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ABCD adjacent altitude angled triangle apply base bisect called centre chord circle circumference coincide common conceive consequently construct corresponding cosine DEM.-Let demonstration describe determine diagonals diameter diedral difference direction distance divided draw drawn edges equal equivalent extremities faces fall feet figure four FUNCTIONS geometrical give given given line greater Hence hypotenuse included increase inscribed intersect joining length less logarithm manner means measured meet middle oblique observe opposite parallel passing perpendicular plane polygon position produced PROP proportional PROPOSITION pyramid radii radius ratio rectangle regular represent respectively revolve right angles sides similar sine solution sphere spherical triangle square straight line student surface symmetrical tangent third triangle triedral values vertex vertices whence
Page 215 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 126 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 29 - Cut out two such triangles and try it Ex. 6. If you have two triangles with only two sides of one respectively equal to two sides of the other, can you make one fit as a pattern on the other ? Try it. Ex. 7. If you have two triangles with two sides in one equal respectively to two sides in the other, and the included angle in one greater than in the other, how is it with the third sides of the triangles ? 76.
Page 105 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Page 102 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Page 246 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 239 - If from any point there extend two lines tangent to a circumference, the angle contained by the tangents is double the angle contained by the line joining the points of contact and the radius extending to one of them.
Page 137 - Hence, the area of a trapezoid is equal to the product of its altitude by the line connecting the middle points of the sides which are not parallel.
Page 77 - In the same or in equal circles, of two unequal chords, the less is at the greater distance from the centre. DEM. — Let CE < AB, then is the perpendicular OD, which measures the distance of CE from the centre, greater than OD' •which measures the distance of AB from the centre.