पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

XVIII.50 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 347
48. In Libra, the gati-s are:

49. In Scorpio, the gati-s are:
    | Degrees | Minutes | Textual (° ') | Calculated (° ') |
    | :--- | :--- | :---: | :---: |
    | 1. Rise to Retro. | 10×3+ 6=36 | 36 + 2=38 | 36 38 | 35 39 |
    | 2. Retro. | 10×1+11=21 | 21 − 7=14 | 21 14 | 21 16 |
    | 3. Retro. to Set. | 10×3+ 4=34 | 34 + 3=37 | 34 37 | 33 38 |
    | 4. Set. to Rise | 10×4+ 2=42 | 42 + 26=68 | 43 8 | 43 6 |
    [धनु:]
    धन्वनि द्विदशावष्टौ, [विंशं], षट्सप्तकं, 'कृतोनं' च ।
    ते ('इषु'युत) 'विषयोनाः' ('शैला' : त्रिंशा) न्विता भागाः ॥ ५० ॥
    48a. A.B. रेकेण
    b. A.B. व्यनखांसां तिथिद्विसंगुणैश्च; C. हीना खाशाग्रिभिर्द्विसंगुणाश्च; D. युता जूके सशून्यतिथिर्द्विसंगुणाश्च |
    d. A.B.C.D. ह्येक (A. ध्येक) त्रिंशद्युताश्चैव |
    49a. A. दशघ्नी; B. दशघ्ना
    b. A.B.C.D. शशिकृत (B. om. त, D. शशिद्विकृत) for त्रिशशि. A.B. दहनाः षड्खरावर्णवाष्टयुताः; C. दहनयुगा वसु-शराणंवाष्टयुताः; D. दहनाः शरार्णवाष्टयुताः |
    c. A. तेशा; B1.3. तेषां. A.B.D. यममुनीशोना; C. यममुनीशेन
    d. A.B. समेना व (B. च)

348 PAÑCASIDDHĀNTIKĀ XVIII.52
50. In Sagittarius, the gati-s are:

51. In Capricorn, the gati-s are:
    | | Degrees | Minutes | Textual | Calculated |
    | :--- | :--- | :--- | :---: | :---: |
    | | | | ° ′ | ° ′ |
    | 1. Rise to Retro. | 20+ 3=23 | 23 + 4=27 | 23 27 | 23 28 |
    | 2. Retro. | 20+ 0=20 | 20 − 4=16 | 20 16 | 20 16 |
    | 3. Retro. to Set. | 20 + 7+18=45 | 45 + 7=52 | 45 52 | 46 54 |
    | 4. Set. to Rise | 20+12=32 | 32 +26=58 | 32 58 | 33 56 |
    [कुम्भः]
    कुम्भे (ऽह्नां) विंशत्या [रूप] युतया 'हुतभुग्वेद'-'द्विदिननाथैः ।
    द्वाविंशतिरंशा पञ्च (दशा-ऽर्थार्थका) षष्टिः ॥ ५२ ॥
    50a. A. धन्वि; B. धन्वनि. A.B. दिच साधाष्टौ (B. याष्टौ); | 51a. A.B. द्युदशं.
    C. दिवसाधार्ष्टौ; D. दिवसानाष्ट्रि षट्कृति षट् | b. A.B.C. मुनिहीनं; D. [मुनियुक्तं]
    b. A.B.C.D. षोडश (A. षोडस) for विंशं | c. A.B.C.D. अंशा रूपेणोनाः
    A.B.C.D. दशोने. A. व for च | d. A.B.C.D. सैकैकाश्रोत्कृति
    c. A1. ते स्फुः; A2.B. ते स्युः. A.B.C.D. शशिविषयोनाः |
    (A.B. नौः) |
    d. A.B.C.D. सैकास्त्रिं (A. त्र्यं) शान्विता. |

XVIII.53 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 349
52. In Aquarius, the gati-s are:

