The Elements of EuclidA. Foulis, 1838 - 466 sider |
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Resultat 1-3 av 37
Side 120
... multiple of E , that KH is of F. by the hypothefis , is the fame multiple of E that CD is of F ; therefore KH is the fame multiple of F , that CD is of F ; wherefore G H 1. Ax . 5. KH is equal to CD , take away the common magnitude CH ...
... multiple of E , that KH is of F. by the hypothefis , is the fame multiple of E that CD is of F ; therefore KH is the fame multiple of F , that CD is of F ; wherefore G H 1. Ax . 5. KH is equal to CD , take away the common magnitude CH ...
Side 312
... multiple whatever of C ; if the multiple of A be greater than the multiple of C , then , by the 5. Def . of B. 5. the multiple of B is also greater than that of C. but from the Hypothefis that A has a greater ratio to C , than B has to ...
... multiple whatever of C ; if the multiple of A be greater than the multiple of C , then , by the 5. Def . of B. 5. the multiple of B is also greater than that of C. but from the Hypothefis that A has a greater ratio to C , than B has to ...
Side 313
... multiple of C , the multiple of A is also greater than the fame , is thus demon- ftrated . Let D , E be equimultiples of A , B , and Fa multiple of C , fuch , that E the multiple of B is greater than F ; D the multiple of A is alfo ...
... multiple of C , the multiple of A is also greater than the fame , is thus demon- ftrated . Let D , E be equimultiples of A , B , and Fa multiple of C , fuch , that E the multiple of B is greater than F ; D the multiple of A is alfo ...
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AC is equal alfo alſo angle ABC angle BAC bafe baſe BC is given becauſe the angle bifected Book XI cafe circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated diameter drawn equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fhall fhewn fide BC fides fimilar fince firft firſt folid angle fome fore fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs leſs likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular prifms Propofition proportionals pyramid rectangle contained rectilineal figure right angles ſhall ſphere ſquare thefe THEOR theſe thro tiple triangle ABC wherefore