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

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Page viii

Position of the

Parabola touches the Line at Infinity 6 . Equation of the Circumscribing Circle 7 .

Equation of the Conic touching the Three Sides of the Triangle of Reference 8 .

Position of the

**Centre**. Condition for a Parabola Condition of Tangency . EveryParabola touches the Line at Infinity 6 . Equation of the Circumscribing Circle 7 .

Equation of the Conic touching the Three Sides of the Triangle of Reference 8 .

Page ix

... Co - ordinates of the

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 ...

... Co - ordinates of the

**Centre**Equation of the Asymptotes Condition for arectangular 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 ...

Page xi

An equation of the nth degree represents a curve of the nth class 6. Equation of a

Conic , touching the three sides of the triangle of reference 7 . Equation of

circumscribed Conic 8 . Equation of the Pole of a given straight line , and of the

An equation of the nth degree represents a curve of the nth class 6. Equation of a

Conic , touching the three sides of the triangle of reference 7 . Equation of

circumscribed Conic 8 . Equation of the Pole of a given straight line , and of the

**centre**. Page 4

The co - ordinates of the

R cos C , where 24 R = a cos A + b cos B + c cos ( " * . 3. The co - ordinates of the

The co - ordinates of the

**centre**of the circumscribed circle are R cos A , R cos B ,R cos C , where 24 R = a cos A + b cos B + c cos ( " * . 3. The co - ordinates of the

**centre**of the inscribe circle are 2A each equal to a + b + c What are the co ... Page 22

... joining the

point of the side BC , is parallel to the straight line joining A with the point of

contact of the circle touching BC externally and AB , AC produced . 6 . On the

sides BC ...

... joining the

**centre**of the circle inscribed in the triangle ABC , with the middlepoint of the side BC , is parallel to the straight line joining A with the point of

contact of the circle touching BC externally and AB , AC produced . 6 . On the

sides BC ...

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### Common terms and phrases

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