| G. Ainsworth - 1854 - 216 pages
...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... | |
| Elias Loomis - Algebra - 1855 - 356 pages
...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- ad=bc.... | |
| Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...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 two... | |
| 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
...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 ad=bc... | |
| Charles Davies, William Guy Peck - Mathematics - 1857 - 608 pages
...portional to the other three taken in their ^ of the means ; and conversely, if the product order. j **of two quantities is equal to the product of two others, the** first two may be taken as the extremes, and the last two as the means, of a proportion. PROPORTION.... | |
| 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.... | |
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