An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page v
... writing on this subject has mainly been to place it on a basis 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 ...
... writing on this subject has mainly been to place it on a basis 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 ...
Page 10
... the equation of the first degree between two variables . Putting gra bc = 1 , TM -q = m , T - r = n , the equation may be written la + mB + ny = 0 . 8. We shall next establish the converse proposition , that 10 MODERN GEOMETRY .
... the equation of the first degree between two variables . Putting gra bc = 1 , TM -q = m , T - r = n , the equation may be written la + mB + ny = 0 . 8. We shall next establish the converse proposition , that 10 MODERN GEOMETRY .
Page 15
... written in the form n m C n - -- = n a C m で n b a m Z b a m b α where it will be seen that the equality of any two members implies that the third is equal to either of them . Multiplying the numerators and denominators of the several ...
... written in the form n m C n - -- = n a C m で n b a m Z b a m b α where it will be seen that the equality of any two members implies that the third is equal to either of them . Multiplying the numerators and denominators of the several ...
Page 17
... we should have aa + bB + cy = 0 . Since af + bg + ch = 2A , this equation may also be written If + mg + nh la + mB + ny = 2A ( aa + bB + cy ) . COR . The general equation of a straight line parallel F. 2 CONDITION OF PARALLELISM . 17.
... we should have aa + bB + cy = 0 . Since af + bg + ch = 2A , this equation may also be written If + mg + nh la + mB + ny = 2A ( aa + bB + cy ) . COR . The general equation of a straight line parallel F. 2 CONDITION OF PARALLELISM . 17.
Page 34
... written , λ α V μ + + β ' γ = 0 , represents a conic , described about the triangle of reference . 3. Let us now inquire how the line βγ + = 0 ע is related to this conic . β If in the equation of the conic we put + μ Y ע - 0 , or ...
... written , λ α V μ + + β ' γ = 0 , represents a conic , described about the triangle of reference . 3. Let us now inquire how the line βγ + = 0 ע is related to this conic . β If in the equation of the conic we put + μ Y ע - 0 , or ...
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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