The Elements of EuclidA. Foulis, 1838 - 466 páginas |
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Página 50
... four rectangles AG , MP , PL , RF are equal to one another , and fo are quadruple of one of them AG . And it was demonftrated that the four CK , BN , GR , RN are quadruple of CK . therefore the eight rectangles which contain the gnomon ...
... four rectangles AG , MP , PL , RF are equal to one another , and fo are quadruple of one of them AG . And it was demonftrated that the four CK , BN , GR , RN are quadruple of CK . therefore the eight rectangles which contain the gnomon ...
Página 113
... four proportionals , and it is inferred , that the fecond is to the firft , as the fourth to the third . Prop . B. Book 5th XV . Componendo , by Compofition ; when there are four proportionals , and it is inferred , that the firft ...
... four proportionals , and it is inferred , that the fecond is to the firft , as the fourth to the third . Prop . B. Book 5th XV . Componendo , by Compofition ; when there are four proportionals , and it is inferred , that the firft ...
Página 463
... four times the fquare of FE is to the fquare of GL , as four times the rectangle BC , CD is to the fquare of BD ; and , by Compo- fition , four times the fquare of FE together with the fquare of GL is to the fquare of GL , as four times ...
... four times the fquare of FE is to the fquare of GL , as four times the rectangle BC , CD is to the fquare of BD ; and , by Compo- fition , four times the fquare of FE together with the fquare of GL is to the fquare of GL , as four times ...
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Términos y frases comunes
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