An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page vii
... Definitions 20 . 21 . ANHARMONIC RATIO . The Anharmonic Ratio of a Pencil is equal to that of the range in which it is cut by any Transversal Definition of an Harmonic Pencil 23 • ib . • 225 25 ARTS . 22 . The Bisectors of any Angle form.
... Definitions 20 . 21 . ANHARMONIC RATIO . The Anharmonic Ratio of a Pencil is equal to that of the range in which it is cut by any Transversal Definition of an Harmonic Pencil 23 • ib . • 225 25 ARTS . 22 . The Bisectors of any Angle form.
Page xi
... equal to the cor- responding angle in the Reciprocal Curve Co - ordinates of the foci of a Conic . . 125 126 · 34 . Double application of the Method of Reciprocal Polars EXAMPLES 128 ib . CHAPTER VII . TANGENTIAL CO - ORDINATES . 1 . 2 ...
... equal to the cor- responding angle in the Reciprocal Curve Co - ordinates of the foci of a Conic . . 125 126 · 34 . Double application of the Method of Reciprocal Polars EXAMPLES 128 ib . CHAPTER VII . TANGENTIAL CO - ORDINATES . 1 . 2 ...
Page 4
... equal to 2A a + b + c ' What are the co - ordinates of the centres of the escribed circles ? 4. The co - ordinates of the centre of gravity are 2A 2A 3a 36 24 · 3c 5. Prove that a sin A + ẞ sin B + γ A sin C is equal to R where R is the ...
... equal to 2A a + b + c ' What are the co - ordinates of the centres of the escribed circles ? 4. The co - ordinates of the centre of gravity are 2A 2A 3a 36 24 · 3c 5. Prove that a sin A + ẞ sin B + γ A sin C is equal to R where R is the ...
Page 7
... equal to the area of the triangle ABC . Hence or PG.AC - PH . AB , bB = cy . This is a relation between the co - ordinates of any point on the line AD , it therefore is the equation of that line . COR . It hence may be proved that the ...
... equal to the area of the triangle ABC . Hence or PG.AC - PH . AB , bB = cy . This is a relation between the co - ordinates of any point on the line AD , it therefore is the equation of that line . COR . It hence may be proved that the ...
Page 15
... equal to either of them . Multiplying the numerators and denominators of the several members of ( 3 ) by l ' , m ' , n ' and adding , we obtain the condition under the form ( mn ' — m'n ) a + ( nl ′ — n'l ) b + ( lm ' — l'm ) c = 0 ...
... equal to either of them . Multiplying the numerators and denominators of the several members of ( 3 ) by l ' , m ' , n ' and adding , we obtain the condition under the form ( mn ' — m'n ) a + ( nl ′ — n'l ) b + ( lm ' — l'm ) c = 0 ...
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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