An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page vii
... Distance between two given Points 4 4-6 . Investigation of Equations of certain Straight Lines 6 7 . . Every Straight Line may be represented by an Equation of the First Degree 9 · 8 . 9 . 10 . 11 . Every Equation of the First Degree ...
... Distance between two given Points 4 4-6 . Investigation of Equations of certain Straight Lines 6 7 . . Every Straight Line may be represented by an Equation of the First Degree 9 · 8 . 9 . 10 . 11 . Every Equation of the First Degree ...
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 , positive if the point lie on the same side of that line as the point A does ...
... 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 , positive if the point lie on the same side of that line as the point A does ...
Page 4
... distance between two given points , in terms of their trilinear co - ordinates . 19 2 ' Let a ,, B1 , Y1 ; α , B , Y , be the co - ordinates of two given points , r the distance between them . -- Then , 2 will be a rational integral ...
... distance between two given points , in terms of their trilinear co - ordinates . 19 2 ' Let a ,, B1 , Y1 ; α , B , Y , be the co - ordinates of two given points , r the distance between them . -- Then , 2 will be a rational integral ...
Page 5
... A , whence r2 – ( ẞı — ẞ2 ) 2 + ( Y1 − Y1⁄2 ) 2 + 2 ( ẞ1 — B2 ) ( Y1 − Y2 ) cos A = - sin2 A a rational integral function of the second degree . where l , m , n are certain functions of DISTANCE BETWEEN TWO POINTS . 5.
... A , whence r2 – ( ẞı — ẞ2 ) 2 + ( Y1 − Y1⁄2 ) 2 + 2 ( ẞ1 — B2 ) ( Y1 − Y2 ) cos A = - sin2 A 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 , suppose these points to be B and C. Then α1 = 0 , B1 = 24 b , 1 = 0 , 2A = ; C α2 = 0 , B2 = 0 , Y2 2 2A 2A also r = a . Hence a2 = - -1 a2bc 442 . Similarly m = ab2c 442 , abc2 n 442 Hence r2 : = abc ...
... distance of which we wish to find , suppose these points to be B and C. Then α1 = 0 , B1 = 24 b , 1 = 0 , 2A = ; C α2 = 0 , B2 = 0 , Y2 2 2A 2A also r = a . Hence a2 = - -1 a2bc 442 . Similarly m = ab2c 442 , abc2 n 442 Hence r2 : = abc ...
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Common terms and phrases
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²