Book contents
- Frontmatter
- ADVERTISEMENT
- Contents
- CLASSIFICATION
- 556 On Steiner's surface
- 557 On certain constructions for bicircular quartics
- 558 A geometrical interpretation of the equations obtained by equating to zero the resultant and the discriminants of two binary quantics
- 559 [Note on inversion]
- 560 [Addition to Lord Rayleigh' paper “On the numerical calculation of the roots of fluctuating functions”]
- 561 On the geometrical representation of Cauchy's theorems of rootlimitation
- 562 On a theorem in maxima and minima: addition [to Mr Walton's paper] by Professor Cayley
- 563 Note on the transformation of two simultaneous equations
- 564 On a theorem in elimination
- 565 Note on the Cartesian
- 566 On the transformation of the equation of a surface to a set of chief axes
- 567 On an identical equation connected with the theory of invariants
- 568 Note on the integrals cos x2 dx and sin x2 dx
- 569 On the cyclide
- 570 On the superlines of a quadric surface in five-dimensional space
- 571 A demonstration of Dupin's theorem
- 572 Theorem in regard to the Hessian of a quaternary function
- 573 Note on the (2, 2) correspondence of two variables
- 574 On Wronski' theorem
- 575 On a special quartic transformation of an elliptic function
- 576 Addition to Mr Walton's paper “On the ray-planes in biaxal crystals”
- 577 Note in illustration of certain general theorems obtained by Dr Lipschitz
- 578 A memoir on the transformation of elliptic functions
- 579 Address delivered by the President, Professor Cayley, on presenting the Gold Medal of the [Royal Astronomical] Society to Professor Simon Newcomb
- 580 On the number of distinct terms in a symmetrical or partially symmetrical determinant; with an addition
- 581 On a theorem in elliptic motion
- 582 Note on the Theory of Precession and Nutation
- 583 On spheroidal trigonometry
- 584 Addition to Prof. R. S. Ball's paper “Note on a transformation of Lagrange's equations of motion in generalised coordinates, which is convenient in Physical Astronomy”
- 585 A new theorem on the equilibrium of four forces acting on a solid body
- 586 On the mathematical theory of isomers
- 587 A Smith's Prize dissertation [1873]
- 588 Problem [on tetrahedra]
- 589 On residuation in regard to a cubic curve
- 590 Addition to Prof. Hall's paper “On the motion of a particle toward an attracting centre at which the force is infinite”
- 591 A Smith's Prize paper and dissertation [1874]; solutions and remarks
- 592 On the Mercator's projection of a skew hyperboloid of revolution
- 593 A Sheepshanks' problem (1866)
- 594 On a differential equation in the theory of elliptic functions
- 595 On a Senate-House problem
- 596 Note on a theorem of Jacobi's for the transformation of a double integral
- 597 On a differential equation in the theory of elliptic functions
- 598 Note on a process of integration
- 599 A Smith's Prize dissertation
- 600 Theorem on the n-th Roots of Unity
- 601 Note on the Cassinian
- 602 On the potentials of polygons and polyhedra
- 603 On the potential of the ellipse and the circle
- 604 Determination of the attraction of an ellipsoidal shell on an exterior point
- 605 Note on a point in the theory of attraction
- 606 On the expression of the coordinates of a point of a quartic curve as functions of a parameter
- 607 A memoir on prepotentials
- 608 [Extract form a] Report on Mathematical Tables
- 609 On the analytical forms called factions
- 610 On the analytical forms called Trees, with application to the theory of chemical combinations
- 611 Report on mathematical tables
- 612 Note sur une formule d'intégration indéfinie
- 613 On the group of points on a sextic curve with five double points
- 614 On a problem of projection
- 615 On the conic torus
- 616 A geometrical illustration of the cubic transformation in elliptic functions
- 617 On the scalene transformation of a plane curve
- 618 On the mechanical description of a Cartesian
- 619 On an algebraical operation
- 620 Correction of two numerical errors in Sohnke's paper respecting modular equations
- 621 On the number of the univalent radicals Cn H2n+1
- 622 On a system of equations connected with Malfatti's problem
- 623 On three-bar motion
- 624 On the bicursal sextic
- 625 On the condition for the existence of a surface cutting at right angles a given set of lines
- 626 On the general differential equation where X, Y are the same quartic functions of x, y respectively
- 627 Geometrical illustration of a theorem relating to an irrational function of an imaginary variable.
- 628 On the circular relation of Möbius
- 629 On the linear transformation of the integral
589 - On residuation in regard to a cubic curve
Published online by Cambridge University Press: 07 September 2011
- Frontmatter
- ADVERTISEMENT
- Contents
- CLASSIFICATION
- 556 On Steiner's surface
- 557 On certain constructions for bicircular quartics
- 558 A geometrical interpretation of the equations obtained by equating to zero the resultant and the discriminants of two binary quantics
- 559 [Note on inversion]
- 560 [Addition to Lord Rayleigh' paper “On the numerical calculation of the roots of fluctuating functions”]
- 561 On the geometrical representation of Cauchy's theorems of rootlimitation
- 562 On a theorem in maxima and minima: addition [to Mr Walton's paper] by Professor Cayley
- 563 Note on the transformation of two simultaneous equations
- 564 On a theorem in elimination
- 565 Note on the Cartesian
- 566 On the transformation of the equation of a surface to a set of chief axes
- 567 On an identical equation connected with the theory of invariants
- 568 Note on the integrals cos x2 dx and sin x2 dx
- 569 On the cyclide
- 570 On the superlines of a quadric surface in five-dimensional space
- 571 A demonstration of Dupin's theorem
- 572 Theorem in regard to the Hessian of a quaternary function
- 573 Note on the (2, 2) correspondence of two variables
- 574 On Wronski' theorem
- 575 On a special quartic transformation of an elliptic function
- 576 Addition to Mr Walton's paper “On the ray-planes in biaxal crystals”
- 577 Note in illustration of certain general theorems obtained by Dr Lipschitz
- 578 A memoir on the transformation of elliptic functions
- 579 Address delivered by the President, Professor Cayley, on presenting the Gold Medal of the [Royal Astronomical] Society to Professor Simon Newcomb
- 580 On the number of distinct terms in a symmetrical or partially symmetrical determinant; with an addition
- 581 On a theorem in elliptic motion
- 582 Note on the Theory of Precession and Nutation
- 583 On spheroidal trigonometry
- 584 Addition to Prof. R. S. Ball's paper “Note on a transformation of Lagrange's equations of motion in generalised coordinates, which is convenient in Physical Astronomy”
- 585 A new theorem on the equilibrium of four forces acting on a solid body
- 586 On the mathematical theory of isomers
- 587 A Smith's Prize dissertation [1873]
- 588 Problem [on tetrahedra]
- 589 On residuation in regard to a cubic curve
- 590 Addition to Prof. Hall's paper “On the motion of a particle toward an attracting centre at which the force is infinite”
- 591 A Smith's Prize paper and dissertation [1874]; solutions and remarks
- 592 On the Mercator's projection of a skew hyperboloid of revolution
- 593 A Sheepshanks' problem (1866)
- 594 On a differential equation in the theory of elliptic functions
- 595 On a Senate-House problem
- 596 Note on a theorem of Jacobi's for the transformation of a double integral
- 597 On a differential equation in the theory of elliptic functions
- 598 Note on a process of integration
- 599 A Smith's Prize dissertation
- 600 Theorem on the n-th Roots of Unity
- 601 Note on the Cassinian
- 602 On the potentials of polygons and polyhedra
- 603 On the potential of the ellipse and the circle
- 604 Determination of the attraction of an ellipsoidal shell on an exterior point
- 605 Note on a point in the theory of attraction
- 606 On the expression of the coordinates of a point of a quartic curve as functions of a parameter
- 607 A memoir on prepotentials
- 608 [Extract form a] Report on Mathematical Tables
- 609 On the analytical forms called factions
- 610 On the analytical forms called Trees, with application to the theory of chemical combinations
- 611 Report on mathematical tables
- 612 Note sur une formule d'intégration indéfinie
- 613 On the group of points on a sextic curve with five double points
- 614 On a problem of projection
- 615 On the conic torus
- 616 A geometrical illustration of the cubic transformation in elliptic functions
- 617 On the scalene transformation of a plane curve
- 618 On the mechanical description of a Cartesian
- 619 On an algebraical operation
- 620 Correction of two numerical errors in Sohnke's paper respecting modular equations
- 621 On the number of the univalent radicals Cn H2n+1
- 622 On a system of equations connected with Malfatti's problem
- 623 On three-bar motion
- 624 On the bicursal sextic
- 625 On the condition for the existence of a surface cutting at right angles a given set of lines
- 626 On the general differential equation where X, Y are the same quartic functions of x, y respectively
- 627 Geometrical illustration of a theorem relating to an irrational function of an imaginary variable.
- 628 On the circular relation of Möbius
- 629 On the linear transformation of the integral
Summary
The following investigation of Prof. Sylvester's theory of Residuation may be compared with that given in Salmon's Higher Plane Curves, 2nd Edition (1873), pp. 133–137:
If the intersections of a cubic curve Us with any other curve Vn are divided in any manner into two systems of points, then each of these systems is said to be the residue of the other; and, in like manner, if starting with a given system of points on a cubic curve we draw through them a curve of any order Vn, then the remaining intersections of this curve with the cubic constitute a residue of the original system of points.
If the number of points in the original system is = 3p, then the number of points in the residual system is = 3q; and if we again take the residue, and so on indefinitely, the number of points in each residue will be = 0 (Mod. 3); viz. we can never in this way arrive at a single point. But if the number of points in the original system be 3p ±1, then that in the residual system will be 3q ∓1; and we may in an infinity of different ways arrive at a residue consisting of a single point; or say at a “residual point,” viz. after an odd number of steps if the original number of points is = 3p -1, but after an even number of steps if the original number of points is =3p+l.
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- The Collected Mathematical Papers , pp. 211 - 214Publisher: Cambridge University PressPrint publication year: 2009First published in: 1896