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

Chapter IV

Subject Matter Classified in the

Brāhmasphuṭasiddhānta

& Khaṇḍakhādyaka

It needs no emphasis that Āryabhaṭa commanded a great influence as an astronomer not only prior to Brahmagupta but during his days also, and we have seen how Brahmagupta quoted this great authority in his writings, sometimes borrowing from him and sometimes contradicting him or improving upon his calculations. Āryabhaṭa's great work is known as the Aryabh- atīyam written in 499 A. D. Āryabhaṭa was born in 476 A. D. ( Kaliyuga Saṁvat 3577 ). The Aryabhaṭīyam is also known as the Aryasiddhānta. For details about Āryabhaṭa the reader is referred to the Chapter entitled "Aryabhaṭa lays Foundations of Algebra" (Founders of Sciences in Ancient India, 1965, Chapter X). This great work was written in Kusumapura, (modern Patna, Bihar).

Divisions of Āryabhaṭīyam

The Aryabhaṭīyam is divided into four chapters called Pāda: (i) the Gītikā Pāda, with ten verses; (ii) the Gaṇita Pāda with 33 verses; (iii) the Kālakriyā Pāda with 25 verses and (vi) the Gola Pāda with 50 verses. In the Gaṇita Pāda, a chapter on mathematics, we have such subjects : squares (varga), cubes (ghana) (verse 3), square-root (vargamūla) (4), cube-root (ghanamūla) (5) ; area of a triangle, volume of a prism (6), area of a circle, volume of a sphere (7), area of a quadrilateral (viṣamacaturasra) (8); circumfe- rence of a circle (10), Rsine (radius x sine) (Jīvā) (11); determina- tion of the Rsine of the zenith distance, the base (bāhu) of a right- angled triangle, and the upright (koṭi) of a right-angled triangle (16); hypotenuse (karṇa) of a right-angled triangle and ardhajyā (17), Reversed-sine (śara) (18), areas of series-figures (śreḍhīphala) (19), rule of three (trairāśika) (23), reduction of fractions (savar- ṇīkaraṇa of bhinna) (27) ; inverse-rule of three (vyasta) (28) ;