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

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Page 1

CHAPTER I. TRILINEAR CO - ORDINATES . EQUATION OF A STRAIGHT LINE .

1 . In the system of co - ordinates ordinarily used , the position of a point in a

plane is

CHAPTER I. TRILINEAR CO - ORDINATES . EQUATION OF A STRAIGHT LINE .

1 . In the system of co - ordinates ordinarily used , the position of a point in a

plane is

**determined**by means of its distances from two given straight lines . Page 6

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

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 2A

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 2A

Q ...

Page 8

It may hence be shewn that the three straight lines drawn through the angular

points of a triangle , perpendicular to the opposite sides , intersect in the point

equations ...

It may hence be shewn that the three straight lines drawn through the angular

points of a triangle , perpendicular to the opposite sides , intersect in the point

**determined**by the equations a cos A = ß cos B = y cos C. 10 6. To find theequations ...

Page 19

tan ( + 1 ) - 1+ M - V Mtul 1 р M Mtu A 2 A .tan usin A v tu cos A v sin A Similarly ,

tan 10 ce 2 M + v cos A Hence , the inclinations of the given straight line to AB ,

AC , are

be ...

tan ( + 1 ) - 1+ M - V Mtul 1 р M Mtu A 2 A .tan usin A v tu cos A v sin A Similarly ,

tan 10 ce 2 M + v cos A Hence , the inclinations of the given straight line to AB ,

AC , are

**determined**. 17. To find the condition that two given straight lines maybe ...

Page 31

The system will be

will also be

as follows . Let p , p ' , q , be the respective distances of the four points from any ...

The system will be

**determined**when two foci , or a centre and focus , are given . Itwill also be

**determined**if two pair of conjugate points be given ; as may be seenas follows . Let p , p ' , q , be the respective distances of the four points from any ...

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### 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