 | Euclides - 1842 - 316 pages
...the ratio of the third to the fourth. Definition of proportion according to Euclid, (Def. V., Book " The first of four magnitudes is said to have the same...second and " fourth ; if the multiple of the first be equal to, greater " than, or less than the multiple of the second, the multiple " of the third is also... | |
 | 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... | |
 | Philip Kelland - Algebra - 1843 - 168 pages
...proportion, as Clavius renders it. the first, and the multiple of the fourth double that of the second. Now if the multiple of the first be greater than that of the second, its double is greater than the double of the other, ie the multiple of the third is greater than that... | |
 | 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,... | |
 | Euclides, 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... | |
 | 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... | |
 | 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... | |
 | 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.... | |
 | 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... | |
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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... 
