Elements of Geometry |
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ABCD adjacent angles allel altitude angles are equal apothem base and altitude bisecting bisector centre chord circumference circumscribed coincide cone CONSTRUCTION cylinder Def.-The Defs.-A diagonals diameter diedral angles distance divided draw equally distant equilateral triangle equivalent Exercise.-The exterior angles face angles figure frustum geometry given line given point given straight line GIVEN TO PROVE Hence Hint.-Apply hypotenuse included angle intersection isosceles triangle lateral area lateral edges lateral faces locus meet middle points number of sides parallel lines parallelogram parallelopiped perimeter PLANE GEOMETRY plane MN polyedral angle polyedron prism prismatic surface pyramid Q. E. D. PROPOSITION quadrilateral radii radius ratio of similitude rectangle regular polygon respectively equal right angles right triangle segment similar sphere spherical polygon square surface symmetrical tangent tetraedron THEOREM third side triangle ABC triangles are equal triangular triangular prism triedral unequal vertex vertices volume
Popular passages
Page xv - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 84 - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Page 131 - 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 166 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.
Page 462 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Page xi - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.
Page 379 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 201 - 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 375 - 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 82 - An angle formed by a tangent and a chord is measured by one-half its intercepted arc.