The Elements of EuclidA. Foulis, 1838 - 466 sider |
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Side 112
... fourth . VI . Magnitudes which have the fame ratio are called proportionals . N. B. When four magnitudes are proportionals , it is ufually expreffed by faying , the firft is to the fecond , as the third to ' the fourth . ' VII . When of ...
... fourth . VI . Magnitudes which have the fame ratio are called proportionals . N. B. When four magnitudes are proportionals , it is ufually expreffed by faying , the firft is to the fecond , as the third to ' the fourth . ' VII . When of ...
Side 113
... fourth ; or that the firft is to the third , as the fecond to the fourth . as is fhewn in the : 6th Prop . of this sth Book . XIV . Invertendo , by Inverfion ; when there are four proportionals , and it is inferred , that the fecond is ...
... fourth ; or that the firft is to the third , as the fecond to the fourth . as is fhewn in the : 6th Prop . of this sth Book . XIV . Invertendo , by Inverfion ; when there are four proportionals , and it is inferred , that the fecond is ...
Side 141
... fourth ; and the fifth to the fecond the fame ratio which the fixth has to the fourth ; the first and fifth together shall have to the fecond , the fame ratio which the third and fixth together have to the fourth . Let AB the first have ...
... fourth ; and the fifth to the fecond the fame ratio which the fixth has to the fourth ; the first and fifth together shall have to the fecond , the fame ratio which the third and fixth together have to the fourth . Let AB the first have ...
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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