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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE

Trivandrum 695 018, India (0471-2490149) www.iish.org , www.iishglobal.org

BHARATHEEYA VIJNANA / SAASTRA

DHAARA ( HANDBOOK OF ANCIENT INDIAN SCIENTIFIC BOOKS )

DR. N. GOPALAKRISHNAN, Ph.D., D.Litt (Scientist, CSIR) INDIAN INSTITUTE OF SCIENTIFIC HERITAGE THIRUVNANTHAPURAM 695018

Heritage Publication Series 78

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PREFACE India is the land of spirituality, science and technology. India is also the land of many languages, customs and rituals. When all other civilizations and culture were vanished from the surface of the globe earth, India still remains with her glory. India was attacked, conquered, plundered and looted for many centuries by foreigners. Still India did not die. Indian heritage was destroyed before the independence by the invaders. After the independence, our own rulers destroyed it. Stil the process of destroying Indian culture and heritage is continuing….. But with all the negatives faced by our motherland, she still serves the mankind with her Vedic messages, with the motherly love and affection, with the noble mantra that Sarve api sukhina santhu . Sarve santhu niraamaya. Sarve bhadraani pasyanthu, Maa kaschit dukhabhag bhavet. Let every one become happy, let everyone become free from diseases, let everyone live with glory, let not anyone suffer from pain….. Bhadram karnebhi srunuyaama devaa: bhadram pasyema askhabhir yajathraa: sthirairangai sthushtuvamsa sthanoobhirvyasema deva hitam yathayu: Let us all hear the glorious news through our ears, let our eyes see glorious sights, let us all do divine and noble missions, through the body made of healthy organs…. We never said haindavaa: samasthaa: sukhino bhavantu let all Hindus become happy. We never said bharatheeya: smasthaa: sukhino bhavantu Let all Indians become happy. We always prayed to the almighty: lokaa: smasthaa: sukhino Bhavanthu Let all the people become happy These are the few among thousands of Indian messages to the world. Like these Indian Rushies have given scientific messages also. A deep and most modern scientific knowledge also include in the list of great Indian contributions. In this book we are giving the abstracts of those scientific knowledge existed in ancient India . We look forward for hearing your comments. In the service of the motherland, Bharath. August 15, 2004 Dr. N. Gopalakrishnan

Detailed descriptions on the subject matter of the most important text books in the subject of astronomy and mathematics are given in the first 30 – 40 pages, after that the smaller and lesser known books on the same subject are described in few lines. TANTRA SANGRAHA OF NILAKANTA SOMAYAAJI

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Nilakanta Somasutwan was a Kerala astronomer, mathematician who has contributed for the subject to a very great extent. His period is exactly known as 1465 – 1545 AD. The book tantra samgraha has 430 stanzas in 8 chapters. The abstract of the book is given here as a model, given in almost all other books. However in many books their abstract presentation will be in the from of contents only. The reader should get an understanding that such a way (as given below) existed in ancient India for giving every astronomical aspects, very rationaly and with the base of pure and applied science. Nilakanta Somayaji, has focused on many aspects of mathematics and astronomy other than applied astronomy. Here the book published by the Visvesvarananda Visva Bahandu Institute of Sanskrit, Hoshiarpur, Punjabi University is followed for presenting the abstract. The text begins with the invocation by the author, then the subject content is followed. The purpose of the astronomical computation, determinants of the time, aim of the astronomical studies, proper approach to the study of astronomy, civil and sidereal day measurements, what is meant by time and detailed explanation on the concept of time, rotation of the celestial spheres, measure of civil and sidereal days, solar and lunar measures of the time, lunar month, solar month, intercalary month, further description on the calculation of the lunar month, nature of the time and month and day very specifically, revolutions of the planets, depiction of numbers, day of the gods, manes and human beings, aeonic revolutions of the planets, etc, civil days and their detailed explaining in a yuga, planetary aeons and the common aeon, theory of intercalation, verification of the number of revolutions through planetary conjunctions, verification of the number of revolutions by inference, etc., planetary revolution in circular orbits, computation of kali days, rationale of the computation of kali days, mathematical operations like addition and subtraction, multiplication and division , squaring and determining square root, fractions, positive and negative numbers, fractions of the fractions, associated and dissociated fractions, addition and subtraction of fractions, multiplication of fractions division of fractions, squaring, etc., of fractions operation with zero, theory of numbers, rationale of division, rationale of squaring, rationale of square root, rationale of the operation for the square root, operation for the square root, ten rules for mathematical derivations, rationale of fractions, positive and negative numbers, rationale of fractions of fractions, rationale of associated and dissociated fractions, rationale of the multiplication of the fractions, rationale of the division of fractions, rationale of the square and cube of the fractions, rationale of the associated fractions, mean planets from Kali days, computation of mean planets, rationale of the rule of three, rationale of the rule of three in the computation of kali days, application of the rule of three of mean planets, in signs, etc, application of the rule of the three in pulverization, application of pulverization in

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org computation of kali days, etc, pulverization using the reduced aeonic revolutions of the Sun and civil days, correction for longitude, situation of the spherical earth, longitudinal time, rationale of the longitudinal time, positive and negative nature of the longitudinal time, zero positions of the planets at the beginning of kali, zero positions of the planets at the ninth minor aeon, rationale of the zero positions at the night aeon, rationale of the reduction of the multipliers and divisors, apogees a of planets, planetary apogees in degrees. These are the subject mattes dealt in the first part of the thantra sangraha. In the second part known as sphutaprakaranam ( true planets); anomaly and order of the quadrants, rotation anomaly and order of the quadrants, computation of risings, and arcs, construction of a circle of diameter equal to the side of a given square, computation of the circumference without the use of square and roots, sum of series, sum of the series of natural numbers, sum of the series of squares of numbers, sum of a series of cubes of numbers, sum of a summation of series, processes relating to Rsines and arcs, computation of the arc of a given Rsine, rationale of the placement of unknown numbers, computation of the circumference of a circle, more accurate methods of the computation of the circumference, different methods for accurate computation of circumference, derivation of Rsines for given Rversed sine and arc, computation of Rsine and arcs, rationale of the computation of Rsines and arcs, Rsines at the intersection of the sine segments, accurate computation of the 24 ordained Rsines, alternate method for Rsines, sectional Rsines and Rsine differences, sum of Rsine differences, summation of Rsine differences, accurate Rsine at a desired point, computation of the arc of an Rsine according to Madhava, computation of Rsine and Rversed sine at desired point without the aid of the ordained Rsines, the explanations of the phrases of Madhava for the computation of desired Rsine and Rversed sine, rationale of the other phrases used by the mathematician Madhavacharya, rationale of Madhava’s method , rationale of the computation of the altitude, the rule of the jiva Parasara for the Rsine of the sum or difference of two angels, derivation of the rule jiva Parasara terms, computation of Rsines without the aid of the radius, rules relating to triangles, rules relating to cyclic quadrilaterals, rules relating to the hypotenuse of a quadrilateral, computation of Rsines without the aid of the radius, computation of the diameter from the area of the cyclic quadrilateral, extension of the rules relating to the area of a cyclic quadrilateral to the area of a triangle, computation of Rversed sine, surface area of a sphere, derivation of Rsine and arc using the chord rule, computation of the desired Rsine, rationale of the computation of the desired Rsines, the true Sun, the ascensional difference, rationale of pranas of ascensional difference, Sun’s daily motion in minutes of arc, application of ascensional difference to true planets, measure of day and night on applying ascensional difference, rationale for the application of the ascensional difference, conversion of the arc of Rsine of the ascensional difference, etc,

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org rationale of the above explanation, situation of the celestial sphere, revolution of the planets in the celestial sphere hypotenuse, related to mandoccha and sighroccha, method for computation of manda karna, alternate method of computation of mandakarna, computation without successive approximation, true Sun through manda hypotenuse, manda correct planet, mean planet from the Sun, rationale of the conjunction of the mean planets from the true Sun, alternate method for mean planets from true Sun, rationale of the alternate, method for mean planets, manda hypotenuse, alternate method, true Sun and Moon at a desired moment, rationale of the true motion of the Sun and the Moon, true asterism at desired time, true lunar day at desired time, karana at desired moment, yoga at desired moment, true Mars, etc , computation of true planets , rationale of true planets, true Mercury and Venus, specialty in the computation of true Mercury and Venus, specialty for Venus, computation of true planets as depicted in glassware, rationale of the computation of true planets, computation of the daily motion of the planets. The third part namely Chhayaprakaranam ( gnomonic shadow) starts with fixing the gnomon invocation, situation of the earth sphere, the atmospheric sphere and the zodiacal sphere, the east west line, north south and other lines, fixing the directions fixing verticality, equinoctial midday shadow, rationale of the above, relation of shadow gnomon and hypotenuse, relation of gnomon, shadow and hypotenuse, latitude and perpendicular, latitude and perpendicular from shadow in the visible celestial sphere, reduction of the latitude and perpendicular in the Draggle to the zodiacal sphere, Rsine latitude and Rcos latitude, prime vertical, equatorial horizon and amplitude at rising, pranas of the rising of the signs at Lanka and at the desired place, rationale of the pranas of the rising of the signs at Lanka, rationale for the pranas of the rising of the signs at the desired place, great gnomon and gnomonic shadow at the desired time, rationale for the computation of the great gnomon and gnomonic shadow from pranas elapsed or to elapse, rationale of the computation of the Rcos and Rsine latitude from the great gnomon and shadow, pranas elapsed or to elapse from the mahasanku, rationale of the above, midday shadow, rationale of the deriving the midday shadow using the declination of latitude, true Sun from the midday shadow, precession of the equinoxes, rationale of the precision of the equinoxes at any desired times, latitude from parallax in latitude and declination rationale of the above, ascertainment of Rsine of the above, Ascertainment of Rsine shadow and the directions, Rationale of the above, Graphical presentation of the path of the shadow of the 12 digit gnomon, method of drawing the path of the shadow, alternate method for Rsine shadow, great gnomon when the Sun is at the prime vertical true Sun from mahasanku,. Samasanku and true Sun there from, hypotenuse of samasanku in inches, rationale of the 12 inch gnomon hypotenuse in relation to the samasanku, alternate method for the hypotenuse of the samasanku, pranas elapsed and to elapse calculated from samasanku, pranas of zenith distance

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org from samasanku, latitudinal triangles, pranas gone and to go and the zenith distance from samasanku, alternate method for pranas of zenith distance, earthsine from samasanku, the ten shadow problems great gnomon and zenith distance from declination, amplitude at rising and latitude, rationale of the derivation of great gnomon, Rsine zenith distance and the rationale of its derivation, great gnomon and declination from zenith distance, amplitude art rising and latitude, rationale of the above, great gnomon and amplitude at rising from zenith distance, declination and latitude, rationale of the above, great gnomon and latitude from zenith distance, declination and amplitude at rising, rationale of the above, zenith distance an declination from great gnomon, amplitude at rising and latitude, rationale of the above, zenith distance and amplitude at rising from great gnomon declination and latitude, rationale of the above statement, zenith distance and latitude from great gnomon, declination and amplitude, declination and amplitude at rising from great gnomon, zenith distance and latitude, declination and latitude and amplitude at rising and latitude respectively, from the other three, great shadow in any direction, rationale of the above, shadow of corner, gnomon, rationale of the shadow of the corner gnomon, rising point of the ecliptic at the east or orient ecliptic, non usability of the rule of the three in the derivation of the rising point of the ecliptic, inaccuracy of orient ecliptic desired by the rule of three, kalagna, situation of the zodiacal sphere at the region of the rising of the sign, ecliptic zenith distance, rationale of deriving the drkkshepa, drkkshepa lagna, rationale for the rising and setting of the point of the signs, drkkshepa lagna, meridian ecliptic point, rationale of the derivation of madhyalanga apropose the situation of zodiacal sphere, madhylagna without repeated approximation.. with these explanations the third part comes to an end. The fourth part is lunar eclipse known as Chandra grahana prakaranam. In this chapter the following subjects are discussed: moment of conjuction in lunar eclipse, innovation, rationale of the moment of conjuction true Sun and Moon as sygyzy, necessity of accurate true longitude in computation of an eclipse, true Sun and Moon by repeated approximation, radius of the orbits of the Sun and the Moon in yojanas, rationale of the above, radius of the orbits of the earth , Sun and the Moon in yojanas, rationale of the true hypotenuse in yojanas of the Sun and the Moon, second true hypotenuse in yojanas of the Sun and the Moon, situation, in the zodiacal sphere, of the Sun, the Moon and the higher apses and their motion, rationale of the second true hypotenuse in yojanas, angular diameters in minutes of the orbits of the Sun and the Moon, rationale of the above explanations, diameter of the earth’s shadow in minutes, rationale of the above, Moon’s latitude and Moon’s rate of motion, probability of an eclipse, rationale of the probability of eclipse calculation, total eclipse and rationale of the explanation given for total eclipse, half duration and first and last contacts, successive approximation of sthityuardha, sparsa and moksha of the eclipse, rationale for the above three

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org eclipse phenomenon, points of contacts and points of release in eclipse, and their method of calculation, visibility of the contact in the eclipse at Sunrise and Sunset, parameters for determination of the visibility of the contact and release of the eclipse, points of first and last contacts, desired immersion and mid eclipse, rationale of deriving the desired immersion, contingency of the invisibility of an eclipse, possibility of the deflection, deflection due to latitude and that due to declination, nature of valana, deflection due to latitude, deflection due to declination, rationale of true valana, graphical representation of the lunar eclipse, rationale of the above eclipse, details, thus ends the fourth part in thantra sangraha. The fifth part is on solar eclipse ( ravigrahaprakaranam); possibility of a solar eclipse, drggati and sine drkkshepa, parallax in longitude in nadikas and the correction there to, minutes of parallax in latitude of the Sun, minutes of parallax in latitude of the Moon,. Probability of the solar eclipse and maximum measure of the eclipse, middle of the eclipse, time of first contact by successive approximation, time of the last contact by successive approximation, half duration and times of submergence and mergence, reduction to observation of computed eclipse, mid eclipse, non prediction of an eclipse, graphical representation of the eclipse, The sixth part known as vyatipata describes the astronomical phenomenon as follows: possibility of vytipata, sine declination of the Sun and the Moon at a desired time, specialty in sine declination of the Moon at a desired time, alternate method for sine, declination of the Moon at a desired time, probability of vyatipata, regional of the non occurrence of the vyatipata, regional of the probable occurrence of the vytipata, mid vytipata, beginning and end of vyatipata, inauspiciousness of the latter half of vyatipata, inauspiciousness of the latter half of the vyatipata, inauspicious of the three types of vyatipatas, viz , lata, vaidrta and sarpamastaka. The seventh part explanations are: the two types of reduction to observation 1. due to latitude of the observer and 2. due to the position of the ecliptic, celestial latitude of the planets at a desired time, reduction to observation of true planets, alternate method for reduction to observation, kalagna and degree of time, visibility and non visibility of the planets and their entrance and exit across the Sun’s orbit. The last part is known as selection of the lunar horns : Revised true Moon celestial latitude and parallax in latitude and lunar orbital differed, orbital difference for computing the illuminated part of the Moon, illuminated part of the Moon deflection of the illuminated part of the Moon, graphical representation of the elevation of the lunar horns, time of Moonrise after Sunset, computation of the orbits etc., of Mars, Mercury and Venus, visual verification of the measure of the orbits and also the conclusion. II. COMMENTARY FOR ARYABHATEYAM:

