| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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