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 The present volume, issued as Part I of Vateśvara-siddhānta and Gola, contains the Sanskrit text of all the eight chapters (adhikaras) of the Vateśvara-siddhānta, written by astronomer Vațeśvara, son of Mahadatta resident of Vadnagara in northern Gujarat, in 904 A. D. It contains also the Sanskrit text of the first five chapters of the Gola (Spherics) written by the same astronomer. The Sanskrit text of the remaining chapters of Vateśvara's Gola has not survived.


Two manuscripts of the Vateśvara-siddhānta have been discovered so far and these have been used for the present edition. Both are incomplete but one is larger than the other. The larger one will be called Ms. A and the shorter one Ms. B. MANUSCRIPT A. This is No. 46608 of Lucknow University Library, Lucknow, and may be described as follows :

  Substance-Paper. Character-Modern Devanāgari. Size-the first 43 leaves 28 cm. x 12.2 cm., the remaining ones 27 cm. x 12.2 cm., (approx). Extent-103 folios; 9 lines per page, and about 40 letters per line. The first 71 folios are numbered as l to 71, the folio-numbers being written on the verso or the left-hand pages of the folios at the top on the left hand margin and also at the bottom on the right hand margin. The first page of the manuscript is left blank and the writing is started from the second page. The folios numbered as 58 to 71 have vateśva (the tachygraphic abbreviation of Vateśvara-siddhānta) written just above the folio number on the left hand margin, the word rāma occurring just above the folio-number on the right hand margin on all folios of the manuscript. The folios occurring subsequent to folio 71, which are slightly darker in colour, were originally numbered as 99 to 129, the verso of the last folio being blank and left unnumbered. These folios were later renumbered as 72 to 103, the last folio (originally unnumbered) being also numbered this time and “vateśvarasiddhānta' written just below the folio-number 103. The renumbering is done in a different hand and only on the left hand margin at the top. The object of renumbering was evidently to provide continuous numbering to the whole manuscript. The discontinuous numbering, 1 to 71 and then 99 to 129, suggests that the manuscript consists of fragments of two different manuscripts, carefully put together to form one single manuscript. This is also proved by the fact that the last folio of the first of these two manuscripts, which bears the folio-number 71, ends with :

(पाणभूगुता च साधयेव । तीक्षालिकादेणभूतोय.मज्पाचायंस्वविक्षेयवियुक्तमतत्भिन्नोत्प)
(दिक्त्थशशिनोपमोयंस्पष्टोफजीवाद्यमृतोर्कवत्स्पात् शीतगोरुदवदृग्विलग्नकात्षद्भयुग्दू)

and the first folio of the second manuscript, which bears the folio number 99, begins with the repetition of the same matter. To get rid of this repetition the matter of folio 71 which is repeated on folio 99 has been enclosed within brackets ( ). The second manuscript has the bare folio-number at the top on the left hand margin and the folio-number with the word rāma just above it at the bottom on the right hand margin.

  As regards the numbering of the verses, only the first 14 verses of Chapter I Section 1, 9 verses of Chapter I Section 2, and 4 verses of Chapter I Section 3, are numbered. The numbering of the first 14 verses is correct; that of the other verses, wrong. The verses numbered 26, 27, 28, and 29 are really the 36th, 37th, 38th and 39th verses when counted from the beginning. These are the last numbered verses.

  The manuscript is written, as usual, along the length of the paper and the written matter is bordered on both sides of the pages by four vertical lines, pairwise in juxtaposition, throughout the manuscript.

  The manuscript is incomplete, but as far as the Vateśvara-siddhānta proper is concerned it is complete and contain all the eight chapters of the Vateśvara-siddhānta. In addition it contains five extra chapters, which really do not form part of the Vateśvara-siddhānta, but were composed and appended to the Vateśvara-siddhānta by Bhatta Govinda, son of Vahnika and resident of Dauranda, the scribe of the original manuscript, as supplement to Chapter III of the Vateśvara-siddhānta, as well as the first five chapters of Vatesvara's Gola which occur in disconnected and disarranged fragments towards the end of the manuscript. The manuscript breaks off in the midst of the last quarter of verse 22 of the Golāvasanā; the remaining verses of the Golāvasanā and and the verses of the next chapter entitled Bhūgolah, which should have occurred thereafter, wrongly occur earlier in the manuscript. The manuscript is incomplete as far as the remaining chapters of Vatesvara's Gola are concerned.  The manuscript begins as follows:

