 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...  The First Six Books with Notes - Page 168by Euclid - 1822 - 179 pagesFull view - About this book
 | James Ryan - Algebra - 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 - Algebra - 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 - Mathematics - 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 - Algebra - 1826 - 430 pages
...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 is 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... | |
 | 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... | |
 | 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... | |
 | Robert Simson - Trigonometry - 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 - Industrial arts - 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 - Euclid's Elements - 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 - Geometry - 1829 - 548 pages
...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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