An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page xi
... EXAMPLES 128 ib . CHAPTER VII . TANGENTIAL CO - ORDINATES . 1 . 2 . Definition of the Tangential Co - ordinates of a Straight Line . 131 Interpretation of the Negative Sign . Equations of certain points . · ib . 3 . General Equation of ...
... EXAMPLES 128 ib . CHAPTER VII . TANGENTIAL CO - ORDINATES . 1 . 2 . Definition of the Tangential Co - ordinates of a Straight Line . 131 Interpretation of the Negative Sign . Equations of certain points . · ib . 3 . General Equation of ...
Page xii
... EXAMPLES Tangential rectangular Co - ordinates 15. Tangential polar Co - ordinates 1-3 . 4-7 . 8 . EXAMPLES 141 142 144 145 CHAPTER VIII . ON THE INTERSECTION OF CONICS , AND ON PROJECTIONS . Any two conics intersect in four points ...
... EXAMPLES Tangential rectangular Co - ordinates 15. Tangential polar Co - ordinates 1-3 . 4-7 . 8 . EXAMPLES 141 142 144 145 CHAPTER VIII . ON THE INTERSECTION OF CONICS , AND ON PROJECTIONS . Any two conics intersect in four points ...
Page xiii
... EXAMPLES ib . 159 • ib . 160 CHAPTER IX . MISCELLANEOUS PROPOSITIONS . ON THE DETERMINATION OF A CONIC FROM FIVE GIVEN GEOMETRICAL CONDITIONS . 2 . If five points be given , one conic only can be drawn 162 • 3 . · If four points and one ...
... EXAMPLES ib . 159 • ib . 160 CHAPTER IX . MISCELLANEOUS PROPOSITIONS . ON THE DETERMINATION OF A CONIC FROM FIVE GIVEN GEOMETRICAL CONDITIONS . 2 . If five points be given , one conic only can be drawn 162 • 3 . · If four points and one ...
Page xiv
... vertex of a circumscribed triangle , whose other ver- tices move each along a fixed straight line Trilinear co - ordinates of the Foci • · 176 177 MISCELLANEOUS EXAMPLES 179 AGE 171 173 171 176 177 179 TRILINEAR CO - xiv CONTENTS .
... vertex of a circumscribed triangle , whose other ver- tices move each along a fixed straight line Trilinear co - ordinates of the Foci • · 176 177 MISCELLANEOUS EXAMPLES 179 AGE 171 173 171 176 177 179 TRILINEAR CO - xiv CONTENTS .
Page 3
... 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 REFERENCE . 3.
... 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 REFERENCE . 3.
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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