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acute adjacent altitude applied base called centre chord circle circumference coincide common construct contained convex surface Corollary cylinder Definitions denote described diameter difference divided Draw drawn equal equal distances equiangular equilateral equivalent extremities faces fall figure formed four frustum given given polygon greater half the product Hence homologous sides included infinitely small inscribed intersection isosceles Join less mean measure meet middle number of sides opposite parallel parallel planes parallelogram parallelopipeds passes perimeter perpendicular plane pole polyedron preceding prism Problem Proof proportional prove pyramid radii radius ratio rectangles regular polygon respectively right angles right triangle sector segment side BC similar similar polygons solid angle solidity Solution sphere spherical triangle square straight line Suppose surface Take tangent Theorem third triangles ABC vertex vertices whence
Page 138 - 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 73 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 132 - Theorem. Every section of a sphere made by a plane is a circle.
Page 131 - A sphere is a solid terminated by a curved surface, all the points of which are equally distant from a point within called the centre.
Page 88 - Theorem. Similar sectors are to each other as the squares of their radii. Proof. The similar sectors AOB, A'&B ' (ng. 136) are, by the same reasoning as in § 97, the same parts of their respective circles, which the angle O= O...
Page 29 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 92 - To construct a parallelogram equivalent to a given square, and having the difference of its base and altitude equal to a given line.
Page 38 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 146 - 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'.