XVIII.69 XVIII. STAR-PLANETS 357 Note 2. The cycle given for each planet is only the period of the planet’s synodic revolution con- verted into the solar days, i.e., it is the synodic period × 360° ÷ 365-15-30, nearly. When so con- verted, we have: | | Mercury | Venus | Mars | Jup. | Saturn | | The regular synodic days: | 115-52-45 | 583-55 | 779-57 | 398-53 | 378-6 | | Converted into solar days: | 114 6/29 | 575½ | 768-45 | 393 1/7 | 372 2/3 | The second set is given for the respective planet, saying that the synodic period is so many ‘days’. Not knowing this TS have remarked that they do not understand why there is so much difference in the periods from the regular days generally known. Also, they say they cannot dismiss them as wrong, since the numbers given are checked in the computation itself. (See pages lxiii-lxiv of Intro- duction in TS’s edition). NP have understood that the cycles are in solar ‘days’. But, they have remarked that ‘VM’ has con- fused the days and degrees, not realising that there is a purpose in giving the cycles in the solar day units. These units have been used because, now, the ‘days’ and the ‘degrees’ will have the same meaning, and they can be combined without, at every point, instructing it. Thus, ultimately, the combined value is the degrees of the true planet. Example 1. Days from epoch 1,20,553. Find the ‘days’, and assuming the Sun at epoch as zero, find the Sun at the end of 1,20,553 days. 1,20,553 × 360 ÷ 365-15-30 = 1,18,187.5 ‘days’. This plus zero, and divided out by 360° = 17°.5, Sun’s longitude. [कुजस्फुट:] ‘नवयम (गुणर्तु’ हीने) ‘कृता’ (ह) ते ‘विषयसप्तखाग्नि’हृते । भूयो (हृ)ते चतुर्भिः [निरंश] दिवसा महीजस्य ॥ ६७ ॥ ‘षड् (विषयै)’ ‘स्ति (थ्यू)’नः दृष्टो ‘वसुधृति’ [भि]-रंशकाः (ष)ष्टिः अष्टशतेन(च)षष्टिः सप्तत्या(त्र्य)धिकया नवतिः ॥ ६८ ॥ षष्ट्याष्टयुक्तया (श) तदलं च ‘खाश्वि द्विकै’: ‘स्वराद्रि’ (घ्राः) । अस्तमितोऽतः सप्ताष्टकेन तिथयो’ निरंशग (गतिः) ॥ ६९ ॥ || कुजः || Motion of Mars 67. Subtract 6329 from the ‘days’. Multiply the remainder by 4 and divide out by 3075. Take the remainder and divide by 4. These are the ‘days’ after con- junction (i.e., the anomaly of conj.) for Mars. 68-69. After 56 ‘days’ it goes behind the Sun by 15°, and becomes observable, (i.e., the heliacal setting ends). In 188, 108, 73, 68, 220, ‘days’ Mars lags behind by 60°, 60°, 90°, 50°, 70°, respectively. Then it sets heliacally, and in 56 ‘days’ lags 15° behind and goes into conjunction.

358 PAÑCASIDDHĀNTIKĀ XVIII.69 Note 1. I generally agree with TS's emendations. But in verse 68, I give ṣaḍviṣayaiḥ for ṣaḍtriṁśat- savaiḥ, which latter is both meaningless and has one mātrā extra. TS's ṣaḍvargaiḥ does not agree with the last saptāṣṭakena, for the numbers should agree or at least nearly agree. saptatyā dvyadhikayā has been emended by me into saptatyā tradhikayā, and khābdhi into khāśvi. These will not only make the total correct, but also bring about agreement with the Siddhāntas, which all generally agree with the actual as given by modern astronomy.

XVIII.72 XVIII. STAR-PLANETS 359 (d) The rising and setting are given by observation at different regions and different conditions of the atmosphere, and therefore vary among the siddhāntas. (e) In the case of the inferior planets the degrees should add upto zero. When the degrees are positive and greater than the days, the planet is gaining upon the Sun, and the total gain is its elon- gation. When the degrees are less than the ‘days’, the planet is lagging behind. When the degrees are negative and numerically greater than the ‘days’, the planet is retrograde and comes at the middle of the cycle, if the cycle begins and ends at superior conjunction. Example 2. Compute Mars at 1,20,553 days from epoch. The solar days are, 1,20,553 × 360 ÷ 365-15-30 = 1,18,817.5, and the Sun is 17°.5, taking the sun at epoch as zero, which it nearly is as already shown. 1,18,817.5 − 6329 = 1,12,488.5 1,12,488.5 × 4 ÷ 3075 leaves the remainder 1004. 1004 ÷ 4 = 251, real remainder of ‘days’. During this period we get the movement: − 15° in 56 ‘days’, − 60° in 188 ‘days’, and − 4° for the 7 ‘days’ remaining, total − 79°. Adding − 79° to the Sun, 17°.5, True Mars = 298.5°. [बुधस्फुटः] वि‘शशिवसुरसे(न्द्रे)’ ‘नव(यम)’गुणितेऽर्करा[म]गुण'भक्ते । गुणकारहृते लब्धान्यहानि शीतांशपुत्रस्य ॥ ७० ॥ दशभिर्द्वादशही(नः) प्रागुदितो ‘म(नु)’भिरून'(नन्दां'शाः) । ‘धृति’भिः(स)नवोऽस्तमितः त्रिंशद्भिरुदेति स'(शराश्विः)' ॥ ७१ ॥ अष्टाद(श)भिः(स)नवः षोडशभिश्चा(र्क)वर्जितोऽस्तमितः । पश्चा‘द्वसू’भिर्नववर्जितो निरं(शं) बुधो याति ॥ ७२ ॥ ॥ बुधः ॥ Motion of Mercury 70. Subtract 14,681 from the ‘days’. Multiply the remainder by 29, and divide out by 3312. Take the remainder and divide by 29. The ‘days’ for Mercury in the cycle is got. 70a. A.विंशशि. A.B.रसेन्द्रा; D. [रसेन्दौ] 71a. A.दशभिद्वा०. A.B.हीनाः b. A.B.1.2.नवनवगुणिते. A.B.1.2.०रागुणभक्ते b. A. मनिभिरूनभश्वांशाः; B. र्मनाभीरूनत्तश्वांशाः; c. A.B.हृते C. मनु[भिरूनिताश्वांशाः]; D. मनु [भिर्विषयश्वांशाः] c-d. B1.2.०ब्यान्य-gap-तांशु०; c. A. शनवो; B. ०भिः-gap-नवो; D. [०भिर्मनवो] B3.०ब्युनाशि-gap-तांशु० d. A. ०रुदेत्ति. A.B. सरसाश्वः (B. श्वाः); C. [सरसांशः]; D. [स रसांशाः]

