The Elements of EuclidA. Foulis, 1838 - 466 páginas |
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Página 25
... equal to the angle DEF ; therefore the base GC is equal to the base DF , anda . 4. 1 . the triangle GBC to the triangle DEF , and the other angles to the other angles , each to each , to which the equal fides are oppofite ; therefore ...
... equal to the angle DEF ; therefore the base GC is equal to the base DF , anda . 4. 1 . the triangle GBC to the triangle DEF , and the other angles to the other angles , each to each , to which the equal fides are oppofite ; therefore ...
Página 219
... equal to the folid angle at D contained by the three plane angles EDC , EDF , FDC , Take the equal ftraight lines AB , DE , and join HB , KB , FE , GE . and becaufe FG is perpendicular to the plane EDC , it makes right angles with every ...
... equal to the folid angle at D contained by the three plane angles EDC , EDF , FDC , Take the equal ftraight lines AB , DE , and join HB , KB , FE , GE . and becaufe FG is perpendicular to the plane EDC , it makes right angles with every ...
Página 236
... equal to the angle ABH . and the angle HAB is equal to the angle MDE . there- fore in the two triangles HAB , MDE there are two angles in one equal to two angles in the other , each to each , and one fide equal to one file , oppofite to ...
... equal to the angle ABH . and the angle HAB is equal to the angle MDE . there- fore in the two triangles HAB , MDE there are two angles in one equal to two angles in the other , each to each , and one fide equal to one file , oppofite to ...
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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