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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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Manual of Euclid: Books IV, V, VI, and Propositions 1-21 of Book XI

Euclid - 1868 - 141 páginas
...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 - 1868 - 410 páginas
...; 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 Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...but F is any multiple whatever of C; and D, E are any equimultiples whatever of A, B ; therefore 2. C is to A, as C is to B (V. Def. 5). Therefore, equal magnitudes, &c. QED PROPOSITION 8.— Theorem. Of two unequal magnitudes, the greater...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 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 geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...Therefore if F be greater 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...whatever of A and B. Therefore C is to A as C is to B (V. Uef. 5). Therefore, equal magnitudes, &c. QED PROP. VIII. THEORKM. Of vntgual magnitudes, the greater...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 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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