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ABCD ABCD &c altitude applied base called centre chord circle circumference coincide common cone consequently construct contained Corollary cylinder Definitions Demonstration denote describe diameter difference divided draw equal equal distances equiangular equilateral equivalent extremities faces fall formed four frustum give given greater half Hence included infinitely small inscribed intersection Join less mean measure meet middle number of sides opposite parallel parallel planes parallelogram parallelopiped passes perimeter perpendicular plane polyedron polygon ABCD preceding prism Problem proportional prove pyramid quantities radii radius ratio rectangles regular polygon remainder respectively right angles right triangle sector segment side BC similar solid solid angle Solution sphere spherical triangle square straight line Suppose surface Take tangent Theorem third triangles ABC vertex vertices whence
Σελίδα 148 - 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'.
Σελίδα 24 - 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.
Σελίδα 40 - One side and two angles of a triangle being given, to construct the triangle. Solution.
Σελίδα 79 - Construct, by § 145, a right triangle, of which the hypothenuse BC (fig. 79) is equal to the side of the greater square, and the leg AB is equal to the side of the less square ; and AC is the side of the required square.
Σελίδα 142 - THEOREM. If two triangles on the same sphere, or on equal spheres, are mutually equiangular, they will also be mutually equilateral. Let A and B be the two given triangles; P and Q their polar triangles. Since the angles are equal in the triangles A and B, the sides will be equal in. their polar triangles P and Q (Prop.
Σελίδα 70 - 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.
Σελίδα 5 - A surface is that which has length and breadth, without thickness. 6. A plane is a surface, in which any two points being taken, the straight line joining those points lies wholly in that surface.