## An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |

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Page x

area of the Conic . Criterion to distinguish between an Ellipse and an Hyperbola

EXAMPLES 91 92 CHAPTER V. TRIANGULAR CO - ORDINATES . I. 94 2 .

**Directrix**of a Parabola To find the magnitudes of the axes of the Conic To find thearea of the Conic . Criterion to distinguish between an Ellipse and an Hyperbola

EXAMPLES 91 92 CHAPTER V. TRIANGULAR CO - ORDINATES . I. 94 2 .

Page 47

... two straight lines is given by the equations * If the coefficients of ß2 and g be

equal , and the triangle of reference be right - angled at A , the form of the

equation shews that A will be a focus of the conic , and BC the corresponding

... two straight lines is given by the equations * If the coefficients of ß2 and g be

equal , and the triangle of reference be right - angled at A , the form of the

equation shews that A will be a focus of the conic , and BC the corresponding

**directrix**. Page 112

If d be the distance from S of the corresponding

MPM ' , the angle between the asymptotes of the reciprocal hyperbola will be the

...

If d be the distance from S of the corresponding

**directrix**, 1 R * 2 p ka d р or , the**directrix**is the polar of the centre of the circle MPM ' . If S lie without the circleMPM ' , the angle between the asymptotes of the reciprocal hyperbola will be the

...

Page 113

If two conics have a common focus and

21 , and another conic , having the same focus , be described 4ll ' so as to touch

both of them , its latus - rectum will be and the envelope of its

If two conics have a common focus and

**directrix**, and their latera - recta be 21 ,21 , and another conic , having the same focus , be described 4ll ' so as to touch

both of them , its latus - rectum will be and the envelope of its

**directrix**will be a ... Page 116

Prove that the locus of the point of intersection of the variable tangents is a

straight line . If the fixed point be a focus , the locus will be the corresponding

GEOMETRY .

Prove that the locus of the point of intersection of the variable tangents is a

straight line . If the fixed point be a focus , the locus will be the corresponding

**directrix**. 5. Chords are drawn to a conic , subtending a 116 MODERNGEOMETRY .

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angle angular points appears Author become BOOKS called Cambridge centre Chap chapter chord circle cloth co-ordinates coefficients coincide College common condition conic conic section considered constant corresponding Crown 8vo curve denoted described determine distance draw drawn eliminating equal equation Examples expressed find the equation fixed point focus follows given point given straight line gives harmonic Hence imaginary line at infinity locus meet observed obtained opposite sides pair parabola parallel passing pencil perpendicular point of intersection points of contact polar pole positive produced projection prove ratio reciprocal relation represented respect result right angles satisfy Schools second degree sides similar Similarly student taken tangents term theorem third three points tion touch Treatise triangle of reference values whence writing written