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

102 PAÑCASIDDHĀNTIKĀ IV. 30
[लङ्कोदयराशिमानम्]
[राशिज्या] ऽपक्रमज्या(कृ)तिवि(श्ले)षमूल[हत] वि(स्ता)रात् ।
द्यु(व्या)स(ह)ता(च्चापं) 'दिग्घ्नं' राश्यु(द्ग)मविनाड्यः ॥ २९ ॥
'वसुमुनिपक्षा' 'व्येकं शतत्रयं' 'त्रिद्विकाग्नय' [श्राङ्का] (त्) ।
परतस्त एव वामाः षडुत्क्रमात्ते तुलाद्यर्धे ॥ ३० ॥
Rt. ascensional difference
29. Square the sine of the longitude of a point on the ecliptic, and deduct
from it the square of the sine of the declination of the point. Find its root,
multiply it by the diameter and divide by the day-diameter. Find the arc of the
resulting sine in degrees. Multiply the degrees by 10. The Right ascension of
the point is obtained in vināḍīs. deducting the right ascension of the next rāśi
from that of the previous, the right ascentional difference of the rāśis are
obtained.
30. The vināḍis of right ascentional difference for the three signs from Meṣa
are 278, 299 and 323. In the next quadrant they are the same in the reversed
order, viz. 323, 299 and 278. In the half of ecliptic beginning from Libra, the
difference are those of the first half, taken in the reverse order.
The formula is:
Sin Right ascension = 240' × √(sin²longitude − sin² dec) ÷ day-diameter.
The degrees of right ascension multiplied by 10, are the vināḍis of right ascension.
The differences as calculated, are, for Aries etc. 278, 299, 323, 323, 299, 278, 278, 299, 323, 323,
299, 278.
Now, what is the meaning of saying that in the second half the differences are in the reverse order
of those in the first half, when reversing the order does not make any difference? True. But the
author must have meant this statement for ascensional difference in general, for, then, owing to
the subtraction and addition of half day-differences (carārdha) in the first and second quadrants,
the reverse order becomes different.
Further, the vināḍis mentioned here are sidereal and not mean solar, because the vināḍis per
degree are obtained by dividing the time of a full revolution by 360, and the time of a full revolution
of the stellar sphere is a sidereal day, and not a mean solar day which is the time of the diurnal
revolution of the mean Sun.
30. Quoted by Utpala on BS 2, p.61.
29a. A. भपक्रमज्या; C. मेषाद्यपक्रमज्या; D. भापक्रमज्या
b. A. क्रतिविशेषमूलविस्तारात्; C. कृतिविशेषमूलगुणविस्तरात्;
D. कृतिविश्लेषमूल [गणिताद्] विस्तारात्
c. A. द्युद्वासहताचाप; C.D. द्युव्यासहताच्चापं
30b. A. ०काग्रयश्चाजान्; C.D. ०काग्रयश्चाजात्. U. श्राङ्काः
C.A. वाभाः
d. A. षड्गक्रमास्ते नुताद्यर्द्धे