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

96 BRAHMAGUPTA'S KHAṆḌAKHĀDYAKA mandocca of the Sun). The value given in the Pañcasiddhān- tikā, IX.7-8) is also the same. Let us compare it with the present value. According to the astronomical constants as given in the Conn. des Temps., the longitude of the Sun's apogee in 499 A.D. (i.e. 1,400 years before 1900 A.D.) was —77° 19′19.44″ according to Conn.des Temps’ equation. —76° 40′37.22″ according to Newcomb's equation. The mean of these two values is very nearly 77⁰ as given by Brahmagupta in the Uttara text. Thus the value given by Brahmagupta is more correct than the value given by Āryabhaṭa. The Āryabhaṭīya gives the value 78⁰ which is less correct. Brahmagupta more correct than Āryabhaṭa (iii) Brahmagupta detected that Āryabhaṭa had made the Moon's apogee quicker and nodes slower, than they really are. In both the cases, Brahmagupta made rather an over-correction. We shall give the extract from Uttara-Khaṇḍakhādyaka in this connection : Multiply the ahargaṇa by 110, increase the product by 511 and divide by 30, 31; subtract the result taken as revolutions, etc., from the mean Moon; the final result is the Moon's apogee.¹ Evidently Brahmagupta assumes that the anomalistic month = 3031/110 days. This convergent to the anomalistic month was known to the author of the Vasiṣṭha Siddhānta as summarised in the Pañcasiddhāntikā² (II-2-6). According to Brahmagupta, the length of the anomalistic month = 1582236450000—4320000000 days. (BrSpSi. I.15,16,18, ───────────────────────── and 20) 577533000000—488105858 = 27.55454641 days which is for 1900 A. D. = 27.5545502 days according to Radau. = 27.554602 according to the Āryabhaṭīya.

1. द्युगणात् ख रुद्र गुणिताद् भवशरयुक्ताच्छशित्रिखाग्नि हृतात् । भगणादि फलं शोध्यं घसचन्द्राच्छशाङ्कोच्चम् ॥ (UKK. IX. 5)