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acute altitude axis base called centre chord circle circumference construct contained convex surface Corollary cubes cylinder Definitions denote described diameter difference divided Draw equal equal distances equiangular equilateral equivalent extremities faces fall formed four frustum given given polygon given square greater half the product Hence homologous sides included infinitely small intersection isosceles Join less maximum mean measure meet middle number of sides opposite parallel parallel planes parallelogram parallelopipeds passes perimeter perpendicular plane pole polyedron portion preceding prism Problem Proof proportional prove pyramid pyramid or cone radii radius ratio rectangles regular polygon respectively right angles sector segment side AC similar solid angle solidity Solution sphere spherical triangle square straight line Suppose surface Take tangent Theorem third triangle ABC triangular vertex vertices whence
Page 133 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 80 - Problem. To construct a polygon similar to a given polygon, and having a given ratio to it.
Page 31 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 87 - To construct a parallelogram equivalent to a given square, and having the difference of its base and altitude equal to a given line.
Page 141 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 6 - Your geometry states it as an axiom that a straight line is the shortest way from one point to another; and astronomy shows you that God has given motion only in curves.
Page 31 - In the same circle or in equal circles, equal chords subtend equal arcs; and of two unequal chords the greater subtends the greater arc. In the equal circles whose centres are 0 and 0', let the chords AB and A'B' be equal, and the chord AF greater than A'B'. To prove that 1. arc AB = arc A'B'; 2.
Page 40 - The three sides of a triangle being given, to construct the triangle. Draw the straight line...