The Elements of EuclidJ. M. Dent & sons, 1933 - 298 páginas |
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Página 29
... Hypothesis . the two sides GB , BC are equal to the two sides DE , EF , each to each ; and the angle GBC is equal to the angle DEF ; [ Hypothesis . therefore the triangle GBC is equal to the triangle DEF , and the other angles to the ...
... Hypothesis . the two sides GB , BC are equal to the two sides DE , EF , each to each ; and the angle GBC is equal to the angle DEF ; [ Hypothesis . therefore the triangle GBC is equal to the triangle DEF , and the other angles to the ...
Página 30
... Hypothesis . the two sides AB , BH are equal to the two sides DE , EF , each to each ; and the angle ABH is equal to the angle DEF ; [ Hypothesis . therefore the triangle ABH is equal to the triangle DEF , and the other angles to the ...
... Hypothesis . the two sides AB , BH are equal to the two sides DE , EF , each to each ; and the angle ABH is equal to the angle DEF ; [ Hypothesis . therefore the triangle ABH is equal to the triangle DEF , and the other angles to the ...
Página 255
... hypothesis of the other . Thus in I. 5 the hypothesis is the equality of the sides , and one conclusion is the equality of the angles ; in I. 6 the hypothesis is the equality of the angles and the conclusion is the equality of the sides ...
... hypothesis of the other . Thus in I. 5 the hypothesis is the equality of the sides , and one conclusion is the equality of the angles ; in I. 6 the hypothesis is the equality of the angles and the conclusion is the equality of the sides ...
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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