The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 130
... equiangular pentagon ABCDE . Wherefore a circle has been described about the given equilateral and equiangular pentagon . Q.E.F. PROPOSITION 15. PROBLEM . To inscribe an equilateral and equiangular hexagon in a given circle . Let ABCDEF ...
... equiangular pentagon ABCDE . Wherefore a circle has been described about the given equilateral and equiangular pentagon . Q.E.F. PROPOSITION 15. PROBLEM . To inscribe an equilateral and equiangular hexagon in a given circle . Let ABCDEF ...
Página 186
... equiangular to the triangle DEF . For , if the triangle ABC be not equiangular to the triangle DEF , at the point B , in the straight line AB , make the angle ABG equal to the angle DEF . [ I. 23 . Then it may be shewn , as in the first ...
... equiangular to the triangle DEF . For , if the triangle ABC be not equiangular to the triangle DEF , at the point B , in the straight line AB , make the angle ABG equal to the angle DEF . [ I. 23 . Then it may be shewn , as in the first ...
Página 197
... equiangular to the triangle CFD . Again , at the point B , in the straight line BG , make the angle GBH equal to the angle FDE ; and at the point G , in the straight line BG , make the angle BGH equal to the angle DFE ; [ I. 23 ...
... equiangular to the triangle CFD . Again , at the point B , in the straight line BG , make the angle GBH equal to the angle FDE ; and at the point G , in the straight line BG , make the angle BGH equal to the angle DFE ; [ I. 23 ...
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ABCD 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 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 whole angle