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Nilakanta Somasutwan has written a commentary for Aryabhateeya which was his first book. All the four padas mentioned in the Aryabhteeya has been further critically analyzed and many more infromation are added to that to form an excellent commentary on the book. III. SIDDHANTA DARPANA OF NILAKANTA SOMASUTWAN In three chapters Nilakanta has given detailed description of the astronomical knowledge , in this books. The first part is known as upadesa bhaga which is the theory section. After the upadesa bhaga , the invocation , revolutions of the planets, revolutions of the apses and the ascending nodes, maximum latitudes, epicycles of the apses and the conjunctions, measure of the aeons, segments of a revolutions, linear velocity of planets of yojana, diameters of the earth, Moon and Sun, position of the city of Avanti, orbit of the stars, the position of the ecliptic, precision and procession of the equinoxes, position of equinoxes at a specific date, epicycles of the equations of the center and of conjunction are given in the first part In the second part known as the practical section, eccentric and orbital cycles, definition of the sine values, geocentric positions of a planet, declination, vyatipaata , lata etc, are described, the lunar crescent, eclipses, etc, and finally Nilakanta has given the conclusion. IV. JYOTHIRMIMAMSA OF NILAKANTA SOMAYAJI :The book described here has been published with English translation by the Visweswarananda Indological Institute, Punjab. Brief description of the content of yothirmimamsa is given in the first part of the book, the nature of the astronomical and mathematical work, the divine intuition, the experimental details of the science, corrections to the planetary parameters, reasons for the corrections for the planetary revolutions, Vedic authority for inference in astronomy, relative accuracy of different systems, correction through eclipses, true motion, position, etc., of planets, relation of the sides and hypotenuse, reduction of angular distances, the beginning of the work on jyothirmimamsa, missing portions of the books, and the omission done at the end of the book is given as a separate part, in the publication, authorities on astronomy , nonastronomical works, are described in the part one of the introduction by the author. The title of each subject area goes like this in the Nilakanta’s book: the use of revising the astronomical constants at intervals for correcting the parameters connected with astronomy, the meaning of devatha prasada, which indicates in the intuition of the astronomers, required for getting the analytical values and approach in the astronomy, the experimental determinations of the astronomical values, the tools used for arriving at the values, the need and importance of conducting experiments in the astronomical studies for arriving at better results on each aspects, significance of the astronomical books and the base of collecting data from

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org those books, application of corrections for the astronomical figures called bija correction, the corrections given based on the period of Aryabhatta, which is known as the Bhatta correction, justification of the changes made by another very famous astronomer Lallacharya in his book Sishyaddhi vruddhi tantra, reasons for difference in the mean planets though the revolutions are identical, indication of Lalla by Suryadeva, Vedic authority for inference as a means to derive the number of planetary revolutions, different systems of astronomy, the number of planetary revolutions enunciated by Sripati and Brahmagupta, the planetary revolutions in a Kalpa, revolutions of apogees in a kalpa( kalpa is a period of 14 x 72 x 4320000 years ) revolutions of the nodes in a kalpa, number of days in a kalpa, zero points of the planets at the commencement of kaliyuga, corrections to planetary revolutions. Relative accuracy of the different astronomical systems, mean planets according to the Sunrise system of Aryabhatiya, mean planets according to siddhantasekhara, Moon’s apogee according to siddhanta sekhara, Moon’s node according to siddhantasekhra, application of the above values in the astronomical calculations, astronomical corrections given on the bases of the eclipses, eclipses observed by Parameswaracharya, method of corrections given by other astronomers, demonstration of the validity of those corrections through eclipses, precision equinox, calculation and the correction, discussions of the second true positions of the planets, correction of the periphery of the manda epicycle, discussion on the precision of the equinoxes, corrections due to the precession of the equinoxes, sine table for praanakalaantara, beginning with dhiyo nu (katapayaadi number system) sine table for the ascensional differences beginning with gunodyana ( same number system), application of the correction, derivation of the 36 Rsines, graphic proof for the relation of the sides and hypotenuse, reason for the reduction of the minutes of arc of the planetary orbital to the visible celestial sphere, discussion on the reduction of the minutes of arc of the visible celestial sphere to those of the zodiacal sphere. Thus ends the jyothir mimamsa written in the 14th century V. CHANDRA CCHAYA GANITHA OF NILAKANTA SOMAYAJI This book is reviewed based on the publication of the Visveswarananda Institute. In the introduction the Hindu astronomy it is described. This books has focused on the shadow of the Moon. In the two chapters of the book namely the chandra cchaya ganitham and second chapter dealing with the time from shadow descriptions are given on Moon’s true latitude, Moon’s second inequality corrections, correction to daily motion, kalagana and orient ecliptic point, zenith distance of the nonagesimal, Moon’s shadow and alternative method for Moon’s shadow. In the second part the bases for viparitacchaya that is the movement of shadow in the opposite direction is described, after that the four main R sines, Reduction to the polar longitude,

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org approximate orient ecliptic point etc and their correction, time determination from the shadow and the conclusions of all the astronomical observations are given systematically This is a very small book, having 25 pages but containing deep science in that. VI. GOLASARA OF NILAKANTA SOMAYAJI There are three sections in gola sara. The section one deals with the civil days and revolutions of the planets, positions of the higher apses , positions of the ascending nodes, maximum mean latitudes, epicycles of the equation of apses, epicycles of the equation of conjunction , diameters of the Sun, Moon and earth, motions in terms of signs , etc, orbits of the planets . In the second section, the explanations are given on the situation of the celestial sphere. In the third section detailed introduction on the mathematical concepts are given. The Pythagoras theorem and the Rsine values for various angles are given as a table, approximate arc and circumference, computation of tabular Rsines are also given in the end of the book PANCHASIDDHANTIKA OF VARAHAMIHIRA In the 18 chapters of pancha siddhantika Varahamihiracharya has given the detailed scientific concepts of mathematics and astronomy, both basic and applied knowledge. He has started the explanation with the aim of compiling the five Siddhantas, five schools of astronomy, contents of the work, days from epoch according to Romaka, Paulisa, Soura, etc., yuga of the Sun and the Moon as given by Romaka and Saura siddhanta, Lord of the year, month, and Hora, etc., names of the 30 days of the parsi months. True sun, true Moon, nakshatra and tithi, day time, gnomonic shadow, lagna from shadow and vice versa according to Vasishta siddhanta. According to Paulisa siddhanta, the true Sun, true motion of Moon, equation of the center, chara or oblique ascension, day time, desantara, local Sunset time, nakshatra computation, Sun’s daily motion, karanas, vyatipata and vaidrta, sadaiti punyakala, solstices, sankranti kala, tridinasprg yoga, rahu the nodes, Moon’s latitude, defect in Bhadravishnu, padaditya and Romaka siddhantas according to Paulisa siddhatna The three problems are described in the 4th chapter, table of sines, declination of the Sun and the Moon gnomonic shadow , latitude from shadow, Rsine zenith distance, sine, colatitudes and day diameter, chara or oblique ascension, latitude from chara, Rt ascensional difference rising signs, time to reach the prime vertical great gnomon, and its shadow, astronomer’s qualification, gnomonic shadow and the prime verticals, agra, sine amplitude, latitude from agra, shadow at desired time, time after Sunrise, time for Sunset, shadow from time, Moon’s shadow, directions from shadow, Sun from shadow.

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In Paulisa siddhanta: the Moon’s cusps during lunar eclipse, Sun and Moon of equal longitude probability of an eclipse, duration of the eclipse, total obscuration, direction of the eclipse, moment of the eclipse and its color, diagrammatic representation, lunar and solar eclipses. Paulisa sidhanta on solar eclipse,. parallax of longitude , parallax in latitude eclipse computation. In Romaka siddhanta, the solar eclipse is explained as follows: the true Sun, the true Moon, daily motion of the Sun and the Moon, rahu, parallax in longitude declination of the nonagesimal, parallax correction and orbital diameters, true diameter of the orbits, moment of the eclipse, eclipse diagram. The solar eclipse in Saura siddhanta: mean Sun, mean Moon, rahu, maximum latitude, true Sun and Moon, epicyclic theory, bhujantara correction, udayantara correction, desantra correction, mean motion of the Sun and the Moon, motion of Moon’s anomaly, true motion of Sun and Moon, kaksha of the Sun and the Moon measure of the orbits, sin zenith distance of meridian point, drkshepa of the Sun , gnomon, parallax corrected new Moon, parallax in latitude , duration of the eclipse, According to Saura siddhanta the lunar eclipse: diameter of the shadow, duration of the eclipse, obscuration at any desired moment, time of total obscuration. Marking the ecliptic, etc, marking of points of contact, etc., conversion of minutes into angles, The description given in Pitamaha siddhanta: days from epoch, tithi, nakshatra, vytipata, duration of a day etc. situation of the earth cosmogony, situation of the earth correct explanation, rotation of the earth, situation of the gods and asuras, signs and yojanas, position of Lanka and Ujjayini, measures of the earth, etc, visibility of the Sun, astronomical observation, Moon’s visibility, the planets and their situation, lords of the months, days and year. The graphical methods and astronomical instruments, ascensional differences of the zodiacal signs, Rsine of the Sun’s zenith distance for the given time, Rt ascensions of the signs, gnomon, local latitude from the equinoctial midday shadow, Sun’s longitude, Vshape of the yasti, Moon’s longitude, cardinal directions by means of a gnomon, the celestial sphere, hemispherical bowl and its use, hoop and its use, armillary sphere, Sun’s northward and southward journeys, instruments for measuring time, local longitude in terms of time, the nadir or ghati, conjuction of the Moon with the star, positions of certain junction stars, digits between the Moon and star in conjunction and time of conjunction, heliacal rising of canopsus, Detailed description of astronomical parameters are given under the 15th chapter known as the secrets of astronomy, eclipses, situation at the poles, weekday, day reckoning, description of mean positions of the star planets, Varahamihira’s bija corrections, further description on true planets

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org based on saura siddhanta, epicycles of the planets, true planets, special work for Mercury and Venus, retrograde motion, heliacal rising, latitudes of planets, Vasishta and Paulisa siddhanta on rising and setting of planets. Rising and setting of Venus, Jupiter, Saturn, Mars, Mercury, and some parameters connected with this astronomical phenomenon Some more information are given on the true planets of Mars, Mercury, Jupiter, Saturn and Venus The above description is taken from the contents of the Varahamihira’s panchasiddhantika compiled and translated by professor K. V. Sarma GANITAYUKTHAYA OF UNKNOWN AUTHORSHIP: In this book the rationales of Hindu astronomy are described very systematically. Computation of the Moon’s shadow and in rationalistic exegesis, derivation of the midday shadow, derivation of the sides and hypotenuse of the triangle relating to the elevation of the Moon’s horns, application of the rule for the derivation of the true planets to the derivation of parallax in longitude, parallaxes in latitude and longitude and the planetary latitude, declination, true longitude computation on the sphere of zodiac, planetary deflection and elongation of the Moon’s, horns, motion of planetary latitude, computation of the Moon for the determination vyatipata, sphere of planetary latitude, planetary latitude in the computation of true planets, choice of lump day of zero correction, Moon’s descriptions and the terms used for that description, the formula for the correction of the divisor for correcting zero positions, corner shadow, aphorisms on the subject of shadow, interpolation on the basis of data, derivation of planetary deflection and descritpiton of planetary deflection, parallax of latitude and longitude, calculations relating to a stump from a pole, equation of the center, correction to the computation of the mean planets, computation of true planets, computation of planetary deflection, the rationale of all the above 27 points are given in details. Here one can see how the methodologies are adopted in ancient Indian astronomical calculation to arrive at the very specific values and calculations. Very interestingly, the author has quoted and stressed with the support of the equations from Sangama grama Madhavacharya, Parameswaracharya, Damodara, Nilikanta Somayaji, Jyeshtadeva, Achyuta Pisharoti, Putumana Somayaji, and many others. SPHUTANIRNAYA OF ACHYUTHA PISHARATI There are six important chapters in sphuta nirnaya tantra of Achyta Pisharati. In the first chapter Pisharati starts with the invocation and continues the explanations from the subject of revolutions of the planets, revolutions of the higher apses, the revolution of the ascending nodes and civil days, measure of the aeons, the explanations connected with kruta,

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org threta, dvapara and kaliyugas, the bases of the duration of manvanthara, the epicycles of the equation of the apses, epicycles of the equation of conjunctions, maximum latitudes of the planets, diameters of the planetary orbits. The first chapter is known as bhaganaadi sankhyakathanam ( astronomical constants) In the second chapter the zero positions at the 0 day of kaliyuga, the weekday on the 0 day of kali, completed kali years, zero positions at the beginning of the current year, weekday at the beginning of the current year and its determination, completed civil days on a particular epoch era, the mean Sun, correction for terrestrial longitude, mean Moon, etc., are explained. In the third chapter the computation of the true positions of the celestial bodies particularly the planets are given. The computation of the Rsines etc, of the Sun, Moon, etc, the definition of anomaly, derivation of Rsines and R cosines, derivation of the arc from the Rsine and equation of the apses, equation of the center corrected mean planet, equation of the center corrected daily motion, equation of the center corrected hypotenuse, alternative view on mandasphuta, alternative view on mandasphuta gati, precision of the equinoxes, Sun’s Rsine of the declination and of the diurnal circle, right assensional differences, Rsine and Rcos terrestrial latitude, declinational ascensional difference, reduction to true Sunrise, etc, are also explained in the third d chapter In the fourth chapter following subjects are discussed and this chapter is known as “true planet on the celestial sphere”: equation of the center corrected celestial latitude, true Moon, true Mars, true latitude of Mars, true daily motion of Mars, true Mercury and Venus, true motion of Mercury and Venus, true distance of the planets, alternative view on application of equation of conjunction,. In the fifth chapter following subjects are discussed under the title “true planet, relative to earth’s center”: true planets related to earth’s sphere, correction for celestial latitude, related to earth’s sphere, motion of planets to related earth’s sphere, true planet related to earth’s surface, In the sixth chapter following subjects are discussed: Sidereal time + 90 degree, zenith distance of the nonagesimal, orient ecliptic point, determination of zenith distance of the noagesimal zenith distance of the planet using cosine and sine angles connected with the radius, R cos zenith distance of the planet, Rsine altitude of the planet, hypotenuse on the zenith planet circle, vertical circle, conclusion, In the end of the text, abstract of some of the important astronomical parameters is given : Resume of the sphuta nirnaya, planetary revolutions according to sphutanirnaya, derivation of revolutions from Tantrasangraha, multipliers and divisors for sphutanirnaya mean planets from Parahita constants, computation of mean planets equal to those of sphutanirnaya,

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lump days and zero positions based on sphutanirnaya, two positions at 0 kali day according to sphutanirnaya and the diagram for true positions of planets, on the shadow . MAHASIDDHANTA OF ARYABHATTA II In the 18 chapters of Mahasiddhanta of Aryabhatta II, the first chapter treats with madhyamadhikara representation of number by alphabet as explained by Aryabhatta I. The revolutions of the planets, number of solar days in a kalpa, the number of revolutions of great bear and ayanagraha, in a kalpa etc., the number of kalpa years elapsed before the commencement of the kali era is calculated as 1972944000, in the 55 slokas of the first chapter and detailed description of the preliminary principles of astronomy is given. In the second chapter., the period of Aryasiddhanta and the true positions of the planets when this book was composed are given. Then the adhimasa and the revolutions of the planets according to Parasara, methods of finding the mean position of the planets, ahargana calculation and other interesting method of finding out the mean positions of the planets by aid of the ahargana or number of solar years in a kalpa and the variety of calculations, are given with rationale . In the third chapter various sine values are given by taking the radian value as 3438. The square of the radius and sine of 24 degree, the method of finding the Rsine and R cos angles, sine of a given declination, precision by the Ayanagraha, the number of revolution of the Ayanagraha, application of mandaphala and chara correction for finding out the true position of the Sun, the method for finding out the mandaphala of the Moon and other planets and the sighraphala of the Mars and other planets, by the knowledge of their distance from the earth’s center. Once again the application of the same methods for Mars and other planets as given by Bhaskaracharya is given. The true motion of the planets including Mars, the retrograde motions, rising and setting of the Mars and other planets, latitude and declination of the true position of a planet, the greatest latitude of the Moon and other planets and finding the tithies of the day based on above calculations, the time of rising of the Sun in Lanka ( which is in the equator) are narrated with strong mathematical support.

