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A B C ABCD adjacent altitude base called centre chord circle circumference common cone consequently contained corresponding Cosine Cotang described diagonal diameter difference distance divided draw drawn edge equal equal Prop equivalent EXAMPLES exterior angle extremities faces feet figure four frustum given gles greater half height hence homologous hypothenuse inches included inscribed intersect join length less logarithm magnitudes manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid radius ratio rectangle regular right angles rods Scholium segment shown side A B sides similar sine solidity sphere spherical triangle square straight line taken Tang tangent THEOREM third triangle ABC vertex whole
Page 17 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 155 - The convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude (Prop.
Page 28 - 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 = e :f Now ab = ab (1) and by Theorem I.
Page 118 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Page 98 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 144 - The convex surface of this prism is equal to the perimeter of its base multiplied by its altitude, AG (Prop.
Page 176 - Find the area of the sector having' the same arc with the segment, and also the area of the triangle formed by the chord of the segment and the radii of the sector. Then...
Page 14 - Straight lines which are parallel to the same line are parallel to each other. Let the straight lines AB, CD be each parallel to the line EF ; then are they parallel to each other.