An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page 8
... seen that we have here or = = sin DAF = cos B ; DE AD = sin DAE = cos C , DF AD ᎠᎬ Cos C Hence PG cos C = DF cos B ' PH Cos Bi .. PG cos BPH cos C , B cos By cos C. This will be the equation of the straight line , drawn through A , at ...
... seen that we have here or = = sin DAF = cos B ; DE AD = sin DAE = cos C , DF AD ᎠᎬ Cos C Hence PG cos C = DF cos B ' PH Cos Bi .. PG cos BPH cos C , B cos By cos C. This will be the equation of the straight line , drawn through A , at ...
Page 14
... seen hereafter . We shall sometimes , in future investigations , speak of the straight line represented by the equation la + mẞ + ny = 0 , as the straight line ( l , m , n ) . Adopting this phraseology , it will be seen that the ...
... seen hereafter . We shall sometimes , in future investigations , speak of the straight line represented by the equation la + mẞ + ny = 0 , as the straight line ( l , m , n ) . Adopting this phraseology , it will be seen that the ...
Page 15
... seen that the equality of any two members implies that the third is equal to either of them . Multiplying the numerators and denominators of the several members of ( 3 ) by l ' , m ' , n ' and adding , we obtain the condition under the ...
... seen that the equality of any two members implies that the third is equal to either of them . Multiplying the numerators and denominators of the several members of ( 3 ) by l ' , m ' , n ' and adding , we obtain the condition under the ...
Page 16
... seen that , q , r , denoting the distances from A , of the points in which the straight line ( l , m , n ) cuts AC , AB respectively , qr b - - gra bc 1 , gr q = m , C b bc m С bc whence = a ar ī a aq c am b an or = 1 - 1 " bl q cl r ...
... seen that , q , r , denoting the distances from A , of the points in which the straight line ( l , m , n ) cuts AC , AB respectively , qr b - - gra bc 1 , gr q = m , C b bc m С bc whence = a ar ī a aq c am b an or = 1 - 1 " bl q cl r ...
Page 25
... seen that , if an harmonic pencil be cut by a transversal , the four points of section will form an harmonic range . And if four points , forming an harmonic range , be joined with a fifth point , the four joining lines will form an ...
... seen that , if an harmonic pencil be cut by a transversal , the four points of section will form an harmonic range . And if four points , forming an harmonic range , be joined with a fifth point , the four joining lines will form an ...
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Common terms and phrases
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²