## Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with Practical Exercises |

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ABCD adjacent altitude applied axis base bisect called centre chord circle circumference coincide common conceived cone considered construct convex COROLLARY corresponding cylinder DEMONSTRATION determine diagonals diameter diedral difference direction distance divided draw drawn edges equal equivalent extremities faces facial angles fall figure four Geometry given given line greater Hence homologous included inscribed intersect joining lateral length less lune manner measured meet method moving parallel parallelogram pass path perpendicular placed plane polygon portion position prism produced proportional PROPOSITION prove pyramid quadrilateral radii radius ratio reason rectangle regular represent respectively revolved right angles segment sides similar solid SOLUTION sphere spherical triangle squares straight line supplement surface tangent Theorem.-The third triangle triedrals vertex vertices volume whence

### Popular passages

Page 284 - A Sphere is a solid bounded by a surface every point in which is equally distant from a point within called the Centre.

Page 136 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side belongs to the triangle having the greater included angle.

Page 14 - LEMMA 4. — A common divisor of two numbers is a divisor of their sum and also of their difference.

Page 303 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.

Page 295 - A spherical angle is measured by the arc of a great circle described from its vertex as a pole, and included between its sides, produced if necessary.

Page 298 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.

Page 325 - A spherical sector is the portion of a sphere generated by the revolution of a circular sector about any diameter of the circle of which the sector is a part.

Page 171 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.

Page 108 - In every isosceles spherical triangle, the angles opposite the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles.