Schultze and Sevenoak's Plane and Solid Geometry |
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Page 106
... circumscribed about the polygon . The center of the circumscribed circle is called the circumcenter of the polygon . E C PROPOSITION II . THEOREM 188. In the same circle , or in equal circles , equal arcs are subtended by equal chords ...
... circumscribed about the polygon . The center of the circumscribed circle is called the circumcenter of the polygon . E C PROPOSITION II . THEOREM 188. In the same circle , or in equal circles , equal arcs are subtended by equal chords ...
Page 109
... circumscribe a circle about a given triangle . * B C Given △ ABC . Required to circumscribe a circle about △ ABC . Construction . Draw the perpendicular bisectors of the sides AC and AB . They will intersect at some point E. ( 83 ) ...
... circumscribe a circle about a given triangle . * B C Given △ ABC . Required to circumscribe a circle about △ ABC . Construction . Draw the perpendicular bisectors of the sides AC and AB . They will intersect at some point E. ( 83 ) ...
Page 116
... circumscribed about a circle if all its sides are tangent to the circle ; as ABCDE . The circle is then said to be ... circumscribed quadri- lateral is equal to the sum of the other two sides . Ex . 540. If hexagon ABCDEF is ...
... circumscribed about a circle if all its sides are tangent to the circle ; as ABCDE . The circle is then said to be ... circumscribed quadri- lateral is equal to the sum of the other two sides . Ex . 540. If hexagon ABCDEF is ...
Page 134
... Construct an equilateral triangle , having given ( a ) the altitude . ( b ) the radius of the inscribed circle . ( c ) the radius of the circumscribed circle . PROPOSITION XXIII . PROBLEM 250. To construct a triangle , 134 PLANE GEOMETRY.
... Construct an equilateral triangle , having given ( a ) the altitude . ( b ) the radius of the inscribed circle . ( c ) the radius of the circumscribed circle . PROPOSITION XXIII . PROBLEM 250. To construct a triangle , 134 PLANE GEOMETRY.
Page 137
... circumscribed circle in a point which is equidistant from the other two vertices of the triangle and the center of the inscribed circle . Ex . 618. A circle is inscribed in a triangle whose sides are 9 , 8 , and 9 . Find the distances ...
... circumscribed circle in a point which is equidistant from the other two vertices of the triangle and the center of the inscribed circle . Ex . 618. A circle is inscribed in a triangle whose sides are 9 , 8 , and 9 . Find the distances ...
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Common terms and phrases
altitude angle equal angle formed angles are equal annexed diagram bisect bisector chord circumference circumscribed congruent cylinder diagonals diagram for Prop diameter dihedral angles divide draw drawn equiangular polygon equilateral triangle equivalent exterior angle face angles Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inscribed intersecting isosceles triangle lateral area lateral edge line joining locus median parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism PROPOSITION prove Proof pyramid Q. E. D. Ex quadrilateral radii ratio rectangle reflex angle regular polygon respectively equal rhombus right angles right triangle segments sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal trihedral vertex angle vertices
Popular passages
Page 222 - 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 208 - The area of a rectangle is equal to the product of its base and altitude.
Page 183 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 160 - A line parallel to one side of a triangle divides the other two sides proportionally.
Page 82 - 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 70 - 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 188 - Pythagorean theorem, which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
Page 409 - 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 333 - The sum of any two face angles of a trihedral angle is greater than the third face angle.
Page 193 - 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.