Conic Sections, Treated Geometrically |
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Page 12
... length . For the two triangles TSM , TSM ' have the angles TMS , TSM respectively equal to the angles TM'S TSM ' , and the side TS common ; and therefore the other sides are equal , and TM = TM ' . 14. PROP . VIII . If from any point T ...
... length . For the two triangles TSM , TSM ' have the angles TMS , TSM respectively equal to the angles TM'S TSM ' , and the side TS common ; and therefore the other sides are equal , and TM = TM ' . 14. PROP . VIII . If from any point T ...
Page 16
... length PL is equal to the semi - latus rectum . P L F S G P Produce PS to meet the curve in P ' ; let F be the point of intersection of the tangents at P and P ' , and join SF . Draw the normals PG , P'G ' , and draw GL , G'L ' at right ...
... length PL is equal to the semi - latus rectum . P L F S G P Produce PS to meet the curve in P ' ; let F be the point of intersection of the tangents at P and P ' , and join SF . Draw the normals PG , P'G ' , and draw GL , G'L ' at right ...
Page 20
... length of X which is LK . Then if the other end of the string be fastened to S , S and the bar be made to slide along the directrix , a pencil at P , keeping the string stretched against the bar , will trace out a portion of a parabola ...
... length of X which is LK . Then if the other end of the string be fastened to S , S and the bar be made to slide along the directrix , a pencil at P , keeping the string stretched against the bar , will trace out a portion of a parabola ...
Page 37
... length of the ordinate at that point produced to meet the tangent at the end of the latus rectum . 9. PT being the tangent at P , meeting the axis in T , and PN the ordinate , prove that TY . TP = TS . TN . 10. If SE be the ...
... length of the ordinate at that point produced to meet the tangent at the end of the latus rectum . 9. PT being the tangent at P , meeting the axis in T , and PN the ordinate , prove that TY . TP = TS . TN . 10. If SE be the ...
Page 38
... , a point P on the curve , and the length of the perpendicular from the focus on the tangent at P , find the vertex . 27. A circle is described on the latus rectum as diameter , and a common tangent QP is drawn to it and 38 The Parabola .
... , a point P on the curve , and the length of the perpendicular from the focus on the tangent at P , find the vertex . 27. A circle is described on the latus rectum as diameter , and a common tangent QP is drawn to it and 38 The Parabola .
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Conic Sections, Treated Geometrically (Classic Reprint) William Henry Besant No preview available - 2016 |
Common terms and phrases
AC² asymptotes auxiliary circle BC² bisects the angle Cambridge CD² centre chord of contact cone confocal conic section conjugate diameters conjugate hyperbola constant ratio double ordinate draw drawn parallel ellipse equally inclined fixed point focal chord focal distances foci focus four points given point given straight line Hence J. W. DONALDSON latus rectum line joining locus major axis meet the axis meet the curve meet the directrix meet the tangent middle point normal parabola parallelogram passes perpendicular plane point of contact point of intersection point Q polar produced meet PROP prove rectangle rectangular hyperbola right angle semi-latus rectum shew shewn St John's College subtends tangent at Q tangents be drawn theorem Third Edition touching transverse axis triangle Trinity College vertex