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

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Page ix

Pascal's

CONIC REPRESENTED BY THE GENERAL EQUATION OF THE SECOND

DEGREE . 2 . 3 . 4 , 5 . 6 . 72 73 74 76 7 . 8 . To find the Point in which a Straight

Line ...

Pascal's

**Theorem**EXAMPLES 65 66 ib . IO . II . ib . 68 70 CHAPTER IV . ON THECONIC REPRESENTED BY THE GENERAL EQUATION OF THE SECOND

DEGREE . 2 . 3 . 4 , 5 . 6 . 72 73 74 76 7 . 8 . To find the Point in which a Straight

Line ...

Page x

Equation of the Polar Reciprocal of one Conic with regard to another Instances of

Transformation Brianchon's

formed by four intersecting straight lines , is the same as that of the range formed

...

Equation of the Polar Reciprocal of one Conic with regard to another Instances of

Transformation Brianchon's

**Theorem**13 . The anharmonic ratio of the Pencil ,formed by four intersecting straight lines , is the same as that of the range formed

...

Page 58

We shall , however , only state and prove such elementary

necessary in our future investigations ; referring the reader who may be desirous

of fuller information to Salmon's Lessons on the Higher Algebra ; Spottiswoode ...

We shall , however , only state and prove such elementary

**theorems**as will benecessary in our future investigations ; referring the reader who may be desirous

of fuller information to Salmon's Lessons on the Higher Algebra ; Spottiswoode ...

Page 59

We may remark in passing that we shall obtain the same result by eliminating 2 ; ,

between the equations a , 1 , + 5,1 % = 0 , azł , + 6,1 , = 0 . and we get Hence ago

by а ,, а , a , b , 3/4 b ,, bg A like

We may remark in passing that we shall obtain the same result by eliminating 2 ; ,

between the equations a , 1 , + 5,1 % = 0 , azł , + 6,1 , = 0 . and we get Hence ago

by а ,, а , a , b , 3/4 b ,, bg A like

**theorem**will be proved to be true for all ... Page 64

For , referring to the relation between determinants of n and n - i rows , given in

Arts . 3 and 4 , it will be seen that this

if it be true for one of n - 1. But it is true for three rows , therefore it is universally ...

For , referring to the relation between determinants of n and n - i rows , given in

Arts . 3 and 4 , it will be seen that this

**theorem**is true for a determinant of n rows ,if it be true for one of n - 1. But it is true for three rows , therefore it is universally ...

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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