t *»* 3 
Scholium. 
In like manner, as the Arches of the Polygons ferv£ 
to determine the Arch of the Circle, fo by comparing 
the Areas of the circumfcribed and infcribed Poly- 
gons, \nrT and \nTZ y the Area of the Sedor of a 
Circle may be found. For if T , T and Z are the 
Tangent, Sine and Cofine of the Arch A ; then by the 
fecond Lemma the Area of the circumfcribed Polygon 
_ 1 jr, 
r -j— t\u — r — r| n 
will be found to be ~ » r f x — t — — " y— ~ 
and the Area of the infcribed will appear to be 
z + 
z — v\ n 
rz. 
4 r n 
But upon the Expanfion of thefe Binomials it will 
appear, that no Number n can be taken fo large as to 
make the one fo big, or the other fo little, as the Area 
denoted by the Series. 
. t* t7 is. 
Xnnt 
2 
3 r r * 5 i' 
So that this Area being larger than any infcribed, 
and fmaller than any circumfcribed Polygon, muft be 
equal to the Area of the Sedor. 
It may further be obferved, that as the Arch or 
Area is found from the Sine, Cofine or Tangent of 
the Arch, by means of the limiting Polygons, fo 
may the Sine, Cofine or Tangent be found from 
the Length of the Arch by the fame Method. 
Thus, if A be the Arch whofe Tangent T \ Sine T, 
and Cofine Z, are to be determined, then will the 
Tangent 
