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

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ABCD adjacent altitude angle included angles are equal axis base and altitude bisect centre chord circumference coincide conceived cone construct convex surface COROLLARY 2.-The COROLLARY.-The cylinder diagonals diameter dicular diedral distance draw drawn equal angles equally distant equiangular equilateral equivalent exterior angles faces facial angles four right angles frustum Geometry given angle given line given point greater Hence homologous sides inscribed intersect isosceles Let ABC middle point number of sides oblique lines opposite sides parallelogram parallelopiped pass pendicular perimeter perpen plane MN prism Problem.-To produced PROPOSITION VII prove pyramid Q. E. D. PROPOSITION quadrilateral radii ratio rectangle regular polygon revolved right angles S-ABC SCHOLIUM segment semi-circumference similar slant height solid solid angle sphere spherical angle spherical polygon spherical triangle square straight line supplement tangent Theorem Theorem.-The triedrals vertex vertices whence ليا

### Popular passages

Page 286 - A Sphere is a solid bounded by a surface every point in which is equally distant from a point within called the Centre.

Page 134 - 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 298 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.

Page 169 - 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 323 - 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 106 - In an isosceles triangle the angles opposite the equal sides are equal.

Page 158 - Theorem. — The area of a trapezoid is equal to the product of its altitude...