An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page xiii
... PROPOSITIONS . ON THE DETERMINATION OF A CONIC FROM FIVE GIVEN GEOMETRICAL CONDITIONS . 2 . If five points be given , one conic only can be drawn 162 • 3 . · If four points and one tangent be given , two conics can be drawn ib . · · 4 ...
... PROPOSITIONS . ON THE DETERMINATION OF A CONIC FROM FIVE GIVEN GEOMETRICAL CONDITIONS . 2 . If five points be given , one conic only can be drawn 162 • 3 . · If four points and one tangent be given , two conics can be drawn ib . · · 4 ...
Page 3
... proposition arises from its enabling us to express any 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 ...
... proposition arises from its enabling us to express any 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 ...
Page 7
... will be represented by the equations bB = cv , cy = aa , aa = Bb , and , therefore , all pass through the point for which aa = bB = cy . In the next three propositions the reader will easily be EQUATIONS OF THE BISECTORS .
... will be represented by the equations bB = cv , cy = aa , aa = Bb , and , therefore , all pass through the point for which aa = bB = cy . In the next three propositions the reader will easily be EQUATIONS OF THE BISECTORS .
Page 8
... propositions the reader will easily be able to draw a figure for himself , by comparison with fig . 5 . 5. To find the equation of the straight line drawn through one of the angular points of the triangle of reference , perpen- dicular ...
... propositions the reader will easily be able to draw a figure for himself , by comparison with fig . 5 . 5. To find the equation of the straight line drawn through one of the angular points of the triangle of reference , perpen- dicular ...
Page 10
... the equation of the first degree between two variables . Putting gra bc = 1 , qr = m , qr — r = n , b с the equation may be written la + mB + ny = 0 . 8. We shall next establish the converse proposition , that 10 TRILINEAR CO - ORDINATES .
... the equation of the first degree between two variables . Putting gra bc = 1 , qr = m , qr — r = n , b с the equation may be written la + mB + ny = 0 . 8. We shall next establish the converse proposition , that 10 TRILINEAR CO - ORDINATES .
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Common terms and phrases
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²