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"The Hindus had certainly made distinguished pro- gress in the science so early as the century immediately following that in which the Grecians taught the rudi- ments of it. The Hindus had the benefit of a good arithmetical notation ; the Greeks the disadvantage of a bad one. Nearly allied as algebra is to arithmetic, the invention of the algebraic calculus was more easy and natural where arithmetic was best handled. No such marked identity of the Hindu and Diophantine systems is observed, as to demonstrate communication. They are sufficiently distinct to justify the presump- tion that both might be invented independently of each other. " If, however, it be insisted that a hint or suggestion, the seed of their knowledge, may have reached the Digitized by 374 PAURANIK PERIOD. [BOOK V. Hindu mathematicians immediately from the Greeks of Alexandria, or mediately through those of Bactria, it must, at the same time, be confessed, that a slender germ grew and fructified rapidly, and soon attained an approved state of maturity in Indian soil. " • Equally worthy of our consideration are the same author's remarks on Hindu Astronomy. " The Hindus had undoubtedly made some progress at an early period in the astronomy cultivated by them for the regulation of time. Their calendar, both civil and religious, was governed chiefly, not exclusively, by the moon and sun ; and the motions of these luminaries were carefully observed by them : and with such success that their determination of the moon's synodical revolu- tion, which was what they were principally concerned with, is a much more correct one than the Greeks ever achieved. They had a division of the ecliptic into twenty-seven or twenty-eight parts, + suggested evident- ly by the moon's period in days ; and seemingly their own : it was certainly borrowed by the Arabians. Being led to the observation of the fixed stars, they obtained a knowledge of the position of the most remarkable ; and noticed for religious purposes, and from supersti- tious notions the heliacal rising with other phenomena of a few. The adoration of the sun, of the planets, * Algebra <SrY., from the Sanscrit. London 1817. P. xxii. fThis Lunar Zodiac was fixed, as we have seen before, in the Epic Period, about 1200 B. C. See Vol. I, pages 267 to 270. Digitized by Google CHAP. IX.] ASTRONOMY AND MATHEMATICS. 375 and of the stars, in common with the worship of the elements had a principal place in their religious observ- ances, enjoined by the Vedas : and they were led con- stantly by piety to watch the heavenly bodies. They were particularly conversant with the most splendid of the primary planets ; the period of Jupiter being introduced by them in conjunction with those of the sun and moon, into the regulation of their calendar, sacred and civil, in the form of the celebrated cycle of sixty years. " * While Hindu astronomy is as old as the Vedas, there can be little doubt that after the Christian Era, the science received much development from Greek sources. We have seen in Chapter XIII of the last Book that the Siddhdntas of the Buddhist Age were 1 greatly indebted to Greek astronomy. The Solar Zodiac, for instance, adopted by the Hin- dus, was undoubtedly of Greek origin. This Hindu " divi- sion of the zodiac into twelve signs, represented by the same figures of animals, and named by words of the same import with the zodiacal signs of the Greeks," leaves little doubt that the Hindus after the Christian Era 11 received hints from the astronomical schools of the Greeks." f Aryabhatta is the first Hindu writer on algebra and astronomy in the Pauranik Age. He was born, as he * Hindu Algebra^ &c. P. xxii, et stq. t /did P. xxiv. 376 PAURANIK PERIOD. [BOOK V. tells us himself, in A. D. 476. He wrote the Arya- bhattiya consisting of the Gttikapdda, die Ganitapada, the Kalakriyapdda, and the Golap&da. The work has now been edited by Dr. Kern, and in this work the astronomer boldly maintains the theory of the revolution of the earth on its own axis, and the true cause of solar and lunar eclipses- * As a person in a vessel, while moving forward, " says Aryabhatta, " sees an immovable object moving backward ; in the same manner do the stars, though immovable, seem to move daily. " Aryabhatta's ex- planation of the eclipses seems to have been generally accepted by his contemporaries, for we find Kalid&sa in his Raghuvansa (XIV, 40) weaving the astronomi- cal discovery into one of his apt similes, and stating 4t what in reality is only the shadow of the earth is * regarded by the people as an impurity of the pure moon." In his Golap&da Aryabhatta gives us the names of the twelve divisions of the solar zodiac. Aryabhatta's calculation of the earth's circumference, (3300 Yojanas of four Krosas each ) is not wide of the mark. Aryabhatta was born in P&taliputra, the ancient capital of Asoka the Great, and wrote early in the sixth century A. D. The revival of learning in that century was not confined to Ujjayini, although that city carried away the palm under the auspices of the illustrious Vikram&ditya. Digitized by Google CHAP. IX.] ASTRONOMY AND MATHEMATICS. 377 Aryabhatta's successor, Varithamihira, was a true born son of Avantt He was born in Avanti and was the son of Adftya D&sa, himself an astronomer. The Ujjayini list compiled by Dr. Hunter as well as Alberuni, give A. D. 505 as Var&hamihira's date, and it is probable that this was the date of his birth. We have already stated before that he was one of the " nine gems " of Vikrama's court, and it has been ascertained by Dr. Bhao Daji that the astronomer died in 587 A. D. He compiled in his famous Panchasiddh^ntikd five older Siddoantas, vis., Paulisa, Romaka, Vasishtha, Saura, and Pait&maha. We have spoken of these Siddodntas in the last Book. Var&hamihira is also the author of Brihat Sanhit£, which has been edited by Dr. Kern. It is a work consisting of no less than 106 chapters dealing with various subjects. The first twenty chapters relate to the sun, moon, earth, and planets ; chapters 21 to 39 deal with rain, winds, earthquakes, meteors, rainbow, dust- storms, thunderbolts, &c; chapters 40 to 42 treat of plants and vegetables, and commodities which are available in different seasons ; chapters 43 to 60 speak of various miscellaneous matters, including portents, house-build- ing, gardening, temples, images, &c. ; chapters 61 to 78 deal with various animals, and with men and women, &c. ; chapters 79 to 85 treat of precious stones, furni- ture, &c. ; chapters 86 to 96 treat of various omens ; Digitized by Google 37^ PAURANIK PERIOD. [BOOK V. and chapters 97 to 106, of various matters including marriages, the divisions of the zodiac, &c. The above enumeration of contents carries no ade- quate idea of the encyclopaedic nature of this great work. The amount of general information which it contains, apart from its merit as an astronomical work, is of the utmost value to the historian. Thus, chapter 14 is a complete geography of India of the sixth century, and mentions the names of numerous provinces and towns. Chapters 41 and 42 contain an enumeration of a vast number of commodities, vegetable and manufactured, which is of the utmost value for a detailed examination of the civilization of the age. So chapters 61 to 67 speak of various animals, and chapters 79 to 85 of various articles from a diamond to a toothbrush ! Chapter 58 is of special in- terest to us, because it lays down rules for the construc- tion of various images, viz., R£ma, Bali, Vishnu with 8 or 4 or 2 hands, Baladeva, a goddess between Krishna and Baladeva, S&mba, Brahmd with four faces, Indra, Siva and his consort, Buddha, the god of the Arhats (Buddhist saints), the Sun, the Linga, Yama, Varuna, Kuvera, and Ganesa with his elephant head. And in chapter 60 we are told that Bhdgavatas worship Vishnu, the Magas worship the Sun, and the twice-born, smear- ed with ashes worship Siva ; the Mdtris are worshipped by those who know them, and Br&hmans worship Brahml The Sakyas and the naked Jainas worship igitized by Google CHAP. IX.] ASTRONOMY AND MATHEMATICS. 379 the all-benevolent and calm-souled god (Buddha). "Each sect should worship, according to its peculiar rules, the deity whom it worships." These passages attest the toleration of the 6th century A.D. ; a Hindu after the time of Sankardch&rya would not thus enumerate the "all-benevolent" and "calm-souled" Buddha in the list of deities. In the following century Brahmagupta wrote (in 628 A. D. ) his Brahma Sphuta Siddh&nta. The work comprises twenty-one chapters. The first ten contain an astronomical system, describing the true places of the planets, the calculation of lunar and solar eclipses, the position of the moon's cusps, the conjunctions of planets and stars, &c. The next ten chapters are sup- plementary ; and the last chapter explains the astron- omical system in a treatise on spherics. The twelfth and eighteenth chapters have been translated by Cole- brooke. After Brahmagupta came the long period of the dark ages and political convulsions. When these ended in the establishment of Rajput power in India, another great mathematician arose. The renowned Bh&skar&ch&rya was born, as he tells us, in 1 1 14 A. D., and completed his great work known as the Siddhanta Siromani in 1150 A. D. The preliminary portions of this work are the Vljaganita (algebra) and the Lil&vati (arith- metic ), and have been translated by Colebrooke ; and the Gol&dhy&ya portion on spherical trigonometry Digitized by Go PAURANIK PERIOD. [BOOK V. has been translated by Wilkinson and revised by the renowned mathematician, Pundit Bapudeva S&stri.