 | James Ryan - 1824 - 550 pagina’s
...D Therefore mrA : A : : ?nrB : B. in like manner we prove that rA :?iA : : rB : nB. PROP. A. THEOR. If the first of four magnitudes has the same ratio to the second which (he third has to the fourth ; then if the first lie greater than the second, the third is also greater... | |
 | James Ryan, Robert Adrain - 1824 - 542 pagina’s
...ratio of A to B. The Fifth Definition according to Euclid. The first of four magnitudes is said to have the same ratio to the second which the third has to the. fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
 | Peter Nicholson - 1825 - 1046 pagina’s
...less can IK- multiplied so as to exceed the other. V. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
 | James Ryan - 1826 - 430 pagina’s
...; Therefore mrA : A : : rnrB : B. in like manner we prove that rA : nA : : rB : nB. PROF. A. THEOR. If the first of four magnitudes has the same ratio...the second which the third has to the fourth ; then if the first be greater than the second, the third is also greater than the fourth ; if equal, equal... | |
 | Euclides - 1826 - 226 pagina’s
...Оr r— = — Оr - = -r. QEI». • 1 Ax. 5. PROPOSITION XXIV. THEOREM. If the first magnitude have the same ratio to the second which the third has to the fourth; and the fifth, the same ratio to the second, which the sixth has to the fourth; then the first and... | |
 | Euclid - 1826 - 234 pagina’s
...T- or - = TQKI>. • 1 Ax. 5. be/ e be fe cf PROPOSITION XXIV. THEOREM. If the first magnitude have the same ratio to the second which the third has to the fourth, ; and the fifth, the same ratio to the second, which the sixth has to the fourth ; then the first and... | |
 | Euclid, John Playfair - 1826 - 326 pagina’s
...; whenee also mB=mnC, and by hypothesis A=mB. therefore A=nwC. Therefore, &e. QED PROP. IV. THEOR. If the first of four magnitudes has the same ratio to the seeond whieh the third has to the fourth, and if any equimultiples whatever be taken of the first and... | |
 | Perry Fairfax Nursey - 1827 - 588 pagina’s
...of the proposition <>f Euclid. Book 5, " If the first of four magAbGEBBAIUAL BQtATIOX. 537 nitudes has the same ratio to the second, which the third has to the fourth, theu, if the first be greater thiin the second, the third is also greater than the fourth ; and if... | |
 | Robert Simson - 1827 - 546 pagina’s
...the less can be multiplied so as to exceed the other. V. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
 | Euclid, Dionysius Lardner - 1828 - 542 pagina’s
...= 2C:3D (Def. V.) : and the same reasoning is generally applicable. COR. — Likewise, if the first has the same ratio to the second, which the third has to the fourth, then also any equimultiples whatever of the first and third shall have the same ratio to the second and... | |
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The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple... 
