Elements of Plane and Solid Geometry
American Book Company, 1908 - Geometry - 384 pages
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AABC ABē ABC and DEF ABCD ACē altitude angle formed angles are equal apothem base bisector bisects chord circum circumference cone COROLLARY cylinder decagon DEFINITION diagonals diameter dihedral angles divided Draw EFGH equal angles equally distant equiangular polygon equilateral triangle equivalent EXERCISE exterior angles Find frustum given circle given line given point hexagon homologous hypotenuse inscribed angle inscribed polygon isosceles triangle lateral area lateral edges Let ABC line joining middle points number of sides opposite sides parallelogram parallelopiped Pass a plane perimeter perpendicular plane MN point of intersection polyhedral angle polyhedron prism prolonged PROPOSITION Prove ABC Prove Proof pyramid quadrilateral radii radius rectangle regular inscribed regular polygon rhombus right angles SCHOLIUM secants segments Show slant height sphere spherical square straight line surface tangent tetrahedron THEOREM trapezoid triangle ABC trihedral unequal vertex volume Whence
Page 185 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 186 - The area of a rectangle is equal to the product of its base and altitude.
Page 161 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 53 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Page 201 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Page 11 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the center.
Page 61 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.
Page 68 - 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 15 - 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.
Page 31 - If two triangles have three sides of the one equal respectively to three sides of the other, the triangles are equal in all -respects. Let ABC and DEF be two A, having AB = DE, BC = EF, and AC = DF. To Prove A ABC and DEF equal in all respects. Proof. Place A ABC...