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 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 . ) . R T Q D P 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 . ) . R T Q D P 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 ...
... 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 g 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 g 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 altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles 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 measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular 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 slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex