[ *0 9 1 
The Tangent of \a will be £rFI;~~« ? 
y-j-r| « -j~r — r 
i jl 
The Sine of * ^ will be 
2 r 71 
For thefe Equations will arife from the TranfpolP* 
tion and Redu&ion of the former for the Tangent and! 
Sine of the Multiple Arch, upon the Subftitution of 
t,y, z and A ; for T , T, Z and n 't A. 
Corollary 3 Hence regular Polygons of any given 
Number of Sides may be infcribed within, or circum- 
fcribed without, a given Arch of a Circle. For if the 
Number n exprefs the double of the Number of Sides 
to be infcribed within, or circumfcribed about, the 
given Arch A ; then one of the Sides infcribed wilh 
be the double of the Sine, and one of die Sides cir- 
cumfcribed the double of the Tangent of the Sub- 
multiple part of the Arch, viz. % A . 
Lemma II. 
To find the Length of the Arch of a Circle wit him 
certain Limits , by means of the Tangent and Sine 
of the Arch . 
Let t be the Tangent, / the Sine and z the Coline 
of the Arch A y whofe Length is to be determined., 
and let v be expounded as before 3 then, if any 
Number n be taken, the Arch of the Circle will be. 
I T 
always lefs than 
7--j-7|7Z r — t|* 
T~ i i 
r T \ n Hh f * — tJ# 
1 1 
and bigger than 
— 2: — *v\ 
Dd 2 
Fox 
