An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
From inside the book
Results 1-5 of 26
Page 8
... seen that we have here DE = AD sin DAE = cos C , DF = AD sin DAF = cos B ; DE = cos C DF cos B PG PH Hence cos C cos B or .. PG cos BPH cos C , B cos By cos C. This will be the equation of the straight line , drawn through A , at right ...
... seen that we have here DE = AD sin DAE = cos C , DF = AD sin DAF = cos B ; DE = cos C DF cos B PG PH Hence cos C cos B or .. PG cos BPH cos C , B cos By cos C. This will be the equation of the straight line , drawn through A , at right ...
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 ( 1 , m , n ) cuts AC , AB respectively , gra bc = 1 , qr qr q = m , C b whence 218 b = bc m C bc ar τ a or - r = n ; n -- = a aq с 018 am b an ...
... seen that , q , r , denoting the distances from A , of the points in which the straight line ( 1 , m , n ) cuts AC , AB respectively , gra bc = 1 , qr qr q = m , C b whence 218 b = bc m C bc ar τ a or - r = n ; n -- = a aq с 018 am b an ...
Page 25
... seen that , if an harmonic pencil be cut by à 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 à 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 ...
Other editions - View all
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