The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 29
... to each ; and the angle ABC is equal to the angle DEF ; [ Hypothesis . therefore the base AC is equal to the base DF , and the third angle BAC to the third angle EDF . [ I. 4 . Next , let sides which are opposite to equal angles BOOK I. 26 ...
... to each ; and the angle ABC is equal to the angle DEF ; [ Hypothesis . therefore the base AC is equal to the base DF , and the third angle BAC to the third angle EDF . [ I. 4 . Next , let sides which are opposite to equal angles BOOK I. 26 ...
Página 98
... equal angles stand on equal arcs , whether they be at the centres or circumferences . Let ABC , DEF be equal circles ; and let BGC , EHF be equal angles in them at their centres , and BAC , EDF equal angles at their circumferences : the ...
... equal angles stand on equal arcs , whether they be at the centres or circumferences . Let ABC , DEF be equal circles ; and let BGC , EHF be equal angles in them at their centres , and BAC , EDF equal angles at their circumferences : the ...
Página 125
Euclid Isaac Todhunter, Robert Simson. be equal to the angle at F , and each of the angles ACD , ADC equal to the angle at Gor H ; [ IV . 2 . and therefore each of the angles ACD , ADC is double of the angle CAD ; F bisect the angles ...
Euclid Isaac Todhunter, Robert Simson. be equal to the angle at F , and each of the angles ACD , ADC equal to the angle at Gor H ; [ IV . 2 . and therefore each of the angles ACD , ADC is double of the angle CAD ; F bisect the angles ...
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Términos y frases comunes
ABCD angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC BC is equal 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 whole angle