In the 4th chapter, determination of the cardinal points, gnomonic shadow in the most accurate method, the gnomonic hypotenues, names of the right angled triangle which are created by these astronomical phenomena, determination of the sines of latitude and colatitude from these right triangles, the hour angle determination for the Sun and its complement, the method of finding out declination, latitude, etc., from the mid shadow, finding out the right ascensions of the thirty sixth part of the ecliptic,

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org determination of ascending , lagna at a given time of the day, determination of the time of the day from the given position of the Sun and the ascendant and the 12 zodiacal signs are given. In the fifth chapter the subject matter of discussion is the lunar eclipse: The determination of the following astronomical and geographical values and aspects are given scientifically,in the first part. Determination of the tithi on the eclipse days, positions of the moon for determining the thithi, the diameter of Sun, Moon and the earth’s shadow, magnitude of the total or partial eclipse, duration of an eclipse and the time for which the Sun or the Moon is totally eclipsed, time of the first contact of the eclipse and the beginning of the eclipse, half duration of the eclipse, method for finding out the duration of the eclipse by an unrepeated process, latitude at the time of first contact, portion eclipsed at a given time and the total duration of the eclipse, determination of akshavalana, are described using applied mathematics The sixth chapter discusses on solar eclipses: determination of the parallax, true parallax known as nati and true latitude, half duration of the solar eclipse, insignificant eclipse and color of the eclipsed body, correct valana, finding out the illuminated portion of the Moon during the partial eclipse, determination of koti ( R cos) and karana for the diagram of solar or lunar eclipse . The seventh chapter describes the diagrams of the solar and lunar eclipses and the diagram for the horn of the Moon, in the next chapter directions of the rising and setting of the planet, kalamsa of a planet, method for determining whether a planet has risen or set and the value of the longitude and latitude of the star Agastya are given. In the ninth chapter the ascendant of the rising and setting of a planet, method for finding out the times of the rising and setting of a planet, and planet’s shadow, the rising and setting of canopus – agastya and other stars, in the 10th chapter the values of the mean diameters of the Mars and other planets, time of conjunction of two planets, the distance between the centers of the two planets in their conjunction,etc., are discussed. In the 11th chapter, longitude and latitude of important stars, the method for determination of conjunction of planets with star/s occurred or will occur, zenith distances of stars when they cross the meridian, method for the determination of the length of a day from the known position of a star, the visibility/ invisibility of stars, and the probability of the star coming in conjunction with tauri’s wagon are the subject discussed In the next chapter following subjects are discussed in detail: vaidhruta and vyatipata, the true quadrants of the Moon’s diurnal circles, and the entering of one quadrant and leaving to the other. With these explanations the first part of Aryasiddhanta is completed and second part

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starts with Goladhyaaya from chapter 13 onwards: the first 57 slokas in the first chapter very specifically discuss the mathematics, geography and the ahargana and the mean position of the planets. In the next chapter arithmetics, additions, subtraction, multiplication, division, determination of squares and square roots, etc are given, similarly cube , cube root, and many basic mathematical calculations, arithmetic progression, geometrical progression, preliminary geometry for the determination of sides, areas, diagonals, perimeters, etc., of triangles, rhombus, segments, square, circles, spheres, quadrilaterals, etc The fifteenth chapter is describing exclusively the volumes of ditch, irregular ditch, cones, well, cylindrical and prism ditches, spheres and number of bricks in a heap of bricks, and number of layer in a heap, etc.

The 16th chapter describes geography, the orbits of planets, earth’s position in space, position of meru, position of Lanka, yamakoti, siddhapura and romaka, islands and oceans on the globe earth, importance of Bharatha varsha, distance between one’s own place and equator, the circumference of earth, measurement of earth’s diameter, circumference and surface of the earth, local time at different places when Sunrises in Lanka , finding out the cardinal points, terrestrial positions, layer when clouds/ lightning occurs above the surface of the earth. The 17th chapter is exclusively the questions on spherical trigonometry and related mathematical problems. In the 18th chapter the indeterminate equations are given including solving the indeterminate equations, method for finding out the correctness of a product, quotient of division, square, square root etc,. KARANARATNA OF DEVACHARYA Karanaratna consists of 8 chapters and detailed descriptions on the common man’s astronomy is given here. The first chapter discusses, the Sun and Moon and connection with panchanga. It begins with the aim of writing such a book,. Ahargana, mean longitude of Sun, Sun’s apogee, Moon, Moon’s apogee and ascending nodes, sakabda, kalpa and manwanthara corrections, R sine differences, Rsine and Rversed sines, equation of the center for the Sun and the Moon, bhujajya and longitude corrections for Moon, longitude correction in general for that, local longitude in time, local place relative to prime meridian, the prime meridian mean and true motions of the Sun and Moon, Uijjayini from Lanka equinoctial midday shadow, accessional differences of the signs, motion of the solstices or equinoxes, the declination table, northern and southern hemispheres, lengths of day and night, cara correction, planet’s longitude for desired time, elements of the panchanga tithi, nakshtra, yoga, three vyatipatas and karana, table of Moon’s latitude,

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org equalization of longitudes of Sun and Moon, and the abstract of all these infromation is given in the first chapter. The lunar eclipse is discussed in detailed in the second chapter, which begins with the invocation and introduction, diameters of the Sun, Moon and rahu, Moon’s latitude, times of first and last contacts, possibility of a lunar eclipse, prediction of eclipse, duration of totality/ semi duration of eclipse by iteration, graphical representation of eclipse, path of eclipsing body, ishta grasa and its graphical representation. In the third chapter solar eclipse is discussed. The iterated lambana and its application, local latitude, meridian ecliptic point, of meridian ecliptic point, parallax in latitude , Moon’s true latitude, impossibility of solar eclipse, Moon’s latitude for first and last contacts, the three valanas, true semi duration of a solar eclipse, measure of eclipse, the eight phases of a solar eclipse and the abstract are the subjects. In the fourth chapter the problems based on the gnomonic shadow are discussed. Meridian shadow from planets longitude, declinations in vinadis, the zenith distance in vinadis, the meridian zenith distance, differences corresponding to shadow angulas, meridian shadow, right and oblique ascensions of the signs, time from Lanka, shadow from times, shadow of man, time from shadow, Lanka from time are discussed in this chapter. In the fifth chapter Moonrise and Moon’s horns are explained. Moon’s longitude and latitude at Sunset, the visibility corrections, Moonrise relative to Sunset, time of Moonrise , Moon’s shadow etc. In the next chapter the elevation of Moon’s horns are described after the invocation and introduction. Heliacal visibility of Moon, Moon’s illuminated part and sankuagra, agras of Sun and Moon and koti of elevation triangle, graphical representation of Moon are given are given In the seventh chapter the mean longitudes of Mars, etc., the four corrections for the planetary positions, planets’ ascending nodes, inclinations of planetary orbits, special instruction for the solar eclipse apogees of the planets, sighrocca of Mars, Jupiter and the Saturn, manda and sighra epicycles, the true epicycles, the true longitude In the last chapter, description is on planetary motion and planetary conjunction. Heliacal rising and setting commencement and conclusion of regression, mean and true daily motions, conjunction of planets, the celestial latitude, distance between planets in conjunction of the victor. Thus, karanaratana is an outstandingly excellent book to refer for any student of astronomy. PAATIGANITA OF SRIDHARACHARYA

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This is a mathematics book written by Sridharacharya in which the ganitha is given in the most systematic way. He started the text without any invocation and directly enters into the notational places, table of money measure, table of weights, table of measure of capacity, table of linear measure and time measurement. These are given in the first part In the second part known as prakarama the addition, subtraction, multiplication, division, squaring, square root, cubing, cube root, operations for fractions, reduction of fractions, rule of three, inverse rule of three, rules of five, seven and nine, barter of commodities, sale of living beings, are given Determinations pertaining to mixture of things are the next part, simple interest, valuation of pieces of gold, partnership, purchase and sale, meeting of two travelers, wages and payments, the cistern problem, wages paid from the commodity, combination of savors, certain special types of problems, series in arithmetic progression, series in geometric progressions, miscellaneous problems on series in arithmetic progression, series of savors cubes and successive sums of natural numbers, series of squares and cubes of the terms of an arithmetic series, are the prime focus of this chapter. In the last part, determinations pertaining to plain figures, area of quadrilateral with equal altitudes and of the triangle, area of the quadrilateral with unequal altitudes are given with a series of problems and their answers KARANAPADDHATI OF PUTHUMANA SOMAYAJI Puthumana Somayaji was from Alathur village of Palakkad district, Kerala. He has written this great book on mathematics and astronomy, known as Karanapaddhati in the 14th century in ten chapters. The book starst with invocation to lord. Then describes the rotation and revolutions of the planets in one mahayuga, the number of civil days in mahayuga , the solar months, lunar months, intercalary months, kalpa and the four yugas and their durations, the details of kaliyuga, calculation of the Kali era from the Malayalam Era known as kolla varsham, calculation of Kali days, the comparison given as mentioned in LaghuBhaskareeya, the true and mean position of planets, simple methods for the mathematical calculations, mean positions of planets and its calculations, converting the months to saka era, the details of the orbits of planets, measuring mean position of the planets based on the day and date, constants to be used for the calculation of various parameters for various planets, etc are described in the first chapter. In the second chapter parameters connected with Kali era and the positions of the planets, their angular motions, various parameters connected with Moon, etc., are described.

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In the third chapter the mean center of Moon and various parameters of Moon based on the latitude and longitude of the same, the constants connected with Moon, are given in Katapayadi number system. In the fourth chapter, the perigee and apogee of the Mars, corrections to be given at different occasions for the Mars, constants for Mars, Mercury, Jupiter, Venus, Saturn in the respective order, the apogee and perigee of all these planets, their conjunction, their conjunctions possibilities , divisors, etc., are given In the fifth chapter, division of the kalpa based on the revolution of the planets, the number of revolutions during the course of this kalpa, the number of civil and solar days of earth since the beginning of this kalpa, the number and other details of the manuantharas for this kalpa, further details on the four yugas are the subject. In the sixth chapter many theorems are given which are literally a feast for a mathematician. Calculation of the circumference of a circle using variety of methods, the division of the circumference and diameters, calculation of various parameters of a circle and their relation, a circle, the arc, the chord, the arrow, the angles, their relations among a variety of parameters, descriptive use of Rsine, R cosine, and tangent of the angles and their relations, their constants and how to memorize all these factors using the katapayadi numbers, are given. In the seventh chapter, the epicycles of the Moon and the Sun, the apogee and perigee of the planets ( here the planets are known as thara graha – which are Mars, Mercury, Jupiter, Venus and Saturn - thara graha does not include the Moon and the Sun). The sign calculation based on the Sign/Rasi in which the planets are present, the chord connected with rising, setting, the apogee, perigee, etc. The method for determining the end time of a month that is the entering of the Sun in the next sign, the sankranti calculations, the star - sankaranti relations. The chords of the epicycles and apogee for all the planets, their karana/ hypotenuse and many other points where an equivalent English translation is impossible , are also given in this chapter In the eighth chapter, methods for the determination of the latitude and longitude are given for various places on the earth, the Rsine and cosine of the latitude and longitude, their arc, chord and variety of constants are given in katapayadi number system. In the ninth chapter the details of the Alpha aeries sign, calculation of the positions of the planets in correct angular values, calculation of the position of the stars, the parallax connected with latitude and longitude for various planets, Sun, Moon and others stars , are given

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In the tenth chapter the shadows of the planets and calculation of various parameters connected with the shadows are given. Calculation of the precision of the planetary positions are the most important points in this part of the book. And at the end the book merits of learning the Karanapaddhati are described The most crucial fact connected with Karanapaddhati is that, one should have thorough knowledge on the katapayadi number system for knowing the descriptions and variety theorems given in this book. In fact the Kelvin’s theorems, Newton’s’ theorems, Lebnitz theorems and variety of other theorems known in the name of foreign scientists have been given by Puthumana Somayaji. Apastamba Sulbasutram: This is a part of the Apastamba srouta sootra, which describes the sacrificial rituals. The sacrificial altars/vedi etc are constructed based on the directions given in the sulbasootra. In short the geometrical part of the sacrifice is given in this book. Even though the knowledge of the book existed many centuries before, it has been written into this from, probably during 800 BC . In this book 223 sutras are given for constructing the sacrificial altars and they give variety of geometrical rules for making circles, triangles, squares, rectangles, and figures inscribed in other structures. The rules mainly describe various types of vedis, their spatial magnitudes, relative positions and such other constructional details and provide geometrical propositions and rules for achieving these details ARYABHATEEYA OF ARYABHATTA I In the history of Indian astronomy and mathematics, the contribution of Aryabhatta I is something unique. He could put forward variety of new hypothesis accurately with the supporting mathematical calculations and evidences. He was borne in 476 AD and wrote his book Aryabhteeya in 499 AD at the age of 23. It is also mentioned that he has written another book known as Suryaasiddhantaprakasa. A commentary for the book on suryasiddhanta. He starts the text with invocations to the divine powers and to all the planets. The Aryabhateeya alphabetical systems for writing numbers, revolution – numbers and zero point of planets, kalpa and beginning of kali era, planetary orbits, Earth’s rotation, liner diameters, obliquity of the ecliptic and inclinations of orbits, ascending nodes and apogees, manda and sighra epicycles, Rsine differences, and the aim of the dasagitika sutra, mentioned above are given in the first chapter of Aryabhateeya known as gitika section.

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In the second part known as ganita or mathematics, invocation and introduction, the first ten notational places square and squaring, cube and cubing, square root, cube root determination, areas of a triangle, volume of right pyramids, area of a circle, volume of sphere ( this fromulae is wrong) area of trapezium and plane figures, chord of one sixth of circles, circumference- diameter relation, computation of Rsine table geometrical derivation of Rsine – differences, construction of circles, etc and testing of level and verticality, Radius of the shadow sphere, gnomonic shadow due to lamp post, tip of the gnomonic shadow from the lamp post and height of the latter, theorems of the square of hypotenuse and on square of half chord, arrows of intercepted arcs of interesting circles, sum of the series of an arithmetic progression, number of terms in a series in AP, sum of variety of arithmetical and geometric progressions, product of factors from their sums and squares, quantities from their difference and product, interest on principal- rule of three, simplification of quotients or fractions, reduction of two fractions to a common denominator, method inversion, unknown quantities from sums of all but one, unknown quantities from equal sums, meeting of two moving bodies, pulveriser residual pulverizes, non residual pulverisor are given in the second part. The third part known as kalakriya or the reckoning of time, the division of time, and circular divisions are given followed by conjunctions of two planets in a yuga, vyatipatas in a yuga, anomalistic and synodic revolutions, jovian years in a yuga, solar years and lunar, civil and sidereal days, intercalary months and omitted lunar days, days of men, manes and god and of Brahma, utsarpini, apasarpini, susamaa and dussama and date of Aryabhata are given as the first part. Then, beginning of the yuga, year and month and day, equality of the linear motion of the planets, consequences of equal linear motion of the planets, non equality of the linear measures of the circular division, relative positions of asterisms and planets, lords of the hours and days, motion of the planets explained through eccentric circles, motion of epicycles, addition and subtraction of mandaphala and sighraphala, a special precorrection for the superior planets, procedure of mandapahala and sighraphala correction for the superior planets and inferior planets are given separately with the distance and velocity of the planets. In the fourth chapter, namely gola the celestial spheres are explained. The position of ecliptic, motion of the nodes, the Sun and the earth’s shadow, motion of the Moon and the planets, visibility of the planets, bright and dark sides of the earth and the planets, situation of the earth, its constitution and shape, earth compared with kadamba flower, increase and decrease in the size of the earth, apparent motion of the starts due to the earth’s rotation, description of the meru mountain, the meru and the badavamukha, the four cardinal cities, positions of lanka and ujjayini, visible and invisible portions of

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org the bhagola, motion of the bhagola from the north and south poles, visibility of the Sun to the gods, manes and men. The prime vertical, meridian and horizon, equatorial horizon, the observer in the khagola, the observer’s drnmandala and drkksheparvrutta, the automatic sphere known as globe or golayantra, the latitude triangle, radius of the day circle, the right ascension of Aries, Taurus and Gemini, earthsine, rising of the four quadrants and the individual signs, Rsine of the altitude sankvagra, Sun’s agra, Rsine of the Sun’s prime vertical altitude, Sun’s greatest gnomon and the shadow thereof, the parallax in solar eclipse, Rsine of the zenith distance of the central ecliptic point, drggatijyas of the Sun and the Moon, parallax of the Sun and the Moon, the visibility correction for akshadrkkarma for the Moon, and that of ayanadrkkarma of the Moon, eclipses of the Moon and the Sun, constitution of the Moon, Sun earth and shadow, and the eclipsers of the Sun and the Moon, occurrence of an eclipse, length of the shadow, earth’s shadow at the Moon’s distance, half duration of a lunar eclipse, half duration of the totality of the lunar eclipse, the part of the Moon not eclipsed, measure of the eclipse at the given time, akshavalana, ayanavalana for the first contact, colour of the Moon during eclipse, conditions when the Sun’s eclipse is not to be predicted, planets determined from observations, acknowledgement to Brahma and the conclusions are given as the last part of Aryabhateeya. BHAKSHALI MANUSCRIPTS: They are the manuscripts obtained during excavation of the city of Peshwar in 1881. the Bhakshali manuscripts are written in the birch bark, a considerable portion of the manuscript had been destroyed and only some 70 leaves of birch bark of which a few again were mere scraps, survived at the time of its discovery, it is now in the Bodliean library oxford. Many people have studied the same and have made detailed report out of that. It contains mathematical work of rules, with illustrative examples and their solutions, for arithmetical, algebra and geometrical operations. The major portion deals with arithmetics, fractions, square roots, progressions, income and expenditure, profit and loss, computation of gold, interest, rule of three, and summation of complex series, the discussion of algebra operations includes simple equations , simultaneous, liner equations, quadratic, linear equations and indeterminate equations of the second degree. Problems relating to mensuration and miscellaneous subjects have also been dealt with. BHOUDHAYANA SULBASUTRA This is book written by Maharshi Boudhaya on constructing the altars for sacrificial rituals. This is a part of Boudhayana sroutha sootra written probably during 1000 BC or before that.. It is the earliest of all subasutras.

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It has 525 sutras and divided in three chapters. The first chapter contains 116 sutras which give geometrical positions necessary for the construction of the sacrificial altars and deal briefly with the relative positions and spatial magnitudes of various vedis. The second chapter consists of 86 sutras of which the major portion is devoted to the description of the special relation in the different constructions of the agnis and the remaining portion explains the construction of several agnis, the third chapter in 323 sutras, describes mainly the construction of ( again) agnis. The work is of considerable importance owing to the various mathematical rules and principles implied in the descriptions and rules concerning the sacrificial altars. Some of which involve irrational numbers, the so called Pythagoras theorem, squaring the circles, indeterminate problems and elementary treatment of surds, are given. Variety of geometrical structures describing the circles, triangles, squares, rectangles etc connected with the vedis are described here, with examples. LAGHUBHASKAREEYAM OF BHASKARACHARYA I Bhaskaracharya begins the great masterpiece in astronomy and mathematics by giving homage to the Sun and to Aryabhatta, appreciation of Aryabhatta I’s work follows. Followed by these, the calculation of the ahargana, revolution number of planets, calculation of mean longitudes of the planets, positions of apogees of planets, epicycles of planets, Hindu prime meridian, a rule for the distance from the prime meridian and its criticism and criticism of another rule, longitude in time criterion for knowing whether the local place is to the east or to the west of the prime meridian, the longitude correction and its application, another rule for distance from the prime meridian, alternative rule for the longitude correction, justification of the longitude correction, demonstration of the same, consequences of improper application of the longitude correction, comparison of corrections for longitude and parallax - lambana – etc., are given in the first chapter. In the second chapter true longitudes of the planets, Sun’s mean anomaly and its Rsine, Sun’s equation of the center, Sun’s correction for the equation of the time due to the eccentricity of the ecliptic, true distances of the Sun and the Moon, true daily motion of the Sun and Moon by various methods, Sun’s declination, earthsine, and ascensional differences, correction for the Sun’s ascensional difference, length of a day and night, corrections for the Moon, nakshatra, tithi, karana, the three kinds of vyatipatas, corrections for the planets, Mars, etc, criterion for knowing whether a planet is stationary, retrograde and or in direct motions,etc., are given in the second chapter In the third chapter determination of directions, latitudes and colatitudes of the local place, ascensional differences of the signs times of rising of the signs, at the equator, times of rising of the signs at the local place, Sun’s zenith

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org distance and the shadow of the gnomon for the given time, time corresponding to the given shadow in the forenoon or afternoon, Sun’s sankuagra, longitude of the rising point of the ecliptic for the given time and vice versa, the Sun’s agra, Sun’s altitude and longitude when it is on the prime vertical, reduction of R sine to the corresponding arc, midday shadow from the Sun’s declination and the latitude of the place, Sun’s declination and its relation with the longitude and the latitude of the local place from the midday shadow of the gnomon are discussed. Here ends the third chapter The fourth chapter is on lunar eclipses. It begins with the explanations of longitudes of the Sun and Moon when they are in opposition or conjunction in longitude. Distance of the Sun and Moon, diameters of the Sun, Moon and earth, length of the earth’s shadow, diameter of the earth’s shadow where the Moon crosses it, Moon’s latitude, measure of the Moon’s diameter unobscured by the shadow, sparsa or touching the shadow during the eclipse and the moksha the relieving of the eclipses and duration of contact during the eclipse ( that is the beginning and ending of the eclipse before and after the eclipse), time calculation of the first contact and the last contact, duration of the totality before and after the time, projection of an eclipse, akshavalana, ayanavalana, resultant valana, corrected valana, valana for the middle of an eclipse, conversion of minutes of arc into angulas, construction of the figures of an eclipse, construction of the phase of an eclipse for the given time are the prime subject in this chapter. The fifth chapter is exclusive discussion on the solar eclipse, longitude of the meridian ecliptic point, drikshepa of the time of the geocentric conjunction in longitude of the Sun and Moon, drggatijya for the same time, lambana for the time of the apparent conjunction of the Sun and Moon, nati for the same time, Moon’s true latitude for the same, sparsa and mokshas of eclipses which is the duration of eclipse before and after the time of apparent conjunction, condition for the impossibility of a solar eclipse. The sixth chapter is on the visibility, phase and rising and setting of the Moon. The visibility correction, minimum distance of the Moon from the Sun, in degrees of time at which she becomes visible, measures of illuminated and unilluminated parts of the Moon, elevation of the lunar horns, Moon’s sankuvagra for Sunset, Moon, true declination and agra, the base of the elevation triangle, construction of the figure exhibiting the elevation of the lunar horns, duration of the Moon’s visibility in the light half of the month, time of Moonrise on the full Moon day, shadow of the gnomon due to the Moon at different time of the Moonrise in the dark half of the month, arte discussed . The seventh chapter discusses, in Laghu Bhaskareeya, on the visibility and conjunction of the planets, minimum distances of the planets from the Sun, in degrees of the time at which they become visible, degrees of time between the Sun and a planet, time and common longitude of the two places,

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org etc., are discussed in connection with the visibility of each and every planet and that too at the time of conjunction of the planets, latitudes of those planets for that time , distance between two planets when they are in conjunction in longitude. The eighth chapter discusses with the conjunction of a planet and a star. The longitudes of the 27 junction stars, conjunction of a planet with a star, celestial latitudes of the junction, the twenty seven nakshatra constellations and the number of stars, definition of absolute conjunction of the Moon with a star, celestial latitudes of the Moon when the Moon occults some of the prominent stars of the zodiac, two astronomical problems on indeterminate equation, subject scope and authorship of the book. Thus ends laghu Bhaskareeya of Bhaskaracharya I, who was born in 629 AD. MAHABHASKAREEYA OF BHASKARACHARYA. I : Mahabhaskareeya of Bhaskaracharya is also known as Bruhat Bhaskariya. It is an astronomical treatise dealing with the duration of day and night, the method of testing the accuracy of a given position of the planets, the mode of finding out the excess lunar month in a year etc.It discusses the grahakarma, a subject which was practically neglected by Aryabhatta I., Mahabhaskareeya is the earliest known work to have systematically deal with the method of operation for determining the position of the planets, using the principles of arithmetical calculations enunciated by Aryabhata I in the ganitapada of his work. This work is divided into eight chapters . In the first chapter, mean longitude of a planet and planetary pulveriser are discussed after giving homage to Lord Siva, planets and stars. Further ahargana calculation, mean longitude of a planet, Sun, Moon, Moon’s apogee, ascending nodes, etc., the pulversor for planetary motions, week day, time, general solutions, interpolator calculations etc are discussed. In the second chapter the longitude correction is discussed followed by places on the Hindu prime meridian, distance from prime meridian, criticism of other rules, longitude and time, details connected with prime meridian, longitude correction and its application... In the third chapter direction, place and time, junction stars of the zodiacal asterism and conjunction of planets with them are the prime subjects. Setting up of the gnomon, finding the direction from the shadow of the gnomon, various parameters of the shadow, finding latitude and longitude, Sun’s declination, day radius, eathsine, and ascensional difference, times of rising of the signs at the local place, Sun’s meridian altitude, declination and longitude, latitude from the Sun’s meridian zenith distance and declination, Sun’s altitude for the given time and also in the night, time corresponding to the Sun’s altitude, longitude of the rising point of the ecliptic, longitude of the setting point of the ecliptic, time for these parameters, hour

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org angle, prime vertical, locus of the shadow , Sun’s agra, midday shadow and the local latitude there from, finding the longitude of a planet or star with the help of that of another planet or star, longitude of the junction stars of the nakshastras, celestial latitudes of the junction stars, conjunction in longitude of a planet and a star and distance between them, occultation of certain stars by the motion. In the fourth chapter, true longitude of a planet is discussed. Sun’s mean anomaly and its Rsine, Rsine of an arc, functions equation of the center, Sun’s correction for the equation of time due to the eccentricity of the ecliptic, bahu and koti due to anomaly, true distance of the Sun and Moon, true daily motions of the Sun and Moon and true distance of the Sun or Moon by the eccentric theory, Sun’s true longitude by the eccentric theory, Sun’s correction for the equation of time due to the eccentricity of the ecliptic under the eccentric theory, an approximate fromula for the Sun’s declination are discussed in the first part. Semi durations of the day and night corrections of the Moon, tithi, karana, nakshatra, phenomena of vyatipata, manda and sighra anomalies, from the planets, corrected manda and sighra epicycles, calculation of the true longitude of the planets, calculation of the true longitude of the planet, true daily motion of the planets, etc. are discussed in the second part. In the fifth chapter, eclipses are discussed, distances of the Sun and Moon, diameters of the earth , Sun, Moon and shadow, longitude of the meridian ecliptic point, the five Rsines relating to the Sun and to the Moon, time of apparent conjunction of the Sun and Moon, finding the Moon’s latitude corrected for parallax, possibility of a solar eclipse, calculation of an eclipse, sparsa, and moksha, stithyardhas, sparsa and moksha vimardardhas, time of actual visibility of a solar eclipse, projection of an eclipse, akshavana, ayana valana, resultant valna, finding the center of the eclipsing body for the time of the first contact, last contact and middle of the eclipse, differences of procedure in the case of a lunar eclipse, measure of the eclipse, path of the eclipsing body, calculation and construction of the phase of the eclipse for the given time. eclipse of the Moon, diameter of the shadow, sthityardhas and vimardhas, direction of the Moon’s latitude to be used in the projection of lunar eclipse etc., are the subjects discussed in detail in this chapter. In the sixth chapter, rising, setting and conjunction of planets are discussed. Visibility correction known as aksha drkkarna and ayana drkkarma for the Moon, phase of the Moon, true declination, elevation of lunar horns, graphical representation of the elevation of the lunar horns, time of Moonrise on the full Moon day, duration of the Moon’s visibility during the night or time of Moonrise, time of the meridian passage of the Moon, Moon’s meridian zenith distance, elevation of the horns of the half risen or half set Moon, procedures to be adopted in the case of the planets, helical visibility

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org of the planets, minimum distance of the planets from the Sun at which they become visible, conjunction of planets, are the subjects further discussed. In the seventh chapter astronomical constants are discussed. Constants under the Sunrise day reckoning, revolution numbers, intercalary months, omitted lunar days and civil days in a yuga inclinations of orbits, longitudes of ascending nodes and apogees and manda and sighra epicycles of the planets, methods for finding the celestial latitude and manda and sighra anomalies of a planet, method for finding the bahuphala and kotiphala. Without using the Rsine difference table, how to calculate the above parameters, circle of the sky and orbits of the planets, constants under the midnight day reckoning, civil day omitted lunar days and revolution numbers of Mercury and Jupiter in a yuga, diameters of the earth, Sun and Moon, mean distance of the Sun and Moon, and longitudes of the apogees of the planets, manda and sighra epicycles and manda and sighra paatas of the planets. Methods for finding the celestial latitude and the true mean longitude of a planet, circle of the sky and orbits of the planets. In the eighth chapter, quotations from Mahabhabhaskariya in later works and glossary of terms used in the Mahabhaskariya are discussed. ARYABHATEEYA BHASHYA BY BHASKARACHARYA : Bhaskaracharya has also written an extremely important book as the Bhashya for the Aryabhteeya. The commentary for Aryabhteeya. It is literally an amazing contribution made by Bhaskarcharya with variety of examples and elaborations to what is given in Aryabhateeya. BIJAGANITA OF BHASKARACHARYA II Bhaskaracharya was borne in 1114 AD. He was the son of Maheswara and has contributed many books in the filed of mathematics and astronomy. Bijaganita is an important book on algebra. It discusses in detail the following subjects in 11 chapters. The first part is detailed description on the cube of fractions, prime numbers, and whole numbers, etc. Then Sunya vivarana, discussion on the application of zero, powers of numbers at different levels, different types of mathematical calculations, square root and cube root and roots at different levels and the pulverisor are described with examples. LILAVATI : Bhaskaracharya’s Lilavati is a very important book in the list of contribution of ancient Indian mathematicians. The book begins with various measurements like, length, volume, area, money, weight, time, distance, etc. writing numbers, addition, subtraction, multiplication, division, square, square root, cube and cube root determination, fractions and calculations with fractions, loss and profit, all mathematical problems connected with the business and banking, color of gold and precious metals and their evaluation for quality and price fixing, etc are given in the first part

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Then comes the Pythagoras theorem, and rules connected with geometrical problems, , triangle, square, rectangle, trapezium, rhombus, circumference, fine and approximate, and type of geometrical figures, the chord - circumference – diameter - radius- arrow relations in a circle. And variety of other infromations are given including quadratic equation, polynomials, monomials, etc. in Lilavati by Bhaskaracharya II SIDDHANTA SIROMONY: The fourth book of Bhaskarcharya is known as siddhanta siromany written during 1150. It is a very important work of Bhaskaracharya II. The first part describes in detail the mathematical part of planets or applied mathematics in astronomy. The real planets, the Moon and the Sun, the method for determining the correct position of the planets, the lunar eclipse, solar eclipse, the shadow of the planets and various parameters connected with the shadow of earth, rising of the planets, the path of revolution of the shadow and the planets,etc are the subject discussed in the first part. In the second part known as Goladyaya following subjects are discussed. All about the planets, size, shape, diameter, etc. the median and exact position of the planets, the eclipses of the planets, the parallax in the visibility, eclipse, rising and setting period are further discussed. In the second part of the book there are 14 chapters. Each chapter is discussing the subject separately. Many professors from the west and east have conducted a series of studies on the subject matter discussed in siddhanta siromany. Hence it has attracted world attention during these days. KARANAKUTUHALA: The fifth book of Bhaskaracharya is Karanakutuhala. This book is known in many names grahaagamakutuhala, Brahmatulya, Brahmatulya siddhantatulya, etc. It was composed in 1183 AD and deals with the subject of planetary motions. BRAHMADEVAGANAKA’S KARANAPRAKASA This book was composed in 1092 AD. It is an astronomical work describing the method of calculating the positions of the places from aharganana following the work of Aryabhatta I, with corrections suggested by Lallacharya. It has 10 chapters in which the subjects connected with the calculations of position, rotation, revolution of planets and the Sun and Moon are precisely done. Next part deals with the lunar and solar eclipses. In the last chapter the details of the author and his parentage are given precisely in two stanzas. BRAHMAGUPTA’S BRAHMASPHUTA SIDDHANTA: One of the most prominent Indian contributions in the filed of mathematics and astronomy, written during 628 AD. This books has been divided into 24 chapters in which variety of subjects connected with the positions of the planets, Sun, Moon, are discussed first. Then the lunar and

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org solar eclipses are described in detail. The detailed description of the shadow of the Moon, the planets coming together, determination of the true position and mean position of the planets and the applied mathematics on the spherics, are discussed in the second part, detailed description of the instruments used in the calculation of astronomical and geographical parameters, in the 12th chapter. (This chapter is known as yantrandhyaya) There is an unusual chapter in this book known as dhyana graha adhyaya on the ground that “he, the divine power tries to solve the problems by speculation not by mathematical calculation”. This work exerted considerable influence in the renaissance of Arab astronomy and mathematics in the 8th century. Many translations and commentaries for this book is available in English and also in other Indian and foreign languages. KHANDAKHADYAKA: The second book of Brahmagupta is Khandakaadya or khandakhadyaka written in saka year 587 i.e 665 AD. This book has eight chapters, the first describing the thithis and then onwards on the mean and true positions of planets, on the three problems relating to the diurnal motion, on lunar eclipses, on solar eclipses on the rising and setting of planets, on the position of the Moon’s cusps, on the conjunction of planets, respectively are the eight chapters. This book also has many followers in the filed and there is also the standard method of Brahmagupta for the calculation of variety of parameters connected with astronomy. GANESA DAIVAJNA’S BRIHAT CHINTAMANY Ganeswara daivajna has written four books connected with the subject of astronomy. The first book appears to be Brhat chintamani written in 1507 which is a short description on the preparation of a lunar calendar in 11 chapters where some instruments are mentioned in the first, then the sankranti details, paksha and thithi relation, lunar and solar eclipse, aynamsa, thithi calculation, etc.., are described. In the second book Buddhi vilasini, daivajna has described the mathematical concepts existed in India as a commentary to Lilavati of Bhaskaracharya II The third book is the commentary on the dhruva bhramanayantra of Padmanabha known as Dhruvabhramanayantravyakhya The fourth book of the author is grahalaghava, which is also known as siddhantarahasya an astronomical work in 145 chapters. The subject matter of this book is true and mean position of the planets, lunar and solar position calculation, eclipses of Moon and Sun, sankranti point of the movement of the Sun, the marking point of the signs, the rising and setting of the planets, detailed calculation of the shadows, making of panchangas and calculations of various parameters on panchanga,

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The smaller works of Daivajna are grahalaghava vrutti an astronomical work, laghuchintamani an abstract of his own work known as bruhat chintamani, patasarini deals with the astronomical calculation tables. The eighth book is pratodayantra. A small book on 143 tools describing a special class of astronomical instruments called pratodyantra made of ivory or simsa wood. These instruments were in use for quick measurements of the movement of the heavenly bodies, etc and for the determination of the time. Few scientists have described it as a chronometer and Eggling, a foreigner - scholar noted its use in military operations also. GANITAYUKTIBHASHA BY AN ANOMOUS AUTHOR: This book was supposed to be written in 1500 AD ( 1475 –1575) in Malayalam, which is also known as Yuktibhasha. The subject matters are presented in seven chapters, which commence with invocation to the lord. The number systems are explained and as a continuation the addition, subtraction, division, multiplication and taking square root, cube root and variety of the similar explanation are given in the first chapter In the second chapter namely dasaprasnottara, ten problems are explained in detail, in the third chapter all the explanations connected with fractions are given. This include additions, subtractions, divisions, multiplication of all the type of fractions. In the fourth chapter the rule of the three is given in the name of vyasta thrairasikam. In the fifth chapter detailed descriptions and mathematical calculations connected with astronomy are given. Here the details and problems are all given in katapayadi number system. Sixth chapter of Yuktibhasha is something unique . The details connected with R sine and R cosine, their additions, additions of squares, R tan and their relation with the Rcosine and Rsin, designing a circle from square and rhombus, measuring the circumference of a circle from the known and unknown diameter of two circles, variety of mathematical problems connected with Rsine, R cosine and R tangent of the circles where the radius of a circle is playing the key point, in all these calculations. The seventh chapter discusses with most complicated applied mathematics of the astronomical parameters . These are all connected with the latitude and longitude and colatitudes of the place and their calculation based on the Sunrise and Sunset. The description of the celestial and terrestrial latitudes and longitudes are also given with mathematical application. Cyclic quadrilateral and other cyclic geometrical pictures are described in the seventh chapter. Other than the above the spherics, shadow

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org based calculation, planets based calculation, their arrow, chord, circumference, etc are given KATYAYANA SULBASUTRAM This is a part of the Katyayana srouta sutra . The sulba sutra describes, in the similar way to that described in Bhoudhyana sulbam. The altar making and relative structures for the sacrificial fire/ yagas. The Katyayana sulba sutra book consists of 102 sutras in six parts. The geometrical proportions, the different measures, relative positions and spatial relations of various vedis ( fire altars) in connection with different types of yagas are mentioned . It also gives different geometrical figures, like triangle, square, rectangle, rhombus, trapezium, circle, semi circle and structures inscribed inside and outside. The Pythagoras theorem, the method for the determination of square root of 2 and 3 etc are also described here giving examples. The period of this book can be somewhere before 500 BC. LAGADHA’S VEDANGA JYOTHISHA There are three available Vedanga Jyothisha known as Archa jyothisa connected with Rk Veda, Yajusha Jyothisha connected with yajurveda and Sama jyothishsa belonging to the Samaveda. These are probably the oldest of jyothishsa books. LALLACHARYA’S SIHYADHI VRUDDHI TANTRA This is another very important ancient Indian astronomical book written in the first millennia AD. The first chapter is detailed description on the applied mathematics, mean planets, true Sun and true Moon, true planets, three problems, lunar and solar eclipses, possibility of an eclipse, rising and setting of planets, cusps of the Moon, conjunction of planets, conjunction of stars and planets, vyatipata and vaidhrut, rationale of corrections, etc., are the subject matter dealt in the first chapter. In the second section graphical representation of the motion of the planets, construction of the armillary sphere, rationale of rule on mean motions, sphere of earth, motion of the celestial sphere, description of the earth, false notions, astronomical instruments and astronomical problems are described. As the additional points, revolutions of the Sun in a yuga, solar months, etc in a yuga, apogees of the Sun etc, manda and sighra epicycles of the Sun, sighra angles, for regression and rising in the east and west, kalamsa of the planets, nodes of planets, polar longitudes of stars, polar latitudes of stars, true longitudes of the Sun and the Moon, true longitudes of the planets, mean and true daily motions, glossary of the technical terms are also described in the book. KHANDAKHADYAKA PADDHATI: The second book of Lallacharya is Khandakhadyaka paddhati, which is a commentary for Brahmagupta’s

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Khandakhadyaka. As it is a commentary, it gives the description with further elaboration on the contribution of Brahmagupta. MAHENDRA SURI’S YANTRA RAJA The book written in 1320 AD deals with the astronomical methods used for preparing instruments by means of which the time of day and night may be accurately ascertained. The work is in 5 chapters, which very systematically follow the method later adopted even in the most modern system. However it is important to note that this is the first book, where prototype making and designing are mentioned very systematically. In the five chapters, first chapter discusses various aspects on the mathematical calculation for designing an instrument, the second chapter the composition of the instrument, and the third chapter known as yantrarachana discusse the drawing of the instruments, and the fourth chapter is yantrasodhana which is the prototype construction of the instrument and the fifth chapter is vicharana determination of various parameters using the instrument. MANJULACHARYA’S LAGHUMANASA This book was written during 662 AD. This book has been published by Indian National Science Academy and the commentator on the subject content gives crisp fine observations. There are nine chapters in this book. They are respectively dhruvaka nirupana adhikaarana, Madhygatyadhikarana,sphutagatyuadhikarana, prakeernaka adhikarana, triprasnaadhikarana, grahayuti grahadvaya prilekhanadhikarana, grahodayadhikarana, mahapaataadhikarana, chandrasrngonnatyadhikarana. In all these chapters with very few tips , Manjulacharya has given the positions of the planets on Mesha sankrati day. The mean position of the planets, true positions of the planets, graphical presentation and actual explanations and observations of eclipses, the rising and setting of the planets, the path of revolutions of the planets are the most important subjects described by Manjulacharya. He has also described miscellaneous subjects in the 4th chapters and three problems (triprasna) in the fifth chapter. His calculation on the conjunction of two planets, eclipses and the graphic presentation of the eclipses are excellent narration of the actual facts in astronomy. PARAMESWARACHARYA’S BHATTADIPIKA Bhatadipika is the first book of Parameswara in which he has given the commentary for Aryabhatta’s Aryabhateeyam. This book is said to be written in 1430 AD. In 1431, Parameswaracharya has written another book known as drugganita which is the astronomical work. The third book is Goladipika written in 1443 AD. There are two version for this book. One is a bigger work divided into four chapters. In the first chapter details of the planets are

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org discussed. In the second chapter graha chara nirupana, critical evaluation of the motion of the planets is done. The third chapter discusses on the position and nature and geographical infromation on earth. The content of the fourth chapter is not well known except that it also deals with astronomy. SRIPATI’S SIDDHANTA SEKHARA This book was written in 1039 AD in 20 chapters, as in the previous astronomical books Sripati has given detailed description of astronomy and applied mathematics. Revolution and rotation of the planets, the true and mean position of the plants, correct position of the planets, the lunar and solar eclipses, rising and setting of the planets, chapters devoted to Moon, the Sun, mathematics, spherics, shadows of the Moon, earth, etc, instrumentations and the last chapter has question and answers. Sripati’s second book is ganita tilaka in which detailed application of mathematics as in the modern subject is described. In his book Dhruvamanasa written in 1057 astronomical subject based on laghumanasa of Manjulacharya is discussed. Dhikoti karana is the fourth work of Sripati, where a commentary type of description of Aryabhateeya and Lallacharya’s Sishyadhi vruddhi tantra is given. SURYASIDDHANTA OF ANONYMOUS AUTHOR The book suryasiddhanta has influenced the development of the Indian astronomy to a very great extent. Many astronomers have written commentary for this book, both from India and abroad. The text has 14 chapters and the first chapter onwards the subject matters are as follows. Mean and true motion of the planets, the true position of the planets, the direction and position of the planets, Sun and the Moon, the eclipse of Sun and the Moon, the graphical presentation of the planets, the detailed description of the stars, the rising and setting of the planets, the orbits of the planets, description of the earth, the instruments for the determination of the planets pathway and parameters of the astronomy, the determination of the periods and the time measurements. VATESWARA SIDDHANTA OF VATESWARACHARYA Vateswara was born in 880 AD and has written the book known as Vateswara siddhanta. In the first chapter Mean Motions of the planets are given. In Sec.1. Revolutions of the planets are discussed in detail after giving Homage and introduction, acknowledgement to divine sages and aim of the work, astronomy as the eye of the Veda and highly honored scent definition of Siddhanta, creation of asterisms and planets, time measures and circular measures,

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org duration of Brahma’s life, age of Brahma in the beginning of the Saka era, revolutions of planets. revolutions of the Seven Sages (or stars of the Great Bear), revolutions of planets’ apogees and nodes, nodes of Mercury and Venus, their actual revolutions, time of author’s birth and age at composition of this work. In the Sec.2. the time measurements are given : Sidereal and civil days, lunar month and solar year, intercalary months and omitted days. days of manes, gods and demons, Jovian years and Vyatipatas. Utsarpini Apasarpini., Susama and Dussama, constants for kalpa or life of Brahma, the zero point, nine modes of time reckoning, use of time reckonings. In the sec.3 Calculation of the Ahargana i.e the date starting from the epoch date is discussed. General method (for calculating Ahargana since the birth of Brahma or beginning of kalpa or yuga), shorter method (without using intercalary months and omitted days), other methods, when adhimasasesa is known, (another shorter methods), when adhimasasesa and avamasesa are known, when omitted days elapsed including the residual fraction are known, when Sun and Moon are known, (lord of the solar year), when suddhi is known Ahargana for the end of mean solar year, shorter Ahargana, Ahargana since Brahma’s birth lord of current day by backward counting, lunar and solar Ahargana, other methods for the Ahargana. In the sec. 4. Computation of Mean Planets is given both theoretically and also using practical method. General method, mean planets from shorter Ahargana, one planet from another, Sun and Moon without using Ahargana: (1) from avamasesa and adhimasasesa,) from avamasesa, other methods for Sun and Moon, other methods for planets, miscellaneous topics, positions of planets at the beginnings of Brahmas day, current kalpa, and Kaliyuga, actual positions of planets’ apogees and ascending nodes in the beginning of Kaliyuga. In the sec.5 the subject of Suddhi or intercalary fraction, for solar year etc. are discussed. Suddhi for solar year : residual intercalary, residual civil and residual days, relation between residual intercalary, residual civil and residual omitted days, past intercalary months and suddhi, lord of solar year, lord of lunar year, lords of solar and lunar years derived from each other’ planets for the end of solar year, planets derived from the Sun (first method), calculation of shorter Ahargana, planets for the end of solar month. Suddhi for solar month: residual civil, residual omitted and residual intercalary days, lord of solar month, shorter Ahargana and lord of current day, planets for the end of solar day. Suddhi for solar day: residual civil and residual omitted days, suddhi, Ahargana and lord of day, avamasesa for the current day, Moon for the end of solar year or solar month, Sun for the end of lunar month, lord of lunar month, monthly motion of the planets, daily motion from monthly motion, conversion of lunar days into civil days, planets for the end of lunar day. Suddhi for Jovian year: suddhi for the beginning of Jovian year (1) in terms of

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org civil days, (2) in terms of lunar days etc, lord of Jovian year, avamaghatis for the beginning of current Jovian year, shorter Ahargana (reckoned since the beginning of the current Jovian year), planets for the end of Jovian year. Miscellaneous topics : mean daily motion of the planets, planets derived from the Sun. (second method), days elapsed since the fall of omitted by day and intercalary month, Ahargana reckoned from the beginning of Caitra, Sun and Moon without using Ahargana, planets from Ahargana since Caitradi, lords of degrees of zodiacal signs. Sec.6 describes the Methods of a Karana Work. Days corresponding to residual fractions of intercalary months, omitted days, and planetary revolutions, multipliers, divisors and additives, additive, subtractive dhanagana and ksayagana for planets’ revolutions’ additives and subtractives for intercalary months and omitted days, calculation of a planet’s longitude, calculation of Ahargana since Caitradi, planet’s longitude by alternative method, true longitude, technique of writing a karana work. The sec. 7 narrates, Mean planets by the Orbital Method. Linear measures, sky lighted by the Sun, orbit of the sky, orbit of the asterisms, orbits of Sun and Moon, orbits of planets in yojanas, planet’s daily motion in yojana, yojanas of planets daily motion, planet’s longitude by orbital method, time taken in traversing the circle of asterisms and the circle of the sky, equality of orbits of Mercury and Venus with that of the Sun explained, identity of the sighroccas of Mars Jupiter and Saturn and the Sun explained, order of planets and their motion at Lanka and elsewhere, succession of lords of hours etc. (counted from Saturn in the order of increasing velocity), succession of lords of days etc. (counted from Moon in the order of increasing distance), difference in revolution periods of planets and difference in sidereal and civil days explained. Sec. 8 deals with the subject of the longitude correction. Prime meridian, Earth’s diameter and circumference, ancient rule for longitude and longitude correction its criticism, criticism of other views, longitude in time, longitude correction, commencement of day (varapravrtti), desantara, bhujantara and cara corrections, lords of civil year and civil month, lords of hour, etc.. Sec.9 Examples on Chapter I are given. Sec. 10 Comments on the Siddhanta of Brahmagupta as a commentary of appreciation and critical evaluation . Chap. II of Vateswara siddhanta describes in details the True Motion of planets. In the Section 1. of the second chapter the Correction of Sun and Moon are given. Introduction, Rsines at intervals of 56’ 15”, R versed sines at intervals of 56’ 15”159 radius, square of radius and Rsine 240, manda and sighra epicycles, manda and sighra anomalies, Rsines of bhuja and koti anomaly, other forms of bhujajya and kotijya computation of the Rsine,

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org computation of the arc by simple interpolation, computation of the arc by second order interpolation, true longitudes of Sun and Moon: bhujaphala and bhujantara corrections, cara correction, true motion of Sun and Moon: definition, jivabhukti for Sun karnabhukti, particular fromulae for jivabhukti, jivabhukti for Moon. In the Sec. 2. Correction of planets Under the Epicycle Theory are described with their constants. Correction of Mars, Jupiter and Saturn, correction of Mercury and Venus, sighrakarna and mandakarna of the planets, true daily motion of the planets, mandaphala and sighraphala corrections, correction of planets derived from risings of a star or rising of a planet: the longitude correction, the bhujantara correction, the cara correction. In this Sec. 3 Correction of Planets Under the Eccentric Theory are described. Introduction, antyaphalajya, karna or hypotenuse,kotijya and true koti, correction of the planets, the four quadrants, true daily motion of the planets, sighraphala and mandaphala, mean planet from true planet. In Sec. 4. Correction of Planets Without Using the Rsine Table are described . Introduction, pindarasi or sine of bhuja, mandaphala and sighraphala, are from Rsine, eight types of planetary motion, sighra anomalies for retrograde and direct motionsn periods of retrograde and direct motion, synodic periods of the planets, sighra anomalies of planets at rising in the east and setting in the west, sighra anomalies of Mercury and Venus at rising in the west, periods of heliacal setting and rising In Sec. 5 Correction of Planets by the Use of Mandaphala and Sighraphala Tables are given. Introduction, mandaphala and sighraphala corresponding to the tabular Rsine differences, true longitude of a planet, computation and application of sighraphala, mandaphala and sighraphala (alternative method), true motion of manda anomaly for a retrograde planet, sighra anomaly at a stationary point, graphical representation of retrograde motion: stationary points, kotiphala for stationary points, bahuphala for stationary points, upakoti, upabhuja, upakarna and kutilakarna, particular cases of stationary karna other particular cases of the karma, computation of retrograde motion, bhujajya and kotijya : (1) when their sum is given, (2) when their difference is given, (3) when their sum and difference are given, sighra anomaly at planet’s heliacal rising, periods of heliacal setting and retrograde motion, periods of heliacal rising, computation of planet’s true longitude miscellaneous methods : (1) Brahmagupta’s method, (2) Aryabhata I’s method for inferior planets, (3) method of suryasiddhanta, computation of mandakarna, (4) unknown author’s method computation of sighrakarna without using koti The sec. 6 is a very important applied astronomy part of Vateswara Siddhanta where the Elements of the Pancanga are given in details. Calculation of tithi, calculation of naksatra, true lengths of naksatras, length of Abhijit, calculation of true naksatra, situation of naksatra Abhijit, conjunction

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org of Moon with the naksatras, calculation of karana, immovable karanas, calculation of yoga Vyatipata and Vaidhrta , days elapsed or to elapse, possibility of occurrence of Pata , special instruction for declination , Pata past or to come, calculation of time of Pata , true tithi from mean tithi equalization of Sun and Moon, Sun and Moon at the ends of tithi, karana, full Moon and new Moon, occurrence of omitted days , time taken by Sun’s disc in transiting a sign end , time taken by Moon disc in transiting the end of tithi, karana or yoga, periods of occurrence of intercalary months and omitted days In the sec. 7. Examples on Chapter II are explained with solid proof and application. In chap. III Three Problems are described which is the applied mathematics in astronomy. In all the astronomical text books this chapter has importance, as it deals with the applied mathematics . The sec. 1 Cardinal Direction and Equinoctial Middy Shadow are the important points described. Introduction, latitude triangles , determination of cardinal directions , hypotenuse of shadow, determination of equinoctial midday shadow, latitude (from Sun’s zenith distance at midday and declination) . Here in the sec. 2. Latitude and Colatitudes are described with examples . Latitude and colatitudes by various methods latitude is always south, ayanacalana or precession of the equinoxes . In the sec. 3 The Sun’s Declinations are described. And in sec. 4 Day Radius or Radius of the Diurnal Circle. In the sec. 5 Earth sine followed by sec. 6 Agra or Rsine of Amplitude at Rising and the important astronomical parameter of sec.7 Ascensional Difference, Ascensional difference by various methods , lengths of day and night , ascensional differences of the signs . In the Sec. 8 Lagna Or Rising Point of the Ecliptic is the subject of discussion. Right ascensions of the signs or times of rising of the signs at Lanka , oblique ascensions of the signs or times or rising of the signs at the local place , time of setting and transiting the meridian by the signs at the local place , lagna or rising point of the ecliptic – , lagnakala (istakala) or time corresponding to the given lagna , astalagna or setting point of the ecliptic, lagna and lagnakala (istakala) when Sun and lagna are in the same sign, madhyalagna and time elapsed since Sunrise, lagna and lagnakala at night , lagnakala without the use of oblique ascensions of the signs, kalamsa or timedegrees . In sec. 9 Midday Shadow in the applied way is described. Altitude triangle for midday, direction of midday shadow , midday shadow and hypotenuse or midday shadow, dhrti and antya for midday, Rsine of meridian altitude from dhrti or antya Rsine of meridian altitude from sankutala ,

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org midday shadow and hypotenuse of midday shadow , dhrti, antya and day radius In sec. 10 Shadow for the Desired Time , which is purely an applied astronomy is given. Natakala and unnatakala: unnatajiva or unnatajya , svantya or istantya, svadhrti or istadhrti , Sun’s altitude , shadow and hypotenuse of shadow, dhrti, unnata and unnatakala , rules concerning multiplicand, multiplier and divisor , method of inversion . In sec. 11 Sun on the Prime Vertical are connected. Sun’s altitude when Sun’s digjya, Sun’s agra 386, is altitude of the upperlimb , samasanku or Rsine of Sun’s prime vertical altitude, samakarna or hypotenuse of the prime vertical shadow , locus of the Sun’s sanku, locus of the gnomonic shadow, prime vertical zenith distance and prime vertical shadow from the shadow locus, unnatakala or day elapsed or to elapse, nata or hour angle . The sec. 12 describes the Sun’s Altitude in the Corner Directions. Calculation of corner altitude, general method , alternative method (process of iteration) , calculation of konasanku: (1) by taking palakarna for the radius , (2) by taking agra for the radius , (3) by taking taddhrti for the radius, (4) by taking dhrti for the radius, (5) by taking istakarna for the radius, konasanku and its shadow . The sec. 13 the position of the Sun from the Shadow. Sun’s hemisphere, Sun’s ayana , Sun’s declination Sun’s bhuja , perpetual daylight , unknown planet from a known one, tithies elapsed, Sun’s longitude from Sun’s bhuja , seasons , equinoxes and solistices, sankrantis , seasons defined and named, Vedic names of months . The ancient procedure of graphical explanation is given in the sec. 14 known as the Graphical Representation of Shadow. Agra, bhuja, and sankutala for the shadow circle, construction of path of shadow and path of gnomon, shadows in various directions, motion of gnomon and shadow tip and that of the Sun’s sanku , observation of Sun through an aperture in the roof, or in oil, mirror or water, or through a hollow tube, observation of planets and stars, equinoctial midday shadow and its hypotenuse in the shadow circle , construction of the shadow circle, astronomical parameters by observation. This part of Vateswara Siddhanta the sec. 15 gives examples on chapter III Introduction, distance of a planet, distances of Sun and Moon, true distances of Sun and Moon , diameters of Sun and Moon , diameter of Earth’s Shadow , true angular diameters of Sun, Moon and Shadow , Moon’s latitude , the eclipser and measure of eclipse, total or partial eclipse, measure of uneclipsed portion of Moon , sthityardha and vimardardha, beginning and end of eclipse , istagrasa or eclipse for the given time, grasa for immersion and emersion, time at the given grasa asksavalana ayanavalana , resultant valana , relation

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org between minutes and angulas, conversion of minutes into angulas, side eclipsed first Chap. V gives detailed descriptions on the Solar Eclipse: The first section under solar eclipse deals with the parallax known as Lambana: Sec. 1 Lambana or Parallax in Longitude: Introduction, existence of lambana and avanati, drkksepajya, drgjya, madhyajya, and udayajya, madhyalagna or meridianecliptic point, madhyajya, drggati and laghudrggati, lambana, lambana for midday or smaller lambana, other froms for drggati . In this section also parallax itself is explained as sec. 2 Nati or Parallax in Latitude. Preliminary calculations, Moon’s drkksepa , nati or parallax in latitude, Moon true nati and Moon’s true latitude . Sec. 3 Sthitardha and Vimardardha , istagrasa for istakala , correction to Moon’s diameter, valana etc, reversal of directions explained . Practicals on the graphical methods are given in the Sec. 4 known as Parilekha or diagram. Introduction, construction of three circles, laying off valana in the trijyavrtta , laying off of Moon’s latitude in the mandaikyardhavrtta, contact and separation points and madhyagrasa , path of eclipsing body and istagrasa, diagram for total eclipse , the eclipse triangle, difference between lunar and solar eclipses, Parilekha in the trijyavrtta, Parilekha in the manialyardhavrtta, Parilekha in the grahyavrtta, laying off of koti in the trijyavrtta or mandaikyardhavrtta, istagrasa from istanadis, celestial latitude from istanadis, istaghatikas from istakarna, eclipsed and eclipsing bodies from sthityardhanadis, Parilekha in the circle of arbitrary radius, colour of eclipsed body invisible part of eclipse . Sec.5 Parvajnana or Determination of Parva. Possibility of eclipse, Moon’s latitude, measure of eclipse, sthityardha and vimardardha (for lunar eclipse), sthityardhas without iteration, lambana and apparent conjunction, nati and Moon’s true latitude, sthityardhas and vimardardhas (for solar eclipse), six monthly ksepas for Sun, Moon and Moon’s ascending node, six monthly ksepa for time. Sec. 6 Computation with Lesser Tools of astronomy: Computation of true tithi , mean anomalies of Sun and Moon (alternative methods) , computation of Yuti or Moon plus Moon’s ascending node , computation of lambana , computation of nati and Moon’s true latitude, aksavalana and ayanavalana, other approximate methods . Sec.7 Examples On Chapter IV and V. The practicals on the above chapters. Chap. VI. Heliacal Rising and Setting : Rising and setting in the east or west, time degree for heliacal visibility, inclinations of planets’ orbit, computation of celestial latitude, visibility correction ayanadrkkarma , visibility .

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In the Chap. VII. Detailed description of the Elevation of Lunar Horns are given. Sec. 1 (1) Diurnal Rising and Setting of the Moon. Introduction, time of Moonrise or Moonset, Moonrise on full Moon day, rising Moon and setting Sun on full Moon day . (2) Moon’s Shadow: Suitable time for calculation, planet’s nychthemeron, Moon’s shadow, Moon’s hour angle, altitude of Moon’s upper or lower limb, time of Moon’s meridian passage (3) Elevation of Lunar Horns: The srngonnati triangle, sita or measure of Moon’s illuminated part parilekhasutra or radius of inner boundary of illumination, reduction to angulas. (4) Diagram of Lunar Horn: When the Sun is not on the horizon, when the Sun in the horizon the elevated horn, the halfilluminated Moon, rising and setting of the elevated horn, the crescent Moon. Se. 2 Examples on Chapter VII are given. Chap. VIII Conjunction of Heavenly Bodies: Sec. 1 Conjunction of Two Planets, diameters of planets, distance between two planets in conjunction, bheda or eclipse of a planet, aksadrkkarma for the time of conjunction , reduction of minutes into cubits . Samaprotiyayuti : introduction , ghatis elapsed since or to elapse before samapr tiyayuti Sec. 2 Conjunctions of Star and Planet: Polar positions of junction stars of naksatras polar positions of Canopus and Sirius, conjunction past or to occur, polar latitudes of junction stars of naksatras, polar latitudes of Sirius and Canopus, bheda or occultation, occultation of Rohini and its junction star, number of stars in the naksatras, shapes of naksatras, the pole star , star’s udayalagna and astalagna , heliacal rising and setting of stars Astarka and Udayarka, days of star’s invisibility, heliacally ever visible stars, circumpolar or always visible or invisible stars, mean declination and true declination, heliacal rising and setting of Canopus, shadow etc. of planets and stars, planets’ sankranti, revolutions of the Seven Sages, Arundhati or Mizar, conclusion Vatesvara’s Gola is the second part of the Vateswara siddhanta. It appears to be a separate book in Vateswara’s contribution. Hence it starts as a separate set of chapters Chap. I Appreciation of Gola or Spherics: Introduction, appreciations of spherics, spherics and what it teaches , aim of the present work . Cha. II Graphical Demonstration of Planetary Motion Through Eccentrics and Epicycles Cha. III Construction of the Armillary Sphere, Grahagola or Spheres of the Planets, Samanyagola or the general Armillary Sphere, right angled triangles, the lambana triangle, situation at Lanka and Poles, fixed or immovable circles, movable circles .

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Chap V Spherical Rationale: Mean motion, planetary corrections , right ascensions of the signs, oblique ascensions of the signs, rising and setting of the signs, visibility and invisibility of the signs, solar eclipse, phases of the Moon, elevation of lunar horns, appearance of the Sun, visibility correction, planetary conjunction, concluding stanza Chap V. The Terrestrial Globe: Cause of Earth’s creation, Earth spherical and supportless in space, not falling down , cities in the equator and abodes of gods and demon, Earth like the bulb of the Kadamba flower . Thus ends the most renowned Indian contribution in the mathematics and astronomy, namely Vateswara Siddhanta. Any one who goes through this book will never in his life say that Indian knowledge in the field is meager or small.

CHEMISTRY There are many books written in chemistry or about chemicals. The books describing the rasa method of treatment also contain details about chemicals and their preparations. Some of the books coming under the above category are Rasendra mangala, rasarathnakara, karshaputa, lohasastra, kakachandeesvarathanthra, etc. Yogaratnamala of Nagararaja of Vikramasila, Rasarnava, the 10th century book written by Bhairavanand yogi, Rasahrudaya thanthra by Bhagavad Govindapadacharya, Jagadguru Sanksaracharya’s Guru in the second half of the 7th century etc., deal with many chemicals and some type of special chemicals. Goraksha samhita, the 12th century text by Ghoraknath has detailed decription on manthra, thanthra, yanthra and the second part known as bhoothiprakarana has been completely devoted for the chemistry. Rasendra choodamany is the 12th century book written by Acharya Somadev. Description of Rasoparasas, ratna pareeksha etc are also in this text. Rasprakash sudhakar is the 12th century book by Acharya Yasodhara Bhatta. There are 13 chapters in which Mercury, Rasoparasas, Sadharana rasas, ynatras, mooshas and metals and precious stones are described in detail. In Rasaratnakara, the 13th century book written by Nityanath in 5 kandas details of mercury and many type precious stones, like emerald, diamond, etc …are described. Their oxides, sulphates and the camphor, safforn, etc are also included in the text. In the fifth khanda of the above book detailed description of the mercury, extraction, complex fromation with mercury, chemistry, etc are mentioned

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Rasahrudaya is a book written in 13th century, by Acharya Kankal yogi. He has described in his book, the mercury, silica, sulphur, camphor, mica, compounds of the above. Rasachintamany is a book in which the mercury processing method is described in detail. This is a 15th century book written by Acharya Ananda Dev. 177 types of oxides used in curing the diseases are mentioned here. Rasendra chintamany and Rasamanjari written separately by Dumdumkanathan and Salinathan describe in detail the medicines prepared from chemicals. Bhavaprakasha is the 16th century book written by Acharya Bhava Misra having two parts poorva kanda and uttara kanda. Detailed description on various metals and their products used in the treatment are given here. Rasakoumudi is written by Jnanachandra in which four parts describe in detail, the science of chemicals including mercury, sulphur, silk, mica, silica, etc RASATHARANGINI BY SREE SADANANDA SARMA The book starts by describing the qualities of the Rasa teacher and the students, teacher student relation, explanation of a perfect laboratory, instrumentation room, translation and glossary of the chemical words in Sanskrit, classification of crucibles, furnaces, and process in relation with the chemical processing. Different types of yantras such as dola- urdhwapaata- adhapaata- thiryakpaata- bhasma- kacchapa –bhoodhara- mrudanga- baaluka- lavanaputa- yantras - used for different types of processing such as filtration, evaporation, condensation , sublimation, oxidation, filtration using cloth, sand bath heating, solidification, crystallization , heating, etc. Variety of puta yantras and used for heating the materials are thus described: ishtika jarana somanala hamsapaka naabhee dhoopakoshtivalabhee swedana paatanaushna yantras which are used for sand heating, direct heating, flame heating, boiling, smoking, steam heating, sublimation type of heating , warming, etc. Variety of processing for the mercury and other materials are described here as sodhana, mardhana, moorchana, paatana, urdhwapaatana, adhapaatana, bhodhana, niyaamana, deepana, jaarana, etc. The extract of many materials are described: mudgarasa, rasapushpa, rasakarpoora, rasaarpatika,etc Then the processing of mercury is given and material processing with mercury also. Parada marana, rasasevana, etc. the description of sulphur processing of materials are further described as sulphur oil, sulphur water emulsion etc. Variety of hingula, production, purification, various processing, etc.

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Abhraka which is the mica is described as naga bhraka, mandookabraka, vajrabhraka and variety of processing with mica. Harataala, thalaka, paatra thala, thaalasodhana, thaalaka, etc are described in detail. The conch shell powder, making fine powder, properties, uses, etc making variety of drugs using the same. Preparation of variety of oxides known as kshaara, arka-thila- apamrgasnuhika kshara, palaasa kshara, sandhava kshara, samudra lavana kshara, etc. Detailed descriptions of gold and salts of gold are given in the 5th chapter. Similarly detailed description on silver and silver production in the next chapter, complete description of copper including metallurgy as in the other cases., tin metal, lead, iron, gold related alloys are described in the next series of chapters, including gold ores, metallurgy, purification, application properties, and their medicinal uses. The 21st chapter gives the description of sulphates of gold, copper, silver, tin, lead, and zinc. 22nd chapter gives 22 types of brass. Many types of jewels are described in the 23rd chapter including precious stones of different variety The 24th chapter describes the poisons of natural origin mineral and organic types. Thus ends the rasatarangini RASARATNAKARA OF MADHAVA. This is a 17th century text in which rasa processing and their qualities are described in details. Its 12 qualities are specifically mentioned as an important factor to be scrutinized before prescribing this as a medicine. 18 types of processed mercury products , 21 types of processing, like mardhana, swedana, moorchana, utsapana, urdhapaathana, adhapaatana, bodhana, niyaamana, sandeepoana, anupaasana, are mentioned for zinc, tin, sulphur, gold, various types of plant products,. Rasa sindoora rasa karpoora, etc are also mentioned here. RASARATNA DEEPIKA This text book describes the production of mercury and their properties and the properties and medicinal application of gold, silver, copper, zinc, sulphur and a variety of their alloys. The medicines, their application and the precautions to be taken for the application/consumption of the rasa based medicines are clearly mentioned in the book. RASENDRA SARASANGRAHA OF GOPALA BHATTA.

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Rasendra sarasangraha is a 13th century chemistry and health based science book. The first chapter of the book describes the mercury and detailed processing techniques of mercury, including the extraction and purification. In the second part, the processing of sulfur and compounds with sulfur are described. Then the vajra processing and manasila processing are explained, processing and compound formation with silica, mica, sulphates, iron oxide, arsenic oxide, etc are given as vimala sodhana- kaaseesa sodhana- maakshika sodhana –sila sodhana -tangana sodhana- swarna, rajata, thamra, loha sodhanas, etc Further description is on the health science and medicines which are given in the respective portions, below. RASAKAMADHENU The chemistry book of the 17th century gives detailed description of the yantras – instruments- used in chemistry in the first part. Followed by this, the mercury processing, detailed descriptions of various types of poisons, classification of materials, quality of chemistry teacher, student, laboratory assistant and making of a laboratory or workplace, etc., are given. Explanation of the iron, gold, silver, copper, zinc, lead, brass and alloys of these metals and their properties, quality description of various types of metals and alloys are also given. Then the extracts of natural products and their compounds are given. Variety of processing methods like heating, vaporization, sublimation, direct and indirect heating etc are also described in the end of the book. RASACHINTAMANI Variety of oxides of metals and their alloys are described in the first part. The plant products and the combination of various types of chemicals and their curative effects are explained further. As in the previous books, description of the metals, their compounds and alloys are given as a continuation of the above subjects. The 7th and 8th chapters are entirely devoted for different types of metallic product preparations. This type of compounds are not seen in other rasa based books written by ancient Indian Rishies. In the 9th chapter the description given is on diseases and curative effects of various types of medicines, both medicinal plant based and mineral based products. RASASAARAM OF GOVINDACHARYA The first chapter gives the religious rituals to be performed by a rasa expert, second chapter explains the qualities and properties of the materials

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and alloys. The third chapter is full of processing of rasa and metals as explained in the above books. It is interesting to note that 48 types of processing methods are given in the fifth chapter. In the last chapter different methods for the purification of the metals and mercury are given. RASARATNAKARAM The merits of the rasa chikitsa, that is the treatment with metal based chemicals, their merits and the demerits, etc., are described in the first chapter. Further, chapter wise description of the subject matters is as follows: removal and the purification of the chemicals used as medicines, processing by heating the materials, different types of yantras - that is- the instruments used in the chemistry laboratory, processing with sulphur and diamond and the product qualities, application of mica and their products in chemical based treatment, uses of haritala and manasila, explanation of gold- silver-mercury- copper-lead- copper salts- zinc- etc. are further given. Detailed descriptions with properties of the impure metals and pure metals, iron based loha asavam, metal oxide preparation, metallic sulphate preparation, etc., are also given in the 9th chapter of the book. RASARATNA SAMUCCHAYA In Rasaratna samuchaya, the author has mentioned the names of many books on chemistry and medicines . The names of the ancient rasa books mentioned are: Rasaparijatha, Rasaratna pradeepa, Rasaratnakara, Brahmasiddhanta, Kapilasiddhanta, Lankesasiddhanta, Chandra sena siddhanta, Nagarjuna siddhanta, Mahadeva siddhanta, Hareeswara siddhanta, kakachandeeswara siddhanta, Maruthasthana bhairava siddhanta, Swacchantha bhairava thantra, Datthathreya thantra, Kamadhenu thanthra, Marasana thanthra, Rudrayamalathanthra, Goraksha samhita, Nasathya samhita, Agasthya samhita, Dathathreya samhita, etc. The first chapter in this book gives detailed description on Himalayas, extraction method of mercury, many extracts, processes, methods, extraction of gold, silver, zinc, lead, brass, bronze, etc are described in the following chapters . Rasavidya, the teaching and learning of rasa sastra, teacher- student- education- academic institution for rasa studies, installation of various types of yantras in the laboratories and in the production centers, variety of heating methods, crucibles, furnaces, etc., are the subjects described upto 12th chapter of the book. Further descriptions in the next few chapters are on the health problems and the medicines used for curing the diseases. That part is given below under the health science part, separately. OTHER BOOKS ON RASASAASTRA There are a series of books on the subject of chemistry. Few among them have been mentioned by the author of Rasaratna samucchaya . Herewith

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org a list of the books available at the oldest ayurvedic Institute in Trivanrum : The Government Ayurveda College, is given. I wish the reader will remember that the subject matter content will be almost the same as explained in the above books. However additions, deletions, modifications, corrections and rationalization would have been undertaken in each of the book. More than that, some of the books might deal with the subject as the specialized subject area focusing book, as seen in the modern health science . Rasachandrika, Rasa chikitsa, Rasachikitsa vivaras, Rasapadhati prakasika in two volumes, Rasajalanidhi in 5 volumes, Rasa kamadhenu, Rasamrutha, yet another version of Rasamrutha, Rasapada vidhi, Rasaprakasa sudhakaram, Rasajata chintamany, Rasaraja mahodhadhi, Rasaraj mahodaya, Rasatarangini in two volumes, Rasaratnakara in two versions, Rasaratanakarantargata, by two authors, Rasaratna pradeepika, Rasarnvakalpa, Rasarnava sudhakara, Rasarnava and Rasa sankethakalika, Rasathanthra sara, Rasathantra sara siddha prayoga sangraha- part I and II, Rasa tarangini part I and II, Rasatarangini bhasha, Rasatatwa darsana, Rasavijnana prakasa, Rasayana kanda, Rasayana samhita, Rasayana tantra, Rasayana sara, Rasayana tathwa vislesham, Rasendra bhaskaram, Rasendra chintamany, Rasendra pranama, Rasendra sambhava Rasendra sampradaya, Rasendra sara sangraha, Rasopanishad, Rasasastra , iatrochemistry, Agastya vaidya chandrika, Ananda kanda, Anubhootha yoga mala, Siddhachikitsa, Ayurveda prakasam, Ayurveda sudhakaram, Ayurvedeeya siddha chikitsa, Ayurvedic materia medica, Ayurvedic system of physics and chemistry, Bhaishajya ratnavali, Bharateeya rasa paddhati, Bharateeya rasa saastra, Bruhat yoga tharangini, Sarngadhara samhita, Abhinava rasa sastra, etc. These are the few names among a large number of books available in ayurveda and ayurveda based chemistry. Here, one can see chemistry, metallurgy, medicines and treatment systems adopted for diseases are included in a single title of rasa saastra. The periods of the above books vary from 200 AD to 1700 AD.

METALURGY A large number of chemistry books are mentioned above in which detailed descriptions of metals, their properties and their alloys are mentioned. Most commonly described metals in all the above books are copper, gold, silver, tin, lead, zinc, and iron. Interestingly ancient Indian mines functioning many thousand years ago were known to produce extremely high quality metals and alloys. Hence theoretical and applied knowledge on the metallurgy existed during then, in India . Rasopanishad gives detailed explanation of tin in the 16th chapter known as Vanga samsodhanadhyayam.

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Rasakamadhenu gives detailed reports on the iron, gold, silver, copper, zinc, lead, brass and the alloys of the above metals and their properties, quality description of various types of metals and alloys are also included. In Rasachintamani, detailed descriptions on the metals are given in the 7th and 8th chapters in which different types of explanation on the metallic product preparations, not seen in other books, are also given. In the Rasendra sara sangraha, detailed descriptions, as chapter wise, on the processing of gold and gold compounds are given. In a descriptive way the metallurgy of silver, copper, brass, lead, zinc iron and their general method of processing, purification, alloy making etc., is also given. This is a text book written by Gopal Bhat in 13th century In the second part of the Rasachandrika , detailed descriptions of various types of putas used for processing metals are given. In fact this is the most authentic book which describes in detail the mooshas used for producing high temperature, required for metallurgical purposes. It describes, the method of making furnaces/kilns / mooshas. The commonly used kilns are mahagajaputa, gaja puta, varaha puta, kukkuta puta, kapotha puta, gocharaputa, bhanda puta, baluka puta, bhoodhara puta, lavaka puta, etc.. In Rasarnavakalpa, in the first part descriptions on copper, lead, gold, silver, and their medicinal powers is given. Sulphur and arsenic sulphide are described. A variety of minerals used for curing different type of diseases are further described. HEALTH SCIENCES, MEDICINES, DISEASES ETC. It can be seen that almost all the Rasa based books explained above in this part as chemistry carries as their second part, the health based information, both diseases and the treatment methods. This also include the diagnosis method, pathyas or control of the life style , processing of drugs in small and large scale. SUSRUTHA SAMHITA OF SUSRUTHA MAHARSHI The book starts with the explanation on the aim of Ayurveda and the principle followed in the diagnosis and treatment of the diseases. The date of composition of the Susrutha samhita and also the authority of the book, the scope and subdivision of the Susrutha samhita are further explained, then the concepts and theories. Ayurveda in relation to cosmic evolution, embryonic conception, body, life and soul, rules and the principles of genetics are then discussed in details. The vata, pitta, kapha principles of the body which is known as tridosha siddhanta, the sleep and dream and their effect. Time and age of an individual.

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The embryonic growth and obstetrics and post natal measures are further discussed in detail giving specific importance to each and every point. The anatomy and physiology of human body are discussed in detail., The food, food values of different edible and potable substances, and their uses in health and curing the diseases. Health and longevity, hygienic rules, care of eyesight, the three ages (childhood, youth and old age) of man, anatomical features and physiological characteristics, rejuvenation and longevity. The subjects are discussed with great accuracy and looking into minute points. The diseases, their origin and classification, diagnosis of diseases, symptoms of a disease indicating the imminent death, fundamental principles of ayurvedic treatment, some diseases meriting special mention, dental diseases, mental and psychic disorders, etc. some of the diseases are further discussed with more details in the 9th part of the book. In the tenth part, poisons and antidotes are discussed, some special reciepes formula are carried in the 11th part of the book . In the 12th part, the living creatures and their classification are the subject. One can see how seriously the ancient Indians have looked the subject. Plant classification, ecology, morphology, taxonomy are discussed in the 13th chapter. And 14th part carries the information on the pharmacology and materia medica of the health science. In this part medicines, applications of medicinal preparations and some important medicinal preparations. The 15th part is the detailed discussion of the surgery. General principles and methods of practical training of surgeon, surgical instruments, surgical importance of certain vulnerable parts, special surgical methods, ophthalmic surgery, dental surgery, and post surgical measures are included in the descriptions.

In the 16th chapter convalescence, and their causes remedies are discussed. And in the last part the explanations on the training methods, duties of the physicians , surgeons, and nurses are given. CHARAKA SAMHITA OF MAHARSHI CHARAKA This is a very ancient book on ayurveda which is similar in content and explanation to Susruta samhita. All the divisions as sthanas are given here also.

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Soothrasthaanam: Learning of Ayurveda, Ayurveda as the upaveda and its methodology of presenting the information, materials and their properties, body and mind, the thridosha siddhanta and its explanation, the medicinal extracts and decoctions,, variety of oils, salts, decoctions, medicinal plants, etc. are mentioned as the abstract information. Medicines used for vomiting and for many other purposes like, curing vata, head injuries, fever, effect of poisonous, body ailments, etc, Nineteen types of mahakashayass which are decoctions and their specific uses. Detailed description on the food and components in the food. Smoking and the bad effect of smoking the poisonous materials and good effect of using the ayurvedic drugs for smoking , which is a method of medical treatment. Use of special types of medicated oils at different times, different ages, before or after different customs and traditions and also for different parts of the body. Body care , change of food, different customs and traditions to be followed and use of varying garments, etc, during seasonal variations. Process of treating each disease and how to proceed in the diagnosis, five sensory and functional organs, panchabhoota, pancha prana etc, Collecting the correct proof , intensive observation of a patient and comparing with his on health state, the method for noting the healthy state and unhealthy state through variety of observation techniques, effect and merits of exercises and apt exercise for men and women at different ages and other conditions, the quality of a physician-drug-nurse-material and surrounding., the diagnosis through direct and indirect observations for certain specific diseases, classification of drugs and physicians, the illness connected with vayu as one of the components of tridosha (vata) Properties and medicinal effect of variety of oils when used directly or used after converting into medicated oils, detailed description of the treatment in which the sweating techniques are used, treatment in which cleaning the intestine and vomiting techniques are followed, description of health and the opinion of different Rishies on the cause and effect of diseases and ill health. Variety of diseases like: diseases caused by worms, microorganisms, due to bad food, etc. Various diseases connected with bowels, urinary bladder, reproductive organs, lungs, etc. and their symptoms. Hundreds of illness/diseases are explained here. Diseases of lean and fat individuals, sleeping and limitless sleeping as a symptom of good/ill health .

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Detailed description of blood and blood based diseases, variety of extracts used as a part of food and their merits, extracts of leaves, fruits, seeds, bark, vegetables etc., are all included in this list. Food and qualities of the food to be maintained for good health. Various types of cereals, pulses, meat products, various birds meat, vegetables, roots, fruits, different types of fermented food/liquid, milk and fermented milk products of various animals, various types of water collected for different sources, the sweetening agents, causes and bases of diseases, etc. are explained in the soothrasthanam part of Charaka samhita Nidaanasthaanam: as mentioned earlier each and every part of Charaka Samhita describes in detail various topics precisely. Here the description o jwara nidanam on fever, raktapitta nidhanam or blood based diseases, prameha nidhanam pancreas based, kushta nidanam, sohasanidanam, unmada nidanam, apamsara nidanam, like this related illness are described very systematically under specific classification. Vimanasthaanam: Detailed description of six rasas (flavours), curative effects of various rasas or flavors from different types of materials, quality parameters to be followed for every medicinal components, depending upon the place, time and season of collection and processing. The importance of drugs and counseling in the treatment, three types of special knowledge about the illness (nature of patient- diseases-drugs to be used), psychological diseases, etc. Tests to assessing the knowledge of the students and examination, evaluation of the text books prescribed for the studies, the examination for ayurveda teachers and students, tests for understanding the analytical capacity of the physician and students, the method of learning and teaching ayurveda, the ethical points to be followed by a physician, the method to be followed for discussion, the pledge to be taken after completing the academic course of physician, the viva voce examination and evaluating viva voce method based on 25 ways of expression and answering by the student, etc. are systematically presented. Sareerasthanam: various types of human body and its nature, the body and mind, the body – mind and jeevatama relation, the cause of happiness and unhappiness, disproportional body, the conceiving and the development of embryo in the womb of the mother, problems of growth during different periods in the womb, the masculine character of the body, the body (janma vasana) character of the body, special qualities of specific individuals, detailed description of pregnancy and the development of the embryo -human body- in the womb of the mother, full details of the baby/embryo, heart beat of the baby, death of baby in the womb, birth, namakarana, jathakarma, milking of the baby, disinfecting the dresses of the bay, cleaning of the resting places of baby, all the information connected with the newly born baby are descried very systematically.

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Indriyasthanam: body organs, sensory and functional organs, the prakruti and vikruti of the body, analyses of ears, eyes, teeth, skin, nose, etc., and the connected diseases. Chikitsasthanam: medicines, the method of curing and treatment, variety of ayurvedic drugs and their components, gooseberry, various rasayanas, rejuvenation of the body, treatment of the fevers, blood diseases and treatment, diabetics, leprosy of various types, blood pressure, epilepsy, psychological problems and treatment, anemia, weakness, stomach based problems and treatment, skin diseases, lungs problems, vomiting and dysentery, treatment for poisons, injuries- wounds - skin related problems, paralyses and Parkinson’s diseases, sex diseases and those connected with sex organs , are described in details specifying each and every point in the analyses, diagnosis and medicament. Kalpasthanam: variety of kalpas of making the drugs, their applications and uses for specific health problems are described here. Siddhisthanam:panchakarma, vasti, netra vasti, etc., are described including variety of special treatments. Thus the Charaka Samhita explaines very systematically almost all aspect of health and ill health as a huge and voluminous book.. This book might have composed probably 2500 years ago. ASHTANGA SANGRAHA OF VAGBHATACHARYA The period of Vagbhatacharya is supposed to be somewhere between 1st century AD and 3rd century. In Ashtanga sangraha also the subject matters are classified into soothra sthana, sareerasthana, nidanasthaana, chikitsasthaana, kalpasthaana and uttarasthaana. Here comes only 6 parts. Totally there are 150 chapters. The unique way of presentation of subject matter in Ashtanga sangraha is the specialty of this book. Here the author has meritoriously presented the information in sootras as done by Patanjalai in the yoga sutra. Vagbhatacharya has taken the authentic subject matter for the body treatment , from Charaka samhita and for surgery, he has followed Susrutha samhita. Of course he has further improved and simplified the subject matter. At random he has also given statements in prose for describing the subject matter other than the poetic method of presenting. Many commentaries are available for Ashtanga sangraha and also many additions and modifications have been done by others to improve the subject matter. ASHTANGAHRUDAYA OF VAGBHATACHARYA In this book the subject matters are presented as follows: sootrasthaanam, sareerasthanam, nidanasthanam, chikitsasthanam in which the kayachikitsa ( treatment for the body) balachikitsa (child care and treatment) grahachikitsa (mainly connected with mental disorders and some

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diseases presumed during those days based on planetary position in the horoscope), urdhwanga chikitsa ( treatment of the body parts) and salyachikitsa ( surgery). Then the kalpasthanam and uttarasthanam are described as 6 parts, as mentioned in the ashtanga sangraham. The details given in Charaka samhita and other books are further improved and said to be presented in more systematic methods in Ashtanga hrudaya. Here, on each and every aspect of diagnosis and treatment, the opinion mentioned by the acharyas of earlier works were quoted and then the irrational views were removed giving logic conclusion and then the authors view points are presented. After giving the rational basis of selection and diagnosis, he himself tells that “this is not my opinion, but the opinion given by great ancient Rishies”. The selection of drugs are done with utmost care, the explanation given on the treatment through vamana and samana are very interesting to understand and analyze. Every modern physician should have to have a look at this book, so that he or she can take many information from this great work of Indian scientist. About the authorship of the book, there are many opinions. As the student of Indian heritage one need not bother too much about the bit points of the authorship, if he is interested in the subject matter only. Other than Charaka Samhita, Susruta Samhita, Ashtanga Hrudaya, Ashtanga sangraha, the books connected with rasa chikitsa give detailed description of the body, diseases and treatment methods. For citing the examples a few explanations are given below.

HEALTH SUBJECTS IN RASARATNAKARA Description of plant products, variety of natural inorganic and organic poisons are given in the 10th chapter of Rasaratnakara. In the 11th chapter, the qualifications of a doctor, student, patient, nurses, rajavaidya, diagnostic methods, different types of ailments, etc., thridosha siddhanta is described in detail. Treatment for the three types of patients are given. From here onwards description of the treatment is given upto last chapter of the book. Varity of diseases: connected with lungs, sound box, blood, heat, liver, intestine, digestive systems, epilepsy, urinary problems, stomach problems, body ache, leprosy, bone problems, chicken pox and small pox, ophthalmic problems, specific problems related with ladies, babies and old aged people are described .

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Fever, typhoid, anemia and infectious diseases due to microorganism and worms, contagious diseases, etc., are also mentioned with their symptom and diagnostic methods.

HEALTH SCIENCE IN RASARATNA SAMUCHAYA From 13th chapter onwards health, diseases and curation are described. Cancer, lungs problems, typhoid, TB, vomiting, heart problems, stomach-intestine-liver-pancreas- ailments, urinary bladder problems, sex diseases, ear- eyes- borne- intestine- problems, etc., are described here upto 26th chapter. 26th chapter is exclusively for rasayana chikitsa, 27th chapter for vajeekarana or rejuvenation, 29th chapter exclusively deals with poisons, and 30th chapter devoted for mercury based drugs and treatments.

HEALTH SCIENCE IN RASENDRA SARA SANGRAHA The second chapter of the book is fully devoted for the diseases and treatment using chemicals, i.e rasa chikitsa. Here description is given as follows: jwara and its treatment, various types of fevers, various types of contageous diseases caused by worms and microorganisms, treatment for breathing problems, throat- thirst-epilepsy and convulsions- bile related problems, skeletal joints, heart problems, urinary problems, diabetics, leprosy, hyper acidity, ear- nose-throat-neck-eyes-head-brain- problems etc. The third chapter discusses the subject of diseases for the children as now known as pediatrics/ child specialist. The fourth chapter is treatment for poisons and the fifth chapter for rasayana vajeekarnam

HELTH SCIENCE IN RASA CHANDRIKA In the first part of this book, detailed description and treatment for diabetics, the stomach problems and for few other diseases are given. The rest of the book describes only on furnaces and processing the rasas for using as medicines.

HEALTH SCIENCE IN RASARNAVAKALPA Rasarnavakalpa is a text book of 10th or 11th century AD. The first part of this book, as explained earlier gives details of metallurgical process and the use of the metals and their compounds for treatment. In the second part in 77 verses explains the tantric method of rasayanas and their benefits. From 78 to 207 verses discussion of the mercurial preparation for the treatment of

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INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org variety of diseases are given, from 213 verses onwards the use of medicinal plants are given with and without minerals and metals. The order of further discussion in this book is as follows, the mercury and its various preparations used as such or with other products for treatment. Medicinal plants and classification of medicinal plants. 64 families of the plants are explained here. The medicinal preparations of metallic compounds using rubbing, roasting, heating, steaming, digestion, calcinations, filtration, etc., are explained. The use of abraka/mica as medicine, and other chemicals used for the same purpose like, kanta loha, cinnabar, makshika, gold pyrites, lead compounds, copper compounds, orpiment, borax, iron pyrites, etc., are explained. BOOKS ON CIVIL ENGINEERING Many south Indian temples, cave temples in middle India, marble structures and buildings in Rajasthan and very many constructions in various other parts of India, give us a good idea about the knowledge existed in ancient India in the construction work and construction materials. These knowledge might have been preserved in printed,written, traditional or any other non printed forms, or atleast in palm leaves. The branch of science dealing with the subject of construction and civil engineering is known as sthaapathya veda. There are many books particularly written in regional languages for the specific regional needs of the people . Here comes the construction work explanation of temples and dwellings. The subject matter is also included in Vaastu vidya. The book known by the same name has 16 chapters in which detailed description about the measurements, qualities of a worker, the nature and merits of the land selected for construction, the processing required prior to starting the construction on the land, analyses of the soil, measurements connected with the area, sides and height of the building to be constructed, the measurements for houses after considering the proportional extrapolation or intrapolation required, the gate and the gate house, the boundary fixing, the trees to be planted in different sides and corners, the specific types of buildings, specific details of the roofing and wood cuttings for the roof making, the slopes and pyramidal structures, the method of fixing all the wooden joints, and the precautions to be taken for such joints, the covering of the roof, the slope calculation on all sides and corners, etc are given very systematically and after analyzing the environmental parameters. The auspicious dates for foundation stone laying, fixing the doors, grahapravesa- house warming ceremony, etc for houses, are also described. The book also gives the details of the construction work of temples connected with dwaja stambha pratishta, and the temple related rooms, varandas, mandapas, halls, sreekovil-sanctum sanctorum, etc

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MANUSHYALAYA CHANDRKA This is an important book discussing the subject of construction of the human dwellings, all the aspects as given in the vastu vidya mentioned above, have been suitably modified, corrected as adoptable to the situation in Kerala are discussed in the book manushyalaya chandrika.

VISWAKARMEEYA Yet another book describing the construction of the houses, public places, roads, with specific reference to the measurements to be followed by adjusting with the neighboring houses, road, etc., is the visvakarmeeyam.

SAMARANGANA SOOTHRA DHARA This book is supposed to be written by Bhojadeva about 1100 years ago. Detailed discussion of the land, ground work, soil, trees, ups and downs in the level of ground, measurements to be followed in constructing houses and other types of buildings are discussed here. The religious customs to be performed before starting the construction and also during construction and after the construction work , are discussed specifically.

MAYAMATAM In 34 chapters, Maya wrote this book, hence it is known as the opinion of Maya on house construction. The name Maya is also connected with Mayas of the Mexico and surroundings, all the ancient constructions mentioned in puranas and epics are connected with the Deva silpi, Maya. Here too , as mentioned above discussion of land, ups and downs on the level of the ground, nature of soil, water availability, directions to be followed, dates and times to be kept for performing the religious rituals connected with the construction work etc are given. In many Artha sastra books the construction of palaces, temples, pagodas, forts, etc., are given in detail.

BOOKS ON PLANT SCIENCE Katyayana has written a book known as Vrukshayurveda, in which description on various types of plants are given. In Bruhat samhita written by Varahamihira, one chapter is fully devoted for the plant science. Sarngadhara has written the Vrukshayurveda book which is a detailed compilation of the plant sciences running in hundreds of pages. The Parasara’s book on Vrukshayurveda , even though a small compilation, it gives large quantum of information of the plant science.

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BOOKS ON CLAYS AND CERAMICS Few explanations on the science and technology of ceramics can be seen in the Rasa based chemistry books, where variety of mooshas are made using specific types of clays and ceramics. Description of the clay compositions and method of preparing the bricks required for performing yagas are given in the Sulbasutra texts. Since variety of ceramics and glass materials are available from Mohan jo daro, Harappa, Lothal, etc, it is sure that the information of the clays and ceramics would have been available in manuscripts, palm leaves or in the printed forms also.

MISCELLANEOUS BOOKS CONTAINING SCIENTIFIC SUBJECTS The vedic food concept of Vedas is some thing unique. The Upanishads give lot more information of psychology, philosophy, etc. The Kalpa sastra gives a number of customs and rituals which are excellent sources of health based informations. Arthasastra of Chanakya and many other scholars give very many information on metals, alloys, coin making, industrial estates, cotton, textiles, etc Dhanurveda gives the technology of weapon making coming under the classification of mukta-amukta-vimukta-muktaamukta- astras. Gandharva Veda texts described fine methods for the manufacture/making of musical instruments. There are dozens of books coming under the subject mentioned in Gandharva Veda. Vaseshika darsana gives the structure of compounds and elements as the basic principles. Patanjali’s yoga sastra gives detailed descriptions on different aspects of health and exercises. Puranas give many relevant information of the scientific aspects also. Similarly our itihasas also project variety of scientific and technological information.

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