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

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Page v

My object in

altogether independent of the ordinary Cartesian system , instead of regarding it

as only a special form of Abridged Notation . A desire not unduly to increase the

size of ...

My object in

**writing**on this subject has mainly been to place it on a basisaltogether independent of the ordinary Cartesian system , instead of regarding it

as only a special form of Abridged Notation . A desire not unduly to increase the

size of ...

Page 10

... in the most general form of the equation of the first degree between two

variables . Putting gra qr = 1 , -q = m , 4 - r = n , bc the equation may be

+ mß + ny = 0 . C 8. We shall next establish the converse proposition , that 10

MODERN ...

... in the most general form of the equation of the first degree between two

variables . Putting gra qr = 1 , -q = m , 4 - r = n , bc the equation may be

**written**la+ mß + ny = 0 . C 8. We shall next establish the converse proposition , that 10

MODERN ...

Page 15

These two equations are equivalent to one only , since they may be

form cm cl - an cl - an ' 0 bn ' - cm n m 7 n 1 m Ā C ī a C a 1 n 1 ' n . m b m 7 C a a

where it will be seen that the equality of any two members implies that the third ...

These two equations are equivalent to one only , since they may be

**written**in theform cm cl - an cl - an ' 0 bn ' - cm n m 7 n 1 m Ā C ī a C a 1 n 1 ' n . m b m 7 C a a

where it will be seen that the equality of any two members implies that the third ...

Page 17

... if it did , we should have aa + b + cy = 0 . Since af + bg + ch = 2A , this equation

may also be

general equation of a straight line parallel F. 2 ' CONDITION OF PARALLELISM .

... if it did , we should have aa + b + cy = 0 . Since af + bg + ch = 2A , this equation

may also be

**written**la + mß + ny = If + mg + nh ( aa + bB + cy ) . 24 Cor . Thegeneral equation of a straight line parallel F. 2 ' CONDITION OF PARALLELISM .

Page 34

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

0 , B n represents a conic , described about the triangle of reference . 3. Let us

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 us

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

...

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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