A geometrical treatise on conic sections, with numerous examplesFor the use of schools and students in the universitiesWith an appendix on harmonic ratio, poles and polars, and reciprocation . draw thedouble ordinates RQvq, RQvq parallel to PP meeting OVin v and v ; then Qq and Q q are bisected in v and v Now i?P2 : RP2 RP : BPQO : 0 Q RQ . Rq : .## . Rq Rv2-Qv2: Rv2- Qv2Ov2 : Ov2OR2 : OR2OR : ORQO : OQ .. QQ is divided harmonically in (9, 0; and therefore also(see Prop. II.) 0 0 is divided harmonically in Q and Q. 160 APPENDIX. Coe. If the conic is a parabola, 0 V is drawn parallel to theaxis
A geometrical treatise on conic sections, with numerous examplesFor the use of schools and students in the universitiesWith an appendix on harmonic ratio, poles and polars, and reciprocation . draw thedouble ordinates RQvq, RQvq parallel to PP meeting OVin v and v ; then Qq and Q q are bisected in v and v Now i?P2 : RP2 RP : BPQO : 0 Q RQ . Rq : .## . Rq Rv2-Qv2: Rv2- Qv2Ov2 : Ov2OR2 : OR2OR : ORQO : OQ .. QQ is divided harmonically in (9, 0; and therefore also(see Prop. II.) 0 0 is divided harmonically in Q and Q. 160 APPENDIX. Coe. If the conic is a parabola, 0 V is drawn parallel to theaxis. If an ellipse or hyperbola, 0 V is drawn through thecentre. If the point 0 be the centre of the hyperbola, then,OP, OP are asymptotes, and the line PP* is at infinity, andany chord QQ through G is bisected at C, while the fourthpoint which with C harmonically divides QQ is at an in-finite distance. Ppop. VII. 76. The locus of the point of intersection of the tangentsat the extremities of any chord drawn through a given pointeither within or without a conic is a straight line. Let 0 be the given point. Through 0 draw any chordQOQ, and bisect QQ in V. First let the curve be a Through 0 and V draw OPO and VWK parallel to theaxis of the parabola meeting the curve in P and WK equal to V Wand PO equal to PO APPENDIX. 1G1
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Keywords: ., bookcentury1800, bookdeca, booksubjectconicsections, bookyear1887
