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 . (1.) Let Q be a point on the concave side of the SQ, SQ, and let SQ meet the curve in P; join SP;then since SQ = SP+ PQ, and SQ < SP -f PQ, 76 CONIC JS s A A .-. SQ- SQ> SP- SP- SP= A A,• ?? SQ- SQ>AA\ (2.) Let Q be a point on the convex side of the curve,nearer to S than a; join SQ, SQ, and let SQ meet thecurve in P; join SP; then £<?< SP+ PQ,and tf# = .SP
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 . (1.) Let Q be a point on the concave side of the SQ, SQ, and let SQ meet the curve in P; join SP;then since SQ = SP+ PQ, and SQ < SP -f PQ, 76 CONIC JS s A A .-. SQ- SQ> SP- SP- SP= A A,• ?? SQ- SQ>AA\ (2.) Let Q be a point on the convex side of the curve,nearer to S than a; join SQ, SQ, and let SQ meet thecurve in P; join SP; then £<?< SP+ PQ,and tf# = .SP + P&.-. SQ-SQ< SP- SP,but £P- SP=AA, ? -. SQ- SQS than S, we can show that SQ - SQ < AA; Cor. Conversely a point will be on the concave or convex-side of the hyperbola, according as the difference of itsdistances from the foci is greater or less than A A. 50. Def. If a point P be taken on the hyperbola nearto P (see fiii. Prop. V.) and PP be joined, the line PP pro-duced, in the limiting position which it assumes when P ismade to approach indefinitely near to P, is called the Tangentto the hyperbola at the point P. Pkop. V. If the tangent to the hyperbola at any point P meet thedirectrix in the point Z, and if S be the focus correspondingto the directrix on which Z is situated, then SZ will be atright angles
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Keywords: ., bookcentury1800, bookdeca, booksubjectconicsections, bookyear1887
