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

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Page 22

On the sides BC , CA , AB of the triangle ABC , respectively , pairs of points are

of ČA with C , A ,, and of AB with 4 B lie in a straight line ; BC , CB , intersect in L ...

On the sides BC , CA , AB of the triangle ABC , respectively , pairs of points are

**taken**, B. , C ; C ,, 4 ,; 45 , B .; such that the points of intersection of BC with B , C ,,of ČA with C , A ,, and of AB with 4 B lie in a straight line ; BC , CB , intersect in L ...

Page 30

Let O be a point in a given straight line , and let P , P , Q , Q , R , R ' ...... be a

series of points on that line so

constant ka suppose . Then these points are said to form a system in involution . If

K be a ...

Let O be a point in a given straight line , and let P , P , Q , Q , R , R ' ...... be a

series of points on that line so

**taken**that OP.OP ' = 0Q . OQ = OR . OR ' = = aconstant ka suppose . Then these points are said to form a system in involution . If

K be a ...

Page 39

For , if they be

conic will become a perfect square , as may be ascertained by substitution , and

the conic will degenerate into a straight line , or rather into two coincident straight

...

For , if they be

**taken**otherwise , the left - hand member of the equation of theconic will become a perfect square , as may be ascertained by substitution , and

the conic will degenerate into a straight line , or rather into two coincident straight

...

Page 65

will be observed , moreover , that each term is the product of n factors , one

from each line and from each column , and that the coefficients of one half of the

terms are +1 , of the other - 1. To determine the sign of any particular term we ...

will be observed , moreover , that each term is the product of n factors , one

**taken**from each line and from each column , and that the coefficients of one half of the

terms are +1 , of the other - 1. To determine the sign of any particular term we ...

Page 98

The theory is especially valuable when the conic , with respect to which the poles

and polars are

given straight lines is the straight line which joins the poles of those straight lines

...

The theory is especially valuable when the conic , with respect to which the poles

and polars are

**taken**, is a circle . 2 . The polar of the point of intersection of twogiven straight lines is the straight line which joins the poles of those straight lines

...

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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