53. In Pisces, the gati-s are:
    | | Degrees | Minutes | Textual (° ') | Calculated (° ') |
    | :--- | :---: | :---: | :---: | :---: |
    | 1. Rise to Retro. | 18 + 1=19 | 20 | 19 20 | 19 19 |
    | 2. Retro. | 18 + 5=23 | 13 | 23 13 | 23 14 |
    | 3. Retro. to Set. | 43=43 | 50 | 43 50 | 43 52 |
    | 4. Set. to Rise | 3 × 8=24 | 49 | 24 49 | 24 47 |
    [बुधगतीनां निर्णयः]
    (अस्तो)दयान्तरांशा बुधस्य दिवसाश्चतुर्थ [या] गत्या ।
    उदयाद् वक्रं प्रथमा तृतीयगत्याऽऽनुवक्र(मस्तमयान्तम्) ॥ ५४ ॥
    52a. A.कुंभेह्ना. A1.त्रिंशत्या; D.त्रिकृत्या
    b. A.B.दगतभुग्विदेवदिननाथैः; C.D.हुतभुग् द्विवेद (D.दिनेश) दिननाथैः
    d. A.B.C.पञ्चवर्गमथाब्ध्रिका षष्टिः (C.र्गमर्थाब्ध्रिका)ः D.पञ्चवर्गं सुराधिपाः षष्टिः
    53b. A.B.C.D.मीने त्र्यष्टकमह्नां
    b. for सागरका;, A1.संशरं; B1.शशीष्टं, B2.शासशिष्टं; B3.शशीरं; C.D.संयुक्तम्
    c. A.B.C.D.त्र्यष्टककृतिर्विंशत्या (D.विंशत्याः)
    d. B2.शनार्थ. A.B. मष्टां स्युः

350 PAÑCASIDDHĀNTIKĀ XVIII.56
Specifications of the gati-s of Mercury
54. From setting to rising the degrees and days are given by the fourth gati.
From rising to vakra (beginning) is (given by) the first gati. The third gati is
(from) anuvakra (i.e., end of retrogression) to setting.
It will be seen that this verse explains what the four gati-s indicate a fact which has not been men-
tioned earlier. Actually, there is no direct reference to the second gati. But it can be inferred that
this gives the retrogression period and the degrees.
TS have made some emendations but have not translated them but say that they are not able to
comprehend the meaning of these verses. NP have adopted the emendations of TS and have just
translated them as they are and that does not make any sense. They comment: "We cannot connect
any rational procedure with the verses XVII, 54-56".
गतिविश्लेषकृतिघ्नैरंशैर्गतिवर्गभाजितैर्लब्धम् |
हित्वा राशिभ्यो भुक्तं प्रथमगतौ वक्रपश्चाच्च || ५५ ||
वक्रगतौ पूर्वार्धे तृतीयगत्यां च यत्कृति गुणितैः |
भागैर्गतिकृतिभक्तैः फलमनुपाताच्चतुर्थगतौ || ५६ ||
55. By the square of the difference in gati-s (days) multiply the degrees and
divide by the square of the gati-s. The result is to be subtracted from the
degrees and that gives the degrees gone in the first gati and in the second half
of vakra-gati.
56. In the first half of vakra-gati and in the third gati multiply the square (of
the days passed) by the degrees and divide by the square of the gati-s (days).
For the fourth gati the result is obtained by (direct) proportion [since the
motion in this section is practically uniform.]
54a. A. अष्टो; C. अर्कौ; D. अथो. A.B.C. न्तरांशान् 55a. B. ॰रंसैगत॰
b. A.B.C.D. दिवसाथतुर्थगत्या occurs as c. They c. B. भुक्तं
have as b, बुधस्य कालांश (A.B. कालांश) d. A. गातौ. A. वक्रपश्वाद्वा; B. वक्रपश्चाच्च;.
कांस्त्रिगत्यूनान् (A.B. गत्यूनात्, D. गतीनाम्) D. वक्रपश्चात्
d. A.B.C.D. अनुवक्रमजमीनयोर्मन्दम् (A. योन्दम्,
B. योर्मदम्). 56a. A. वर्गाक्रगतौ; B. चक्रगतौ
b. A.C. गत्या च; D. गत्याश्च
A. यात्कृतं; B. तक्षत. C. गुणितम्; D. [यात्कृति गुणितैः]
c. A.B. गतिकृति (B. क्रति). B1. भत्यै; B2.3. भृत्यै
d. D. ॰मनुपाञ्च च. A.B. ॰र्थभागगतौ (B2.3. गतौ)

