The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 203
... similar and similarly described rectilineal figure on the second . PROPOSITION 21 . THEOREM . Rectilineal figures which are similar to the same recti- lineal figure , are also similar to each other . Let each of the rectilineal figures ...
... similar and similarly described rectilineal figure on the second . PROPOSITION 21 . THEOREM . Rectilineal figures which are similar to the same recti- lineal figure , are also similar to each other . Let each of the rectilineal figures ...
Página 211
... similar to the whole triangle CBA , and to one another . [ VI . 8 . B D And because the triangle CBA is similar to the triangle ABD , [ VI . Def . 1 . therefore CB is to BA as BA is to BD . And when three straight lines are ...
... similar to the whole triangle CBA , and to one another . [ VI . 8 . B D And because the triangle CBA is similar to the triangle ABD , [ VI . Def . 1 . therefore CB is to BA as BA is to BD . And when three straight lines are ...
Página 296
... similar ; thus it is required to apply to the given straight line AB a parallelogram equal to the given rectilineal figure C and deficient by a parallelo- grammic figure which is similar to D. Let AB be bisected at the point E , and on ...
... similar ; thus it is required to apply to the given straight line AB a parallelogram equal to the given rectilineal figure C and deficient by a parallelo- grammic figure which is similar to D. Let AB be bisected at the point E , and on ...
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ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC bisected centre circle ABC circumference Constr Construction Corollary Definition 15 demonstration diameter double draw equal angles equal to F equiangular equimultiples Euclid Euclid's Elements exterior angle fourth given circle given straight line gnomon greater ratio greater than F Hypothesis less Let ABC Let the straight meet multiple opposite angle parallel to BC parallelogram perpendicular polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION rectangle contained remaining angle right angles segment shewn sides similar and similarly Simson square described square on AC straight line &c straight line AB THEOREM tiples touches the circle triangle ABC triangle DEF twice the rectangle Wherefore