Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 7
Page 143
... slant height of the pyramid . 16. The diagonal of a polyedron is a straight line joining the vertices of two solid angles which are not adjacent to each other . 17. Two polyedrons are similar when they are contained by BOOK VII . 143.
... slant height of the pyramid . 16. The diagonal of a polyedron is a straight line joining the vertices of two solid angles which are not adjacent to each other . 17. Two polyedrons are similar when they are contained by BOOK VII . 143.
Page 146
... slant height . For , since the pyramid is regular , the point O , in which the axis meets the base , is the centre of the polygon ABCDE ( Def . 14. ) ; hence the lines OA , OB , OC , & c . drawn to the vertices of the base , are equal ...
... slant height . For , since the pyramid is regular , the point O , in which the axis meets the base , is the centre of the polygon ABCDE ( Def . 14. ) ; hence the lines OA , OB , OC , & c . drawn to the vertices of the base , are equal ...
Page 147
... slant height of the pyramid : hence the area of all the tri- angles , or the convex surface of the pyramid , is equal to the perimeter of the base multiplied by half the slant height . Cor . The convex surface of the frustum of a ...
... slant height of the pyramid : hence the area of all the tri- angles , or the convex surface of the pyramid , is equal to the perimeter of the base multiplied by half the slant height . Cor . The convex surface of the frustum of a ...
Page 171
... slant height SG ( Book VII . Prop . IV . ) . Let now the number of sides of the inscribed polygon be indefinitely increased ; the perimeter of the inscribed polygon will then become equal to circ . OA , the slant height SG will become ...
... slant height SG ( Book VII . Prop . IV . ) . Let now the number of sides of the inscribed polygon be indefinitely increased ; the perimeter of the inscribed polygon will then become equal to circ . OA , the slant height SG will become ...
Page 172
... slant height fh ( Book VII . Prop . IV . Cor . ) . A di I Let now the number of sides of the inscribed polygons be indefinitely increased : the perimeters of the polygons will be- come equal to the circumferences BIA , EGD ; the slant ...
... slant height fh ( Book VII . Prop . IV . Cor . ) . A di I Let now the number of sides of the inscribed polygons be indefinitely increased : the perimeters of the polygons will be- come equal to the circumferences BIA , EGD ; the slant ...
Other editions - View all
Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex