 | Robert Simson - 1806 - 546 σελίδες
...Stc. PROP. C. THEOR. See N. 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... | |
 | John Playfair - 1806 - 320 σελίδες
...QED Bookv, PROP. B. 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 to the fourth. First, if mA and mB be equimultiples of the magnitudes A and B, mA : A : : »iB : B.... | |
 | Euclid - 1810 - 554 σελίδες
...PROP. C. THEOR. See Note. 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. A E Let the first A be the same multiple of B the second, that C the third is of the fourth D: A is... | |
 | John Mason Good - 1813 - 714 σελίδες
...inversely. 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 second, a* the third is to the fourth. Prop. D. Theor. If the fust be to the second as the third to the fourth,... | |
 | Charles Butler - 1814 - 582 σελίδες
...PROPORTION. 83. The foregoing articles treat of the properties of what is called DIRECT PROPORTION, where the first is to the second as the third is to the fourth ; but when the terms are so arranged, ' It must he understood, tbat what we have delivered on proportion,... | |
 | Euclides - 1816 - 588 σελίδες
...D H PROP. C. THEOR. Se«N. 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... | |
 | Daniel Cresswell - 1819 - 446 σελίδες
...THEOREM. If the first of four magnitudes be the same multiple of the second, or the same part ofit, that the third is of the fourth, the first is to the second, as the third is to the fourth. First, let A •= pB, and C = pD ; then A : B :: C:D. Let there be taken of A and C any equi-multiples... | |
 | John Playfair - 1819 - 350 σελίδες
...&c. Q, ED PROP. B. 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 to the fourth. First, if mA, mB be equimultiples of the magnitudes A and :B, mA : A : : mB : B. Take... | |
 | James Ryan, Robert Adrain - 1824 - 542 σελίδες
...: rB. QED PROr. C. THEOR. If the first be (lie 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. DEMONSTRATION. t 1. Supposing m lo be any integer greater than unity, let w»A the lirst be the same... | |
 | James Ryan - 1824 - 550 σελίδες
...: rB. QED PROP. C. THEOfl. If the first be the satne multiple of the second, or 1he same part of it that the third is of the fourth ; the first is to. the second as the third is to the fourth. DEMONSTRATION. I. Supposing m to be any integer greater than unity, let mA the first be the same multiple... | |
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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... 
