An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page vii
... EXAMPLES · 21 19 . ANHARMONIC RATIO . Definitions • 23 20 . The Anharmonic Ratio of a Pencil is equal to that of the range 21 . in which it is cut by any Transversal Definition of an Harmonic Pencil 228585 ib . ARTS . 22 . 23 . 24 . 25 .
... EXAMPLES · 21 19 . ANHARMONIC RATIO . Definitions • 23 20 . The Anharmonic Ratio of a Pencil is equal to that of the range 21 . in which it is cut by any Transversal Definition of an Harmonic Pencil 228585 ib . ARTS . 22 . 23 . 24 . 25 .
Page x
... equal to the correspond- ing angle in the Reciprocal Curve 113 22 . Co - ordinates of the foci of a Conic · 115 EXAMPLES 116 23 . Double application of the Method of Reciprocal Polars 118 RTS . I. 2 . 3 . 4 . CHAPTER X CONTENTS .
... equal to the correspond- ing angle in the Reciprocal Curve 113 22 . Co - ordinates of the foci of a Conic · 115 EXAMPLES 116 23 . Double application of the Method of Reciprocal Polars 118 RTS . I. 2 . 3 . 4 . CHAPTER X CONTENTS .
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 2A " 3a 36 3c • Prove that a sin A + ẞ sin B + y sin C is equal to 2R 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 2A " 3a 36 3c • Prove that a sin A + ẞ sin B + y sin C is equal to 2R where R is the ...
Page 7
... equal to the area of the triangle ABC . or Hence 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 . or Hence 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 8
... equal to the area of the triangle ABC . or Hence PG.AC cos B PH.AB cos C ; B cos B = Y cos C. This will be the equation of the straight line , drawn through A , at right angles to BC . COR . It may hence be shewn that the three straight ...
... equal to the area of the triangle ABC . or Hence PG.AC cos B PH.AB cos C ; B cos B = Y cos C. This will be the equation of the straight line , drawn through A , at right angles to BC . COR . It may hence be shewn that the three straight ...
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Common terms and phrases
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα