 | Admiralty - 1845 - 152 páginas
...equation, Divide by 13 .-. ж=12 61. An equation may be formed from 4 proportional quantities, by making the product of the means equal to the product of the extremes. Let the proportional quantities be x, y, a, b ; or x : y : : a : b. Vy-J (Art. 15.) .-. bx=ay. (Art.... | |
 | Jeremiah Day - 1846 - 356 páginas
...given, they are frequently stated in the form of a proportion. But it is commonly necessary that ihis first proportion should pass through a number of transformations...products, will not destroy the proportion. Thus, if a : 6 : : c : d, the order of these four quantities may be varied, in any way which will leave ad=bc.... | |
 | Jeremiah Day - 1846 - 356 páginas
...given, they are frequently stated in the form of a proportion. But it is commonly necessary that ihis first proportion should pass through a number of transformations...which will leave the product of the means equal to fhe product of the extremes. It is evident, in the first place, that any alteration in the arrangement,... | |
 | James Bates Thomson - 1847 - 266 páginas
...is evident that the terms of a proportion may undergo any change which will not destroy the equn ity of the ratios ; or which will leave the product of the means equal to the product of the extremes. These changes are numerous, but they may be reduced to a few general principles. CASE I. Changes in... | |
 | Jeremiah Day, James Bates Thomson - 1848 - 264 páginas
...proportional. 343. It is evident that the terms of a proportion may undergo any change which will not destroy the equality of the • ratios ; or which will leave...of the means equal to the product of the extremes. These changes are numerous, but they may be reduced to a few general principles. CASE I. Changes in... | |
 | Jeremiah Day - 1848 - 354 páginas
...demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which wiil leave the product of the means equal to the product of the extremes. 380. If four quantities are proportional, THE ORDER OF THE MEANS, OR OF THE EXTREMES, OR OP THE TERMS... | |
 | Jeremiah Day - 1850 - 356 páginas
...it is commonly necessary that ihis first proportion should pass through a number of trans formations before it brings out distinctly the unknown quantity,...quantities may be varied, in any way which will leave ad— be. Hence, 330. If four quantities are proportional, THE ORDER OF THE MEANS, OR OF THE EXTREMES,... | |
 | Jeremiah Day - 1850 - 348 páginas
...quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not afiect the equality of the ratios; or which will leave the...quantities may be varied, in any way which will leave ad— be. Hence, 380. If four quantities are proportional, THE ORDER OP THE MEANS, OR OF THE EXTREMES,... | |
 | Joseph Ray - 1852 - 366 páginas
...square pile. (10, Here we have the proportion v ея(n+1)(я+2) ; 'я(я+1)(2П+1) : : 6 : 11. Placing the product of the means equal to the product of the extremes, and canceling ¿я(я+1) on each side, we have 12ra+6= llя+22, whence ra=16, the number of balls in... | |
 | 1855 - 424 páginas
...proportional. It is evident that the terms of a proportion may undergo any change which will not destroy the equality of the ratios, or which will leave the product of thu means equal to the product of the extremes. These changes ate numerous, but they may be reduced... | |
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But it is commonly necessary that this first proportion should pass through a number of transformations before it brings out distinctly the unknown quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect... 
