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adjacent angles angle formed angle inscribed angle opposite angles are equal arcs intercepted base and altitude bisector Book circles touch circumscribed circle Complementary angles construct a square construct a triangle construct the triangle COROLLARY diagonals diameter distance dividing a line double the number equal arcs equal circles equilateral polygon equilateral triangle exterior angles forming equal angles four quantities given angle given circle given line given point given square given triangle homologous sides hypotenuse Illustration included angle inscribed angle inscribed circle intercepted arc line drawn line joining measured by half median middle point number of sides oblique lines opposite angles opposite side parallel lines perimeter perpendicular PLANE GEOMETRY point equally distant Problem proportion Proposition XVIII quadrilateral radii forming equal ratio rectangle regular polygon right angles right triangle SCHOLIUM segments straight line supplementary angles SUPPLEMENTARY PROPOSITIONS tangent Theorem third side triangle in terms triangles are equal variable
Page 47 - If from, a point without a circle a secant and a tangent are drawn, the tangent is a mean proportional between the whole secant and the external segment.
Page 35 - An angle formed by two tangents is measured by half the difference of the intercepted arcs.
Page 24 - If four quantities are in proportion, they will be in proportion by INVERSION ; that is, the second will be to the first as the fourth to the third.
Page 14 - Any exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Page 59 - The side of a regular inscribed hexagon is equal to the radius of the circle.
Page 28 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Page 25 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 36 - Given, two sides of a triangle, and the angle opposite one of them, to construct the triangle. Let A and B be the given sides, and G the given angle.