 | Charles Hutton - Arithmetic - 1818 - 646 pages
...compounding, or adding, in def. 86. THEOREM THEOREM IA VI. Equimultiples of any two Quantities hare the same Ratio as the Quantities themselves. LET A. and B be any two quantities, and WA, ms, any equimultiples of them, m being any number whatever : then will mA and NIB have the same... | |
 | Charles Hutton - Mathematics - 1825 - 608 pages
...the sense opposed to compounding, or addine, in def. 86. THEOREM THEOREM LXVI. Equimultiples of any two Quantities have the same Ratio as the Quantities themselves. Let A and E be any two quantities, and in\, me, any equimultiples of tliem, m being any number whatever : then... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...Since -r-=-r, Hyp . aa 1~~b a c i~~d Qt C b f ab=ba, : .'. ad=bc, q/=6e. PROP. LXX. THEOR. 15 . 5 *„. Equimultiples of two quantities have the same ratio as the quantities themselves. Let ma and mb be equimultiples of a and b; then will a : b :: ma : mb. For — ——. b mb a ma That is,... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...-=-=—, Hyp. oa a _a bb ct c ~b = ~d Ct € ab=ba, : .-. ad=bc, af=be. PROP. LXX. THEOR. j 5 . 5 Eu. Equimultiples of two quantities have the same ratio as the quantities themselves. Let ma and nib be equimultiples of a and /<; then will a : b :: ma : mb. For -T=-T. b mb a ma That is,... | |
 | William Frothingham Bradbury - Algebra - 1868 - 264 pages
...af-6:cfd=a — 6 : e — d Hence, by Theorem III. a -\-b : a — b= c -\- d : c — d THEOREM X. 211. Equimultiples of two quantities have the same ratio as the quantities themselves. For by Art. 83, ?=^ * 6 mb ie a:b = ma:mb Cor. It follows that either couplet of a proportion may be... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...THEOREM. If four quantities are proportional, they are also p *j by division. Let A : BC : D ; vJisn wil. A — B : A : : C— D : C. For, since A : B...Equimultiples of two quantities have the same ratio as tf<t quantities themselves. Let A and B be any two quantities, and »iA, »zB then equimultiples ;... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...by means of (15) and (11), If a : b = c : d then a-\-b : a — 6 = e -\-d : c — d THEOREM VII. 20. Equimultiples of two quantities have the same ratio as the quantities themselves. a ma For - = — b mo that is a : b = ma : mb 21 i Corollary. It follows that either couplet of a proportion... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...(18), by means of (15) and If a : b = c : d then a-\-b : a — 6 =: c -\-d:c — d THEOREM VII. 20. Equimultiples of two quantities have the same ratio as the quantities themselves. a ma For - = — I mb that is a : b = ma : mb 21 . Corollary. It follows that either couplet of a proportion... | |
 | William Frothingham Bradbury - 1875 - 280 pages
...6:c + rf=a — b : с — d Hence, by Theorem III. a -\- b : a — 6=c-(-rf:c — d THEOREM X. 211. Equimultiples of two quantities have the same ratio as the quantities themselves. For by Art. 83, -. = —. J b mb ie a : 6 = ma : т Ъ Cor. It follows that either couplet of a proportion... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...quantity, and A+C+E as a single quantity. Therefore, by Pr. 1, A: B:: A+C+E: B+D+F. PROPOSITION X. THEOREM. Equimultiples of two quantities have the...'quantities themselves. Let A and B be any two quantities of the same kind, and m any number, entire or fractional, we have the equality AmA or, A : B : : mA... | |
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It follows that either couplet of a proportion may be multiplied or divided by any quantity, and the resulting quantities will be in proportion. And since by... 
