An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page ix
... Terms of a Determinant 64 8 . Sign changed by interchange of two Consecutive Lines or Columns 9 . • Multiplication of a Determinant by a given Quantity IO . Minors of a Determinant · 5625 65 66 ib . II . Condition that a Quadratic ...
... Terms of a Determinant 64 8 . Sign changed by interchange of two Consecutive Lines or Columns 9 . • Multiplication of a Determinant by a given Quantity IO . Minors of a Determinant · 5625 65 66 ib . II . Condition that a Quadratic ...
Page 3
... ordinates , B and y for example , and this may be made homo- geneous in a , ß , y by multiplying each term by ax + bB + cy 2A raised to a suitable power . Thus , the equation 1-2 AREA OF THE TRIANGLE OF REFERENCE . 3.
... ordinates , B and y for example , and this may be made homo- geneous in a , ß , y by multiplying each term by ax + bB + cy 2A raised to a suitable power . Thus , the equation 1-2 AREA OF THE TRIANGLE OF REFERENCE . 3.
Page 4
... terms of their trilinear co - ordinates . Let a1 , B11 ; a2 , B2 , Ya , be the co - ordinates of two given points , r the distance between them . - Then , r2 will be a rational integral function of α , — ɑ2 , B1 - B1 Y1- Y2 , of the ...
... terms of their trilinear co - ordinates . Let a1 , B11 ; a2 , B2 , Ya , be the co - ordinates of two given points , r the distance between them . - Then , r2 will be a rational integral function of α , — ɑ2 , B1 - B1 Y1- Y2 , of the ...
Page 17
... terms , - and can only be admitted as a limiting form to which possi- ble equations may continually tend . 15. To find the equation of a straight line , drawn through a given point , parallel to a given straight line . Let ( l , m , n ) ...
... terms , - and can only be admitted as a limiting form to which possi- ble equations may continually tend . 15. To find the equation of a straight line , drawn through a given point , parallel to a given straight line . Let ( l , m , n ) ...
Page 25
... term harmonic is employed on account of the cir- cumstance , that if the points P , Q , R , S form what is above defined as an harmonic range , PR will be an harmonic mean between PQ and PS . For PQ.RS = PS . QR ; .. PQ ( PS - PR ) = PS ...
... term harmonic is employed on account of the cir- cumstance , that if the points P , Q , R , S form what is above defined as an harmonic range , PR will be an harmonic mean between PQ and PS . For PQ.RS = PS . QR ; .. PQ ( PS - PR ) = PS ...
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Common terms and phrases
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα