Proposition 7. 289. ff four quantities are in proportion, they are in proportion by composition and division; that is, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. Plane and Solid Geometry: Inductive Method - Page 126by Arthur A. Dodd, B. Thomas Chace - 1898 - 406 pagesFull view - About this book
| Charles Butler - 1814 - 582 pages
...as the 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 :: t+d : c—d; for a + bc + da —... | |
| James Wood - Algebra - 1815 - 338 pages
...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,... | |
| 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... | |
| James Wood - Algebra - 1825 - 322 pages
...a :: cd : 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 Art. 179, °—... | |
| George Lees - 1826 - 276 pages
...therefore, 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 : d, therefore,... | |
| John Playfair - Geometry - 1829 - 210 pages
...•'• 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,...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... | |
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