Elements of Geometry and Trigonometry |
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Page 28
... gles EFG , FGH , have a common side , and two adjacent angles in each equal ; hence these triangles are equal ( Prop . VI . ) ; therefore , the side EG , which measures the distance of the parallels AB and CD at the point E , is equal ...
... gles EFG , FGH , have a common side , and two adjacent angles in each equal ; hence these triangles are equal ( Prop . VI . ) ; therefore , the side EG , which measures the distance of the parallels AB and CD at the point E , is equal ...
Page 57
... gles DAE , DAC , that the angle CAE is measured by half the arc AC , included between its sides . PROBLEMS RELATING TO THE FIRST AND THIRD BOOKS . PROBLEM I. To divide a given straight line into two equal parts . Let AB be the given ...
... gles DAE , DAC , that the angle CAE is measured by half the arc AC , included between its sides . PROBLEMS RELATING TO THE FIRST AND THIRD BOOKS . PROBLEM I. To divide a given straight line into two equal parts . Let AB be the given ...
Page 65
... gles inscribed in it , shall be equal to the given angle . Let AB be the given straight line , and C the given angle . M E -D Ꮐ B K E M G B K Produce AB towards D ; at the point B , make the angle DBE = C ; draw BO perpendicular to BE ...
... gles inscribed in it , shall be equal to the given angle . Let AB be the given straight line , and C the given angle . M E -D Ꮐ B K E M G B K Produce AB towards D ; at the point B , make the angle DBE = C ; draw BO perpendicular to BE ...
Page 67
... gles . With equal radii describe the arcs CD , EF , to serve as mea- sures for the angles : proceed afterwards in the comparison of the arcs CD , EF , as in the last D CL problem , since an arc may be cut off from an arc of the same ...
... gles . With equal radii describe the arcs CD , EF , to serve as mea- sures for the angles : proceed afterwards in the comparison of the arcs CD , EF , as in the last D CL problem , since an arc may be cut off from an arc of the same ...
Page 70
... , are equivalent , being halves of equivalent parallelograms . PROPOSITION III . THEOREM . Two rectangles having the same altitude , are to each other as their bases . Let ABCD , AEFD , be two rectan D gles 70 GEOMETRY .
... , are equivalent , being halves of equivalent parallelograms . PROPOSITION III . THEOREM . Two rectangles having the same altitude , are to each other as their bases . Let ABCD , AEFD , be two rectan D gles 70 GEOMETRY .
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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