| Euclides - 1845 - 546 pages
...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 - Geometry - 1853 - 176 pages
...; 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 pages
...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 pages
...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 - Geometry, Plane - 1860 - 380 pages
...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 pages
...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 pages
...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 pages
...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 pages
...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 - Euclid's Elements - 1867 - 424 pages
...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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