 | Sir John Leslie - 1809 - 522 σελίδες
...B—A:B:: D—C:D. PROP. XI. THEOR. The terms of an analogy are proportional by conversion ; that is, the first is to the sum or difference of the first and second, as the third to the sum or difference of the third and fourth. Let A: B:: C: D, and suppose A^B; then A: A=fcB:... | |
 | Bewick Bridge - 1818 - 254 σελίδες
...consequently, by Art. 99, a±b : b :: c±d : d. и Тн. 7. " If four quantities he proportional, U\K first is to " the sum or difference of the first and second, as the third to " the sum or difference of the third and fourth." For by THEOR. 6. a+b : b : : c±d : d, and alternately... | |
 | Bewick Bridge - 1821 - 284 σελίδες
...<-±— vdb ==—=--, consequently, by Art. 99, a + b : b : : c+_d : d. Тн. 7. "If four quantities be proportional, the first is to " the sum or difference of the first and second, as the third to " the sum or difference of the third and fourth." For by THEOR. 6, a+_l : b : : с ± d : d, and... | |
 | Rev. John Allen - 1822 - 516 σελίδες
...preceding, and theor. 3. 15. 5, it follows, that, "if four magnitudes be proportional, " by converting, the first, is to the sum or difference of the first...the sum or difference of the third " and fourth." PROP. XIX. THEOR. If the wAoie (^U), be to the wiwle (CD), as apart (-AE) taken away, is to apart(CF)... | |
 | Euclid - 1822 - 222 σελίδες
...difference between the third and fourth to the fourth. Cor. 2. Prop. 25. 18. By conversion, when we infer that if there be four magnitudes proportional, the...or difference of the first and second, as the third to the sum or difference of the third and fourth. Prop. 21 and 25 and Cor. 1. Prop. 25. 19. Ex sequali,... | |
 | Peter Nicholson - 1823 - 210 σελίδες
...orders. THEOREM 42. 122. If four quantities, a, b, c, d, be proportionals, the first will be to the sum of the first and second as the third is to the sum of the third and fourth. For, since a, b, c, d, are proportionals, ad=be. To each side of this equation... | |
 | George Peacock - 1830 - 732 σελίδες
...magnitudes be proportionals, they shall be proportionals also convertendo, or the first shall be to the difference of the first and second as the third is to the difference of the third and fourth." Let a : b :: c : d, then also a : a — b :: c : c—d. VI* a... | |
 | Euclid - 1833 - 216 σελίδες
...difference between the third and fourth to the fourth. Cor. 2. prop. 25. 18. Byconversion; when we infer that if there be four magnitudes proportional, the...or difference of the first and second, as the third to the sum or difference of the third and fourth. Prop. 21, and 25. and Cor. 1. prop. 25. 19. Ex asquali,... | |
 | George Darley - 1836 - 172 σελίδες
...to the fourth, 117. ART. 174. In a series of four proportional right lines, the first is to the sum of the first and second as the third is to the sum of the third and fourth, ibid. ART. 175. In a series of four proportional right lines, the first is... | |
 | Andrew Bell - 1837 - 290 σελίδες
...the third, together with the fourth, is to the fourth. 24. By addition, when the first is to the sum of the first and second, as the third is to the sum of 'the third and fourth. second, is to the second, as the excess of the third above the fourth, is... | |
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Convertendo ; when it is concluded, that, if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth. 
