The Elements of EuclidA. Foulis, 1838 - 466 páginas |
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Página 263
... cone , of which the base is the circle ABCD . but it is alfo lefs , for the pyramid is contained within the cone ; which is impoffible . Nor can the cylinder be less than the triple of the cone . let it be lefs if poffible . therefore ...
... cone , of which the base is the circle ABCD . but it is alfo lefs , for the pyramid is contained within the cone ; which is impoffible . Nor can the cylinder be less than the triple of the cone . let it be lefs if poffible . therefore ...
Página 264
... cone , and so on , there See N. 1 A H G muft at length remain fome fegments of the cone which together shall be less than the excess of the cone above the third part of the cylinder . let these be the fegments upon AE , EB , BF , FC ...
... cone , and so on , there See N. 1 A H G muft at length remain fome fegments of the cone which together shall be less than the excess of the cone above the third part of the cylinder . let these be the fegments upon AE , EB , BF , FC ...
Página 271
... cone EFGHN.n therefore the cone EFGHN has to a folid which is lefs than the cone i . 14. 5 . ABCDL , the triplicate ratio of that which EG has to AC , which was demonstrated to be impoffible . therefore the cone ABCDL has not to any ...
... cone EFGHN.n therefore the cone EFGHN has to a folid which is lefs than the cone i . 14. 5 . ABCDL , the triplicate ratio of that which EG has to AC , which was demonstrated to be impoffible . therefore the cone ABCDL has not to any ...
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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