 | Robert Simson - Trigonometry - 1806 - 546 pages
...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... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...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... | |
 | John Mason Good - 1813 - 714 pages
...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... | |
 | Euclides - 1816 - 588 pages
...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... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...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.)... | |
 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...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... | |
 | James Ryan - Algebra - 1826 - 430 pages
...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... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...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... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...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... | |
 | John Martin Frederick Wright - Euclid's Elements - 1829 - 206 pages
...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... | |
| |
F is of B, and that magnitudes have the same ratio to one another which their equimultiples have; (v. 
