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 1
... EQUATION OF A STRAIGHT LINE . 1. IN the system of co - ordinates ordinarily used , the position of a point in a ... Let P be the given point , and first suppose it to lie within F. 1 the triangle of reference ( fig . 1 ) . 831 CHAPTER ...
... EQUATION OF A STRAIGHT LINE . 1. IN the system of co - ordinates ordinarily used , the position of a point in a ... Let P be the given point , and first suppose it to lie within F. 1 the triangle of reference ( fig . 1 ) . 831 CHAPTER ...
Σελίδα 3
... equation in a form homogeneous with respect to the trilinear co - ordinates of any point to which it relates . Any locus may be represented , as in the ordinary system , by means of a relation between two co- ordinates , B and y for ...
... equation in a form homogeneous with respect to the trilinear co - ordinates of any point to which it relates . Any locus may be represented , as in the ordinary system , by means of a relation between two co- ordinates , B and y for ...
Σελίδα 4
... equation B2 + hy + k2 = 0 is equivalent to the homogeneous equation 4A3ß2 + 2Ahy ( ax + bB + cy ) + k2 ( ax + bB + cy ) 2 = 0 . The following examples may familiarize the reader with this system of co - ordinates . 1. Prove that the co ...
... equation B2 + hy + k2 = 0 is equivalent to the homogeneous equation 4A3ß2 + 2Ahy ( ax + bB + cy ) + k2 ( ax + bB + cy ) 2 = 0 . The following examples may familiarize the reader with this system of co - ordinates . 1. Prove that the co ...
Σελίδα 6
... reference , so as to bisect the opposite side . Let D be the middle point of the side BC , we have then to investigate the equation of the straight line AD . EQUATIONS OF THE BISECTORS . 7 In AD take any 6 TRILINEAR CO - ORDINATES .
... reference , so as to bisect the opposite side . Let D be the middle point of the side BC , we have then to investigate the equation of the straight line AD . EQUATIONS OF THE BISECTORS . 7 In AD take any 6 TRILINEAR CO - ORDINATES .
Σελίδα 7
... let a , B , y be its co - ordi- Fig . 5 . H F P D B E nates . From D , P draw DE , PG perpendicular to AC , DF PH ... equation of that line . COR . It hence may be proved that the three straight lines , drawn through the angular points ...
... let a , B , y be its co - ordi- Fig . 5 . H F P D B E nates . From D , P draw DE , PG perpendicular to AC , DF PH ... equation of that line . COR . It hence may be proved that the three straight lines , drawn through the angular points ...
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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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