,< >85 ) 
But yet Mr. Leifantd, never took any furthermotice ofliis 
having received rhefe Series, nor how his own differed from 
them, nor ever produced any other Series then thofe which 
he received from Mr Oldenburgh , or numeral Series deduced 
from them in particular Cafes. And what he did with 
Mr. Gregory's Series for finding the Arc whofe Tangent is 
given, he has told us in the Aft a Eruditorum menfs Aprilis 
1691. pag 178. jam anno 1 6 y$, faith he, compoftumha.be- 
bam o'pufcuium Quadrature Arithmetical ab amicis ah illo tempore 
leffum, Sec. By a Theoreme for tranfmuting of Figures, 
like thofe of Dr. Bar rove and M r. Gregory, he had now found 
a Demonffration of this Series, and this was the Subject of 
his Opufculum. But he ftill wanted a Demonffration of the 
reff : and meeting with a Pretence to ask for what he wanted, 
he wrote to Mr. Oldenburg the following Letter, dated at 
Paris May i ' i . 1676 . 
Cum Georgias Mohr Eanus nobis attulerit communicatam fibi 
a DocUfimo Collinio vefro cxprdffionem rationis inter arcum & 
fitium per inf nit as Series fequentcs ; pofeto fnu x, area z, radio 1, 
z — x J r U 3 + iix* + X 7 -h ff-x 9 + &c. 
x = z - ;Z ! + L* - ^ - ®C. 
Hsc, I NQJ 7 A M , -cum nobis attulerit ille, que mihi vdde 
ingeniofa videntur , & pofterior imprimis Series -elegantiam quan- 
dam fngularem habeat : ideo rem gr at am mihi feceris, Vir cla- 
rijfime, f demon frationem tranjmiferis. Habebis vicijjim mea 
ab his longe diver [a circa hrnc rem meditata, de quibus jam aliquot 
abhinc annis ad te perfcripfffe credo, demonfratione tamen non 
addita , quam nunc polio-. Oro ut Clarijfmo Collinio mult am- a me 
falutcm dicas : is facile tiki matcriam fnppeditabit fatisfaciendi 
defiderio meo. Here, by the Word / N OU AM, one would 
think that he had never feen rhefe two Series before, and 
that his diver [a circa hanc rem meditata were fomething elf® 
than one of che Series which he had received from 
H h 3 
