Posted on: 4 January 2015

Digital Rare Book:
History of Hindu Mathematics - A Source Book
By Bibhuthibhusan Datta and Avadesh Narayan Singh
Published by Asia Publishing House, Bombay - 1935

Read Book Online:


Little is known at present to historians of mathematics regarding the achievements of the early Hindu mathematicians and our indebtedness to them. Though it is now generally admitted that the decimal place-value system of numeral notation, was invented and first used by the Hindus, it is not yet fully realized to what extent we are indebted to them for our elementary mathematics. This is due to the lack of a reliable and authentic history of Hindu mathematics. Our object in writing the present book has been to make up' for this deficiency by giving a comprehensive account of the growth and development of the science of mathematics in India from the earliest known times down to the seventeenth century of the Christian era.

The subject is treated by topics. Under each topic are collected together and set forth in chronological order translations of relevant Sanskrit texts as found in the Hindu works. The texts have been elucidated, wherever necessary, by adding explanatory notes and comments, and also by illustrative examples culled from original sources. We have tried to avoid repetition as far as has been consistent with our aim. However, on several occasions it has been considered desirable to repeat the same rule in the words of different authors in order to emphasize the continuity or rather the gradual evolution of mathematical thought and terminology in India. Comparative study of this kind has helped us to throw light on certain obscure Sanskrit passages and technical terms whose full significance had not, been understood before. In translating the texts we have tried to be as literal and faithful as possible without sacrificing the spirit of the original. Sometimes it has not been possible to find exact parallels to Sanskrit words and technical terms in English. In all such cases we have tried to maintain the spirit of the original in the English version.

The above plan of the book has been adopted in pursuance of our intention to place before those who have no access to the Sanskrit sources all evidence, unfavourable as well as favourable, so that they can judge for rhemselves the claims of Hindu mathematics, without depending solely on our statements. In order to facilitate comparison with the development of mathematics in other countries the various topics have been arranged generally in accordance with the sequence in Professor D. E.Smith's History of Mathematics, Vol. II. This has sometimes necessitated divergence from the arrangement of topics as found in the Hindu works on mathematics.

In search of material for the book we had to examine the literature of the Hindus, non-mathematical as well as mathematical, whether in Sanskrit or in Prakrit (Pali and Ardha Magadhi). Very few of the Hindu treatises on mathematics have been printed so far, and even these are not generally known. The manuscript works that exist in the various Sanskrit libraries in India and Europe are still less known. We have not spared labour in collecting as many of these as we could. Sanskrit mathematical works mentioned in the bibliography given at the end of this volume have been specially consulted by us. We are thankful to the authorities of the libraries at Madras, Bangalore, Trivandrum, Trippunithura and Benares, and those of the India Office (London) and the Asiatic Society of Bengal (Calcutta) for supplying us transcripts of the manuscripts required or sending us manuscripts for
consultation. We are indebted also to Dr. R. P. Paranjpye, Vice Chancellor of the Lucknow University, for help in securing for our use several manuscripts or their transcripts from the state libraries in India and the India Office, London.

This page is a copy of a manuscript of the Lilavati of Bhaskara II (1114-1185). This manuscript dates from 1650.

This page from the Lilavati gives another illustration of the Pythagorean Theorem.

Source: Mathematical Association of America

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Pythagoras of Samos 570 – c. 495 BC This is a page from a manuscript of the Lilavati of Bhaskara II (1114-1185). This manuscript dates from 1650. This page from the Lilavati gives another illustration of the Pythagorean Theorem.

Digital Rare Book: History of Hindu Mathematics - A Source Book By Bibhuthibhusan Datta and Avadesh Narayan Singh Published by Asia Publishing House, Bombay - 1935 DOWNLOAD PDF BOOK: -------------------------------------------------------------------------------- How the Hindu Numbers Came to the Arabs (Circa 776) Regarding the transmission of Hindu numbers to the Arabs, al-Qifti's 'The History of the Learned Men' written around the end of the 12th century, but quoting earlier sources, stated: ". . . a person from India presented himself before the Caliph al-Mansur in the year 776 who was well versed in the siddhanta method of calculation related to the movement of the heavenly bodies, and having ways of calculating equations based on the half-chord [essentially the sine] calculated in half-degrees ... Al-Mansur ordered this book to be translated into Arabic, and a work to be written, based on the translation, to give the Arabs a solid base for calculating the movements of the planets. . ." (Mactutor article on The Arabic numeral system). The book from which the early Indian scholar presented may have been the Brahmasphutasiddhanta (The Opening of the Universe), written in 628 by the Indian mathematician Brahmagupta, which had used Hindu Numerals with the zero sign. (Source:

Digital Rare Book: Ta'rikh al-hukama (History of Learned Men) By Ibn Al-Qifti Translated by Dr.Julius Lippert Published by Dieterich'sche Verlagsbuchhandlung, Leipzig - 1903 Read Book Online: Download pdf Book: Image: The colophon of a copy made in 1636/1045 of the Ta’rīkh-i ḥukamā’ (The History of Learned Men) written by Ibn al-Qifṭī in the 13th century. In this colophon it is stated that Ibn al-Qifṭī's treatise was edited in the month of Rajab in the year 647 [October-November 1249] by Muḥammad ibn ‘Alī ibn Muḥammad al-Khaṭībī al-Zawzanī, and that this copy was completed on 16 Sha‘ban 1045 [25 January 1636] by the copyist Muḥammad ibn shaykh ..?.. ibn shaykh ‘Umar al-Akhrawi. Source: U.S. National Library of Medicine

Please do not let your wonderful page be hijacked by bigots.


Sai Deepak Iyer J. Please take a look.


Cannot read any of these. Sites blocked by Government of India. Rare Book Society of India The Brahmasphutasiddhanta refered by you in a comment above does not mean the opening of the universe. It simply means Explanation of Brahmagupta's Proposition. Your translation may imply that Indians knew the secrets of big bang.

I am afraid the source for this translation is from this site. A large number of western writers seem to translate it in this manner.

We are soon planning to arrange the download of all these books posted on this FB page from the RBSI website instead of the Internet Archive site.

And maybe the Indians did know the secrets of the big bang! As the the vedic seer in the Rig Vedic hymn on creation (Nasadiya sukta) finally says..."Who really knows?..." Nasadiya Sukta नासदासीन्नो सदासीत्तदानीं नासीद्रजो नो व्योमा परो यत् । किमावरीवः कुह कस्य शर्मन्नम्भः किमासीद्गहनं गभीरम् ॥ १॥ Then even nothingness was not, nor existence, There was no air then, nor the heavens beyond it. What covered it? Where was it? In whose keeping Was there then cosmic water, in depths unfathomed? न मृत्युरासीदमृतं न तर्हि न रात्र्या अह्न आसीत्प्रकेतः । आनीदवातं स्वधया तदेकं तस्माद्धान्यन्न परः किञ्चनास ॥२॥ Then there was neither death nor immortality nor was there then the torch of night and day. The One breathed windlessly and self-sustaining. There was that One then, and there was no other. तम आसीत्तमसा गूहळमग्रे प्रकेतं सलिलं सर्वाऽइदम् । तुच्छ्येनाभ्वपिहितं यदासीत्तपसस्तन्महिनाजायतैकम् ॥३॥ At first there was only darkness wrapped in darkness. All this was only unillumined water. That One which came to be, enclosed in nothing, arose at last, born of the power of heat. कामस्तदग्रे समवर्तताधि मनसो रेतः प्रथमं यदासीत् । सतो बन्धुमसति निरविन्दन्हृदि प्रतीष्या कवयो मनीषा ॥४॥ In the beginning desire descended on it - that was the primal seed, born of the mind. The sages who have searched their hearts with wisdom know that which is is kin to that which is not. तिरश्चीनो विततो रश्मिरेषामधः स्विदासीदुपरि स्विदासीत् । रेतोधा आसन्महिमान आसन्त्स्वधा अवस्तात्प्रयतिः परस्तात् ॥५॥ And they have stretched their cord across the void, and know what was above, and what below. Seminal powers made fertile mighty forces. Below was strength, and over it was impulse. को अद्धा वेद क इह प्र वोचत्कुत आजाता कुत इयं विसृष्टिः । अर्वाग्देवा अस्य विसर्जनेनाथा को वेद यत आबभूव ॥६॥ But, after all, who knows, and who can say Whence it all came, and how creation happened? the gods themselves are later than creation, so who knows truly whence it has arisen? इयं विसृष्टिर्यत आबभूव यदि वा दधे यदि वा न । यो अस्याध्यक्षः परमे व्योमन्त्सो अङ्ग वेद यदि वा न वेद ॥७॥ Whence all creation had its origin, he, whether he fashioned it or whether he did not, he, who surveys it all from highest heaven, he knows - or maybe even he does not know.[9]

Nasadiya Sukta is **BOTH** a statement on big bang and what is now known as Godel's incompleteness theorem. This naturally, is of all my heritage -- the piece which seems to bind me to my past completely and in one seamless continuum, more than my fav, a verbal expounding of what my soul would most probably be like.

