| James Ryan - 1824 - 550 pages
...treat of propov\\ov\, i the method of PROP. IV. THEOR. -4' •* ,' It'tlictirft of four magnitudes has **the same ratio to the second which the third has to the fourth** ; then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples... | |
| James Ryan, Robert Adrain - 1824 - 542 pages
...method of demonstration adopted in this essay. PROP. IV. THEOR. If the first of four magnitudes has **the same ratio to the second which the third has to the fourth;** then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples,... | |
| Peter Nicholson - 1825 - 1046 pages
...and С have been taken certain equimultiples K, L ; and of В and О 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 have the sam« ratio to the second and... | |
| James Ryan - 1826 - 430 pages
...ratio of C to D ; or that the ratio of C to D is less than the ratio of A ta B. The Fiftli Definition **according to Euclid. The first of four magnitudes...said to have the same ratio to the second which the** tnird has to the four h, when any equimultiples whatsoever of the first and third being taken, and... | |
| Euclid - 1826 - 234 pages
...— = 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 pages
...- 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... | |
| Robert Simson - 1827 - 546 pages
...greater ratio to the second, than the fifth has to the sixth. PROP. XIV. THEOR. See N. If the Jirst **have the same ratio to the second which the third has to the fourth;** then, if the first be greater than the third, the second shall be greater than the fourth ; and if... | |
| Perry Fairfax Nursey - 1827 - 588 pages
...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... | |
| Euclid, Dionysius Lardner - 1828 - 542 pages
...Propositions are introduced by SIMSON. PROPOSITION A. THEOREM. (480) If the first of four magnitudes **have the same ratio to 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 ; and if... | |
| Euclid, Robert Simson - 1829 - 548 pages
...said to have a ratio to one another, when 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** scoond, which the third has to the fourth, when any equimultiples whatsoever of the first and third... | |
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