The Elements of EuclidA. Foulis, 1838 - 466 sider |
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Side 114
... second is to the third of the first rank , fo is the second to the third of the other ; and fo on in order , and the inference is as mentioned in the preceding Definition ; whence this is called Ordinate Propor- It is demonftrated in ...
... second is to the third of the first rank , fo is the second to the third of the other ; and fo on in order , and the inference is as mentioned in the preceding Definition ; whence this is called Ordinate Propor- It is demonftrated in ...
Side 324
... second to the third , and fo on to the last , is only a name or expreffion by which the ratio which the first A has to the last D is fignified , and by which at the fame time the ratios of all the magnitudes A to B , B to C , C to D ...
... second to the third , and fo on to the last , is only a name or expreffion by which the ratio which the first A has to the last D is fignified , and by which at the fame time the ratios of all the magnitudes A to B , B to C , C to D ...
Side 407
... second , fo is the other fide of the second to the ftraight line to which the other fide of the first has the fame ratio which the first parallelo- gram has to the fecond . and confequently if the ratio of the first parallelogram to the ...
... second , fo is the other fide of the second to the ftraight line to which the other fide of the first has the fame ratio which the first parallelo- gram has to the fecond . and confequently if the ratio of the first parallelogram to the ...
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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