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

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Page 4

co - ordinates of the centre of gravity are 2A 2A 2A За 36 3c >

B sin B + y sin C is equal to where R is the radius of the circumscribing circle .

**Prove**that the co - ordinates of the middle point of the line BC are 0 , ъ 2. ... Theco - ordinates of the centre of gravity are 2A 2A 2A За 36 3c >

**Prove**that a sin A +B sin B + y sin C is equal to where R is the radius of the circumscribing circle .

Page 6

44 % ab2c Similarly 442 abc 442 " abc Hence pa { a ( B.-B. ) ( y - 7 ) + b ( 7-7 ) ( a

, – Q. ) + c ( Qz - Q ) ( B.-B. ) } . This is one form of the expression for r . It may also

ke

44 % ab2c Similarly 442 abc 442 " abc Hence pa { a ( B.-B. ) ( y - 7 ) + b ( 7-7 ) ( a

, – Q. ) + c ( Qz - Q ) ( B.-B. ) } . This is one form of the expression for r . It may also

ke

**proved**in a similar manner that abc g2 447 { a cos A ( an - Qn ) + b cos B ... Page 7

It hence may be

points of a triangle to bisect the opposite sides , intersect in a point . For these

straight lines will be represented by the equations or b = oy , cy = an , αα = bß ,

and ...

It hence may be

**proved**that the three straight lines , drawn through the angularpoints of a triangle to bisect the opposite sides , intersect in a point . For these

straight lines will be represented by the equations or b = oy , cy = an , αα = bß ,

and ...

Page 9

... points may be shewn to be respectively the centres of the inscribed and

escribed circles . We shall hereafter

bisectors of each angle respectively intersect the sides opposite to them , lie in

the same ...

... points may be shewn to be respectively the centres of the inscribed and

escribed circles . We shall hereafter

**prove**that the points , in which the externalbisectors of each angle respectively intersect the sides opposite to them , lie in

the same ...

Page 16

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

. 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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### 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