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acute adjacent altitude base bisecting Book called centre chord circle circumference circumscribed coincide common constant contained Conversely Corollary DEFINITIONS described diagonals diameter diedral angles difference direction distance divided draw drawn edges equal equally distant equilateral equivalent extremities feet figure formed four frustum given angle given line given point greater half hence homologous lines hypothenuse included inscribed intersection isosceles triangle less locus mean measure meet number of sides opposite opposite sides parallel parallelogram parallelopiped pass perimeter perpendicular plane plane M N polygon prism PROBLEM produced proportion proposition proved pyramid quantity radius ratio rectangle regular polygon respectively right angles right triangle segments sides similar sphere spherical triangle square straight line tangent THEOREM third triangle A B C triangular triedral vertex vertices volume
Page 166 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 41 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d...
Page 198 - Each side of a spherical triangle is less than the sum of the other two sides.
Page 75 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 203 - In an isosceles spherical triangle, the angles opposite the equal sides are equal. In the spherical triangle ABC, let AB equal AC.
Page 220 - If one angle of a triangle is equal to the sum of the other two, the triangle can be divided into two isosceles triangles.
Page 136 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Page 199 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.
Page 162 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. GM is a right section of oblique prism AD', and GM.' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =0= GM'. Proof. The lateral edges of GM