VOL. XXX.] PHILOSOPHICAL TRANSACTIONS. 3Q7 



An Apology against M. John Bernoulli, Math. Profes. Basil. By Dr. Brook 

 Taylor, R. S. S. N° 36o, p. 955. Translated from the Latin. 

 In an "Epistle for an eminent mathematician, Act. Leips. 17 16, among 

 others, 1 am accused of plagiarism, as if I arrogated to myself the inventions 

 of M. John Bernoulli and others. Let them produce their examples, and then 

 they shall have an answer. I have indeed treated of many things in common 

 with others ; but I have by no means used other men's inventions as my own. 

 I have everywhere used my own analysis, except in the problem of the isoperi- 

 meters; so that I have no ways defrauded others. They should have named the 

 authors, from whom I have taken my methods. I have so great a veneration 

 for the illustrious names of Huygens, Hospital, Varignon, Leibnitz, &c. that I 

 may have erred on the contrary side, and been wanting to myself, having 

 always thought it an honour to quote such men as these. There may have been 

 some little negligence in the matter, that being wholly intent on things of im- 

 portance, I omitted some little historical matters. What problems I have 

 treated of in common with Bernoulli, are on the funicularia, on the centre of 

 oscillation, and on isoperimeters. In the two former of these I have used my 

 own analysis entirely. In the isoperimeters used that of the author James 

 Bernoulli, a man very deserving in the mathematics, to whom I now pay his due 

 honour. My solution of the problem on the centre of oscillation, was com- 

 municated to my friends from the beginning of the year 1712, as can be wit- 

 nessed by the letters of Dr. Keill. And my book was in the possession of the 

 Royal Society, and communicated to our mathematicians, from April 1714: 

 which I think necessary to mention here, lest John Bernoulli should claim that 

 solution also to himself. His two solutions were published the same year; the 

 one of them so perfectly agreeing with mine in the principles, that it might be 

 said they were both invented by the same person. The matter of the isoperi- 

 meters was invented by James Bernoulli, as hinted above ; and his solution, 

 with the analysis, is in the Leipsic Journal for 1701. His brother John's 

 analysis is in the Memoirs of the Paris Acad, for 1706; and another solution is 

 in my book. Jo. Bernoulli has lately published a commentary on the same 

 subject, in the Leipsic Acts of 17 18. There, lest he should seem to be doing 

 the same thing over again, he spitefully endeavours to detract both from my 

 solution and his brother's, objecting prolixity to the latter, and obscurity to 

 mine. He promises great things by those new undertakings ; that by means of 

 a certain principle of the law of uniformity, which he pretends no person has 

 hitherto observed, he will complete the whole matter with very little trouble, 

 and almost without calculation : but I know not by what fatality, in this affair 

 of the isoperimeters, he never finds the gods propitious : for first, that former 

 analysis of his, from beginning to end, consists of one continued blunder : 



