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

### From inside the book

Page viii

Equation of the Circumscribing

Three Sides of the Triangle of Reference 8 . Position of the Centre . Condition for

a Parabola 9 . Condition of Tangency Equations of the Four

the ...

Equation of the Circumscribing

**Circle**7 . Equation of the Conic touching theThree Sides of the Triangle of Reference 8 . Position of the Centre . Condition for

a Parabola 9 . Condition of Tangency Equations of the Four

**Circles**which touchthe ...

Page ix

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

Conditions for a

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

points ...

Page x

Polar reciprocal of one

respect to a Point Instances of Transformation of Theorems by Reciprocation with

respect to a

radius ...

Polar reciprocal of one

**Circle**with regard to another 19. Reciprocation withrespect to a Point Instances of Transformation of Theorems by Reciprocation with

respect to a

**circle**Corresponding Points and Lines . The angle between theradius ...

Page xi

Circular points at infinity Conditions for a

rectangular Co - ordinates 14 . Tangential polar Co - ordinates EXAMPLES 125

126 IO . 127 ib . 128 129 130 132 ib . . CHAPTER VIII . ON THE INTERSECTION

...

Circular points at infinity Conditions for a

**Circle**EXAMPLES II - 13 . Tangentialrectangular Co - ordinates 14 . Tangential polar Co - ordinates EXAMPLES 125

126 IO . 127 ib . 128 129 130 132 ib . . CHAPTER VIII . ON THE INTERSECTION

...

Page xii

Any two conics may be projected into conics of any eccentricity , or into

141 19 . Projection of the foci and directrices of a Conic ib . The anharmonic ratio

of any pencil or range is unaltered by projection 142 Any two lines , which make ...

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 . The anharmonic ratio

of any pencil or range is unaltered by projection 142 Any two lines , which make ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### 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