| Bewick Bridge - Algebra - 1818 - 254 pages
...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,... | |
| Bewick Bridge - Algebra - 1821 - 284 pages
...± 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... | |
| Bewick Bridge - Algebra - 1821 - 648 pages
....'. 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... | |
| John Playfair - Geometry - 1829 - 210 pages
...A :: D± C : C, •'• 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...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), .-. A + B : C •+... | |
| John Darby (teacher of mathematics.) - 1829 - 212 pages
...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 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. If four quantities be proportionals,... | |
| George Peacock - Algebra - 1830 - 732 pages
...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 is to their difference...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' x, , a + bc + da... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...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... | |
| John D. Williams - Algebra - 1840 - 634 pages
...: 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... | |
| John D. Williams - Algebra - 1840 - 216 pages
...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... | |
| Bewick Bridge - Algebra - 1841 - 260 pages
...: 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 £=... | |
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