The Elements of EuclidA. Foulis, 1838 - 466 páginas |
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Página 215
... manner , the other folid angles of the figures are equal to one another . If then the solid figure AG be applied to ... manner , the figure AH coincides with the figure KR , and the ftraight line DH with NR , and the point H with the ...
... manner , the other folid angles of the figures are equal to one another . If then the solid figure AG be applied to ... manner , the figure AH coincides with the figure KR , and the ftraight line DH with NR , and the point H with the ...
Página 321
... manner in which the Definitions of Duplicate and Triplicate ratio are given , viz . " that as in feveral magnitudes that are continual proportionals , Eu- " clid named the ratio of the first to the third , the Duplicate ratio " of the ...
... manner in which the Definitions of Duplicate and Triplicate ratio are given , viz . " that as in feveral magnitudes that are continual proportionals , Eu- " clid named the ratio of the first to the third , the Duplicate ratio " of the ...
Página 351
... manner , the pyramid EBCM has to the pyramid LGHN the tri- plicate ratio of that which EB has to LG . therefore as the pyramid EABM is to the pyramid LFGN , fo is the pyramid EBCM to the pyramid LGHN . in like manner , as the pyramid ...
... manner , the pyramid EBCM has to the pyramid LGHN the tri- plicate ratio of that which EB has to LG . therefore as the pyramid EABM is to the pyramid LFGN , fo is the pyramid EBCM to the pyramid LGHN . in like manner , as the pyramid ...
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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