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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 Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...has a greater ratio to B than E has to F. Wherefore, If the first tsc. QED Con. Also, 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 shewn, in like...
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The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ...

Thomas Gaskin - Geometry, Analytic - 1847 - 301 pages
...second, but the multiple of the third not greater than the multiple of the fourth ; hence the first has a greater ratio to the second than the third has to the fourth. 3. Euclid, Prop. 19, Book i. If A : B :: B : C, then the ratio of A to C is that compounded of the...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...shall also have to the second a greater ratio than the fifth has to the sixth. 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 geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...ratios to the sum of the consequents will be respectively greater or less than that other ratio. 7. If the first of four magnitudes have a greater ratio to the second than the third has to the fourth ; then, (a) The second will have to the first a less ratio than the fourth to the third : — (6) The...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...two extremes, and the second and third the two means. vn. The first of four magnitudes is defined to have a greater ratio to the second than the third has to the fourth (or, what is the same thing, the third to have a less ratio to the fourth than the first has to the...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 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 geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...ratio to B, than E has to F (V. Def. 7). Wherefore, if the first, &c. QED COROLLARY. — 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, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 pages
...fourth, but the third to the fourth a greater ratio than the fifth has to the sixth. 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. If any number of magnitudes...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 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 with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...fourth, but the third to the fourth a greater ratio than the fifth has to the sixth. 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. If any number of magnitudes...
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