Great to read this. Beginning to make sense of lots of bits we have been learning over a lifetime. At last this generation is bringing the knowledge our ancestor's have carried. So glad for the internet being a source of understanding that is much needed now.

Rare of the rare.

Sir, as life cannot in any circumstance originate from matter, the universe too has not originated from mass of gases & dust. This is very simple to understand - but somehow the big bang theory stays afloat as suggested by the so called 'scientists'. For a detailed description of the creation of the universe, please refer to Srimad Bhagavatam, 2nd Canto.

Sir I am agree with Mohan sundar

Wow! Just amazing. Thanks for sharing.

I am convinced that everything has come down to us from the banks of the Ganga – astronomy, astrology, spiritualism, etc. It is very important to note that some 2500 years ago at the least Pythagoras went from Samos to the Ganga to learn geometry.” – Francis M. Voltaire

What about Euclid ...?

Puttezhath Sunil Menon Himanshu Trivedi Nitin Basrur

Voltaire :-) those words are spoken in excitement during the first flush of the 'discovery' of Sanskrit by the west. What was true was exchange of ideas all around. At the centre of the highway, playing both the crossroads and the nucleus, was ancient Sumer. While there is plenty evidence of sophisticated mathematics in ancient India, the likelihood of some of the basic precepts having come from Sumer is very high, and at any rate it coexisted and co-evolved with Anatolia-Greece, China, Egypt. Spirituality had nothing to do with. It was practical knowledge that evolved. It wasn't divine revelation that entered anyone's brain on the banks of any river.

Pardon the grammar. Typed in a hurry. The practical concerns relating to the construction of fire-altars in various geometric shapes seems to have had a large role yo play in it. It's paradoxical that stage props for ritual almost forced rational thinking out of the practitioners. Just like astrological concerns, which have no basis, led to rather acute astronomical skills. It's best for all of us to try and appreciate things as they were rather construct some hocus-pocus around it.

very important

Great post. The evolutionary process is very subtly narrated through Srichakra in श्रीविद्या॥

Proud to be a hindu

हिंदी अनुवाद भी दें तो अधिक लोग पढ सकेंगे।

Thank you all !!

very nice

And we live in a time and place where the population is 1/6th of the entire planet, and hardly anyone understands "Shouny" :)

Digital Rare Book: History of Hindu Mathematics - A Source Book By Bibhuthibhusan Datta and Avadesh Narayan Singh Published by Asia Publishing House, Bombay - 1935 DOWNLOAD PDF BOOK:

Anand Rajadhyaksha ji

I know some oldest rare books in shanskrit and some other language with hand written including aayurvedic treatment (medical) n gems mankind ideas like gold etc ...approx five hundred year atleast old ......any body ready to buy ? After satisfaction in all ? ........very rare

Kalindi Shukla

recently I bought The Shulbhasutras, Translated by S N Sen & A K Bag, for some reason. I became stunned after seeing their perfection and dedications to make a perfect alter.& this is a perfect geometry book with no hocus focus too :P

Real treasure

Yeah Air India the airlines mainly for the Maharaja's of today! Still dying with Vedic Sciences and traditions!

Hari Bol.


@kingrakshit , I am interested in the book, please quote

thanks Abha for the information


Wish I could understand this.

very nice.

True. It is practical and Vedas do have ups Vedas and all knowledh

And all knowledge has been classified in Vedas . it is not abrahamic religion where some angel handed over or emperor Constantine created. All we are saying acknowledge the material scir

Acknowledge the material science in vedas

It's a very long answer. There's nothing particularly in the Vedas that I know of that classifies as knowledge. There's plenty of literature from thereafter though, a lot of which is secular in nature. The distinction with Abrahamic religions does not apply here as far as I can see. That's a theological thing.

YOU CAN GET AND DOWNLOAD - SAVE for you http ://www.wilbourhall. org/pdfs/RekhaganitaVOL_II_DLI.pdf http://www.wilbourhall.o rg/in dex.htm l#aryabhatiya There is an Ancient Mathamatics Book in SANSKRIT called "REKHA GANITA " part1-2 . A linear mathamatics in English is developed from that translation 2 centuries ago, Linear, s eries , log series, Area, ciecles, Earth and Space trignometry every thing is explained.

all this should be kept in school level just glimps , from my child hood gandhi till today we r only spoiling our country not others they preserved it..before eating andy thin give to others means ...?