360 PAÑCASIDDHĀNTIKĀ XVIII.72 71. In 10 ‘days’ Mercury falls back by 12°, and rises in the east. In 14 ‘days’ more it lags by 9°. Then in 18 ‘days’ it gains 9°. Then it sets, and in 30 ‘days’ gains 25° and rises heliacally. 72. Then in 18 ‘days’ it gains 9°. In 16 ‘days’ it lags 12°, and sets in the west. Then in 8 ‘days’ it lags 9°, and gets into conjunction. Note 1. In verses 71 and 72 my corrections are based on the need to conform as nearly as possible to reality, and they are also, as far as possible, kept close to the text. śarāsviḥ, 25, may also be jalāśviḥ, 24. The values are:

XVIII.75 XVIII. STAR-PLANETS 361 [गुरुस्फुटः] रहिते 'द्वियमशरा[ष्ट्यां]' '(नगा)'हृते 'द्विविषय(स्व)राश्वि'हते । सप्तहृते देवगु(रोः) भवन्ति दिवसा [निरंशस्य] ॥ ७३ ॥ सर्वे(ऽर्का)त् संशोध्यः षोडशभिर्द्वादशोदितः प्रा(च्याम्) । 'कृतविषयैः' 'कृतवेदाः' सप्तत्या 'सार्णवाः षष्टिः' ॥ ७४ ॥ 'नवदिग्भिः' 'शून्यार्काः' '[सा]ष्टाशीत्या' 'रसस्वरा' [श्चैव] । 'शून्यकृ(तै)'र्द्वात्रिंशत् (ततोऽस्तगः) षोडशभि'र्काः)' ॥ ७५ ॥ ॥ जीवः ॥ Motion of Jupiter 73. Deduct 16,552 from the 'days'. Multiply the remainder by 7 and divide by 2752. Divide the remainder here by 7. The 'days' from conjunction are got. 74-75. All degrees given are to be subtracted from the sun. In 16 'days' it moves 12° and rises in the east. Then in 54, 70, 49, 88, 40 days it moves 44°, 64°, 120°, 76°, 32°. Then it sets in the west, moves 12° in 16 days and joins the Sun. Note 1. The first foot of verse 73 is faulty containing 3 mātrās extra, and corrupt. So it has been corrected. The rest of verses 73 and 74 are TS's emendations. In 75, all emendations are TS's, excepting those for grammar. Note 2. The cycle is 2752 ÷ 7 = 393 1/7 days. The days and degrees are:

362 PAÑCASIDDHĀNTIKĀ XVIII.78 [शुक्रस्फुट:] 'नयनार्क [धृतीन्दू]' ने द्विगुणे (रू) पेन्द्रि [येश्रु] रै' र्भक्ते | शे(षं) यत्त(द्द) लितं भृगुतनयनिरांशदिवसाः स्युः || ७६ || 'विषयै' र्नवकविहीनः प्रागुदित'स्तिथि' [भि] 'रेक (य) म' हीनः | 'वसुकृत्या' 'ति(थ्यूनः)' 'कृताष्टिभिः' स (पञ्चकास्त्रिंशत्) || ७७ || (पञ्चा) [ष्ट] केन सद(शः) निरं[शगो] ऽतो विलोमगः पश्चात् | उ(दे)ति (नि)रंशका(ले) (प्रया)ति (चा)स्तं वि(लोम)गतिः || ७८ || || शुक्रः || Motion of Venus 76. Deduct 1,18,122 from the 'days'. Multiply by 2 and divide by 1151. Take the remainder and divide by 2. We have the 'days' from the conjunction of Venus. 77-78. In 5 'days' Venus lags by 9°, and rises in the east. In 15 days it lags 21°. In 64 days it lags 15°. In 164 days it gains by 35°. Then it sets in the east. Then in 40 days it gains 10°, and joins the Sun. Then, moving in accordance with the reversed order of the days for cycles given, it rises, after the days given from setting to conjunction (i.e., 40 days), in the west, and moves till it reaches the setting in retrograde (and getting into the inferior conjunction) section. Note 1. I have corrected mitīndu into dhṛtīndu for agreement with the Sun in superior conjunction which alone fits. TS's correction (also NP's) mahīndu does not bring agreement with the Sun either at superior conj. or inferior conj. There can be another possible correction matīndu (mati is 8). In the 64 days, flanking the retrograde, the days may be a little more or less, since a small error of observation can produce a difference of a large number of days. The lacunae is filled by me with sapañcakāstriṃśat, meaning 35°, to fit the number of degrees wanted to make up the total zero, and fitting the number of days given. TS's emendation, kṛtāṣṭabhiḥ will be far from fitting the total. 76a. A.B. ॰र्कमितिदुने; C.D. ॰र्कमहीन्दूने 78a. A.B.C. ष (B. स) ष्टाष्टकेन सदश (B. सदृश); b. A.B. रूपेन्द्रियैः स्वरै र्भ (B2. भ) ते D. षष्टाष्टकेन स दश c. A1. शेषः. A1. यत्तदलितं; B. यकृदलितं b. A. निरंसतोतो; B. निरंशतातो d. B. ॰वसा स्युः c. A. उदयति तिथिनिरंशकालो; 77a. B3. नवका B. उदयतिथिनिरंशकालो b. A.B. तिथिरकपम (B. यम) हीनः c-d. C. उदयति निरंशकालेन, याति; c. A. तिथ्यून D. उदयति निरंशकालात्र याति d. A.B. ॰ष्टिभिः स, rest of verse missing: d. A.B. नयति (B. भवति) वास्तं D. नः कृत (ष्ट्रै) स्त्रिभिः स A.B. विनाथगतिः; D. [दिनानाथ] गतिः C. ॰भिः [सेषुरस्तगतः]; D. ॰भिः [सपञ्चास्तगः]

