An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 31
... called the centre of the system . Two points , such as P , P ' , are said to be conjugate to one another . It is evident that each focus is conjugate to itself , and that the conjugate of the centre is at an infinite distance , and that ...
... called the centre of the system . Two points , such as P , P ' , are said to be conjugate to one another . It is evident that each focus is conjugate to itself , and that the conjugate of the centre is at an infinite distance , and that ...
Page 33
... called a conic section ; and then , before proceeding further with the consideration of the general equa- tion , shall investigate the nature of the curve corresponding to certain special forms of the equation . PROP . Every curve ...
... called a conic section ; and then , before proceeding further with the consideration of the general equa- tion , shall investigate the nature of the curve corresponding to certain special forms of the equation . PROP . Every curve ...
Page 48
... called vertices of the quadrangle , or of the system of circumscribing conics . It will be seen , from the preceding investigation , that any two conics which intersect in four real points can be reduced , by a proper choice of the ...
... called vertices of the quadrangle , or of the system of circumscribing conics . It will be seen , from the preceding investigation , that any two conics which intersect in four real points can be reduced , by a proper choice of the ...
Page 53
... called the line ww ' . 23. To find the equation of the line ww ' . Let the required equation be ka + mB + ny = 0 , we have then to determine m and n . Since , when ka = wß , ka = 1 7 , * This mode of expression is given by Salmon in his ...
... called the line ww ' . 23. To find the equation of the line ww ' . Let the required equation be ka + mB + ny = 0 , we have then to determine m and n . Since , when ka = wß , ka = 1 7 , * This mode of expression is given by Salmon in his ...
Page 59
... called the determinant of the given system of equations . We proceed to investigate the law of its formation . 3. First , suppose we have two equations , а ̧x1 + Ⴄ ̧ = 0 , b1x ̧ + b ̧x ̧ = 0 . Multiply the first by b ,, the second by ...
... called the determinant of the given system of equations . We proceed to investigate the law of its formation . 3. First , suppose we have two equations , а ̧x1 + Ⴄ ̧ = 0 , b1x ̧ + b ̧x ̧ = 0 . Multiply the first by b ,, the second by ...
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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