An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page x
... Locus of the intersection of two Tangents at right angles to one another . To find the magnitudes of the axes of the Conic 315 93 94 22 . To find the area of the Conic . Criterion to distinguish be- tween an Ellipse and an Hyperbola ...
... Locus of the intersection of two Tangents at right angles to one another . To find the magnitudes of the axes of the Conic 315 93 94 22 . To find the area of the Conic . Criterion to distinguish be- tween an Ellipse and an Hyperbola ...
Page xiii
... LOCUS OF THE CENTRE OF A SYSTEM OF CONICS WHICH SATISFY FOUR CONDITIONS . 11 . Four points given 12. Three points and a tangent 13 . 14 . 15 . Two points and two tangents . One point and three tangents . Four tangents · 165 • 167 168 ...
... LOCUS OF THE CENTRE OF A SYSTEM OF CONICS WHICH SATISFY FOUR CONDITIONS . 11 . Four points given 12. Three points and a tangent 13 . 14 . 15 . Two points and two tangents . One point and three tangents . Four tangents · 165 • 167 168 ...
Page xiv
... Locus of a vertex of a circumscribed triangle , whose other ver- tices move each along a fixed straight line 174 • • 176 20 . Trilinear co - ordinates of the Foci . 177 MISCELLANEOUS EXAMPLES 179 TRILINEAR CO - ORDINATES . CHAPTER I ...
... Locus of a vertex of a circumscribed triangle , whose other ver- tices move each along a fixed straight line 174 • • 176 20 . Trilinear co - ordinates of the Foci . 177 MISCELLANEOUS EXAMPLES 179 TRILINEAR CO - ORDINATES . CHAPTER I ...
Page 3
... locus may be represented , as in the ordinary system , by means of a relation between two co- ordinates , B and y for example , and this may be made homo- az + bB + cy geneous in a , B , y by multiplying each term by 2A " raised to a ...
... locus may be represented , as in the ordinary system , by means of a relation between two co- ordinates , B and y for example , and this may be made homo- az + bB + cy geneous in a , B , y by multiplying each term by 2A " raised to a ...
Page 10
... locus of a point which moves in such a manner , that the sum of the areas of the triangles PAQ , PAR is constant . Let AQ = q , AR = r , then the areas of the triangles PAQ , PAR will be respectively represented by 198 , dry , and the ...
... locus of a point which moves in such a manner , that the sum of the areas of the triangles PAQ , PAR is constant . Let AQ = q , AR = r , then the areas of the triangles PAQ , PAR will be respectively represented by 198 , dry , and the ...
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Common terms and phrases
angular points asymptotes ax+bB+cy b₁ b₂ C₁ Cambridge centre Chap co-ordinates coefficients College common tangents conic section Crown 8vo determinant directrix Edition equation Fcap find the equation fixed point follows four points given conic given point given straight line Hence imaginary investigated Let the equation line at infinity line joining locus meets the conic nine-point circle numerous Illustrations obtain opposite sides Owens College pair parabola Pascal's Theorem perpendicular point f points of intersection pole Professor prove radical axis ratios rectangular hyperbola represented respect right angles second degree shewn similar and similarly sin POS tangents tangents drawn term a,b,c theorem three straight lines tion touches the line triangle of reference Ua² ux² V'ca v'f+u'g+wh va² values Vb² vß² W. K. CLIFFORD W'ab whence wy² λα