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

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Page ix

... Centre Equation of the Asymptotes Condition for a rectangular

Conditions for a Circle All Circles pass through the same two points at infinity All

Conics , similar and similarly situated to each other , intersect in the same two

points ...

... Centre Equation of the Asymptotes Condition for a rectangular

**Hyperbola**Conditions for a Circle All Circles pass through the same two points at infinity All

Conics , similar and similarly situated to each other , intersect in the same two

points ...

Page x

Criterion to distinguish between an Ellipse and an

CHAPTER V. TRIANGULAR CO - ORDINATES . I. 94 2 . Definition of the

Triangular Co - ordinates of a Point Formulæ relating to Straight Lines Formulæ

relating ...

Criterion to distinguish between an Ellipse and an

**Hyperbola**EXAMPLES 91 92CHAPTER V. TRIANGULAR CO - ORDINATES . I. 94 2 . Definition of the

Triangular Co - ordinates of a Point Formulæ relating to Straight Lines Formulæ

relating ...

Page xii

Any two intersecting conics may be projected into

eccentricity ib . 18 . Any two conics may be projected into conics of any

eccentricity , or into circles 141 19 . Projection of the foci and directrices of a

Conic ib .

Any two intersecting conics may be projected into

**hyperbolas**of any assignedeccentricity ib . 18 . Any two conics may be projected into conics of any

eccentricity , or into circles 141 19 . Projection of the foci and directrices of a

Conic ib .

Page 82

To find the condition that the conic may be a rectangular

equations of the asymptotes be la + mß + ny = 0 , l'a + m'p + n'y = 0 , the condition

of their perpendicularity is Il + mm ' + nn ' - ( mn ' + m'n ) cos A - ( nl ' + n'l ) cos B -

( lm ...

To find the condition that the conic may be a rectangular

**hyperbola**. If theequations of the asymptotes be la + mß + ny = 0 , l'a + m'p + n'y = 0 , the condition

of their perpendicularity is Il + mm ' + nn ' - ( mn ' + m'n ) cos A - ( nl ' + n'l ) cos B -

( lm ...

Page 83

It hence appears , that the condition that the conic u'ßry + o'rya + w'aß = 0 ,

described about the triangle of reference , may be a rectangular

cos A + o ' cos B + w ' cos C = 0 ) ; that is , the conic must pass through the point ...

It hence appears , that the condition that the conic u'ßry + o'rya + w'aß = 0 ,

described about the triangle of reference , may be a rectangular

**hyperbola**, is u'cos A + o ' cos B + w ' cos C = 0 ) ; that is , the conic must pass through the point ...

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### Common terms and phrases

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