The Elements of EuclidA. Foulis, 1838 - 466 páginas |
Dentro del libro
Resultados 1-3 de 89
Página 121
... lefs , less . Take any equimultiples of each of them , as the doubles of each . then by Def , 5th of this Book , if the double of the first be greater than the double of the fecond , the double of the third is greater than the double of ...
... lefs , less . Take any equimultiples of each of them , as the doubles of each . then by Def , 5th of this Book , if the double of the first be greater than the double of the fecond , the double of the third is greater than the double of ...
Página 128
... lefs , lefs . Again , because C is to a . 5. Def . 5. D , as E is to F , and H , K are taken equimultiples of C , E ; and M , N of D , F ; if H be greater than M , K is greater than N ; and if equal , equal ; and if lefs , lefs . but if ...
... lefs , lefs . Again , because C is to a . 5. Def . 5. D , as E is to F , and H , K are taken equimultiples of C , E ; and M , N of D , F ; if H be greater than M , K is greater than N ; and if equal , equal ; and if lefs , lefs . but if ...
Página 20
... lefs than a right angle . Q. E. D. Cafe 2. Let AB be greater than a quadrant , make AE a qua- drant , and let a great circle pafs through C , E. ECA is a right angle as before , and BCA is greater than ECA , that is , greater than a ...
... lefs than a right angle . Q. E. D. Cafe 2. Let AB be greater than a quadrant , make AE a qua- drant , and let a great circle pafs through C , E. ECA is a right angle as before , and BCA is greater than ECA , that is , greater than a ...
Otras ediciones - Ver todas
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