 | James Ryan - 1826 - 430 σελίδες
...THKOR. If the first be the same multiple of the second, or the same part of it that the third is oi' the fourth ; the first is to the second as the third is to the fourth. DEMONSTRATION. 1. Supposing m to be any integer greater than unity, let mA the first be the same multiple... | |
 | Euclid, John Playfair - 1826 - 326 σελίδες
...QED ' -. /—PROP. B. THEOR. If the first be the same multiple of the seeond, or the same part of it, that the third is of the fourth ; the first is to the seeond as the third to the fourth. First, if mA, mB be equimultiples of the magnitudes A and B, mA:... | |
 | John Playfair - 1832 - 358 σελίδες
...C. Therefore, PROP. B. THEOR. If the first be the same multiple of the second, or the samep\ of it, that the third is of the fourth; the first is to the second the third to the fourth. First, ifmA. mB be equimultiples of the magnitudes A and «A:A::mB:B. Take... | |
 | Euclid - 1835 - 540 σελίδες
...THEOR. If the first of four magnitudes be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to...the fourth. Let the first A be the same multiple of B the second, that C the third is of the fourth D; then A is to B as C is to D. For, of A and C take... | |
 | 1836 - 488 σελίδες
...taken inversely. B. If the first be the saine multiple of the second, or the same part of it, thut the third is of the fourth; the first is to the second as the third to the fourth. C. If the first be to the second as ths tlu'rd to the fourth ; and if the first be a... | |
 | Robert Mudie - 1836 - 524 σελίδες
...of the first divided by the second is equal to the quotient of the third divided by the fourth, then the first is to the second as the third is to the fourth, or the ratio of the first and second is equal to the ratio of the third and fourth ; because these... | |
 | Robert Mudie - 1836 - 542 σελίδες
...of the first divided by the second is equal to the quotient of the third divided by the fourth, then the first is to the second as the third is to the fourth, or the ratio of the first and second is equal to the ratio of the third and fourth ; because these... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...magnitudes, &c. PROP. C. THEOR. IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to...the fourth. Let the first A be the same multiple of B the second, that C the third is of D the fourth ; then A : B : : C : D. Take of A and C any like... | |
 | Andrew Bell - 1837 - 290 σελίδες
...C. PROPOSITION B. THEOREM. If the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second as the third to the fourth. First, if mA, mB, be equimultiples of the magnitudes A and B, mA : A : : mB : B. Take... | |
 | Robert Simson - 1838 - 434 σελίδες
...magnitudes, &c. QED PROP. C. THEOR. IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to...the fourth.* Let the first A be the same multiple of B the second that C the third is of the fourth D : A is to B as C is to D. Take of A and C any equimultiples... | |
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THEOR. IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth... 
