 | Charles Lutwidge Dodgson - 1874 - 96 pages
...¿>C, .•. , substituting, ->1 ; QED by c, a>c. Similarly, if A = C, a=c; and if A<C, a<c. PROP. XXI. If there be three magnitudes and other three, which, taken two and two in a cross order, have the same ratio : then, if the first be greater than the third, the fourth is... | |
 | Euclides - 1884 - 434 pages
...17 .-. A - C: B - D = C: D, by alternation; V. 16 .-. A- C:B - D = A:BF 11 PROPOSITION 20. THEOREM. If there be three magnitudes, and other three, which, taken two and two in direct order, have the same ratio; if the first be greater than the third, the fourth shall be greater... | |
 | Joseph Battell - Force and energy - 1903 - 722 pages
...if 9:3: : 12:4, then 9:9 — 3(6): : 12: : 12—4(8). See Axiom 1 1. PROPOSITION XX. ' If there are three magnitudes, and other three, which taken two and two have the same ratio ; if the first is greater than the third, the fourth is greater than the sixth ; if equal, equal ; and if less, less.'... | |
 | Euclid - Mathematics, Greek - 1908 - 456 pages
...perturbed, then, if ex aequali the first magnitude is greater than the third, the fourth will also be greater than the sixth; if equal, equal; and if less, less. Let there be three magnitudes A, B, C, and others D, E, F equal to them in multitude, which taken two... | |
 | Euclid - 452 pages
...are in the same ratio, and if ex aequali the first be greater than the third, the fourth will also be greater than the sixth; if equal, equal ; and, if less, less. Let there be three magnitudes A, B, C, and others D, E, F equal, to them in multitude, which taken... | |
 | Peter M. Engelfriet - Mathematics - 1998 - 516 pages
...perturbed, then, if ex aequali the first magnitude is greater than the third, the fourth will also be greater than the sixth; if equal, equal; and if less, less. [If A:B=E:F, and B:C=D:E, then, accordingly as A>=<C, also D>=<F] Heath If there be any number of magnitudes... | |
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XX. THEOR. IF there be three magnitudes, and other three, which, taken two and two, have the same ratio ; if the first be greater than the third, the fourth shall be greater than the sixth ; and if equal, equal ; and if less, less... 
