An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page viii
... Triangle of Refer- 33 • ence 34 · · 4 . Position of the Centre . Condition for a Parabola 35 • 5 . Condition of ... Reference . 39 · 8 . Position of the Centre . Condition for a Parabola 40 9 . Condition of Tangency 42 10 . Equations of the ...
... Triangle of Refer- 33 • ence 34 · · 4 . Position of the Centre . Condition for a Parabola 35 • 5 . Condition of ... Reference . 39 · 8 . Position of the Centre . Condition for a Parabola 40 9 . Condition of Tangency 42 10 . Equations of the ...
Page xi
... triangle of reference . ib . 8 . Equation of circumscribed Conic 138 · 9 .. Equation of the Pole of a given straight line , and of the centre . Condition for a Parabola 139 10 . Circular points at infinity ib . Conditions for a Circle ...
... triangle of reference . ib . 8 . Equation of circumscribed Conic 138 · 9 .. Equation of the Pole of a given straight line , and of the centre . Condition for a Parabola 139 10 . Circular points at infinity ib . Conditions for a Circle ...
Page 1
... triangle of reference , its sides , lines of reference , and the distances of a point from its three sides will be called the trilinear co - ordinates of that point . We shall usually denote the angular points of the triangle of ...
... triangle of reference , its sides , lines of reference , and the distances of a point from its three sides will be called the trilinear co - ordinates of that point . We shall usually denote the angular points of the triangle of ...
Page 2
The Method of Reciprocal Polars, and the Theory Projections Norman Macleod Ferrers. the triangle of reference ( fig . 1 ) . Join PA , PB , PC , and draw PD perpendicular to BC . Then PD = a , and aa = twice the area of the triangle PBC ...
The Method of Reciprocal Polars, and the Theory Projections Norman Macleod Ferrers. the triangle of reference ( fig . 1 ) . Join PA , PB , PC , and draw PD perpendicular to BC . Then PD = a , and aa = twice the area of the triangle PBC ...
Page 3
... - ordinates , B and y for example , and this may be made homo- aa + bB + cy geneous in a , ẞ , y by multiplying each term by 24 raised to a suitable power . Thus , the equation 1-2 AREA OF THE TRIANGLE OF REFERENCE . 3.
... - ordinates , B and y for example , and this may be made homo- aa + bB + cy geneous in a , ẞ , y by multiplying each term by 24 raised to a suitable power . Thus , the equation 1-2 AREA OF THE TRIANGLE OF REFERENCE . 3.
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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