 | John Playfair - 1806 - 320 σελίδες
...magnitudes, taken separately, be proportionals, they will also be proportionals when taken jointly, that is, if the first be to the second as the third to the fourth, the first and second together will be to the second, as the third and fourth together to the fourth.... | |
 | Robert Simson - 1806 - 546 σελίδες
...taken separately, be proportionals, see N. they shall also be proportionals when taken joindy, that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together to the fourth.... | |
 | John Mason Good - 1813 - 714 σελίδες
...taken separately, he proportionals, they shall also be proportionals, when taken jointly, that is, if the first be to the second, as the third to the fourth, the first and second together shall he to the second, as the third and fourth together to the fourth.... | |
 | Charles Butler - 1814 - 540 σελίδες
...one or two more particulars will require an explanation. If four numbers are proportionals, that is, if the first be to the second as the third to the fourth, then will the first be to the third аз the second to the fourth; and this accounts for the usual... | |
 | Euclides - 1814 - 560 σελίδες
...is to B, as C is to D: Therefore, if the first be the same multiple, A. &c. QED CD H PROP. D. THEOR. IF the first be to the second as the third to the s«- N. fourth, and if the first be a multiple or part of the second ; the third is the same multiple,... | |
 | Charles Hutton - 1815 - 686 σελίδες
...equal to the fourth; if greater, greater; if less, less." " Prop. 2. If the first df four magnitudes be to the second as the third to the fourth, and if any equimultiples whatever of the first and third be taken, and also any equimultiples of the second... | |
 | Euclides - 1816 - 588 σελίδες
...is to B, as C is to D : Therefore, if the first be the same multiple, A. &c. QED CI) PROP. D. THEOR. IF the first be to the second as the third to the See N. fourth, and if the first be a multiple or part of the second ; the third is the same multiple,... | |
 | Bewick Bridge - 1818 - 254 σελίδες
...с : b : d, and b : d :; a.: c. cd cd, с а Тн. 5. "If there be six proportional quantities, and the " first be to the second as the third to the fourth ; and the third " to the fourth as the fifth to the sixth ; then will the first " be to the second as the... | |
 | John Playfair - 1819 - 350 σελίδες
...demonstrated, A : C : : B : D, and inversely (A. 5.) C : A : : D : B. Therefore, &c. q. ED PROP. C. THEOE. If the first be to the second as the third to the...if the first be a multiple or a part of the second, ihe third is the same multiple or the same part of the fourth. Let A : B : : C : D, and first let A... | |
 | Daniel Cresswell - 1819 - 446 σελίδες
...B:A::D:C; .-. (S. 2. 5.) A:B::C:D. PROP. IV. 4. THEOREM. If the first of four proportional magnitudes be a multiple, or a part, of the second, the third is the same multiple, or the same part, of the fourth. If A:B::C: D, and if A = pB, then C = pD. For (hyp. and S. 3. 5.) A :... | |
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IF the first be to the second as the third to the fourth, and if the first be a multiple, or part of the second; the third is the same multiple, or the same part of the fourth... 
