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

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Page viii

Equation of the Conic

the Centre . Condition for a Parabola Condition of Tangency . Every Parabola

touches the Line at Infinity 6 . Equation of the Circumscribing Circle 7 . Equation

of ...

Equation of the Conic

**described**about the Triangle of Reference 4 . Position ofthe Centre . Condition for a Parabola Condition of Tangency . Every Parabola

touches the Line at Infinity 6 . Equation of the Circumscribing Circle 7 . Equation

of ...

Page 34

Hence the equation λβη + μγα + ναβ = 0 , or , as it may also be written , a M + - =

0 , B n represents a conic ,

now inquire how the line By + M is related to this conic . V + 0 If in the equation of

...

Hence the equation λβη + μγα + ναβ = 0 , or , as it may also be written , a M + - =

0 , B n represents a conic ,

**described**about the triangle of reference . 3. Let usnow inquire how the line By + M is related to this conic . V + 0 If in the equation of

...

Page 48

Hence also , if any number of conic sections be

quadrangle * , and the diagonals of that quadrangle intersect in A , while the

sides produced intersect ' in B and C , then A , B , C form , with respect to each of

the ...

Hence also , if any number of conic sections be

**described**about the samequadrangle * , and the diagonals of that quadrangle intersect in A , while the

sides produced intersect ' in B and C , then A , B , C form , with respect to each of

the ...

Page 56

A triangle is

angular point with the point of contact of the opposite side , intersect in a point . 3

. Find the equations of the normals to the conic aby + uyar + vaß = 0 , drawn at ...

A triangle is

**described**about a conic ; prove that the straight lines , joining eachangular point with the point of contact of the opposite side , intersect in a point . 3

. Find the equations of the normals to the conic aby + uyar + vaß = 0 , drawn at ...

Page 57

If R be the radius of the circle

the circle with respect to which 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

...

If R be the radius of the circle

**described**about the triangle of reference , ö that ofthe circle with respect to which 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

...

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### 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