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Lengths and Curvitiesof curve Lines and curvilinear Figures, 
and this without taking away Radicals, and to extend to 
the like Problems in Curves ufually called Mechanical, 
and to inverfe Problems of Tangents and others more diffi- 
cult, and to almofl all Problems, except perhaps fome Nu- 
meral ones like thofe of Dicphantus. And Mr. Leibnitz, in 
his Letter of Aug . 2.7. 1676, reprefented that he could not 
believe that Mr. Newton * s Method was fo general; 
Mr. Newton in the Firfl of his three Letters fet down his 
Method of Tangents deduced from this general Method, 
and illuflrated it with an.Example, and faid that this Me- 
thod of Tangents was but a Branch or Corollary of his Ge- 
neral Method, and that he took the Method of Tangents of 
Slujius to be of the fame kind : and thereupon Mr. Leibnitz , 
in his Return from Paris through England and Holland into 
Germany, was confidering how to improve the Method of 
Tangents pf Slujius, and extend it to all forts of Problems, 
as we fhewed afcove out of his Letters. And in his third • 
Letter Mr. Newton illuflrated his Method with Theorems 
for Quadratures and Examples thereof. And when he had 
made fo large an Explanation of his Method, thajt Mr. Lett* 
nitz had got Light into it, and had in his Letter of June xi. 
1677 explained how the Method which he was fallen into 
anfwered to the Defcription which Mr. Newton had given of 
his Method, in drawing of Tangents giving the Method of 
Slujius, proceeding without taking away* Fradiions and Surds, 
and facilitating Quadratures ; for him to tell the Germans that 
in the Year 1684, when he firfl publifhed his Differential , 
Method, he knew nothing more ofMri Newtons mvention, 
than that he had a certain Method of Tangents, is very extra- 
ordinary and wants an Explanation. . 
. At that time he explained nothing more concerning his 
own Method, than how to draw Tangents and determin 
Maxima and Minima without taking away Fractions or Surds, 
He certainly knew that Mr, Newtons Method would do all 
• • shic 
