 | Euclides - 1845 - 546 σελίδες
...if less, less : but F is any multiple whatever of C, and D, E are any equimultiples whatever of A, B; therefore, C is to A as C is to B. (v. def. 5.) Therefore, equal magnitudes, &c. QED PROPOSITION VIII. THEOREM. Of two unequal magnitudes, the greater... | |
 | Euclides - 1853 - 176 σελίδες
...; if less, less. And f is any multiple whatever of c, and d, e are any equimultiples whatever of a, b. Therefore c is to a as c is to b (v. def. 5). Therefore, equal magnitudes, &c. QED cf PROPOSITION VIII. — THEOREM. Of unequal magniiudes the greater... | |
 | Euclides - 1855 - 270 σελίδες
...likewise greater than E ; if equal, equal ; and if less, less. But F is any multiple whatever of С, and D and E are any equimultiples whatever of A and B. Therefore С is to A as С is to B (V. lief. 5). Therefore, equal magnitudes, &c. QED PROP. VIII. THEOREM. Of... | |
 | Euclid - 1859 - 150 σελίδες
...greater than D, F is likewise greater than E ; if equal, equal ; and if less, less. But F is any multiple of C, and D and E are any equimultiples whatever of A and B. Therefore С is to A as С is to B (Def. VI.). Therefore, equals have the same ratio, &c. QED Annotation. The... | |
 | Robert Potts - 1860 - 380 σελίδες
...equal; if less, less; but lPis any multiple whatever of C, and D, E are any equimultiples whatever of A, B; therefore, C is to A as C is to B. (v. def. 5.) Therefore, equal magnitudes, &c. QED PROPOSITION VIII. THEOREM. Of two unequal magnitudes, the greater... | |
 | Euclides - 1863 - 122 σελίδες
...Therefore if F be greate, than D, F is likewise greater than E; if equal, equal; and if less, less. But F is any multiple whatever of C; and D and E are...and B. Therefore C is to A as C is to B (V. Def. 5). Therefore, equal magnitudes, &c. QED PEOP. VIII. (THEonEM.)— Of unequal magnitudes (AB,BC), the greater... | |
 | Euclides - 1864 - 448 σελίδες
...if less, less ; but .Fis any multiple whatever of C, and D, E are any equimultiples whatever of A, B; therefore, C is to A as C is to B. (v. def. 5.) Therefore, equal magnitudes, &c. QED PROPOSITION VIII. THEOREM. Of two unequal magnitudes, the greater... | |
 | Euclides - 1865 - 402 σελίδες
...and if less, less; but F is any multiple whatever of C, and D, E are any equimultiples whatever of A, B ; therefore, C is to A as C is to B. (v. def. 5.) Therefore, equal magnitudes, &c. QED PEOP. Vm.— THEOREM Of unequal magnitude!, the greater has a... | |
 | Robert Potts - 1865 - 528 σελίδες
...if less, less ; but F is any multiple whatever of C, and D, E are any equimultiples whatever of A, B; therefore, C is to A as C is to B. (v. def. 5.) Therefore, equal magnitudes, &c. QED PROPOSITION VIn. THEOREM. Of two unequal magnitudes, the greater... | |
 | Euclid, Isaac Todhunter - 1867 - 424 σελίδες
...E. Therefore if F be greater than D, F is greater than E ; and if equal, equal ; and if less, less. But F is any multiple whatever of C, and D and E are any equimultiples whatever of A and B; [Construction. therefore C is to A as C is to B. [V. Definition 5. Wherefore, equal magnitudes &c.... | |
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F is greater than E; and if equal, equal; and if less, less. But F is any multiple whatever of C, and D and E are any equimultiples whatever of A and B; [Construction. 
