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 , ß , 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 , ß , 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 , - Im ̧n - l ̧m ̧n + lm ̧n ̧ — l ̧m ̧n ̧ + 1 ̧ ̧n — l ̧m ̧n ̧ = 0 , the required condition . - The identity of form between the conditions that three straight lines should ...
... gives , eliminating a , B , y by cross - multipli- cation , - Im ̧n - l ̧m ̧n + lm ̧n ̧ — l ̧m ̧n ̧ + 1 ̧ ̧n — l ̧m ̧n ̧ = 0 , the required condition . - The identity of form between the conditions that three straight lines should ...
Page 33
... give us a quadratic for the determination of , to each of the Y 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 real ...
... give us a quadratic for the determination of , to each of the Y 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 real ...
Page 43
... conic may become the in- scribed circle . At the centre of this circle we have , as we know , a = ẞ = y . This gives , by the result of Art . 8 Equations of the Four Circles which touch the Three Sides the Triangle of Reference.
... conic may become the in- scribed circle . At the centre of this circle we have , as we know , a = ẞ = y . This gives , by the result of Art . 8 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 + Ђ C = bc " N L r + 210 210 = a ca L M + · b 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 + Ђ C = bc " N L r + 210 210 = a ca L M + · b ab Adding together the last two of these equations , and ...
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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