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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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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 pagina’s
...of the second and fourth, these like parts will likewise be proportionals. PROP. 17. (Eue. v. 15.; Magnitudes have the same ratio to one another which their equimultiples have. For, if от А, от В be any equimultiples whatever of A, B, it is evident, that any part P of В...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...any like parts of the second and fourth, these like parts will likewise be proportionals. PROP. [17]. Magnitudes have the same ratio to one another, which their equimultiples have. Let M, N be equimultiples of А, В : that is, let А в м в M, N contain А, В the | same number...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pagina’s
...by the first case; wherefore, B is less than D. Therefore, " if the first," &c. QED 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 is to F, as AB to DE. Because AB is the same multiple...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 pagina’s
...than the third, the second shall be greater than the fourth ; if equal, equal ; and if less, less. XV. Magnitudes have the same ratio to one another which their equimultiples have. XVI. If four magnitudes of the same kind be proportionals, they will also be proportionals when taken...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 pagina’s
...(V. 10). In the same manner, it is proved, that if A = C, B = D; and if A PROPOSITION XV. THEOREM. Magnitudes have the same ratio to one another which their equimultiples have. If A and B be two magnitudes, and m any number, A : B : : mA. : mB. ( V. 12), or A : B : : 2 A : 2B....
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...(v. Prop. 10). In the same manner it is proved, that if A = C, B = D ; and if A^C, PROP. XV. THEOR. Magnitudes have the same ratio to one another which their equimultiples have. If A and B be two magnitudes, and m any number, A : B : : mA : mB. Because A : B : : A : B ; A : B...
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The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - 1841 - 98 pagina’s
...the same way it may be readily shown, if A be :zr or -3 С, В will be =r or -3 D. PROP. XV. THEO. Magnitudes have the same ratio to one another which their equimultiples have. Let Q and Д ^e two magnitudes ; then, О : D - M'O : М'ПF О : D = О : D .-. О:П :: 4O: And...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 pagina’s
...B, by the first case; wherefore B is less than D. Therefore, if the first, &c. QED 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 is to DE. Because AB is the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 pagina’s
...B7D (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. If A and B be two magnitudes, and m any number, A : B . : mA : mB. Because A : B : : A : B (7. 5.)...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...less than the least that can be assigned. Thus it may be considered that m : A :: n : BQED PROP. I. MAGNITUDES have the same ratio to one another which their equimultiples have. Let A and в be two magnitudes, and CG and DL equimultiples of them : A : B::GG : DL. Let P be a common...
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