 | John Keill - Logarithms - 1723 - 444 pages
...THEOREM. Proportions that are one and the fame to any "Third, are alfo the fame to one another. T ET A be to B as C is to D, and C to D as E ••-1 to F. I fay A is to B as E is to F. For take G, H, K, Equimultiples of A, C, E ; and H KB—... | |
 | Euclid, John Keill - Geometry - 1733 - 444 pages
...demon Crated. PROPOSITION xi. THEOREM. Proportions that are one and the fame to any third, are alfo the fame to one another. LET A be to B as C is to D, and C to D as E to F. I fay, A is to B as E is to F. For take G, H, K, Equimultiples of A, C, E j and CH KAC — EBD FLM... | |
 | Robert Simson - Trigonometry - 1762 - 488 pages
...than A. That magnitude therefore, &c. D. PROP. XL THEOR. ATI OS that are the fame to the fame ratio, are the fame to one another. Let A be to B, as C h to D ; and as C to D, fo let E be to F ; A is to B, as E to F. Take of A, C, E any equimultiples... | |
 | Robert Simson - Trigonometry - 1775 - 534 pages
...magnitude, therefore, &c. Q^ED b 4. Ax 5. R PRO P. XI. THEO R. ATIOS that are the fame to the fame ratio, are the fame to one another. Let A be to B as C is to D ; and as C to D, fo let E be to F ; A is to B, as E to F. Take of A, C, E, any equimultiples whatever G,... | |
 | Euclid - Geometry - 1776 - 326 pages
...not equal or greater than A, it muft be lefs. Wherefore, &c. P BOOK V; PROP. XL THEO R. ROPORTIONS that are the fame to any third, are the fame to one another. Let A be to 6, as C is to D, and C to D as E to F ; then A will be to B as E to F. For, let G, H, K, be any equimultiples... | |
 | Robert Simson - Trigonometry - 1781 - 534 pages
...That magnitude therefore, &c. QED -. E R PRO P. XL THEO R. ATIOS that are the fame to the fame ratio, are the fame to one another. Let A be to B, as C is to D} and as C to D, fo let E be to F; A is to B, as E to F. Take of A, C, E any equimultiples whatever G, H,... | |
 | Euclid - 1781 - 552 pages
...magnitude, therefore, &c. Q^ED B R PROP. XI. T II EO R. AT1OS that are the fame to the fame ratio, are the fame to one another. Let A be to B, as C is to D ; and as C to D, fo let E be to ' F ; A is to B, as E to F. Take of A, C, E, any equimultiples whatever G,... | |
 | John Keill - Geometry - 1782 - 476 pages
...PROBLEM. Proportions that are one and (be fame to any third, are alfo the Jams to one another. TETA be to B, as C is to D ; and C to D, as •*-' E to F. 1 fay, A is to B, as E is to F. For, take G, H, and K, Equimultiples of A, C, and GHK p N E; and L,... | |
 | Euclid - Euclid's Elements - 1789 - 296 pages
...r PROP. XL THEOREM. Ratios which are the fame to the fame ratio, are the fame to each other. FH Nv Let A be to B as c is to D, and c to D as E is to F ; then will A be to B as E is to F. For, of A, c and E take any equimultiples whatever G, H... | |
 | John Bonnycastle - 1803 - 306 pages
...PROP. XI. THEOREM. Ratios which are the fame to the fame ratio, are the fame to each other. tif AiLet A be to B as c is to D, and c to D as E is to F ; then will A be to B as E is to F. For, of A, c and E take any equimultiples whatever G, H... | |
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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 is to B, as E to F. 
