SHRI BRAHMAGUPTA VIRACITA
BRĀHMA-SPHUṬA
SIDDHĀNTA
WITH
Vāsanā, Vijñāna and Hindi
Commentaries
Vol. I
FOREWORD
By
DR. SAMPURNANANAD
Governor-Rajasthan
Edited By
A Board of Editors headed by
ACHARYAVARA RAM SWARUP SHARMA
Chief Editor and Director of the Institute
Published by
Indian Institute of Astronomical and
Sanskrit Research
2239, Gurudwara Road, Karol, Bagh, New, Delhi-5.

Published by
Indian Institute of Astronomical
and Sanskrit Research
2239, Gurudwara Road, Karol Bagh,
New Delhi-5. (India)
☉
Aided by
Ministry of Education,
Government of India
☉
Editorial Board
Shri Ram Swarup Sharma
Chief Editor, Director of the Institute.
Shri Mukund Mishra Jyotishacharya
Shri Vishwanath Jha Jyotishacharya
Shri Daya Shankar Dikshita Jyotishacharya
Shri Om Datt Sharma Shastri, M.A.,M.O.L.
Introduction by
Dr. Satya Prakash D.Sc.
☉
Copy right by publishers
1966
☉
Price Rs. 80.00
☉
Printed by
Padam Shree Prakashan & Printers
12. Chamelian Road.
Delhi.

Dedicated to
Shri S. K. Patil
Union Minister for Railways

The provided image is completely blank (solid white), and there is no text or content visible to transcribe. Please upload a clear image of the page you would like transcribed.

श्रीब्रह्मगुप्ताचार्य-विरचित
ब्राह्मस्फुटसिद्धान्तः
(संस्कृत-हिन्दी-भाषायां वासनाविज्ञानभाष्याभ्यां समलंकृतः सोपपत्तिकः)
प्रथमो भागः
प्राक्कथन :
डा० सम्पूर्णानन्द-राज्यपाल-राजस्थान
प्रधानसम्पादक :
आचार्यवर पंडित रामस्वरूप शर्मा
(सञ्चालक-इण्डियन इंस्टीट्यूट आफ़ ऐस्ट्रानौमिकल एण्ड संस्कृत रिसर्च)
प्रकाशक :
इण्डियन इन्स्टीट्यूट आफ़ ऐस्ट्रानौमिकल एण्ड संस्कृत रिसर्च
२२३६, गुरुद्वारा रोड, क़रौलबाग़, न्यू देहली-५

प्रकाशक—
इंडियन इंस्टीट्यूट आफ़ ऐस्ट्रानौमिकल
एण्ड संस्कृत रिसर्च
२२३६, गुरुद्वारा रोड, करौल बाग़,
नई दिल्ली-५ (भारत)
⊙
भारत सरकार के शिक्षा मन्त्रालय द्वारा
प्रदत्त अनुदान से प्रकाशित ।
©
सम्पादक मण्डल—
श्री रामस्वरूप शर्मा सञ्चालक
प्रधान सम्पादक
डा० सत्यप्रकाश डी० एस-सी०
प्रस्तावना-लेखक
श्री मुकुन्दमिश्र ज्योतिषाचार्य
श्री विश्वनाथ झा ज्योतिषाचार्य
श्री दयाशंकर दीक्षित ज्योतिषाचार्य
श्री ओंदत्त शर्मा शास्त्री
एम. ए., एम. ओ. एल.
⊙
प्रथम संस्करण
१९६६
⊙
मूल्य रु० ८०.००
⊙
मुद्रक :
पद्म श्री प्रकाशन एण्ड प्रिन्टर्स
१२ चमेलियन रोड़,
दिल्ली ।

समर्पण :
श्रीयुत एस० के० पाटिल
यूनियन मिनिस्टर फ़ार रेल्वेज़
को
सादर समर्पित

The provided image is completely blank and contains no visible text or content to transcribe.

