The Elements of EuclidA. Foulis, 1838 - 466 páginas |
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Página 20
... greater than AB . wherefore the greater angle , & c . Q. E. D. b . 18. 1 . PROP . XX . THEOR . See N. a . 3. 1 . b . 5.1 . C. 19. 1 . See N. ANY two fides of a triangle are together greater than the third fide . Let ABC be a triangle ...
... greater than AB . wherefore the greater angle , & c . Q. E. D. b . 18. 1 . PROP . XX . THEOR . See N. a . 3. 1 . b . 5.1 . C. 19. 1 . See N. ANY two fides of a triangle are together greater than the third fide . Let ABC be a triangle ...
Página 130
... greater than N , G is greater than K ; and if equal , equal ; and if lefs , lefs ; but b . 5. Def . 5. G is greater than K , therefore M is greater than N. but H is not greater than L ; and M , H are equimultiples of A , E ; and N , L ...
... greater than N , G is greater than K ; and if equal , equal ; and if lefs , lefs ; but b . 5. Def . 5. G is greater than K , therefore M is greater than N. but H is not greater than L ; and M , H are equimultiples of A , E ; and N , L ...
Página 336
... greater than A , from each of thefe taking away B , C , the remaining one D must be greater than the excess of A above B and C. take therefore any magnitude D which is less than A , B , C together , but greater than the excess of A ...
... greater than A , from each of thefe taking away B , C , the remaining one D must be greater than the excess of A above B and C. take therefore any magnitude D which is less than A , B , C together , but greater than the excess of A ...
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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