## Elements of Geometry |

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### Contents

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### Common terms and phrases

ABCD adjacent angles allel altitude angles are equal apothem axis bisecting bisector centre chord circumference circumscribed coincide construct Def.—The Defs.—A diagonals diameter diedral angles distance divided draw equally distant equilateral triangle equivalent Exercise.—The face angles figure Find the area frustum geometry given circle given line given point given straight line given triangle GIVEN—the Hence homologous hypotenuse isosceles triangle lateral area lateral edges lateral faces locus meet middle points number of sides parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyedral angle polyedron prism prismatic surface PROVE pyramid Q. E. D. PROPOSITION quadrilateral radical axis radii radius ratio of similitude rectangle regular polygon respectively equal right angles right triangle segment similar slant height sphere spherical polygon square straight line joining surface symmetrical tangent tetraedron THEOREM triangle ABC triangles are equal triangular prism triedral vertex vertices volume

### Popular passages

Page 40 - If two triangles have two sides and the included angle of one, equal respectively to two sides and the included angle of the other, the triangles are equal. C...

Page 476 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.

Page 325 - The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and a mean proportional between the two bases of the frustum.

Page 215 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.

Page 46 - ... 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 389 - 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...

Page 148 - ... twice the product of one of these sides and the projection of the other side upon it.

Page 67 - 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 145 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.

Page 157 - The product of two sides of a triangle is equal to the product of the diameter of the circumscribed circle and the altitude upon the third side.