Foreword

The Indian Institute of Astronomical & Sanskrit Research
has done a very useful piece of work by publishing the Brāhma
Sphuṭa Siddhānta. This is an original work on Astronomy
written about twelve hundred years ago. Mainly devoting himself
to Astronomy as was natural, the author, Brahma Gupta, has
also given considerable space to such branches of Mathematics as
in his opinion are particularly applicable to Astronomy. Brahma
Gupta is not a mere theoriser. His work bears ample evidence of
close observation of astronomical phenomena, though he did not
have at his disposal any large and well equipped Vedhālaya or
Observatory. He has had to find fault with some of his predece-
ssors. The main reason for his criticism was as stated by him :
ब्रह्मोक्तं ग्रहगणितं महता कालेन यत् श्लथीभूतम् ।
अभिधीयते स्फुटं तज्जिष्णुसुतब्रह्मगुप्तेन ॥
The creator Brāhma himself had given certain calculations
in his book namely Brahma Siddhānta. But in the course of many
years these calculations have been found to have bocome inaccu-
rate. Of course, in referring to calculations, the author is referr-
ing to the bases of these calculations, the main data of astronomy.
The excellent and fairly exhaustive introduction by Dr. Satya
Parkash is of very great help in understanding the book because
it brings out clearly the various points on which Brahma Gupta
has laid stress, particularly those on which he differs from other
great astronomers.
A great controversy still rages between two schools of Indian
astronomers which for want of better names may be called the
schools of Arya Bhata and Brahma Gupta. Some years ago the
Indian Institute of Astronomical & Sanskrit Research published
the Vateshwar Siddhānta which is supposed to be associated with
the Arya Bhata School. It is, therefore, in the fitness of things
that it should now publish the present standard volume of the
other school.
To my mind the Publication of such books is of great value
from two points of view. It helps to remove the ignorance of
average educated Indian of today about the achievements of his
ancestors. In the field of two important branches of science,
Mathematics and Astronomy, it is really surprising how those
ancient astronomers could reach such heigts of accuracy with the
help of instruments which seem to be laughably crude compared
to those that modern astronomers have at their disposal. At the
same time a study of such literature is a very salutary corrective

( २ )
to the vanity of those who feel that in astronomy as in certain
other subjects the last word was said by those writers who have
written in Sanskrit. We learn how far behind we are in certain
very important directions in the field of knowledge.
It is interesting by the way to find that the author of this
great work was a Vaishya. This shows how diffused knowledge
even of the most abstract subjects was in those days and how
Scholarship was honoured irrespective of caste. Not one the
critics of Brahma Gupta has taunted him on the ground of his not
being a Brahmana.
Sampurnanand
Governor-Rajasthan
Raj Bhavan,
Jaipur,
Dated May 4, 1966.
—:०:—

Observations
of
Dr. K. M. Munshi
President of the Reception Committee
The Author Shri Ram Swaroop Sharma has given to the
world of scholars an excellent and valuable treatise on the famous
Astronomer Brahma-Gupta, son of Jiṣṇugupta, born in 589 A. D.
in Bhillamala or Srimala now in Southern Marwad close to the
northern frontier of modern Gujarat. The work is divided into
13 chapters and at the end of each, the learned author has given
reference to other works and treatises for further study as also
in support of his various conclusions. He has described Astro-
nomy in Ancient India in the light of the knowledge of the
subject available in different countries in his time.
After giving personal details of Brahma-gupta, the author
starts on a critical study of the works of that Astronomer-parti-
cularly his Brahma-sphuṭa-siddhānta and Khaṇḍana-Khādya.
The author has also discussed the Indian Luni-solar Astronomy,
the Greek and Hindu methods in spherical Astronomy and the
Epicyclic theory of ancient Indians. Discussing in detail the
contribution of Brahma Gupta in Arithmetic, Algebra, in Astro-
nomy and the Astronomical instruments that he used, the author
has brought out the various highlights of his work and achieve-
ments in comparison with those of his predecessors, successors and
contemporaries in other countries.
The author deserves to be congratulated for this scholarly
contribution on the subject of Ancient Indian mathematics and
Astronomy.
—K.M. Munshi
Bhartiya Vidya Bhawan
Bombay

