Schultze and Sevenoak's Plane and Solid Geometry |
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Page 83
... hexagon ; seven sides , a heptagon ; eight sides , an octagon ; ten sides , a decagon ; twelve sides , a dodecagon . All the polygons discussed are understood to be convex , i.e. such that no side produced will enter the polygon . 157 ...
... hexagon ; seven sides , a heptagon ; eight sides , an octagon ; ten sides , a decagon ; twelve sides , a dodecagon . All the polygons discussed are understood to be convex , i.e. such that no side produced will enter the polygon . 157 ...
Page 84
... angles is 1000 st . ? 200 rt . ? 24 rt . ? 720 ° ? Ex . 385. How many degrees are in each angle of an equiangular quadrilateral ? pentagon ? hexagon ? decagon ? PROPOSITION XLII . THEOREM 160. If the sides of any 84 PLANE GEOMETRY.
... angles is 1000 st . ? 200 rt . ? 24 rt . ? 720 ° ? Ex . 385. How many degrees are in each angle of an equiangular quadrilateral ? pentagon ? hexagon ? decagon ? PROPOSITION XLII . THEOREM 160. If the sides of any 84 PLANE GEOMETRY.
Page 98
... then and AB = BC , AE = CD , LA = LC , BE = BD , LE = LD . D E Ex . 448. Two equilateral triangles are equal if the altitude of one equals the altitude of the other . Ex . 449. If the opposite sides of a hexagon 98 PLANE GEOMETRY.
... then and AB = BC , AE = CD , LA = LC , BE = BD , LE = LD . D E Ex . 448. Two equilateral triangles are equal if the altitude of one equals the altitude of the other . Ex . 449. If the opposite sides of a hexagon 98 PLANE GEOMETRY.
Page 99
... hexagon are parallel , and two of opposite sides are equal , all opposite sides are equal . Ex . 450. If from the ends of the base BC of an isos- celes triangle ABC , equal parts , BD and CE , be laid off on one arm and the prolongation ...
... hexagon are parallel , and two of opposite sides are equal , all opposite sides are equal . Ex . 450. If from the ends of the base BC of an isos- celes triangle ABC , equal parts , BD and CE , be laid off on one arm and the prolongation ...
Page 107
... . Ex . 508. The radii drawn to the vertices of an inscribed equilateral hexagon divide the figure into six equilateral triangles . PROPOSITION III . THEOREM 190. A radius perpendicular to a THE CIRCLE - CONSTRUCTIONS 107.
... . Ex . 508. The radii drawn to the vertices of an inscribed equilateral hexagon divide the figure into six equilateral triangles . PROPOSITION III . THEOREM 190. A radius perpendicular to a THE CIRCLE - CONSTRUCTIONS 107.
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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.