 | Euclid, Robert Simson - 1821 - 514 σελίδες
...first to that taken from the other: the demonstration is contained in the preceding. PROP. E. THEOR. ~4 IF four magnitudes be proportionals, they are also...first is to its excess above the second, as the third to its excess above the fourth. Let AB be to BE, as CD to DF; then BA is to A AE, as DC to CF. | Because... | |
 | Euclid - 1822 - 222 σελίδες
...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. Cor. 2. If there be four magnitudes proportional, AF,g, 34. to B as... | |
 | George Crabb - 1823 - 704 σελίδες
...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... | |
 | James Ryan, Robert Adrain - 1824 - 542 σελίδες
...fourth is to the fourth. XVII. Convertendo, by conversion, or conversely, when it is inferred that the first is to its excess above the second, as the third to its excess above the fourth. XVIII. Ex aequali (sc. distaritia), or ex aequo, from equality of distance,... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...taken from the 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, tJutt is, thf fini ii to ilt excess above the second, as the third to itt excess above the fourth.... | |
 | George Lees - 1826 - 276 σελίδες
...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,... | |
 | Robert Simson - 1827 - 546 σελίδες
...taken from the first to that taken from the other. The demonstration is contained in the preceding. PROP. E. THEOR. If four magnitudes be proportionals,...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 - 1828 - 542 σελίδες
...therefore A— C : BD = C : D. The following proposition is added by Simson. PROPOSITION E. THEOREM (498) If four magnitudes be proportionals, they are also...first is to its excess above the second as the third to its excess above the fourth. Let A : B = C : D, then A : A— B = C : C— D. For by division A—... | |
 | John Playfair - 1832 - 358 σελίδες
...but A: B: : C: D, therefore (11. 5.) AC: B— D: :A:B. Therefore, &c. QED COR. AC: BD::C:D. 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.... | |
 | Euclid - 1833 - 216 σελίδες
...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... | |
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THEOB.—If four magnitudes be proportionals, they are also proportionals by conversion; that is, the first is to its excess above the second, as the third to its excess above the fourth. Let AB be to BE, as CD to DF: then BA shall be to AE, as DC to... 
