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

### From inside the book

Results 1-5 of 13

Page 1

We shall usually

letters A , B , C , the lengths of the sides respectively opposite to them by a , b , c ,

and the distances of any point from BC , .CA , AB respectively by the letters a , b ,

y .

We shall usually

**denote**the angular points of the triangle of reference by theletters A , B , C , the lengths of the sides respectively opposite to them by a , b , c ,

and the distances of any point from BC , .CA , AB respectively by the letters a , b ,

y .

Page 16

By referring to the investigation of Art . ( 7 ) it will be seen that , q , r ,

distances from A , of the points in which the straight line ( 1 , m , n ) cuts AC , AB

respectively , gra qr 1 , mi q = m , -q = n ; bc b с 3 C bc n whence - bc m = ar ī a a

...

By referring to the investigation of Art . ( 7 ) it will be seen that , q , r ,

**denoting**thedistances from A , of the points in which the straight line ( 1 , m , n ) cuts AC , AB

respectively , gra qr 1 , mi q = m , -q = n ; bc b с 3 C bc n whence - bc m = ar ī a a

...

Page 20

... lbc Now , let a

– 2qr cos A ) * a ' +98 + rh = ( af + bg + ch ) , af + bg + ch_gh á ' 72 qr bc 2 1 ma r с

or 7 a boft f + 65 ) 3+ ( 1-2 ) h a lbc ( If + mg + nh ) . And from the values of q and ...

... lbc Now , let a

**denote**the distance from ( f , g , h ) to ( l , m , n ) . Then ( 2 ° +72– 2qr cos A ) * a ' +98 + rh = ( af + bg + ch ) , af + bg + ch_gh á ' 72 qr bc 2 1 ma r с

or 7 a boft f + 65 ) 3+ ( 1-2 ) h a lbc ( If + mg + nh ) . And from the values of q and ...

Page 53

Hence any point on the conic may be expressed by giving the value of the ratio

ka B ' ka If w be the value of this ratio at any point , that point may be

the letter w * . The line joining the two points w , w ' may be called the line ww ' .

or ...

Hence any point on the conic may be expressed by giving the value of the ratio

ka B ' ka If w be the value of this ratio at any point , that point may be

**denoted**bythe letter w * . The line joining the two points w , w ' may be called the line ww ' .

or ...

Page 57

... the triangle of reference is self - conjugate , prove that pS + 4R * cos A cos B

cos C = Ö . 7 If BC , 04 , AB be three given tangents to a conic , P , Q , R three

points on the curve , and if the areas of the triangles PBC , PČA , PAB be

by ...

... the triangle of reference is self - conjugate , prove that pS + 4R * cos A cos B

cos C = Ö . 7 If BC , 04 , AB be three given tangents to a conic , P , Q , R three

points on the curve , and if the areas of the triangles PBC , PČA , PAB be

**denoted**by ...

### 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