 | Wales Christopher Hotson - 1842 - 306 pages
...:: a + c + e ... : 6 + d +/... 149. Geometrical Definition of Proportion. (Euclid, book v. def. 5). The first of four magnitudes is said to have the same...first and third being taken, and any equimultiples whatsover of the second and fourth ; if the multiple of the first, be less than that of the second,... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...mB=mnC, and by hypothesis A=mB, therefore A=wmC PROP. IV. THEOR. If the first of four magnitudes has the same ratio to the second which the third has to the fourth, and if any equimultiples whatever be taken of the first and third, and any whatever of the second and... | |
 | George Peacock - Algebra - 1842 - 426 pages
...of the second, the multiple of the thii will be equal to that of the fourth : and if the multiple of first be less than that of the second, the multiple of the will be less than that of the fourth. It is this proposition which is deduced as a necessary consequence... | |
 | Scottish school-book assoc - 1845 - 444 pages
...geometrical magnitudes, and therefore it is necessary to substitute another, which is as follows: — Def. The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples whatever of the first and third being taken,... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...whatever of G, H: therefore (V. def. 5) as E : G : : F : H. Therefore, &c. Cor. Likewise, if the first have the same ratio to the second, which the third has to the fourth, then also any like multiples whatever of the first and third have the same ratio to the second and... | |
 | Euclides - 1845 - 546 pages
...is to G, so is F to H. (v. def. 5.) Therefore, if the first, &c. QED COB. 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... | |
 | Euclid - Geometry - 1845 - 218 pages
...ratio to the second, than the fifth has to the sixth. PROPOSITION XIV. THEOR. — If the first has 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... | |
 | Dennis M'Curdy - Geometry - 1846 - 168 pages
...having some common property ^ can have a ratio to one another. 5. The first of four magnitudes has the same ratio to the second which the third has to the fourth, when equimultiples of the first and third, also of the second and fourth, being taken ; if the multiple... | |
 | Dennis M'Curdy - Geometry - 1846 - 166 pages
...multiple, &c. QED Recite (a) definitions 1, 2, A of b 5 -B D-0 H4 Th. If the first of four magnitudes have the same ratio to the second which the third has to the fourth ; then any equimultiples of the antecedents shall have the same ratio as any equimultiples of the consequents.... | |
 | Euclides - 1846 - 292 pages
...has a greater ratio to the second than the fifth has to the sixth. PROP. XIV. THEOR. If the first has 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 equal,... | |
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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... 
