An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page vi
... AND CAIUS COLLEGE , July , 1861 . ERRATA . Page Line 21 I after m insert ) 21 7 52 12 56 5 for 2mn cos A read 2mna cos A for lu read 2μ after values insert of CONTENTS . CHAPTER I. TRILINEAR CO - ORDINATES . ARTS vi PREFACE .
... AND CAIUS COLLEGE , July , 1861 . ERRATA . Page Line 21 I after m insert ) 21 7 52 12 56 5 for 2mn cos A read 2mna cos A for lu read 2μ after values insert of CONTENTS . CHAPTER I. TRILINEAR CO - ORDINATES . ARTS vi PREFACE .
Page 6
... values of l , m , n are independent of the positions of the points , the distance of which we wish to find , sup- pose these points to be B and C. Then 2A α = 0 , B1 = 1 = 0 , - = - b α2 = 0 , B2 = 0 , Y2 also r = a . Hence 2A = ; 2A 2A ...
... values of l , m , n are independent of the positions of the points , the distance of which we wish to find , sup- pose these points to be B and C. Then 2A α = 0 , B1 = 1 = 0 , - = - b α2 = 0 , B2 = 0 , Y2 also r = a . Hence 2A = ; 2A 2A ...
Page 12
... values of a , ß , y , at the point of intersection . 10. To find the equation of the straight line , passing through two given points . Let f , g , h ; f ' , g ' , h ' , be the co - ordinates of the two given points , and suppose the ...
... values of a , ß , y , at the point of intersection . 10. To find the equation of the straight line , passing through two given points . Let f , g , h ; f ' , g ' , h ' , be the co - ordinates of the two given points , and suppose the ...
Page 14
... values of a , ß , y.ˆ This gives , eliminating a , B , y by cross - multipli- cation , - Im ̧n - l ̧m ̧n + lm ̧n ̧ — l ̧m ̧n ̧ + 1 ̧ ̧n — l ̧m ̧n ̧ = 0 , the required condition . - The identity of form between the conditions that three ...
... values of a , ß , y.ˆ This gives , eliminating a , B , y by cross - multipli- cation , - Im ̧n - l ̧m ̧n + lm ̧n ̧ — l ̧m ̧n ̧ + 1 ̧ ̧n — l ̧m ̧n ̧ = 0 , the required condition . - The identity of form between the conditions that three ...
Page 16
... values of a , B , y , since , as we have already proved ( Art . 2 ) , aa + bB + cy = 2A . Hence the equa- tion ( 4 ) may be looked upon as an expression of the fact that two equations la + mB + ny = 0 , l'a + m'B + n'y = 0 , cannot be ...
... values of a , B , y , since , as we have already proved ( Art . 2 ) , aa + bB + cy = 2A . Hence the equa- tion ( 4 ) may be looked upon as an expression of the fact that two equations la + mB + ny = 0 , l'a + m'B + n'y = 0 , cannot be ...
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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