An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page xiv
... points , forming a con- 171 • 18 . jugate triad . Envelope of a side of an inscribed triangle whose other sides ... point • · 173 · 174 19 . 20 . Locus of a vertex of a circumscribed triangle , whose other ver- tices move each along a fixed ...
... points , forming a con- 171 • 18 . jugate triad . Envelope of a side of an inscribed triangle whose other sides ... point • · 173 · 174 19 . 20 . Locus of a vertex of a circumscribed triangle , whose other ver- tices 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 - B - 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 - B - g , Pn = y - h ...
Page 104
... 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 109
... 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 110
... ' . The student will find the above mode of transformation , in which a Again , turn to Example 4 , on page 56 110 TRILINEAR CO - ORDINATES . Envelope of a side of an inscribed triangle whose other sides pass each through a fixed point.
... ' . The student will find the above mode of transformation , in which a Again , turn to Example 4 , on page 56 110 TRILINEAR CO - ORDINATES . Envelope of a side of an inscribed triangle whose other sides pass each through a fixed point.
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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