The Elements of EuclidA. Foulis, 1838 - 466 sider |
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Side 118
... equimultiples whatever of the first and third fhall have the fame ratio to any equimultiples of the second and fourth , viz . the equimultiple of the first shall have the fame ratio to that of the fecond , which the equimultiple of the ...
... equimultiples whatever of the first and third fhall have the fame ratio to any equimultiples of the second and fourth , viz . the equimultiple of the first shall have the fame ratio to that of the fecond , which the equimultiple of the ...
Side 129
... equimultiples of B , D , F ; if G be greater Book V. than L , H is greater than M , and K greater than N ; and if equal , equal ; and if lefs , lefs " . Wherefore if G be greater than L , then a . 5. Def . 5 . G , H , K together are ...
... equimultiples of B , D , F ; if G be greater Book V. than L , H is greater than M , and K greater than N ; and if equal , equal ; and if lefs , lefs " . Wherefore if G be greater than L , then a . 5. Def . 5 . G , H , K together are ...
Side 133
... equimultiples , and of EB and FD , HX and MP are equimultiples ; if , GK be greater than HX , then LN is greater than MP ; and if equal , equal ; and if lefs , lefs . but if GH be greater than KX , by adding the common part HK to both ...
... equimultiples , and of EB and FD , HX and MP are equimultiples ; if , GK be greater than HX , then LN is greater than MP ; and if equal , equal ; and if lefs , lefs . but if GH be greater than KX , by adding the common part HK to both ...
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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