Determination of Ascensional Difference in the Lagnaprakaraṇa
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Ancient Indian Leaps Into Mathematics Editors B.S
B.S. Yadav Man Mohan Editors Ancient Indian Leaps into Mathematics Editors B.S. Yadav (Deceased) Man Mohan Ramjas College University of Delhi 110 007 New Delhi India [email protected] ISBN 978-0-8176-4694-3 e-ISBN 978-0-8176-4695-0 DOI 10.1007/978-0-8176-4695-0 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010937771 Mathematics Subject Classification (2010): 01A32, 01A16, 01A17, 01A25, 01A27, 01A29 c Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper www.birkhauser-science.com Dedicated to the memory of U. N. SINGH The Founder of the Indian Society for History of Mathematics U. N. Singh (November 19, 1920 – April 9, 1989) Professor B. S. Yadav (31 July 1931 – 24 February 2010) B. S. Yadav was born in Mathura, India. He dedicated his whole life to the cause of mathematics and the history of mathematical sciences. -
Aryabhatiya with English Commentary
ARYABHATIYA OF ARYABHATA Critically edited with Introduction, English Translation. Notes, Comments and Indexes By KRIPA SHANKAR SHUKLA Deptt. of Mathematics and Astronomy University of Lucknow in collaboration with K. V. SARMA Studies V. V. B. Institute of Sanskrit and Indological Panjab University INDIAN NATIONAL SCIENCE ACADEMY NEW DELHI 1 Published for THE NATIONAL COMMISSION FOR THE COMPILATION OF HISTORY OF SCIENCES IN INDIA by The Indian National Science Academy Bahadur Shah Zafar Marg, New Delhi— © Indian National Science Academy 1976 Rs. 21.50 (in India) $ 7.00 ; £ 2.75 (outside India) EDITORIAL COMMITTEE Chairman : F. C. Auluck Secretary : B. V. Subbarayappa Member : R. S. Sharma Editors : K. S. Shukla and K. V. Sarma Printed in India At the Vishveshvaranand Vedic Research Institute Press Sadhu Ashram, Hosbiarpur (Pb.) CONTENTS Page FOREWORD iii INTRODUCTION xvii 1. Aryabhata— The author xvii 2. His place xvii 1. Kusumapura xvii 2. Asmaka xix 3. His time xix 4. His pupils xxii 5. Aryabhata's works xxiii 6. The Aryabhatiya xxiii 1. Its contents xxiii 2. A collection of two compositions xxv 3. A work of the Brahma school xxvi 4. Its notable features xxvii 1. The alphabetical system of numeral notation xxvii 2. Circumference-diameter ratio, viz., tz xxviii table of sine-differences xxviii . 3. The 4. Formula for sin 0, when 6>rc/2 xxviii 5. Solution of indeterminate equations xxviii 6. Theory of the Earth's rotation xxix 7. The astronomical parameters xxix 8. Time and divisions of time xxix 9. Theory of planetary motion xxxi - 10. Innovations in planetary computation xxxiii 11. -
Aryabhatta Date an Analytical Study
ARYABHATTA’S DATE AN ANALYTICAL STUDY Dr. M.L. Raja, M.B., B.S., D.O., AVINASH English ARYABHATTA’S DATE AN ANALYTICAL STUDY By- Dr. M.L. Raja Published by AVINASH Printed at Sankav Offset Printerss, Erode Cover Design & Type setting A.P. Nallashivam Published in January 2016 Yugabdom 5117 IPrice `160. ISBN: 978-93-84582-54-8BN: 978i AVINASH Academy on Vibrant National Arts & Scientific Heritage Erode, Tamilnadu Ph : 94433 70129 E-mail : [email protected] PREFACE In the history our Nation, we can find thousands and thousands of great scholars and their works, in almost all fields of science. We can cite examples, at least a few hundred in each century, scattering over a very long period of time, exceeding a minimum of ten thousand years. Their works in the various fields of science are remarkably outstanding, highly astonishing and fully scientific with thorough and clear knowledge, exceeding the modern scientific achievements, at least in a few aspects. But, the most unfortunate thing is, we are very much ignorant of our ancestor’s glorious antiquity, Himalayan achievements, high technological skill and the vast knowledge and wisdom and their highly admirable scientific works are not at all included in our Nation’s educational curriculum. So, it is right time or even if late, it is better late than never, to bring forth these ancient scientific works of our glorious Nation, in the day-light, amongst the present and the future generations of our Nation. With that motive in mind, this book on Âryabhaa is a very small, but a firm step in that direction, where the actual date and name of Âryabhaa and his texts are detailed. -
Editors Seek the Blessings of Mahasaraswathi
OM GAM GANAPATHAYE NAMAH I MAHASARASWATHYAI NAMAH Editors seek the blessings of MahaSaraswathi Kamala Shankar (Editor-in-Chief) Laxmikant Joshi Chitra Padmanabhan Madhu Ramesh Padma Chari Arjun I Shankar Srikali Varanasi Haranath Gnana Varsha Narasimhan II Thanks to the Authors Adarsh Ravikumar Omsri Bharat Akshay Ravikumar Prerana Gundu Ashwin Mohan Priyanka Saha Anand Kanakam Pranav Raja Arvind Chari Pratap Prasad Aravind Rajagopalan Pavan Kumar Jonnalagadda Ashneel K Reddy Rohit Ramachandran Chandrashekhar Suresh Rohan Jonnalagadda Divya Lambah Samika S Kikkeri Divya Santhanam Shreesha Suresha Dr. Dharwar Achar Srinivasan Venkatachari Girish Kowligi Srinivas Pyda Gokul Kowligi Sahana Kribakaran Gopi Krishna Sruti Bharat Guruganesh Kotta Sumedh Goutam Vedanthi Harsha Koneru Srinath Nandakumar Hamsa Ramesha Sanjana Srinivas HCCC Y&E Balajyothi class S Srinivasan Kapil Gururangan Saurabh Karmarkar Karthik Gururangan Sneha Koneru Komal Sharma Sadhika Malladi Katyayini Satya Srivishnu Goutam Vedanthi Kaushik Amancherla Saransh Gupta Medha Raman Varsha Narasimhan Mahadeva Iyer Vaishnavi Jonnalagadda M L Swamy Vyleen Maheshwari Reddy Mahith Amancherla Varun Mahadevan Nikky Cherukuthota Vaishnavi Kashyap Narasimham Garudadri III Contents Forword VI Preface VIII Chairman’s Message X President’s Message XI Significance of Maha Kumbhabhishekam XII Acharya Bharadwaja 1 Acharya Kapil 3 Adi Shankara 6 Aryabhatta 9 Bhadrachala Ramadas 11 Bhaskaracharya 13 Bheeshma 15 Brahmagupta Bhillamalacarya 17 Chanakya 19 Charaka 21 Dhruva 25 Draupadi 27 Gargi -
GIPE-043972-Contents.Pdf (1.117Mb)
REPORT OF THE CALENDAR REFORM I:DMMITTEE GOVERNMENT OF INDIA Council of Scientific and Industrial Research, Old Mill Road, • New Delhi. 1955 REPORT OF THE l:llLENDAR REFORM l:OMMITTEE · GOVERNMENT OF INDIA Council of Scientific and Industrial Research, Old Mill Road, New Delhi. 1955 Pub~shed by The Council of Scientific and Industrial Reaearch, Old Mill Road, New Delhi. Printed by Sri Hari Narayan Dey, Sree Gopal Printing Works, 25/IA, Kalidas Singhee Lane,· Calctitta-9. M E S S A G E. I am glad that the Calendar Reform Committee has started its lab~urs. The Government of India has entrusted to it the work of examining the different calendars followed in this country and to submit proposals to the Government for an accurate and uniform calendar based on a scientific study for the whole of India. I am told that we have at present thirty different calendars, differing from each other in various ways, including the methods of time reckoning. These calendars are the natural result of our past political and cultural history an1 partly represent past political divisions in the country. Now that we have attained independence, it is obviously desirable that there should be a certain uniformity in the calendar for our civic, social and other purposes and that this should be based on a scientific approach to this problem. It is true the.t for governmental and many other public p~poses we follow the Gregorian calendar, which is used in the greater part of the world. The mere fact that it is largely used, makes it important. -
Ancient Indian Mathematics – a Conspectus*
