 | Robert Simson - 1838 - 434 σελίδες
...first case ; and therefore D is less than F. Therefore, if there be three, &c. QED PROP. XXI. THEOR. IF there be three magnitudes, and other three, which...same ratio taken two and two, but in a cross order, if the first magnitude be greater than the third, the fourth shall be greater than the sixth ; and... | |
 | Euclid - 1838 - 470 σελίδες
...equal, equal; and if less, less.* Let A, B, C be three magnitudes, and D, E, F other three, which nave the same ratio, taken two and two, but in a cross order, viz. as A is to B, so is E to F, and as B is to C, so is D to E. If A be greater than C, D shall be... | |
 | Euclides - 1840 - 192 σελίδες
...E, and B : A : : E : D ; therefore, by the first case, if C/'A, ¥-7D, that is, if PROP. XXI. THEOR. If there be three magnitudes, and other three, which have the same ratio taken two and two, but irregularly ; if the first magnitude be greater than the third, the fourth is greater than the sixth... | |
 | Oliver Byrne - 1841 - 144 σελίδες
...er-, =, or -3 then will < c-, —, or (14 B. v.) . If there be three magnitudes, &c. PROP. XXI. THEO. If there be three magnitudes, and other three which...first magnitude be greater than the third, the fourth shall be greater than the sixth ; and if equal, equal ; and if less, less. Let Г"), \^_), [_}, be... | |
 | Euclides - 1841 - 378 σελίδες
...than the sixth: and if equal, equal; and if less, less. Let A, B, C be three magnitudes, and D, E, F other three, which have the same ratio, taken two and two, but in a cross order, viz, as A is to B, so is E to F, and as B is to C, so is D to E: then if A be greater than C, D shall... | |
 | John Playfair - 1842 - 332 σελίδες
...: : E : D ; therefore, by the first case, if C7 A, F 7D, that is, if A/; C, D/F. PROP. XXI. THEOR. If there be three magnitudes, and other three, which...same ratio taken two and two, but in a cross order; if the first magnitude be greater than the third, the fourth is greater than the sixth; if equal, equal... | |
 | Euclid, James Thomson - 1845 - 382 σελίδες
...; that is, D is less than F. Therefore, if there be three magnitudes, &c. BC PROP. XXI. THEOR. — If there be three magnitudes, and other three, which...same ratio taken two and two, but in a cross order ; if the first be greater than the third, the fourth is greater than the sixth ; if equal, equal ;... | |
 | Euclides - 1845 - 546 σελίδες
...than the sixth ; and if equal, equal ; and if less, less. Let A, B, C be three magnitudes, and D, E, F other three, which have the same ratio, taken two and two, but in a cross order, viz. as A is to B, so is E to F, and as B is to C, so is D to E. If A be greater than C, D shall be... | |
 | Euclid - 1845 - 218 σελίδες
...and two, but in a crost order ; if the first magnitude be greater than the third, the fourth shatt be greater than the sixth ; and if equal, equal ; and if less, less. EUCLID S ELEMENTS. A D EV B is to C, so is D to E. If A be greater than C, D shall be greater than... | |
 | Euclid, John Playfair - 1846 - 334 σελίδες
...and B : A : : E : D ; therefore, by the first case, if C/A, F/D, that is, if A^C, PROP. XXI. THEOR. If there be three magnitudes, and other three, which...have the same ratio taken two and two, but in a cross frder; if the first magnitude be greater than the third, the fourth is greater than the sixth; if equal,... | |
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... If there be three magnitudes, and other three, which have the same ratio taken two and two, but in a cross order; then if the first magnitude be greater than the third, the fourth shall be greater than the sixth: and if equal, equal; and if less,... 