XVIII.79 XVIII. STAR-PLANETS 363 Moreover, their filling the lacuna by seṣuḥ, meaning 5° is quite inadequate to make up zero. I have emended saṣṭāṣṭakena into pañcāṣṭakena, meaning 5 × 8 = 40, which will fit the number of days. Also, 10° synodic motion there requires 40 days and it is also the period from setting to going into superior conjunction. ṣaṣṭa is patently wrong spelling, and ṣaṣṭāṣṭakena is meaningless. But TS and NP keep it, which is wrong. That this is the segment of heliacal setting to conj. can be inferred from udayati given for the next segment, and 10° for heliacal setting and rising at superior conj. is given by many siddhāntas. The other minor emendations are TS's. Note 2. 1,18,122 seems to be a very large subtractive constant, equal to more than 300 years, while all others are very near VM's time. But I cannot think of any other number to fit, Note 3. The maximum elongation is seen to be 45°, correctly. (Cf. Table).

364 PAÑCASIDDHĀNTIKĀ XVIII.81 अष्टनव(त्या) नवतिर्दलं च 'मनु'भिस्त्रयोदशविहीनाः | 'गुणरुद्रै': 'शून्यार्का' द्व्यूनेन शतेन 'शशिनवकम्' || ८० || अति जग[त्या सार्धा]र्का(न)स्तमे(त्य)तो 'नव(कु)भि'(र्नि)रंशम् | षोडश सार्धा(न् सौ)रश्चरति रखेः सर्वदा हीनः || ८१ || || शनैश्चरः || Motion of Saturn 79. Subtract 16,518 from the 'days', multiply by 3 and divide by 1118. Take the remainder here and divide by 3. The days left over in the cycle are got. In 18 days Saturn lags behind by 16½°, and rises in the east. 80-81. In 98, 14, 113, 98, and 13 'days', it falls behind 90½°, 13°, 120°, 91°, and 12½°, respectively. Then Saturn sets in the west, and joins the Sun passing 16½° in 19 days. Note 1. In verse 79, ṣaṭkavarka is patently extra, forming syllables not required for the foot, and has been deleted by me as also by TS. aṣṭābhiḥ is corrected into aṣṭiḥ by me, as also by TS, to conform to grammar and facts. In the rest of the minor corrections there is no difference between our corrections. In verse 80, I have retained the dvi in dvyūnena, while TS have made it dyu, meaning one day, which is not necessary, and which leads into trouble later, needing further correction. The minor corrections are common to both. In 81, I have filled up the lacuna by (tyā sārdha), while TS have made it (tibhirardhā). The word is atijagatī, and not atijagatīḥ, which alone can justify TS's tibhiḥ. Also, only sārdhārka can mean 12½, but their ardhārka can mean only 6. I have corrected navati into navaku keeping the nava. But TS have corrected it into atidhṛti, making unnecessary changes in the lettering, though both of us mean the same. The rest of the corrections are minor, and are acceptable. 79a. A.B.C. ॰रसषट्कवर्क (B.वक्रे) शशाङ्के 81a. A1. जग---र्का b. B.भाजिताग्नि (B3.घ्नि) a-b. A.1.3. ॰र्कारस्त (B.स्ते) मेत्यंतो (B3.मेसंतो); c. A.सौरस्य. A.B.धृतिभिरष्टाभि (B1.2.भिः) C. ॰र्दर्द्धार्कानस्तमेत्यतो; D.[॰र्कार्कान् सार्धानस्तमेति] d. A.C.सार्धार्क; B.सार्द्धार्क; D.सार्धार्काद् b. A1.B.नवतिभिर्विंशं; 80a. A.नवर्तिर्ज्या नवति॰; C.D.नवर्तिर्नवतिः C.ऽतिधृतिर्निरांशम्; D.नव[दश]भिर्निरांशम् b. A1.B.C.D.विहीनः c. A1.सार्धात्सौर; B.सार्द्धात्सौर c. B2.शून्यर्का d. A1.रचेः d. C.D.[द्यूनेन]; Ms. A2. breaks off here. A1.शाशि

XVIII.81 XVIII. STAR-PLANETS 365 Note 2. The following is the table of motions:

[इति पञ्चसिद्धान्तिकायाम् अष्टादशोऽध्याये

प्रक्षेपभागः समाप्तः] ॥ Col. A1.B.D. पौलिशसिद्धान्ते (B3 न्तो) ताराग्रहाः (B adds एवम् | C. इति पौलिशसिद्धान्ते ताराग्रहा नामाष्टदशोऽध्यायः Post-Colophonic statements: A1. इत्याचार्य-वराहमिहिरकृता पंचसिद्धांतिका समाप्ता संवत् १६७३ वर्षे शाके १५३८ प्रवर्तमाने द्वितीयाश्विनशुदि २ बुधे अद्येह स्तंभतीर्थे वास्तवं | पंडित-श्रीपीतांवर[:] तत्सूनुः श्री-श्रीरंग[:], तत्पुत्रः पंडित नाना | तत्तनेयो पंडितगोविन्दः | तस्यात्मजेन शंकरेणेयं पंचसिद्धांतिका लिखिता । आत्मपठ (ठ) नार्थ तथा [परो] पकृतये च । शुभं भवतु ।। B1.2.3. इत्याचार्यवराहमि[हि]रकृतायां (B3. om. यां) पञ्चसिद्धान्तिका समाप्ता । (B3. संवत् १९२८ शाके १७९३ प्रवर्तमाने माघशुक्ला २ शुक्रे | ज्योतिर्विदूत्तमरामदुर्लभरामेण लिखिता || अमदावाद-निवासिना मुंबई- बन्दरमध्ये इंद पुस्तकं लिखितं || श्री || C. इति वराहमिहिराचार्यकृता पञ्चसिद्धान्तिका समाप्ता । D. इत्याचार्यवराहमिहिरकृता पंचसिद्धान्तिका समाप्ता ||

Thus ends Chapter XVIII 61-81: A Spurious Supplement entitled ‘Computation of the Star Planets in Brief’, to the Pañcasiddhāntikā of Varāhamihira

1 Page blank APPENDIX I INDEX OF VERSES

अंशाशीत्या 9.7 अक्षे क्षिप्तां लेखां 14.3 अक्षोक्षिप्तस्योदृक् 14.25 अणुमात्रदर्शन 15.12 अतिजगत्या 18.81 अधिमासकेषु 1.13 अधिमासकोन 15.24 अध्यर्धशतं 18.14 अनयोर्विश्लेषांशान् 18.41 अनुवक्रि परि गत्वा 18.5 अनुवक्रोऽशीत्या 18.13 अन्याद्ययोः 10.7 अन्यच्च भवेद् भूमेः 13.7 अन्यद्रोमक 15.25 अपमान्तरविक्षेपा 5.5 अपमान्तरसंयुक्ता 5.1 अपमोनयुताक्ष 4.22 अपवृषमिथुना 4.24 अभिमतदेशाक्ष 14.29 अर्केन्दुदृष्टि 15.6 अर्केन्दुभुक्ति 10.5 अर्केन्दुयोगचक्रे 3.20 अर्कोदद्यन्तारांशान् 18.54 अर्धेनालिख्य 8.18 अर्हत्प्रोक्ते 13.8 अलिनि दशघ्नाः 18.49 अवनतिवर्गं 8.16; 9.26 अविचार्यैवं 15.29 अविदितसंस्था 15.2 अविशेषाद् दृक्क्षेपं 9.24 अष्टगुणे दिनराशौ 3.28 अष्टनहत्या 18.80 अष्टादशभिः 18.65, 72 अष्टौ भागा लिप्ता 16.6 असितात् सितात् 13.38 अस्तोदयन्तारांशा 18.54

अस्माकमुदय 15.8 आकरणाद् रवि 18.66 आवन्त्यकः 18.61 आश्लेषार्धादासीत् 3.21

इष्टक्रान्तिज्याघ्न 4.39 इष्टांशद्विगुणोन 4.5 इष्टा नाड्यो द्यु 4.50 इष्टेऽहनि बुद्ध्वा 14.10c इष्टोत्तरगोलाप 4.32

उक्तश्च संहितायां 15.10 उज्जयिनी लङ्कायाः 13.17 उत्तरगोलेऽर्क 4.35 उत्तरमक्षाच्छुद्धं 8.12 उदगयनं मकरादा 3.25 उदगयने पूर्वार्धे 7.3 उदयगुणिता 18.22 उदयनवांशं 18.7 उदयात् प्रभृति च 8.10 उदयो यो लङ्कायां 15.23

ऋक्षं लिप्ताष्टशती 3.16 ऋजुशङ्कु 13.31

एकादशाष्ट 3.2 एकेन्द्रियवसु 18.34 एकैकोंऽशो 13.15 एवं कृते ग्रहान्त 18.58 एवं कृत्वा हन्यात् 4.43 एवं च नवत्यंशैः 13.16 एवं व्यर्काच्चन्द्रा 5.9 एवं स्फुटमध्याख्यं 17.9, एष निशार्धे 16.1

कन्यांशान् षट् 18.2

कन्यायामुत्कृत्या 18.47 कन्यायामृतुकृत 18.47 कमलोद्भवप्रजेशौ 1.24 कर्कटकादिषु भुक्तं 2.9 कर्कटसिंहयो 18.31 कर्किणि दिग्घ्नैः 18.45 कालापेक्षा 3.36 काष्ठघ्न्यार्क 4.53 किन्वन्तरांशहीनौः 6.5 कुम्भाधर्कारं ताम्रं 14.32 कुम्भेऽह्नां विंशत्या 18.52 कृतगुणमृत्तु 2.1 कृतदिग्ग्रहणे 4.38 कृतियोगपदं 10.6 कृत्वा चतुर्भिरुद्यान् 18.37 fn. क्लैवं क्षयवृद्धी 5.10 केन्द्रान्तरज्या 9.13 क्रमशः मध्यः 18.8 क्षेप्याः स्वरेन्दु 16.10

खखरूपाष्टगुण 8.4 खजिनघ्नी क्रान्ति 4.34 खनवनगाः शशि 8.7 खार्काधिकं भवेद् 3.6

गगनमुपैति 13.4 गणितविषयोपलब्ध 14.41 गतमयनादुत्तरतो 12.5 गतिविश्लेषकृति 18.55 गत्यर्धे भगणार्ध 2.5 गवि द्विकृत 18.43 गवि वेदयम 18.43 fn. गुणरसनवका 4.10 गुणशिखिगुणाम्नि 3.17 गुणसलिलपांशु 14.27 गुरुभूतनया 17.14