GENERAL ARTICLE Ancient Indian Mathematics – A Conspectus* S G Dani India has had a long tradition of more than 3000 years of pursuit of Mathematical ideas, starting from the Vedic age. The Sulvasutras (which in- cluded Pythagoras theorem before Pythagoras), the Jain works, the base 10 representation (along with the use of 0), names given to powers of 10 S G Dani is a Distinguished up to 1053, the works of medieval mathematicians Professor at the Tata motivated by astronomical studies, and ¯nally Institute of Fundamental Research, Mumbai. He the contributions of the Kerala school that came obtained his bachelor’s, strikingly close to modern mathematics, repre- master’s and PhD degrees sent the various levels of intellectual attainment. from the University of Mumbai. His areas of There is now increasing awareness around the world that interest are dynamics and as one of the ancient cultures, India has contributed sub- ergodic theory of flows on stantially to the global scienti¯c development in many homogeneous spaces, spheres, and mathematics has been one of the recognized probability measures on Lie groups areas in this respect. The country has witnessed steady and history of mathematics. mathematical developments over most part of the last He has received 3,000 years, throwing up many interesting mathemati- several awards including cal ideas well ahead of their appearance elsewhere in the the Ramanujan Medal and the world, though at times they lagged behind, especially in TWAS Prize. the recent centuries. Here are some episodes from the fascinating story that forms a rich fabric of the sustained * This is a slightly modified ver- intellectual endeavour. -
Water Clock and Steelyard in the Jyotiṣkaraṇḍaka
International Journal of Jaina Studies (Online) Vol. 14, No. 2 (2018) 1-49 WATER CLOCK AND STEELYARD IN THE JYOTIṢKARAṆḌAKA Sreeramula Rajeswara Sarma for Professor Nalini Balbir in friendship and admiration 0 Introduction Mahāvīrācārya, the great Jain mathematician who flourished in Karnataka in the ninth century, at the beginning of his mathematical work Gaṇitasārasaṃgraha, pays homage to Jina Mahāvīra who illuminated the entire universe with saṃkhyā-jñāna, the science of numbers. 1 Indeed, saṃkhyā-jñāna plays an important role in Jainism which seeks to comprehend the entire universe in numerical terms. In this process, the Jains conceived of immensely large numbers, making a very fine and subtle classification of transfinite numbers and operating with laws of integral and fractional indices and some kind of proto-logarithms.2 Kāla-jñāna or kāla-vibhāga is an important part of the saṃkhyā-jñāna, for time too needs to be comprehended in numbers. Jains measured time from the microscopic samaya, which cannot be sub-divided any further,3 to the macroscopic śīrṣa-prahelikā, a number indicating years which is said to occupy 194 or even 250 places in decimal notation.4 But for vyāvahārika or practical purposes, especially for the calendar, the early Jain literature makes use of a five-year cycle or yuga. The basic problem in astronomical time- measurement is that the apparent movements of the two great luminaries who determine the passage of time, namely the Sun and the Moon, do not synchronize. The lunar year falls short of about eleven days in comparison to the solar year and does not keep step with the passage of seasons. -
Śrīpati's Arithmetic in the Siddhāntaśekhara And
ŚRĪPATI’S ARITHMETIC IN THE SIDDHĀNTAŚEKHARA AND GAṆITATILAKA: EDITION, TRANSLATION, AND MATHEMATICAL AND HISTORICAL ANALYSIS Rev. Jambugahapitiye Dhammaloka Thero A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics Department of Mathematics and Statistics University of Canterbury New Zealand 2019 Abstract The literature on the exact sciences in Sanskrit in the second millennium is significant from a his- torical point of view because of the emergence of innovative ideas, systematization of the traditional knowledge, advanced technicality, creativity of the scientific writing style, and so on. Śrīpati, a mathematician-astronomer, is the first known writer of exact sciences in this era. He lived inthe 11th century most probably in Maharashtra and he wrote in a vast range of subjects from