454 -Mh glenie’s Method of comparing 
pendicularly to vo, or otherwife if in the fame angle ; and 
let the redtangles or parallelograms MR, np, be com- 
pleted. Let lm be a fourth proportional to op, mn and 
nr- op; and let the rectangle or parallelogram LQ.be 
completed. 
Then (14. e. 6.) lt is equal to tr, and confequently 
LQ_to mr. But (23. e. 6.) mr has to np the ratio com- 
pounded of the ratios of mn to no and nr to op. There- 
fore (1. e. 6.) ln has to no the ratio compounded of the 
ratios of mn to no and nr to op. But ln is equal to 
mn+ mn. NR 0? w , or A + A.ppp by conftru&ion. Whence 
it appears, that a magnitude of the fame kind with a 
and e, which has to b the ratio compounded of the ratios 
of a to b and c to d, is expreffed by a + a. 
In like manner let e, f, be reprefented by rn, op, re- 
fpedtively, and let lk be a fourth proportional to op, ln, 
and qr. Then (14. e. 6.) kx is equal to xr or tr and xs 
together. But fince ln hath already been fhewn to be 
equal to a + a.^~ , lk is a fourth proportional to F, e-f, 
and a + a.— — ; that is equal to a,— ^— + A. -p-* — — • by 
conftrudtion. Wherefore kn being equal to lk + ln is 
equal to a + a.— + a. — - + a. • * And fince 
1 D F D F 
XQ. is equal to lr, kn has to no a ratio compounded of 
the 
x 
