A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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... Euclid , he may find it an easy and interesting con- tinuation of his geometrical studies . With a view also of rendering the work a complete Manual of what is required at Cambridge , I have either embodied into the text , or inserted ...
... Euclid , he may find it an easy and interesting con- tinuation of his geometrical studies . With a view also of rendering the work a complete Manual of what is required at Cambridge , I have either embodied into the text , or inserted ...
Page 7
... ( Euclid , VI . Prop . A. ) Now when P ' is indefinitely near to P , and PP ' becomes the tangent at the point P , the angle PSP ' becomes indefinitely small , while the angle QSF approaches two right angles , and therefore the angle P'SZ ...
... ( Euclid , VI . Prop . A. ) Now when P ' is indefinitely near to P , and PP ' becomes the tangent at the point P , the angle PSP ' becomes indefinitely small , while the angle QSF approaches two right angles , and therefore the angle P'SZ ...
Page 11
... ( Euclid , VI . 8 Cor . ) AN But TN 2 AS ( Prop . VII . ) AS and NG = 2 AN ( Prop . VIII . ) .. PN2 = 4 AS . AN . PROP . X. 7'ir SNS . 12. If the tangent at any point P intersect the tangent at the vertex in Y , then SY will bisect PT at ...
... ( Euclid , VI . 8 Cor . ) AN But TN 2 AS ( Prop . VII . ) AS and NG = 2 AN ( Prop . VIII . ) .. PN2 = 4 AS . AN . PROP . X. 7'ir SNS . 12. If the tangent at any point P intersect the tangent at the vertex in Y , then SY will bisect PT at ...
Page 12
... ( Euclid , VI . 8 Cor . ) But ST = SP , ( Prop . VII . ) .. SY SP . SA . = COR . If PM be drawn at right angles to the directrix , and MY be joined , then since SP , PY = MP , PY , each to each , and the angle SPY = the angle MPY , ( Prop ...
... ( Euclid , VI . 8 Cor . ) But ST = SP , ( Prop . VII . ) .. SY SP . SA . = COR . If PM be drawn at right angles to the directrix , and MY be joined , then since SP , PY = MP , PY , each to each , and the angle SPY = the angle MPY , ( Prop ...
Page 19
... ( Euclid , II . 5 , ) So Q'0.0q ' Hence Q0 . Oq = QV2 - RW , - 4 SP . PV – 4 SP.PW , ( Prop . XV . ) = 4 SP.RO. = - = 4 SP ' . RO . Q'O . Oq ' : 4 SP : 4 SP ' . By Euclid , II . 6 , the same may C 2 CONIC SECTIONS . 19 PROP. XVII. ...
... ( Euclid , II . 5 , ) So Q'0.0q ' Hence Q0 . Oq = QV2 - RW , - 4 SP . PV – 4 SP.PW , ( Prop . XV . ) = 4 SP.RO. = - = 4 SP ' . RO . Q'O . Oq ' : 4 SP : 4 SP ' . By Euclid , II . 6 , the same may C 2 CONIC SECTIONS . 19 PROP. XVII. ...
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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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