The Elements of Euclid, Libros 1-6;Libro 11 |
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From this it is manifest , that the straight line which is drawn at right angles to the diameter of a circle from the extremity of it , touches the circle ; ( III . Def.2 . and that it touches the circle at one point only , because if ...
From this it is manifest , that the straight line which is drawn at right angles to the diameter of a circle from the extremity of it , touches the circle ; ( III . Def.2 . and that it touches the circle at one point only , because if ...
Página 114
A circle is said to be described about a rectilineal figure , when the circumference of the circle passes through all the angular points of the figure about which it is described . 7. A straight line is said to be placed in a circle ...
A circle is said to be described about a rectilineal figure , when the circumference of the circle passes through all the angular points of the figure about which it is described . 7. A straight line is said to be placed in a circle ...
Página 248
If this process be continued , and the triangles be supposed to be taken away , there will at length remain segments of circles which are together less than the excess of the circle EFGH above the space S , by the preceding Lemma .
If this process be continued , and the triangles be supposed to be taken away , there will at length remain segments of circles which are together less than the excess of the circle EFGH above the space S , by the preceding Lemma .
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ABCD angle ABC angle ACB angle BAC Axiom base BC is equal bisected Book centre circle circle ABC circumference common Construction contained Corollary Definition demonstration described diameter divided double draw drawn edition Elements equal equal angles equiangular equilateral equimultiples Euclid exterior angle extremities fall figure four fourth given straight line greater half Hypothesis impossible join less Let ABC magnitudes manner meet multiple namely parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals Q.E.D. PROPOSITION ratio reason rectangle rectangle contained rectilineal figure right angles segment shewn sides similar Simson solid square straight line &c suppose Take taken THEOREM third touches the circle triangle ABC Wherefore whole