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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...
Volledige weergave - 1876
ABCD adjacent angles altitude apothem base bisects called centre of similitude chord circumference circumscribed coincide common cone convex Corollary cylinder Definition denote diagonals diameter dicular diedral angle distance divided draw equally distant equilateral equivalent exterior angle faces figure find the locus fixed point frustum given circles given plane given point given straight line hence homologous hypotenuse indefinitely inscribed angle isosceles Let ABC measure medial lines middle point number of sides one-half opposite sides parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN plane passed polar pole polyedral angle polyedron prism PROPOSITION pyramid quadrilateral radical axis radii radius rectangle regular polygon respectively right angles right triangle Scholium secant segment similar sphere spherical polygon square straight line drawn straight line joining surface symmetrical tangent tetraedron theorem three given triangle ABC triedral vertex vertices volume
Pagina 243 - It will be shown that every section of a sphere made by a plane is a circle...
Pagina 214 - 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.
Pagina 127 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Pagina 217 - THEOREM. 611. -A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Pagina 42 - Every point in the bisector of an angle is equally distant from the. sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle.
Pagina 115 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Pagina 261 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180į and less than 540į. (gr). If A'B'C' is the polar triangle of ABC...
Pagina 105 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.