The Elements of EuclidA. Foulis, 1838 - 466 páginas |
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Página 148
... triangles ABC , ACD , and the parallelograms EC , CF have the fame altitude , viz . the perpendicular drawn from the point A to BD . then as the bafe BC is to the bafe CD , fo is the triangle ABC to the triangle ACD , and the ...
... triangles ABC , ACD , and the parallelograms EC , CF have the fame altitude , viz . the perpendicular drawn from the point A to BD . then as the bafe BC is to the bafe CD , fo is the triangle ABC to the triangle ACD , and the ...
Página 418
... triangle has a given obtufe angle ; the excess of the fquare of the fide which fubtends the obtuse an- gle above the fquares of the fides which contain it , fhall have a given ratio to the triangle . Let the triangle ABC have a given ...
... triangle has a given obtufe angle ; the excess of the fquare of the fide which fubtends the obtuse an- gle above the fquares of the fides which contain it , fhall have a given ratio to the triangle . Let the triangle ABC have a given ...
Página 425
... triangle ABC is fimilar f to the triangle POQ . f . 1. Cor . Otherwise , Let the triangle ABC have the given angle BAC , and let the ratio of the rectangle BA , AC to the fquare of BC be given ; the triangle ABC is given in fpecies . 77 ...
... triangle ABC is fimilar f to the triangle POQ . f . 1. Cor . Otherwise , Let the triangle ABC have the given angle BAC , and let the ratio of the rectangle BA , AC to the fquare of BC be given ; the triangle ABC is given in fpecies . 77 ...
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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