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भास्करः I


General Editor

Professor of Mathematics, Lucknow University





महाभास्करीयम् लखनऊ विश्वविद्यालयस्य गणिताध्यापकेन एम०ए०, डी० लिट्० इत्युपाधिधारिणा श्री कृपाशंकर शुक्लेन अाङ्ग्लानुवाद-व्याख्या-टिप्पण्यादिभिः सहितं सम्पादितम्। W लखनऊ विश्वविद्यालयस्य गणित-ज्योतिष-विभागेन प्रकाशितम् efo २०१७ वि० First Edition 1960 Price Rs.15/- $ వీరి • Printed at Nav Jyoti Press Pandariba, Lucknow. PREFACE The object of the “Hindu Astronomical and Mathematical Texts Series' is to bring out authoritative and critical editions of important unpublished works dealing with ancient Indian astronomy and mathematics. The present edition of Bhaskara I's Maha-Bhaskariya is No. 3 of this series. The idea of bringing out the above series is due to Dr. A. N. Singh, late Professor of Mathematics, Lucknow University, who organised a scheme of research in the history of Hindu mathematics and astronomy in the Department of Mathematics, Lucknow University, with the object of collecting, studying, and editing important works on Hindu mathematics and astronomy. Under his able guidance remarkable progress was made in this direction and a number of manuscripts were acquired, studied and edited. In 1954 he submitted to the Government of the Uttar Pradesh a detailed plan for the publication of the work carried out under the above scheme of research in a series to be called the “Hindu Astronomical and Mathematical Texts Series'. The plan was approved by the Government and a sum of Rs. 1000/- was sanctioned in the name of Bharata Ganita Parisad to undertake the publication of the series. In the year 1955 the Government of the Uttar Pradesh was generous enough to sanction the remaining sum of Rs. 9000/- to the Department of Mathematics and Astronomy, Lucknow University, for the said publication. The scheme of research in the history of Indian mathematics and astronomy referred to above has been financed by the Government of the Uttar Pradesh through the kind help of Dr. Sampurnanand, its then Education Minister, for which we express our sincere thanks to them. We are specially grateful to Dr. Sampurnanand who, a great scholar of Jyotisa as he himself is, has been taking keen interest in the progress of this research and helping us with necessary funds and encouragement from time to time. R. Ballaibh CONTENTS Introduction Sanskrit Text प्रथमोऽध्यायः द्वितीयोऽध्यायः तृतीयोऽध्यायः चतुर्थोऽध्यायः पञ्चमोऽध्यायः षष्ठोऽध्यायः सप्तमोऽध्यायः अष्टमोऽध्यायः शब्दानुक्रमणिका छन्दानुक्रमणिका English Translation Chapter I. MEAN LONGITUDE OF A PLANET AND PLANETARY PULVERISER Homage to God Siva, planets and stars 1-Appreciation of the Aryabhatiya and the pupils of Aryabhata 1-Ahargana 2-6-Meanlongitude of a planet by various methods 6-7, 15Mean longitudes of Sun and Moon 8,9-Mean longitude by simplified rules 16-28-Correction to the mean longitudes of Moon's apogee and ascending node 28-Planetary pulveriser 29-Methods for solving a planetary pulveriser 30-36-Weekday pulveriser 36-Time-pulveriser 38-General solution of a pulveriser 40-When the interpolator is positive 41-When the residues of two or more planets are given 43. Chapter II. THE LONGITUDE-CORRECTION Places on the Hindu prime meridian 47-Distance from the prime meridian 49,55-Criticism of two rules 51-Longitude in time 52, 53-Criteria for knowing whether the local place is to the east or to the west of the prime meridian 54 Lóngitude-correction and its application 55. Page զo ፄኛ २२ २९ ३७ እ፩`(ፉ Yፏe ५३ ६६ 47 CONTENTS Page Chapter III. DIRECTION, PLACE AND TIME. JUNCTION STARS OF THE ZODIACALASTERISMS AND CONJUNCTION OF PLANETS WITH THEM 56 Setting up of the gnomon 56-Finding the directions from the shadow of the gnomon 57, 59–Hypotenuse of the shadow 60-Finding the latitude of the place and the Sun's altitude 61--Sun's declination, day-radius, earthsine, and ascensional difference 62-Ascensional differences of the signs 65-Times of rising of the signs at the equator 68Times of rising of thesigns at the local place 69-Sun's meridian altitude, declination, and longitude 70-73,76-Latitude from the Sun's meridian zenith distance and declination 74Sun's altitude for the given time 74,77-78--Sun's altitude in the night 79—Time corresponding to the Sun’saltitude 80—Longitude of the rising point of the ecliptic 81—Longitude of the setting point of the ecliptic 82-To find the time from the longitudes of the Sun and the risingpoint of the ecliptic 82Sun's altitude, hour angle, and longitude when the Sunison the prime vertical 84-88-Locus of the shadow-end 89-92-Sun's agra and Sahkyagra and derivation of the equinoctial midday shadow therefrom 92-93-Finding the Sun's agra and Sahkyagra by the observation of the Sun and deriving the equinoctial midday shadow and the local latitude therefrom 94Finding the longitude of a planet or star with the help of that of another planet or star 95-Longitudes of the junction-stars of the naksatras 98-Celestial latitudes of the junction-stars 102-Conjunction in longitude of a planet and a star, and distance between them 102-Occultation of certain stars by the Moon 104. Chapter IV. TRUE LONGITUDE OF A PLANET 106 Sun's mean anomaly and its Rsine 106-Rsine of an arc 107-Sun's equation of the centre 110, 111-Sun's correction for the equation of time due to the eccentricity of the ecliptic 114—Bāhu and koți due to anomaly lo True distance of the Sun or Moon 115-True daily motion of the Sun or Moon 119-122-. True distance of the Sun or Moon by the eccentric theory 122-Sun's true longitude by the eccentric theory 125-Sun's correction for the equation of time due to the eccentricity of the ecliptic CONTENTS Page under the eccentric theory 126-An approximate formula for the Sun’s declination 127—Correction due to the Sun’s ascensional difference 127-Semi-durations of day and night 128-Corrections for the Moon 129.