...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 + bbc + dd fractions,...

...± 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,...of " the third and fourth is to their difference." For by _ ., a + bc + d , a— t c—d . , ,, , THEOR. 6, — : — =• , and — — = — — : invert...

....'. 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...of " the third and fourth is to their difference." For by THEOR. 6, ^~=^—, and ^- =^^-; invert the two last bdba , , bd , a+bb c+dd fractions, then...

...•'• 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,...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), .-. A + B : C •+ D : : B : D (36). Again,...

...fourth is to the fourth. 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...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. If four quantities be proportionals,...

...B:: C + D:C — D: that is, if four numbers be proportional, the sum of the first and second terms is to their difference, as the sum of the third and fourth terms \a to their difference. It is evident that if B be greater than A, the analogy will become B...

...a±4 : a :: c±d : c; .-. inversely a : a±b ;• c TH. 8. If four quantities be proportional, then the sum of the first and second is to their difference...sum of the third and fourth is to their difference. For, by theorem 6, ~|~ ~\ • od , a — bb — d , . . . . . bd and — ; — = — j- ; invert the...

...: c±rf : с ; .•. inversely a : «z±& : : с Тн. 8. If four quantities be proportional, then the sum of the first and second is to their difference...sum of the third and fourth is to their difference. For, by theorem 6, g ' c~*~ ; ; ' bd . a — bb — d ... bd and — — — ; invert the last two...

...: c±d : c, .-. inversely a : a±6 : : c : c±d. TH. 8. " If four quantities be proportional, then the sum of the first and second is to their difference...sum of the third and fourth is to their difference." For by TH. 6^ — =— = — =- , and od — T— = — — ; invert the last two fractions, then £=...

...inversely, a : a - b :: с : с — d. 236. When four quantities are proportionals, the sum of the ßrst and second is to their difference, as the sum of the third and fourth is to their difference. By Art. 233, a + bc + d • , . a -b с- d and by Art. 234, — ~ — = - ; therefore ^±5 н~ ^ -...