An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page xiv
... points , forming a conjugate triad 18. Envelope of a side of an inscribed triangle whose other sides pass each through a fixed point 19. Locus of a vertex of a circumscribed triangle , whose other vertices move each along a fixed ...
... points , forming a conjugate triad 18. Envelope of a side of an inscribed triangle whose other sides pass each through a fixed point 19. Locus of a vertex of a circumscribed triangle , whose other vertices move each along a fixed ...
Page 11
... fixed point D on the locus of the equation , a , ẞ , y those of any point P. Draw DE , PM perpendicular to AC , DF , PN perpendi- cular to AB . Also draw Dm , Dn , perpendicular respectively . to PM , PN . Then Pm - 8 - g , Pn - y - h ...
... fixed point D on the locus of the equation , a , ẞ , y those of any point P. Draw DE , PM perpendicular to AC , DF , PN perpendi- cular to AB . Also draw Dm , Dn , perpendicular respectively . to PM , PN . Then Pm - 8 - g , Pn - y - h ...
Page 103
... point , may be deduced those of another curve which is always touched by the polar of this moving point with regard to a fixed conic . The theory is especially valuable when the conic , with respect to which the poles and polars are ...
... point , may be deduced those of another curve which is always touched by the polar of this moving point with regard to a fixed conic . The theory is especially valuable when the conic , with respect to which the poles and polars are ...
Page 108
... fixed point , the three points lying in the same straight line , the third angular point will move along a straight line , passing through the intersection of the straight lines along which the other angu- lar points move . " The ...
... fixed point , the three points lying in the same straight line , the third angular point will move along a straight line , passing through the intersection of the straight lines along which the other angu- lar points move . " The ...
Page 109
... fixed straight lines , along which two of the angular points of the first triangle move , will be fixed points ... point , along which the angular points of the reciprocal triangle always move . Hence the data of the reciprocal proposition ...
... fixed straight lines , along which two of the angular points of the first triangle move , will be fixed points ... point , along which the angular points of the reciprocal triangle always move . Hence the data of the reciprocal proposition ...
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Common terms and phrases
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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