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

BRAHMAGUPTA A GREAT CRITIC 323 then the roof and hills would come down, which is contrary to our observation.¹ Obviously Brahmagupta is not justified in his criticism. 13. Brahmagupta points out to the differences in his calcu- lations and the calculations of Āryabhaṭa in the peripheries of the manda and śīghra epicycles of planets in the odd and even quadrants. (This difference we have shown in Table V, p. 313)² 14. Āryabhaṭa I and Bhāskara I have both given a rule for the determination of the dṛkkṣepajyās of the Sun and the Moon : Take the product of the Sun's or Moon's own madhya- jyā and udayajyā, then divide the product by the radius and then take the square of the quotient. Sub- tract that from the square of the own madhyajyā ; the square-root of that difference is known as the Sun's or Moon's dṛkkṣepajyā.³ The Sun's dṛkkṣepajyā is the Rsine of the zenith distance of that point of the ecliptic which is at the shortest distance from the zenith (this point is called nonagesimal or the central ecliptic point). The Moon's dṛkkṣepajyā is the Rsine of the zenith distance of that point of the Moon's orbit which is at the short- est distance from the zenith. The rule given above is only approximate and has been criticised by Brahmagupta.⁴ 15. In the Āryabhaṭīya, there is a rule in the Golapāda for finding the Rsine of the agrā of the true Sun; and also for the

1. प्राणेनैति कलां भूर्यदि तर्हि कुतो ब्रजेत् कमध्वानम् । आवर्त्तनमुर्व्याश्चेन्न पतन्ति समुच्छ्रयाः कस्मात् ॥ —BrSpSi. XI. 17
2. औदयिको यः परिधिर्विषमेऽन्योमेऽन्यः समे भुजस्य गुणः । तदसद्विषमान्तफलं यतो न युग्मादि फलतुल्यम् ॥ विषमेऽन्योऽन्यो युग्मे परिधिर्गुणकः क्रमोत्क्रमज्यानाम् । चक्रार्धे फलनाशो न भवति यस्मादसत् तदपि । —BrSpSi. XI. 18-19
3. स्वमध्यज्योदयाभ्यासं विष्कम्भार्धाप्तवर्गितम् ॥ मध्यज्यावर्गंतोऽपास्य स्वदृक् क्षेपं पदं विदुः ॥ —Mbh. V. 19
4. वित्रिभलग्ने दृक्क्षेपमण्डलं तदपमण्डलयुतौ ज्या । मध्याद्दक्क्षेपज्या नार्थभटोक्ताऽनया तुल्या ॥ दृक्क्षेपज्याऽतोऽसव तन्नाशादवनतेर्नांशः । अवनतिनाशात् ग्रासस्योनाधिकता रविग्रहणे ॥ —BrSpSi. XI. 29-30