Tangent Tbe 
[ 212 ] 
i A 3 
i As 
Sine T 
Cofine Z 
For it may be made to appear, from the firft Lemma y 
and its Corollaries , that if in any of thefe Theorems, 
as fuppofe in the Firft, the Quantity A ftand for the 
Bow of the circumferibed Polygon, then will the 
Quantity T exhibited by the Theorem, be always 
bigger; but if for the Bow of the infcribed, always 
lefs than the Tangent of the Arch, how great foever 
the Number n be taken ; and confequently, if A ftand 
for the Length of the Arch itfelf, the Quantity T muft 
be equal to the Tangent > and the like may be fhewn 
for the Sine,, and, mutatis mutandis , for the Cofine. 
Thefe Principles, from whence I have here derived 
the Quadrature of the Circle, which is wanted in the 
Solution of the Problem in hand, happen to be upon 
another Account abfolutely requifite for the Reduction 
of it to a manageable Equation. But I have inlarged, 
more than was necefiary to the Problem itfelf, on the 
Ufes of this fort of Quadrature by the limiting Poly- 
gons, becaufe it is one of that kind which requires no 
other Knowledge but what depends on. the common. 
Properties of Number and Magnitude and fo may 
ferve as an Inftance to fhew that no other is requifite 
for the Eftablithment of Principles for Arithmetick and 
Geometry. A Truth, which though certain in itfelf, 
may perhaps feem doubtful from the Nature and Ten- 
dency of the prefent Inquiries in Mathematicks. For 
among the Moderns fome have thought it necefiary,. 
for 
