Elements of Geometry and Trigonometry |
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Page 17
... Hence , the point D , falling at the same time in the two straight lines BA and CA , must fall at their intersection A : hence , the two triangles EDF , BAC , coincide with each other , and re therefore equal ( Ax . 13. ) . Cor ...
... Hence , the point D , falling at the same time in the two straight lines BA and CA , must fall at their intersection A : hence , the two triangles EDF , BAC , coincide with each other , and re therefore equal ( Ax . 13. ) . Cor ...
Page 23
... hence the third sides , CF and CA are equal ( Prop . V. Cor . ) . But ABF , being a straight line , is shorter than ACF , which is a broken line ( Def . 3. ) ; therefore , AB , the half of ABF , is shorter than AC , the half of ACF ; hence ...
... hence the third sides , CF and CA are equal ( Prop . V. Cor . ) . But ABF , being a straight line , is shorter than ACF , which is a broken line ( Def . 3. ) ; therefore , AB , the half of ABF , is shorter than AC , the half of ACF ; hence ...
Page 27
... 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 same manner it may be ...
... 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 same manner it may be ...
Page 28
... Hence AB and CD are . perpendicular to the same straight line ; hence they are parallel ( Prop . XVIII . ) . . A R T Q D B PROPOSITION XXIII . THEOREM . Two parallels are every where equally distant . Two parallels AB , CD , being C H ...
... Hence AB and CD are . perpendicular to the same straight line ; hence they are parallel ( Prop . XVIII . ) . . A R T Q D B PROPOSITION XXIII . THEOREM . Two parallels are every where equally distant . Two parallels AB , CD , being C H ...
Page 29
... hence the angle DEF is equal to BAC ( Ax . 1. ) . Scholium . The restriction of this proposition to the case where the side EF lies in the same direction with AC , and ED in the same direction with AB , is necessary , because if FE were ...
... hence the angle DEF is equal to BAC ( Ax . 1. ) . Scholium . The restriction of this proposition to the case where the side EF lies in the same direction with AC , and ED in the same direction with AB , is necessary , because if FE were ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex