VOL. XXX.] PHILOSOPHICAL TRANSACTIONS. SOQ 



These stars are only 3 or 4 in all former catalogues, but the British of Mr. 

 Flamsteed increases them to l6; to them we have added 3 others, somewhat 

 smaller. If the times of the occultations of any one of these stars, or even of 

 any two of them in the same night, be accurately observed under distant meri- 

 dians, the difference of those meridians may thence be truly obtained, especially 

 since the moon's parallax, and all other requisite parts of her theory, are at 

 present sufficiently stated and known. 



Solution of a Problem, lately proposed by M. Leibnitz to the English Geometri- 

 cians. By Dr. B. Taylor, Seer. R. S, N° 354, p. 695. Translated from 

 the Latin. 



Though the late M. Leibnitz, in the controversy about the inventor of thg 

 method of fluxions, which he chooses to call the differential method, and 

 obstinately to appropriate the invention to himself, has given no answer to 

 those arguments which are alleged in favour of Mr. Newton as the inventor; 

 yet by his encouragement Mr. John Bernoulli has proposed a problem to be 

 solved by the English geometricians. But whether the problem be solved by 

 them or not, it can be no argument against the right of Mr. Newton. How- 

 ever, that they may not take occasion to triumph on this problem not being 

 attempted by the English, I venture to give my solution, such as it isj though 

 the problem is nowise remarkable either for its use or difficulty. 



The problem at first proposed by M. Leibnitz, was understood to mean no- 

 thing more than that conic hyperbolas, described with the same centre and 

 vertices, should be cut at right angles. But when he was informed that this 

 case had been immediately solved by some Englishmen, he replied, that it was 

 not the solution of a particular case, but a general solution that was required. 

 For which reason those particular solutions were not published, though in the 

 Philos. Trans. N*^ 347, a very general solution appeared. But M. Leibnitz and 

 his partisans were not content with this, but seemed rather to despise it, as if 

 the author was not able to apply it to any particular case. But if they could 

 not perceive how equations were to be deduced from it, that is to be imputed 

 to their own unskilfulness. A little before the death of M. Leibnitz, the fol- 

 lowing problem at last came out; which may be solved after different manners, 

 by pursuing the steps of the general solution just mentioned; but at present we 

 shall solve it in the following manner : 



The Problem. " On the right line ag, fig. 7, pi. 8, as an axis, from the 

 point a to draw an infinite number of curves, as abd, of such a nature, that 

 the radii of curvature bo, drawn from every point b, may be cut by the axis ag. 



