 | Algebra - 1853 - 380 pages
...of the two means. 179. If four quantities, A, B, C, and D, are so related to each other that A x D = BXC, we shall also have, — = -^-, AC and hence,...quantities, two of them may be made the extremes, and tht other two the means of a proportion. 180. If we have three proportional quantities, A : B : : B... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...PROPOSITION II. THEOREM. If the product of two magnitudes be equal to the product of two other magnitudes, two of them may be made the extremes and the other two the means of a proportion. If we have Hx Q=NxP; then will M : N : : P : Q. For, if P have not to Q, the ratio which M has to N",... | |
 | 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 obtain т-=т4 „... | |
 | 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 other product, the... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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.... | |
 | 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.... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...PROPOSITION II. THEOREM. If the product of two magnitudes be equal to the product of two other magnitudes, two of them may be made the extremes and the other two the means of a proportion. If vre have Mx Q=NxP ; then will M : N : : P : Q. For, if P have not to Q, the ratio which M has to... | |
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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. 
