If a straight line touches a circle, and from the point of contact there is drawn across, in the circle, a straight line cutting the circle, then the angles. Stoicheia is a mathematical treatise consisting of books attributed to the ancient greek mathematician euclid in alexandria, ptolemaic egypt c. The first three books of euclids elements of geometry from the text of dr. Let ab be the given straight line, and the angle at c the given rectilinear angle. Propositions from euclids elements of geometry book iii tl heaths. On a given straight line to describe a segment of a circle admitting an angle equal to a given rectilinear angle. The books cover plane and solid euclidean geometry. An obtuse angle of a triangle is greater and an acute angle less than the sum of the other two angles. Then, since a straight line ef touches the circle abcd at b, and ba has been drawn from the point of contact.
It is a collection of definitions, postulates, propositions theorems and constructions, and mathematical proofs of the propositions. The exterior angle of a triangle equals the sum of the two opposite interior angles. The sum of the angles in a triangle equals 180 degrees. Euclids proposition 22 from book 3 of the elements states that in a cyclic quadrilateral opposite angles sum to 180. Proposition 32 if a straight line touches a circle, and from the point of contact there is drawn across, in the circle, a straight line cutting the circle, then the angles which it makes with the tangent equal the angles in the alternate segments of the circle. If a straight line touches a circle, and from the point of contact. If a straight line passing through the center of a circle bisects a straight line not passing through the center, then it also cuts it at right angles. With links to the complete edition of euclid with pictures in java by david joyce, and the well known comments from heaths edition at the. Proposition 32 in any triangle, if one of the sides is produced, then the exterior angle equals the sum of the two interior and opposite angles, and the sum of the three interior angles of the triangle equals two right angles. It is required to describe on the given straight line ab a segment of a circle admitting an angle equal to the angle at c. In the first proposition, proposition 1, book i, euclid shows that, using only the.
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