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ABCD adjacent altitude apply base bisect called centre chord circle circumference coincide common conceive cone consequently construct Converse corresponding DEM.-Let demonstration describe diagonals diameter diedral difference direction distance dividers draw drawn edge equal equiangular equivalent extremities faces facial angles fall feet figure four given given line greater Hence homologous inches included inscribed intersect joining latter length less lune manner mean measured meet oblique opposite parallel parallelogram passing path perpendicular plane pole polygon position prism produced PROP proportional PROPOSITION pyramid quadrilateral radii radius ratio reason rectangle regular represent respectively revolve right angles sides similar solid sphere spherical triangle square straight line student supplement surface tangent Theorem.-The third triangle triedral vertex vertices volume whence
Page 213 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 203 - A sphere is a solid, bounded by one continued convex surface, every point of which is equally distant from a point within, called the centre.
Page 132 - Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other.
Page 121 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Page 161 - Oblique lines drawn from a point to a plane, meeting the plane at equal distances from the foot of the perpendicular, are equal; and of two oblique lines meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Page 216 - 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 viii - LEMMA 4. — A common divisor of two numbers is a divisor of their sum and also of their difference.