॥ ॥ श्री कृष्णाय नमः ॥ ॥ ब्रह्मावनीन्दुबुधशुक्रदिवाकरारजीवार्कसूनुभगुरून्पितरौ च नत्वा। ब्राह्म ग्रहक्षगणितं महदतसूनुर्वेक्ष्पैखिल स्फुटमतीव वटेश्वरोह ॥ १ ॥
and ends thus:
प्रागपरकयालयोः कुफललम्छनं क्षयमतस्खम्भुदलप्टष्टगनरयोदृक्साम्पालम्छनं न मध्याही उपपत्तियाप्राक्ता प्रागपरे लम्छनेन तिथिविरहे लम्छने विरहेवनते याम्पो
 The colophons at the ends of the chapters of the Vateśvara-siddhānta run as follows:
 (1) श्रीमदानंदपुरोयमट्टमदतसुतवटेश्वरावेरचिते स्वनामसंज्ञिते स्फुटस्मिद्धांते

मध्यगतिः प्रथमोधिकारः ॥ ॥

 (2) श्रीमदानंदपुनायभट्टमहदत्तसुतवेश्वटेरविरचिते स्फुटसिद्धांते स्वनामसंज्ञिति

- - - टगत्पधिकरोयः ॥ ॥

 (3) श्रीमदानन्पयुरायभट्टमहदत्तसृतवठोश्चरविरचिते स्वनामसंशिते स्फुटसिद्धान्ते

भट्टगोविन्दावतारिते त्रिप्रश्नाध्पापस्तृतीयः ॥ ॥

 (4) श्रीमदानंदपुरीयभट्टमहदत्तसुतवटेश्वरकिचिते स्वनामसंज्ञिते स्फुटसिद्धांते

भट्टगोविन्दाचतारिते चंद्रग्रहणाधिकारश्चतुर्थ: ॥ ॥
 (5) श्रीमदानन्दयुरीयभट्टमहदत्तसुतचटेश्चरविरचिते स्वनामसंज्ञिते स्फुटसिद्धान्त
भट्टगोविन्दावतारिते रविग्रहणाधिकारः पंचमः ॥

 (6) श्रीमदानन्दपुरीयभट्टमहदत्तसुतवटेश्चरविरचिते स्वनामसंज्ञिते स्फुटसिद्धान्ते

भट्टगोविन्दावतारिते उदयास्तमयाधिकारष्षष्ठः ।

 (7) श्रीमदानन्दपुरीयभट्टमदतसुतोवटेश्वरविचिते स्वनामसंज्ञिते स्फुटप्रसिद्धान्ते

भट्टगोविन्दावतारिते श्रृङ्गोन्नत्पथिकारस्सप्तमः ।

 (8) श्रीमदानन्दपुरीयभट्टमहदत्तसुतवदेश्वरविरचिते स्वनामसंज्ञिते भट्टगोविन्दा

वतारिते समागमाधिकारोष्टम: ।

॥ समाप्तेदं कालक्रियायट्टम् ॥

 The manuscript is very defective. The words are generally misspelt and there are omissions, repetitions as well as distortions. These defects and the occurrence of the chapters of Vatesvara's Gola in fragments, in wrong sequence, and in wrong places, indicate that our manuscript did not come from the hands of Bhatta Govinda, the scribe of the original manuscript, who had good knowledge of astronomy. It must have been copied from an incorrect copy of the manuscript originally written by Bhatta Govinda.

 The manuscript was originally discovered by me in the collection of the late Pandit Girish Chandra Awasthi, Head of the Oriental Department, Lucknow University, Lucknow. It was later presented to the Lucknow University Library.

 MANUSCRIPT B. No. 45866 of the Lucknow University Library, Lucknow. This is really a photostat copy of Ms. No. 3784 of the Sanskrit Section of the (West) Panjab University Library, Lahore, and was acquired before the partition of the country. It may be described as follows:

 Substance- paper. Character- Modern Devanagari. Size- 27 cm. x 12 cm. Extent- 66 folios: 9 lines per page and 40 letters per line. Incomplete; runs up to the end of the first quarter of verse 14 of Chapter VII Section 1 of the Vateśvara-siddhānta.

