Elements of Geometry and Trigonometry |
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Page 109
... surfaces are to each other as the squares of those sides ( Book IV . Prop . XXVII . ) . Scholium . The angle of a regular polygon , like the angle of an equiangular polygon , is determined by the number of its sides ( Book I. Prop ...
... surfaces are to each other as the squares of those sides ( Book IV . Prop . XXVII . ) . Scholium . The angle of a regular polygon , like the angle of an equiangular polygon , is determined by the number of its sides ( Book I. Prop ...
Page 116
... surface . Let Q be the side of a square less than the given surface . Bisect AC , a fourth part of the circumference , and then bi sect the half of this fourth , and proceed in this manner , always bisecting one of the arcs formed by ...
... surface . Let Q be the side of a square less than the given surface . Bisect AC , a fourth part of the circumference , and then bi sect the half of this fourth , and proceed in this manner , always bisecting one of the arcs formed by ...
Page 117
... surface . Cor . 1. A circumscribed regular polygon , having a given number of sides , is greater than the circle , because the circle makes up but a part of the polygon : and for a like reason , the inscribed polygon is less than the ...
... surface . Cor . 1. A circumscribed regular polygon , having a given number of sides , is greater than the circle , because the circle makes up but a part of the polygon : and for a like reason , the inscribed polygon is less than the ...
Page 119
... surfaces of these polygons are to each other as the squares of the homologous sides AB , ab ; they are therefore likewise to each other as the squares of AO , ao , the radii of the circumscribed circles , or as the squares of OD , od ...
... surfaces of these polygons are to each other as the squares of the homologous sides AB , ab ; they are therefore likewise to each other as the squares of AO , ao , the radii of the circumscribed circles , or as the squares of OD , od ...
Page 122
... surface to a circle , the radius of which is known . Now it has just been proved , that a circle is equivalent to the rectangle contained by its circumference and half its radius ; and this rectangle may be changed into a square , by ...
... surface to a circle , the radius of which is known . Now it has just been proved , that a circle is equivalent to the rectangle contained by its circumference and half its radius ; and this rectangle may be changed into a square , by ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex