( >84 ) 
In the End of February or beginning of March 1677. 
Mr. Leibnitz, went from London to turir, and continuing his 
Correfpondence with Mr Oldenburg and Mr. Collin , wrote in 
July 1674. that he had a wonderful Theoreme, which gave 
the Area of a Circle or any Sector thereof exactly in a Series 
of rational Numbers; and in Oftober following, that he had 
found the Circumference of a Circle in a Series of very fimple 
Numbers, and that by the fame Method (fo he calls thefaid 
Theoreme) any Arc whofe Sine was given might be found 
in a like Series, though the Proportion to the whole Circum- 
feietree be not known His Thcforetoie therefore was for find- 
ing any Se&or or Arc whofe Sine wiis given. If the Pro- 
portion of the Arc to the whole Circumference was not 
known, the Theoreme or Method gave him only the Arc ; 
if it was known it gave him alfo the whole Circumference: 
and therefore it ivas the firfl: of Mr. Norton’s twoTheOremes 
above-mention’d. But the Demonfiration of this Theoreme 
Mr Leibnitz wanted. For in his Letter of May n. 1675. 
he defired Mr. Oldinburgh to procure the Demonfiration from 
Mr Collins , meaning the Method by which Mr. Newton had 
invented it. 
In a Tetter compos’d by Mr. Collins and dated April 1 y. 
1675’. Mr. Cldenburgh (ent to Mr. Leibnitz Eight of 
Mr Newtons and Mr. Gregorys Scries, amongft which were 
Mr. Newton' s two Series above mention’d for finding the Arc 
whofe Sine is given, and the Sine whofe Arc is given; and 
Mr. Gregorys two Series above mentioned for finding the 
Arc whofe Tangent is given, and the Tangent whole Arc 
is given. And Mr. Leibnitz in his Anfwer, dated May 20. 
1 67 y. acknowledged the Receipt of this Letter in thefe Words. 
Liter as tuas mrtlta fruge Algebraica refertas accepi, pro qttibus ti- 
bi drdcffijjimo Collinio gratias ago. Cum nunc prater tr dinar i- 
as curas Mcchanicis imprimis negotiis difirahar, non potui exa- 
minare Series quas mi ft (l is ac cum meis comparare. Ub't fecero 
perferibam tibi (ententiammedm ; n am aliquot jam anni funt quod 
invent me as via qua dam Jic ( atisjtngulari . But 
