An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
From inside the book
Results 6-10 of 16
Page 112
... focus . " This angle will be found , by reciprocating Euc . III . 20 , to be one - half of the angle sub- tended at the focus by the portion of the corresponding directrix intercepted between the two fixed tangents . Again , it is easy ...
... focus . " This angle will be found , by reciprocating Euc . III . 20 , to be one - half of the angle sub- tended at the focus by the portion of the corresponding directrix intercepted between the two fixed tangents . Again , it is easy ...
Page 113
... focus and directrix , and their latera - recta be 27 , 27 ′ , and another conic , having the same focus , be described so as to touch both of them , its latus - rectum will be and the envelope of its directrix will be a conic , having ...
... focus and directrix , and their latera - recta be 27 , 27 ′ , and another conic , having the same focus , be described so as to touch both of them , its latus - rectum will be and the envelope of its directrix will be a conic , having ...
Page 115
... focus is a circle , it will follow from the above reasoning that the family of conics obtained as above must , if ( f , g , h ) be a focus , be circles also . Applying the conditions for a circle investigated in Art . 14 , Chap . IV ...
... focus is a circle , it will follow from the above reasoning that the family of conics obtained as above must , if ( f , g , h ) be a focus , be circles also . Applying the conditions for a circle investigated in Art . 14 , Chap . IV ...
Page 116
... focus in that case . EXAMPLES . 1. HAVING given a focus and two points of a conic section , prove that the locus of the point of intersection of the tangents at these points will be two straight lines , passing through the focus , and ...
... focus in that case . EXAMPLES . 1. HAVING given a focus and two points of a conic section , prove that the locus of the point of intersection of the tangents at these points will be two straight lines , passing through the focus , and ...
Page 117
... focus , and which touch the three sides of the several triangles ABC , AEF , BFD , CDE , have their latera - recta equal . 8. Two conics are described with a common focus and their corresponding directrices fixed ; prove that , if the ...
... focus , and which touch the three sides of the several triangles ABC , AEF , BFD , CDE , have their latera - recta equal . 8. Two conics are described with a common focus and their corresponding directrices fixed ; prove that , if the ...
Other editions - View all
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