The Elements of EuclidJ. M. Dent & sons, 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
Euclid Isaac Todhunter. PROPOSITION 26. THEOREM . In equal circles , 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 ...
Euclid Isaac Todhunter. PROPOSITION 26. THEOREM . In equal circles , 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 ...
Página 192
Euclid Isaac Todhunter. Next , let the angle FBD be equal to the angle EBG , and let the sides about the equal angles be reciprocally proportional , namely , DB to BE as GB is to BF : the parallelogram AB shall be equal to the parallelo ...
Euclid Isaac Todhunter. Next , let the angle FBD be equal to the angle EBG , and let the sides about the equal angles be reciprocally proportional , namely , DB to BE as GB is to BF : the parallelogram AB shall be equal to the parallelo ...
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AB is equal ABCD adjacent angles 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 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