An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page vii
... relation between the Trilinear Co - ordinates of a Point ib . Distance between two given Points • Investigation of Equations of certain Straight Lines Every Straight Line may be represented by an Equation of the First Degree • 4 • • 6 9 ...
... relation between the Trilinear Co - ordinates of a Point ib . Distance between two given Points • Investigation of Equations of certain Straight Lines Every Straight Line may be represented by an Equation of the First Degree • 4 • • 6 9 ...
Page viii
... Relation of Points and Lines 29 • 26 . ON INVOLUTION . Definitions 30 · · • 27-29 . Anharmonic Properties of Points and Lines in Involution 31 · 3383 CHAPTER II . SPECIAL FORMS OF THE EQUATION OF THE SECOND DEGREE . 1. Every Equation of ...
... Relation of Points and Lines 29 • 26 . ON INVOLUTION . Definitions 30 · · • 27-29 . Anharmonic Properties of Points and Lines in Involution 31 · 3383 CHAPTER II . SPECIAL FORMS OF THE EQUATION OF THE SECOND DEGREE . 1. Every Equation of ...
Page xi
... relation between the co - ordinates of any straight Line An equation of the nth degree represents a curve of the nth class · ib . 133 134 136 · 7 . Equation of a Conic , touching the three sides of the triangle of reference ib . 8 ...
... relation between the co - ordinates of any straight Line An equation of the nth degree represents a curve of the nth class · ib . 133 134 136 · 7 . Equation of a Conic , touching the three sides of the triangle of reference ib . 8 ...
Page 1
... relation exists , which we proceed to investigate . If A denote the area of the triangle of reference , a , ß , y , the trilinear co - ordinates of any point , then ax + bB + cy = 2A . Let P be the given point , and first suppose it to ...
... relation exists , which we proceed to investigate . If A denote the area of the triangle of reference , a , ß , y , the trilinear co - ordinates of any point , then ax + bB + cy = 2A . Let P be the given point , and first suppose it to ...
Page 3
... relation between two co- ordinates , B and y for example , and this may be made homo- ax + bB + cy geneous in a , B , y by multiplying each term by 2A raised to a suitable power . Thus , the equation 1-2 AREA OF THE TRIANGLE OF ...
... relation between two co- ordinates , B and y for example , and this may be made homo- ax + bB + cy geneous in a , B , y by multiplying each term by 2A raised to a suitable power . Thus , the equation 1-2 AREA OF THE TRIANGLE OF ...
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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