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

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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

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

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

Page 16

Hence the equation ( 4 ) may be looked upon as an

two equations la + mß + ny = 0 , l'a + m'ß + n'y = 0 , cannot be simultaneously

satisfied by any values of Q , B , y , or , in other words , that the two straight lines ...

Hence the equation ( 4 ) may be looked upon as an

**expression**of the fact thattwo equations la + mß + ny = 0 , l'a + m'ß + n'y = 0 , cannot be simultaneously

satisfied by any values of Q , B , y , or , in other words , that the two straight lines ...

Page 17

This is often

equivalent equation a sin A + B sin B + y sin C = 0 , represents the straight line at

infinity . This phraseology is very convenient , and free from objection , if the ...

This is often

**expressed**by saying that the equation ad + b3 + cy = 0 , or theequivalent equation a sin A + B sin B + y sin C = 0 , represents the straight line at

infinity . This phraseology is very convenient , and free from objection , if the ...

Page 21

1 * 6 * c a = 1 Hence If + mg + nh ( 72 + m + n ? – 2mn cos A – 2nl cos B - 2 lm

cos C ) } } the required

manifestly ...

1 * 6 * c a = 1 Hence If + mg + nh ( 72 + m + n ? – 2mn cos A – 2nl cos B - 2 lm

cos C ) } } the required

**expression**. It will be observed , that the numerator of this**expression**vanishes if the point ( f , g , h ) lie upon the line ( l , m , n ) , asmanifestly ...

Page 23

If OP , OQ , OR , OS be four straight lines intersecting in a point , the ratio sin POQ

.sin ROS sin POS.sin QOR is called the anharmonic ratio of the pencil OP , OQ ,

OR , OS , and is

If OP , OQ , OR , OS be four straight lines intersecting in a point , the ratio sin POQ

.sin ROS sin POS.sin QOR is called the anharmonic ratio of the pencil OP , OQ ,

OR , OS , and is

**expressed**by the notation { 0. PQRS ) * . DEF . 2. If P , Q , R , S ...### What people are saying - Write a review

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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