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ABCD altitude angle base bisect called centre chord circ circle circumference circumscribed coincide common cone consequently construction contained convex corresponding cylinder denote described diagonal diameter difference distance divided double draw equal equilateral equivalent exterior angle extremities figure follows formed four given gives greater hence included inscribed intersection join length less lines drawn magnitude manner mean measured measured by half meet multiplied opposite parallel parallel lines parallelogram parallelopipedon pass perimeter perpendicular plane plane MN polygon portion position prism Problem produced Prop proportional PROPOSITION pyramid radii radius ratio rectangle remain respectively right-angles sector segment shown sides similar solid angle sphere spherical square straight line suppose surface taken tangent Theorem third triangle ABC vertex VIII whole
Page 227 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Page 13 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Page 24 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Page 229 - The volume of a cylinder is equal to the product of its base by its altitude. Let the volume of the cylinder be denoted by V, its base by B, and its altitude by H.
Page 272 - THEOREM. Two triangles on the same sphere, or on equal spheres, are equal in all their parts, when they have each an equal angle included between equal sides. Suppose the side...
Page 116 - 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 14 - If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another.
Page 228 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.