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

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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 ,

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

This

7 m , + , m , -2,3,7 = 0 , the required condition . The identity of form between the

conditions that three straight lines should intersect in a point , and that three ...

This

**gives**, eliminating a , ß , y by cross - multiplication , l , m ,, -1,2,3 , + 1,3,7 , -1,7 m , + , m , -2,3,7 = 0 , the required condition . The identity of form between the

conditions that three straight lines should intersect in a point , and that three ...

Page 33

To find where the curve , of which this is the equation , is cut by the straight line la

+ m + ny = 0 , we may eliminate a between the two equations . This will

quadratic for the determination of , to each of the g two values of this ratio , real ...

To find where the curve , of which this is the equation , is cut by the straight line la

+ m + ny = 0 , we may eliminate a between the two equations . This will

**give**us aquadratic for the determination of , to each of the g two values of this ratio , real ...

Page 43

... for the determination of the centre , obtained in Art . 8 . Thus , let it be required

to find the ratios of L , M , N in order that the conic may become the inscribed

circle . At the centre of this circle we have , as we know , a = B = y . This

the ...

... for the determination of the centre , obtained in Art . 8 . Thus , let it be required

to find the ratios of L , M , N in order that the conic may become the inscribed

circle . At the centre of this circle we have , as we know , a = B = y . This

**gives**, bythe ...

Page 44

This

equations , put each member equal to r , we then get M N ū + ris : 18 N L + > с a

ca r L M b = ab + a Adding together the last two of these equations , and ...

This

**gives**, by the result of Art . 8 , Nb + Mc = Lc + Na = Ma + Lb. To solve theseequations , put each member equal to r , we then get M N ū + ris : 18 N L + > с a

ca r L M b = ab + a Adding together the last two of these equations , and ...

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### Common terms and phrases

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