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

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Page vii

Straight Lines 6 7 . Every Straight Line may be represented by an Equation of the

First Degree 9 8 . Every Equation of the First Degree represents a Straight Line 9

.

**Distance**between two given Points 4-6 . Investigation of Equations of certainStraight Lines 6 7 . Every Straight Line may be represented by an Equation of the

First Degree 9 8 . Every Equation of the First Degree represents a Straight Line 9

.

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 determined by means of its

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 3

... y for example , and this may be made homoaa + bB + oy geneous in a , b , y by

multiplying each term by 24 raised to a suitable power . Thus , the equation 1-2

AREA OF THE TRIANGLE OF REFERENCE . 3

Points.

... y for example , and this may be made homoaa + bB + oy geneous in a , b , y by

multiplying each term by 24 raised to a suitable power . Thus , the equation 1-2

AREA OF THE TRIANGLE OF REFERENCE . 3

**Distance**between two givenPoints.

Page 4

Let 04 , B. , % ; Qg , B2 , yz , be the co - ordinates of two given points , r the

B. - By , - Yg , of the second degree * . * This , if not self - evident , may be proved

as ...

Let 04 , B. , % ; Qg , B2 , yz , be the co - ordinates of two given points , r the

**distance**between them . Then , gut will be a rational integral function of a , - og ,B. - By , - Yg , of the second degree * . * This , if not self - evident , may be proved

as ...

Page 5

... ( B1 - B2 ) + ( 71-72 ) 2 + 2 ( B1 – B2 ) ( 71-72 ) cos A whence ge sin ? A a

rational integral function of the second degree . 1 - ; also r = a . - where

... ( B1 - B2 ) + ( 71-72 ) 2 + 2 ( B1 – B2 ) ( 71-72 ) cos A whence ge sin ? A a

rational integral function of the second degree . 1 - ; also r = a . - where

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### Common terms and phrases

angle angular points Arithmetic asymptotes auxiliary become BOOKS called Cambridge centre Chap chapter chord circle cloth co-ordinates coincide College condition conic conic section considered constant corresponding Crown 8vo curve denoted described determine directrix distance equal equation Examples expressed fixed point focus follows four points given conic given point given straight line gives harmonic Hence hyperbola imaginary line at infinity locus meet move obtain opposite sides pair parabola parallel passing pencil perpendicular plane point of intersection points of contact polar pole positive produced projection proposition prove ratio reciprocal relation represented respect result right angles satisfy Schools second degree seen sides similar Similarly suppose taken tangents term theorem third three points tion touch Treatise triangle of reference values whence writing written