...first above the second is to the first, as the excess of the third above the fourth to the fourth. 70. If four quantities be proportionals, the sum of the...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 u + li c 4 </ a...

...inversely, a : a—b :: c : c — d., (182.) When four quantities are proportionals, the sum of the Jirst and second is to their difference, as the sum of the third and fourth, to their difference. Let a : b :: c : d ; then, ' + b : ab :: c + d: «— d. G Ey ac , If possible,...

...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 last udud .. . , bd , a...

...± d : c, ,'. 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, — : — =• , and —...

....'. inversely a : a+_b : : c : c£d. TH. S. " If four quantities be proportional, then the .•mm " of the first and second is to their difference, as the sum of " the third and fourth is to their difference." For by THEOR. 6, ^~=^—, and ^- =^^-; invert the two last bdba , , bd , a+bb c+dd...

..., that is, ab : a :: cd : c; and inversely, a : ab :: с : c — d. (182.) When four quantities are proportionals, the sum of the first and second is...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 Art. 179, °—...

...— d, and, therefore, by again alternating, a: a — b::c:c — rf. 116. When four quantities are proportionals, the sum of the first and second is...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 : d, therefore,...

...still be a true one. _ а с ас a^-bc^-d For T=-d-'- b^=^1' or —=Т' Or, a*rb : b : : c~rd : d. 64. If four quantities be proportionals, the sum of the first and second is to their difterence,.as the sum of the third and fourth is to their difference. * The terms are similarly designated...

...•'• 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. ForA + B:B::C +D;D(37),...

...= =-, and mvertcndo, ac ac a — bc — d' or a : a — b :: c : c — d. 411. " If four magnitudes be proportionals, the sum of the first and second...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 : c — d. T. .ac Forif 6-3'...