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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 College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...whatever G, 1 1, K ; and of B, D, F any equimultiples whatever L, M, N. DEMONSTRATION 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,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pages
...PROPOSITION XI. THEOREM. \lai.ios that are the tame to the same ratio, are the same to me 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. 0 H KAC EBD FLM NTake of A, C, E, any equimultiples...
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The Principles of Psychology, Volume 2

Herbert Spencer - Psychology - 1873
...ratio are equal to one another," it will be needful to quote in full.* It is as follows : — • " Let A be to B as C is to D ; and as C ia to D so let B be to F. Then A shall bo to B as E to F. GH KAC ED • F— M • N — Take of...
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The Principles of psychology, Volume 2

Herbert Spencer - 1873
...same ratio are equal to one another," it will be needful to quote in full.* It is as follows : — " Let A be to B as C is to D ; and as C is to D so let E he to F. Then A shall be to B as E to F. -G : HA CL MTake of A, C, E, any equimultiples...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...PROPOSITION 11. — 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. QHK E_ D- F. IMN Construction. Take...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1876 - 403 pages
...QED PROPOSITION XL THEOREM. Satins 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. 8Tako of A, C, E, any equimultiples whatever...
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Works, Volume 3

Herbert Spencer - 1881
...same ratio aro equal to one another," it will be needful to quote in full.* It is as follows : — " Let A be to B as C is to D ; and as C is to D so let E be to F. Then A shall be to B as E to F. G HA CB DL LiTake of A, C, E, any equimultiples...
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The Principles of Psychology, Volume 2

Herbert Spencer - Psychology - 1882
...same ratio are equal to one another," it will be needful to quote in full.* It is as follows : — " Let A be to B as C is to D ; and as C is to D so let E DO to F. Then A shall be to B as E to F. GHK AC MTake of A, C, E, any equimultiples...
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The Principles of Psychology, Volume 2

Herbert Spencer - Psychology - 1906
...same ratio are equal to one another," it will be needful to quote in full.* It is as follows: — " Let A be to B as C is to D; and as C is to D so let E be to F. Then A shall be to B as E to F. G HA CL MTake of A,C,E, any equimultiples...
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Principles of psychology

Herbert Spencer - Philosophy - 1910
...same ratio are equal to one another," it will he needful to quote in full.* It is as follows: — " let A be to B as C is to D; and as C is to D so let E be to F. Then A shall be to B as E to F. G— HA CM Take of A,C,E, any equimultiples...
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