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

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Page vii

Distance from a Point to a Straight Line EXAMPLES 19 . ANHARMONIC RATIO .

Definitions The Anharmonic Ratio of a Pencil is

which it is cut by any Transversal ib . Definition of an Harmonic Pencil 25 . 20 21 .

Distance from a Point to a Straight Line EXAMPLES 19 . ANHARMONIC RATIO .

Definitions The Anharmonic Ratio of a Pencil is

**equal**to that of the range inwhich it is cut by any Transversal ib . Definition of an Harmonic Pencil 25 . 20 21 .

Page x

The angle between the radius vector and tangent in any curve is

corresponding angle in the Reciprocal Curve Co - ordinates of the foci of a Conic

EXAMPLES 23 . Double application of the Method of Reciprocal Polars 109 IIO

II2 ...

The angle between the radius vector and tangent in any curve is

**equal**to thecorresponding angle in the Reciprocal Curve Co - ordinates of the foci of a Conic

EXAMPLES 23 . Double application of the Method of Reciprocal Polars 109 IIO

II2 ...

Page 4

Thus , the equation B2 + hy + k + = 0 ) is

equation 44 ° 22 + 2Ahy ( aa + bB + cy ) + k * ( aa ... The co - ordinates of the

centre of the inscribe circle are 2A each

ordinates of the ...

Thus , the equation B2 + hy + k + = 0 ) is

**equivalent**to the homogeneousequation 44 ° 22 + 2Ahy ( aa + bB + cy ) + k * ( aa ... The co - ordinates of the

centre of the inscribe circle are 2A each

**equal**to a + b + c What are the co -ordinates of the ...

Page 7

AB , for each is

bB = cy . This is a relation between the co - ordinates of any point on the line AD ,

it therefore is the equation of that line . COR . It hence may be proved that the ...

AB , for each is

**equal**to the area of the triangle ABC . Hence PG . AC = PH . AB ,bB = cy . This is a relation between the co - ordinates of any point on the line AD ,

it therefore is the equation of that line . COR . It hence may be proved that the ...

Page 8

AB ; cos B cos C each of these fractions being

ABC . as an Hence PG.AC PH . AB i cos B cos C th or B cos B = y cos C. ar а This

will be the equation of the straight line , drawn through A , at right angles to BC .

AB ; cos B cos C each of these fractions being

**equal**to the area of the triangleABC . as an Hence PG.AC PH . AB i cos B cos C th or B cos B = y cos C. ar а This

will be the equation of the straight line , drawn through A , at right angles to BC .

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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