45 6 Mr. glenie’s Method of comparing 
C— D E F C — D E F , - 
2. a+ a. — + a.—- + a. — . — , when three are 
compounded. 
3. AH- A.— - + 
0 D 
C D E F G — H C — D G — F C — D* 
A-— + A.— + A. — --7“ + A.— 
G — H E — F G — H 
+ A. 
H 
— n C D E F G H , r 
— + a. — - . — . — - , when four ratios 
ri D r H * 
are compounded, 8cc. See. 
By continuing this operation much farther, I found 
upon examination that the number of terms in which A 
is connected with the differences c-d, e-f, g-h, See. 
taken one by one, two by two, three by three, Sec. if p 
denote the number of ratios compounded, is expreffed 
refpedtively by *=- r > ^ ^ ^=- 3 > 8cc. Thus 
if the ratio of a to b be fuppofed equal to the ratios of 
c to d, e to f, g to h, 8cc. refpe&ively, thefe exprefiions 
will give the following ones. 
2 — I A — B 
I. A + .A. 
l B 
2 1 A B 2 — I 2 — 2 A — B> 
2. A+- . A.— i“— — . .A.—— 
I B I 2 B 
0 , . -4—i « „ A ~ e1 , 4-i 4—2 4—3 
3» A 4- • A. t . • A . 4“ " • • 
u 1 B12 b 1 2 2 
A— i) 
a. — — ; for magnitudes of the fame kind with A 
and b, which have to b refpedlively the duplicate, 
triplicate, and quadruplicate ratio of a to b ; where p 
is fucceffively equal to a, 3, and 4. And univerfally, 
by the fame geometrical reafoning, it is found, that 
A + 
> 1 A B 
—.A.—— 
+ 8ec. 
A. 
has to 
B fuch 
