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{This Lunar Zodiac was fixed, as we have seen before, in the Epic Period, about 1200 B. C. See Vol. I, pages 267 to 270. CHAP, 1X] 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 Jed 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 greatly indebted to Greek astronomy. . The Solar Zodiac, for instance, adopted by the Hin- dus, was uhdoubtedly 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 “ 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 seg. ¢ Jdid P. xxiv. 376 PAURANIK PERIOD. [BOOK v. tells us himself, in A.D. 476. He wrote the Arya. bhattiya consisting of the Gitikapada, the epnleee the K4lakriyap4da, and the Golapada. - 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.| “Asa 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 K4liddsa in his Raghuvansa (XIV, 40) weaving the astronomi- ‘cal discovery into one of his apt similes, and stating “what in reatity is only the shadow of the earth is regarded by the people as an impurity of the pure moon.” In his Golapada 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 reach) is not wide of the mark. . Aryabhatta was born in PaAtaliputra, the ancient capital of Asoka the Great, and wrote early in the sixth century A. D. The revival of tearing in that century was not confined to Ujjayini, although that city carried away the palm under the auspices of the illustrious Vikramaditya. CHAP. 1X.] ASTRONOMY AND MATHEMATICS. 377 Aryabhatta’s successor, Varahamihira, was a true born son of Avanti. He was born in Avanti and was the son of Aditya D&sa, himself an astronomer. The Djjayini list compiled by Dr. Hunter as well as Alberuni, give A. D. 505 as Varahamihira’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 ‘Panchasiddhdntikt five older Siddoantas, viz., Paulisa, Romaka, Vasishtha, Saura, and Paitamaha. We have apeaee of these Siddodntas in the last Book. Varahamihira is also the author of Brihat Sanhita, which has been edited by Dr. Kern, - It isa 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, &.; chapters 86 to 96 treat of various omens; 378 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 encyclopedic 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, wz, RAma, Bali, Vishnu with 8 or 4 or 2 hands, Baladeva, a goddess between Krishna and Baladeva, Samba, Brahm4é 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 Bhagavatas worship Vishnu, the Magas worship the Sun, and the twice-born, smear- ed with ashes worship Siva; the Matris are worshipped by those who know them, and Brahmans worship Brahma. The Sakyas and the naked Jainas worship . 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 Sankaracharya 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 tunar 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 Bhaskaraécharya was born, as he tells us, in 1114 A, D., and completed his great work known as the Siddhanta Siromani ia — 1150 A. D. The preliminary portions of this work are ‘the Vijaganita (algebra) and the Lildvati (arith- metic ), ‘and have been translated by Colebrooke ; and the Golidhyaya portion on spherical trigonometry 380 PAURANIK PERIOD. {BOOK Vv. has been translated by Wilkinson and revised by the renowned mathematician, Pundit Bapudeva SAstri. There are solutions of remarkable problems in Bhaskaricharya which were-not achieved in Europe till the 17th and 18th centuries.* The science of algebra indeed received a remarkable degree of development in India ; the application of algebra to astronomical investi- gations and to geometrical demonstrations is a pecu- liar invention of the Hindus ; and their manner of con- ducting it has received the admiration of modern European mathematicians. While such was the progress made in India in astron- omy, . algebra, arithmetic, and trigonometry, the science of geometry was lost! The Hindus had dis- covered the first elementary laws of geometry in the eighth century before Christ, and imparted it te the Greeks ; but as the construction of altars according to * A striking history hasbeen told of the problem, to find x so that ax3+6 shall be a square number. Fremat made somé progress towards solving this ancient problem, and sent it as a defiance to the English algebraists in the 17th century. Euler finally solved it, and arrived exactly at the point attamed by Bh&skara in 1150! A particular solution of another problem given by Bh&skara is exactly the same as was dis- covered in Europe by Lord Brounker in 1657; and the general solu- tion of the same problem given by Brahmagupta in the 7th century A. D, was unsuccessfully attempted by Euler, and was only accom- plished by De Ja Grange in 1767 A.D. The favorite process of the Hindus known as the Xwuétaka was not known in Brees till published by Bachet de Mezeriac in 1624 A. D. CHAP, IX.] ASTRONOMY AND MATHEMATICS. 381 * geometrical rules fell into disuse, geometry was neglect- ed, and geometrical problems were solved by algebra: ’ Arabian writers translated Hindu works on algebra in the eighth century A. D., and Leonardo of Pisa, first introduced the science to modern Europe. In trigonometry, too, the Hindus seem to have been the earliest teachers in the world; and in arithmetic they invented that system of decimal notation which the Arabians borrowed from them and taught in Europe, and which is now the property of the human race. De aipemmenenmenemened CHAPTER X. MEDICINE.