A Treatise on the Geometry of the Circle and Some Extensions to Conic Sections by the Method of Reciprocation: With Numerous Examples |
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Page 3
... ( 3 ) are termed the Anharmonic Ratios of the four points on the line ; and those on the right the Anharmonic Ratios of the pencil O. ABCD . Their equivalence is expressed thus : -A variable line drawn INTRODUCTION . 3 GO Anharmonic Ratios,
... ( 3 ) are termed the Anharmonic Ratios of the four points on the line ; and those on the right the Anharmonic Ratios of the pencil O. ABCD . Their equivalence is expressed thus : -A variable line drawn INTRODUCTION . 3 GO Anharmonic Ratios,
Page 4
... variable line drawn across a pencil is cut in a constant anharmonic ratio ; or any pencil and transversal to it are Equianhar- monic . The foot of the perpendicular from a point on a line is the Projection of the point on the line , and ...
... variable line drawn across a pencil is cut in a constant anharmonic ratio ; or any pencil and transversal to it are Equianhar- monic . The foot of the perpendicular from a point on a line is the Projection of the point on the line , and ...
Page 6
... variable PQ is bisected at Q ' the locus of Q ' is a parallel to OQ and 1 " 1 + = PAT PB 1 PQ Hence for any three lines A , B , C we find in the same manner that 1 1 1 1 + PA ' PB + PC = PQ " where ' describes a right line . 8. For any ...
... variable PQ is bisected at Q ' the locus of Q ' is a parallel to OQ and 1 " 1 + = PAT PB 1 PQ Hence for any three lines A , B , C we find in the same manner that 1 1 1 1 + PA ' PB + PC = PQ " where ' describes a right line . 8. For any ...
Page 7
... @ = yd , t . t ' = i . y . d . It is obvious that either the transverse common tangent to the circles or their angle of intersection is imaginary . Let AX be a variable chord passing through a fixed INTRODUCTION . 7 Examples,
... @ = yd , t . t ' = i . y . d . It is obvious that either the transverse common tangent to the circles or their angle of intersection is imaginary . Let AX be a variable chord passing through a fixed INTRODUCTION . 7 Examples,
Page 8
With Numerous Examples William J. M'Clelland. Let AX be a variable chord passing through a fixed point A at which a tangent is drawn . According as the X A X T chord AX and angle TAX diminish in magnitude X approaches the tangent . When ...
With Numerous Examples William J. M'Clelland. Let AX be a variable chord passing through a fixed point A at which a tangent is drawn . According as the X A X T chord AX and angle TAX diminish in magnitude X approaches the tangent . When ...
Contents
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Other editions - View all
A Treatise on the Geometry of the Circle: And Some Extensions to Conic ... William J. M'Clelland No preview available - 2017 |
A Treatise on the Geometry of the Circle and Some Extensions to Conic ... William J. M'Clelland No preview available - 2018 |
Common terms and phrases
ABCD bisected bisector Brocard points centre of similitude centres of perspective circum-centre circum-circle coaxal system coincide common tangents concurrent concurrent lines conic constant corresponding cyclic polygon cyclic quadrilateral denote diagonals diameter distances equal equation equianharmonic ex-circles fixed point given circles hence hexagon in-circle infinity inscribed inverse points Isogonal Conjugates isosceles limiting points line at infinity lines joining locus maximum mean centre median median triangle meet middle point minimum multiples opposite sides orthocentre orthogonally pair of inverse parallel pedal triangle perpendiculars point of intersection points of contact polar polygon prove r₁ radical axis radius reciprocal rectangle right angles segments sides of ABC similar triangles Similarly Simson lines species squares subtend symmedian point system of points tangents Theorem transversal triangle ABC triangle PQR vertex vertical angle
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