--Tithi 130-Karana 131-Naksatra 132-Phenomena of vyatipata 132-Manda and sighra anomalies (kendra) for the planets 134-Corrected manda and sighra epicycles 134-Calculation of the true longitudes of the planets 136—Calculation of the true longitudes of the planets under the eccentric theory 141-145Mandakarna and sighrakarna 146-Direct and retrograde motions of a planet 146-True daily motion of the planets 148-Longitudes of the Sun and Moon at the end of the parva-tithi 152. Chapter V. ECLIPSES 53 Distances of the Sun and Moon 153-Diameters of the Earth, Sun, Moon and the shadow 153-157-Longitude of the meridian-ecliptic point 157-The five Rsines relating to a the Sun and to the Moon 158-162-Time of apparent conjunction of the Sun and Moon 162-Finding the Moon's latitude corrected for parallax (true nati) 166—Possibility of a solar eclipse 167-Calculation of an eclipse: Sparsa and moksasthityardhas 167-Sparsa and moksa vimardārdhas 168-Time of actual visibility of a solar eclipse 169Projection of an eclipse: Aksa-valana 169-Ayana-valana 171-Resultant valana 172-Finding the centre of the eclipsing body for the time of the first contact, last contact and middle of the eclipse 173-Difference of procedure in the case of a lunar eclipse 74-Measure of the eclipse 175Path of the eclipsing body 175-Calculation-and construc-. tion of the phase of the eclipse for the given time 175, 176Eclipse of the Moon: Diameter of the shadow 177 -Sthityardhas and vimardardhas 180-Direction of the Moon's latitude to be used in the projection of a lunar eclipse 180. Chapter VI. RISING, SETTING AND CONJUNCTION OF PLANETS 182 Visibility-corrections known as aksa-drikkarma and ayanadikkarma 182, 184-Visibility of the Moon 186-The phase of the Moon 187—Moon’s true declination 188-Elevation of the lunar horns 189-Graphical representation of the eleva CONTENTS Page tion of the lunar horns 190-193-Time of moonrise on the g full moon day 193-Duration of the Moon's visibility during the night, or time of moonrise 194-96-Time of meridian passage of the Moon 197-Moon's meridian zenith distance 198-Elevation of the horns of the half-risen or halfset Moon 198-Procedure to be adopted in the case of the planets 198-Heliacal visibility of the planets 199-200Minimum distances of the planets from the Sun at which they become visible 199-Conjunction of planets 200-204. Chapter VII. ASTRONOMICAL CONSTANTS 205 Constants under the sunrise day-reckoning: Revolutionnumbers, intercalary months, omitted lunar days, and civil days in a yuga 205-Inclinations of orbits, longitudes of ascending nodes and apogees, and manda and sighra epicycles of the planets; methods for finding the celestial latitude and manda and sighra anomalies of a planet 206-Method for finding the bahuphala and kotiphala, etc., without using the Rsine-difference table 207-Circle of the sky and orbits of the planets 210. Constants under the midnight day-reckoning: Civil days, omitted lunar days, and revolution-numbers of Mercury and Jupiter in a yuga; diameters of the Earth, Sun, and Moon; mean distances of the Sun and Moon; and longitudes of the apogees of the planets211-Manda and sighra epicycles and manda and sighrapatas of the planets 212-Methods for finding the celestial latitude and the truemean longitude of a planet; Circle of the sky and orbits of the planets 213. Chapter VIII. EXAMPLES 24 Quotations from the Maha-Bhaskariya in later works. 226 Glossary of terms used in the Maha-Bhaskariya 230 Short : Long: A nusvara : Visarga : Non-aspirant: Classified: Unclassified: Compound : TRANSLTERATION 3. a lत्च्kक् य् क्षम् kş WOWELS 砂 e = h S - CONSONANTS ख् ग् घ् ड् kh g gh i হু ज् झ् व् ch j jih ट् ड् 京 णू th d dh थ् द् 驱 r th d dih in फू बृ भू म् ph b bh. m. र् ल् व् श् l ዒሀ s त्र् ज्ञ ' έγ η স্ত্রী अौ Á BJ BrSpSi BrSam GL KK IKKanu KKu KPr LBh LIM MBh MS MoC PS PS SK ŠiL)Vr S?Sფ, SiŚe Sន៍ STW SãS? TS WS VM VVS. LIST OF ABBREWIATIONS Aryabhatöaya Brhajjataka Brahma-sphuta-siddhanta Bhat-saiahita Graha-laghaca Khanda-khadyaka Karana-kaustubha Karama-kutahala Karama-prakasa Laghu-Bhaskariya |Lagһи-татаsa Maha-Bhaskariya Maha-siddhanta Muhйrta-cіntamaryi Pitamaha-siddhanta (of Visnudharmottara-purama) Paica-siddhantika Sarvananda-karana Sisya-dh-orddhida Siddhanta-sarvabhauma Siddhanta-Sekhara Siddhanta-Siromani Siddhanto-tat'a-vijeka Surya-siddhanta Tantra-sagraha Watesvara-siddhanta Widya-Madhaviya Vrddha-Vasistha-siddhanta INTRODUCTION This Part contains the text with English translation, notes, short comments, and explanations, where necessary, of the Maha-Bhaskariya (“the bigger work of Bhaskara I')." Sanskrit Tect. The text has been edited on the basis of the following five manuscripts collected by the late Dr. A. N. Singh: MSS. A and B -Containing the text only; MS. C. --Containing the text together with a commentary entitled Bhäsya of Govinda Svāmi; The present work has been divided into four parts: Part IGeneral Introduction (containing a general study of the life and works of Bhāskara I); Part II—Mahā-Bhāskariya; Part III—Laghu-Bhāskariya (“The smaller work of Bhāskara I") edited with English translation, critical notes and comments, etc.; Part IV--Bhāskara II's commentary on the Aryabhatiya of Aryabhata 1.

  • Bhaskara I, the author of the Maha-Bhaskariya, was a different person from his namesake of the twelfth century A. D., the author of the Siddhanta-Siromani and Lilavati, etc. He lived in the seventh century of the Christian era and was a contemporary of Brahmagupta (628 A.D). He wrote three works on astronomy which were composed in the following order: (1) the Maha-Bhaskariya, (2) a commentary on the Aryabhatiya, and (3) the Laghu-Bhaskariya. His commentary on the Aryabhatiya was written in 629 A. D., i.e., one year after the completion of the Brahma-sphuta-siddhanta of Brahmagupta.

Bhaskara I was a follower of Aryabhata I, the author of the Aryabha fiya. His works provide us with a detailed exposition of the astronomical methods taught by Aryabhata I and throw light on the development of astronomy during the sixth and early seventh century A. D. in India. For details regarding the life and works of Bhaskara I, the reader is referred to Part I of the present work. ÎNTRODUCTION MS. D -Containing a commentary known as Prayoga-racana and also supplying the beginnings of the passages commented upon; MS. E -Containing the commentary Karmadipika of Paramesvara and also the beginnings of the passages commented upon. MSS. A. and B, which contain the text only, are in agreement in so far as the extent of the two is concerned. In other respects also they are almost the same. Both of them contain 396 verses. Agreement between the two manuscripts seems to indicate that they are perhaps derived from the same source. There are other reasons also for this conjecture. Verse iii. 45, which has been misplaced in one of them, occupies the same wrong position in the other also. Moreover, six and a half verses', which have been commented upon by Govinda Svami (MS. C), Paramesvara (MS. E), and in the Prayoga-racana (MS. D), and are included in the text of MS. C, are absent from both MSS. A. and B. MS. C contains 394 and a half verses. Its text has evident gaps at some places, for a few verses, some of which have been actually commented upon in the commentary at their proper places, are missing from the text. These are amongst those verses which belong to MSS. A and B and have been explained in the Prayoga-racana (MS. D), and in the commentary of Paramesvara (MS. E). MSS. D and E contain commentaries of the Maha-Bhaskariya. In these manuscripts only the beginnings of the passages commented have been given; the full text is not given. The following table will show at a glance how far the above manuscripts have differed from one another: viz. i. 12; v. 18, 26-27(1), 47-48(i); vi, 14(ii)-15G), 58(iii). INTRODUCTION Chapters Whether MS C Whether comand verses available Whether mented upon of the in MSS. available in the in edited text and B' Text comm. MSD Ms. E . Chapter I Werses 1-7 Yes Yes Yes Yes. Yes Verse 8 Yes No s p 2. Werses 9-li s Yes 92. s 29 Verse 12 No ' . yy z 29 Werses 13-52 Yes 99 99 Chapter II Werses 1-10 z y y MS. de- s fective Chapter III Verses 1-74(i) s 29 s Yes , 29 Verse 74(ii) No No s No Versè 75(i) 22 No Yes ኃኃ Yes Chapter IV Verse 1 s Yes ን፵ s Verse 2(i) s No s s Verses2(ii)-12 , Yes Verse 13 2. No s No, but mentioned Werses 14-64 9 Yes Yes Chapter W Werses 1-17 29 99. 25 s לל Werse 18 No y 99 s 92 Werses 19-25 Yes Verses 26-27(i) No y s 99 Werses 27(ii)-46 Yes 92 sy s Verses 47-48(i) No 99 s s V INTRODUCTION MS. C. Chapters Whether Whether Whether comand verses available available mented upon of the in MSS. A in the in edited text and B Text Comm. MS. D MS. E. Werses 48(ii)-78 Yes Yes Yes Yes Yes Chapter VI Verses -14(i) לל לל Werses 14(ii)-15(i) No த9 و جو כל s Werses A. 15(ii)-18 Yes 5 ל s s Verse 19(i) y No 39 Verses 19(ii)-25 Yes s Verse 26 22 No sy 2 לל Werses 27-36(i) 23 Yes ነኃ y Werse 36(ii) s No 2 29 לל Werses 37-40 Yes %》 ፵ ፵ 99 Verse 4 و او No s s 9ي Werses 42-58(i) Yes s 3ל Werses 58(ii) No 2 ללጳ ኃ ; Werses 59-62 Yes s s Chapter VIII Werses -35 ፵ ጋ ፵ 3 22 s ... 3 Chapter VIII Werses -22 9. s 5, s Verses 23-24 s No No Verses 25-27 Yes Yes sy ל 2 ܢ sy 2 y לל NTRODUCTION V The edited text of the Maha-Bhaskariya contains 402 and a half verses, of which 387 and a half occur in all manuscripts. The remaining fifteen verses, which occur either in MSS. A and B or in MS. C, are of the following categories : (1) Those which have been commented upon by all commentators, viz. i. 8, 12; iii. 75(i); iv. 2(i); v. 18, 26-27(i), 47-48(i); vi. 14(ii)-15(i), 19(i), 26, 36(ii), 4 I, and 58(iii). (2) Those which have been commented upon in one or two commentaries only, viz. iii. 74(ii); iv. 13 ; viii. 23-24. Inclusion in the edited text of the verses of the first category requires no explanation. Those of the second category have been taken as genuine for the following reasons: Half-verse iii. 74(iii). This has been regarded as genuine because it is relevant to the context and the subject matter contained in it has its counterpart in the author's smaller work, the Laghu-Bhaskariya. It occurs in MSS. A. and B and forms part of a passage vv. 71-75(i) which describes the occultation of certain stars by the Moon. This description is a statement of facts and hardly requires any explanation, which explains why the half-verse in question has been left unexplained by Govinda Svami and Paramesvara. The author of the commentary Prayoga-racana has simply paraphrased it. Verse iv. 13. The genuineness of this verse is evident from the mention of the word “athava' (meaning “or') in the beginn ing of the next verse 14, which shows that verse 14 gives an alternative method. Verse 13 is thus indispensable, for if it is removed verse 14 would no longer be an alternative method. The author of the Prayoga-racana, commenting on these two Verses, states : W NTRODUCTION “viskambhardha etc. Here the author finds the true daily motion.' “antyajiva etc. This is an alternative method.' So also, commenting upon the verse 14, Paramesvara, writes: “The author sets forth the method of finding the true daily motion by another method.' Absence of the verse in question from the text of MS. C seems to be due to the carelessness of the scribe. Werses viii. 23-24. These verses are taken as genuine because they occur in MSS. A. and B and have been mentioned in MSS. D and E. Moreover, they have been mentioned and the examples contained therein have been solved in MS. Cin Chapter I under verses 49 and 50 respectively. It seems that like so many other verses these also have been left out from MS. C due to the carelessness of the scribe. There is no doubt that they were composed by Bhaskara I, because they occur in his commentary on the Aryabhatiya along with several other verses containing similar examples. There is one more verse which requires consideration here. It is not included in the numbered verses of the edited text. This verse marked 24 occurs after verse 24 of Chapter VIII. It does not occur in any of the available manuscripts of the Maha-Bhaskariya, but I have taken the liberty to include it in the edited text, though I have not given it any specific number. My reasons for including this verse in the text are as follows: (l) The preceding verse 24 contains an example which