Publisher’s Note

It is with pride and pleasure that the Indian Institute of
Astronomical & Sanskrit Research brings out its second monumental
work ‘Brāhma Sphuṭa Siddhānta’. The Institute, set up on the 23rd
November, 1957, with the object of promoting research into ancient
Indian manuscripts on Astronomy and allied Sciences, started its
programme of publication with the preparation of a critical edition of
Vateshwara Siddhānta running into more than 700 pages. It was far
back in early forties that the idea of reviving the treasures of know-
ledge hidden in ancient manuscripts came to my mind. In 1945 I could
succeed in editing and publishing ‘Trailokya Prakāśa’ of Acharya Hema
Prabha Sūri.
Ālbruni’s Travel Accounts of India contain a reference to
Vateshwara Siddhānta and this fact was responsible for prompting me to
arrange publication of Vateshwar Siddhanta. It was rather difficult to
search out this manuscript and the clue given by Mahamahopadhyaya
Sudhākar Dwivedi (a great Mathematician and Astronomer of 19th
century) that the manuscript was available in Gwalior did not lead me
to any results. I kept my search on and found a copy of this text in the
collection of manuscripts inherited by a Brahman widow of Gujranwala
District in west Pakistan. The same style of copy was later seen by me
in the Panjab University Library at Lahore.
Vateshwarāchārya, the great writer of Vateshwara Siddhānta, has
criticised Brāhma Sphuṭa Siddhānta of Brahma Gupta, in his work.
This naturally aroused my curiosity to procure and publish Brahma
Sphuṭa Siddhānta so as to provide right perspective to the students of
ancient Indian Scientific literature. Moreover, in one of my
discussions with the late Dr. K. S. Krishnan, Director,
National Physical Laboratories, New Delhi, he refer-
rred to Dr. Colebrook (a German Writer) as having translated into
English two chapters of ‘Brāhma Sphuṭa Siddhānta’, namely, Vyakta
(Arithmetic)and Ayakta(Algebra). The late Dr. Krishnan showed keen
interest in this manuscript and encouraged me in taking up preparation
of a critical edition of this text. The Institute is grateful to the Govt.
of India (Department of Cultural Affairs) for meeting part of the
expenditure on this publication and thereby enabling us to complete
our task.
I shall be failing in my duty if I do not mention the great and
invaluable contribution made for the success of the Institute by its
founder President the late Shri Brijlal Nehru. It was under his able
guidance that the Institute started functioning and its various progr-
ammes were finalised. His passing away has been a big and irreparable
loss to us The Institute will keep his memories always alive by follow-
ing his ideals and by executing with zeal the programmes inspired by
him.

( ii )
I must take this opportunity to express my heartfelt gratitudes to
Shri B. B. Varma, Member Parliament, who has never shirked in
shouldering the responsibilities of managing the affairs of the Institute
first as a member of its Executive Council and now as its President.
I am also thankful to Dewan Hari Krishan Das, Chairman of the Exe-
cutive Council and Shri F.C. Bedi Treasurer of the Institute for their
ungrudging support to the cause of the Institute.
My thanks are also due to Dr. Sampurnanand, Governor Rajasthan,
who has blessed the Institute by inaugurating it and has now been kind
to write a foreword for the present book. I am also indebted to Dr.
Satya Prakash, Head of the Deptt. of Chemistry, Allahabad University
for his having spared time to write an introduction in English for this
publication. He has always been cheerfully allowing us to draw on his
rich experience and wealth of knowledge. I am also grateful to Pt.
Mukund Mishra, Pt. Vishwa Nath Jha, Shri Daya Shankar Dixit and
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. The volume
also contains a Sanskrit Bhumika from the Chief Editor and an Index
of Shlokas. Volume II comprises of the first nine chapters of Brāhma
Sphuṭa Siddhānta containing only those readings which we have
considered as correct. It also includes Vāsanā commentary of Pṛthūdaka
Swāmī and Vigyān Bhashya in Sanskrit with Hindi translation.
Volume III includes chapters 10 to 16. This volume also contains
Nutan Tilak commentary of Sudhakar Dwivedi and Vigyan Bhashya
in Sanskrit with Hindi translation. Volume IV comprises of chapters
17 to 24 and also an Index of Shlokas contained in Volumes II, III and
IV. It also includes an appendix on Dhayāna Grhaopadeshādadhyāya.
Another appendix in this volume contains Vāsanā commentary on
Golādhyāya.
The Institute has planned to add to its list of publications,
shortly, Samrāṭ Siddhānta (3000 pages and already in press), Bṛhad
Yavan Jātaka (2000 pages) and Panch Siddhāntikā (1600 pages).
The Indian Institute of Astronomical & Sanskrit Research
considers it a proud priviledge to dedicate Brāhma Sphuṭa Siddhānta to
Shri S. K. 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. M. Munshi and Shri Wadilal Chaturbhuj 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 Lal H. Shah, Hony. 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. I also owe a debt of grati-

( iii )
tude to the Patrons of the Institute : His Majesty the King of Nepal,
Abhinaya Samrat, Shri Prithvi Raj Kapoor, Shri Dhairyasinh, R.
Morarji, Chairman Dharamsi Morarji & Co., Bombay, Shri Pranlal
Bhogilal, Patel Bombay for their invaluable help. I am also grateful to
the life members of the Institute : H.H. Maharaja Manabendra Shah of
Tehri Garhwal, Yuvraj P.C Dev, Shri B.N. Bhaskar, Shri R.K. Batra,
Shri Sada Jivatlal Chandulal, Shri Shiv Kumar Bhuvalka, Shri Jamna
Das H. Moorjani, Shri Shantilal K. Somaiya, Shri Kisonlal M. Diwanji,
Solicitor, Shri N. K. Jalan, Shri D. R. Nayar, Shri Vadilal C. Gandhi,
Shri Devi Prasad Khandelval, Shri Ram Prasad Khandelval, Shri B. K.
Jalan, Shri Amir Chand T. Gupta, Shri Laxman Vaman Apte, Smt.
Padma Koregaonkar, Shri Yodh Raj Bhalla for their support to the
Institute.
I must make a special mention here of shri A. N. Jha, Chief
Commissioner, Delhi, who has greatly encouraged me in my task of
publishing old manuscripts. His help in solving the various problems
faced by me, has been invaluable. I am highly grateful to him for
his support in my cause. I am also grateful to H. H. Maharaja
Manabedra Shah of Tehri Garhwal, Seth Sadajivat Lal, Smti. Padma
Koregaonkar, Lala Yodh Raj Bhalla, Shri F.A Fazalbhai, Shri Morar J.
Vaidya, Shri N. J. Aggarwal, Shri P. S. Naulakha, Shri R. L.
Maheshwari, Shri D. N. Bhattacharjee, Shri P. A. Narielwala,
Shri P. M. Aggrawal, Shri Shiv Kumar Bhuvalka, Shri Navin
Bhai Khandwala and Smti. Nirmala Gomte, Lala Jagan Nath Jr,
Shri L.S. Aggarwal, Shri B.N. Saxena, Shri R.B. Shah, Shri L.O. Joshi,
Shri T.S. Krishnamurti, Shri R. S. Chitkara, Dr. Ram Karan Sharma,
Shri V.P. Agnihotri, Shri K.L. Handa and Shri K.G. Somayya for their
help and advice at various occasions.
Ram Swarup Sharma
Bombay
17-5-1966.
—:o:—

विषयानुक्रमणिका

1. Foreword
2. Observations of Dr. K. M. Munshi
3. Publisher's Note
4. Index
5. भूमिका
6. Introduction 1—344
   CONTENTS PAGE
7. Astronomy in ancient nations 1—45
8. Personal references of Brahmagupta. 47—56
9. Brāhma Sphuṭa-Siddhānta & Khaṇḍakhādyaka. 57—94
10. Brahmagupta's Originality in the Khaṇḍakhādyaka. 95—104
11. Indian Luni-solar Astronomy. 107—124
12. Greek & Hindu methods in Spherical Astronomy. 125—145
13. Epicyclic theory of Ancient Indians. 147—152
14. Brahmagupta & Arithmetic. 153—187
15. Brahmagupta as an Algebraist. 189—276
16. Arabic & Indian divisions of the Zodiac. 277—288
17. Brahmagupta's Astronomy : its highlight 289—314
18. Brahmagupta—a great critic. 317—330
19. Brahmagupta and Astronomical Instruments. 331—344
20. ब्राह्मस्फुटसिद्धान्त ... ... १—३२२
    १. मध्यमाधिकारः १—२२
    २. स्पष्टाधिकारः २३—४८
    ३. त्रिप्रश्नाधिकारः ४९—७१
    ४. चन्द्रग्रहणाधिकारः ७२—७७
    ५. सूर्यग्रहणाधिकार ७८—८४
    ६. उदयास्ताधिकारः ८५—९०
    ७. चन्द्रशृंगोन्नत्यधिकारः ९१—९८

