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

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Page 30

OQ = OR . OR ' = = a constant ka suppose . Then these points are said to form a

system in involution . If K be a point such that OK = k , K is called a

system . If k * be positive , there will evidently be 30 MODERN GEOMETRY .

OQ = OR . OR ' = = a constant ka suppose . Then these points are said to form a

system in involution . If K be a point such that OK = k , K is called a

**focus**of thesystem . If k * be positive , there will evidently be 30 MODERN GEOMETRY .

Page 31

It is evident that each

centre is at an infinite distance , and that a point and its conjugate will be on the

same , or different sides of the centre , according as the foci are real or imaginary

.

It is evident that each

**focus**is conjugate to itself , and that the conjugate of thecentre is at an infinite distance , and that a point and its conjugate will be on the

same , or different sides of the centre , according as the foci are real or imaginary

.

Page 47

The intersection of these two straight lines is given by the equations * If the

coefficients of ß2 and g be equal , and the triangle of reference be right - angled

at A , the form of the equation shews that A will be a

the ...

The intersection of these two straight lines is given by the equations * If the

coefficients of ß2 and g be equal , and the triangle of reference be right - angled

at A , the form of the equation shews that A will be a

**focus**of the conic , and BCthe ...

Page 57

Hence prove that the circle , which passes through the points of intersection of

three tangents to a parabola , passes also through the

ELIMINATION BETWEEN LINEAR EQUATIONS . 1. EXAMPLES . 57.

Hence prove that the circle , which passes through the points of intersection of

three tangents to a parabola , passes also through the

**focus**. CHAPTER III . ONELIMINATION BETWEEN LINEAR EQUATIONS . 1. EXAMPLES . 57.

Page 113

If two conics have a common

21 , and another conic , having the same

both of them , its latus - rectum will be and the envelope of its directrix will be a ...

If two conics have a common

**focus**and directrix , and their latera - recta be 21 ,21 , and another conic , having the same

**focus**, be described 4ll ' so as to touchboth of them , its latus - rectum will be and the envelope of its directrix will be a ...

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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