 The first page of the manuscript has the script vaţesvarasiddhăntaprarambhah at its centre. The writing is started on the second page and the numbering of the folios occurs on the verso or left hand pages of the folios at the top on the left hand margin and also at the bottom on the right hand margin, the word rama being written just above the folio-number on the right hand margin as in Ms. A. The numbering of the verses in this manuscript is exactly the same as in Ms. A. The same verses have been numbered and in the same way. The manuscript is written along the length of the paper and the Written matter in every page is bordered by four pairwise juxtaposed vertical lines on either sides, as in the case of Ms. A.

 The manuscript begins as follows:

। ॥ श्रीकृष्णाय नमः ॥ ॥ व्रह्मावनीन्दुवुधशुकदिवाकरारजीवार्कसूनुभगुरून्पितरौ च नत्वा ब्राह्म ग्रहक्षगणित महदत्तसूनुर्वक्ष्पेखिल स्फुटमतीव वटेश्वरोह ॥ १ ॥

 It ends on page 13t (i.e. recto of folio 66) as follows:

वरास्फसमीरितं बुधैर्गणितस्कन्दविशेषभाजनैः दिनशेषविधूंघासवस्सहितारात्रिगृतासवोप्पलम् रविवन्नरकर्णदीप्तयोर्मावन्दधमेणभुजादि च । प्राग्लग्नदृक्चंद्रमसौविलग्न

On page 132 there occurs the following statement in the centre:

 वटेम्वरसिद्धान्तः मल्लारिज्योतिविदाम् श्रीराम

le, "(This copy of) the Vateśvara-siddhānta belongs to astronomer Malāri. Sri Rāma.”

 The last folio 66 is numbered as usual at the bottom on the right ۔۔ hand margin but at the top on the left hand margin we have the number 1825 instead of the folio-number. This number 1825 probably indicates the year when the manuscript was copied and the statement in the centre on page 132 shows that the manuscript belonged to astronomer Malläri. The colophons at the ends of the various chapters run as follows:

 (1) श्रीमदानंदपुरोयभट्टमदत्तसुतवटेश्वरावरचिते स्वनामसंज्ञिते स्फुटस्मिडांते

मध्यगतिः प्रथमोधिकारः

 (2) श्रीमदानंदपुनायभट्टमहदत्तसुतवेश्वटेरविरचिते स्फुटसिद्धांते स्वनामसंज्ञिति

---टगत्पधिकारोयः ॥ ॥

 (3) श्रीमदादन्पपुरीयभट्टमहदत्तसुतवठोश्चरविरचिते स्वनामसंज्ञिते स्फुटसिद्धान्ते

भट्टगोविंदाबतारिते त्रिप्रश्नाध्यापस्तृतीयः । ।

 (4) श्रीमदानंदपुरीयभट्टमहदत्तसुतवटेश्चरकिचिते स्वनामसंज्ञिते स्फुट सिद्धांत

भट्टगोविन्दाचतारिते चंद्रग्रहणाधिकारश्चतुर्थः । ।

 (5) श्रमदानंदयुरीयभट्टमहदत्तसुतचटेश्चरविरचिते स्वनमसंज्ञिते स्फुट सिद्धान्त

भट्टगोविंदावतारिते रविग्रहणाधिकारः पंचमः । ।

 (6) श्रीमदानन्दपुरीयभट्टमहदत्तसुतवटेश्चरविरचिते रवनामसंज्ञिते स्फुट सिद्धान्ते

भट्टगोविन्दावतारिते उदयास्तमयधिकारषष्ठः ।

 Mss. A and B bear striking similarity. The differences are trivial. Both begin with obeisance to God Krsna and have the same colophons at the ends of the chapters. Both bear the same incorrect punctuation and in both of them the same verses are numbered in the same way. Thus there is no doubt that they were copied from copies of the same original. A glaring proof of this is that the rule contained in vs. 25 of Chapter I, Section 5, which is missing from MsA is also missing from MsB. It has been inserted editorially to fill the gap.


  The manuscripts described above, which were used for the present edition, being full of errors, omissions, repetitions and distortions, a large number of rules stated in the Vateśvara-siddhānta being new, having no counterpart in any other work on Hindu astronomy, and there being no commentary of the text to serve as a guide in deciphe ring the text, the task of editing the text was extremely difficult, almost impossible. Attempt has been made to emend and correct the text where necessary, without making drastic alteration in the original text exhibited by the manuscripts used. Three main considerations were kept in mind while editing the text, firstly that the edited text should be correct as far as the subject matter was concerned, secondly that it should be perfect as far as the metre of the verses was concerned, and thirdly that it should be grammatically sound and as near the original text as possible. The edited text is printed in the upper half of the page (in antique types) and the text as found in Ms. A is printed below (in roman types) followed by variants in Ms. B, if any. This arrangement will enable the interested reader to see for himself how far the editor has been successful in deciphering and editing the text correctly. Additional matter inserted in the edited text by Way of filling the gaps and omissions has been enclosed within square brackets. The text has been presented completely and exactly as found in the manuscripts used. Not a single verse or part thereof has been omitted.

 The entire text in the manuscripts used was set out, as usual, in the form of running matter. Even the words were not properly separated. The edited text as well as the original manuscript text has been displayed properly, the verses being given in two lines (as far as possible) and the words properly spaced. In the edited version the verses dealing with the same topic or giving the same rule have been put together and prefixed by an introductory heading in Sanskrit briefly summarising their contents. These introductory headings have been enclosed within square brackets [ ]. Alternative rules have been separated by providing a little more space between them.

 For the convenience of the reader, the chapter-heading has been mentioned at the top on the left hand page and the section-heading (or the subject of the chapter) at the top on the right hand page. The chapter-number and the section-number (or verse-number) are also mentioned at the top on every page.  Towards the end of this Part are given three appendices, containing Index of Half-verses, List of Word-numerals and Glossary of Terms used by Vatesvara, and General Index. It is hoped that these will prove useful to the reader.


 The present publication is sponsored by the Indian National Science Academy, New Delhi. I am greatly indebted to Professor F. C. Auluck, then Vice-Chairman, National Commission for the Compilation of History of Sciences in India, who requested me to edit the Vateśvara-siddhānta for the Academy. The credit for the publication of this work is indeed due to him. All workers in the field of Indian mathematics and astronomy must be grateful to him. My first and most cordial thanks are due to him.

 I must offer my cordial thanks to Dr. A. K. Bag, Asst. Executive Secretary, Indian National Science Academy, New Delhi, who evinced keen interest in the preparation and publication of this book and offered all possible help.

 I am under great obligation to Pandit Markandeya Mishra, Jyotishacharya, my former colleague and friend, whose scholarly assistance and advice was of great help in the editing of the text. My heartiest thanks are due to him. My thanks are also due to Dr. K. V. Sarma, Honorary Professor of Sanskrit, Adyar Library and Research Centre Adyar, Madras, for his suggestions regarding the arrangement of the textual matter, and to my student Shri Yukio Ohashi for his assistance in proof-reading on various occasions and for help in preparing the General Index.

 I am grateful to the late Pandit Girish Chandra Awasthi, formerly Head of the Oriental Department, Lucknow University, Lucknow, for kindly making the manuscript (Ms. A) of the Vateśvara-siddhānta of his collection available to me for my use and later presenting it to the Lucknow University Library at my suggestion. I am indebted to the authorities of the (West) Panjab University Library, Lahore, who were kind enough to supply the photostat of Ms. B and to the authorities of the Lucknow University Library, Lucknow, for their cooperation in procuring transcripts of manuscripts for my use from time to time.

 I remember with respect and gratitude my teacher, late Dr. A. N. Singh, formerly Professor and Head of the Department of Mathematics and Astronomy, Lucknow University, Lucknow, for his guidance, help and blessings and for placing at my disposal all manuscripts, transcripts and books of his collection.

 I am also thankful to the many scholars whose works were consulted and found helpful during the preparation of this work.

 Lastly, I express my thanks to the proprietor and staff of the industrial Printing Works, Raniganj, Lucknow, for the excellent composing, printing and get-up of the book.

K. S. Shukla