Magnitudes of any Kind together . 453 
•or diminifhed, fuch as ratios , velocities, powers, &c. As 
1 fhall frequently, for the fake of concifenefs and con- 
■veniency, be obliged to make ufe of particular modes of 
expre fling geometrical magnitudes, I here obferve, once 
for all, that by fuch expreflions as thefe a. a.-~ b > 
A. ? , a.———, &c. I mean refpeftively a third pro- 
portional to B and a ; a fourth proportional to b, a, and 
the difference of A and b ; a fourth proportional to d, a, 
and the' difference of c and d ; a fourth proportional to b, 
- £ 
a. — — and a-b, Sec. 
To proceed then in the order in which I firft invefti- 
gated thefe theorems ; let a, b, c, d, e, f, g, h, See. be 
any number of magnitudes of the fame kind, taken two 
y z s R 
A 
I X 
T 
Q. 
C—I> 
A.— — 
D 
-E 
A 
C F 
B 
V K M L M NO 
.and two from the firft ; and let mm, no, nr, op, refpec- 
stively reprefent a, b, c, d. Let nr, op, be drawn per- 
pendicularly 
