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 la + mß + 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 la + mß + ny = 0 , l'a + CONDITION OF PARALLELISM . 15.
Page 19
... result of the last article , - tan -na ) + ( ma - lb ) 2 tan 0 ( lcna ) — ( ma - lb ) = tan e ' = ( l'cn'a ) - ( m'a — l'b ) - - ( l'c — n'a ) + ( m'a — l'b ) - tan And , if these be at right angles to one another , Hence 1 + tan 0 tan ...
... result of the last article , - tan -na ) + ( ma - lb ) 2 tan 0 ( lcna ) — ( ma - lb ) = tan e ' = ( l'cn'a ) - ( m'a — l'b ) - - ( l'c — n'a ) + ( m'a — l'b ) - tan And , if these be at right angles to one another , Hence 1 + tan 0 tan ...
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 ...
... 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 ...
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 + Ђ C = bc " N L r + 210 210 = a ca L M + · b ab Adding together the last two of these equations , and sub- tracting ...
... result of Art . 8 , Nb + McLc + Na = Ma + Lb. To solve these equations , put each member equal to r , we then get M N + Ђ C = bc " N L r + 210 210 = a ca L M + · b ab Adding together the last two of these equations , and sub- tracting ...
Page 54
... result of the preced- ing article , by simply putting w ' = w . 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 , w ' . It is therefore given ...
... result of the preced- ing article , by simply putting w ' = w . 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 , w ' . It is therefore given ...
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Common terms and phrases
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα