 | James Ryan, Robert Adrain - 1824 - 542 σελίδες
...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 σελίδες
...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... | |
 | Euclid, John Playfair - 1826 - 326 σελίδες
...repeated m times=mnC ; 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... | |
 | Euclid - 1826 - 234 σελίδες
...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... | |
 | Euclides - 1826 - 226 σελίδες
...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... | |
 | Perry Fairfax Nursey - 1827 - 588 σελίδες
...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 σελίδες
...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 σελίδες
...= 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... | |
 | Pierce Morton - 1830 - 584 σελίδες
...magnitude of the other ; and conversely (ax. 1, 2, 3, 4).* ' " The first of fonr magnitudes is enid to bare the same ratio to the second, wh'ich the third has to the fourth, when any equimultiples whatsoever of the fir>t aiid third being taken, ¡ind any equimultiples whatsoever... | |
 | Euclid - 1833 - 216 σελίδες
...controversy among geometers. Euclid defines them thus : The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equi-multiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
| |
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... 
