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

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Page 15

... C = 0 , a form which we shall occasionally use . It will be observed that this

condition is the same in form as that which

between the equations 1 la + mß + ny = 0 , l'a + CONDITION OF PARALLELISM .

15.

... C = 0 , a form which we shall occasionally use . It will be observed that this

condition is the same in form as that which

**results**from the elimination of a , B , ybetween the equations 1 la + mß + ny = 0 , l'a + CONDITION OF PARALLELISM .

15.

Page 19

And these straight lines must be perpendicular to each other . If 0 , o be the

respective inclinations of these straight lines to the internal bisector of the angle A

, then , by the

+ ...

And these straight lines must be perpendicular to each other . If 0 , o be the

respective inclinations of these straight lines to the internal bisector of the angle A

, then , by the

**result**of the last article , ( lc - na ) - ( ma - 76 ) A tan 0 = tan ( lc - na )+ ...

Page 43

0 , is identical with the condition that the point ( 1 , m , n ) should lie in the conic

L M N + + B g :( ) ; a a

To find the equations of the four circles which touch the three sides of the triangle

of ...

0 , is identical with the condition that the point ( 1 , m , n ) should lie in the conic

L M N + + B g :( ) ; a a

**result**analogous to that obtained in Art . 13 , chap . I. 10 .To find the equations of the four circles which touch the three sides of the triangle

of ...

Page 44

This gives , by the

equations , put each member equal to r , we then get M N ū + ris : 18 N L + > с a

ca r L M b = ab + a Adding together the last two of these equations , and ...

This gives , by the

**result**of Art . 8 , Nb + Mc = Lc + Na = Ma + Lb. To solve theseequations , put each member equal to r , we then get M N ū + ris : 18 N L + > с a

ca r L M b = ab + a Adding together the last two of these equations , and ...

Page 54

This is obtained at once , from the

putting w ' = w . It will then be seen to be w'B + y = 2w.ka . 25. To find the pole of

ww ' . The pole of ww ' is the point of intersection of the tangents at w , w ' .

This is obtained at once , from the

**result**of the preceding article , by simplyputting w ' = w . It will then be seen to be w'B + y = 2w.ka . 25. To find the pole of

ww ' . The pole of ww ' is the point of intersection of the tangents at w , w ' .

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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