Elements of Geometry and Trigonometry |
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Page 48
... fall from the centre upon this tangent would be shorter than CA ; hence this supposed tangent would enter the circle , and be a secant . * PROPOSITION X. THEOREM . Two parallels intercept equal arcs on the circumference . There may be ...
... fall from the centre upon this tangent would be shorter than CA ; hence this supposed tangent would enter the circle , and be a secant . * PROPOSITION X. THEOREM . Two parallels intercept equal arcs on the circumference . There may be ...
Page 51
... fall on D , and the point B on E. But , in that case , the arc AB must also QQ fall on the arc DE ; for if the arcs did not exactly coincide , there would , in the one or the other , be points unequally distant from the centre ; which ...
... fall on D , and the point B on E. But , in that case , the arc AB must also QQ fall on the arc DE ; for if the arcs did not exactly coincide , there would , in the one or the other , be points unequally distant from the centre ; which ...
Page 58
... fall a perpen- dicular on this line . Let A be the point , and BD the straight line . From the point A as a centre , and with a radius sufficiently great , describe an arc cutting the line BD in the two points B and D ; then mark a ...
... fall a perpen- dicular on this line . Let A be the point , and BD the straight line . From the point A as a centre , and with a radius sufficiently great , describe an arc cutting the line BD in the two points B and D ; then mark a ...
Page 62
... , and there would be but one solution . The problem would be impossible in all cases , if the side B were less than the perpen- dicular let fall from E on the line DF . PROBLEM XII . The adjacent sides of a parallelogram , 62 GEOMETRY .
... , and there would be but one solution . The problem would be impossible in all cases , if the side B were less than the perpen- dicular let fall from E on the line DF . PROBLEM XII . The adjacent sides of a parallelogram , 62 GEOMETRY .
Page 64
... the point 0 ; from the point 0 , let fall the perpendiculars OD , OE , OF , on the three sides of the triangle : these perpendiculars will all be equal . For , by construc- D B E F tion , we have the angle DAO = OAF , 64 GEOMETRY .
... the point 0 ; from the point 0 , let fall the perpendiculars OD , OE , OF , on the three sides of the triangle : these perpendiculars will all be equal . For , by construc- D B E F tion , we have the angle DAO = OAF , 64 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