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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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The Elements of Plane and Solid Geometry

Henry William Watson - 1871 - 285 pagina’s
...of a triangle is half the area of a parallelogram upon the same base and between the same parallels, and because magnitudes have the same ratio to one another which their equimultiples have, therefore the areas of triangles between the same parallels are to one another as their bases. Corollary...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...equimultiples whatever G and 11. Demonstration. 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 1. A is to B, as E is to F; but as A is to B so is C to D (hyp.) ; wherefore 2....
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Elements of Geometry Containing Books I. to VI. and Portions of Books XI ...

James Hamblin Smith - 1876
...to B as A, C, E... together is to B, D, .F... together. V. Def. 5. QBD PROPOSITION XL (Eucl. v. 15.) Magnitudes have the same ratio to one another which their equimultiples have. Let A be the same multiple of C that B is of D. Then must C be to D as A to B. Divide A into magnitudes...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 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; (v. 15.) therefore A is to B, as E is to F: but as A is to B so is Cto D; (hyp.) wherefore as C is...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...parallelogram CF is to CE. It is plain that ABC is to ACD as CF is to CE. PROP. XVI. COROLLARY. 5. Magnitudes have the same ratio to one another, which their equimultiples have. It is plain that ABC to ACD as parallelogram CF to CE and CF and CE are equimultiples of ABC and ACD....
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...be proved that if A = C, B = D ; and if A be less than C, B is less than D. PROPOSITION 15. THEOREM. Magnitudes have the same ratio to one another which their equimultiples have. Let A and B be two magnitudes, and m any number : it is required to prove A : B — mA : mB. Because...
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Ellen: Or, Whisperings of an Old Pine, Volume 1

Joseph Battell - 1903
...greater than, equal to, or less than the other, its consequent must be equally so. PROPOSITION' XV. ' Magnitudes have the same ratio to one another which their equimultiples have.' " Because the mutual relation of the magnitudes to each other in respect of quantity is the same. "...
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A Text-book of Euclid's Elements for the Use of Schools, Boek 1

Euclid - 1904 - 456 pagina’s
...if A > B, then C : A< C : B ; v. 5. which is contrary to the hypothesis ; .-. A < B. PROPOSITION 8. Magnitudes have the same ratio to one another which their equimultiples have. Let A, B be two magnitudes ; then shall A : B : : mA : mB. If p, q be any two whole numbers, then in...
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