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" PROP. XV. THEOR. 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 shall be to F, as AB to DE. "
A new supplement to Euclid's Elements of geometry, by the author of 'A new ... - Pagina 41
door Joseph Denison - 1840 - 84 pagina’s
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 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...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...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...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...that is, B is less than D. Wherefore, If the first %c. QED . . . * DAB c DAB c PROP. XV. THEOR. Magnitudes have the same ratio to one another which their equimultiples have. Let AB and DE be equimultiples of C and F : C shall be to F as AB to DE. For, because AB is the same...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 317 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...
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THE SOLUTIONS OF GEOMETRICAL PROBLEMS

THOMAS GASKIN, M.A., - 1847
...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...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...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...
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Alternate circles and their connection with the ellipse

Edward Adolphus Seymour (11th duke of Somerset.) - 1851
...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...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...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...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 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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