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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. "
Elements of Geometry: Containing the Principal Propositions in the First Six ... - Página 143
por Euclid - 1789 - 272 páginas
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...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...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 páginas
...; 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...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...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...
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Manual of Euclid: books iv., v., vi., by J.A. Galbraith and S. Haughton

Euclides - 1859
...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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 páginas
...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...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...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...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...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...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...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...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 páginas
...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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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 páginas
...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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