Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with Practical Exercises |
Other editions - View all
Common terms and phrases
ABCD ABCDEF adjacent adjacent angles altitude angle included angles are equal apothem arc CB bisect centre chord circumference coincide conceived construct COROLLARY 1.-The diagonals diameter diedral distance draw drawn edges equal angles equally distant equiangular equilateral equivalent exterior angles facial angles figure frustum Geometry given angle given line given point given sides greater Hence homologous sides inscribed inscribed angle intersect Let ABC lune measured by arc middle point number of sides oblique lines opposite sides parallel parallelogram pass pendicular perimeter perpen perpendicular prism Problem.-To produced PROPOSITION VII prove pyramid Q. E. D. PROPOSITION quadrilateral radii ratio rectangle regular polygon revolved right angles SCHOLIUM segment similar solid sphere spherical angle spherical triangle square straight angle straight line supplemental surface tangent Theorem.-The transversal triedrals vertex vertices whence ليا
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 triangle which has the greater included angle has the greater third side.
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 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.
Page 186 - It follows from § 259 that if through a fixed point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Page 160 - The area of a trapezoid is equal to the product of its altitude...