An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page vii
... Distance between two given Points 4 4-6 . Investigation of Equations of certain Straight Lines 6 7 . · 8 . 9 . Every Straight Line may be represented by an Equation of the First Degree . Every Equation of the First Degree represents a ...
... Distance between two given Points 4 4-6 . Investigation of Equations of certain Straight Lines 6 7 . · 8 . 9 . Every Straight Line may be represented by an Equation of the First Degree . Every Equation of the First Degree represents a ...
Page 1
... distances from two given straight lines . In the system of which we are about to treat , the position of a point in a ... distance of a point from the line BC , as positive if the point lie on the same side of that line as the point A ...
... distances from two given straight lines . In the system of which we are about to treat , the position of a point in a ... distance of a point from the line BC , as positive if the point lie on the same side of that line as the point A ...
Page 4
... distance between two given points , in terms of their trilinear co - ordinates . 19 Let a ,, B1 , Y1 ; a ,, B , Y , be the co - ordinates of two given points , r the distance between them . Then , r2 will be a rational integral function ...
... distance between two given points , in terms of their trilinear co - ordinates . 19 Let a ,, B1 , Y1 ; a ,, B , Y , be the co - ordinates of two given points , r the distance between them . Then , r2 will be a rational integral function ...
Page 5
... ) cos A , ( B1 − B2 ) 2 + ( Y1 − Y2 ) 2 +2 ( ẞ1 − B2 ) ( Y1 − Y1⁄2 ) cos A sin2 A whence 2 a rational integral function of the second degree . - where l , m , n are certain functions of DISTANCE BETWEEN TWO POINTS . 5.
... ) cos A , ( B1 − B2 ) 2 + ( Y1 − Y2 ) 2 +2 ( ẞ1 − B2 ) ( Y1 − Y1⁄2 ) cos A sin2 A whence 2 a rational integral function of the second degree . - where l , m , n are certain functions of DISTANCE BETWEEN TWO POINTS . 5.
Page 6
... distance of which we wish to find , sup- pose these points to be B and C. Then 24 = - α1 = 0 , ẞ1 = = = b 2 Y1 = 0 , 2A = ; also ra . Hence Similarly 2A 2A a2 = -l ; a2bc 4A2 ab2c m = - 4A2 , abc2 n = - 4A ** abc Hence r2 4A2 - { a ( B1 ...
... distance of which we wish to find , sup- pose these points to be B and C. Then 24 = - α1 = 0 , ẞ1 = = = b 2 Y1 = 0 , 2A = ; also ra . Hence Similarly 2A 2A a2 = -l ; a2bc 4A2 ab2c m = - 4A2 , abc2 n = - 4A ** abc Hence r2 4A2 - { a ( B1 ...
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angular points asymptotes ax+bB+cy b₁ b₂ C₁ Cambridge centre Chap co-ordinates coefficients College common tangents conic section Crown 8vo determinant directrix Edition equation Fcap find the equation fixed point follows four points given conic given point given straight line Hence imaginary investigated Let the equation line at infinity line joining locus meets the conic nine-point circle numerous Illustrations obtain opposite sides Owens College pair parabola Pascal's Theorem perpendicular point f points of intersection pole Professor prove radical axis ratios rectangular hyperbola represented respect right angles second degree shewn similar and similarly sin POS tangents tangents drawn term a,b,c theorem three straight lines tion touches the line triangle of reference Ua² ux² V'ca v'f+u'g+wh va² values Vb² vß² W. K. CLIFFORD W'ab whence wy² λα