| Euclid - 1859 - 150 pages
...àiroiovovv ToXXaя-Xaíriaff/iov, rev áurоv i'Ctí Xóyov Xq^öivra raráXXqXa. If the first has the same ratio to the second which the third has to the fourth; any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of... | |
| Eucleides - 1860 - 396 pages
...the first case in Euclid. G. (c) V. 2. PROPOSITION A. THEOREM. — 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 equal,... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...is to G, so is F to H. (v. def. 5.) Therefore, if the first, &c. QED Cos, 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... | |
| Robert Fowler - 1861 - 426 pages
...those m = 16 j cases. PROPOKTION. 133. Def. — If there be four quantities, such that the first has the same ratio to the second which the third has to the fourth, then the four quantities are said to be proportionals. Thus if а, Ъ, с, d be the four quantities,... | |
| Euclides - 1861 - 464 pages
...the same ratio, as Ato I}; ie A : B = C : x. PROP. A, — THEOR. If the first of four magnitudes has 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 greater than the fourth ; and if equal, equal... | |
| George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...and therefore e ; / : ; g : A. Therefore, if the first, &c.— QED 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 same ratio to the second and... | |
| Euclides - 1863 - 122 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...whatsoever of the first and third being taken, and auy equimultiples whatsoever of the second and fourth; if the multiple of the first b« IMS than that... | |
| Euclides - 1864 - 448 pages
...being any integers, no, no, ' or mAl : na, : : mAt : no,. That is, 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... | |
| Euclides - 1865 - 402 pages
...has to the second a greater ratio than the fifth has to the sixth . . . . . V. 13. 10. If the first 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 is greater than the fourth ; and if equal,... | |
| Robert Potts - 1865 - 528 pages
...is to G, so is Fto H. (v. def. 5.) Therefore, if the first, &c. QED 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... | |
| |