 | Euclides - 1865 - 402 σελίδες
...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 - 1865 - 528 σελίδες
...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 .4 shall bo to If, as £ to jFl OHK . BD — r LMN Take of A, C, E,... | |
 | Robert Potts - 1868 - 434 σελίδες
...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 - 1873 - 670 σελίδες
...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 - 678 σελίδες
...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 - 342 σελίδες
...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 - 1876 - 446 σελίδες
...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 - 756 σελίδες
...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 - 1882 - 722 σελίδες
...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 - 1906 - 788 σελίδες
...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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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. 
