[ 3°5 ] 
X -jp E being the coefficient of that term of the 
binomial ci q- $ expanded in which occurs a 1 ? • 
Wherefore, the ratio of RQW^ to A C F H is 
» V n 
Put G now for the coefficient of the middle term of 
the fame binomial, and if p — q = A } E — G, ^ 
= 4 - = b the area R QW h is equal to half ACFH; 
for then Qj', F/, CJ are all equal, and confequently 
the aieas RQW/6, HD b and AD/6. Wherefore, the 
feries B- — is equal to ^Lul ^ — . But the 
3 A n + i G 
B 3 
feries B y 4. ©V.^becaufe B 2 — ^ does not alter 
whatever p and q are, whilft their fum 11 remains the 
fame. Wherefore, in all cafes, the ratio of R Q W h 
to ACFH is^S X 4 ^ X 2". 
n Cj 
I r. By Prop. 1 o. Art. 4. of the Effiay, the ratio 
of ACFH to HO* is — h— x p; and by Art. 9. the 
ratio of R ht Qjo H O is ab q X ^Zf x « * — 
_ »-/ » 
Z 3 « — 2 ;« 5 Z 5 
3 + "77" x — 7“ & Cr Wherefore, the ratio of 
* It is hoped that the imperfection of the figure all along re- 
ferred to will be excufed. The lines R h and D b fhould appear 
APnr?!?/ f/ 11 be found P rerentl y> that the curve line 
j rr “ 10u d have been drawn from F and C convex to- 
wards A H. 
V ol. LIV. Rr Rbt 
