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Mathematics in Ancient and Medieval India c4.s3.t5: Brahmagupta (c. 628 A.D.)

Mathematics in Ancient and Medieval India c4.s3.t5

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Brahmagupta (c. 628 A.D.)

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The most prominent of Hindu mathematicians belonging to the school of Ujjain was Brahmagupta. His father’s name was Jiṣṇu. He wrote in 628 A.D. his *Brāhmasphuṭasiddhānta* at the age of thirty¹ and the other astronomical work, *Khaṇḍakhādyaka* in 655 A.D.² He lived during the reign of Śrīvyāghramukha, the greatest king of the Cāpa dynasty.

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¹ *śrīcāpavaṁśatilake śrīvyāghramukhe nṛpe śakanṛpālāt/* *pañcāśatsaṁyaktairvarṣaśataiḥ pañcabhiratītaiḥ//* *brāhmaḥsphuṭasiddhāntaḥ sajjanagaṇitagolavit prītyai/* *triṁśadvarṣeṇa kṛto jiṣṇusutabrahmaguptena//* (*Brāhmasphuṭasiddhānta*, *Ch.* 24, *v.* 7-9) “In the reign of Śrī Vyāghramukha, of the Śrī Cāpa dynasty, five hundred and fifty years after the Śaka king (i.e., 628 A.D. having passed, Brahmagupta, the son of Jiṣṇu, at the age of thirty, composed the *Brāhmasphuṭasiddhānta*, for the gratification of mathematicians and astronomers”.

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² Vide. P. C. Sengupta’s tr. of the *Khaṇḍakhādyaka*, Introduction, p. XXVII, University of Calcutta, 1934.

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The *Brāhmasphuṭasiddhānta*³ which is complete in twentyfour chapters includes two chapters on mathematics namely; *Gaṇitādhyāya* (chapter on mathematics) and *Kuṭṭakādhyāya* (chapter on indeterminate equations). Many other details of mathematical interests have been found in other chapters of this work. The *Gaṇitādhyāya* deals with cyclic triangle and quadrilateral, rules for arithmetical operations involving zero, negative numbers; quadratic equations. The *Kuṭṭakādhyāya*, contains solutions of the indeterminate equations of both first and second degree. The *Spaṣṭādhikāra* chapter contains, however, trigonometrical notations including sine table. In chapter IX of his *Khaṇḍakhādyaka*, Brahmagupta gave a method of obtaining from the given table of sines, the sines of intermediate angles.

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³ Ed. with commentary of Sudhākara Dvivedi, Benaras, 1902; Published originally in the *Pandit*, (n.s.) 23-24, 1901-2; tr. into English (a portion only) by H. T. Colebrooke, vide his *Algebra with Arithmetic and Mensuration from the Sanskrit of Brahmagupte and Bhascara*, London, 1817; Ed. with *Vāsanābhāṣya* by Ram Swarup Sarma and a board of editors and with notes by Satya Prakash. 4 vols. Indian Institute of Astronomical and Sanskrit Research, New Delhi, 1966.

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Brahmagupta was a bitter opponent of Āryabhaṭa I, though in his *Khaṇḍakhādyaka*, in his old days he seems to have recognised Āryabhaṭa's merit and adopted one of the system of Āryabhaṭa's astronomy. Brahmagupta holds a place in the history of Indian Civilisation. His works which were translated into Arabic seem to have influenced Arabian astronomy and mathematics in the 8th century A.D. possibly before Arabian scholars came to know about Ptolemy's work.¹

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¹ Arabian *Sindhind* and *Alarkand* were probably translations of *Brāhmasphuṭasiddhānta* and *Khaṇḍakhādyaka*. According to some scholars, *Sindhind* may be a translation of the *Sūryasiddhānta*, or some other work bearing the title *siddhānta* ( Smith, D. E. History of Math., *1*, p. 167-8. Dover Publication ).

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