| Sir John Leslie - Geometry, Plane - 1809 - 493 pages
...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 - Algebra - 1818 - 227 pages
...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 - Algebra - 1821 - 288 pages
...<-±— 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 - Astronomy - 1822 - 516 pages
...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 - 179 pages
...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 - Architecture - 1823 - 210 pages
...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 - Algebra - 1830 - 732 pages
...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 - Euclid's Elements - 1833 - 183 pages
...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 - Euclid's Elements - 1836 - 172 pages
...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 - Euclid's Elements - 1837 - 240 pages
...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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