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" 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... "
A Supplement to the Elements of Euclid - Side 284
av Daniel Cresswell - 1819 - 410 sider
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 sider
...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,...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...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,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sider
...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,...
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - 1817 - 436 sider
...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...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Euclid, Rev. John Allen - 1822 - 494 sider
...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...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Euclid, Rev. John Allen - 1822 - 494 sider
...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...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - 1824 - 516 sider
...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,...
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An Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan, Robert Adrain - 1824 - 516 sider
..., , 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,...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 sider
...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,...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...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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