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Mukund Mishra, Pt. Om Datt Sharma, the learned scholars who helped me in preparing this work. The book has been published in four volumes. Volume I includes introduction in English by Dr- Satya Prakash followed by the text as given in the copy of the manuscript obtained from the Bhandarkar Research Institute, Poona, with footnotes to collate the various versions found in the copies of the manuscripts procured from the Royal Asiatic Society, Bombay, the Oriental Research Institute, Baroda and the Vishweshwaranand Vedic Research Institute, Hoshiarpur. Volume II comprises of the first nine chapters of Brahma Sphuta Siddhanta containing only those readings which we have considered as correct.

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Volume III includes chapters 10 to Ill and IV. Another appendix in this volvme contains Vssai. The Institute has planned to add to its list of publications, shortly, Samrat Siddhanta pages and already in press. Brhad Yavan Jataka pages and Panch Siddhanuka pages. Patil, Union Minister for Railways.

I am highly grateful to him for his having consented to this dedication. I am also grateful to Shri K. Munshi and Shri Wadilal Chaturbhu] Gandhi for their kindly agreeing to my request to be President and Chairman respect- ively of the Reception Committee. My heart felt thanks are also due to Shri Kanti Lai H. Secy, of the Organising Committee and to all the members of the organising and the Reception Committees for their help and cooperation in my work.

Shri Prithvi Raj Kapour.

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Shri Dhairyasinh, R. Shri Pranlal Bhogilal, Patel Bombay for their in valuable help.

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I am also sjrauM'ul to the life members of the Institute : H. C Dev, Shri H. Bhaskar, Shri R. Moorjani, Shri Shantilal K. Somaiya, Shri fCisonlal M.

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Solicitor, Shri N. Jalan, Shri D. Nayar, Shri Vadilal Gandhi. Padma Koregaonkar. Jha, Chief Commissioner, Delhi, who has greatly encourago I me in my task of publishing old manuscripts. I am highly grateful to him for his support in my cause. I am also firat!

Shri F.

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Vaidya, Shri N. Shri P. Naulakha, Shri R. Maheshwari, Shri D. Bhattacharjee, Shri P. Aggarwal, Shri B. Saxena, Shri R. Shri T. Krishnamurti, Shri R. Chitkara, Dr. Ram Karan Sh'irmm Shri V. Agnihotri, Shri K. L, Handa and Shri K. Somnyyn fur their help and advice at various occasions.

Ram Swarup Sharma Bombay Foreword 2. M' Munshi 5. Publisher's Note 4. Index 5. Introduction 1— Contents Page 1 Astronomy in ancient nations 2 Personal references of Brahrnagupta. Indian Luni-solar Astronomy. Epicyclic theory of Ancient Indians. Brahrnagupta as an Algebraist. Brahmagupta's Astronomy : its highlight 10 Brahrnagupta — a great critic.

Brahrnagupta and Astronomical Instruments. T- sfaqreq? T7f T? Al Beruni records this testimony in his great book on India.. It is doubtful that astronomy had its birth in Greece and China. This knowledge must have spread from their common cradle home where man for the first time developed his culture and civilisation.

Dawn of Astronomy Th'e earliest man must have been the primitive astro- nomer. These phenomena not only raised feelings of admiration, but in different sections of human society often feelings of superstitious alarm. By and by stars became guides for the traveller by land and sea. In the midst of these observations, one discovered various cycles : cycle of day and night, cycle of seasons and cycle of other details. The Vedic. Aryans also discovered the variations in the duration of the day along different latitudes, and the time of sunrise in places of different longitudes.

In fact the idea of longitudes and latitudi scame suffi- ciently afterwards. Man discovered month as related to thr varia- tion of light with the Moon's phases. In temperate regions, where probably the first astronomical observations were systematically made, the changing length of the day or the directum of the Sun at rising or setting or the lengths of shadows cast at midday, would show that the Sun's daily path in the sky altered through- out the year, a time interval which was already marked by the changing vegetation.

According to Sir W,C. Dumpier, "attempts were made to determine the number of months in the cycle of the seasons in Babylonia about B. About B. The old inspired sages like Dlrghatamas discovered for the observing man the Vedic Era and intercalation. It is impossible to assign an age to these old traditions.

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One might aWsay that a considerable period might have R elapsed before it was noticed that at a particular season of ZODIAC 3 the year, the same stars are seen at corresponding hours of the night. Of course this circumstance was less conspicuous than the regular variation of the Sun's altitude in the sky as the year progresses. It is the surmise that the striking naked-eye cluster, the Pleiades, must have been one of the earliest noted star- groups, and it became the first star-group for providing the first fairly close determination of the length of the year as approxim- ately days.

The rising of this cluster in the evening was a mark of the coming winter to primitive man ; and the husband- man judged the time of reaping by its rising, and of ploughing by its setting in very ancient times ; Sirius. Arcturus, the Hyades and Orion were similarly equally useful to him. Do not exclude us from the sacrifice! Let us have a share in the sacrifice! The gods, not approving, the seasons went to the Asuras, the malignant, spiteful enemies of the gods.

The divi- sion into twelve parts, each corresponding to a month of the Sun's movement, was made ; and their connection with the solar course during the year was found by observations of heliacal risings or settings. In the case of Sinus, the brightest fixed star, these would happen when the Sun was about ten degrees below the horizon.

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For the less bright stars the angle would be a larger one. It must have been almost simultaneously observed that the Moon in going like the Sun round the heavens. After a time, however, it must have been noted by careful observers that this path was not con- stant, but deviated from the centre line of the Zodiac, getting away from that line up to a maximum deviation on either side but slowly returning to it. In the course of a number of years, it must have become evident that the Moon's path among the stars does not lie always in the same line on the celestial sphere, but in a zone or band about twenty moon breadths 10" wide, occu- pying the middle of the Zodiacal zone itself.

Among the bright stars Mercury, Venus, Mars, Jupiter and Saturn the first two of which are never seen very far from the Sun in the sky soon must have been noted to be moving in the Zodiac with varying periods. The English name planet is de- rived from Greek planetes, meaning a wanderer, since the planets change their positions among the Zodiacal stars.