An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page xiv
... 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. TRILINEAR CO - xiv CONTENTS .
... 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. TRILINEAR CO - xiv CONTENTS .
Page 10
... 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 area of QAR by A. gr bc ...
... 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 area of QAR by A. gr bc ...
Page 57
... move along a given straight line , the other will describe a conic about the triangle . Hence prove that the circle , which passes through the points of intersection of three tangents to a parabola , passes also through the focus , 11 ...
... move along a given straight line , the other will describe a conic about the triangle . Hence prove that the circle , which passes through the points of intersection of three tangents to a parabola , passes also through the focus , 11 ...
Page 104
... moving point , may be deduced those of another curve which is always touched by the polar of this moving point with regard to a fixed conic . The theory is especially valuable when the conic , with respect to which the poles and polars ...
... moving point , may be deduced those of another curve which is always touched by the polar of this moving point with regard to a fixed conic . The theory is especially valuable when the conic , with respect to which the poles and polars ...
Page 105
... move in any manner whatever , its polar will move in a manner dependent upon the motion of the point , and the curve which the polar always touches ( its envelope , as it is called ) will have certain definite relations to the path ...
... move in any manner whatever , its polar will move in a manner dependent upon the motion of the point , and the curve which the polar always touches ( its envelope , as it is called ) will have certain definite relations to the path ...
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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