XVIII.58 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 351
[दृकर्म—आक्षम्]
ज्याविधिविक्षेपघ्ना (च्च) रकाला‘म्बराष्टवेदां’शम् |
जह्यात् क्षिपेच्च याम्योत्त(रे) ग्रहे खं यथा(काष्ठम्) || ५७ ||
एवं कृते [ग्रहान्त]रांशकैरस्तदर्शनं तेषाम् |
Correction for mean elongation in heliacal rising
57. Find the R sine of the latitude of the body. Multiply the (maximum) half-
cara (i.e. the half difference between the half day-time or night-time from 15
(nāḍis.) in vināḍis, by this R sine, and divide by 480. Add this or subtract this
(to or from the Moon or star-planet) if the latitude is north or south, according
to the proper direction, (i.e. according as the phenomenon of setting or rising,
takes place in the west or east, respectively).
58a-b. When this is done, their setting or rising happens according to the
interval in degrees (between the Sun, and the planet given in XVII.12, or the
Moon).
Note 1. There is a lot of lacunae in verse 57. The half-cara-vināḍīs meant is the maximum for the
place. yathākakṣam is meaningless here and is corrected into yathākāṣṭham, i.e. according to the direc-
tion, but the direction is not mentioned. If north latitude, the addition is for the Moon or planet in
the west. Also if north latitude, the subtraction from the Moon or star planet is to be done for the
east. If south latitude, the subtraction is for the west, and the addition for the east. These things can
be got by a little reflection.
Note 2. The amount of degrees to be applied can simply be got by multiplying the degrees of
latitude of the body by the tangent of the latitude of the place. (The equinoctial mid-day shadow
of the 12" gnomon ÷ 12, is tan. latitude of a place). The amount got is very rough.
The degrees wanted = Sin. half cara (i.e., tan latitude of place x tan. declination of the Sun) ×
sin (90° – angle for heliacal rising), nearly. The last term is neglected here, tan declination is
roughly taken as 48', half-cara is converted into degrees by division by 10, and the conversion into
sine-function is applied to the latitude of the planet instead of the half-cara, as roughly equal.
Note 3. This application is what is technically called Ākṣa-dṛkkarma. The Āyana-dṛkkarma is
neglected.
Note 4. The heliacal rising of the Moon, and of Venus and Mercury when retrograde, takes place
in the west. The heliacal setting of the Moon and retrograde Venus and retrograde Mercury takes
place in the east. Otherwise, all star-planets set in the west and rise in the east. (This Siddhānta does
not envisage the setting or rising of Venus and Mercury when retrograde, no separate degree for
that being given).
57a. B1.3. ज्याविधिविधि d. A. ०्तरं; B. ०तंर०. C. स्वे. D. [कक्ष्यम्]
b. A.B. च for च्च A. ०दंबराष्ट; B. चरकादि 58a-b. A.B.C.D. ग्रहार्कन्तरांशकैः
(B2. कालादि) चराष्टवेदांशं B. ०तिष्ठतितिथ०
c. A. जह्याक्षि. A. यान्मो
26

352 PAÑCASIDDHĀNTIKĀ XVIII.60
चन्द्रादीनां 'द्वादश मनुरवितिथ्यष्टतिथि'संज्ञैः ॥ ५८ ॥
58c-d. The setting and rising (mentioned above in verse 58a) is by 12°, 14°,
12°, 15°, 8° and 15° for the Moon etc.
Note 1. This has to be taken with verse 58a. The degrees given here separately are according to
the Vāsiṣṭha-Pauliśa, which do not instruct the correction due to the latitude of the planet or for
even the latitude of place (ākṣa-valana). The result will therefore be very rough.
Note 2. These degrees are necessarily arbitrary as mentioned already, and the correctness of the
numbers cannot be verified in the absence of the original siddhāntas which are now lost. But we can
guess the probable values as we are sure of the relative luminosities of the planets. The numbers
seem to have been misplaced. They should be dvādaśa, tithi, manu, ravi, aṣṭa, tithi (12°, 15°, 14°, 12°,
8°, 15° for Moon etc.) All siddhāntas give 17° for Mars instead of 15°. The rest are nearly correctly
given, according to one siddhānta or other.
[कालभागानां क्षेत्रभागकरणम्]
(त्रि) शतविनाडीगुणितै (रू) द (य) [वि] नाडीप्रमाणहृतैः ।
लब्धांशकप्रमाणादुदयोऽस्तं वा स्फुटं वाच्यम् ॥ ५९ ॥
Conversion of time-degrees into distance-degrees
59. Multiply the degrees by 300 and divide by the vināḍīs of oblique ascen-
sional difference of the sign, rising at that moment, (near sunset or sunrise,
as the case may be), and get the respective degrees. When the distance bet-
ween the sun and planet is that much, the respective setting or rising takes
place.
Note 1. This work is what is known as the conversion of time-degrees (kālabhāga) into degrees of
distance on the ecliptic (kṣetrabhāga). Since the rule has to apply commonly to Saura on the one hand
and the Vāsiṣṭha-Pauliśa on the other, it has been placed last.
Note 2. Since the positions of the Sun, Moon and planets are given only on the ecliptic, this con-
version is necessary to measure distances.
ज्ञसिताऽऽरेज्या (र्व्यू) नाः शशिनः प्रत्युत्तरं खरां (शुश्च) ।
ज्ञात्वैवं विक्षेपादादेशमनागतं कुर्यात् ॥ ६० ॥
60. (The rising takes place in the east when) Mercury, Venus, Mars, Jupiter
and Saturn are less in longitude than the Sun, and the Sun is less than the
Moon in the opposite direction, (i.e., west). Making the computation according
to the instruction given above using the latitude etc, the phenomenon should
be predicted.
60a. A.B.C. र्ज्यकोर्नाः
59a. A. त्रिंशत; B. त्रिशति. B. विनाडी b. A.B. खरांशोना; C. खगांशेन; D. [खंशाश्च]
b. A. घदशनाडी; B. श्रदशनाडीं d. B. मनागमतत्

XVIII.63 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 353
Note. The verse is very corrupt. But knowing what it is about we can give the meaning, making
possible corrections. The rising is mentioned here as it is more important for application to dharma-
śāstra etc. But rising also envisages setting with the word 'less' taken for 'more', and 'more' for 'less'.
Example 1. The latitude of the moon is 3° 45' N. The maximum half-cara of the place is 150 vināḍīs. The
oblique ascensional difference of the rising sign is 280 vināḍīs near sunset. Find the ecliptic distance between
the Sun and Moon, for the heliacal rising of the Moon.
The time-degrees for the moon is 12°. The heliacal rising of the Moon takes place in the evening.
R sin 3° 45′ × 150 ÷ 480 = 7 38/60 × 150 ÷ 480 = 2° 23′.
This is additive since the Moon's latitude is north, and the phenomena pertains to the west.
Therefore, the corrected time-degrees = 14°.
14° × 300 ÷ 280 = 15° is the distance on the ecliptic between the Sun and the Moon, required.
Example 2. For the same place, (i.e., max. half-cara 150 vināḍis) find the ecliptic distance required for
heliacal rising, given: the latitude of Mars 1° 15' N, and the oblique ascensional difference near sunrise at that
time is 330 vināḍis.
The latitude correction to the time degrees (17° for Mars) = R sin 1° 15′ × 150 ÷ 480 = 2′ 33 ″
× 150 ÷ 480 taken as degrees = 48′.
As the latitude is north, and the phenomenon pertains to the east, (since it is the rising of Mars
that is considered), it is subtractive.
∴ 17° − 48′ = 16° 12′ is the corrected time-degrees. 16° 12′ × 300 ÷ 330 = 14° 44′, is the distance
on the ecliptic required.
[पञ्चसिद्धान्तिकोपसंहारः]
आवन्त्यकः समासा (च्छि) ष्यहितार्थं स्फुटाङ्कसमम् ।
चक्रे वराहमिहिरः ताराग्रहकारिकातंत्रम् ॥ ६१ ॥
प्रद्युम्नभूमितनये जी (वे) (सौरैऽथ वि) जयनन्दिकृते ।
बुधे (च भग्नो) [त्साहः] स्फुटमिदं करणं भजतात् ॥ ६२ ॥
दृष्टं वराहमिहिरेण सुखप्रबोधं
..............................
..............................
.............................. ॥ ६३ ॥
61. For the good of his disciples, Varāhamihira, belonging to the Avanti
country (Ujjain region), wrote this section dealing with the star-planets, briefly
but with the constants agreeing with the original (siddhāntas).
62. A learner, discouraged by the computation of Mars by the astronomer
Pradyumna, the computation of Jupiter according to the Saura siddhānta, and

Here is the transcription of the page, formatted line by line in clean Markdown:

354 PAÑCASIDDHĀNTIKĀ XVIII.63
the computation of Mercury by Vijayanandi, can have recourse to this section
of the manual.
63. By Varāhamihira has been seen, (i.e., written) (this karaṇa) easy to under-
stand,......................
Note 1. Verses 61 and 62 clearly close the section dealing with the star-planets. Since VM says that
he has improved on the earlier authors, he must be referring to Chapter XVI and XVII, dealing
with the Saura. His reference to his improvement on the Saura itself in the case of Jupiter must
refer to the bīja correction made by him in XVI. Indeed, his dissatisfaction with the Jupiter of the
Saura is reflected in his formula for computing Jupiter to give the years of the sixty-year Jovian
cycle, given in his Bṛhatsaṃhitā, in the chapter dealing with the motion of Bṛhaspati (Jupiter). As
for chap. XVIII, he could not have meant the Vāsiṣṭha-Pauliśa star-planets there as an improve-
ment, they being crude.
Note 2. Verse 63 evidently closes the Pāñcasiddhāntikā, as indicated by the Vasantatilakā metre of
the verse instead of the regular āryā metre. But unfortunately the last three feet are missing.
Perhaps it is a purposely done ‘black-out’ by a later astronomer-scribe, to add his spurious verses
64-81 in continuation (see below) and, unfortunately, only his manuscript has survived as the
archetype of the few extant manuscripts,
61a. B. आयंतकः समांसाः
b. A. छिष्णहिं०; B. छिसंध्यं हिं०; B2.3. छिसंख्यं हिं०
A.B. ०र्थं तमद्गस्फु०; C. र्थं [ततः] स्फु०;
D. ०थं [वियद्गस्फुटांशम्]
c. A.B. मिहरः
62a. A. प्रद्यम्र. B. भुमि
b. A.B. जीवै (B3. जीवे)
A. शौरयवावीजय०; B. सौरे यवविजयं
D. सौरैऽथवा विजय०
c-d. A. बुधे वनग्रास्फुट; B. छुधे च मग्रास्फुटं; D. बुधो भग्नः
स्फुटमिदं करणं भजति दृष्टं वराहमिहिरेण || ६२ ||
d. C. प्रस्फुटमिदं, om. करणं. A.B. भजतां;
D. drops the word.
63a. A.B.C. मिहरेण. B. प्रबोधां
b-d. A.B.C. gap indicated for the three
quarters of the verse.
D. Ignores the expression सुखप्रबोधं
in this verse and constitutes a new
half verse for the previous verse.
as: बुधो भग्नः स्फुटमिदं करणं भजति दृष्टं
वराहमिहिरेण || In consequence, the
numbering of verses than in A is one
less in D, hereforward.
[इति पञ्चसिद्धान्तिकायां वराहमिहिरविरचितायां
ग्रहोदयास्तो नाम अष्टादशोऽध्यायः ]
Thus ends Chapter Eighteen entitled ‘(Vāsiṣṭha-) Pauliśa-Siddhānta
— Rising and Setting of Planets’, in the Pañcasiddhāntikā composed
by Varāhamihira

Chapter Eighteen 64-81 (A Spurious Supplement)
Computation of the Star-Planets in brief
[पञ्चसिद्धान्तिकायां प्रक्षेपः — ताराग्रहाः]
Spuriousness of this Section
That verses 64-81 of Pāñcasiddhāntikā form only an appendage to a manuscript of the work and
not a composition of Varāhamihira, is evident from its occurring after the work has closed in the
customary way with a concluding colophonic verse, with its metre changed to Vasantatilakā from
the āryā metre in which all the previous verses of the chapter had been couched, and with the author
speaking about himself in this concluding verse. It is also to be noted that the set of verse 64 to 81
begin with a new salutation. Had these verses really belonged to the PS, the customary colophonic
verse must have come at their end, and significantly there is no such colophonic verses at the end.
Further, in verse 65 it is said that the author considers this as a superior set containing a previous
method or matter and that he was giving it out, with a liberal mind, to the generality of astronomers
without hiding it from them. But actually it is inferior stuff, and can give only very rough results
since the equation of the centre is dispensed with, only the equation of conjunction being given,
which makes it valueless. The author boasts here that he has made things easy, and takes credit for
this which only a novice could have done. Fancy VM speaking thus, when in verse 62 he is so intent
on accuracy that he says, "Let people who have been dissatisfied with the inaccuracy of astronomers
like Pradyumna, Vijayanandi etc., have recourse to his treatment of the Saura." Further, there are
mistakes in the computation of Venus and Mercury, unpardonable in any astronomer. (See below,
Note 2 under verses 70-72). The above-mentioned aspects of verses 64-81 have escaped the notice
both of TS and NP, who both take them as genuine compositions of VM. Moreover, NP obliterate
verse 63, the concluding genuine verse of PS, by not including it in their text, though a few words
thereof are present in all the manuscripts of the work and in some of the manuscripts it bears a
serial number; thus, verses 64 to 81 are numbered in NP as 63 to 80.
These spurious verses are dealt with below for the sake of completeness of the text as found in
the parent manuscript of the PS from which all its manuscripts available now have been derived.
[उपक्रमः]
प्रस्तावेऽपि न दोषा [न्] जान (न्न) पि न वक्ति यः परोक्षस्य ।
प्रथयति गु(णां) श्च तस्मै सुजनाय न(मः) परहिताय ॥ ६४ ॥
अष्टादशभिर्बद्धान्त्या ताराग्रहतंत्रमेतदार्याभिः ।
(वरमिति) वराहमिहिरो ददाति निर्मत्सरः करणम् ॥ ६५ ॥
Salutation
64. Salutation to the good people, ever interested in the welfare of others,
who even when knowing the faults of others, and even when there is an
opportunity, do not mention their faults, but proclaim their good qualities.

