An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page xiv
... , whose other ver- • 174 20 . tices move each along a fixed straight line Trilinear co - ordinates of the Foci . · • 176 • · 177 MISCELLANEOUS EXAMPLES 179 TRILINEAR CO - ORDINATES . CHAPTER I. TRILINEAR CO - xiv CONTENTS .
... , whose other ver- • 174 20 . tices move each along a fixed straight line Trilinear co - ordinates of the Foci . · • 176 • · 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 qß , ry , 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 qß , ry , 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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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