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

326 BRAHMAGUPTA A GREAT CRITIC
dṛkkṣepajyā
= [ (madhyajyā)² - { udayajyā × madhyajyā / R }² ]^(1/2)
where R is the radius of the celestial sphere.
(iv) The dṛgjyā is the Rsine of the zenith distance (of the
Sun) and is given by :
dṛgjyā = [ R² - { dṛggatijyā × R sin (L - θ) / R }² ]^(1/2)
where L is the longitude of the horizon ecliptic in the east and
θ the longitude of the Sun.
(v) The dṛggatijyā is the Rsine of the altitude of the central
ecliptic point, and is given by :
dṛggatijyā = [R² - (dṛkkṣepajyā)²]^(1/2)
where R is the radius of the celestial sphere.
In the Mahābhāskarīya¹, the expression for the Sun's
dṛggatijyā is :
(Sun's dṛggatijyā)²
= (Sun's dṛgjyā)² - (Sun's dṛkkṣepajyā)²
and similar is the expression for the the Moon's dṛggatijyā.
Now lambana, which is the difference of the parallaxes,
in longitude, of the Sun and the Moon, is given by the expres-
sion :
Lambana = Moon's lambana - Sun's lambana.
Sun's lambana
= Sun's dṛggatijyā × Earth's semidiameter / Sun's true distance in yojanas
Moon's lambana
= Moon's dṛggatijyā × Earth's semi-diameter / Moon's true distance in yojanas
These lambanas are in terms of minutes of arc etc².

1. स्वदृग्दृक्क्षेप गुणयोर्वर्गे विश्लेषजे पदे ।
   दृग्गतिज्ये भवेतां ते भास्करामृत तेजसः ॥ -MBh. V, 23
2. स्वदृग्गतिज्यया व्यास भेद संवर्ग संभवम् ।
   पृथग्योजन कर्णाप्तं लिप्ताद्यं लम्बनं विदुः ॥
   (Cont. on Page 225}