A Text-book of Geometry
Ginn & Company, 1894 - Geometry - 437 pages
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ABCD altitude angle axis base bisector bisects called centre chord circle circumference circumscribed coincide common cone construct contained curve cylinder denote describe diagonals diameter difference dihedral angles distance divide draw drawn edges ellipse equal equidistant equilateral equivalent exterior extremities faces fall feet figure Find formed four frustum given point greater height Hence homologous hypotenuse inches included indefinitely inscribed intersection isosceles joining lateral legs length less limit measured meet middle point opposite parallel parallelogram pass perimeter perpendicular plane polygon polyhedron prism PROBLEM Proof proportional PROPOSITION prove prove Proof pyramid radii radius ratio rectangle regular polygon respectively right angle segment sides similar sphere spherical square straight line Suppose surface tangent THEOREM third touches triangle unit vertex vertices volume
Page 96 - Any two sides of a triangle are together greater than the third side.
Page 270 - The acute angle which a straight line makes with its projection upon a plane is the least angle which it makes with any line of the plane.
Page 333 - The volume of a frustum of a circular cone is equivalent to the sum of the volumes of three cones whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and the mean proportional between the bases of the frustum. Let V denote the volume, B the lewer base, b the upper base, H the altitude of a frustum of a circular cone.
Page 187 - Two triangles having 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.
Page 64 - 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 46 INTERCEPTS BY PARALLEL LINES.
Page 134 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Page 283 - An oblique prism is equivalent to a right prism whose base is equal to a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. r Let FI be a right section of the oblique prism AD', and FI' a right prism whose lateral edges are equal to the lateral edges of AD'.
Page 352 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Page 403 - Show that the locus of a point which moves so that the sum of its distances from two h'xed straight lines is constant is a straight line.
Page 215 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.