 | National cyclopaedia - 1884 - 670 pages
...fourth term) can be obtained as easily ; for be . ad , ad a=— ,6 = — , and c = — . dcb Conversely, if the product of two quantities is equal to the product of two others, these four are proportionals ; example, 4 times 6 = 3 times 8 ; whence we see that 3 is to... | |
 | Elias Loomis - Algebra - 1886 - 396 pages
...: d. Then | = |, Art. 292. Multiplying each of these equals by bd, we have ad=bc. 300. Conversely, if the product of two quantities is equal to the product...of two other quantities, the first two may be made Hie extremes, and the other two the means of a proportion. Let ad=bc. Dividing each of these equals... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...be a : b = b : c. Then by §242, 62=ac. Whence, b = Vac. PROPOSITION II. THEOREM. 244. CONVERSELY, if the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad =... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...the product of the means). Whence, extracting the square root, 6.= Vac. QED PROPOSITION III. 297. // the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion in which the other two are made the means.... | |
 | Algebra - 1888 - 492 pages
..., bc . ad ad From this equation, a = -=• , d =. — , о = — , с ==-=-• aa с b 368. IV. // the product of two quantities is equal to the product of two others, the factors of either product ni.ay be made the extremes, and the factors of the other product... | |
 | Charles Davies - Algebra - 1889 - 330 pages
...Conversely, if we divide both members of ( 2 ) by ca, we shall have, - . = - ; or, a : b : : c : d. Hence, ac If the product of two quantities is equal to the product,...quantities, the first two may be made the means, and the second two the extremes, of a proportion. It follows, that of three proportional quantities, the square... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...A Theorem. 119. If the product of two quantities equals the product of two other quantities, either two may be made the means and the other two the extremes of a proportion. Proposition IV. A Theorem. 120. If four quantities are in proportion, they will be in proportion by... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...A Theorem. 119. If the product of two quantities equals the product of two other quantities, either two may be made the means and . the other two the extremes of a proportion. Proposition IV. A Theorem. Proposition V. A Theorem. 121. If four quantities are in proportion, they... | |
 | Webster Wells - Algebra - 1890 - 560 pages
...mean is equal to the product of the extremes divided by the other mean. 384. (Converse of Art. 381.) If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad =... | |
 | Seth Thayer Stewart - Geometry - 1891 - 426 pages
...— C becomes • — r— = — ^— ; or, AL SECTION II.— EQUAL PRODUCTS. PROPOSITION VI. 318. Theorem: If the product of two quantities is equal to the product of two other quantities, the two quantities that form either product may be made the extremes, and the other two quantities, the... | |
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If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad. 
