An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 111
... auxiliary circle lies within , without , or upon , that to be reciprocated . This agrees with what has been already shewn , Art . 9 . Let 2a , 2b , be the axes of the conic , 27 its latus - rectum , e its eccentricity . To determine ...
... auxiliary circle lies within , without , or upon , that to be reciprocated . This agrees with what has been already shewn , Art . 9 . Let 2a , 2b , be the axes of the conic , 27 its latus - rectum , e its eccentricity . To determine ...
Page 112
... auxiliary circle affects the absolute , but not the rela- tive , magnitudes , or positions of the various lines in the reci- procal figure . As our theorems are , for the most part , inde- pendent of absolute magnitude , we may ...
... auxiliary circle affects the absolute , but not the rela- tive , magnitudes , or positions of the various lines in the reci- procal figure . As our theorems are , for the most part , inde- pendent of absolute magnitude , we may ...
Page 114
... auxiliary circle ) , and the tangent at Fig . 20 . that point , is equal to the angle between the radius vector of , and tangent at , the corresponding point of the reciprocal • curve . For , if P be the given point , PY the tangent at ...
... auxiliary circle ) , and the tangent at Fig . 20 . that point , is equal to the angle between the radius vector of , and tangent at , the corresponding point of the reciprocal • curve . For , if P be the given point , PY the tangent at ...
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Common terms and phrases
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