| Robert Simson - Trigonometry - 1806 - 518 pages
...has a greater ratio to B than E has to Fe. Wherefore, if the first, &c. QED CoR. And if the first has **a greater ratio to the second, than the third has to the fourth,** but the third the same ratio to the fourth, which the fifth has to the sixth ; it may be demonstrated,... | |
| Euclides - 1814 - 558 pages
...greater c 7 Def.5. ratio to B, than E has to F c . Wherefore, if the first, &c. QED C0R. And if the first **have a greater ratio to the second, than the third has to the fourth,** but the third the same ratio to the fourth, which the fifth has to the sixth; it may be demonstrated,... | |
| Euclides - 1816 - 528 pages
...greater « 7 Def. 5. ratio to B, than E has to Fc. Wherefore, if the first, &c. QED COR. And if the first **have a greater ratio to the second, than the third has to the fourth,** but the third the same ratio to the fourth, which the fifth has to the sixth; it may be demonstrated,... | |
| Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...ratio than the second has to the fourth. PROP. XVII. (iv.) If the first, together with the second, **of four magnitudes, have a greater ratio to the second, than the third,** together with the fourth, has to the fourth, the first shall have a greater ratio to the second than... | |
| Rev. John Allen - Astronomy - 1822 - 516 pages
...in like manner, be proved, not to be less than the same ; it is therefore equal to itTheor. 4. — **If the first, of four magnitudes, have a greater ratio to the second, than the third has to the fourth** ; by inverting, the second has a less ratio to the first, than the fourth has to the third. For, in... | |
| Rev. John Allen - Astronomy - 1822 - 508 pages
...like manner, be proved, not to be less than the same ; it is therefore equal to it. Theor. 4.—If **the first, of four magnitudes, have a greater ratio to the second, than the third has to the fourth** ; by inverting, the second has a less ratio to the first, than the fourth has to the third. For, in... | |
| James Ryan - Algebra - 1824 - 516 pages
...since by hypothesis ^p= r; > CE and AE therefore we have^g >rr. or tj*. I'j. I). COR. And if the first **have a greater ratio to the second than the third has to the fourth,** but the third the same ratio to the fourth which the fifth has to the sixth ; it may be demonstrated,... | |
| James Ryan, Robert Adrain - Algebra - 1824 - 516 pages
..., , CE • and also -fj>pT> AF therefore we have-R >;?r. r\ vr\ D r y. &. L/. COR. And if the first **have a greater ratio to the second than the third has to the fourth,** but the third the same ratio to the fourth which the fifth has to. the sixth ; it may be demonstrated,... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...greater ratio to B, than E has to F. (7. Def. 3 ) Wherefore, if the first, Sec. QED COR. And if the first **have a greater ratio to the second, than the third has to the fourth,** but the third the same ratio to the fourth, which the fifth has to the sixth ; it may be demonstrated,... | |
| Euclides - 1826 - 226 pages
...but the multiple of the third does not exceed the multiple of the fourth, then the first is said to **have a greater ratio to the second, than the third has to the** fourth.f 8. Proportion is a similitude of ratios. 9. Proportion consists of three terms at least. 10.... | |
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