astrology to astronomy. In spite of his prolific writings and influence in the early stages of the second millennium, Śrīpati has been understudied. Śrīpati is the first author who wrote a separate mathematical text while still retaining all the main mathematical rules in theoretical astronomical texts. It is Śrīpati who used different elegant metrical forms in versification of mathematical rules. Most importantly, he invented several rules in arithmetic and provided inspiration for successive mathematicians and astronomers especially Bhāskara II. In this thesis we provide a critical edition of the 13th chapter of Śrīpati’s Siddhāntaśekhara, an astronomical work, consulting the published edition and three manuscripts and his Gaṇitatilaka, his arithmetic text, based on the published edition. They are followed by the critical translation and the commentary where mathematical analysis of all the rules is given. -
Understanding Ancient Indian Mathematics - the Hindu 2/9/14 3:18 PM
Understanding ancient Indian mathematics - The Hindu 2/9/14 3:18 PM S & T » Science Published: December 26, 2011 02:58 IST | Updated: December 26, 2011 03:02 IST ! Understanding ancient Indian mathematics S.G. Dani A portion of a dedication tablet in a rock-cut Vishnu temple in Courtesy: Bill Casselman Gwalior built in 876 AD. The number 270 seen in the inscription features the oldest extant zero in India. It is high time we studied our mathematical heritage with diligence and objectivity Quite often I find that conversations, with people from various walks of life, on ancient Indian mathematics slide to “Vedic mathematics” of the “16 sutras” fame, which is supposed to endow one with magical powers of calculation. Actually, the “16 sutras” were introduced by Bharati Krishna Tirthaji, who was the Sankaracharya of Puri from 1925 until he passed away in 1960, associating with them procedures for certain arithmetical or algebraic computations. Thus, this so-called “Vedic mathematics (VM)” is essentially a 20th century phenomenon. Neither the “sutras” nor the procedures that they are supposed to yield, or correspond to, have anything to do with either the Vedas, or even with any post-Vedic mathematical tradition of yore in India. The image that it may conjure up of ancient rishis engaged in such arithmetical exercises as are taught to the children in the name of VM, and representing the solutions through word-strings of a few words in modern styled Sanskrit, with hardly any sentence structure or grammar, is just too far from the realm of the plausible. -
The Myth of the Holy Cow
IWU * ** The Myth of the Holy Cow D.N. Jha navayana The Myth of the Holy Cow © D.N.Jha Published by Navayana Publishing, 2009 First published by Matrix Books, New Delhi, 2001 ISBN: 978-8189059163 All rights reserved. No part of this book may be reproduced or utilised in any form without the prior permission of the publisher. Printed by Sanjiv Palliwal, New Delhi Navayana Publishing M-100, 1 Floor, Saket, New Delhi 110017 navayana.org [email protected] Distributed by IPD Alternatives (www.ipda.in) and WestLand Books Pvt. Ltd. Chennai gam alabhate[2]; yajno vai gauh; . yajnarn eva labhate; atho annam vai gauh; annam evavarundhe. Taittiriya Brahmana, III. 9.8.2-3 (Anandasrama- sanskritgranthavalih 37, vol. Ill, 3rd.edn., Poona, 1979). ‘ (At the horse-sacrifice) he (the Adhvaryu) seizes (binds) the cow (i.e. cows). The cow is the sacrifice. (Consequently) it is the sacrifice he (the Sacrificer) thus obtains. And the cow certainly is food. (Consequently) it is food he thus obtains.’ English translation by Paul-Emile Dumont, Proceedings of the American Philosophical Society, 92.6 (December 1948), p. 485. ‘. Silver foil or “varak” used for decorating sweets has more than just a pleasing look to it. It is made by placing thin metal strips between steaming intestines of freshly slaughtered animals. The metal is then pounded between ox-gut and the sheets are carefully transferred in .’ special paper for marketing. Bindu Jacob, ‘More to it all than meets the Eye’, The Hindu, 5 June 2001 (A news item based on a publication of the Animal Welfare Board of India under the Ministry of Social Justice and Empowerment, Government of India). -
Zone Wise List of Fellows & Honorary Fellows
The National Academy of Sciences, India (The Oldest Science Academy of India) Zone wise list of Fellows & Honorary Fellows (2020) 5, Lajpatrai Road, Prayagraj – 211002, UP, India 1 The list has been divided into six zones; and each zone is further having the list of scientists of Physical Sciences and Biological Sciences, separately. 2 The National Academy of Sciences, India 5, Lajpatrai Road, Prayagraj – 211002, UP, India Zone wise list of Fellows Zone 1 (Bihar, Jharkhand, Odisha, West Bengal, Meghalaya, Assam, Mizoram, Nagaland, Arunachal Pradesh, Tripura, Manipur and Sikkim) (Section A – Physical Sciences) ACHARYA, Damodar, Chairman, Advisory Board, SOA Deemed to be University, Khandagiri Squre, Bhubanesware - 751030; ACHARYYA, Subhrangsu Kanta, Emeritus Scientist (CSIR), 15, Dr. Sarat Banerjee Road, Kolkata - 700029; ADHIKARI, Satrajit, Sr. Professor of Theoretical Chemistry, School of Chemical Sciences, Indian Association for the Cultivation of Science, 2A & 2B Raja SC Mullick Road, Jadavpur, Kolkata - 700032; ADHIKARI, Sukumar Das, Formerly Professor I, HRI,Ald; Professor & Head, Department of Mathematics, Ramakrishna Mission Vivekananda University, Belur Math, Dist Howrah - 711202; BAISNAB, Abhoy Pada, Formerly Professor of Mathematics, Burdwan Univ.; K-3/6, Karunamayee Estate, Salt Lake, Sector II, Kolkata - 700091; BANDYOPADHYAY, Sanghamitra, Professor & Director, Indian Statistical Institute, 203, BT Road, Kolkata - 700108; BANERJEA, Debabrata, Formerly Sir Rashbehary Ghose Professor of Chemistry,CU; Flat A-4/6,Iswar Chandra Nibas 68/1, Bagmari Road, Kolkata - 700054; BANERJEE, Rabin, Emeritus Professor, SN Bose National Centre for Basic Sciences, Block - JD, Sector - III, Salt Lake, Kolkata - 700098; BANERJEE, Soumitro, Professor, Department of Physical Sciences, Indian Institute of Science Education & Research, Mohanpur Campus, WB 741246; BANERJI, Krishna Dulal, Formerly Professor & Head, Chemistry Department, Flat No.C-2,Ramoni Apartments, A/6, P.G. -
Nptel Course on Mathematics in India: from Vedic Period
NPTEL COURSE ON MATHEMATICS IN INDIA: FROM VEDIC PERIOD TO MODERN TIMES Lecture 39 Mathematics in Modern India 1 M. D. Srinivas Centre for Policy Studies, Chennai 1 Outline I Continuing tradition of Indian Astronomy and Mathematics (1770-1870) I Surveys of indigenous education in India (1825-1835) I Survival of indigenous education system till 1880 I Modern Scholarship on Indian Mathematics and Astronomy (1700-1900) I Rediscovering the Tradition (1850-1900) I Development of Higher Education and Modern Mathematics in India (1850-1910) 2 Outline I Srinivasa Ramanujan (1887-1920) I Brief outline of the life and mathematical career of Ramanujan I Hardy’s assessment of Ramanujan and his Mathematics (1922, 1940) I Some highlights of the published work of Ramanujan and its impact I Selberg’s assessment of Ramanujan’s work (1988) I The saga of Ramanujan’s Notebooks I Ongoing work on Ramanujan’s Notebooks I The enigma of Ramanujan’s Mathematics 3 Background: Continuted Development of Mathematics in Medieval India I Gan. itas¯arakaumud¯ı (in Prakrita) of T. hakkura Pher¯u (c.1300) and other works in regional languages such as Vyavah¯aragan. ita (Kannada) of R¯aj¯aditya, P¯avul¯uri- gan. itamu of P¯avul¯uriMallan. a in Telugu. I Gan. itakaumud¯ı and B¯ıjagan. it¯avatam. sa of N¯ar¯ayan. a Pan. d. ita (c. 1350) I M¯adhava (c.1350): Founder of the Kerala School. Infinite series for π, Sine and cosine functions and fast convergent approximations to them. I Works of Parame´svara (c.1380-1460) I Works of N¯ılakan.