The Elements of EuclidA. Foulis, 1838 - 466 páginas |
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Página 113
... proportionals . ' XIII . Permutando , or Alternando , by Permutation , or alternately ; this word is used when there are four proportionals , and it is infer- See N. red , that the firft has the fame ratio to the third , which the fe ...
... proportionals . ' XIII . Permutando , or Alternando , by Permutation , or alternately ; this word is used when there are four proportionals , and it is infer- See N. red , that the firft has the fame ratio to the third , which the fe ...
Página 164
... proportionals . Let the four straight lines AB , CD , E , F be proportionals , viz . as AB to CD , fo E to F ; the rectangle contained by AB , F ' is e- qual to the rectangle contained by CD , E. a E From the points A , C draw AG , CH ...
... proportionals . Let the four straight lines AB , CD , E , F be proportionals , viz . as AB to CD , fo E to F ; the rectangle contained by AB , F ' is e- qual to the rectangle contained by CD , E. a E From the points A , C draw AG , CH ...
Página 171
... proportionals . Wherefore the recti- lineal figures A and B are equiangular , and have their fides about b . 1. Ax . f , the equal angles proportionals . Therefore A is fimilar to B. c . 11. 5 . Q. E. D. IF PROP . XXII . THEOR . F four ...
... proportionals . Wherefore the recti- lineal figures A and B are equiangular , and have their fides about b . 1. Ax . f , the equal angles proportionals . Therefore A is fimilar to B. c . 11. 5 . Q. E. D. IF PROP . XXII . THEOR . F four ...
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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