368 PAÑCASIDDHĀNTIKĀ गुरूचपलाय 14.28 गोमिथुनतौलिक 18.30 ग्रहणेन्दोः 10.4 घनषोडशहत 2.3 चक्रात् पतितं वक्त्रम् 9.6 चतुराधिकेन शतेन 18.40 चत्वारिंशच्छशि 18.27 चत्वारिंशद्रामा 4.9 चन्द्रच्छेदक 6.13 चन्द्रत्मोव्यास 10.20 चन्द्रादूर्ध्वं बुध 13.39 चन्द्राम्बरान्तर 11.2 चरखण्डपक्षांश 4.27 चरदलकाल 4.31 चरनाडीक्रम 4.51 चित्रार्धाष्टमभागे 14.37 छायाद्वादश 4.45 छायार्कवर्गयोगा 4.52 छायार्को नाडीभिः 4.49 छाया समरेखा 4.55 छायाहरिजाभ्यन्तर 14.6 छेद्यवदर्धकपालं 14.19 छेद्यार्धयष्टि 14.12 जह्यादुदय 18.15 जीवस्य शता 16.2 जीवाध्यर्ध 4.16 ज्ञसितारेज्या 18.60 ज्याविधिना विक्षेपं 9.25 ज्याविधिविक्षेप 18.57 झषवृश्चिका 18.29 तज्ज्या तिर्यग्रेखा 14.11 तज्ज्या स्थितज्य 4.42 [

APP.I: INDEX OF VERSES 369 नवकृत्या षष्टिः 18.39 बहुलचतुर्दश्यर्था 3.19 यवनान्तरजा 3.13 नवतिस्त्रियुता 4.18 बहुला षष्ठांशान्ते 14.34 यष्ट्या विद्ध्यात् 11.1 नवतस्सप्तशती 9.11 बुध्वा शशिविक्षेपं 14.33 याम्योदग्रेखायां 14.24 नवदिग्भिः 18.75 भागनवत्या राहो 3.31 याम्योदग्विक्षेपा 5.8 नवयमगुण 18.67 भागविशेषात्तिथि 9.23 याम्योदक्समसूत्रा 14.2 नवयमवसुभिः 18.38 भ्रमति भ्रमिस्थितिव 13.6 युगवर्षमासपिण्डं 1.16 नववसुरार्मर्मध्यं 18.38 fn. येष्टेवोदङ् 13.13 नवशतगुणिते 9.3 मकरादौ गुण 2.8 योजनपञ्चनवांशां 13.23 नवशतसहस्त्र 9.2 मध्याज्याकृति 9.20 योजनशतानि 13.18 नव सार्धाः 18.11 मध्यममाना 8.15 नष्टच्छायाप्येवं 13.11 मध्यात् पुनर्वि 17.8 रविकक्षा नवति 10.1 नाड्यः षड्घ्न्यो भागा 14.5 मध्यार्कलम्बित 9.17 रविशशिनोः पञ्च 12.1 नाभ्याः शङ्कुच्छाया 14.14 मध्याह्नं भद्राश्वे 15.22 रविशशिनोः स्फुट 8.2 नित्यमध्यस्थ 13.35 मध्याह्नच्छायार्धं 2.10 रविशशिमान 8.17 नैश्यास्तिथि 6.1 मध्याह्नार्कमयूखं 14.22 रव्युदये लङ्कायां 15.19 मध्याह्ने प्राक् तथा 14.8 रसगुणनवेन्दु 2.2 पञ्चघ्नात् त्रिघ्ना 7.2 मनुभवयम 8.6 रसभववसू 17.2 पञ्चत्रिंशत् त्र्यष्टक 4.25 रसविषयकृत 18.9 पञ्चमहाभूत 13.1 मनुविषयतिथि 4.15 रहिते द्वियम 18.73 पञ्चाब्द्येयो 16.11 मन्दग्रहान्तरज्या 17.13 राशिचतुष्टय 16.5 पञ्चाशता त्रिभिः 9.10 मार्गादिपेत 3.34 राशिज्याप्रक्रमज्या 4.29 पञ्चाशीतिं कृत्वा 18.23 मासाधिपा यथोर्ध्वं 13.42 राहुमुखोनं चक्रं 6.10 पञ्चाष्टकेन 18.78 मासीकृते सम्प्राप्ते 1.9 राहोः सषट्कृति 6.2; 7.5 पदमैकोनं पञ्चा 3.5 मिथुनान्ते च 13.10 रुद्रदस्रमनु 1.10 पर्य्येति शशी 13.41 मीने त्र्यष्टकमह्नां 18.53 fn. रोमकयुगमर्केन्द्वोः 1.15 पूर्वाचार्यमतेभ्यो 1.2 मीनेऽष्टादशमह्नां 18.53 रोमकसूर्यो 8.1 पौलिशतिथि 1.4 मनुयोजे व्येकान्ते 4.12 रौमकमहर्गणं 3.35 पौलिशरोमक 1.3 मुनिकृतगुणेन्द्रिय 9.15 प्रचयः स्वराग्नि 18.17 मुनियमयमद्रि 1.17 लग्नत्र्यगुविवर 8.11 प्रतितेन भवति 13.32 मेरोर्न दिग्विभागः 15.11 लङ्कार्धरात्र 15.20 प्रतिदिवसमेव 13.37 मेरोस्सममुपरि 13.5 लङ्कास्था भूलग्नां 13.26 प्रतिविषयमुदृक् 13.20 मेषतुलादौ विषुवं 3.23 लब्धं द्वादशहीनं 2.13 प्रद्युम्नभूमि 18.62 मेषवृषमिथुन 13.12 लब्धं विषुवज्जीवा 4.21 प्रस्तावेऽपि न 18.64 मेषस्तेषां नित्यं 13.28 लब्धाङ्गुलानि कोटि 4.54 प्रागधं पर्व 12.4 मेषादिषु तदुप 3.11 लम्बकगुणिता 4.56 प्रागुदये षट् 18.25 मेषे दिनषट्कृत्या 18.42 लिप्ताद्वयेन 11.6 प्रोक्ता शशाङ्क 6.12 मेषे विक

16.9 11. सिंहे गुणेन्दु 18.46 fn. 12. सिंहे बाणगुणा 18.46 13. सितबहल्योः 3.18 14. सितवज्जलधेः 3.18 fn. 15. सितशीघ्रं 16.8 16. सूत्रद्वयसम्पात 14.20 17. सूत्रेण बिन्दुकत्रय 14.15 18. सूर्यस्यार्धा 15.26 19. सूर्येन्दुभगण 15.1 20. सैकत्रिंशे द्युगणे 12.3 21. सैकाजे पञ्चाशत् 4.7 22. सौरस्य सहस्र 16.3 23. सौर्यं स्थापित 9.9 24. स्थितिदलनविमर्दे 6.6 25. स्फुटगणितविदिह 3.37 26. स्फुटदिनकर 17.12 27. स्फुटमध्यम 18.24 28. स्फुटयित्वैवं 17.7 29. स्वपरिधिगुणिते 17.5 30. स्वप्रत्ययेन 13.34 31. स्वरवसुमुनीन्द्र 9.16

APPENDIX II INDEX OF PAÑCASIDDHĀNTIKĀ VERSES QUOTED BY LATER ASTRONOMERS

1. Makkibhaṭṭa's Com. on the Siddhāntaśekhara of Śrīpati : PS XIII.36; XV.17-20 (5 verses)
2. Nīlakaṇṭha Somayāji in his Jyotirmīmāṃsā : PS I.3, 4; XV.20 (3 verses)
3. Nīlakaṇṭha Somayāji in his Bhāṣya on the Āryabhaṭīya : PS III.21; XIII.1, 10; XV.20 (4 verses) Nīlakaṇṭha quotes two more verses from the Pañcasiddhāntikā, which, however are not to be found in the present edition of the work : See Nīlakaṇṭha on ABh IV.10 : अत एवोक्तं वराहमिहिरेण पञ्चसिद्धान्ताख्ये करणे कर्तारिकाध्याये — संख्या तु तेषां चिरजीविदृष्टा संवादहीना यदि यत्नभाजः । यंत्रैर्मयोक्तैः खगचारसूक्ष्मैस्तंत्रं विना सिद्ध्यन्ति खेचराणाम् ॥ Again, तदुक्तं कर्तारिकाध्याये — यत्नतः प्रतिनिवृत्तिकालतः सौम्यतश्च विदितं यदन्तरम् । भास्करस्य दलितं यदेव हि क्रान्तिमाहुरधिकं पुरातनाः ॥
4. Parameśvara's Com. on the Āryabhaṭīya : PS XIII.12 (1 verse)
5. Pṛthūdakasvāmin's Com. on the Khaṇḍakhādyaka of Brahmagupta : PS. XIII.2-3, 5-6, 9, 12, 27, 35 (8 verses)
6. Sūryadevayajvan's Com. on the Āryabhaṭīya : XIII.1, 3, 36.
7. Utpala's Com. on the Bṛhatsaṃhitā of Varāhamihira : PS. I.1, 8-10, 16-22; II.13; III.1, 10, 21, 25; IV.20-23, 27-28, 30-33, 35-36, 38, 41-44; 48-49; V.1-10; VI.9-10, 15; VIII.1, 9-18; IX.1; XII.1-3; XIII.1-34, 39-42; XIV.33, 39-40; XV.15, 18-29; XVII.4-5 (117 verses)

APPENDIX III BHŪTASAṄKHYĀ (OBJECT NUMERALS) Used in the Pañcasiddhāntikā akṣa (अक्ष) 5 | caraṇa (चरण) 4 | randhra (रन्ध्र) 9 akṣi (अक्षि) 2 | jala (जल) 4 | ravi (रवि) 12 agni (अग्नि) 3 | jaladhi (जलधि) 4 | rasa (रस) 6 aṅka (अङ्क) 9 | jina (जिन) 24 | rāma (राम) 3 atijagatī (अतिजगती) 13 | tanu (तनु) 8 | rudra (रुद्र) 11 adri (अद्रि) 7 | tithi (तिथि) 15 | rūpa (रूप) 1 anala (अनल) 3 | tīkṣṇāṃśu (तीक्ष्णांशु) 12 | lavaṇoda (लवणोद) 4 abdhi (अब्धि) 4 | darśa (दर्श) 2 | vasu (वसु) 8 [

APPENDIX IV INDEX OF PLACES, PERSONS AND TEXTS Cited in Pañcasiddhāntikā

Arkasiddhānta : See Saurasiddhānta Arhat, XIII.8 Avanti, XVIII.61 Āryabhaṭa, XV.20 Āvantyaka : See Varāhamihira Ujjayinī, XIII.17, 21 Kukaraṇakāra, III.37 Kuru, XV.22 Ketumālā, XV.22 Jayanandi, XVIII.62 Pādāditya, III.33, (34), Pūrvācārya-s, I.2, Paitāmaha-siddhāntā, I.3; XII.1 Pauliśa-siddhānta, I.3, 4, 10, 11 Pradyumna, XVIII.62 (Bṛhat) Saṁhitā, XV.10 Bhadraviṣṇu, III.32 Bhadrāśva. IV.22

Bhāratavarṣa, XV.22 Meru, XIII.5, 12, 18, 21, 27; XV.5, 6, 11 Yamakoṭi, XV.23 Yavana, III.13; XV.19 Yavanapura, I.8; III.13; XV.18, 25 Romaka, XV.23, 25, Romakaviṣaya, XV.23, 25 Romaka-siddhānta, I.3, 4, 10, 15; III.35; VIII.1 Laṅkā, XIII.9, 17, 19, 26, 29, 32; XV.19, 20, 23, 25 Lāṭadeva, Lāṭācārya, I.3; XV.8 Varāhamihira, Āvantyaka, XVIII.61, 63, 65 Vārānasi, III.13 Śaka, Śakendra, I.8; XII.2 Sāvitrā : see Saurasiddhānta Siddhapura, XV.23 Saura-siddhānta, Arkasiddhānta, Sāvitra, I.3, 4, 14; IX.1; XVI.1 Himādri, III.12 Horātantra, I.22

APPENDIX V BIBLIOGRAPHY Āryabhaṭa, C. Nīlakaṇṭha Somayāji The Āryabhaṭīya of Āryabhaṭācārya with the Bhāṣya of Gārgya-Kerala-Nīlakaṇṭha Somasūtvan, Trivandrum, 3 vols., 1930, 1931, 1957. (Triv.Skt.Ser. Nos. 101, 110, 185) Āryabhaṭa, C. Parameśvara Āryabhaṭīya with the com. Bhaṭadīpikā of Paramādīśvara, ed. by H. Kern, Leiden, 1874 Āryabhaṭa, C. Sūryadeva Yajvan Āryabhaṭīya of Āryabhaṭa with the com. of Sūryadeva Yajvan, Ed. by K.V. Sarma, New Delhi, INSA, 1976 Brahmagupta, C. Āmarāja Khaṇḍakhādyakam by Brahmagupta, with the commentary called Vāsanābhāṣya by Āmarāja, Ed. by Babua Miśra, Calcutta, Univ. of Calcutta, 1925 Fleet. J.F. The Topographical list of the Brihat Saṁhitā, Ed. (with notes) by Kalyan Kumar Dasgupta, Calcutta, Pub. Semushi, 1973 Nīlakaṇṭha Somayāji Jyotirmīmāṁsā (Investigations on astronomical theories) by Nīlakaṇṭha Somayāji, Ed. K.V. Sarma, Hoshiarpur, VVBISIS, 1977 Pṛthuyaśas, C. Utpala Pṛthuyaśas’ Ṣaṭpañcāśikā with Bhaṭṭotpala’s commentary, Bombay, 1864 Shastri, Ajay Mitra India as seen in the Bṛhatsaṁhitā of Varāhamihira, Delhi, MLBD, 1969 Varāhamihira and his times, Kusumanjali Prakashan, Jodhpur, 1991 Sastry, T.S. Kuppanna Collected Papers on Jyotisha, Tirupati, Kendriya Vidyapeetha, 1989 Śrīpati, C. Makki Bhaṭṭa The Siddhāntaśekhara ... Ed. with the com. of Makkibhaṭṭa .... by Babuāji Miśra, Calcutta, Univ. of Calcutta, 2 vols., 1932, 1947 Vākyakaraṇa with the com. Laghuprakāśikā by Sundararāja, Ed. T.S.K. Sastry and K.V. Sarma, Madras, K.S.R. Institute, 1962

BIBLIOGRAPHY 375 Varāhamihira The Pañcasiddhāntikā, the astronomical work of Varāhamihira. The text ed. with an original com. in Skt. and an Eng. trans. by T.G. Thibaut and MM Sudhākara Dvivedi, Rep. Ch. Skt. Series Office, Varanasi, 1968 The Pañcasiddhāntikā, of Varāhamihira, Ed. and Tr. by O. Neugebauer and D. Pingree, Kobenhavn, Munksgaard, 1970, 2 vols., Samāsasaṁhitā known through quotations. Ṭikaṇikā-yātrā of Varāhamihira, ed. by V.K. Pandit, Jl. of the Bombay Univ., 20 (Arts 26) (1951) 40-63 Vaṭakaṇikā known through quotations Vivāhapaṭala, Mss. Nos. 35161, 35162, Des. Catal. of Skt. Mss. Vol. IX, Sanskrit University, Varanasi. Die Yogayātrā des Varāhamihira [Ed. and Tr. by H. Kern] Indische Studien 10 (1868) 161-212; 14 (1876) 312-58; 15 (1878) 167-84 [Text in Roman characters and Tr.] Yogayātrā ... Ed. ... by Jagadish Lal Shastri, Lahore, 1944 Varāhamihira, C. Rudra (Bṛhajjātakam) Horāśāstram, with the com. Horāvivaraṇa by Rudra, Ed. S. Kunjan Pillai, 2nd edn., Trivandrum, 1958 (Triv. Skt. Ser., No. 91) Varāhamihira, C. Utpala Bṛhadyātrā of Varāhamihira, ed. (with a fragment of Utpala's com.) by David Pingree, Madras, Govt. Or. Mss. Library, 1972 Varāhamihira, C. Utpala Varāhamihira's Bṛhajjātaka with Bhaṭṭotpala's com. Jagaccandrikā, Bombay, 1874 Varāhamihira, C. Utpala Bṛhat Saṁhitā by Varāhamihira, with the com. of Bhaṭṭotpala, Ed. by Avadha Vihari Tripathi, Varanasi, 1968, Varanaseya Skt. Vishvavidyalaya, 2 vols. Varāhamihira, C. Utpala Laghujātakam, with com. of Utpala and a Bengali Tr. by Rajanikanta Acharya, Calcutta, 1910

APPENDIX VI

SUBJECT INDEX

Abhra, 24 Adar, 24 Adhikamāsa, 17 Ādityadāsa, xxviii Agastya, xxix Agastyodaya, xxix, 278-81 Agni, 24 Agrā, 113-14, 126, 131, 133, 135, 136 Ahargaṇa, xxvii, 241, 243 Aharmāna, xxvii, 34-35, 51-52, 246-47 Ahurmazd, 24 Aja, 24 Ākṣadṛkkarma, 143, 148, 150, 351 Akṣakṣetras, 129 Akṣāṃśa, 267-68 Ākṣavalana, 184, 185 Alexandria, 10, 288 Almagest, 10 Amordad, 24 Amplitude, 114, 126, 131 Anala, 24 Aneran, 24 Aṅgiras, 4 Anna, 24 Anuvakra, 334, 335 Anuvarṇana, 240 Anuvatsara, 242 Apamaṇḍala, 236-38 Ardhakapālayantra, 271 Ārdharātrika (rātra)-pakṣa, 4, 17, 197, 200, 209, 210, 289, 293, 294, 311 Ardibahesht, 24 Arhat, 250 Arkāgrā, 131 Armillary sphere, 272-73 Aruṇa, 4 Āryabhaṭa, xxvii, 17, 92, 196, 197, 198, 200, 210, 252, 289, 311 Āryabhaṭīya, xxvii, xxviii, 3, 5, 10, 26, 42, 44, 59, 60, 61, 62, 196, 198, 205, 210, 223, 289, 292, 299, 371 Āryabhaṭīya-bhāṣya, xviii Ascending node, 67 Ascensional differences, 261-62 Ashisvang, 24 Ashtad, 24 Asman, 24 Astronomer, bad, 74; qualifications of, 112 Astronomical observation, 257-58 Asura, 248, 249, 251 Ativakra, 334, 335 Atri, 4 Audayika-pakṣa, 293 Avan, 24 Avanti, xxi, 353. See also Ujjain Āyana-dṛkkarma, 143, 150, 351 Ayanāṃśa, 68, 73 Āyana-valana, 164 Babylonian astronomy, 316 Babylonians, 291 ‘Bāhu’, 126 Baladeva, 24 Bālava, 57 Banaras, 51, 52, 53 See also Vārāṇasī ‘Base’, 126, 132, 135 Baudhāyana, 139 Bava, 57 Behram, 24 Bhadrāśva-varṣa, 290 Bhadraviṣṇu, 71 Bhadra (viṣṭi), 57 Bhagola, 85-87 Bhārata-varṣa, 290 Bhāskara I, 4, 62, 129 Bhāskara II, 118, 129, 207 261 Bhaṭṭotpala, 4, 10, 179, 187, 244, 292, 293, 301, 310. See also Utpala Bhau Daji, 10 Bhava, 24 Bhoga-rekhā, 272 Bhṛgu, 4 Bhūbhramaṇa, 249-50 ‘Bhuja’, 131, 132, 133, 143, 144, 145, 146 Bhujāntara, 54, 209 Bhūmi, 24 Bhūtasaṅkhyā, 372 Bīja correction of VM for planets, 299 Bimbamāna, 189-90, 215-16 Brahmā, 4, 5, 24 Brahmagupta, xxvii, xxviii, 4, 5, 196, 197, 289 Brahman, 24 Brahmasiddhānta, 5 Brāhmasphuṭasiddhānta, xxvii, xxviii, 3, 5, 60, 70, 293 Bṛhadyātrā, xxix Bṛhadyogayātrā, xxix Bṛhajjātaka, xxviii, xxix, 286 Bṛhatsaṃhitā, xxviii, xxix, 3, 4, 10, 17, 22, 62 68, 179, 293, 354, 371 Budhacāra, 340 Budhasphuṭa, 342-60 Burgess, J., xix Caitra-pakṣa, 44 Cakrayantra, 272 Calendar reform, 73 Candracchāyā, 123-25

PAÑCASIDDHĀNTIKĀ 377 Candragrahaṇa, xxvii See also Eclipse, Lunar eclipse Candrāṁśa, 269 Candrasphuṭa, xxviii, 27 Candraśṛṅgonnati, 137-51 Canopus, 278-81 Cara, 48-49, 57, 98 ff., 261 Cara-karaṇa, 57 Carakhanda, 48, 49 Cara-vināḍī, 49, 50, 100, 105 Cardinal directions, 269-70 Catuṣpāda, 57 Celestial equator, 86 Celestial sphere, 270-71 Chāyā, 284 Chedyaka, 267-81 Chedyakayantrāṇi, 267-81 Christian Calendar, 73 Comet, 69 Conjunction of the Moon with a Star, 276-78 Correction for the Equation of the centre, 54 Cosmogony, 248-61 Cyavana, 4 Daily motion of the Sun and the Moon, 185 Dakṣiṇāyana, 60, 176, 177, 248 Dakṣiṇottara, 271 Day, duration of, 246-47 Day, lord of, 21-23, 287, 291 Day-diameter, 96-98 Day-reckoning, 289 Days from Epoch, 5, 8, 10, 11, 25, 26, 197, 241-43 Day-time, 34-35, 51-52 Declination, 85-90 Declination of the Moon 87-90 Declination of the Sun, 87-90 Demons, 248, 249 Depadar, 24 Depdin, 24 Depmohr, 24 Deśāntara, 51-53, 209, 274 Deśāntara-nāḍī, 51 Descending Node, 67, 69 Devas, 248, 249 Dhana, 78 Dhanada, 24 Dharma-śāstra, 10, 69, 74, 139, 251 Dhātrī, 24 Dhruva, 286-87 Dhruvakaraṇī, 77 Dhūmaketu, 68 Dig-jyā, 113-15 Dikshit, S.B., xix, 10 Din, 24 Dinagaṇanā, 288-91 Dina-vyāsa, 96-98 Diophantine equation, 293 Directions from shadow, 126-32 Directions, problems of, 76-130 Dragon's head, 67 Dragon's tail, 67 Drekkāṇa, 258 Dṛkṣepa, 187-89 Dṛkṣepa of the Sun, 219-20 Druma, 24 Duration of a day, 246-47 Duration of the Eclipse, 230-35 Duryavana, 4 Dvādaśāṁśa, 258 Dvāpara, 293 Dvivedi, See also 5, 19, 20; Sudhakara Dvivedi, TS Dyauḥ, 24 Dyugaṇa, 7 Earth, 248 Earth, measures of, 253 Earth, situation of, 248 Earth's shadow, 228-30 Earth-sine, 118-21 Eclipse diagram, 236-40 Eclipse, duration of, 225-27 Eclipses, 195-96, 232-86 Ecliptic, xxvi, 236-38 Egypt 10, 288 Epicycles of the planets, 300-1 Epicyclic theory, 206-9 Epoch, 7, 30, 59 Epoch constant (kṣepa) for Jupiter, 297 Epoch constant for Mars, 297 Epoch constant for Mercury, 298 Epoch constant for Saturn, 297 Epoch constant for Venus, 298 Equation of the centre, 47-48 Farwardin, 24 First point of Aries, 73 First sine, 118-21 Five Schools of Astronomy, 4 Five siddhāntas, compara- tive study, xxvi-vii Gaṇitakaumudī, 265 Garga, 4 Gārgya, 4 Gati, 27, 312 passim. Gavām-ayana-satra, 60 Ghana, 13, 27, 28, 30, 31 Ghaṭī-yantra, 275-76 Gnomon, 91-220 ff., 267-68 Gnomonic shadow, 35 ff. 90-136, 113 Go, 24 God, 250