8 o Mr. glenie’s Proportions . 
is equal to the fquare of ab multiplied by 2 ; the fquare 
of ae equal to the fquare of ad or ac multiplied by 2 ; 
that is, equal to the fquare of ab multiplied by 4, and fo 
on. Thus the fquares of ac, ae, ag, ai, al, Sec. are re- 
fpeCtively equal to the fquare of ab multiplied by the 
terms of the following feries 2, 4, 8, 16, 32, 64, Sec. 
where the fixty-third term gives the fquare of ab mul- 
tiplied by the laft term of sessa’s Series for the Chefs- 
board. 
If cx be drawn parallel to ap, the fquares of a a , Ad , 
a c , a d , Sec. will be refpeCtively equal to the fquare of 
ab multiplied by 3, 5, 9, 17, 33, 65, 129, Sec. Alfo 
if Ag be taken equal to a <7, and^ ^ be drawn parallel to 
ec, and this be repeated, the fquares of Ae, Sec. will be 
equal refpedtively to the fquare of ab multiplied by 
6, 1 2, 24, 48, Sec. And the fquares on a 0, Sec. will be 
equal to fquare on ab multiplied by 4, 7, 13, 25, 49, 
Sec. In like manner, if am be taken equal to Ad, and mn 
be drawn parallel to bc, the fquares on an, Sec. will be 
equal refpedtively to the fquare on ab multiplied by 
10, 20, 40, 80, 160, Sec. And the fquares on as, Sec. 
will be equal refpeCtively to the fquare on ab multiplied 
by the terms of the following feries: 6, 11,21,41,81, 
1 61, Sec. 
In the fame way, if right lines be drawn from e, e , g, 
n, 1, l, Sec. there will arife numberlefs other feries. And 
if bc be taken equal to ab multiplied by any number, 
fiird, fractional, or mixed, there will be obtained a great 
variety of feries, confuting refpeCtively of terms, which 
are 
