The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 28
... angle contained by the sides of that which has the greater base , shall be greater than the angle contained by the ... EDF . For if not , the angle BAC must be either equal to the angle EDF or less than the angle EDF . But the ...
... angle contained by the sides of that which has the greater base , shall be greater than the angle contained by the ... EDF . For if not , the angle BAC must be either equal to the angle EDF or less than the angle EDF . But the ...
Página 99
... angles BAC , EDF at their circumferences , stand on equal arcs BC , EF : the angle BGC shall be equal to the angle EHF , and the angle BAC equal to the angle EDF . B H If the angle BGC be equal to the angle EHF , it is manifest that the ...
... angles BAC , EDF at their circumferences , stand on equal arcs BC , EF : the angle BGC shall be equal to the angle EHF , and the angle BAC equal to the angle EDF . B H If the angle BGC be equal to the angle EHF , it is manifest that the ...
Página 183
... angle GEF , and the angle GEF is equal to the angle ABC , [ Constr . therefore the angle ABC is equal to the angle ... EDF in the other , and the sides about those angles proportionals , namely , BA to AC as ED is to DF : the triangle ABC ...
... angle GEF , and the angle GEF is equal to the angle ABC , [ Constr . therefore the angle ABC is equal to the angle ... EDF in the other , and the sides about those angles proportionals , namely , BA to AC as ED is to DF : the triangle ABC ...
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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