An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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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 , try , and the area of QAR by qr bc A ...
... 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 , try , and the area of QAR by qr bc A ...
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 ...
... 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 ...
Page 98
... 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 99
... 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 ...
Page 100
... move along E , its polar will envelope L. In other words , I may be generated from E , as E was from L. In this consists the reciprocity of the curves . The process of generating E from L , or L from E , is called reciprocating L or E ...
... move along E , its polar will envelope L. In other words , I may be generated from E , as E was from L. In this consists the reciprocity of the curves . The process of generating E from L , or L from E , is called reciprocating L or E ...
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a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα