INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org 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 1 INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org 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 2 INDIAN INSTITUTE OF SCIENTIFIC HERITAGE www.iish.org 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 3 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, 4 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