 | James Wood - Algebra - 1815 - 338 pages
...and b and c the means. (172.) When four quantities are proportionals, the product of the extremes is equal to the product of the means. Let a, b, c, d, be the four quantities ; then, since ac they are proportionals, 7 = 3 (Art. 171) ; and by multiplying both... | |
 | Bézout - Arithmetic - 1825 - 258 pages
...9, and the square root 6 of the product 36 is the mean proportional sought. * In every geometrical proportion, the product of -the extremes is equal to the product of the means. Let us take, for example, the geometrical proportion 12: 3 :: 16 : 4; I say that 12X4=3X16. In effect,... | |
 | William Whewell - 1837 - 226 pages
...6, c is greater than d. 39. When four quantities are proportionals, the product of the extremes is equal to the product of the means. Let a, b, c, d be the four quantities ; then, since ac they are proportionals, = - ; and by multiplying both sides by bd,... | |
 | Horatio Nelson Robinson - Algebra - 1850 - 256 pages
...correspondence, the principle or the operation is true — otherwise, false. PROPOSITION I. In every proportion, the product of the extremes is equal to the product of the means. Let a : 6=c : d represent any proportion, Then, -=- must be a true equation. ac Multiply both members of... | |
 | James Haddon - Algebra - 1850 - 210 pages
...柄 卯 ・ Propotitiotu. 1. If four quantities are proportionals， the product of the extremes is equal to the product of the means. Let a : b :: c : d be the proportion， &d th en 竺 言 三 ， 血 d ， muMpl y hgbothmembersoftMsequa ・ 虹 onbybd ，... | |
 | 1852 - 970 pages
...has been applied. ARITHMETIC. 1. Prove the fundamental property of proportionals, viz. : that when four quantities are in proportion, the product of the extremes is equal to the product of the means. State and prove its converse. 2. Write down the rule for stating and for... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...in continued proportion. (212.) If four quantities are proportional, the product of toe extremes is equal to the product of the means. Let a : b : : c : d. Then will ad=bc. For, since the four quantities are proportional, Multiplying each of these equals... | |
 | Isaac Todhunter - Algebra - 1858 - 530 pages
...and b and с the means. 38G. When four quantities are proportionals, the product of the extremes is equal to the product of the means. Let a, b, c, d be the four quantities ; then since they are prost С portionals r = -j, (Art. 385); and by multiplying both... | |
 | Elias Loomis - Algebra - 1858 - 394 pages
...in continued proportion. (212.) If four quantities are proportional, the product of Inf. extremes is equal to the product of the means. Let a : b : : c : d. Then will ad=bc. For, since the four quantities are proportional, ac b=d" Multiplying each of these... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...to that of C to D ; and, (by Def. 3), A : B : : C : D. THEOREM II. If four magnitudes constitute a proportion, the product of the extremes is equal to the product of the means. Let the four magnitudes A, B, C, and D form the pioportion A : B : : C : D ; we are to prove that A x £... | |
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In any proportion the product of the extremes is equal to the product of the means. Let the proportion be a : b = с : d. 
