Plane and Solid Geometry |
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Page 76
... inscribed in a circle , if all its ver- tices are in the circumference . The circle is then said to be circumscribed about the polygon . PROPOSITION II . THEOREM 177. In the same circle , or equal circles , equal arcs are subtended by ...
... inscribed in a circle , if all its ver- tices are in the circumference . The circle is then said to be circumscribed about the polygon . PROPOSITION II . THEOREM 177. In the same circle , or equal circles , equal arcs are subtended by ...
Page 77
... inscribed in a circle are equal . Ex . 310. The radii drawn to the vertices of A B an inscribed equilateral hexagon divide the figure into six equilateral triangles . Ex . 311. If two chords bisect each other , the arcs intercepted by ...
... inscribed in a circle are equal . Ex . 310. The radii drawn to the vertices of A B an inscribed equilateral hexagon divide the figure into six equilateral triangles . Ex . 311. If two chords bisect each other , the arcs intercepted by ...
Page 78
... inscribed polygon are equal , the polygon is equilateral . Ex . 315. If from a point without a circle two equal lines are drawn to a circumference , the bisector of the angle they form passes through the center of the circle . Ex . 316 ...
... inscribed polygon are equal , the polygon is equilateral . Ex . 315. If from a point without a circle two equal lines are drawn to a circumference , the bisector of the angle they form passes through the center of the circle . Ex . 316 ...
Page 83
... a portion of a circle bounded by a chord and its arc . A sector of a circle is a portion of a circle bounded by two radii and their intercepted arc . ] Ex . 328. The side of an equilateral hexagon inscribed THE CIRCLE 83 888.
... a portion of a circle bounded by a chord and its arc . A sector of a circle is a portion of a circle bounded by two radii and their intercepted arc . ] Ex . 328. The side of an equilateral hexagon inscribed THE CIRCLE 83 888.
Page 84
... inscribed in a circle is nearer to the center than the side of an equilateral heptagon inscribed in the same circle , and more remote from the center than the side of an equi- lateral pentagon inscribed in the same circle . Ex . 329 ...
... inscribed in a circle is nearer to the center than the side of an equilateral heptagon inscribed in the same circle , and more remote from the center than the side of an equi- lateral pentagon inscribed in the same circle . Ex . 329 ...
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Common terms and phrases
ABCD altitude angles are equal bisect bisector chord circumference circumscribed cone construct a triangle cylinder diagonals diagram for Prop diameter diedral angles divide draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle face angles find a point Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inches inscribed intersecting isosceles triangle joining the midpoints lateral area lateral edges line joining mean proportional median opposite sides parallel lines parallelogram parallelopiped perimeter perpendicular plane MN point equidistant polyedral angle polyedron PROPOSITION prove Proof quadrilateral radii ratio rectangle regular polygon respectively equal rhombus right angles right triangle SCHOLIUM segments sphere spherical polygon spherical triangle square straight angle straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal triedral vertex
Popular passages
Page 148 - 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 150 - If, from a point without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment.
Page 180 - 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 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 337 - 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 305 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes ; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.
Page 312 - The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their radii. Let S, S' denote the lateral areas, T, T...
Page 149 - If, from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other and its external segment.
Page 328 - Every section of a sphere made by a plane is a circle.
Page 257 - If two intersecting planes are each perpendicular to a third plane, their intersection is perpendicular to that plane.