373 



VIGA GANITA. 



VIGA GANITA. 



371 



a manufactory of falsified history on his own premises, from which his 

 opponent could destroy the genuineness of any passage he pleased. 

 Mr. Bentley doea not tell us in what language he talked with this 

 native, but we strongly suspect that they misunderstood each other. 



On the grounds of the complete absence of all reference to autho- 

 rity, the certainty of all the conclusions (for there is rarely an admis- 

 sion of auy degree of probability less than certainty), and the temper 

 of the writer, who sees nothing but folly or fraud in every one who 

 differs from him, we should feel justified in assuming that Bentley is 

 no authority whatsoever in the matter. But Colebrooke answered Mr. 

 Bentley's work, in the 'Asiatic Journal" for March 1826; and though 

 the answer does not occupy more than seven pages of the periodical 

 above cited, it sets in array such a number of inconsistencies, as well 

 as of simple unsupported assertions, as to satisfy us that our opinion 

 of Bentley as derived from his writings was a correct one. With 

 respect to the asserted forgery of the ' Brahma Sphuta Siddhanta,' 

 Colebrooke says it is " an idle guess, untrue in all its particulars." 

 But he turns the tables on his opponent, as follows : " Bontley has 

 reasoned on a treatise in his possession, which he calls the Arya Sid- 

 dhanta, and asserts to have been written by Aryabhatta." Colebrooke 

 says that none but Bentley had seen this work, that the manuscript 

 was not forthcoming, that Bentley himself did not understand Sanskrit, 

 that the natives about him well knew his notions, and that he was as 

 likely as his friend Colonel Wilford (who from his ignorance of Sanskrit 

 had had some very curious impostures palmed upon him) to have 

 been imposed upon. With regard to his own manuscript Colebrooke 

 adverts to the fact of its being (with the rest of his Oriental library) 

 deposited at the India House, in a situation accessible to Sanskrit 

 scholars. And with respect to Bentley's celebrated test, namely, that 

 tables must have been constructed at the time when they best repre- 

 sent the state of the heavens, Colebrooke adverts to an instance in 

 which Bentley himself was obliged to abandon it, because it would 

 have proved that a certain set of tables, which now exist, were 

 written fourteen hundred years hence. But as we have nothing here 

 to do with Bentley, except to give sufficient reason for not taking as 

 an authority a writer whose name is very well known (perhaps bettor 

 than that of any recent writer) in connection with our subject, we 

 refer the reader to the 'Asiatic Journal' (March, 1826, vol. xxi.) for 

 further information. 



The writers who are most cited by Hindoo astronomers bear the 

 names of Varaha-mihira and Brahmegupta. The astronomers at Ujein 

 place BKAHMEGUPTA at A.D. 628, and Mr. Colebrooke, from his own 

 description of the position of certain stars with respect to the equinox, 

 thiuks he lived towards the end of the 6th century. His work, 

 called the Brahma Sphuta Siddhanta, generally referred to under the 

 name of Brahma Siddhanta, which appears to be a correction of a 

 treatise of the latter name, was found in an imperfect state by Mr. 

 Colebrooke. He informs us that it consists in the computation of 

 mean motions and true places of the planets ; solution of problems 

 concerning time, the points of the horizon, and the position of places; 

 calculation of lunar and solar eclipses ; rising and setting of the planets; 

 position of the moon's cusps ; observation of altitudes by the gnomon; 

 conjunctions of planets with each other and with stars ; the astrono- 

 mical sphere and its circles ; the construction of sines ; the rectifica- 

 tion of the apparent planet (?) from mean motions ; the cause of lunar 

 and solar eclipses ; and the construction of the armillary sphere. It 

 also contains algebra and mensuration. 



From his astronomical data Colebrooke infers that VAKAHA- 

 MIHIBA wrote at the end of the 5th century, which is also the date 

 assigned to him by the astronomers at Ujein. He is the author of a 

 system of astrology (including astronomy), which he declares he has 

 compiled from earlier writers. There is another Vahara-mihira, whom 

 the same astronomers place in A.D. 200. But popular tradition places 

 Varaha-mihira in the time of Vikramaditya (B.C. 56), and names, as 

 hereafter noticed, several of his contemporaries. No historical 

 evidence tending to impeach this tradition has yet been put forward, 

 not prominently at least. 



AKYTABHATTA, known to the Arabs under the name of Arjabahar, is 

 placed by Colebrooke, after much discussion, at not later than the 

 5th century, possibly not far from the first. He wrote both on 

 astronomy and algebra, but none of his writings have been found, 

 except in citations. 



Authors prior to or contemporary with the last named are men- 

 tioned by name, and even cited ; such are Palisa, Parasara, and others, 

 but none of their writings are preserved. 



BHASCARA ACUABYA, the author of the Liliwati, Viga Ganita, 

 Siddhanta-siromani (of which the two former are parts), and other 

 works, is very confidently placed by Colebrooke A.D. 1150. 



The celebrated work on astronomy, the Surya-siddhanta, is o: 

 uncertain date. The term siddhanta means a system of astronomy 

 and surya is the sun. The oldest writings mention a work of this 

 name, and the Arabs state that among the systems of astronomy o: 

 the Hindoos there is one called Area (or solar). The tables mentioned 

 at the beginning of this article are generally admitted to have been 

 substantially taken from the Surya-siddhanta, as it now exists, or 

 from a common source ; but whether the work which now exists is 

 that which was mentioned by the ancient writers may be strongly 

 doubted. Bentley (in one of his early papers, before he became bis 



eader's sole authority) has discussed the question ; and assuming that 

 he age of a table is most probably that at which, one result with 

 mother, it best represents the Leavens, has deduced the year A.D. 1000, 

 or thereabouts, for the age of the Surya-siddhanta. The principle is 

 a fair one ; and Colebrooke at one time acknowledged great force in 

 3entley's argument. But it is notorious that the Hindoo writers were 

 n the habit of correcting their works from time to time, without 

 altering their names ; ao that it is very possible that there may 

 always have been a Surya-siddhanta, from the earliest times of Hindoo 

 astronomy. The name of the author, according to Bentley, is Varaha- 

 mihira ; but Colebrooke does not mention any author, aa far as we 

 can find, and certainly disputes Bentley's assertion, which also over- 

 turns itself, thus : Bentley's method (which was also that of Bailly 

 and Playfair, though their conclusions were very different), as applied 

 by himself, throws the tables of Brahmegupta into the 6th century : 

 now Brahmegupta mentions Varaha, who is nevertheless, by Bentley's 

 own conclusion from another source, the author of the .Surya-sid- 

 dhanta in the llth century. Perhaps it was this dilemma which 

 drove its author to assert forgery upon forgery, until he had set all 

 right. 



It thus appears that there is ordinarily good evidence for a succes- 

 sion of writers from the commencement of the Christian era up to 

 the 12th century, with no very great allowance of antiquity to those 

 who are cited by the earliest writers now remaining. There would be 

 nothing extraordinary in the supposition that the chain of authors 

 went back to the time of Alexander at least, since it is certain that 

 the Brahminical system existed before the time of that conqueror. 

 The only question which is worth discussing is, whether anything was 

 received from the Greeks, and if so, whether it was without inter- 

 change, and enough to give us a right to say that the Greeks were the 

 primary instructors of the Hindoos. If not, then it is to be settled 

 whether the Hindoos were the original instructors of the Greeks. It 

 is only with reference to this question that the antiquity of Hindoo 

 astronomy is of much independent interest, as a matter of discussion 

 at least : if the astronomy travelled westward, then we must place a 

 flourishing period of it before the time of Thales, and the only thing 

 to be said is, that we must probably wait for the actual ascertainment 

 of the most active age of Hindoo science, till we know that of other 

 things. But if it travelled eastward, it must be pretty clear, from the 

 dates given above, that it was the science of Hipparchus and his suc- 

 cessors of the period preceding Ptolemy, and not that of Ptolemy, nor 

 of his Saracen followers, which was communicated to the Hindoos. 



There is some evidence of communication between the Greeks and 

 Hindoos, such as it is ; but neither Delambre nor Bentley could pro- 

 duce it. All that can be obtained from the actual theories and methods 

 amounts to very little indeed, in establishing any connection ; while 

 there are hints and processes by the dozen to which there is no resem- 

 blance whatever in the Greek writings. Varaha-mihira, according to 

 Colebrooke, says that the Yavanas (lonians or Greeks) are barbarians, 

 but that this science (astronomy) is well established among them, and 

 they (the learned in it, we suppose) are revered like holy sages. The 

 name of Yavana-charya, which occurs frequently in Hindoo compila- 

 tions, is thought by the same writer to have reference to some 

 European ; and he thinks he sees in a work entitled Komaca-Siddhanta 

 a title which has some allusion to the astronomers of the west. But 

 nevertheless in another place Colebrooke cites one Yavanesvf&ra, as a 

 known Sanskrit writer. Besides this, there are several words of Greek 

 origin, and used in their Greek meaning. First hora, for astrological 

 prediction, in the sense of determining the hour ''Vahara-mihira... 

 derives the word from ahoratra, day and night.... But this formation 

 of a word, by dropping both the first and last syllables, is not conform- 

 able to the analogies of Sanskrit etymology." Next dretchcana, used 

 in the eame astrological sense with the Greek Senavos and Latin 

 decanus. Thirdly, for the minute of a degree, the Hindoos have 

 adopted, besides their own cala, one taken from the Greek Aeirra, 

 hardly altered in the Sanskrit lipta. This word in Sanskrit means 

 smeared, infected with poison, eaten ; and the dictionaries give no 

 interpretation that has any affinity with its special acceptation as a 

 technical term in the writings of Brahmegupta. Cendra, for centre, 

 resembling the Greek nevrpov, is not easily traced to any Sanskrit root. 

 If to all that precedes we add that the Hindoo astronomy employs 

 epicycles about as much as Hipparchus appears to have done, but 

 stops decidedly short of the use of them made by Ptolemy, it seems 

 very likely, especially when we consider the age in which their earliest 

 cited writers must be placed, that they had some communication with 

 the Greeks, or their writings, before or immediately after the Christian 

 era. And this surmise, founded on the points of resemblance between 

 their astronomy and that of the Greeks, receives an additional proba- 

 bility from the state of their political affairs. In the first century 

 before our era was the celebrated prince Vikramaditya of Ujein, from 

 whose reign the years of the Samvat era are counted (B.O. 56). 

 Vahara-mihira, whom Colebrooke leaves somewhere in the 5th 

 century, is the name, according to Professor Wilson, of one of nine 

 who were called the gems of the court of this prince. The prince 

 just mentioned was a noted promoter of knowledge, and the period 

 was a remarkable one. It is not unreasonable to suppose that at this 

 period, which is intermediate between the times of Hipparchus and 

 Ptolemy an effort was made to obtain -information from Greek 



