The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 68
... Let ABC be any triangle , and the angle at B an acute angle ; and on BC one of the sides containing it , let fall the perpendicular AD from the opposite angle : the square on AC , opposite to the angle B , shall be less than the squares ...
... Let ABC be any triangle , and the angle at B an acute angle ; and on BC one of the sides containing it , let fall the perpendicular AD from the opposite angle : the square on AC , opposite to the angle B , shall be less than the squares ...
Página 92
... Let the straight line DE touch the circle ABC at C , and from C let CA be drawn at right angles to DE : the centre of the circle shall be in CA. For , if not , if possible , let F be the centre , and join CF. Then , because DE touches ...
... Let the straight line DE touch the circle ABC at C , and from C let CA be drawn at right angles to DE : the centre of the circle shall be in CA. For , if not , if possible , let F be the centre , and join CF. Then , because DE touches ...
Página 115
... Let ABC be the given circle , and DEF the given triangle : it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF . Draw the straight line GAH touching the circle at the point [ III . 17 . A ; at the ...
... Let ABC be the given circle , and DEF the given triangle : it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF . Draw the straight line GAH touching the circle at the point [ III . 17 . A ; at 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