An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 15
... 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 , y be- tween the equations lx + mB + ny = 0 , l'a + CONDITION OF PARALLELISM . 15.
... 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 , y be- tween the equations lx + mB + ny = 0 , l'a + CONDITION OF PARALLELISM . 15.
Page 19
... result of the last article , = tan tan 0 ' : = - ( lc — na ) — ( ma — lb ) - - ( lc ― na ) + ( ma — lb ) A tan A tan 2 ( l'c — n'a ) — ( m'a — l'b ) - ( l'c - n'a ) + ( m'a - lb ) And , if these be at right angles to one another , Hence ...
... result of the last article , = tan tan 0 ' : = - ( lc — na ) — ( ma — lb ) - - ( lc ― na ) + ( ma — lb ) A tan A tan 2 ( l'c — n'a ) — ( m'a — l'b ) - ( l'c - n'a ) + ( m'a - lb ) And , if these be at right angles to one another , Hence ...
Page 43
... 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 reference . These may be obtained most readily by the employment of the equations for ...
... 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 reference . These may be obtained most readily by the employment of the equations for ...
Page 44
... result of Art . 8 , Nb + McLc + Na = Ma + Lb. To solve these equations , put each member equal to r , we then get M N + 210218 = r N L с L a + + M b = = bc ' r са r ab • Adding together the last two of these equations , and sub ...
... result of Art . 8 , Nb + McLc + Na = Ma + Lb. To solve these equations , put each member equal to r , we then get M N + 210218 = r N L с L a + + M b = = bc ' r са r ab • Adding together the last two of these equations , and sub ...
Page 54
... result of the preced- ing article , by simply putting ww . It will then be seen to be w2ß + y = - 2w.ka. 25. To find the pole of ww ' . The pole of ww ' is the point of intersection of the tangents at w , ტ . It is therefore given by ...
... result of the preced- ing article , by simply putting ww . It will then be seen to be w2ß + y = - 2w.ka. 25. To find the pole of ww ' . The pole of ww ' is the point of intersection of the tangents at w , ტ . It is therefore given by ...
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Common terms and phrases
angular points anharmonic ratio asymptotes auxiliary conic b₁ b₂ C₁ centre Chap chord co-ordinates coefficients common tangents conic section determinant directrix find the equation fixed point fixed straight line follows four points given conic given point given straight line given triangle Hence investigated Let the equation line at infinity line joining locus meets the conic nine-point circle obtain opposite sides parabola Pascal's Theorem perpendicular point f points at infinity points of contact points of intersection PQRS prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree shewn similar and similarly sin POS tangents drawn term a,b,c theorem three points three straight lines triangle of reference ua² uf+w'g+v'h ux² V'ca va² Vb² vß² W'ab whence wy² λα