Elements of Geometry
Harper & brothers, 1897 - Geometry - 354 pages
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ABCD altitude angles are equal approaches base bisects called centre chord circle circumference circumscribed coincide common cone construct contains corresponding cylinder describe diagonals diameter diedral angles difference distance divided draw drawn edges equal equivalent Exercise Exercise.-The extremities faces fall figure Find formed four frustum given given point greater half Hence homologous hypotenuse included indefinitely inscribed intersection isosceles joining lateral area length less limit mean measured meet method middle point parallelogram parallelopiped passed perimeter perpendicular plane polygon prism proportional PROPOSITION PROVE pyramid Q. E. D. PROPOSITION radii radius ratio rectangle regular polygon respectively right angles right triangle segment sides similar sphere spherical square straight line surface symmetrical tangent THEOREM third triangle ABC triangular unequal unit vertex vertices volume
Page 242 - The volume of any prism is equal to the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude of the prism DA'.
Page 12 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.
Page 73 - A line perpendicular to a radius at its extremity is tangent to the circle.
Page 253 - The volume of a triangular pyramid is equal to one-third the product of its base and altitude.
Page 238 - COR. 2. The volume of a rectangular parallelopiped is equal to the product of its base by its altitude.
Page 177 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.
Page 287 - 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 126 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 61 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Page 256 - 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.