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

### From inside the book

Results 1-5 of 10

Page xi

If the four points of intersection be all real , all the

one pair only is real ON PROJECTIONS . 8 . Definition of Projections 9 .

Projection to infinity 10-12 . Any quadrilateral may be projected , in an infinite

number of ...

If the four points of intersection be all real , all the

**common**chords are real ; if not ,one pair only is real ON PROJECTIONS . 8 . Definition of Projections 9 .

Projection to infinity 10-12 . Any quadrilateral may be projected , in an infinite

number of ...

Page 57

Prove that the three tangents at their

which intersect their respective conics in three points lying in a straight line ; and

that the other

Prove that the three tangents at their

**common**point meet the sides of the trianglewhich intersect their respective conics in three points lying in a straight line ; and

that the other

**common**tangents to each pair of conics intersect the sides of the ... Page 100

If any two curves be reciprocated , the polar of any point

both will be a point of intersection of the reciprocal curves . two curves will ...

If any two curves be reciprocated , the polar of any point

**common**to both will be a**common**tangent to the reciprocal curves , and the pole of any tangent**common**toboth will be a point of intersection of the reciprocal curves . two curves will ...

Page 105

Hence the first thing to be proved is , “ That the three straight lines joining the

points of contact of the

lying on the respective conics all pass through a point . ” Again , “ the other ...

Hence the first thing to be proved is , “ That the three straight lines joining the

points of contact of the

**common**tangent with the angular points of the triangle notlying on the respective conics all pass through a point . ” Again , “ the other ...

Page 106

Hence the latter part of the theorem will run : “ And that the same three straight

lines respectively join the other point of intersection of each pair of conics with the

angular point of the triangle

...

Hence the latter part of the theorem will run : “ And that the same three straight

lines respectively join the other point of intersection of each pair of conics with the

angular point of the triangle

**common**to each pair . ” 11. After a little practice , the...

### 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