The Elements of EuclidA. Foulis, 1838 - 466 páginas |
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Página 112
... third to ' the fourth . ' VII . When of the equimultiples of four magnitudes ( taken as in the 5th Definition ) the multiple of the firft is greater than that of the fecond , but the multiple of the third is not greater than the ...
... third to ' the fourth . ' VII . When of the equimultiples of four magnitudes ( taken as in the 5th Definition ) the multiple of the firft is greater than that of the fecond , but the multiple of the third is not greater than the ...
Página 121
... third has to the fourth ; then if the first be greater than the second , the third is also great- er than the fourth ; and if equal , equal ; if lefs , less . Take any equimultiples of each of them , as the doubles of each . then by Def ...
... third has to the fourth ; then if the first be greater than the second , the third is also great- er than the fourth ; and if equal , equal ; if lefs , less . Take any equimultiples of each of them , as the doubles of each . then by Def ...
Página 204
... third planc , and let BD be the common fection of the first two , BD is perpendicular to the third plane . B If it be not , from the point D draw , in the plane AB , the straight line DE at right angles to AD the common fection of the ...
... third planc , and let BD be the common fection of the first two , BD is perpendicular to the third plane . B If it be not , from the point D draw , in the plane AB , the straight line DE at right angles to AD the common fection of the ...
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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