The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 76
... pass through the centre : AC , BD shall not bisect one another . If one of the straight lines pass through the centre it is plain that it cannot be bisected by the other which does not pass through the centre . But if neither of them ...
... pass through the centre : AC , BD shall not bisect one another . If one of the straight lines pass through the centre it is plain that it cannot be bisected by the other which does not pass through the centre . But if neither of them ...
Página 83
... pass through the point A. For , if not , let it pass otherwise , if possible , as FGDH , and join AF , AG . Then , because AG , GF are greater than AF , [ I. 20 . and AF is equal to HF , [ I. Def . 15 . therefore , AG , GF , are greater ...
... pass through the point A. For , if not , let it pass otherwise , if possible , as FGDH , and join AF , AG . Then , because AG , GF are greater than AF , [ I. 20 . and AF is equal to HF , [ I. Def . 15 . therefore , AG , GF , are greater ...
Página 108
... pass through the centre , at right angles , at the point E. Then , if BD be bisected at F , F is the centre of the circle ABCD ; join AF . Then , because the straight line BD which passes through the centre , cuts the straight line AC ...
... pass through the centre , at right angles , at the point E. Then , if BD be bisected at F , F is the centre of the circle ABCD ; join AF . Then , because the straight line BD which passes through the centre , cuts the straight line AC ...
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Términos y frases comunes
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