Talk:Indian mathematics
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editSir William Wilson Hunter wrote: "The Hindus attained a very high proficiency in arithmetic and algebra independently of any foreign influence." The romance of the composition of Lilavati - the standard Hindu text book on Arithmetic by Bhaskaracharya - is very interesting and charming. It deals not only with the basic elements of the science of arithmetic but also with questions of interest, of barter, of permutations and combinations, and of mensuration. Bhaskaracharya knew the law of gravitation. The Surya Siddhanta is based on a system of trigonometry. Professor Wallace says: "In fact it is founded on a geometrical theorem, which was not known to the geometricians of Europe before the time of Vieta, about two hundred years ago. And it employs the sine of arcs, a thing unknown to the Greeks." The 47th proposition of Book I of Euclid, which is ascribed to Pythagoras was known long ago to the Hindus and must have been learnt from them by Pythagoras. (source: Indian Culture and the Modern Age - By Dewan Bahadur K. S. Ramaswami Sastri Annamalai University. 1956 p. 67). [1] [2]
As George Frederick William Thibaut (1848-1914) author of Mathematics in the making in Ancient India, remarked: ...And Thibaut then lays down the principle, which should never be overlooked by Indian historians, that whatever science "is closely connected with the Ancient Indian religion, must be considered as having sprung up among the Indians themselves, and not borrowed from other nations."
(source: Journal of the Asiatic Society of Bengal, 1875. p. 227 and A History of Civilization in Ancient India Based on Sanscrit Literature - By Romesh Chunder Dutt p. 240-243) [3]
Jean-Claude Bailly said: " The motion of the stars calculated by the Hindus before some 4500 years vary not even a single minute from the tables of Cassine and Meyer (used in the 19-th century). The Indian tables give the same annual variation of the moon as the discovered by Tycho Brahe - a variation unknown to the school of Alexandria and also to the Arabs who followed the calculations of the school... "The Hindu systems of astronomy are by far the oldest and that from which the Egyptians, Greek, Romans and - even the Jews derived from the Hindus their knowledge."
(source: The Politics of History - By N. S. Rajaram Voice of India ISBN 81-85990-28-X. 1995 p. 47).[4]
The paper of John Playfair (1748-1819) (FRS and Professor of Mathematics at the University of Edinburgh) is a detailed review (published in 1790) of the book 'Traite de ';astronomie Indienne et Orientale,' by J. S. Bailly (Paris 1787), the famous French historian of astronomy. Taken as if by surprise by Bailly's rather positive evaluation of the origin, antiquity and achievements of Indian astronomy, Playfair states that: "I entered on the study of that work, not without a portion of skepticism....The result was, an entire conviction of the accuracy of the one, and of the solidity of the other.' Both Bailly's book and Playfair's article examine in detail some of the astronomical tables (based on Indian astronomy) that the French had procured from Siam (Thailand), Playfair's main conclusions are the following:
(source: India Through The Ages: History, Art Culture and Religion - By G. Kuppuram p.671-672).[5]
Sir William Hunter (1840-1900) says: "The astronomy of the Hindus has formed the subject of excessive admiration." "Their fame spread throughout the West, and found entrance into the Chronicon Paschale (commenced about 330 A.D. and revised under Heraclius 610-641). "The Sanskrit term for the apex of a planet's orbit seems to have passed into the Latin translations of the Arabic astronomers. The Sanskrit uccha became the aux (genaugis) of the later translators." "The Arabs became their (Hindus) discipline in the 8th century, and translated Sanskrit treatises, Siddhanats, under the name Sindhends." [6] [7]
Albrecht Weber (1825-1901) says:
"The fame of Hindu astronomers spread to the West, and the Andubarius (or probably, Ardubarius), whom the Chronicon Paschale places in primeval times as the earliest Indian astronomer, is doubtless none other than Aryabhatta, the rival of Pulisa, and who is likewise extolled by the Arabs under the name of Arjabahar."
(source: Indian Literature - By Albrecht Weber ISBN: 1410203344 p. 255).[8] [9]
T. N. Colebrooke, has said: "Compared to the scientists of Europe, Kanaada and others Indian scientists were the global masters in this field."
Horace Hyman Wilson (1786-1860) says: "The Hindus have the art of smelting iron, of welding it, and of making steel, and have had these arts from times immemorial."
EJH Mackey (Further Excavations at Mohenjo Daro 1934) has said „It is surprising to find that an instrument was actually used for drawing circles in the indus Valley as early as 2500 BC.“
- Marquis Pierre Simon de Laplace wrote: "Nevertheless the ancient reputation of the Indians does not permit us to doubt that they have always cultivated astronomy, and the remarkable exactness of the mean motions which they assign to the Sun and the Moon necessarily required very ancient observation."
- attributed at [10] , (source: Hinduism and Scientific Quest - By T R. R. Iyengar p. 153-154 South Asia Books ASIN 8124600775).
- Yaqubi, Shiite historian, wrote in the ninth century: "Hindu are more exact in astronomy and astrology than any other people.
- attributed at [11], (source: Hinduism and Scientific Quest - By T R. R. Iyengar p. 153-154 South Asia Books ASIN 8124600775).
William Robertson wrote: "It is highly probable that the knowledge o the twelve signs of zodiacs was derived from India."
Horace Hyman Wilson (1786-1860) wrote: "The science of astronomy at present exhibits many proofs of accurate observation and deduction, highly creditable to the science of the Hindu astronomers. The division of the ecleptic into lunar mansions, the solar zodiac, the mean motions of the planets, the procession of the equinox, the earth's self-support in space, the diurnal revolution of the earth on its axis, the revolution of the moon on her axis, her distance from the earth, the dimensions of the orbits of the planet, the calculations of eclipses are parts of a system which could not have been found amongst an unenlightened people." But the originality of the Hindus is not less striking than their proficiency. Wilson says: "The originality of Hindu astronomy is at once established, but it is also proved by intrinsic evidence, and although there are some remarkable coincidences between the Hindu and other systems, their methods are their own." [12]
- It (Bhaskara’s Cakravala method, today known as "inverse cyclic“ method) is beyond all praise: it is certainly the finest thing achieved in the theory of numbers before Lagrange”. - Herman Hankel (1839 - 1873), the famous German mathematician
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Professor Wallace says: "However ancient a book may be in which a system of trigonometry occurs, we may be assured it was not written in the infancy of the science. Geometry must have been known in India long before the writing of Surya Siddanata." which is supposed by the Europeans to have been written before 2000 B. C. E.