 | Euclid - 1845 - 218 pagina’s
...first case ; wherefore B is less than D. Therefore, if the first, &c. QED PROPOSITION XV. THEOB. — Magnitudes have the same ratio to one another which their equimultiples have. Let AB be the same multiple of C, that DE is of F : C is to F, as AB to DE. Because AB is the same... | |
 | Euclides - 1845 - 546 pagina’s
...the first case ; that is, B is less than D. Therefore, if the first, &c. QED PROPOSITION XV. THEOREM. Magnitudes have the same ratio to one another which their equimultiples have. Let AB be the same multiple of C, that T>E is of F. Then C shall be to F, as AB to DE. Because AB is... | |
 | Euclides - 1846 - 292 pagina’s
...any equimultiples whatever G, H : Then, because E is the same multiple of A that F is of B, and that magnitudes have the same ratio to one another which their equimultiples have (5. 15) therefore A is to B as E is to F : But A is to B as C is to D ; therefore C is to D as E is... | |
 | Dennis M'Curdy - 1846 - 166 pagina’s
...are so divided in the diagram that each may be taken greater or less as the case may require. 15 Th. Magnitudes have the same ratio to one another which their equimultiples have. Given two magnitudes C, F ; and equimultiples of them, AB, DE : C is to F as AB is to DE. Because AB... | |
 | Euclid, John Playfair - 1846 - 334 pagina’s
...B/D (10. 5.). In the same manner, it is proved, that if A=C, B=D ; and if A-/C, B/D. PROP. XV. THEOR. Magnitudes have the same ratio to one another which their equimultiples have. B : : 2A : 2B. And in the same manner, since A : B : : 2A : 2B, A : B : : A+2A : B+2B (12. 5.), or... | |
 | Thomas Gaskin - 1847 - 301 pagina’s
...that xl, yl are co-ordinates of a point in the hyperbola. ST JOHN'S COLLEGE. DEC. 1846. (No. XVII.) 1. MAGNITUDES have the same ratio to one another which their equimultiples have. Give Euclid's definition of equal ratios. Explain why the properties proved in Book v. by means of... | |
 | Euclides - 1848 - 52 pagina’s
...second shall be greater than the fourth; and if equal, equal ; and if less, less. PROP. XV. THEOREM. Magnitudes have the same ratio to one another which their equimultiples have. PROP. XVI. THEOREM. If four magnitudes of the same kind be proportionals, they shall also be proportionals... | |
 | Edward Adolphus Seymour (11th duke of Somerset.) - 1851 - 84 pagina’s
...Proposition. And again, ON =2u; therefore, 2t : 2u :: 2c : 2y. Then, cu = ty, and M : y : : t : c. That magnitudes have the same ratio to one another which their equimultiples have, and that if four straight lines be proportionals, their squares shall also be proportionals ; and if... | |
 | Royal Military Academy, Woolwich - 1853 - 400 pagina’s
...equimultiples whatever G and H : And because E is the same multiple of A, that F is of B, and that magnitudes have the same ratio to one another which their equimultiples have (15. v.) ; therefore A is to B, as E is to F: But as A is to B, so (ffyp.) is C to D ; wherefore as... | |
 | Euclides - 1853 - 176 pagina’s
...equimultiples whatever g and д : and because e is the same multiple of a that f is of b, and that magnitudes have the same ratio to one another which their equimultiples have (v. 15) ; therefore a is to b, as e pg, is to f ; but as a is to b, so is С to d ; wherefore as С... | |
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F is of B, and that magnitudes have the same ratio to one another which their equimultiples have; (v. 
