| George Crabb - Industrial arts - 1823 - 704 pages
...to be BE as CD to EF, then, by division, AE is to EB as CF to FD. Proportion by conversion is when **the first is to its excess above the second as the third to its excess above the fourth.** — Ordiiiate proportion, or proportion ex a:quali,\.e. from equality of distance, is when any number... | |
| James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...D and the ratio of rA-A to rB-B,is and therefore rA : rB : : rA— A : rB— B. QED PROP. E. THEOR. **If four magnitudes be proportionals, they are also...first is to its excess above the second as the third** is to its excess above the fourth. DEMONSTRATION. Let rA, A, rB, B, be the four proportionals, we have... | |
| James Ryan - Algebra - 1824 - 550 pages
...therefore rA : rB : : rA— A : rB— B. PROP. E. THEOR.~jt-*. If four magnitudes be-proportionals, **they are also proportionals by conversion ; that is,...first is to its excess above the second as the third** is to its excess above the fourth. DEMONSTRATION. Let rA, A, rB, B, be the four proportionals. we have... | |
| Peter Nicholson - Mathematics - 1825 - 1046 pages
...Book 5. XVII. Convertendo, by conversion ; when there are four proportionals, and it is inferred, that **the first is to its excess above the second, as the third to its excess above the fourth.** Prop. E. Book 5. XVIII. Ex xquali (se. distentía), or ex tequo, from equality of diittnce; when there... | |
| James Ryan - Algebra - 1826 - 430 pages
...rrrr^ rrs — D (i — I).D ?—, and therefore D rA: rB : : rA— A: rB— B. QED PROP. E. THEOR. **If four magnitudes be proportionals, they are also...first is to its excess above the second as the third** is to its excess above the fourth. DEMONSTRATION. Let rA, A, rB. B, be the four proportional?, we have... | |
| George Lees - 1826 - 276 pages
...a±b'.b:'.c ±d'. <?. 115. Iffour quantities be proportionals, they are also proportionals convertendo, **that is, the first is to its excess above the second, as the third to its excess above the fourth.** For, since a:b :: c:d, a — b:b::c — d:d, (No. 114.) and, alternately, (No. 112.) a — b: c —... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...first to that taken from the other. The demonstration is contained in the preceding. PROP. E. THEOR. **If four magnitudes be proportionals, they are also proportionals by conversion : that is, the** Jirst is to its excess above the second, as the third to its excess above the fourth. Let AB be to... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...(465) XVIII. COnvertendo, by conversion ; when there are four proportionals, and it is inferred that **the first is to its excess above the second as the third to its excess above the fourth.** Proposition E Book V. Conversion consists in substituting the differences of the antecedents A a and... | |
| John Playfair - Euclid's Elements - 1832 - 358 pages
...PROP. D. THEOR. If four magnitudes be proportionals, they are also proportionals by conversion, thai **is, the first is to its excess above the second, as the third to its excess above the fourth.** If A: B: : C: D, by conversion, A: A— B : : C: C— D. For, since A: B::C: D, by division (17. 5.1,... | |
| Euclid - Euclid's Elements - 1833 - 216 pages
...be proved, that, if there be four magnitudes proportional, and the first be greater than the second, **the first is to its excess above the second, as the third to its excess above the fourth.** Fig. 24. Cor. 2. If there be four magnitudes proportional, A to B as C to D, the difference between... | |
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