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" Ratios that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F. "
A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the ... - Page 250
by Thomas Malton - 1774 - 440 pages
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...H, K ; _ p v/ B - D L- - M -- Nand of B, D, F any equimultiples whatever L, M, N: Then, because A is to B as C is to D, and as E to F ; and G, H, K are equimultiples of A, C, E, and L, M, N equimultiples Book v. of B, D, F ; if G be...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 pages
...equimultiples whatever G, H, K; and of B, D, F any equimultiples whatever L, M, N: then because A is to B, as C is to D, and as E to F; and that G, H, K are equimultiples of A, C, E, and L, M, N equimultiples of B, D, F; therefore if G...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...PROPOSITION XI. THEOR. — Ratios that are the same to the same ratio, are the same to one another. Let A be to B, as C is to D ; and as C to D, so let E be to F : A is to B, as E to F. Take of A, C, E, any equimultiples whatever G, H,...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 pages
...whatever G, H, K : and of B, D, F any like multiples whatever L, M, N : then (V. def. 5) because A is to B, as C is to D, and as E to F, and that G, H. K are like multiples of A, C, E ; and L, M, N like multiples of B, D, F ; if G be greater...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...QED PROPOSITION XI. THEOREM. Ratios that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F. QA Then A shall be to B, as E to F. Take of A, C, E, any equimultiples whatever...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...equimultiples whatever G,H,K, and of B, D, F any equimultiples whatever L, M, N : Then, because A is to B as C is to D and as E to F, and that G, H, K are equimultiples of A, C, E, and L, M, N equimultiples of B, D, F, therefore, if...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...PROPOSITION XI. Tin,' M;. Ratios that are tJie same to the same ratio, are the same to one another. Let A be to B, as C is to D ; and as C to D, so let E be to F : A is to B, as E to F. Take of A, C, E, any equimultiples whatever G, H,...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 147 pages
...PROPOSITION XI. — THEOREM. Ratios that are the same to the same ratio are the same to one another. LET a be to b as c is to d ; and as c to d so let e be to f ; a is to b as e to f. Take of a, c, e, any equimultiples whatever g, h, k...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...QED PROPOSITION XI. THEOREM. Ratios that are the same to the same ratio, are the same to one another, Let A be to B as C is to D ; and as C to D, so let E be to F. Then A shall be to B, as E to F. ACE L . MN Take of A, C, E, any equimultiples...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...QED PROPOSITION XI. THEOREM. Ratios that are the tame to the same ratio, are the same to one another Let A be to B as C is to D ; and as C to D, so let E be to F. Then A shall be to B, as E to F. GH KBD FLM NTake of A, C, E, any equimultiples...
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