...excess of the third above the fourth to the fourth. 70. If four quantities be proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth to their difference. Let a : b :: c : d, then will a+b : a—b : : c+d : c—d; for...

...inversely a : a±e : : с : c±.d. Til. 8. " If four quantities be proportional, then the sum " of (.he first and second is to their difference, as the sum of " the third and fourth is to their difference." For by THEOR. 6, £L+Ô=ÎI±^ and ^=£^; invert the two...

...,'. inversely a : a+_b : : с : c+_d. Tн. 8. " If four quantities be proportional, then the sum " of the first and second is to their difference, as the sum of " the third and fourth is to their difference." For by _ ., a + bc + d , a— t c—d . , ,, , THEOR. 6,...

...: c; and inversely, a : ab :: с : c — d. (182.) When four quantities are proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth, to their difference. Let a : b :: с : d; then, a + b : a — b :: c + d : c—d....

...by again alternating, a: a — b::c:c — rf. 116. When four quantities are proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth to their difference. This readily appears from Nos. 114 and 115. For, (No. 114.) a+b:b::c+d...

...A : B j- A : .- C : D ± C. Cor. B^fA^::D^C:C (35). 40. If four quantities be proportional, the sum of the first and second is to their difference, as the sum of the third and fourth is to their difference. Let A : B : : C : D, then (by mixing) A+B:AB::CJ+D:C — D....

...Thus,ifa:6::e;rf; then will a— b ; b : ; c — did. 5. If four quantities be proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth is to thejr difference. Thus, if a;b:;c:d, then will a+b;a— b: ;c+d;c — d. 6....

...a — bc — d' or a : a — b :: c : c — d. 411. " If four magnitudes be proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference." Let a : b :: c : d, then also a + b : a — b :: c + d :...

...whose terms are not equimultiples of a and b. 232. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth to their difference. 234. Express a + b . Jl]. and log, (a + 6 v'~) in the c + «...

...excess above the second, as the third is to its excess above the fourth. 27- By mixing, when the sum of the first and second, is to their difference, as the sum of the third and fourth to their difference. 28. By equality, when there is any number of magnitudes more...