ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

138 GREEK AND INDIAN METHODS
the secondary to the equator cutting it at E'. Both the above
astronomers were content with the idea that AE = AE', or that
AE = the declination of the point A of the ecliptic which is 90°
ahead of S in the above figure. This idea continued till the
time of Bhāskara II (1150 A. D.) who found out the correct
equation.
He recognised that CS, the declination of S = PP'; P'EH is
then the horizon of the station whose north geographical latitude
is CS. Also, the ‘sine’ of EA is the ‘Agrā’ or the sine of the
amplitude of the point A for the latitude CS.
∴ R sin EA = (R sin AE' × R) / (R cos CS) = [R sin (90° + γS) × R sin ω] / R
× R / (R cos CS)
or R sin EA = [R sin (90° + l) × R sin ω] / (R cos δ)
where l stands for γS and δ for CS.
Greek Method :
We give below the Ptolemy's method in a slightly modified
form¹. Let SHA be the triangle and γCE be the transversal ;
then we have,
(sin SC / sin CH) × (sin HE / sin EA) × (sin Aγ / sin γS) = 1
or (sin δ / cos δ) × (sin 90° / sin EA) × [sin (90° + l) / sin l] = 1
∴ sin EA = [sin δ × sin (90° + l)] / (cos δ × sin l) ,
which is readily transformed into Bhāskara's equation. The
originality of Bhāskara would be readily admitted.
Problem VI--
To find the Angle between the
Ecliptic and the Horrizon
Indian Method :
(A) Āryabhaṭa's method. It consists of the following²
steps :--
(1) Determination of the orient point of ecliptic.
(2) Finding the sine of its amplitude.

1. Manitius, ibid, Book I, pp. 104-06.
2. Āryabhaṭa, Gola, 33 : Sūryasiddhānta, V. 5-6.