## The Elements of Geometry |

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AB² AC and BC AC² AD² adjacent angles angles are equal apothem approach the limit arc AB arc arc BC area ABCD base and altitude BC² bisector bisects CD² central angle centre chord circumference circumscribed coincide common point construct the triangle Converse of Prop decagon diameter divided equal angles equal circles equal figures equal respectively equally distant equiangular equilateral triangle EXERCISES exterior angle given point given square given straight line greater Hence homologous homologous sides hypotenuse hypothesis included angle isosceles triangle line joining measured by arc middle point number of sides opposite sides parallelogram perimeter produced PROPOSITION prove quadrilateral radii radius ratio rectangle regular inscribed regular polygon rhombus right triangle ABC secant line segments side BC similar triangles subtended tangent THEOREM third side trapezoid triangles are equal vertex vertical angle Whence ZAOB zoid

### Popular passages

Page 38 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 23 - In general, any side may be taken as the base; but in an isosceles triangle, unless otherwise 'specified, the side which is not one of the equal sides is taken as the base.

Page 65 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.

Page 172 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.

Page 122 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.

Page 123 - In any proportion the terms are in proportion by composition and division ; that is, the sum of the first two terms is to their difference as the sum of the last two terms to their difference.

Page 139 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 58 - The sum of the interior angles of a polygon is equal to twice as many right angles as the polygon has sides, less four right angles.

Page 224 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.

Page 24 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...