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

130 GREEK AND INDIAN METHODS
or mn = (R sinδ × R cosω) / (R sin ω)
∴ R sin R. A. = (MN / mn) × mn = (R / R cosδ) × ((R sinδ × R cosω) / (R sin ω)) (5)
Problem II :—
Sidereal Time-intervals
Indian Method
The problem discussed above provides the method of find-
ing the sidereal time-intervals in which the signs of the zodiac
rise on the equator. To find the corresponding times at any
latitude ϕ, it is necessary to calculate and apply what is the
ascensional difference due to the elevation of the celestial pole.
This ascensional difference is called 'carakāla' or the variation in
the length of half the day. The 'sine' of this 'carakāla' is called
'carajyā.' If ch denotes this 'carakāla,'
then.¹ R. Sin ch = (R sinϕ × R sin δ × R) / (R cos ϕ × R cos δ)
Just as in the solution of the previous problem, the dec-
linational triangles or 'Krānti Kṣetras' were constructed and
used, so in the solution of this and other problems another set
of similar triangles were conceived and constructed and were
given the name 'Akṣa kṣetras.'²
Let NPZH be the meri-
dian (Fig. 7), NOH the north-
south line passing through
the observer O,P the celestial
pole, OQ the trace of the
equator on the meridian
plane, Z the zenith. Join OZ.
From Q draw QM perpendi-
cular to OZ. Then the
triangle QOM is an 'Akṣa-
kṣetra' or a latitudinal right-
angled triangle, as ∠QOM =
ϕ, the latitude of the station.
Another 'Akṣakṣetra' is thus
conceived, in the same figure, let P, P' be the north and
south celestial poles, N, the north point, AB A'B' the diurnal
Fig 7

1. Āryabhaṭīya, Gola, 26; Pañca-siddhāntikā, IV, 34; Brāhmasphuṭasiddhānta.
   II, 57-58; Sūrya-siddhānta, II, 91; Grahagaṇita, VIII, 48-49.
2. Bhāskara, Golādhyāya ( Wilkinson and Bāpudeva Śāstri's tr. ) PP. 173-76;
   also, Bhāskara, Grahagaṇita, Ch. IX. 13-17.