The Elements of EuclidJ. M. Dent & sons, 1933 - 298 páginas |
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Página 11
... remaining angles of the one to the remaining angles of the other , each to each , to D which the equal sides are opposite , E namely the angle ACF to the angle ABG , and the angle AFC to the angle AGB . [ I. 4 . And because the whole ...
... remaining angles of the one to the remaining angles of the other , each to each , to D which the equal sides are opposite , E namely the angle ACF to the angle ABG , and the angle AFC to the angle AGB . [ I. 4 . And because the whole ...
Página 116
... angle it is required to describe a triangle about the circle ABC , equiangular to the triangle DEF Produce EF both ... remaining angle AMB is equal to the re- maining angle DEF . [ Axiom 3 . In the same manner the angle LNM may be ...
... angle it is required to describe a triangle about the circle ABC , equiangular to the triangle DEF Produce EF both ... remaining angle AMB is equal to the re- maining angle DEF . [ Axiom 3 . In the same manner the angle LNM may be ...
Página 185
... angle ABG equal to the angle DEF . [ I. 23 . Then , because the angle at A is equal to the angle at D , [ Hyp . and the angle ABG is equal to the angle DEF , [ Constr . therefore the remaining angle AGB is equal to the re- maining angle ...
... angle ABG equal to the angle DEF . [ I. 23 . Then , because the angle at A is equal to the angle at D , [ Hyp . and the angle ABG is equal to the angle DEF , [ Constr . therefore the remaining angle AGB is equal to the re- maining angle ...
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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