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 are 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 are 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 28
... Hence AB and CD are . perpendicular to the same straight line ; " hence they are parallel ( Prop . XVIII . ) . T Q D B PROPOSITION XXIII . THEOREM . Two parallels are every where equally distant . Two parallels AB , CD , being CH given ...
... Hence AB and CD are . perpendicular to the same straight line ; " hence they are parallel ( Prop . XVIII . ) . T Q D B PROPOSITION XXIII . THEOREM . Two parallels are every where equally distant . Two parallels AB , CD , being CH given ...
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 ...
... 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 ...
Page 31
... hence , when a pentagon is equiangular , each angle is equal to the fifth part of six right angles , or to § of one right angle . Cor . 3. The sum of the angles of a hexagon is equal to 2 × ( 6-2 , ) or eight right angles ; hence in the ...
... hence , when a pentagon is equiangular , each angle is equal to the fifth part of six right angles , or to § of one right angle . Cor . 3. The sum of the angles of a hexagon is equal to 2 × ( 6-2 , ) or eight right angles ; hence in the ...
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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