An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page v
... Co - ordinates , which forms the subject of the greater part of the following work . My object in writing on this subject has mainly been to place it on a basis altogether independent of the ordinary Cartesian system , instead of ...
... Co - ordinates , which forms the subject of the greater part of the following work . My object in writing on this subject has mainly been to place it on a basis altogether independent of the ordinary Cartesian system , instead of ...
Page vii
... CO - ORDINATES . ARTS . 1 . DEFINITION of Trilinear Co - ordinates PAGE 1 2 . 3 . · 4-6 . 7 . Identical relation between the Trilinear Co - ordinates of a Point ib . Distance between two given Points • Investigation of Equations of ...
... CO - ORDINATES . ARTS . 1 . DEFINITION of Trilinear Co - ordinates PAGE 1 2 . 3 . · 4-6 . 7 . Identical relation between the Trilinear Co - ordinates of a Point ib . Distance between two given Points • Investigation of Equations of ...
Page viii
... Co - ordinates of the Centre ib . 19 . Equation of the Circle , with respect to which ́the Triangle of Reference is self - conjugate 51 · 20 . 21 . 23 . 24 . 25 . 26 . 27 . Equation of the Conic which touches two sides of the Triangle ...
... Co - ordinates of the Centre ib . 19 . Equation of the Circle , with respect to which ́the Triangle of Reference is self - conjugate 51 · 20 . 21 . 23 . 24 . 25 . 26 . 27 . Equation of the Conic which touches two sides of the Triangle ...
Page ix
... Co - ordinates of the Pole of a given Straight Line 79 • 10 . Equation of the pair of Tangents drawn to the Conic from a given external Point · 11 . Co - ordinates of the Centre 12 . Equation of the Asymptotes • 13. Condition for a ...
... Co - ordinates of the Pole of a given Straight Line 79 • 10 . Equation of the pair of Tangents drawn to the Conic from a given external Point · 11 . Co - ordinates of the Centre 12 . Equation of the Asymptotes • 13. Condition for a ...
Page x
... CO - ORDINATES . Definition of the Triangular Co - ordinates of a Point Formulæ relating to Straight Lines ri si as 1 . 2 . 3 . Formulæ relating to Conics · 3 . 5 . 6 , 7 . 8 , 10 .. 12 . 13 . CHAPTER VI . RECIPROCAL POLARS . 100 ib ...
... CO - ORDINATES . Definition of the Triangular Co - ordinates of a Point Formulæ relating to Straight Lines ri si as 1 . 2 . 3 . Formulæ relating to Conics · 3 . 5 . 6 , 7 . 8 , 10 .. 12 . 13 . CHAPTER VI . RECIPROCAL POLARS . 100 ib ...
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Common terms and phrases
angular points anharmonic ratio asymptotes auxiliary conic b₁ b₂ C₁ centre Chap chord co-ordinates coefficients common tangents conic section determinant directrix find the equation fixed point fixed straight line follows four points given conic given point given straight line given triangle Hence investigated Let the equation line at infinity line joining locus meets the conic nine-point circle obtain opposite sides parabola Pascal's Theorem perpendicular point f points at infinity points of contact points of intersection PQRS prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree shewn similar and similarly sin POS tangents drawn term a,b,c theorem three points three straight lines triangle of reference ua² uf+w'g+v'h ux² V'ca va² Vb² vß² W'ab whence wy² λα