An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page vii
... relation between the Trilinear Co - ordinates of a Point ib . 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 ...
... relation between the Trilinear Co - ordinates of a Point ib . 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 ...
Page viii
... Relation of Points and Lines • 26 . ON INVOLUTION . Definitions PAGE 25 • 26 27 28 30 . 31 27-29 . Anharmonic Properties of Points and Lines in Involution CHAPTER II . SPECIAL FORMS OF THE EQUATION OF THE SECOND DEGREE . 1. Every ...
... Relation of Points and Lines • 26 . ON INVOLUTION . Definitions PAGE 25 • 26 27 28 30 . 31 27-29 . Anharmonic Properties of Points and Lines in Involution CHAPTER II . SPECIAL FORMS OF THE EQUATION OF THE SECOND DEGREE . 1. Every ...
Page xi
... relation between the co - ordinates of any straight Line 134 • 6 . An equation of the nth degree represents a curve of the nth class 136 7 . Equation of a Conic , touching the three sides of the triangle of reference . ib . 8 . Equation ...
... relation between the co - ordinates of any straight Line 134 • 6 . An equation of the nth degree represents a curve of the nth class 136 7 . Equation of a Conic , touching the three sides of the triangle of reference . ib . 8 . Equation ...
Page 1
... relation exists , which we proceed to investigate . If △ denote the area of the triangle of reference , a , B , v , the trilinear co - ordinates of any point , then aa + bB + cy = 2A . Let P be the given point , and first suppose it to ...
... relation exists , which we proceed to investigate . If △ denote the area of the triangle of reference , a , B , v , the trilinear co - ordinates of any point , then aa + 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- aa + bB + cy geneous in a , ẞ , y by multiplying each term by 24 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- aa + bB + cy geneous in a , ẞ , y by multiplying each term by 24 raised to a suitable power . Thus , the equation 1-2 AREA OF THE TRIANGLE OF ...
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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