An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of ProjectionsMacmillan, 1866 - 182 σελίδες |
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Σελίδα 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 ...
Σελίδα 14
... gives , eliminating a , B , y by cross - multipli- cation , m ̧ ̧ — ̧ ̧n + lm ̧ ̧− m ̧ ̧ + 1 ̧m ̧n — 1m ̧n ̧ = 0 , - the required condition . - - The identity of form between the conditions that three straight lines should intersect in ...
... gives , eliminating a , B , y by cross - multipli- cation , m ̧ ̧ — ̧ ̧n + lm ̧ ̧− m ̧ ̧ + 1 ̧m ̧n — 1m ̧n ̧ = 0 , - the required condition . - - The identity of form between the conditions that three straight lines should intersect in ...
Σελίδα 33
... give us a quadratic for the determination of , to each of the В 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 ...
... give us a quadratic for the determination of , to each of the В 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 ...
Σελίδα 43
... the ratios of L , M , N in order that the conic may become the inscribed circle . At the centre of this circle we have , as we know , a = B = y . This gives , by the result of Art . 8 17 Condition for a Parabola + + +.
... the ratios of L , M , N in order that the conic may become the inscribed circle . At the centre of this circle we have , as we know , a = B = y . This gives , by the result of Art . 8 17 Condition for a Parabola + + +.
Σελίδα 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 C N L L 210 218 + + a - = bc ' 2 ° са M 2 b ab Adding together the last two of these equations ...
... 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 C N L L 210 218 + + a - = bc ' 2 ° са M 2 b ab Adding together the last two of these equations ...
Άλλες εκδόσεις - Προβολή όλων
An Elementary Treatise on Trilinear Co-Ordinates, the Method of Reciprocal ... Norman MacLeod Ferrers Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
aa+bB+cy angular points anharmonic ratio asymptotes b₁ b₂ centre Chap chord coefficients common tangents condition of tangency conic section Crown 8vo curve determine directrix distance escribed circles Fcap find the equation fixed point foci focus four points given conic given point given straight line harmonic pencil Hence imaginary internal bisectors investigated Let the equation line at infinity line joining locus meets the conic nine-point circle obtain opposite sides pair parabola parallel Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact pole prove radical axis reciprocated with respect rectangular hyperbola represented right angles second degree sin POS tangents tangents drawn theorem three points three straight lines touches the line triangle of reference ua² V'ca values vß² W'ab whence wy² λα
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