A Geometrical Treatise on Conic Sections, with a copious collection of examples |
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Page 8
... meet the directrix in the point Z ; join SZ ; then since the angle ZSP is a right angle , ( Prop . IV . ) : . ZS2 + ... produced to R , 8 CONIC SECTIONS .
... meet the directrix in the point Z ; join SZ ; then since the angle ZSP is a right angle , ( Prop . IV . ) : . ZS2 + ... 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 ... meet the directrix in Z. Join SZ ; then by the last Proposition the angle ZSP is a right angle , and .. also the ...
William Henry Drew. COR . 1. If ZP be produced to R , then the angle SPR = the angle MPR . = COR . 2. It is evident that ... meet the directrix in Z. Join SZ ; then by the last Proposition the angle ZSP is a right angle , and .. also the ...
Page 10
... meet the axis 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 ...
... meet the axis 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 ...
Page 17
William Henry Drew. R V T S Produce QV to meet the parabola in Q ' ; and draw the tangents QO , Q'O , meeting VP produced in the point 0 . ( Prop . XIV . ) Also let the tangent at P meet OQ in R , and join SP , SR , and SQ . Now since ...
William Henry Drew. R V T S Produce QV to meet the parabola in Q ' ; and draw the tangents QO , Q'O , meeting VP produced in the point 0 . ( Prop . XIV . ) Also let the tangent at P meet OQ in R , and join SP , SR , and SQ . Now since ...
Page 18
... meet the axis produced in 7 ; then 2 QV2 = 4. SP . PV , But PVST SP , = .. QV 4 SP2 ; = or QV 2 SP , = .. QQ ' = 4 SP . ( Prop . XV . ) ( Prop . VII . ) PROP . XVII . 19. If two chords of a 18 CONIC SECTIONS .
... meet the axis produced in 7 ; then 2 QV2 = 4. SP . PV , But PVST SP , = .. QV 4 SP2 ; = or QV 2 SP , = .. QQ ' = 4 SP . ( Prop . XV . ) ( Prop . VII . ) PROP . XVII . 19. If two chords of a 18 CONIC SECTIONS .
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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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