  • विष्कम्भार्धेनेति स्फुटभुक्ति साधयति । ४ अन्त्यजीवेत्युपायान्तरम्। * स्फुटभुक्त्यानयन प्रकारान्तरेणाह। NRODUCTION W

unlike other examples of that chapter, is of an abstract nature. In order to give that example a concrete form, it is necessary to supply some such data as mentioned in verse 24. (2) Verse 24 occurs in Bhāskara II’s commentary on the Aryabhaiya' and in Govinda $vami's commentary on the Maha-Bhaskariya. At both the places it has been followed by verse 24* and the two verses taken together are treated as forming one complete example. The example has been solved both by Bhaskara I and Govinda Svāmi. Counting this additional verse also, the edited text of the Maha-Bhaskariya consists of 403 and a half verses, which are distributed over the eight chapters as follows: Chapters I II III IV V VI VIII VIII Verses 52 0 74, 64 78 62 35 28 Reading-differences. The question of deciding between differing readings of the text as encountered in the manuscripts consulted by me has in general not presented much difficulty. In my choice between alternative readings I have been guided solely by the criterion of appropriateness, My task has been simplified by the fact that the readings selected and accepted should give the correct mathematical interpretation of the text as well as should fit in the metre. Quotations from the Maha-Bhaskariya are found in other works. I have gathered together such quotations and this has helped me to verify the edited text in a number of cases. ii. 32-33. i. 52.





कलां बिभति क्षणदाकरस्य यः
प्रकाशिताशां शिरसा गभस्तिभिः'।
नमोऽस्तु तस्मै सुरवन्दिताङ्घ्रये
समस्तविद्याप्रभवाय शम्भवे ॥ १ ॥
जयन्ति भानोः कमलावबोधिनः
करा हिंभांशोर्वेनिताननस्विषः'।
धरासुतज्ञापकसितत्विषः पुनः ॥ २
तपोभिराप्तं स्फुटतन्त्रमाश्मक
चिरत्वमभ्येतु जगत् सद्गुणैः ।
चिरं च अध्यासुरपेतकल्मषा'
भटस्य शिष्या जितरागशत्रवः ।। ३ ।।
नवाद्रिरूपाग्नियुतं * महीभुजां
शकेन्द्रनाम्नां गतवसङ्गृहम् ।
द्विषट्कनिघ्नं गतमससंयुतं ।
युगाधिमासैर्णयेद् द्विराशितम् ॥ ४ ॥

गमस्तिनि B. • हिमांशोर्वैनितालतत्विषः A, B, धरासुतज्ञातिसितत्विषं A, B.
स्फुटतन्त्रमात्मकं C. ५ चिरं समभ्येतु A, B. 'जीयासुरपेतकल्मषा A, B. • नवाग्नि-
रूपरग्नियुतं A, B; नावाग्निरूपाग्नियुतं C. ‘युर्गार्धमासैगणयेदिराशितम् B; युगाधि
मासैर्गुणयेद्विराशिकम् C.

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षष्ठोऽध्यायः॥ ४१

तघटीभोगसंयुक्तसूर्येन्द्वन्तर्घटीक्रमात् ।
ततोऽहम्नसंशुद्धिः शेषभोगादिकर्मणा ।।३४॥
अकॅन्दुमध्यनाडीभ्यो' दिनमानं विवर्धते ।
तद्विशेषघटीशेषे दिवा चन्द्रोदयः स्मृतः ।।३५।
अन्तरालोदयप्राणैः कल्प्यं तत्राविशेषणम् ।।३६।।'
चन्द्रादौदयिकात्प्राणा' यावानौदयिक' रविः।
ग्राह्यास्ततोऽपि विश्लेषात् कल्प्यते निश्चलकिया ।।३७।
कृताविशेषनाडीभिर्यावन्नोदेति भास्करः।
तावदाशामुखादर्शः प्राणैराक्रमते शश ।।३८।।
आसन्नौ स्वधियाऽभ्यूह्य' मध्यलग्ननिशाकरौ।
कालेन्दुमष्यलग्नानामविशेषं समाचरेत् ।३९।
नाड्योऽन्तरालजाः‘ साध्या लङ्काराश्युदयैस्तयोः'।
ऊने ' विश्लेषनाडीभ्यः" शुद्धिः क्षेपोऽधिके स्मृतः ।|४०।।
मध्यलग्नसमश्चन्द्रो जायतेऽनेन कर्मणा।
तत्क्षिप्यपक्रमायैस्तु" मध्यच्छाया प्रसाध्यते ।।४१।"
अधोदितस्य चन्द्रस्य तथाऽर्धास्तमितस्य च ।
इन्दूदयास्तलग्नाग्रेः शृङ्गस्योन्नतिकल्पना" ।।४२।।
कर्मेदं शशिनस्तस्य कुर्यादमृतदीधितेः ।
ग्रहाणामपि सर्वेषामिदं कर्म विधीयते ।।४३।
अंशैरन्तरितः सूर्यान्नवभिर्युच्यते भृगुः ।
द्वयधिकैर्युयधिकैद या ज्यौज्ञसौरिधरासुताः ॥४४॥
प्रपन्नवक्रःसद्वर्मा सितो दृश्योऽर्धपञ्चमैः '।
चतुभिर्वाशुमालित्वादंशैरंशुमतोऽन्तरैः ।।४५।

२ °संयुक्तः° A, B. २ अकॅन्दुमध्यनाडियो A; अकॅन्दुभोगनाडिभ्यो B. १ The
second half of verse B6 is missing from C. *चन्द्रादौदयितात्प्राणा B;
चन्द्रादौदयिकाः प्राणा C. ५ द्यावानौदयिको A, B. ‘कृतावशेषनाडी° A, B; कृताविशे-
नाडी° C. " आसन्नस्वधिया ह्यत्र A, B. ‘नाड्योन्तरालजैः A, B; नाड्योऽन्तरा भुजाः
C. ‘लङ्कोर° c. ऊना C. १९ शद्धि A, B. • तत्क्षित्याप° A, B. " Verse
41 is missing from C. " शगस्यो° A, B. " ज्योज्ञसौरिधरासुताः A, B;
शाकंसोरिधरासुतान् C. " प्रपन्नदृश्युः A, B; प्रसन्नवक्त्रः C. t" सदृश्येऽर्ध° C.


पृष्ठम्:महाभास्करीयम्.djvu/६१ पृष्ठम्:महाभास्करीयम्.djvu/६२ पृष्ठम्:महाभास्करीयम्.djvu/६३ पृष्ठम्:महाभास्करीयम्.djvu/६४ ४६

[ महाभास्करोये इष्टग्रहस्य भगणैर्गगनस्य वृत्तं भङ्क्त्वऽथ तस्य परिधिं लभते समन्तात्' ।।२०। निबन्धः कर्मणां प्रोक्तो योऽसावौदयिको विधिः । अर्धरात्रे त्वयं' सर्वो यो विशेषः स कथ्यते ।।२१।। त्रिशती दिने' क्षप्या ह्यवमेभ्यो विशोध्यते । ज्ञगुर्लभंगणेभ्योऽपि' विशतिश्च ततोऽब्धयः ।।२२।। अष्टिश्शतगुणा’ व्यासो योजनानां भुवो रवेः । खाष्टाब्ध्यङ्गानि शीतांशोः शून्यवस्वब्धयस्तथा*।।२३।। वस्विन्द्रियगुणच्छिद्वस्वङ्गानि’ विभावसोः । अङ्गाङ्गष्वेकभूतानि चन्द्र कर्णः प्रकीतितः ।।२४। अष्टिरष्टौ जिना रुद्रा' विंशतिर्युयधिकाः क्रमात् । दशघ्ना गुरुशुक्राकभौमज्ञांशाः" स्वमन्दजाः ।।२५।। मन्दवृत्तानि द्वात्रिंशन्मनवः" षष्टिरेव " च। खद्यो वसुदस्राः स्युः शीघ्रवृत्तान्यथ क्रमात् ।।२६। द्वयद्रयः• खाङ्गनेत्राणि खाब्धयोऽGध्यग्निदस्रका:” । द्वयग्नीन्दवो रवेर्मन्दंॐ शुक्रवद् वृत्तमेव च ।।२७। एकत्रिंशत्क्षपाभर्तुरर्धरात्रे विधीयते । पातभागाश्च विज्ञेयाः पण्डितैः परिकल्पिताः ।२८। मन्दशीघ्रोच्चयोः क्षेप्यं चक्रार्ध बुधशुक्रयोः । राशित्रयं तु शेषाणां पात्यते" पातसिद्धये ॥२९॥ शुक्रकिदेवपूज्यानां भागौ द्वावेव संयुतौ । मन्दपाताच्च शीघ्रोच्चात " सार्धाशस्तु कुजज्ञयोः ॥३०॥ .२१ २१ ३५ परिधिर्लभते समन्तात् A, B, परिधि लभते समानात् C. २ अर्धरात्रेश्चयं A, B. दिने A, B. ५ क्षेप्याऽप्यवमेभ्यो A; क्षेप्याप्यवमे द्यो B. ५ भृगुर्वोमं गणेभ्यो Q. अद्भिश्शतगुणो A, B. ५ शन्यावस्वब्धयः सदा C. “ वस्विन्द्रीय° }; वस्वीन्द्रीय B. अह्रष्ट A,B. • द्रिघ्ना A,B; रुद्र C. १ विशतिद्वयधिकाः B, C. १२ दशघ्नं C. ९ ९भौमज्ञान्धि A, B; भौमज्यांशाः C. १४ मन्दवृत्तान्यथ किशन्मनव A, B; मन्दवृत्तान्यपित्रशन्मनवः C. ५ ~~टुरेव A, B. " वसुरुद्राः C. " द्वयग्नयः A, B, C. “ खश्योऽध्यग्निदस्रकाः A; खायोध्यग्निदस्रकाः B; खाब्धयो ह्यग्नि दस्रकाः C. ९ द्वयद्वन्दवो A, B. ३ रवेर्मन्द A, B, C. २९ ऽभिधीयते C. * वात° A; तेवाभा° B; पात missing from C. २ मन्दोच्चयोः C. २* वारयते B. २५ कीfततो A, B.

[महाभास्करीय ५२
भास्करेण परिचिन्य कृतोऽयं
मन्दबुद्धिपरिबोधसमर्थः ।
स्पष्टवाक्यकरणैः समवेतः ।२६।
स्पष्टार्थानेककरणैः छेद्यके ग्रहणे रवेः ।
यदिहास्ति तदन्यत्र यन्नेहास्ति न तत् क्वचित् ।।२७।

इति महाभास्करीयेऽष्टमोऽध्यायः ।

इति महाभास्करीयं समाप्तम्

१ ततो या C. २ कर्मनिबद्धः A, B. १ स्पष्टानेककरणे C. ॐ छेद्यकेन्द्रगणे A, B.

पृष्ठम्:महाभास्करीयम्.djvu/७२ पृष्ठम्:महाभास्करीयम्.djvu/७३ पृष्ठम्:महाभास्करीयम्.djvu/७४ पृष्ठम्:महाभास्करीयम्.djvu/७५ पृष्ठम्:महाभास्करीयम्.djvu/७६ पृष्ठम्:महाभास्करीयम्.djvu/७७ पृष्ठम्:महाभास्करीयम्.djvu/७८ पृष्ठम्:महाभास्करीयम्.djvu/७९ पृष्ठम्:महाभास्करीयम्.djvu/८० पृष्ठम्:महाभास्करीयम्.djvu/८१ पृष्ठम्:महाभास्करीयम्.djvu/८२ पृष्ठम्:महाभास्करीयम्.djvu/८३ पृष्ठम्:महाभास्करीयम्.djvu/८४ पृष्ठम्:महाभास्करीयम्.djvu/८५ पृष्ठम्:महाभास्करीयम्.djvu/८६ पृष्ठम्:महाभास्करीयम्.djvu/८७ पृष्ठम्:महाभास्करीयम्.djvu/८८ पृष्ठम्:महाभास्करीयम्.djvu/८९ पृष्ठम्:महाभास्करीयम्.djvu/९० पृष्ठम्:महाभास्करीयम्.djvu/९१ पृष्ठम्:महाभास्करीयम्.djvu/९२ MEAN LONGITUDE OF A PLANET

That is to say mean longitude of the desired planet in minutes (mean longitude of the known planet in revolutions, etc., reduced to minutes) x (revolution-number of the desired planet) revolution-number of the known planet This rule and the previous one are based on the following principle. If there are two planets P and g, then revolution-number of P: revolution-number of g

(mean longitude of Pin revolutions etc.) : (mean longitude of g in

revolutions etc.). Alternative rules for deriving the mean longitude of the Moon from that of the Sun and vice vers: Il. Or, multiply the chargeta by the number of intercalary months in a ५ge am divide (the product) by the number of civil days (in a yugg) : bhe result is in terms of revolutions, etc. Add that to tbhirteen times the mean longitude of the Sun. (This is the process) to obtain the mean longitude of the Moon. 12. Or, subtract the result obtained (in revolutions etc.) from the mean longitude of the Moon and take one-thirteenth of the remainder : this is stated to be the mean longitude of the Sun by the mathematicians whose intellect has been awakened by the grace of the teacher. The following is the rationale : We know that intercalary months in a yuga = lunar months in a yuga – solar months in a yuga. But lunar months in a yuga = Moon's revolution-number – Sun's revolution-number; and solar months in a yuga = 12 (Sun's revolution number). • This rule is found also in BrspS, xi. 33; iDV१, , i. 24 (i)Sise ii. 19. पृष्ठम्:महाभास्करीयम्.djvu/९४ पृष्ठम्:महाभास्करीयम्.djvu/९५ पृष्ठम्:महाभास्करीयम्.djvu/९६ पृष्ठम्:महाभास्करीयम्.djvu/९७ पृष्ठम्:महाभास्करीयम्.djvu/९८ पृष्ठम्:महाभास्करीयम्.djvu/९९ पृष्ठम्:महाभास्करीयम्.djvu/१०० पृष्ठम्:महाभास्करीयम्.djvu/१०१ पृष्ठम्:महाभास्करीयम्.djvu/१०२ पृष्ठम्:महाभास्करीयम्.djvu/१०३ पृष्ठम्:महाभास्करीयम्.djvu/१०४ पृष्ठम्:महाभास्करीयम्.djvu/१०५ पृष्ठम्:महाभास्करीयम्.djvu/१०६ पृष्ठम्:महाभास्करीयम्.djvu/१०७ पृष्ठम्:महाभास्करीयम्.djvu/१०८ पृष्ठम्:महाभास्करीयम्.djvu/१०९ पृष्ठम्:महाभास्करीयम्.djvu/११० पृष्ठम्:महाभास्करीयम्.djvu/१११ पृष्ठम्:महाभास्करीयम्.djvu/११२ पृष्ठम्:महाभास्करीयम्.djvu/११३ पृष्ठम्:महाभास्करीयम्.djvu/११४ पृष्ठम्:महाभास्करीयम्.djvu/११५ पृष्ठम्:महाभास्करीयम्.djvu/११६ पृष्ठम्:महाभास्करीयम्.djvu/११७ पृष्ठम्:महाभास्करीयम्.djvu/११८ पृष्ठम्:महाभास्करीयम्.djvu/११९ पृष्ठम्:महाभास्करीयम्.djvu/१२० पृष्ठम्:महाभास्करीयम्.djvu/१२१ पृष्ठम्:महाभास्करीयम्.djvu/१२२ पृष्ठम्:महाभास्करीयम्.djvu/१२३ पृष्ठम्:महाभास्करीयम्.djvu/१२४ पृष्ठम्:महाभास्करीयम्.djvu/१२५ पृष्ठम्:महाभास्करीयम्.djvu/१२६ पृष्ठम्:महाभास्करीयम्.djvu/१२७ पृष्ठम्:महाभास्करीयम्.djvu/१२८ पृष्ठम्:महाभास्करीयम्.djvu/१२९ पृष्ठम्:महाभास्करीयम्.djvu/१३० पृष्ठम्:महाभास्करीयम्.djvu/१३१ पृष्ठम्:महाभास्करीयम्.djvu/१३२ पृष्ठम्:महाभास्करीयम्.djvu/१३३ पृष्ठम्:महाभास्करीयम्.djvu/१३४ पृष्ठम्:महाभास्करीयम्.djvu/१३५ पृष्ठम्:महाभास्करीयम्.djvu/१३६ पृष्ठम्:महाभास्करीयम्.djvu/१३७ पृष्ठम्:महाभास्करीयम्.djvu/१३८ पृष्ठम्:महाभास्करीयम्.djvu/१३९ पृष्ठम्:महाभास्करीयम्.djvu/१४० पृष्ठम्:महाभास्करीयम्.djvu/१४१ पृष्ठम्:महाभास्करीयम्.djvu/१४२ पृष्ठम्:महाभास्करीयम्.djvu/१४३ पृष्ठम्:महाभास्करीयम्.djvu/१४४ पृष्ठम्:महाभास्करीयम्.djvu/१४५ पृष्ठम्:महाभास्करीयम्.djvu/१४६ पृष्ठम्:महाभास्करीयम्.djvu/१४७ पृष्ठम्:महाभास्करीयम्.djvu/१४८ पृष्ठम्:महाभास्करीयम्.djvu/१४९ पृष्ठम्:महाभास्करीयम्.djvu/१५० पृष्ठम्:महाभास्करीयम्.djvu/१५१ पृष्ठम्:महाभास्करीयम्.djvu/१५२ पृष्ठम्:महाभास्करीयम्.djvu/१५३ पृष्ठम्:महाभास्करीयम्.djvu/१५४ पृष्ठम्:महाभास्करीयम्.djvu/१५५ पृष्ठम्:महाभास्करीयम्.djvu/१५६ पृष्ठम्:महाभास्करीयम्.djvu/१५७ पृष्ठम्:महाभास्करीयम्.djvu/१५८ पृष्ठम्:महाभास्करीयम्.djvu/१५९ पृष्ठम्:महाभास्करीयम्.djvu/१६० पृष्ठम्:महाभास्करीयम्.djvu/१६१ पृष्ठम्:महाभास्करीयम्.djvu/१६२ पृष्ठम्:महाभास्करीयम्.djvu/१६३ पृष्ठम्:महाभास्करीयम्.djvu/१६४ पृष्ठम्:महाभास्करीयम्.djvu/१६५ पृष्ठम्:महाभास्करीयम्.djvu/१६६ पृष्ठम्:महाभास्करीयम्.djvu/१६७ पृष्ठम्:महाभास्करीयम्.djvu/१६८ पृष्ठम्:महाभास्करीयम्.djvu/१६९ पृष्ठम्:महाभास्करीयम्.djvu/१७० पृष्ठम्:महाभास्करीयम्.djvu/१७१ पृष्ठम्:महाभास्करीयम्.djvu/१७२ पृष्ठम्:महाभास्करीयम्.djvu/१७३ पृष्ठम्:महाभास्करीयम्.djvu/१७४ पृष्ठम्:महाभास्करीयम्.djvu/१७५ पृष्ठम्:महाभास्करीयम्.djvu/१७६ पृष्ठम्:महाभास्करीयम्.djvu/१७७ पृष्ठम्:महाभास्करीयम्.djvu/१७८ पृष्ठम्:महाभास्करीयम्.djvu/१७९ पृष्ठम्:महाभास्करीयम्.djvu/१८० पृष्ठम्:महाभास्करीयम्.djvu/१८१ पृष्ठम्:महाभास्करीयम्.djvu/१८२ 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पृष्ठम्:महाभास्करीयम्.djvu/२१५ पृष्ठम्:महाभास्करीयम्.djvu/२१६ पृष्ठम्:महाभास्करीयम्.djvu/२१७ पृष्ठम्:महाभास्करीयम्.djvu/२१८ पृष्ठम्:महाभास्करीयम्.djvu/२१९ पृष्ठम्:महाभास्करीयम्.djvu/२२० पृष्ठम्:महाभास्करीयम्.djvu/२२१ पृष्ठम्:महाभास्करीयम्.djvu/२२२ पृष्ठम्:महाभास्करीयम्.djvu/२२३ पृष्ठम्:महाभास्करीयम्.djvu/२२४ पृष्ठम्:महाभास्करीयम्.djvu/२२५ पृष्ठम्:महाभास्करीयम्.djvu/२२६ पृष्ठम्:महाभास्करीयम्.djvu/२२७ पृष्ठम्:महाभास्करीयम्.djvu/२२८ पृष्ठम्:महाभास्करीयम्.djvu/२२९ पृष्ठम्:महाभास्करीयम्.djvu/२३० पृष्ठम्:महाभास्करीयम्.djvu/२३१ पृष्ठम्:महाभास्करीयम्.djvu/२३२ पृष्ठम्:महाभास्करीयम्.djvu/२३३ पृष्ठम्:महाभास्करीयम्.djvu/२३४ पृष्ठम्:महाभास्करीयम्.djvu/२३५ पृष्ठम्:महाभास्करीयम्.djvu/२३६ पृष्ठम्:महाभास्करीयम्.djvu/२३७ पृष्ठम्:महाभास्करीयम्.djvu/२३८ पृष्ठम्:महाभास्करीयम्.djvu/२३९ पृष्ठम्:महाभास्करीयम्.djvu/२४० पृष्ठम्:महाभास्करीयम्.djvu/२४१ पृष्ठम्:महाभास्करीयम्.djvu/२४२ पृष्ठम्:महाभास्करीयम्.djvu/२४३ पृष्ठम्:महाभास्करीयम्.djvu/२४४ पृष्ठम्:महाभास्करीयम्.djvu/२४५ पृष्ठम्:महाभास्करीयम्.djvu/२४६ पृष्ठम्:महाभास्करीयम्.djvu/२४७ TIME OF APPARENT CONJUNCTION OF THE SUN AND MooN 163 them to the time of geocentric conjunction of the Sun and Moon. (Then is obtained the first approximation to the time of apparent conjunction).

The lambama computed for the middle of the day is subtracted from the time of geocentric conjunction when the Moon's udg¢jya is north and added when south.

Repeat this process until the nearest approximation (to the lambama for the time of apparent conjunction) is arrived at:

The corresponding displacements should be given by the learned to (the longitudes of) the Sun and the Moon, as in the case of the tithi (i.e., the time of conjunction of the Sun and the Moon ). The term lambama is the technical term for “parallax in longitude". When used alone in connection with a solar eclipse it generally stands for the difference between the parallaxes in longitude of the Sun and the Moon. The above stanzas aim at finding out the time of apparent conjunc tion of the Sun and Moon. This involves a knowledge of the lambana for that timeFor, time of apparent conjunction = time of geocentric conjunction + lambama in time for the time of apparent conjunction, where + or – sign is taken according as the Sun and the Moon at the time of apparent conjunction lie to the west or east of the central ecliptic point. The lambama for the time of apparent conjunction depends on the time of apparent conjunction itself. But as the time of apparent conjune tion is unknown, the corresponding lambama cannot be obtained directly and recourse is taken to the method of successive approximations stated in the text. 1 The literal translation would run as follows: Repeat this process until the time of apparent conjunction is fixed. A What is meant is that after the first approximation to the time of apparent conjunction is obtained, the corresponding longitudes of the Sun and the Moon should be calculated and the process repeated. पृष्ठम्:महाभास्करीयम्.djvu/२४९ पृष्ठम्:महाभास्करीयम्.djvu/२५० पृष्ठम्:महाभास्करीयम्.djvu/२५१ पृष्ठम्:महाभास्करीयम्.djvu/२५२ पृष्ठम्:महाभास्करीयम्.djvu/२५३ पृष्ठम्:महाभास्करीयम्.djvu/२५४ पृष्ठम्:महाभास्करीयम्.djvu/२५५ पृष्ठम्:महाभास्करीयम्.djvu/२५६ पृष्ठम्:महाभास्करीयम्.djvu/२५७ पृष्ठम्:महाभास्करीयम्.djvu/२५८ पृष्ठम्:महाभास्करीयम्.djvu/२५९ पृष्ठम्:महाभास्करीयम्.djvu/२६० पृष्ठम्:महाभास्करीयम्.djvu/२६१ पृष्ठम्:महाभास्करीयम्.djvu/२६२ पृष्ठम्:महाभास्करीयम्.djvu/२६३ पृष्ठम्:महाभास्करीयम्.djvu/२६४ पृष्ठम्:महाभास्करीयम्.djvu/२६५ पृष्ठम्:महाभास्करीयम्.djvu/२६६ पृष्ठम्:महाभास्करीयम्.djvu/२६७ पृष्ठम्:महाभास्करीयम्.djvu/२६८ पृष्ठम्:महाभास्करीयम्.djvu/२६९ पृष्ठम्:महाभास्करीयम्.djvu/२७० पृष्ठम्:महाभास्करीयम्.djvu/२७१ पृष्ठम्:महाभास्करीयम्.djvu/२७२ पृष्ठम्:महाभास्करीयम्.djvu/२७३ पृष्ठम्:महाभास्करीयम्.djvu/२७४ पृष्ठम्:महाभास्करीयम्.djvu/२७५ पृष्ठम्:महाभास्करीयम्.djvu/२७६ पृष्ठम्:महाभास्करीयम्.djvu/२७७ पृष्ठम्:महाभास्करीयम्.djvu/२७८ पृष्ठम्:महाभास्करीयम्.djvu/२७९ पृष्ठम्:महाभास्करीयम्.djvu/२८० पृष्ठम्:महाभास्करीयम्.djvu/२८१ पृष्ठम्:महाभास्करीयम्.djvu/२८२ पृष्ठम्:महाभास्करीयम्.djvu/२८३ पृष्ठम्:महाभास्करीयम्.djvu/२८४ पृष्ठम्:महाभास्करीयम्.djvu/२८५ पृष्ठम्:महाभास्करीयम्.djvu/२८६ पृष्ठम्:महाभास्करीयम्.djvu/२८७ पृष्ठम्:महाभास्करीयम्.djvu/२८८ पृष्ठम्:महाभास्करीयम्.djvu/२८९ पृष्ठम्:महाभास्करीयम्.djvu/२९० पृष्ठम्:महाभास्करीयम्.djvu/२९१ पृष्ठम्:महाभास्करीयम्.djvu/२९२ पृष्ठम्:महाभास्करीयम्.djvu/२९३ पृष्ठम्:महाभास्करीयम्.djvu/२९४ पृष्ठम्:महाभास्करीयम्.djvu/२९५ पृष्ठम्:महाभास्करीयम्.djvu/२९६ पृष्ठम्:महाभास्करीयम्.djvu/२९७ पृष्ठम्:महाभास्करीयम्.djvu/२९८ पृष्ठम्:महाभास्करीयम्.djvu/२९९ पृष्ठम्:महाभास्करीयम्.djvu/३०० पृष्ठम्:महाभास्करीयम्.djvu/३०१ पृष्ठम्:महाभास्करीयम्.djvu/३०२ पृष्ठम्:महाभास्करीयम्.djvu/३०३ पृष्ठम्:महाभास्करीयम्.djvu/३०४ पृष्ठम्:महाभास्करीयम्.djvu/३०५ पृष्ठम्:महाभास्करीयम्.djvu/३०६ पृष्ठम्:महाभास्करीयम्.djvu/३०७ पृष्ठम्:महाभास्करीयम्.djvu/३०८ पृष्ठम्:महाभास्करीयम्.djvu/३०९ पृष्ठम्:महाभास्करीयम्.djvu/३१० पृष्ठम्:महाभास्करीयम्.djvu/३११ पृष्ठम्:महाभास्करीयम्.djvu/३१२ पृष्ठम्:महाभास्करीयम्.djvu/३१३ पृष्ठम्:महाभास्करीयम्.djvu/३१४ पृष्ठम्:महाभास्करीयम्.djvu/३१५ पृष्ठम्:महाभास्करीयम्.djvu/३१६ पृष्ठम्:महाभास्करीयम्.djvu/३१७ पृष्ठम्:महाभास्करीयम्.djvu/३१८ पृष्ठम्:महाभास्करीयम्.djvu/३१९ पृष्ठम्:महाभास्करीयम्.djvu/३२० पृष्ठम्:महाभास्करीयम्.djvu/३२१ पृष्ठम्:महाभास्करीयम्.djvu/३२२ पृष्ठम्:महाभास्करीयम्.djvu/३२३ पृष्ठम्:महाभास्करीयम्.djvu/३२४ पृष्ठम्:महाभास्करीयम्.djvu/३२५ पृष्ठम्:महाभास्करीयम्.djvu/३२६ पृष्ठम्:महाभास्करीयम्.djvu/३२७ पृष्ठम्:महाभास्करीयम्.djvu/३२८ पृष्ठम्:महाभास्करीयम्.djvu/३२९ पृष्ठम्:महाभास्करीयम्.djvu/३३० पृष्ठम्:महाभास्करीयम्.djvu/३३१ पृष्ठम्:महाभास्करीयम्.djvu/३३२ पृष्ठम्:महाभास्करीयम्.djvu/३३३ पृष्ठम्:महाभास्करीयम्.djvu/३३४ पृष्ठम्:महाभास्करीयम्.djvu/३३५ पृष्ठम्:महाभास्करीयम्.djvu/३३६ पृष्ठम्:महाभास्करीयम्.djvu/३३७ पृष्ठम्:महाभास्करीयम्.djvu/३३८ पृष्ठम्:महाभास्करीयम्.djvu/३३९ पृष्ठम्:महाभास्करीयम्.djvu/३४०

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