 | Jeremiah Day - 1827 - Liczba stron: 352
...the product of the means is, in both cases the same. And if no : b'. '.x : yy then a : b'.'.x : ny. 375. On the other hand, if the product of two quantities...means, and those on the other side, the extremes. If my=nh, then m : n'.'.h : y, that is —=ny For by dividing my=nh by ny, vie have Z^=!L ny ny And... | |
 | James Bryce - 1837 - Liczba stron: 322
...product of the means is equal to the product of the extremes; and if the product of two quantitles be equal to the product of two others, the four quantities will form a proportion. ft f, Let the proportion be a:b::c:d; then -=- = -; and о а clearing of fractions, ad=bc. Again,... | |
 | 1838 - Liczba stron: 372
...other that AxD=B*C, i „ , , BD we shall also have ~T=~r' A. O and hence, A : B : : C : 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.... | |
 | Charles Davies - 1839 - Liczba stron: 272
...each other that AxD=BxC, we shall also have — =— ; A. L> , and hence, A : B : : C : 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.... | |
 | Charles Davies - 1842 - Liczba stron: 368
...related to each other that we shall also have — =— ., jfi O and hence, A : B : : C : 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.... | |
 | Charles Davies - 1842 - Liczba stron: 284
...Thus, if we have the proportion 3 : 6 : : 6 : 12, t we shall also have = 62 = 3xl2=36. QUEST. — 155. If the product of two quantities is equal to the product of two other quantities, may the four be placed in a proportion 1 How ? — 156. If three quantities are proportional,... | |
 | Thomas Sherwin - 1842 - Liczba stron: 326
...Suppose we have ad = bc. Dividing both members by 6 and d, we have r = -, or a : b = c : d. Hence, oa If the product of two quantities is equal to the product of ttca other quantities, the two factors of either product may be made the means, and the two factors... | |
 | James Bates Thomson - 1844 - Liczba stron: 272
...for the product of the means in both cases is the same. So if na:b::x:y, then a : b : : x : ny. 339. On the other hand, if the product of two quantities...others, the four quantities will form a proportion if they are so arranged, that those on one side of the equation shall constitute the means, and those... | |
 | William Scott - 1844 - Liczba stron: 568
...products, and each is divided by irf, ad be acc _ a that is, a : b::c : d, or c '. d:'.a '. b. Wherefore, if the product of two quantities is equal to the product of two others, the four quantities are convertible into a proportion of which the multiplicand and multiplier of either product form the... | |
 | Charles Davies - 1845 - Liczba stron: 382
...other that A x D — B x C, we shall also have, — = — , -AO and hence, A : B : : C : 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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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. 
