 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.  Euclid's Elements of Geometry - Pagina 163door Euclid - 1872 - 261 pagina’sVolledige weergave - Over dit boek
 | Sir John Leslie - 1809 - 522 pagina’s
...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 pagina’s
...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... | |
 | Euclides - 1821 - 294 pagina’s
...C— D : D. This def. is proved by Cor. 2. Prop. 25. Book 5. 18. Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the...to the sum or difference of the third and fourth. Note. . If A : B : : C : D, then A : A± B : : C : C±D. This def. is proved by Prop. 21 & 25 and by... | |
 | Bewick Bridge - 1821 - 284 pagina’s
...<-±— 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 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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... | |
| |
