An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 12
... give the values of a , B , y , at the point of intersection . 10. To find the equation of the straight line , passing through two given points . Let f , g , h ; f ' , g ' , h ' , be the co - ordinates of the two given points , and ...
... give the values of a , B , y , at the point of intersection . 10. To find the equation of the straight line , passing through two given points . Let f , g , h ; f ' , g ' , h ' , be the co - ordinates of the two given points , and ...
Page 14
... gives , eliminating a , B , y by cross - multipli- cation , - - = 1 ̧m ̧n ̧ − 1 ̧m ̧n + lm ̧n ̧− 1 ̧m ̧n ̧ + 1 ̧m ̧n — 1 ̧m ̧n ̧ — 0 , the required condition . The identity of form between the conditions that three straight lines ...
... gives , eliminating a , B , y by cross - multipli- cation , - - = 1 ̧m ̧n ̧ − 1 ̧m ̧n + lm ̧n ̧− 1 ̧m ̧n ̧ + 1 ̧m ̧n — 1 ̧m ̧n ̧ — 0 , the required condition . The identity of form between the conditions that three straight lines ...
Page 33
... give us a quadratic for the determination of B γ " to each of the two values of this ratio , real , equal , or imaginary , one value of a will correspond ; whence it appears that the straight line and the curve cut one another in two ...
... give us a quadratic for the determination of B γ " to each of the two values of this ratio , real , equal , or imaginary , one value of a will correspond ; whence it appears that the straight line and the curve cut one another in two ...
Page 43
... the centre of this circle we have , as we know , a = B = y . This gives , by the result of Art . 8 CONDITION OF TOUCHING A GIVEN STRAIGHT LINE . 43 10 Equations of the Four Circles which touch the Three Sides the Triangle of Reference.
... the centre of this circle we have , as we know , a = B = y . This gives , by the result of Art . 8 CONDITION OF TOUCHING A GIVEN STRAIGHT LINE . 43 10 Equations of the Four Circles which touch the Three Sides the Triangle of Reference.
Page 44
... gives , by the result of Art . 8 , Nb + McLc + Na = Ma + Lb. To solve these equations , put each member equal to r , we then get M N b N L α + + + с L α M b = bc ' r == = ca γ ab · Adding together the last two of these equations , and ...
... gives , by the result of Art . 8 , Nb + McLc + Na = Ma + Lb. To solve these equations , put each member equal to r , we then get M N b N L α + + + с L α M b = bc ' r == = ca γ ab · Adding together the last two of these equations , and ...
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Common terms and phrases
angular points asymptotes ax+bB+cy b₁ b₂ C₁ Cambridge centre Chap co-ordinates coefficients College common tangents conic section Crown 8vo determinant directrix Edition equation Fcap find the equation fixed point follows four points given conic given point given straight line Hence imaginary investigated Let the equation line at infinity line joining locus meets the conic nine-point circle numerous Illustrations obtain opposite sides Owens College pair parabola Pascal's Theorem perpendicular point f points of intersection pole Professor prove radical axis ratios rectangular hyperbola represented respect right angles second degree shewn similar and similarly sin POS tangents tangents drawn term a,b,c theorem three straight lines tion touches the line triangle of reference Ua² ux² V'ca v'f+u'g+wh va² values Vb² vß² W. K. CLIFFORD W'ab whence wy² λα