An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 1
... denote the angular points of the triangle of reference by the letters A , B , C , the lengths of the sides respectively opposite to them by a , b , c , and the dis- tances of any point from BC , CA , AB respectively by the letters a , ẞ ...
... denote the angular points of the triangle of reference by the letters A , B , C , the lengths of the sides respectively opposite to them by a , b , c , and the dis- tances of any point from BC , CA , AB respectively by the letters a , ẞ ...
Page 16
... denoting the distances from A , of the points in which the straight line ( 1 , m , n ) cuts AC , AB respectively , qr C qr b qra bc 1 , -q = m , tr — r = n ; b whence or bc 2133 2018 a C 012 ar = m ī bc | = n ī C " α aq am b an 1 1 bl q ...
... denoting the distances from A , of the points in which the straight line ( 1 , m , n ) cuts AC , AB respectively , qr C qr b qra bc 1 , -q = m , tr — r = n ; b whence or bc 2133 2018 a C 012 ar = m ī bc | = n ī C " α aq am b an 1 1 bl q ...
Page 20
... denote the distance from ( f , g , h ) to ( l , m , n ) . Then ( qa + r2 — 2qr cos A ) * a ' + 99 + rh = L " ( af + bg + ch ) , 1 1 2 cos or + gr bc _ b A 184 af + bg + ch_g á = a bc Դ -- - h = & ƒ + ( − 1 ) + ( − 1 ) x bc α = lbc ...
... denote the distance from ( f , g , h ) to ( l , m , n ) . Then ( qa + r2 — 2qr cos A ) * a ' + 99 + rh = L " ( af + bg + ch ) , 1 1 2 cos or + gr bc _ b A 184 af + bg + ch_g á = a bc Դ -- - h = & ƒ + ( − 1 ) + ( − 1 ) x bc α = lbc ...
Page 53
... denoted by the letter w * . The line joining the two points w , w ' may be called the line ww ' . 23. To find the equation of the line ww ' . Let the required equation be ka + mB + ny = 0 , we have then to determine m and n . Since ...
... denoted by the letter w * . The line joining the two points w , w ' may be called the line ww ' . 23. To find the equation of the line ww ' . Let the required equation be ka + mB + ny = 0 , we have then to determine m and n . Since ...
Page 57
... denoted by P1 , P P respectively , and three of the triangles obtained by successively writing and R in place of P by I , I , I rrr , prove that ( P1L‚ˆ ‚ ) * ~ ( P ̧ ¥ ‚ † ) * + ( P‚2‚ˆ ‚ ) * — ( P ̧ ? , r ) 2 + { P ̧ ¥ ‚ ˆ ‚ ) * — ( P ...
... denoted by P1 , P P respectively , and three of the triangles obtained by successively writing and R in place of P by I , I , I rrr , prove that ( P1L‚ˆ ‚ ) * ~ ( P ̧ ¥ ‚ † ) * + ( P‚2‚ˆ ‚ ) * — ( P ̧ ? , r ) 2 + { P ̧ ¥ ‚ ˆ ‚ ) * — ( P ...
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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