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

306 PAÑCASIDDHĀNTIKĀ XVII.9
Fourth step
An. conj = 17° 18′ − 244° 44′ = 132° 34′. Bhujāṁśa = 180° − 132° 44′ = 47° 26′, Koṭyaṁśa = 42°
34′. Bhuja = 88′ 20″. Koṭi = 81′ 8″. Bhuja-result = 88′ 20″ × 234° ÷ 360° = 57′ 25″. Koṭi-result = 81
8″ × 234° ÷ 360° = 52′ 44″.
As an. of conj. is in 270° to 90°, this is deductive from 120′. So, 120′ − 52′ 44″ = 67′ 16″. 120′ ×
bhuja-result ÷ √(bhuja-result² + 67′ 16″²) = 77′ 32″.
Arc of this taken as sine = 46° 16′, additive because an. conj. is from 0° to 180°.
So, corrected mean arc = 244° 44′ + 40° 16′ = 285° 0′ = geocentric true Mars.
Example 2. Find the geocentric Venus at 1,20,553 days from epoch.
Given:
The śīghra of Venus = 2ʳ 27° 16′ 20″ = 87° 16′
Mean Venus = Mean Sun = 17° 18′
Aphelion of Venus = 2ʳ 20° = 80°.
Epicycle of Conj. of Venus = 260°.
Epicycles of the apsis = 14°.
First step
An. Conj = 87° 16′ − 17° 18′ = 69° 58′.
The Bhuja degrees = 69° 58′. Koṭi degrees = 20° 2′.
Bhuja = 112′ 42″. Koṭi = 41′ 5″.
Bhuja-result = 112′ 42″ × 260° ÷ 360° = 81′ 24″.
Koṭi-result = 41′ 5″ × 260° ÷ 360° = 29′ 40″.
An. Conj. is between 270° and 90°. So the Koṭi-result is additive to 120′.
So, 120′ + 29′ 40″ = 149′ 40″.
Bhuja-result × 120′ ÷ √(81′ 24″² + 149′ 40″²) = 57′ 20″.
Arc 57′ 20″ = 28° 33′. Half arc = 14° 17′, subtractive to aphelion (as An. conj. is from 0° to 180°)
80° − 14° 17′ = 65° 43′ = Half corrected aphelion.
Second step
An. of apsis = mean − half cor. aphelion = 17° 18′ − 65° 43′ = 311° 35′.
The Bhuja degrees are 48° 25′..
Bhuja = 89′ 44″.
Bhuja-result = 89′ 44″ × 14° ÷ 360° = 3′ 29″.
Arc. 3′ 29″ = 1° 40′. Half arc = 50′, subtractive, as an. conj. is from 180° to 360°.
Corrected aphelion = Half-corrected aphelion − 50′ = 65° 43′ − 50′ = 64° 53′.
Third step
An. of apsis = mean-corrected aphelion
= 17° 18′ − 64° 53′ = 312° 25′
Bhuja degrees = 47° 35′. Bhuja = 88′ 33″.
Bhuja-result = 88′ 33″ × 14° ÷ 360° = 3′ 27″.
Arc sine 3′ 27″ = 1° 39′, additive as an. of apsis is 180° to 360°.
So, mean Venus + arc = 17° 18′ + 1° 39′ = 18° 57′, is the eq. cent. corrected mean.