A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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Page 5
... produce it to meet the parabola in P ; join SP ; then since SQ and QP > SP , and SP = PM , .. SQ and QP > PM , .. SQ > QM . COR . Conversely a point will be inside or outside the parabola according as its distance from the focus is less ...
... produce it to meet the parabola in P ; join SP ; then since SQ and QP > SP , and SP = PM , .. SQ and QP > PM , .. SQ > QM . COR . Conversely a point will be inside or outside the parabola according as its distance from the focus is less ...
Page 7
... produce it to meet the directrix in Z ; join SZ . Draw PM , P'M ' at right angles to the directrix ; join SP , SP ; and produce PS to meet the parabola in Q. Then , since the triangles ZMP , ZM'P ' are similar , .. ZP : ZP ' :: MP : M'P ...
... produce it to meet the directrix in Z ; join SZ . Draw PM , P'M ' at right angles to the directrix ; join SP , SP ; and produce PS to meet the parabola in Q. Then , since the triangles ZMP , ZM'P ' are similar , .. ZP : ZP ' :: MP : M'P ...
Page 8
... - PM , .. ZS = ZM ; Now in the triangles ZPS , ZPM , · ZP , PS = ZP , PM , each to each , and ZS = ZM , .. the angle SPZ = the angle MPZ ; or PZ bisects the angle SPM . COR . 1. If ZP be produced to R , 8 CONIC SECTIONS .
... - PM , .. ZS = ZM ; Now in the triangles ZPS , ZPM , · ZP , PS = ZP , PM , each to each , and ZS = ZM , .. the angle SPZ = the angle MPZ ; or PZ bisects the angle SPM . COR . 1. If ZP be produced to R , 8 CONIC SECTIONS .
Page 9
William Henry Drew. COR . 1. If ZP be produced to R , then the angle SPR = the angle MPR . = COR . 2. It is evident that the tangent at the vertex A is perpendicular to the axis . PROP . VI . 8. The tangents at the extremities of a focal ...
William Henry Drew. COR . 1. If ZP be produced to R , then the angle SPR = the angle MPR . = COR . 2. It is evident that the tangent at the vertex A is perpendicular to the axis . PROP . VI . 8. The tangents at the extremities of a focal ...
Page 10
... produced in the point T , and PN be the ordinate of the point P , then NT = 2 AN . M Y P A S N Join SP , and draw PM at right angles to the directrix ; then · the angle SPT = the angle MPT = the angle STP , .. ST = SP . But SP = PM = XN ...
... produced in the point T , and PN be the ordinate of the point P , then NT = 2 AN . M Y P A S N Join SP , and draw PM at right angles to the directrix ; then · the angle SPT = the angle MPT = the angle STP , .. ST = SP . But SP = PM = XN ...
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Common terms and phrases
AC² angle ZSP auxiliary circle BC² BERNARD DRAKE bisects the angle CA² Cambridge CD be conjugate CD² centre circle be described circle described circle of curvature cloth CO.'S PUBLICATIONS cone Conic Sections conjugate diameters conjugate hyperbola CP² Crown 8vo curve cutting plane drawn at right drawn parallel ellipse Euclid Fcap Fellow of St Fellow of Trinity focal chord focus intersect John's College join SP late Fellow latus rectum let the tangent M.A. Fellow MACMILLAN & CO.'S major axis mean proportional meet CD meet the axis meet the directrix meet the ellipse meeting the asymptotes pair of tangents parabola parallelogram perpendicular PN² produced to meet Prop prove QV² radius right angles Second Edition triangle Trinity College University of Cambridge vertex
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