371 



VIGA QANITA. 



VIGA GANITA. 



372 



and that of Vieta better than any description. Accordingly, both 

 Cossali and Libri state the asserted resemblances without specific 

 citation. When will the writer who asserts that Cardan was substan- 

 tially in possession of Vieta's algebra, attempt to substantiate his 

 assertion by putting so much as half a page of the former side by side 

 with one of the latter ? 



VIGA GANITA, the name of the principal Hindoo work on Algebra 

 which remains. In our notice of DIOPHANTUS, the Alexandrian 

 mathematician, we referred to the head Viga Ganita the consideration 

 of the question whether the method of analysis which bears his name, 

 but of which it is impossible to suppose he was the inventor, was 

 borrowed from certain Greek predecessors, or whether he derived 

 the original suggestion from India. We have also referred to this 

 article all matters which relate to the astronomical and arithmetical 

 science of the Hindoos, because there is not enough to be said on the 

 subject or the writers, to make it worth while to distribute what we 

 have to say under heads in a work like the present. We cannot 

 pretend to the knowledge of Oriental matters which is necessary to 

 form the most positive judgment upon the controversy; but it is of 

 more consequence to our readers to see the manner in which the 

 question has been discussed, than to be put in possession of any new 

 statements of opinion ; and it is of some importance that those who 

 may hereafter write on the subject, should see that a disposition to 

 support system is soon pointed out, even in ordinary works of re- 

 ference. 



In 1687 La Loubore, returning from his embassy to Siam, brought 

 home what are called the Siamese Tables. In 1750 Du Champ, a 

 missionary, sent home another set of tables, from Christnabouram (the 

 Kistnabaram of the ordinary maps?), in the Carnatic. About the 

 same time Patouillet, another missionary, sent home another set, 

 nameless, but supposed to answer to the latitude of Narsapur, near 

 Masulipatam. In 1769 the astronomer Le Gentil brought with him 

 from India, where he had been to observe the transit of Venus, the 

 tables of Tirvalore. These were all the documents of Indian astro- 

 nomy which were known when Bailly published his history of that 

 subject. The professed epochs of these tables are Siamese, A.D. 638 ; 

 Christnabouram, A.D. 1491; Narsapur, A.D. 1569; Tirvalore, B.C. 3102, 

 the beginning of the Cali Yug, or fourth great age of the Hindoos. 



These tables, with the exception of some remarks by D. Cassini and 

 Le Gentil, excited no great notice till they impressed the active imagi- 

 nation of Bailly with the idea that the epoch of the Tirvalore Tables 

 was that at which they were actually made, and that consequently 

 they represent actual observation made nearly five thousand years 

 BKO. We have seen, in the article cited, the manner in which he rode 

 this singular hobby, and how he even changed it at last for one still 

 more strange, in inventing a people unknown to history to be the 

 original progenitors of all astronomical science. Bailly had learned 

 from his Indian teachers not to be nice about a few thousand years ; but, 

 as it has been mercifully said that we are not to judge of the tempta- 

 tion to which a man has yielded, without taking into consideration the 

 amount which he may possibly have resisted, we may remember that 

 the Hindoo Calpa was upwards of four hundred millions of years, and 

 that Bailly, when at his wildest, never asked for more than eight or 

 nine thousand. His latest opponent, Bentley, who, as we shall see, had 

 the same sort of fault as himself, petitioned for and obtained a sort of 

 certificate in his own favour from Maskelyne, who states that, to his 

 knowledge, Lalande and Laplace considered Bailly as a superficial 

 astronomer and an indifferent calculator. But Bailly was a better 

 calculator than Laplace, and a better astronomer (in the sense in 

 which Laplace was an astronomer) than Lalande. 



The antiquity of Hindoo astronomy found favour in the eyes of 

 Playfair, and was supported by him in the ' Edinburgh Transactions,' 

 in a paper which is reprinted in his miscellaneous works. It was 

 opposed by Leslie, who regarded everything Indian with abhor- 

 rence: his gross ignorance and reckless assertions were exposed by 

 Colebrooke ('Algebra,' &c. Introduction, p. 59). Playfair's only 

 authority was Bailly ; and his paper amounts to little more than a 

 reiteration, in his own elegant manner, of the main points of Bailly's 

 argument. Sir W. Jones evidently leans to the side of antiquity ; and, 

 placing the foundation of the Indian system about B.C. 2000, seems to 

 suppose that astronomical knowledge was nearly of as old a date ; but 

 he does not enter into the question as a mathematician. We next 

 come to Delambre.a mind the opposite of Bailly's in every particular : 

 he was seduced by the regular and demonstrated systems of the 

 Greeks into the belief that the origin of all astronomy which deserves 

 the name must have been Grecian. Relying upon nothing but con- 

 temporary written documents, his mode of meeting every conjecture, 

 however probable, is simply that of treating it as conjecture. It is 

 evident that the spirit of system is as strong in him as in Bailly, the 

 current only setting in a different direction ; hia mode of arguing 

 equally keeps out truth and falsehood, when it comes on unwritten 

 evidence. The admissions which he is obliged to make in favour of 

 Indian arithmetic and algebra, are evidently wrung from a most 

 unwilling BOU! ; and not content with overthrowing most completely 

 the premises of Bailly's argument, he endeavours to insinuate that all 

 the astronomy of the Eastern world either did come or might have 

 come from the Greeks : in his mind the latter is the same thing as the 

 former. Much of the matter of Delambre's chapters on the subject is 



drawn from the writings of Davis and the earlier writings of Bentley. 

 Colebrooke's 'Algebra,' &c. only appeared in time for him to consider 

 it in the preface to the History of Astronomy in the Middle Ages. He 

 did not see Colebrooke's work : the account of it in the ' Edinburgh 

 Review' was, he says, better for his object (and ho puts it in Italics) 

 than the work itself, on account of the accompanying remarks. It is 

 the only instance that we can find in which an article in a review 

 serves Delambre's purpose better than the historical documents on 

 which it was written. 



Since tho time of Bailly, three Anglo-Indians have written on the 

 subject of Hindoo science, more or less controversially : Samuel Davis, 

 Henry Thomas Colebrooke, and John Bentley. The first two are the 

 only writers in our list who seem to have no personal wish that the 

 astronomy of which they treat should have any particular date. Mr. 

 Colebrooke states that Mr. Davis was the first who opened to the 

 public a correct view of the astronomical computations of the Hindoos. 

 Mr. Colebrooke was one of the most eminent of Sanskrit scholars, an 

 indefatigable Indian antiquary, and more than well informed in mathe- 

 matics and astronomy. His account of the Hindoo systems of philo- 

 sophy, as published in his ' Miscellaneous Essays," is by far the best 

 which exists; and all that he has written on their science is done in 

 the most careful and conscientious spirit. We may even say that it was 

 his bias to allow the least possible weight to his own arguments, and 

 the greatest to all that could make for his opponents. For instance, 

 when he has brought the time of Aryabhatta (presently mentioned) 

 to "some ages before the 6th century," he places him in the 5th 

 century A.c., and requires no other conclusion to be granted. But 

 when he comes to speak of Diophantus (of whom, the earlier he wrote, 

 the more likely is it that he did not borrow his algebra from India), 

 he is willing that it should be " confidently affirmed " that he cannot 

 be later than the 4th century, because (such are his grounds) Suidas 

 sta.tes that Hypatia wrote a commentary on some Diophantus, most 

 likely the writer now known by that name, and an author of uncertain 

 date in the ' Anthologia ' wrote an epigram upon him. Throughout 

 his writings there is this apparent carelessness of making the most of 

 his own argument, and the least of that of his opponents, to an 

 extent which, while it makes us feel we are certainly on the safe side 

 in following him, causes us to regret that so cautious an investigator 

 should not have given us his limits in both directions. We consider 

 him by far the safest guide, both in point of learning and judgment, 

 taking the former from the general report of Oriental scholars ; and 

 accordingly we shall represent him as to dates and facts, even where 

 we do not follow him. 



Mr. Bentley, the last named of the three, is the Bailly of those who 

 oppose the antiquity of Hindoo astronomy. In his earlier writings, 

 which are to be found (as well as those of Davis and some of those of 

 Colebrooke) in the 'Asiatic Researches/ he does not deserve any such 

 epithet ; his opinions, though strong, are accompanied by their sup- 

 ports moderately stated. His paper ' On the Antiquity of the Surya 

 Siddhanta' was published in 1799 : it was not till 1823 that he pub- 

 lished at Calcutta his ' Historical View of the Hindoo Astronomy,' 

 which was reprinted in England in 1825. It is in this work that he 

 has surpassed Bailly in his own line. The Hindoo works are forgeries 

 by the dozen : Bentley knows who forged them, and why. The 

 upholders of Indian antiquity are dupes, or worse ; they are to take 

 the stain (see his preface) of supporting all the horrid abuses and 

 impositions of the Hindoo superstition, " the burning of widows, the 

 destroying of infants, and even" (even !) "the immolation of men." 

 They conspire to overturn the Mosaic account ; and they calumniate 

 the just endeavours of those who attempt to stop the torrent of im- 

 position. It is worth while to state an instance or two of Mr. Bentley's 

 mode of proceeding, as some of our readers may have no other autho- 

 rity on the subject. 



Bhascara, the author of the Liliwati and Viga Ganita, lived, accord- 

 ing to Mr. Colebrooke, who gives his reasons, in the 12th century. A 

 version of the former, by one Faizi, was made, at the command of the 

 emperor Akbar, in 1537. It does not please Mr. Bentley that it should 

 be so, and he accordingly informs us that Bhascara's work was pre- 

 sented to Akbar, the author being then alive ; but that, in order to 

 give a false antiquity to the work, it was represented as that of 

 another Bhascara, who lived some centuries before. Not a single bint 

 at any authority is given ; it is a simple statement, as of the author's 

 own knowledge ; and is only one out of hundreds of the same kind, 

 all of which Mr. Bentley calls in different places " absolute facts," 

 " demonstrated facts," &c. 



Again, Mr. Colebrooke mentions a treatise which he found in his 

 library, the Siddhanta-Sphuta. This is one of Mr. Bentley's mass of 

 forged treatises ; but in this instance he declares he knew the forger. 

 A native, he says, offered his services to him, informed him that his 

 profession was ' book-making,' in rather an odd sense, for he said he 

 could forge any book whatever. This native was, after being con- 

 temptuously dismissed by Mr. Bentley, in the employment of Mr. 

 Colebrooke, at least so the former affirms ; and on this native he fixes 

 the forgery, as he asserts it to be, of the Siddhanta-Sphuta, giving us 

 to understand that the keen and critical eye of Mr. Colebrooke could 

 be deceived by so shallow an artifice as a recent forgery laid among his 

 papers by his own servant. And he makes this adroit native inter- 

 polate other books of Mr. Colebrooke's, so that the latter, in fact, had 



