228 Mr. maseres’s Method of 
respondent perpendicular altitude, or the radius, as 
i .31 1,028,779, - x r is to r, or as 1. 31 1,028,779, 
- &c. is to 1 . 
Art. 25. Hence we may determine the proportion of 
the time of defcent of a pendulum through an arch of 
90° to the time of its defcent through an infinitely fmall 
arch at the bottom of a quadrant, or rather (to fpeak cor- 
rectly) to the limit of the time of defcent through a very 
fmall but finite arch at the bottom of the quadrant, to 
which the faid time continually approaches nearer and 
nearer as the faid fmall arch is taken lefs and lefs, and to 
which it may be made to approach fo nearly, by taking 
the faid fmall arch fufficiently fmall, as to differ from it 
by lefs than any given quantity. For this latter time, or 
limit, is known to be to the time of the fall of a heavy 
body through half the length of the pendulum, or half 
the radius of the circle, as the femi-circumference 
of a circle is to its diameter, that is, as the number 
i - 57 °j 796 , 326 , 794 , 8 cc. is to i. But the time of the 
fall of a heavy body through half the radius of the 
circle is to the time of the fall through the whole radius 
as 1 to s/ a, or 1.414,213, &cc. Therefore, ex tequo, the 
faid limit of the time of defcent of a pendulum through 
a very fmall arch of the circle at the bottom of the qua- 
> drant, is to the time of the fall of a heavy body through 
6 the 
