Elements of Geometry |
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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 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 TO PROVE given triangle Hence hypotenuse lateral area lateral edges lateral faces locus meet middle points number of sides parallel lines parallelogram parallelopiped perimeter perpendicular plane geometry plane MN polyedral angle polyedron prism prismatic surface pyramid Q. E. D. PROPOSITION quadrilateral radical axis radii radius ratio of similitude rectangle regular polygon right angles right triangle segment similar slant height sphere spherical polygon spherical triangle square straight line joining surface symmetrical tangent tetraedron THEOREM triangle ABC triangles are equal triangular prism triedral vertex vertices volume
Popular passages
Page 30 - 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 466 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Page 315 - 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 205 - 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 36 - ... 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 379 - 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 138 - ... twice the product of one of these sides and the projection of the other side upon it.
Page 57 - 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 137 - 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 147 - 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.