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

### From inside the book

Results 1-5 of 27

Page viii

... with respect to which the Triangle of Reference is self - conjugate Equation of

the Conic which touches two sides of the Triangle of Reference in the points

where they

Conic ...

... with respect to which the Triangle of Reference is self - conjugate Equation of

the Conic which touches two sides of the Triangle of Reference in the points

where they

**meet**the third Any Chord of a Conic is divided harmonically by theConic ...

Page ix

To find the Point in which a Straight Line , drawn in a given direction through a

given Point of the Conic ,

given Point Condition that a given Straight Line may touch the Conic Condition

for a ...

To find the Point in which a Straight Line , drawn in a given direction through a

given Point of the Conic ,

**meets**the Curve again Equation of the Tangent at agiven Point Condition that a given Straight Line may touch the Conic Condition

for a ...

Page 20

To find the perpendicular distance from a given point to a given straight line . Let (

f , g , h ) be the given point , ( 1 , m , n ) the given straight line . Then , if q and r be

the distance from A , of the points where this straight line

To find the perpendicular distance from a given point to a given straight line . Let (

f , g , h ) be the given point , ( 1 , m , n ) the given straight line . Then , if q and r be

the distance from A , of the points where this straight line

**meets**AC , AB ... Page 22

... three straight lines AP , BQ , CR are drawn to pass through one point , and

three straight lines AP ' , BQ ' , CR to pass through another point , the points P , P

lying on BC , Q , Qon CA , R , R on AB , BQ , CR

...

... three straight lines AP , BQ , CR are drawn to pass through one point , and

three straight lines AP ' , BQ ' , CR to pass through another point , the points P , P

lying on BC , Q , Qon CA , R , R on AB , BQ , CR

**meet**AP in D , DE ; CR , AP**meet**...

Page 28

Join B'C , BC " , and produce them to

fourth harmonic required . For , let ABC be the triangle of reference , and let the

equation of AD be ß - kry = 0 . " Let the equation of B C be na + ß - koy = 0 .

Join B'C , BC " , and produce them to

**meet**in E. Join AE , then AE shall be thefourth harmonic required . For , let ABC be the triangle of reference , and let the

equation of AD be ß - kry = 0 . " Let the equation of B C be na + ß - koy = 0 .

### 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