 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 = ос.  Plane and Solid Geometry - Page 79by James Howard Gore - 1898 - 210 pagesFull view - About this book
 | G. Ainsworth - 1854 - 216 pages
...a : 6=c : d, then -=-, and multiplying both sides by ac, —= — , Л С ' <to . • . bc=ad. And conversely, if the product of two quantities is equal to the product of two other quantities, the four are proportional. For (by hyp.) ad=bc, and dividing both sides by bd, we... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...immediately from the definition, that the product of the extremes is equal to the product of the menus ; and conversely, if the product of two quantities is equal to the product of two others, the first two may be taken as the structed with a groove in each leg, so that extremes, and the last... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...bd, the expression becomes abd bcd ~b~=~d' or ad=bc. Thus, if 3 : 4 : : 9 : 12, .hen 3X12=4X9. (213.) Conversely, if the product of two quantities is equal to the product of two others, the first two quantities may be made the extremes, and the other two the means of a proportion. Let-... | |
 | 1855 - 424 pages
...means in both cases is the same. So, if na : Ь : : x : y, then a : Ь : : x : ny. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities will form a proportion, if they are so arranged that those on one side of the equation... | |
 | Thomas Sherwin - Algebra - 1855 - 318 pages
...product of the extremes. 2. Suppose we have ad=bc. Dividing both members by b XLIX. PROPORTIONS. 221 If the product of two quantities is equal to the product of two otner quantities, the two factors of either product may be made the means, and the two factors of the... | |
 | Thomas Sherwin - Algebra - 1855 - 262 pages
...ad=bc. If we divide both members by b and d, we have — = —, or bdi a : b = c : d. Therefore, •• If the product of two quantities is equal to the product of two other quantities, the two factors of one product may be made the means, and the two factors of the... | |
 | Elias Loomis - Algebra - 1856 - 280 pages
...by clearing the equation of fractions, we have ad— bc. Thus, if 3:4:: 9:12, then 3x12=4x9. (184.) Conversely, if the product of two quantities is equal to the product of two others, the first two quantities may be made the extremes, and the other two the means of a proportion. Let... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...by the proposition, A xC=B xB, which is equal to B'. PROPOSITION ii. THEOEEM (Converse of Prop. /.). If the product of two quantities is equal to the product of twc other quantities, the first two may be made the extremes, and the other two the means of a proportion.... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...by the proposition, AXC = BXB, which is equal to B1. PROPOSITION n. THEOREM (Converse of Prop. /.). If the product of two quantities is equal to the product of twc other quantities, the first two may be made the extremes, and the other two the means of a proportion.... | |
 | Charles Davies - Algebra - 1859 - 324 pages
...other, that A x D = В x (7, we shall also have, -j = -~ ; А ъ and hence, A : В : : С : D. That is : 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.... | |
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