| Eucleides - 1860
...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 - 361 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... | |
| Euclides - 1861
...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... | |
| Robert Fowler - 1861
...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,... | |
| George Sturton Ward - Geometry, Algebraic - 1862 - 79 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
...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
...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
...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,... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 5. **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 the third being... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 5. **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 the third being... | |
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