The Elements of EuclidJ. M. Dent & sons, 1933 - 298 páginas |
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Página 32
... make the exterior angle EGB equal to the interior and opposite angle GHD on the same side , or make the interior angles on the same side BGH , GHD together equal to two right angles : AB shall be parallel to CD . Because the angle EGB is ...
... make the exterior angle EGB equal to the interior and opposite angle GHD on the same side , or make the interior angles on the same side BGH , GHD together equal to two right angles : AB shall be parallel to CD . Because the angle EGB is ...
Página 184
... equal to the two sides GD , DF , each to each ; and the angle EDF is equal to the angle GDF ; [ Constr . therefore the base EF is equal to the base GF , and the triangle EDF to the triangle GDF , and the re- maining angles to the re- ...
... equal to the two sides GD , DF , each to each ; and the angle EDF is equal to the angle GDF ; [ Constr . therefore the base EF is equal to the base GF , and the triangle EDF to the triangle GDF , and the re- maining angles to the re- ...
Página 286
... VI . 12 . The angle DBF is equal to the angle GBE ; add to each the angle FBE ; [ Hypothesis . therefore the angles DBF , FBE are together equal to the angles GBE , FBE . [ Axiom 2 . But the angles DBP , FBE are together equal to two right ...
... VI . 12 . The angle DBF is equal to the angle GBE ; add to each the angle FBE ; [ Hypothesis . therefore the angles DBF , FBE are together equal to the angles GBE , FBE . [ Axiom 2 . But the angles DBP , FBE are together equal to two right ...
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Términos y frases comunes
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