An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page viii
... Pole of a given Straight Line . Condition of Tangency . Condition for a Parabola Co - ordinates of the Centre ib . 54 ib . ib . 55 EXAMPLES 56 CHAPTER III . ELIMINATION BETWEEN LINEAR EQUATIONS . ARTS . viii CONTENTS .
... Pole of a given Straight Line . Condition of Tangency . Condition for a Parabola Co - ordinates of the Centre ib . 54 ib . ib . 55 EXAMPLES 56 CHAPTER III . ELIMINATION BETWEEN LINEAR EQUATIONS . ARTS . viii CONTENTS .
Page ix
... ELIMINATION BETWEEN LINEAR EQUATIONS . ARTS . PAGE 2 . Definition of a Determinant 58 3—6 . Law of Formation of Determinants 59 7 . Signs of the several Terms of a Determinant 64 8 . Sign changed by interchange of two Consecutive Lines ...
... ELIMINATION BETWEEN LINEAR EQUATIONS . ARTS . PAGE 2 . Definition of a Determinant 58 3—6 . Law of Formation of Determinants 59 7 . Signs of the several Terms of a Determinant 64 8 . Sign changed by interchange of two Consecutive Lines ...
Page 13
... 0 , λα + β + γ = 0 , λας + μβ + γ = 0 , whence , eliminating λ , μ , v , by cross multiplication , ― the required condition . - - - 13 . To find the condition that three straight lines THREE POINTS IN A STRAIGHT LINE . 13.
... 0 , λα + β + γ = 0 , λας + μβ + γ = 0 , whence , eliminating λ , μ , v , by cross multiplication , ― the required condition . - - - 13 . To find the condition that three straight lines THREE POINTS IN A STRAIGHT LINE . 13.
Page 14
... eliminating a , B , y by cross - multipli- cation , - Im ̧n - l ̧m ̧n + lm ̧n ̧ — l ̧m ̧n ̧ + 1 ̧ ̧n — l ̧m ̧n ̧ = 0 , the required condition . - The identity of form between the conditions that three straight lines should intersect in ...
... eliminating a , B , y by cross - multipli- cation , - Im ̧n - l ̧m ̧n + lm ̧n ̧ — l ̧m ̧n ̧ + 1 ̧ ̧n — l ̧m ̧n ̧ = 0 , the required condition . - The identity of form between the conditions that three straight lines should intersect in ...
Page 15
... form which we shall occasionally use . It will be observed that this condition is the same in form as that which results from the elimination of a , B , y be- tween the equations la + mß + ny = 0 , l'a + CONDITION OF PARALLELISM . 15.
... form which we shall occasionally use . It will be observed that this condition is the same in form as that which results from the elimination of a , B , y be- tween the equations la + mß + ny = 0 , l'a + CONDITION OF PARALLELISM . 15.
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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