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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 - Page 284
by Daniel Cresswell - 1819 - 410 pages
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The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...of the fifth definition are violated. In the first of these cases the first magnitude is said d to have a greater ratio to the second than the third has to the fourth ; not that one ratio can be strictly said to be greater than another, but the first magnitude is greater...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 122 pages
...first, &c. QED and whatever multiple K is of I), take N the same multiple of B. Cor.—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 he demonstrated,...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...greater ratio to B, than E has to F, (v. def. 7.) 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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...greater ratio to B, than E has to F. (v. def. 7.) 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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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...of them be the least, the fourth shall be the greatest. 8. 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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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...has a greater ratio to B than E has to F. Wherefore, if the first &c. QED COROLLARY. 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 that the fifth has to the sixth, it may be shewn, in the...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...greater ratio to B, than E has to F. (v. def. 7.) 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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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...greater ratio to B, than E has to F (V. Def. 7). 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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Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...third a greater ratio than the second has to the fourth. 3. 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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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...has a greater ratio to B than E has to F. Wherefore, if thefirst &c. QED COROLLARY. 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 that the fifth has to the sixth, it may be shewn, in the...
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