 | James Bates Thomson - Algebra - 1878 - 322 pages
...e By Art. 363, | = * Clearing of fractions, at = 6s. Again, 9:6:: 6-4, and 4 xg = 62. THEOREM III. If the product of two quantities is equal to the product of two others, the four quantities are proportional j the factors of either product being taken for the extremes,... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...AC, we have, £ = £, or, A:B = C:DL, £ = 5, or, A:C=B:DIL, ~ = ~, or, B : A = D : C III. CA Hence, if the product of two quantities is equal to the product of two other quantities, one pair of factors may be made the extremes, and the other pair the means, of a... | |
 | Horatio Nelson Robinson - Algebra - 1879 - 332 pages
...Conversely. If the product of two quantities be equal to the product of two others, then either two may be taken for the means, and the other two for the extremes of a proportion. Let ad=bc... (1). Dividing by d, a = 7 • ' • (2). Dividing (2) by b, a- = C-. (3). Hence by formula... | |
 | Elias Loomis - Algebra - 1879 - 398 pages
...b : : c : d. Then ~ = -,, Art. 292. oa 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 the extremes, and the other two the means of a proportion.... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...extremes equal to the product of the meaiis ia merely clearing the equation of fractions. THEOREM II. 14i If the product of two quantities is equal to the product of two others, the factors of either product may be made the extremes, and the factors of the other the means of a... | |
 | William James Milne - Algebra - 1881 - 360 pages
...3. What does ad, the first member of the equation, form in the proportion? What be? PRINCIPLE 3. — If the product of two quantities is equal to the product of two otlier quantities, two of them may be made the extremes, and the other two the means, of a proportion.... | |
 | National cyclopaedia - 1884 - 670 pages
...merely the 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 4 as 6 is... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...the proportion 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 = be. Dividing... | |
 | 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 the... | |
 | 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. Let... | |
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Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion. 
