( i8; ) 
thefe two. Let the Radius of a Circle be r, the Arc a, and 
the Tangent t, the Equations for finding the Arc whofe 
Tangent is given, and the Tangent whofe Arc is given, 
will be thefe. 
d = t — — 4- — — — — L t9 — f rc 
* * 3 r* T Sr* ?r s l sr 8 U 
, ^ 4- ii — ' -!2H ! 6 '* 9 l J 
1 ~ a * 3 ^ * r~ ijr* ~ r jijr 4 T*i8j77»-r &*• 
In this Year (1671) Mr. Leibnitz publifhed two Tra&s at 
London , the One dedicated to the Royal-Society, the Ocher 
dedicated to the Academy of Sciences at Parts \ and in the 
Dedication of the Firfl he mentioned his Correfpondence with 
Mr. Oldtnburgh. 
In February 1 67 \ meeting Dr. Pell at Mr. Boyle's, he pre- 
tended to the differential Method of Mouton. And notwich- 
flanding that he was (hewn by Dr. Pell that it was Mouton s 
Method, he perfifled in maintaining it to be his own Inventi- 
on, by reafon that he had found it himfelf without knowing 
what Mouton had done before, and had much improved it. 
When one of Mr. Newtons Series was fenc to Mr. Gregory, 
he tried to deduce it from his own Series combined together, 
as he mentions in his Letter dated December 19. 1670. And 
by fome fuch Method Mr Leibnitz, before he left Lon don , feems 
to have found the Sum of a Series of Fractions decreafing in 
Inf nit um, whofe Numerator is a given Number and Deno- 
minators are triangular or pyramidal or triangulo-triangular 
Numbers, &c. See the Myfl ery ! From the Scries f -f- 1 q - 1 _|_ 
•jri + f 4 * &c* fubdudt all the Terms but the firfl ( viz | _j, 
1 + f +• r ) and there will remain 1 =: 1 — - -f- i -1 * 
+ 7-7+7- ^7^)=^+^+^+^+^. 
And from this Series take all the Terms but the firfl, and 
there will remain ~ = — 1 7— -X ~~ — -! — 4- 
a iXiXi » 1XJX4T3X4XM 4Xfx6l ^ 
And from the firfl Series take all the Terms but the two firfl, 
and there will remain f = ,^ + Tr, +- Hb +~« + & c - 
Hh 2. 
In 
