An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page iii
... , F.R.S. MASTER OF GONVILLE AND CAIUS COLLEGE , HON . LL.D. OF THE UNIVERSITY OF GLASGOW . FOURTH EDITION . London : MACMILLAN AND CO . AND NEW YORK . 1890 [ All Rights reserved . ] First Edition 1861 , Second Edition 1866 , Third Edition.
... , F.R.S. MASTER OF GONVILLE AND CAIUS COLLEGE , HON . LL.D. OF THE UNIVERSITY OF GLASGOW . FOURTH EDITION . London : MACMILLAN AND CO . AND NEW YORK . 1890 [ All Rights reserved . ] First Edition 1861 , Second Edition 1866 , Third Edition.
Page iv
The Method of Reciprocal Polars, and the Theory Projections Norman Macleod Ferrers. First Edition 1861 , Second Edition 1866 , Third Edition 1876 , Fourth Edition 1890 . 1 133536 OCT S LIH F41 1909 PREFACE . HE prominence.
The Method of Reciprocal Polars, and the Theory Projections Norman Macleod Ferrers. First Edition 1861 , Second Edition 1866 , Third Edition 1876 , Fourth Edition 1890 . 1 133536 OCT S LIH F41 1909 PREFACE . HE prominence.
Page vi
... Third Edition , I have rewritten some articles where the demonstrations were imperfect or obscure , and have added some examples , taken from various Cambridge Examination papers . DECEMBER , 1875 . CONTENTS . CHAPTER I. TRILINEAR CO ...
... Third Edition , I have rewritten some articles where the demonstrations were imperfect or obscure , and have added some examples , taken from various Cambridge Examination papers . DECEMBER , 1875 . CONTENTS . CHAPTER I. TRILINEAR CO ...
Page viii
... third Any Chord of a conic is divided harmonically by the Conic , any Point , and its Polar 52 • 53 23 . Equation of a Line joining Two given Points ib . 24 . Equation of the Tangent at a given Point . 54 25 . 26 . 27 . Pole of a given ...
... third Any Chord of a conic is divided harmonically by the Conic , any Point , and its Polar 52 • 53 23 . Equation of a Line joining Two given Points ib . 24 . Equation of the Tangent at a given Point . 54 25 . 26 . 27 . Pole of a given ...
Page 15
... third is 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 ...
... third is 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 ...
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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