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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 Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 pagina’s
...by the first case ; wherefore B is less than D. Therefore, if the first, &c. QED t 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 pagina’s
...it can be proved that if A=*C, B=D ; c JQ. 5. and if A<C, B<D. Therefore, &c, QED 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 : Ba, A : B...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...second shall be greater than the fourth; and if t-qnal, equal ; and if less, less. Prop. XV. Theor. Magnitudes have the same ratio to one another which their equimultiples have. Prop. XVI. Theor. If four magnitudes of the same kind be proportionals, they shall also be proportionals...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pagina’s
...B, by the first case; wherefore B is lass 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 pagina’s
...manner, it is proved, that if A = C, B = D ; and it' AzC, B/.D. Therefore, &c. Q, ED PROP. XV. THEOR. Magnitudes have the same ratio to one another which their equimultiples have. If A and 13 be two magnitudes, and m any number, A : B : : mA : mB. Because A : B : : A : B (7. S.)...
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An Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan, Robert Adrain - 1824 - 516 pagina’s
...suppose rA=rB, then by division A= B: lastly, suppose rA ZrB, then by division A-^: BQED PROP. XV. THEOR. Magnitudes have the same ratio to one another which their equimultiples have. DEMONSTRATION. Let A, B be any two magnitudes of the same kind ; and m being any integer grtiter than...
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An Elementary Treatise on Algebra: Theoretical and Practical ...

James Ryan - 1826 - 383 pagina’s
...suppose rA=rB, then by division A= B : lastly, suppose rA^rB, then by division Av BQED PROP. xv. THEOR. Magnitudes have the same ratio to one another which their equimultiples have. DEMONSTRATION. Let A, B be any two magnitudes of the same kind ; and m being any integer greater than...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 pagina’s
...B, by the first case; that is, 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 to DE. Because AB is the...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 324 pagina’s
...D is greater than B, by the first case ; that is, B is less than D. PROPOSITION XV. THEOREM. (492) 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 : then C : F = AB : D E. Because AB is the same multiple...
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Self-examinations in Euclid

John Martin Frederick Wright - 1829 - 188 pagina’s
...C3 BK = 2 x ^ BCD, •:. •:.-•_ and £Z7 J3F = 2 x ^ AAC; /. 2 ^i BCD : 2 ^\ J34C :; DH: AM. But magnitudes have the same ratio to one another which their equimultiples have (Prop. XV., Book V.) .-. s\ BCD : s\ BAG ;: DH : AM. Also £Z7* upon = bases being double of ^/\* on...
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