( २ )
८. चन्द्रच्छायाधिकारः ६६-१०१
६. ग्रहयुत्यधिकारः १०२ - १०६
१०. भगृहयुत्यधिकारः ११० - १२६
११. तन्त्रपरीक्षाध्याय १३० - १५२
१२. गणिताध्यायः १५३ - १७०
१३. मध्यगतिप्रश्नोत्तराध्यायः १७१ - १८१
१४. स्फुटगत्युत्तराध्यायः १८२ - १८८
१५. त्रिप्रश्नोत्तराध्यायः १८६ - २१५
१६. ग्रहणोत्तराध्यायः २१६ - २२६
१७. शृङ्गोन्नत्युत्तराध्यायः २३० - २३२
१८. कुट्टकाध्यायः २३३ - २४६
१६. शंकुच्छायादिज्ञानाध्यायः २४७ - २७१
२०. छन्दश्चित्युत्तराध्यायः २७२ - २७७
२१. गोलाध्यायः २७८ - २६७
२२. यन्त्राध्यायः २६८ - ३१५
२३. मानाध्यायः ३१६ - ३१८
२४. संज्ञाध्यायः ३१९ - ३२२
8. ध्यानग्रहोपदेशाध्याय ... ... ३२३ - ३३६
9. अकारादि क्रमेण श्लोकानुक्रमणिका ... ३३७ ३५२
:०:

Here is the line-by-line transcription of the text from the image into Unicode Devanagari Markdown:

भूमिका
ब्रह्मगुप्तकृतो ब्राह्मस्फुटसिद्धान्तः
श्रीचापवंशतिलके श्रीव्याघ्रमुखे नृपे शकनृपाणाम् ।
पञ्चाशत्संयुक्तैर्वर्षशतैः पञ्चभिरतीतैः ॥
ब्राह्मः स्फुटसिद्धान्तः सज्जनगणितज्ञगोलवित्प्रीत्यै ।
त्रिंशद्वर्षेण कृतो जिष्णुसुतब्रह्मगुप्तेन ॥
इति ब्राह्मस्फुटसिद्धान्तीयसंज्ञाध्याये आचार्योक्त्या ५२० शाकवर्षे-आचा-
र्यस्य (ब्रह्मगुप्तस्य) जन्म समयस्ततः परं त्रिंशति वर्षेषु गतेषु तेन ब्राह्मस्फुट-
सिद्धान्तसंज्ञको ज्योतिषसिद्धान्तग्रन्थो विरचितः¹। गुर्जरदेशमध्ये भिनमाल नाम
ग्राम एवास्य जन्मस्थानं बहूनां पाश्चात्यानां गवेषणया सिध्यति । गुर्जरदेशीय-
ज्योतिर्विदां मुखकथातोऽपि भिल्लमालकोऽधुना भिनमालनाम्ना प्रसिद्धो ग्राम
एवाऽऽचार्यस्य

( २ )
(१८१७ ख्रीष्टाब्दे) कृत इत्युपलभ्यते। अत्र ब्राह्मस्फुटसिद्धान्तेऽष्टाधिक सहस्र-
१००८मिता आर्याः सन्ति, तथा पूर्वार्धे १. मध्यगतिः। २. स्पष्टगतिः। ३. त्रिप्रश्ना-
ध्यायः। ४. चन्द्रग्रहणाध्यायः। ५. सूर्यग्रहणाध्यायः। ६. उदयास्तमयाध्यायः।
७. चन्द्रशृङ्गोन्नत्यध्यायः। ८. चन्द्रच्छायाध्यायः। ९. ग्रहयुत्यध्यायः, १० भगृह-
युत्यध्यायः, इति दशाध्यायाः सन्ति। परार्धे च १. तन्त्र परीक्षाध्यायः।
२. गणिताध्यायः। ३. मध्यगत्युत्तराध्यायः। ४. स्फुटगत्युत्तराध्यायः।
५. त्रिप्रश्नोत्तराध्यायः। ६. ग्रहणोत्तराध्यायः। ७. छेद्यकाध्यायः। ८. शृङ्गोन्न-
त्युत्तराध्यायः। ९. कुट्टकाकाराध्यायः। १०. छन्दश्चित्युत्तराध्यायः। ११. गोला-
ध्यायः। १२. यन्त्राध्यायः। १३. मानाध्यायः। १४. संज्ञाध्यायः। इति चतुर्दशा-
ध्यायाः सन्ति, पूर्वार्धपरार्धाध्याययोर्योगेन चतुर्विंशतिरध्याया अत्र ग्रन्थे सन्ति।

