 | John Playfair - 1806 - 320 σελίδες
...fourth. 17th prop, book 5. XVIII. Convertendo, by conversion: when there are four proportionals, and it is inferred, that the first is to its excess above...second, as the third to its excess above the fourth. Prop. D. book 5. XIX. Ex sequali (sc. distantia), or ex sequo, from equality of distance ; when there... | |
 | Robert Simson - 1806 - 546 σελίδες
...fourth. 17th prop, book 5. XVII. Convertendo, by conversion ; when there are four proportionals, and it is inferred, that the first is to its excess above the Q Bonk v. second, as the third to its excess above the fourth. Prop. E, *— v— ' books. XVIII. Ex... | |
 | Charles Butler - 1814 - 582 σελίδες
...— — , that is, a—b:b::c—d:d; thii is called 01 viha DESDO. Euclid 17, 5. 68. In like manner, the first is to its excess above the 'second, as the third to its excess above the fourth. a— b c—d , , ,. , . bd Because — ; — = — - — by the preceding, and since — = — , odac... | |
 | Euclides - 1816 - 588 σελίδες
...E. THEOR. 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 istoAE, as DC to CF. Because AB is to BE, as CD to DF, by di•... | |
 | John Playfair - 1819 - 350 σελίδες
...fourth. 17th Prop. Books. XVIII. Convertendo, by conversion : When there are four proportionals, and it is inferred, that the first is to its excess above...second, as the third to its excess above the fourth. Prop. D. Book 5. XIX. Ex aaquali (sc. distantia), or ex aequo, from equality of distance ; when there... | |
 | Daniel Cresswell - 1819 - 446 σελίδες
...THEOREM. 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 A+B : B : : C + D : D ; then A+B : A : : C+D:C. For (dividendo) A : B : : C : D ; .•. (invertendo)... | |
 | John Playfair - 1819 - 354 σελίδες
...fourth. ,17th Prop. Book 5. XVIII. Convertcndo, by conversion : When there are four proportionals, and it is inferred, that the first is to its excess above the second, ns th*. third to its excess above the fourth. Prop. D. Book 5. XIX. Kx aequali (sc. distantia), or... | |
 | 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 C to D ; the difference between... | |
 | 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 of distance, is when any number... | |
 | James Mitchell - 1823 - 666 σελίδες
...equal areas; but it is impossible the sides of the former can all coincide with those of the l.uki CONVERSION of Proportion, is •when of four proportionals it is inferred that the li is to its excess above the 2df as the 3d to its excess above the 4th. CONVEX, round or curved, or... | |
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... when there are four proportionals, and it is inferred, that the excess of the first above the second, is to the second, as the excess of the third above the fourth, is to the fourth. 
