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

### From inside the book

Results 1-5 of 77

Page 2

Adding these equations , we get aa + b3 + cy = 2A . Next , suppose P to lie

between AB , AC produced , and on the side of BC remote from A ( fig . 2 ) . Then

a will be Fig . 2 . D negative , while B , y are positive .

GEOMETRY ...

Adding these equations , we get aa + b3 + cy = 2A . Next , suppose P to lie

between AB , AC produced , and on the side of BC remote from A ( fig . 2 ) . Then

a will be Fig . 2 . D negative , while B , y are positive .

**Hence**2 MODERNGEOMETRY ...

Page 3

have as before aa + b3 + cy = 2A . Thirdly , let P lie between AB , AC , produced

backwards ( fig . 3 ) , so that B , y are negative while a is positive . Twice Fig . 3 .

**Hence**, twice the area PBC will be represented by — ad , and we shall thereforehave as before aa + b3 + cy = 2A . Thirdly , let P lie between AB , AC , produced

backwards ( fig . 3 ) , so that B , y are negative while a is positive . Twice Fig . 3 .

Page 5

-a Similar expressions may be found for ( B.-B. ) , ( Y. - Y ) .

the form 2 ( B - B2 ) ( 7. - Y ) + m ( Y. - Y ) ( Qz - Q ) + n ( az -22 ) ( B - B2 ) , dicular

to AB , PN , QN ' to AC . Draw Qm perpendicular to PM , Qn to PN , and join mn .

-a Similar expressions may be found for ( B.-B. ) , ( Y. - Y ) .

**Hence**, pa will be ofthe form 2 ( B - B2 ) ( 7. - Y ) + m ( Y. - Y ) ( Qz - Q ) + n ( az -22 ) ( B - B2 ) , dicular

to AB , PN , QN ' to AC . Draw Qm perpendicular to PM , Qn to PN , and join mn .

Page 6

Since the values of l , m , n are independent of the positions of the points , 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 , =

Since the values of l , m , n are independent of the positions of the points , 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 . Page 7

of any point on the line AD , it therefore is the equation of that line . COR . It

may be proved that the three straight lines , drawn through the angular points of ...

**Hence**PG . AC = PH . AB , bB = cy . This is a relation between the co - ordinatesof any point on the line AD , it therefore is the equation of that line . COR . It

**hence**may be proved that the three straight lines , drawn through the angular points of ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

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