पृथिव्याश्चलत्वं भगणानां स्थिरत्वं स्वीकृत्य—अहोरात्रासुभिः स्वाक्षो-
परि पृथिव्या भ्रमणं मन्यते आर्यभटेनेति—आवर्तनमुर्व्यश्चेदित्याद्युक्तिः। अन्यत्रा-
नेका अत्युक्तयो दुराग्रहवशात् कुत्रचिद्वाग्बलेन कथिता ब्रह्मगुप्तेन यथा—
स्वयमेव नाम यत्कृतमार्यभटेन स्फुटं स्वगणितस्य ।
सिद्धं तदस्फुटत्वं ग्रहणादीनां विसंवादात् ॥
जानात्येकमपि यतो नार्यभटो गणितकालगोलानाम् ।
न मया प्रोक्तानि ततः पृथक् पृथक् दूषणान्येषाम् ॥
आर्यभटदूषणानां संख्या वक्तुं न शक्यते यस्मात् ।
तस्मादयमुद्देशो बुद्धिमताऽन्यानि योज्यानि ॥
स्वयं ग्रहग्रहणादिवेधकर्त्ता ब्रह्मगुप्तः प्राचीनाचार्येभ्योऽनेकान् विशिष्टान्
ग्रहादिसाधनविधीन् गणितसत्यासत्यपरीक्षार्थं वेधविधींश्च स्वग्रन्थे प्रौढोक्त्या
प्रतिपादयति —
ज्ञातं कृत्वा मध्यं भूयोऽन्यदिने तदन्तरं भुक्तिः ।
त्रैराशिकेन भुक्त्या कल्पग्रहमण्डलानयनम् ॥
यदि भिन्नाः सिद्धान्ता भास्करसंक्रान्तयोऽपि भेदसमाः ।
स स्पष्टः पूर्वस्यां विषुवत्यर्कोदयो यस्य ॥
इत्यादिना वास्तवविचारासक्तः सर्वप्रथमं सर्वतो विशिष्टं विवेचनाबहुलं
सिद्धान्तग्रन्थं ब्रह्मगुप्त एव रचितवानित्युपलब्धज्योतिषसिद्धान्तग्रन्थेभ्यो ज्ञायते ।
‘कृती जयति जिष्णुजो गणकचक्रचूडामणि’ रितिस्वसिद्धान्तशिरोमणेर्गणिता-
ध्यायारम्भे भास्कराचार्येण ब्रह्मगुप्तमभिवन्द्य तत्परमपि बहुत्रस्थले ब्रह्मगुप्त-
मतोल्लेखं कुर्वताऽपि ‘यथाऽत्रग्रन्थे ब्रह्मगुप्तस्वीकृतागमोऽङ्गीकृत’ इत्युक्त्या
तद्ग्रन्थानुसारी ग्रन्थो रचित इति प्रतीयते । ब्रह्मगुप्तेनायनचलनं नोपलब्धमिति
ब्रह्मस्फुटसिद्धान्ततो ज्ञायते । अयनचलनोपलब्धिः प्रत्युत खण्डितेति दृश्यते
यथा—
परमल्पामिथुनान्ते युरात्रिनाड्योऽर्कगतिवशाहतवः ।
नायनयुगमयनवशात् स्थिरमयनद्वितयमपि तस्मात् ॥
वराहमिहिरोऽयनचलनसम्बन्धे सन्दिहान आसीदिति ‘नूनं कदाचिदासी-
द्येनोक्तं पूर्वशास्त्रेषु’ इति तत्कथनेन ज्ञायते । तत्समयेऽश्विन्यादौ क्रान्तिपात
आसीदित्यश्विन्यादि नक्षत्रगणना प्रवृत्ता सैव ब्रह्मगुप्तात्परमद्यावधि प्रचलति ।

पञ्चषष्ट्या वर्षैः क्रांतिपातः प्राय एकमंशं पश्चिमदिश्यपसरति तज्ज्ञानं स्वल्प-
कालेनासम्भव इवेति वेधविज्ञेनापि ब्रह्मगुप्तेनायनचलनं नोपलब्धमिति । आर्य-
भटविरोधी भूत्वापि ब्रह्मगुप्तो ब्राह्मस्फुटसिद्धान्तरचनानन्तरं सप्तत्रिंशत्तमे वर्षे
खण्डखाद्यकं नामकरणग्रन्थं रचितवान् यथा तत्प्रारम्भे --
प्रणिपत्य महादेवं जगदुत्पत्तिस्थितिप्रलयहेतुम् ।
वक्ष्यामि खण्डखाद्यकमाचार्य्यार्य्यभटतुल्यफलम् ॥
प्रायेणार्यभटेन व्यवहारः प्रतिदिनं यतोऽशक्यः ।
उद्वाहजातकादिषु तत्समफललघुतरोक्तिरतः ॥
इति तदुक्तग्रन्थपर्यालोचनया ज्ञायते यत्सर्वत्र व्यवहारकृतां मानवानां
मध्ये प्रचरितार्यभटमत निराकरणमतीव कठिनमासीदिति—'आर्यभटमतानुसारि-
व्यवहरतां तात्कालिकजनानामुपकारायैव व्यावहारिकः करणग्रन्थः खण्डखाद्यक-
नामको रचितो ब्रह्मगुप्तेन । यथोपलब्धेषु प्राचीनज्योतिषसिद्धान्तग्रन्थेषु ब्राह्म-
स्फुटसिद्धान्त आदर्शरूपो ग्रन्थस्तथैव सर्वेषां करणग्रन्थानामादर्शरूपमादिमं वा
इतस्त्रयोदशशतवर्षैः प्राचीनं खण्डखाद्यकं करणम् । अथ ‘ब्रह्माह्वयश्रीधरपद्म-
नाभबीजानि यस्मादति विस्तृतानि' इति बीजगणिते भास्करोक्त्या ज्ञायते
यद्ब्रह्मगुप्तस्य विपुलो बीजगणित ग्रन्थ आसीत्परमयं ग्रन्थः कुत्रापि नोपलभ्यते
न वा श्रूयते । ब्रह्मगुप्त एव सर्वापेक्षया श्रीपतेरादर्शभूतः । ब्राह्मस्फुटसिद्धान्त-
सिद्धान्तशेखरयोः पर्यालोचनया ज्ञायते यद् ब्रह्मगुप्तोक्ताः संक्षिप्ता बहुलार्थयुक्ता
आर्या एव बृहदाकारैश्छन्दोभिरनूदिताः श्रीपतिना। वस्तुतो ब्रह्मगुप्तोक्तं ग्रह-
गणितं सूक्ष्मं ज्ञात्वा सत्यमिव तदेव स्वीकुर्वन् श्रीपतिस्तदुक्तिवैषम्यं स्वसुन्दर-
रचनाभिरपहरन् सुगमतंर ग्रन्थांतरं (सिद्धान्त शेखरं) चकार, नात्र केषामपि
विप्रतिपत्तिः । ग्रन्थरचनासम्बन्धे श्रीपतेर्विशेषतो लल्लाचार्य एवादर्शः । ये केचन
विषया ब्रह्मगुप्तेन न कथिता अथ लल्लेन कथितास्तान् सर्वानिव नियतमेव
श्रीपतिः श्लोकान्तरेण तथैव कथितवान् । वस्तुतो द्वयोर्ग्रन्थयोः (ब्राह्मस्फुट
सिद्धान्तशिष्यधीवृद्धिदयोः) परिशीलनं कृत्वा श्रीपतिना सिद्धान्तशेखरो रचितः ।
ब्राह्मस्फुट सिद्धान्ते येषामाचार्याणां नामानि समागतानि सन्ति तेषां सम्बन्धे
किञ्चिद्विविच्यते । सर्वेषां सिद्धान्तानामादिमः सर्वेभ्यः प्राचीनॊ वा ब्रह्मसिद्धान्त
एव, स एव कैश्चित् पितामहसिद्धान्तनाम्नाप्युच्यते । पञ्चसिद्धान्तिकायां
वराहमिहिरेण द्वादशोऽध्याय आर्यापञ्चात्मकः पैतामहसिद्धान्तः कथितो
यथा—
रविरशिनोः पञ्चयुगं वर्षाणि पितामहोपदिष्टानि ।
अधिमासस्त्रिंशद्भिर्मासैरवमस्त्रिषष्ट्याऽह्नाम् ॥