## Schultze and Sevenoak's Plane and Solid Geometry |

### From inside the book

Results 1-5 of 26

Page 407

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**triangle**P " A " D " , having the hypotenuse P " A " = PA , and one arm D ...**spherical**angle is the angle between two inter- secting great circles . PROPOSITION IX . THEOREM 730 ...**spherical**angle formed by the great THE**SPHERE**407. Page 409

Arthur Schultze, Frank Louis Sevenoak. 733. DEF .

Arthur Schultze, Frank Louis Sevenoak. 733. DEF .

**SPHERICAL**POLYGONS A**spherical**polygon is a portion of the surface ...**triangle**is a**spherical**polygon of three sides . It is called isosceles , equilateral , etc. , in the same ... Page 410

... spherical polygons are sup- posed to be convex polygons unless stated otherwise . 738. Spherical polygons are symmetric if their corresponding polyhedral angles are symmetric ...

... spherical polygons are sup- posed to be convex polygons unless stated otherwise . 738. Spherical polygons are symmetric if their corresponding polyhedral angles are symmetric ...

**spherical triangle**. To prove AB. 410 SOLID GEOMETRY. Page 411

Arthur Schultze, Frank Louis Sevenoak. Given ABC , a

Arthur Schultze, Frank Louis Sevenoak. Given ABC , a

**spherical triangle**. To prove AB + BC > AC . Proof . Draw radii OA , OB , and oc . Then ZAOB + BOC > AOC . ( 548 ) But the central angle is measured by the intercepted arc . .. AB + BC ... Page 413

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**spherical triangle**are equal . A HINT . Bisect the vertex angle and prove that two symmetric triangles are formed . 746. COR . An equilateral**spherical triangle**is also equi- angular . 747. REMARK . Many theorems of Spherical Geometry ...### Other editions - View all

### 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 LAOB lateral area lateral edge line joining locus median parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism produced 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 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 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 192 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.

Page 208 - The area of a rectangle is equal to the product of its base and altitude.

Page 67 - If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side.

Page 177 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 25 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.

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...