Elements of Geometry and Trigonometry |
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Page 116
... circumscribed square is greater than the circumscribed octagon by the four triangles , Cnp , kDg , hEf , Git ; and if a regular polygon of sixteen sides be circum- scribed about the circle , we may prove in a similar way , that the ...
... circumscribed square is greater than the circumscribed octagon by the four triangles , Cnp , kDg , hEf , Git ; and if a regular polygon of sixteen sides be circum- scribed about the circle , we may prove in a similar way , that the ...
Page 117
... circumscribed polygon , and p the in- scribed polygon ; then , since the triangles aOb , AOB , are like parts of P ... circumscribed and inscribed poly- gons may always be made less than a given surface . Cor . 1. A circumscribed regular ...
... circumscribed polygon , and p the in- scribed polygon ; then , since the triangles aOb , AOB , are like parts of P ... circumscribed and inscribed poly- gons may always be made less than a given surface . Cor . 1. A circumscribed regular ...
Page 118
... circumscribed polygon cannot fall within the circle , nor the sides of the inscribed polygon without it , it follows that the perimeters of the polygons will unite on the circumference of the circle , and become equal to it . Cor . 3 ...
... circumscribed polygon cannot fall within the circle , nor the sides of the inscribed polygon without it , it follows that the perimeters of the polygons will unite on the circumference of the circle , and become equal to it . Cor . 3 ...
Page 119
... circumscribed circle , and OD , perpendicular to AB , the radius of the inscribed circle ; let ab , in like manner , be a side of the other polygon , o its centre , oa and od the radii of the circumscribed and the inscribed circles ...
... circumscribed circle , and OD , perpendicular to AB , the radius of the inscribed circle ; let ab , in like manner , be a side of the other polygon , o its centre , oa and od the radii of the circumscribed and the inscribed circles ...
Page 123
... circumscribed , being given ; to find the surfaces of the regular inscribed and circumscribed polygons having double the number of sides . Let AB be a side of the given inscribed polygon ; EF , parallel to E P AB , a side of the ...
... circumscribed , being given ; to find the surfaces of the regular inscribed and circumscribed polygons having double the number of sides . Let AB be a side of the given inscribed polygon ; EF , parallel to E P AB , a side of the ...
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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