Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |
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Page 14
... bisecting it . OF ANGLES . THEOREM I. When a straight line meets or crosses another , the adjacent angles are supplements ; and the opposite angles are equal . A G C B F For , drawing FG perpendicular to AB , we see that the angle AFC ...
... bisecting it . OF ANGLES . THEOREM I. When a straight line meets or crosses another , the adjacent angles are supplements ; and the opposite angles are equal . A G C B F For , drawing FG perpendicular to AB , we see that the angle AFC ...
Page 23
... bisect it . THEOREM XIV . If a line be drawn bisecting a given angle , that is , dividing it into two equal angles : I. Any point in this bisecting line will be equidistant from the sides of the angle . II . Any point without this bisecting ...
... bisect it . THEOREM XIV . If a line be drawn bisecting a given angle , that is , dividing it into two equal angles : I. Any point in this bisecting line will be equidistant from the sides of the angle . II . Any point without this bisecting ...
Page 29
... bisect- ing the angle ACG ( Post . VI . ) , and meet- ing AB at L , draw GL . The two triangles ACL , GCL , are equal ( T. XX . ) , and LG = LA . Therefore , AB = AL + LB = LG + LB , which is greater than BG ( T. VII . ) . Although the ...
... bisect- ing the angle ACG ( Post . VI . ) , and meet- ing AB at L , draw GL . The two triangles ACL , GCL , are equal ( T. XX . ) , and LG = LA . Therefore , AB = AL + LB = LG + LB , which is greater than BG ( T. VII . ) . Although the ...
Page 30
... bisects the vertical angle of an isosce- les triangle , bisects the base perpendicularly , and divides the triangle itself into two equal parts . Cor . II . An equilateral triangle is equi - angular , that is , has all its angles equal ...
... bisects the vertical angle of an isosce- les triangle , bisects the base perpendicularly , and divides the triangle itself into two equal parts . Cor . II . An equilateral triangle is equi - angular , that is , has all its angles equal ...
Page 35
... bisect each other , that is , they divide each other into halves . D E A B C In the two triangles EAB and ECD , we have the angle EAB of the first equal to ECD of the second , being alternate an- gles in reference to the parallels AB ...
... bisect each other , that is , they divide each other into halves . D E A B C In the two triangles EAB and ECD , we have the angle EAB of the first equal to ECD of the second , being alternate an- gles in reference to the parallels AB ...
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Common terms and phrases
ABē ABCD altitude angles equal apothem base bisecting centre chord circle circumference circumscribed circle circumscribed polygon cone consequently corresponding cosec Cosine Cotang cubic cylinder decimal denote diameter dicular distance divided draw drawn equally distant equation exterior angles feet figure frustum GEOMETRY given angle given line gives greater half hence homologous hypotenuse inches included angle intersection logarithm measure middle point multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant quadrilateral radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle Scholium secant similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang Tangent THEOREM three sides triangle ABC volume