Elements of Geometry and Trigonometry |
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Page 23
... ( Prop . V. Cor . ) : therefore , two oblique , lines , equally distant from the perpendicular , are equal . Thirdly . In the triangle DFA , the sum of the lines AC , CF , is less than the sum of the sides AD , DF ( Prop . VIII ...
... ( Prop . V. Cor . ) : therefore , two oblique , lines , equally distant from the perpendicular , are equal . Thirdly . In the triangle DFA , the sum of the lines AC , CF , is less than the sum of the sides AD , DF ( Prop . VIII ...
Page 24
... ( Prop . XV . ) . So , likewise , are the two oblique lines AE , EB , the A two AF , FB , and so on . Therefore every point in the perpendicular is equally distant from the extremities A and B. E oni Secondly , Let I be a point out of the ...
... ( Prop . XV . ) . So , likewise , are the two oblique lines AE , EB , the A two AF , FB , and so on . Therefore every point in the perpendicular is equally distant from the extremities A and B. E oni Secondly , Let I be a point out of the ...
Page 25
... ( Prop . I. ) ; and taking away BAC from both , there will remain the angle ABD = BAE . Again , the angles EGA , BGF , are equal ( Prop . IV . ) ; there- fore , the triangles EGA and BGF , have each a side and two adjacent angles equal ...
... ( Prop . I. ) ; and taking away BAC from both , there will remain the angle ABD = BAE . Again , the angles EGA , BGF , are equal ( Prop . IV . ) ; there- fore , the triangles EGA and BGF , have each a side and two adjacent angles equal ...
Page 27
... ( Prop . XIX . ) , and hence we shall have two lines GB , GH , 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 ...
... ( Prop . XIX . ) , and hence we shall have two lines GB , GH , 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 ...
Page 28
... ( Prop.E XX . Cor . 1. ) ; and since CD is parallel to EF , PR will for a like reason be perpen - C dicular to CD . Hence AB and CD are . perpendicular to the same straight line ; " hence they are parallel ( Prop . XVIII . ) . T Q D B ...
... ( Prop.E XX . Cor . 1. ) ; and since CD is parallel to EF , PR will for a like reason be perpen - C dicular to CD . Hence AB and CD are . perpendicular to the same straight line ; " hence they are parallel ( Prop . XVIII . ) . T Q D B ...
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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