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

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Page 1

... point , then ac + b3 + cy = 24 . Let P be the given point , and first

lie within B and the triangle of reference ( fig . 1 ) . F. 1 MODERN GEOMETRY .

CHAPTER TRILINEAR CO-ORDINATES EQUATION OF A STRAIGHT LINE

ARTE,

... point , then ac + b3 + cy = 24 . Let P be the given point , and first

**suppose**it tolie within B and the triangle of reference ( fig . 1 ) . F. 1 MODERN GEOMETRY .

CHAPTER TRILINEAR CO-ORDINATES EQUATION OF A STRAIGHT LINE

ARTE,

Page 2

1 . : Similarly bB = twice the area of PCA , cy = twice the area of PAB . Adding

these equations , we get aa + b3 + cy = 2A . Next ,

AC produced , and on the side of BC remote from A ( fig . 2 ) . Then a will be Fig .

2 .

1 . : Similarly bB = twice the area of PCA , cy = twice the area of PAB . Adding

these equations , we get aa + b3 + cy = 2A . Next ,

**suppose**P to lie between AB ,AC produced , and on the side of BC remote from A ( fig . 2 ) . Then a will be Fig .

2 .

Page 6

where l , m , n are certain functions of a , b , c , which we proceed to determine .

Since the values of l , m , n are independent of the positions of the points , the

distance of which we wish to find ,

Q ...

where l , m , n are certain functions of a , b , c , which we proceed to determine .

Since the values of l , m , n are independent of the positions of the points , the

distance of which we wish to find ,

**suppose**these points to be B and C. Then 2AQ ...

Page 12

To find the equation of the straight line , passing through two given points . Let f ,

g , h ; f'og ' , h ' , be the co - ordinates of the two given points , and

equation of the required straight line to be La + MB + Ny = 0 . We must then have

...

To find the equation of the straight line , passing through two given points . Let f ,

g , h ; f'og ' , h ' , be the co - ordinates of the two given points , and

**suppose**theequation of the required straight line to be La + MB + Ny = 0 . We must then have

...

Page 13

To find the condition that three points may lie in the same straight line , Let az , B ,

% ; Qz , B. , Y ,; as , Bg , Yo , be the co - ordinates of the three given points , then ,

if these points lie in the same straight line ,

To find the condition that three points may lie in the same straight line , Let az , B ,

% ; Qz , B. , Y ,; as , Bg , Yo , be the co - ordinates of the three given points , then ,

if these points lie in the same straight line ,

**suppose**the equation of that line to ...### What people are saying - Write a review

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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