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3- In like manner, the ratio of HC/ to HO is 
? + 1 * ? + 2^ q + 3 
£ r x r 1 +_/ x p-i X r 4 - 
?+I ?+I £+2 ^+1 £ + 2 q + 3 
occ. 
4* If E be the coefficient of that term of the bi- 
nomical a + b\P + 9 expanded in which occurs aP b 
the ratio of the whole figure A C F H to HO is 
TTTi x £■> n being —p + For, when A/— AH 
^ — 1 5 r — o. Wherefore, all the terms of the fe- 
ries fet down in Art. 2. as expreffing the ratio of 
A C f to H O will vanifh except the laft, and that 
becomes ,7; X ^ x ^ X &c. x But E 
being the coefficient of that term in the binomial 
a -\- b \ expanded in which occurs a p b q is equal to 
X ~y x &c. x 1 . And, becaufe Af is fup- 
pofed to become — AH, AC/=ACH. From 
whence this article is plain. 
5. The ratio of AC f to the whole figure ACFH 
is (by Art . 1. and 4.) « 4. 1 x E x / +X — q X 
p +2 P+Z , ?+' 
* T^Xf-i X a: &c. and if, as x exprefies 
P + 2 . ~ 7 + 3 ~ 
the ratio of Af to AH, X ffiould exprefs the ratio 
of At to AH; the ratio of AF? to ACFH 
- p + I p ~h 2 
would be n 1 X E x X — qX 
P+Z p+ l p+2 2 
X X — &c. and confequently the ratio of tFCf 
P+'i . ,/ 
to ACFH is » 4 1 X E x into the difference 
between 
