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

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Page x

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

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 the

**corresponding**angle in the Reciprocal Curve Co - ordinates of the foci of a ConicEXAMPLES 23 . Double application of the Method of Reciprocal Polars 109 IIO

II2 ...

Page 33

... represented by such an equation , is what is commonly called a conic section ;

and then , before proceeding further with the consideration of the general equaall

investigate the nature of the curve

... represented by such an equation , is what is commonly called a conic section ;

and then , before proceeding further with the consideration of the general equaall

investigate the nature of the curve

**corresponding**to certain special forms of the ... Page 47

... 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 BC the

directrix .

... 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 BC the

**corresponding**directrix .

Page 56

The

ag + b + cy = 2A to be - 2aA 47 bc - a . These values all become infinite when 4K

* bc = a ' , as manifestly ought to be the case , since , as has been shewn in Art ...

The

**corresponding**value of a may be ascertained by substitution in the equationag + b + cy = 2A to be - 2aA 47 bc - a . These values all become infinite when 4K

* bc = a ' , as manifestly ought to be the case , since , as has been shewn in Art ...

Page 60

... the second by Qg , and subtract , we then get ( a , b , - azba ) 18+ ( 0,2 ; – caz )

2g = 0 , re Cydz – caz agbz – azbe or ਮੋਲ , 6,6 – b , c , ' by symmetry .... ( C ) .

Hence , dividing each term of ( B ) by the

... the second by Qg , and subtract , we then get ( a , b , - azba ) 18+ ( 0,2 ; – caz )

2g = 0 , re Cydz – caz agbz – azbe or ਮੋਲ , 6,6 – b , c , ' by symmetry .... ( C ) .

Hence , dividing each term of ( B ) by the

**corresponding**member of ( C ) we get ...### What people are saying - Write a review

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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