 | 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.... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...clearing of fractions, fl £ (2) ad=bc. Therefore, etc. THEOREM H. If the product of two quantities equals the. product of two other quantities, two of them may be made the means, and the other two the extremes of a proportion. Let (1) a x d = b x c; then will a : b :: c... | |
 | 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... | |
 | 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 =... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...product. 6, Conversely, if the product of two numbers is equal to the product of two others, either two may be made the extremes, and the other two the means, of a proportion. For, if we have given ah 9 = a\ then, dividing by bb ' , we obtain Corollary. The terms of a proportion... | |
 | Edward Albert Bowser - Algebra - 1888 - 868 pages
...their product. (2) Conversely, If the product of two quantities be equal to the product of two others, two of them may be made the extremes, and the other two the means, of a proportion. For let ad = be. Dividing by bd, ^ = c-; bd that is, a: b : : c: d. In a similar manner it may be shown... | |
 | 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... | |
 | James Morford Taylor - Algebra - 1889 - 340 pages
...a : b = b : c, then b2 = ac, or b = Va c. 192. Conversely, if the product of two quantities equals the product of two other quantities, two of them may...extremes and the other two the means of a proportion. If ad = cb, then by dividing both members by bd we obtain a : b = c : d . (i.) Inversion : If a : b... | |
 | 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, of two other quantities, the first two may be made the means, and the second two the extremes, of a proportion. It follows,... | |
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If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion. 
