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

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Page viii

Every Equation of the Second Degree represents a

of the Conic described about the Triangle of Reference 4 . Position of the Centre .

Condition for a Parabola Condition of Tangency . Every Parabola touches the ...

Every Equation of the Second Degree represents a

**Conic Section**2 , 3 . Equationof the Conic described about the Triangle of Reference 4 . Position of the Centre .

Condition for a Parabola Condition of Tangency . Every Parabola touches the ...

Page 23

We shall introduce , in this place , a short account of harmonic and anharmonic

section , as a familiarity with this conception is useful in the higher geometrical

investigations . DEF . 1. If OP , OQ ... See his

edition ) ...

We shall introduce , in this place , a short account of harmonic and anharmonic

section , as a familiarity with this conception is useful in the higher geometrical

investigations . DEF . 1. If OP , OQ ... See his

**Conic Sections**, p . 273 ( thirdedition ) ...

Page 33

We shall first prove that every curve , represented by such an equation , is what is

commonly called a

consideration of the general equaall investigate the nature of the curve ...

We shall first prove that every curve , represented by such an equation , is what is

commonly called a

**conic section**; and then , before proceeding further with theconsideration of the general equaall investigate the nature of the curve ...

Page 34

We shall now inquire what are the relations of the

reference , when certain relations exist among the coefficients of the equation .

First , suppose u , v , w , all = 0 . The equation then assumes the form u By + v'rya

+ ...

We shall now inquire what are the relations of the

**conic section**to the triangle ofreference , when certain relations exist among the coefficients of the equation .

First , suppose u , v , w , all = 0 . The equation then assumes the form u By + v'rya

+ ...

Page 46

If we put a = 0 , we get MB = + N ( -1 ) Ny , shewing that BC cuts the

imaginary points . The analytical condition of harmonic

satisfied here also . 13. We may next investigate the equations of the tangents

drawn ...

If we put a = 0 , we get MB = + N ( -1 ) Ny , shewing that BC cuts the

**conic**in twoimaginary points . The analytical condition of harmonic

**section**is , however ,satisfied here also . 13. We may next investigate the equations of the tangents

drawn ...

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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