An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 13
... condition that three points may lie in the same straight line . 29 Let α1 , B1 , Y1 ; α , B2 , Y2 ; as , B. , Y ... condition . - - - 13 . To find the condition that three straight lines THREE POINTS IN A STRAIGHT LINE . 13.
... condition that three points may lie in the same straight line . 29 Let α1 , B1 , Y1 ; α , B2 , Y2 ; as , B. , Y ... condition . - - - 13 . To find the condition that three straight lines THREE POINTS IN A STRAIGHT LINE . 13.
Page 14
... condition . - The identity of form between the conditions that three straight lines should intersect in a point , and that three points should lie in a straight line , is worthy of notice . Its full geometrical mean- ing will be seen ...
... condition . - The identity of form between the conditions that three straight lines should intersect in a point , and that three points should lie in a straight line , is worthy of notice . Its full geometrical mean- ing will be seen ...
Page 15
... condition of parallelism requires that a - f B - g Y - h = = a - ƒ ' B ' - g ' B ' — g' ̄ ̄`'y ' — h ' ' -- Also , recurring to the investigation of Art . ( 8 ) , fig . 7 , a - f bn - cm a ' - f ' bn ' - = = cl B - g - y - h an am bl ...
... condition of parallelism requires that a - f B - g Y - h = = a - ƒ ' B ' - g ' B ' — g' ̄ ̄`'y ' — h ' ' -- Also , recurring to the investigation of Art . ( 8 ) , fig . 7 , a - f bn - cm a ' - f ' bn ' - = = cl B - g - y - h an am bl ...
Page 16
... condition , since the two straight lines are in the same plane . Although , however , no values of a , ß , y exist which will satisfy the equation aa + bB + cy = 0 , yet we can always satisfy the equation la + mẞ + ny = 0 , where the ...
... condition , since the two straight lines are in the same plane . Although , however , no values of a , ß , y exist which will satisfy the equation aa + bB + cy = 0 , yet we can always satisfy the equation la + mẞ + ny = 0 , where the ...
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.
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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