## An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |

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Page vi

... Caius COLLEGE , July , 1861 . ERRATA . Page Line 21 I 2 1 7 after m insert )

for 2mn cos A read 2mna cos A for lu read 24 after

CONTENTS . CHAPTER I. TRILINEAR CO - ORDINATES . EQUATION vi

PREFACE .

... Caius COLLEGE , July , 1861 . ERRATA . Page Line 21 I 2 1 7 after m insert )

for 2mn cos A read 2mna cos A for lu read 24 after

**values**insert of 52 I 2 56 5CONTENTS . CHAPTER I. TRILINEAR CO - ORDINATES . EQUATION vi

PREFACE .

Page 6

Since the

distance of which we wish to find , suppose these points to be B and C. Then 2A

Q = 0 , B. = Y = 0 , 2A Ag = 0 , B , = 0 , Y , = Hence 24 2A a * = - 7 ; b a'bc .

Since the

**values**of l , m , n are independent of the positions of the points , thedistance of which we wish to find , suppose these points to be B and C. Then 2A

Q = 0 , B. = Y = 0 , 2A Ag = 0 , B , = 0 , Y , = Hence 24 2A a * = - 7 ; b a'bc .

Page 12

Where these intersect , we have B g mn ' - m'n ni ' – n'l Im ' - I'm These equations ,

combined with ar + b3 + cy = 2A , give the

intersection . a 10. To find the equation of the straight line , passing through two ...

Where these intersect , we have B g mn ' - m'n ni ' – n'l Im ' - I'm These equations ,

combined with ar + b3 + cy = 2A , give the

**values**of a , b , y , at the point ofintersection . a 10. To find the equation of the straight line , passing through two ...

Page 14

If these three straight lines intersect in a point , the above three equations must

be satisfied by the same

cross - multiplication , l , m ,, -1,2,3 , + 1,3,7 , -1,7 m , + , m , -2,3,7 = 0 , the

required ...

If these three straight lines intersect in a point , the above three equations must

be satisfied by the same

**values**of a , b , y . This gives , eliminating a , ß , y bycross - multiplication , l , m ,, -1,2,3 , + 1,3,7 , -1,7 m , + , m , -2,3,7 = 0 , the

required ...

Page 16

The last of these is , as we know , an equation which cannot be satisfied by any

. Hence the equation ( 4 ) may be looked upon as an expression of the fact that ...

The last of these is , as we know , an equation which cannot be satisfied by any

**values**of a , B , y , since , as we have already proved ( Art . 2 ) , an + b3 + cry = 2A. Hence the equation ( 4 ) may be looked upon as an expression of the fact that ...

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angle angular points appears Author become BOOKS called Cambridge centre Chap chapter chord circle cloth co-ordinates coefficients coincide College common condition conic conic section considered constant corresponding Crown 8vo curve denoted described determine distance draw drawn eliminating equal equation Examples expressed find the equation fixed point focus follows given point given straight line gives harmonic Hence imaginary line at infinity locus meet observed obtained opposite sides pair parabola parallel passing pencil perpendicular point of intersection points of contact polar pole positive produced projection prove ratio reciprocal relation represented respect result right angles satisfy Schools second degree sides similar Similarly student taken tangents term theorem third three points tion touch Treatise triangle of reference values whence writing written