The Elements of Geometry
Leach, Shewell & Sanborn, 1894 - Geometry - 378 pages
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Common terms and phrases
ABCD adjacent altitude approach the limit base bisector bisects Book called centre chord circle circumference circumscribed coincide common cone construct cylinder denote describe diagonals diameter diedral divided draw drawn edges equal respectively equally distant equilateral equivalent EXERCISES extremities faces fall figure Find formed four frustum given given point greater Hence homologous hypotenuse included inscribed intersection isosceles triangle joining lateral area length less line drawn manner measured meet middle point multiplied parallel parallelogram parallelopiped passing perimeter perpendicular plane polygon prism PROBLEM produced Prop proportional PROPOSITION prove pyramid quadrilateral radii radius ratio rectangle regular respectively right angles right triangle segment sides similar sphere spherical triangle square straight line surface tangent tetraedron THEOREM third triangle ABC unit vertex vertices volume Whence
Page 38 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first 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 65 - 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 170 - The areas of two triangles which have 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. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Page 120 - The first and fourth terms of a proportion are called the extremes, and the second and third terms the means.
Page 24 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...
Page 123 - In any proportion the terms are in proportion by composition and division ; that is, the sum of the first two terms is to their difference as the sum of the last two terms to their difference.
Page 322 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...
Page 248 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane.