Elements of Geometry and Trigonometry |
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Page 26
... OGA + GOC , be equal to two right an- gles . For , if OGB + GOD be not equal to two right angles , let IGH be drawn , making the sum OGH + GOD equal to two A I F E B H D right angles ; then IH and CD will be parallel 26 GEOMETRY .
... OGA + GOC , be equal to two right an- gles . For , if OGB + GOD be not equal to two right angles , let IGH be drawn , making the sum OGH + GOD equal to two A I F E B H D right angles ; then IH and CD will be parallel 26 GEOMETRY .
Page 27
... drawn through the same point G and parallel to CD , which is impossible ( Ax . 12. ) : hence , GB and GH should coincide , and OGB + GOD is equal to two right angles . In the same manner it may be proved that OGA + GOC is equal to two ...
... drawn through the same point G and parallel to CD , which is impossible ( Ax . 12. ) : hence , GB and GH should coincide , and OGB + GOD is equal to two right angles . In the same manner it may be proved that OGA + GOC is equal to two ...
Page 28
... Draw PQR perpendicular to EF , and cutting AB , CD . Since AB is parallel to EF , PR will be perpendicular to AB ... drawn , the angles GFE , FGH , considered in refer- ence to the parallels AB , CD , will be alternate angles , and ...
... Draw PQR perpendicular to EF , and cutting AB , CD . Since AB is parallel to EF , PR will be perpendicular to AB ... drawn , the angles GFE , FGH , considered in refer- ence to the parallels AB , CD , will be alternate angles , and ...
Page 30
... drawn to the vertices of all the opposite angles , it is plain that the poly- gon will be divided into five triangles , if it has seven sides ; into six triangles , if it has eight ; and , in general , into as many triangles , less two ...
... drawn to the vertices of all the opposite angles , it is plain that the poly- gon will be divided into five triangles , if it has seven sides ; into six triangles , if it has eight ; and , in general , into as many triangles , less two ...
Page 31
... drawn at pleasure , cannot meet the contour of the polygon in more than two points . PROPOSITION XXVII . THEOREM . If the sides of any polygon be produced out , in the same direc- tion , the sum of the exterior angles will be equal to ...
... drawn at pleasure , cannot meet the contour of the polygon in more than two points . PROPOSITION XXVII . THEOREM . If the sides of any polygon be produced out , in the same direc- tion , the sum of the exterior angles will be equal to ...
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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 convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines 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 sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex