Elements of Geometry and Trigonometry |
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Page 46
... perpendicular to DE , would also be perpendicular to FG , and the angle K would be a right angle ( Book I. Prop . XX . Cor . 1. ) . But BK , the prolongation of BD , is a different line from BF , because the three points A , B , C , are ...
... perpendicular to DE , would also be perpendicular to FG , and the angle K would be a right angle ( Book I. Prop . XX . Cor . 1. ) . But BK , the prolongation of BD , is a different line from BF , because the three points A , B , C , are ...
Page 47
... perpendicular to a radius , at its extremity , is a tangent to the circumference . Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfe - r rence . For , every oblique line CE , is ...
... perpendicular to a radius , at its extremity , is a tangent to the circumference . Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfe - r rence . For , every oblique line CE , is ...
Page 48
... perpendicular to the radius CA ( Book I. Prop , XIV . Sch . ) ; hence in reference to this new tangent , the radius AC would be an oblique line , and the perpendicular let fall from the centre upon this tangent would be shorter than CA ...
... perpendicular to the radius CA ( Book I. Prop , XIV . Sch . ) ; hence in reference to this new tangent , the radius AC would be an oblique line , and the perpendicular let fall from the centre upon this tangent would be shorter than CA ...
Page 49
... perpendicular to the chord which joins the points of intersection , and will divide it into two equal parts . For , let the line AB join the points of intersection . It will be a common chord to the two circles . Now if a perpendicular ...
... perpendicular to the chord which joins the points of intersection , and will divide it into two equal parts . For , let the line AB join the points of intersection . It will be a common chord to the two circles . Now if a perpendicular ...
Page 57
... perpendicular raised from the middle of AB ( Book I. Prop . XVI . Cor . ) . But only one straight line can pass through two given points ; hence the line DE must itself be that perpendicular , which divides AB into two equal parts at ...
... perpendicular raised from the middle of AB ( Book I. Prop . XVI . Cor . ) . But only one straight line can pass through two given points ; hence the line DE must itself be that perpendicular , which divides AB into two equal parts at ...
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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