»er. i.] DISSERTATION SECOND. 9 



after this, in 1704, that Newton himself first published a work 

 on the new calculus, his Quadrature of Curves, more than 

 twenty-eight years after it was written. 



These discoveries, however, even before the press was 

 employed as their vehicle, could not remain altogether un- 

 known in a country where the mathematical sciences were 

 cultivated with zeal and diligence. Barrow, to whom they 

 were first made known by the author himself, communicated 

 them to Oldenburgh, the Secretary of the Royal Society, 

 who had a very extensive correspondence all over Europe. 

 By him the series for the quadrature of the circle were made 

 known to James Gregory, 1 in Scotland, who had occupied 

 himself very much with the same subject. They were also 

 communicated to Leibnitz in Germany, who had become 

 acquainted with Oldenburgh in a visit which he made to 

 England in 1673. At the time of that visit, Leibnitz wag 

 but little conversant with the mathematics ; but having after- 

 wards devoted his great talents to the study of that science, 

 he was soon in a condition to make new discoveries. He 

 invented a method of squaring the circle, by transforming it 

 into another curve of an equal area, but having the ordinate 

 expressed by a rational fraction of the absciss, so that its 

 area could be found by the methods already known. In this 

 way he discovered the series, so remarkable for its simplici- 

 ty, which gives the value of a circular arch in terms of the 



rim clarissirmun rirum voluissc turn ilia, turn alia qua: apud ipsum 

 pretnit edidissc. Cum vero Mud nondum fecerit libel eorum non- 

 nulla hie attingere ne pereanV Among these last is an account 

 of the fluxionary notation, according to which the fluxions of 

 flowing quantities are distinguished by points, and also of certain 

 applications of this new algorithm, extracted from two letters of 

 Newton, written in 1792. — Opera, Tom. II. p. 390, &c— There 

 is no evidence of his notation having existed earlier than that 

 date, though it be highly probable that it did. 



1 Note A, at the end. 



2 



