The Elements of EuclidA. Foulis, 1838 - 466 páginas |
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Página 135
... whole magnitude be to a whole , as a magni- See N tude taken from the firft is to a magnitude taken from the other ; the remainder fhall be to the remain . der as the whole to the whole . Let the whole AB be to the whole CD , as AE a ...
... whole magnitude be to a whole , as a magni- See N tude taken from the firft is to a magnitude taken from the other ; the remainder fhall be to the remain . der as the whole to the whole . Let the whole AB be to the whole CD , as AE a ...
Página 136
... whole AB to the whole CD . Wherefore if the whole , & c . Q. E. D. A F C B D COR . If the whole be to the whole , as a magnitude taken from the firft is to a magnitude taken from the other ; the remainder likewife is to the remainder ...
... whole AB to the whole CD . Wherefore if the whole , & c . Q. E. D. A F C B D COR . If the whole be to the whole , as a magnitude taken from the firft is to a magnitude taken from the other ; the remainder likewife is to the remainder ...
Página 177
... whole line AB by the parallelogram KH fimilar and fimilarly fituated to CE ; AD is greater than AF . DL E First ... whole CH is equal to the whole KE . but CH is equal to CG , becaufe the bafe AC с G A F H a . 26. 6 . b . 43. Is c . 36 ...
... whole line AB by the parallelogram KH fimilar and fimilarly fituated to CE ; AD is greater than AF . DL E First ... whole CH is equal to the whole KE . but CH is equal to CG , becaufe the bafe AC с G A F H a . 26. 6 . b . 43. Is c . 36 ...
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Términos y frases comunes
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