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

88 BRĀHMASPHUṬASIDDHĀNTA & KHAṆḌAKHĀDYAKA ing of Āryabhaṭa I).¹ (viii) A rule for finding the longitude of the true mean planet according to midnight-day reckoning is as follows : Apply half the Śīghraphala and (then) half the mandaphala to the longitude of the planet's own mandocca (reversely). From the resulting longitude of the planet's mandocca cal- culate the (mandaphala and apply it to mean longitude of the planet : the resulting longitude of planet is stated to be) the true-mean longitude of the planet. This is stated to be another difference (of the midnight day-reckoning) ² (ix) Length of the circle of the sky and derivation of the lengths of the orbits of the planets are given as follows : Multiply the revolutions of the Moon (in a yuga) by 3, 240,000 and then discard the zero in the unit's place : (this is the length of the circle of the sky in terms of yojanas). (Severally) divide that by the revolutions of the planets (in a yuga): thus are obtained the lengths of the orbits of the respective planets in terms of yojanas.³ From these stanzas (from 20-35), it is evident that one yojana of the sunrise day-reckoning is one and a half times that of the midnight day-reckoning. Now from stanza 22, it appears that 300 is to be added to the number of civil days in a Mahāyuga. According to the Āryabhaṭīya. the number of civil days in this cycle is 1,577,917, 500, which increased by 300, becomes 1,577,917,800, the number of

1. शोधयित्वा क्रमात् पातान् विक्षेपार्शान् प्रसाधयेत् । —31 योगविश्लेषणोत्पत्तिरेकानेकस्वदिग्वशात् । विक्षेपः स स्फुटो ज्ञेयो ग्रहस्यैकस्य कीर्तितः ॥ —32 अन्यस्याप्येवमेव स्याच्छेषाः प्रागुक्त कल्पनाः । एतत्सर्वं समासेन तन्त्रान्तरमुदाहृतम् ॥ —MBh. VII. 31 (ii)–33
2. शीघ्रमन्दोच्चचापाधैसंस्कृता त् स्वीयमन्दतः । स्फुटमध्यग्रहः स धै विशेषः परिकीर्तितः ॥ —MBh. VII. 34
3. वेदाश्विरामगुणितान्य युताहतानि । चन्द्रस्य शून्यरहितान्यथ मण्डलानि ॥ र : स्वैर्हृतानि भगणैः क्रमश्रो ग्रहाणां । कक्ष्या भवन्ति खलु योजनमण्ड्रस्था ॥ —MBh. VII. 35