The Elements of EuclidA. Foulis, 1838 - 466 páginas |
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Página 359
... magnitude to a given magnitude which is the fame ratio with it can be found . III . Rectilineal figures are faid to be given in fpecies , which have each of their angles given , and the ratios of their fides given . IV . Points , lines ...
... magnitude to a given magnitude which is the fame ratio with it can be found . III . Rectilineal figures are faid to be given in fpecies , which have each of their angles given , and the ratios of their fides given . IV . Points , lines ...
Página 360
... magnitude is faid to be lefs than another by a given magnitude , when this given magnitude being added to it , the whole is equal to the other magnitude . THE PROPOSITION I. HE ratios of given magnitudes to one another is given . a Let ...
... magnitude is faid to be lefs than another by a given magnitude , when this given magnitude being added to it , the whole is equal to the other magnitude . THE PROPOSITION I. HE ratios of given magnitudes to one another is given . a Let ...
Página 368
... magnitude together with that to which another magnitude has a given ratio , be given ; this other is given together with that to which the firft magni- tude has a given ratio . Let AB , CD be two magnitudes of which AB together with BE ...
... magnitude together with that to which another magnitude has a given ratio , be given ; this other is given together with that to which the firft magni- tude has a given ratio . Let AB , CD be two magnitudes of which AB together with BE ...
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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