Magnitudes of any Kind together . 4 57 
b fuch a multiplicate ratio of a to b as is expreffed by 
the number /*. 
In the reafoning above I fixed on b as the magnitude 
to which the reft were to be referred ; but I might as well 
have fixed on a or any of the other magnitudes. Thus, 
r „ p — I B A p 1 p 2 B aT ^ 
for mltance, b+ -—.b, — + — - . - — .b. + &c. 
2 A I Qi A 
B.— — — - has to a fuch a multiplicate ratio of b to a 
as is expreffed by the number p; or a has to b + 
p 1 B A p— I p— 2 B — a! Z - 
- — b. - — * b. + &c. b. the ratio 
I A I 2 A A 
A E 
c 'p — I A — B p — I p — 2 o 
of At- — .A. + — .A.— : + & C. A. 
A — B 
ip— I 
tOB 
that is, fuch a multiplicate ratio of a to b as is expreffed' 
by the number p. Each of thefe, indeed, I demonftrated 
feparately from the fame fort of geometrical reafoning ; 
but for the fake of brevity I omit fetting down thefe 
feparate demonftrations, as they are both contained in 
general reafoning above, which furnifhes likewife a great 
variety of other expreffions, according as certain num- 
bers of the ratios c to d, e to f, g to h, &c. are fuppofed 
to be refpedtively equal to, greater or lefs than, the ratio 
of a to s. 
Vo l. LXVII. 
O o o 
