The Elements of EuclidA. Foulis, 1838 - 466 páginas |
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Página 294
... must be less than the fum , but greater than the difference of the other two , from this he fhews the circles must meet one ano- ther , in one cafe ; and fays that it may be proved after the fame manner in any other cafe . but the ...
... must be less than the fum , but greater than the difference of the other two , from this he fhews the circles must meet one ano- ther , in one cafe ; and fays that it may be proved after the fame manner in any other cafe . but the ...
Página 300
... must be affumed as the center ; and if from this affump- tion an abfurdity follows , as Euclid demonstrates there must ; then it is not true that the point affumed is the center ; and as any point whatever was affumed , it follows that ...
... must be affumed as the center ; and if from this affump- tion an abfurdity follows , as Euclid demonstrates there must ; then it is not true that the point affumed is the center ; and as any point whatever was affumed , it follows that ...
Página 423
... must be greater or lefs than LM or NO . but , as has been fhewn in the preceding demonftration , a triangle fimilar to ABC can be defcribed in the fegment EGF upon the bafe EF , and the ratio of its perpendicular to the base is the fame ...
... must be greater or lefs than LM or NO . but , as has been fhewn in the preceding demonftration , a triangle fimilar to ABC can be defcribed in the fegment EGF upon the bafe EF , and the ratio of its perpendicular to the base is the fame ...
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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