 | Euclid - Geometry - 1765 - 492 pages
...PROP. XV. THEOR. Magnitudes have the fame ratio to one another wbitt their equimultiples have *. For let AB be the fame multiple of C, that DE is of F I fay c is to F, as AB is to D E. For becaufe AB is the fame multiple of C, that DE is of F : there... | |
 | John Keill - Geometry - 1772 - 462 pages
...to D E. But AG is equal to C, and D K. to F. Whence, as C is to F, fo fhall AB be to D E. Therefore, Parts have the fame Proportion as their like Multiples, if taken correfpondently ; which Was to b» demonftrated, PROPROPOSITION XVI. THEOREM. Jf four Magnitudes of the fame Kind are... | |
 | Robert Simson - Trigonometry - 1775 - 534 pages
...'PROP. XV. THEO R. M AGNITUDES- have the fame ratio to one another which their equimultiples have. O Let AB be the fame multiple of C, that DE is of F : C is to F, as AB to DE. Becaufe AB is the fame multiple of C that DE is of F ; there are as many... | |
 | Euclid - Geometry - 1776 - 318 pages
...is equal to' C, B js equal to D ; and, if lefs, lefs. Wherefore, &c> P BOOK V. PROP. XV. THEOR, ARTS have the fame proportion as their like multiples^...each equal to F ; then AG, GH, HB are equal to one another3-, and likewife DK, KL, LE equal to one another ;« A*. therefore AG is to DK as GH is to KL,... | |
 | Euclid - 1781 - 552 pages
...PRO P. XV. THEO R. M AGNITUDES have the fame ratio to one another •which their equimultiples have. Let AB be the fame multiple of C, that DE is of F : C is t» F, as AB to DE. Becaufe AB is the fame multiple of C, that DE is of F; there are as many... | |
 | John Keill - Geometry - 1782 - 476 pages
...; which was to be demonftrated. D PROPOSITION XV. THEOREM. Paris have the Jame Proportion as tbeir like Multiples, if taken correfpondently. LET AB be the fame Multiple of C, as DE is of F. I fay, as C is to F, fo is AB to D E. For, becaufe AB and DE are A Equimultiples of... | |
 | Alexander Ingram - Trigonometry - 1799 - 374 pages
...equimultiples of two others ; any equimultiples of the firft two are alfo equimultiples of the other two. Let AB be the fame multiple of C that DE is of F, and let AG, DH be equimultiples of AB, DE ; then AG is the fame multiple of C that DH is of F. ai.Def.5.... | |
 | Robert Simson - Trigonometry - 1804 - 530 pages
...have the fame ratio to one another which their equimultiples have. D K TJ /~t IT TT ** i»* J-« -C Let AB be the fame multiple of C that DE is of F. C is to F, as AB to DE. Becaufe AB is the fame multiple of C that DE is of F, there are as many magnitudes... | |
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Let AB be the fame multiple of C, that DE is of F : C is to F, as AB to DE. Becaufe AB is the fame multiple of C that DE is of F ; there are as many magnitudes in AB equal to C, as there are in... 