 | Herbert Spencer - Psychology - 1873 - 670 pages
...whatever of B, F ; therefore as A is to B so is E to F." * ID some editions the enunciation runs, — " Ratios which are the same to the same ratio are the same to each other ;" but the above is much the .better. t For the aid of those who have not lately looked... | |
 | Herbert Spencer - 1873 - 678 pages
...whatever of B, F ; therefore as A is to B so is E to F." * In some editions the enunciation runs, — " Ratios which are the same to the same ratio are the same to each other ;" but the above is much the better. i For the aid of those who have not lately looked into'Euclid,... | |
 | Euclides - 1874 - 342 pages
...less than A (V. Ax. 4). Therefore, that magnitude, &c. QED 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_... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...is less than A. (v. ax. 4.) Therefore, that magnitude, &c. 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... | |
 | James McDowell - 1878 - 310 pages
...BC :: KA : AC :: HA : AD, but ratios which are equal to the same ratio are equal to one another (or ratios which are the same to the same ratio are the same to one another, V. 11); therefore or alternately, Similarly, therefore or alternately, GH : BD :: GK : BC, GH : GK... | |
 | Nicholas Patrick Wiseman - 1878 - 568 pages
...the proposition cited, it is " relations " which are considered, since the proposition itself is " ratios which are the same to the same ratio are the same to each other," and it is, therefore, expressly occupied about "ratios," or one kind of " relations."... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...is less than A. [V. 4a»om 4. Wherefore, that magnitude &o. QED 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 let C be to D as E '•& to> : A shall be to B as ^ is to F. H ------... | |
 | Herbert Spencer - 1881 - 756 pages
...B, F ; therefore as A is to B so is E to F." * In some editions the enunciation runs, — " Ration which are the same to the same ratio are the same to each other ;" but the above is much the better. t For the aid of those who have not lately looked into... | |
 | Herbert Spencer - Psychology - 1882 - 722 pages
...whatever of B, F ; therefore as A is to B so is E to I'." * In some editions the enunciation runs, — " Ratios which are the same to the same ratio are the same to each other ;" but the above is much the better. t For the aid of those who have not lately looked into... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...that E is less than D, therefore B is less than A. [V. .Aascmi 4. 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 Z>, and let C be to D as E is to F : A shall be to B as E is to F. A B LTake... | |
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Ratios that are the same to the same ratio, are the same to one another. 
