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

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Results 1-5 of 17

Page 43

0 , is identical with the condition that the point ( 1 , m , n ) should lie in the conic

L M N + + B g :( ) ; a a result analogous to that obtained in Art . 13 ,

To find the equations of the four circles which touch the three sides of the triangle

of ...

0 , is identical with the condition that the point ( 1 , m , n ) should lie in the conic

L M N + + B g :( ) ; a a result analogous to that obtained in Art . 13 ,

**chap**. I. 10 .To find the equations of the four circles which touch the three sides of the triangle

of ...

Page 70

obtain the following theorem : “ If the opposite sides of a quadrilateral , inscribed

in a conic , be produced to meet , and likewise the pairs of tangents at opposite ...

**Chap**. II . Again , by supposing D to coincide with B , and E with C , we readilyobtain the following theorem : “ If the opposite sides of a quadrilateral , inscribed

in a conic , be produced to meet , and likewise the pairs of tangents at opposite ...

Page 72

This equation , as we have shewn ( Art . 1 ,

. 2. To find the point in which a straight line , drawn in a given direction through a

given point of the conic , meets the conic again . Let f , g , h , be the co ...

This equation , as we have shewn ( Art . 1 ,

**Chap**. III ) , represents a conic section. 2. To find the point in which a straight line , drawn in a given direction through a

given point of the conic , meets the conic again . Let f , g , h , be the co ...

Page 76

... that the conic may break up into two straight lines , real or imaginary . For this

purpose it is necessary and sufficient that the expression $ la , B , y should break

up into two factors . The condition for this has been shewn in Art . 9 ,

... that the conic may break up into two straight lines , real or imaginary . For this

purpose it is necessary and sufficient that the expression $ la , B , y should break

up into two factors . The condition for this has been shewn in Art . 9 ,

**Chap**. Page 77

The Method of Reciprocal Polars, and the Theory Projections Norman Macleod

Ferrers. ( see Art . 12 ,

) , ( f .: 92 h , ) respectively , are fi ( ua + w'B + vy ) +9 . ( wa + uß + u'y ) + h , ( u'a ...

The Method of Reciprocal Polars, and the Theory Projections Norman Macleod

Ferrers. ( see Art . 12 ,

**Chap**. I. ) , Again , the equations of the tangents at ( fi , 9 h) , ( f .: 92 h , ) respectively , are fi ( ua + w'B + vy ) +9 . ( wa + uß + u'y ) + h , ( u'a ...

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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