 | 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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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. 
