Elements of Plane and Solid Geometry |
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Common terms and phrases
AABC AB² ABC and DEF altitude angle formed angles equal apothem BC² bisector bisects chord circum circumference circumscribed cone Construct a triangle COROLLARY DEFINITION diagonals diameter dihedral angles divided EFGH equally distant equiangular polygon equilateral triangle equivalent EXERCISE exterior angles Find frustum given angle given circle given line given point hexagon hypotenuse inscribed angle intercepted isosceles triangle joining the middle Let ABC Let To Prove line joining mean proportional medians meet middle points number of sides opposite sides parallelogram parallelopiped pass perimeter perpendicular plane point of intersection prism prolonged PROPOSITION Prove ABCD Prove Proof pyramid quadrilateral radius ratio rectangle regular inscribed regular polygon rhombus right angles right-angled triangle SCHOLIUM secants segments Show similar polygons similar triangles straight line tangent THEOREM trapezoid triangle ABC unequal vertex vertical angle Whence
Popular passages
Page 185 - Any two rectangles are to each other as the products of their bases by their altitudes.
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 178 - In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.
Page 68 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Page 186 - The area of a rectangle is equal to the product of its base and altitude.
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 72 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.
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 17 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.