356 PAÑCASIDDHĀNTIKĀ XVIII.66
65. In eighteen āryā verses, Varāhamihira, without feeling any jealousy,
gives this manual to the world, ending with the treatment of the planets,
thinking that it is good.
Note 1. The emendations are TS's also.
Note 2. Verse 64 is a paranomasia and means also, "Salutation to the good science of astronomy
called technically parahita-gaṇita (prevalent in Kerala in South India), which at the beginning deals
only with mean motions, though knowing its defective nature as not being true motions, and which
furnishes tabular values of equations going by the means, mandajyā (R sine table of the equation of
the centre), karkijyā (R sine table of the equation of conjunction for the anomaly 90° to 270°) and
makarajyā (R sine table of the equation of conjunction for the anomaly 270° to 90°)."
This meaning being not obvious to the ordinary reader, I give the phrase by phrase meaning:
prastāve (granthārambhe), parokṣasya (asphuṭagrahasya) doṣān (asphuṭatvādi-doṣān) jānann api yaḥ na
vakti (jānann api na vadati, madhyagater eva prakṛtatvāt) guṇān (mandajyā, karkijyā, makarajyā ityādi-
guṇaśabda-vācyā jyāḥ) prathayati (prakaṭīkaroti, gaṇayitvā likhatīti yāvat), tasmai sujanāya (tasmai
śobhanajanmane) parahitāya (parahitagaṇitāya) namaḥ (namo 'stu).
Note 3. These two verses also form part of the 18 verses mentioned. So, actually there are only 16
verses (66 to 81), giving the computation.
[सौरदिनम्]
आकरणाद् रविभागा दिवसा (श्रा) रंशका रवौ कार्याः ।
अधिका (य) दा दि(ने) भ्यो भागा ज्ञेयास्तदा चक्रात् ॥ ६६ ॥
‘Sun’s day’ (Sauradina)
66. From the epoch, to the time of computation of the planet, find the Sun’s
degrees passed. These are to be technically called ‘days’, (and used in the com-
putation). Find the remainder after dividing by the cycle number given for
the respective star-planet. Take the ‘days’ of motion corresponding to the set
of motions given to the respective planet. These are degrees of planetary
motion. Add this to the Sun's longitude. The true planet is got.
Note 1. The ‘days’ mentioned here is only what is called sauradina (‘Sun’s day’) as distinguished
from the sāvana or civil day, and are actually degrees. (This is like the word ‘light-year’, which is
used as a unit of distance). This instruction is given with respect to all planets.
64a. A.B. दोषाः c. A. वराहमिह वराहमिहिरो (A2. ०म्पितिहरो);
b. A. जानन्नापि न; B. जानानापि (B. जुना०). B. मिहरवराहमिहरो; C. ०म्हिहरो
A. पटोक्षस्य d. B. निमत्सरः
c. B. प्रथयाति. A, गुणाश्च तस्मै; B. गुणास्तस्मै 66b. A. दिवमाश्ररांशका; B. दिवसाश्चंशका
d. A. सुजनयानमपर; B. सुजनया तमः. B. परिहिताया B. कार्या
65a. A. ०र्वद्धा; B. ०र्वंधा c. A. ०कार्यदा दितेभ्यो; B. ०कार्यदा दिनेभ्यो
b. B. दायाभिः d. A.B. वक्रात्

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

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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