The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 93
... reason the angle FEC is double of the angle EAC . Therefore the whole angle BEC is double of the whole angle BAC . Next , let the centre of the circle be without the angle BAC . Then it may be shewn , as inthe first case , that the ...
... reason the angle FEC is double of the angle EAC . Therefore the whole angle BEC is double of the whole angle BAC . Next , let the centre of the circle be without the angle BAC . Then it may be shewn , as inthe first case , that the ...
Página 126
... reason the angles at the points B , D are right angles . And because the angle FCK is a right angle , the square on FK is equal to the squares on FC , CK . [ I. 47 . For the same reason the square on FK is equal to the squares on FB ...
... reason the angles at the points B , D are right angles . And because the angle FCK is a right angle , the square on FK is equal to the squares on FC , CK . [ I. 47 . For the same reason the square on FK is equal to the squares on FB ...
Página 201
... reason the triangle ECD is similar to the triangle LHK . Therefore the similar polygons ABCDE , FGHKL may be divided into the same number of similar triangles . Also these triangles shall have , each to each , the same ratio which the ...
... reason the triangle ECD is similar to the triangle LHK . Therefore the similar polygons ABCDE , FGHKL may be divided into the same number of similar triangles . Also these triangles shall have , each to each , the same ratio which the ...
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ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC 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