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

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Page 5

... ( B1 - B2 ) + ( 71-72 ) 2 + 2 ( B1 – B2 ) ( 71-72 ) cos A

rational integral function of the second degree . 1 - ; also r = a . - where

DISTANCE BETWEEN TWO POINTS . 5.

... ( B1 - B2 ) + ( 71-72 ) 2 + 2 ( B1 – B2 ) ( 71-72 ) cos A

**whence**ge sin ? A arational integral function of the second degree . 1 - ; also r = a . - where

DISTANCE BETWEEN TWO POINTS . 5.

Page 11

... of any point P. Draw DE , PM perpendicular to AC , DF , PN perpendicular to

AB . Also draw Dm , Dn , perpendicular respectively to PM , PN . Then Pm = B - 9

, Pn = y - h . Also , since f , g , h is a point on the locus , If + mg + nh = 0 ,

la ...

... of any point P. Draw DE , PM perpendicular to AC , DF , PN perpendicular to

AB . Also draw Dm , Dn , perpendicular respectively to PM , PN . Then Pm = B - 9

, Pn = y - h . Also , since f , g , h is a point on the locus , If + mg + nh = 0 ,

**whence**la ...

Page 12

... through two given points . Let f , g , h ; f'og ' , h ' , be the co - ordinates of the two

given points , and suppose the equation of the required straight line to be La +

MB + Ny = 0 . We must then have Lf + Mg + Nh = 0 , Lf ' + Mg ' + Nh ' = 0 ;

...

... through two given points . Let f , g , h ; f'og ' , h ' , be the co - ordinates of the two

given points , and suppose the equation of the required straight line to be La +

MB + Ny = 0 . We must then have Lf + Mg + Nh = 0 , Lf ' + Mg ' + Nh ' = 0 ;

**whence**...

Page 13

...

2.B.72 + ax B.72 – QBxy = 0 , the required condition . 13 . To find the condition

that three straight lines THREE POINTS IN A STRAIGHT LINE . 13 Condition that

...

...

**whence**, eliminating 2 , l , v , by cross multiplication , QB : 7 : - 0,337 , + aß.7 . –2.B.72 + ax B.72 – QBxy = 0 , the required condition . 13 . To find the condition

that three straight lines THREE POINTS IN A STRAIGHT LINE . 13 Condition that

...

Page 16

By referring to the investigation of Art . ( 7 ) it will be seen that , q , r , denoting the

distances from A , of the points in which the straight line ( 1 , m , n ) cuts AC , AB

respectively , gra qr 1 , mi q = m , -q = n ; bc b с 3 C bc n

...

By referring to the investigation of Art . ( 7 ) it will be seen that , q , r , denoting the

distances from A , of the points in which the straight line ( 1 , m , n ) cuts AC , AB

respectively , gra qr 1 , mi q = m , -q = n ; bc b с 3 C bc n

**whence**- bc m = ar ī a 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