Book contents
- Frontmatter
- PREFATORY NOTE
- ARTHUR CAYLEY
- COUESES OF LECTURES DELIVERED BY PROFESSOR CAYLEY
- Contents
- CLASSIFICATION
- 486 Note on Dr. Glaisher's paper on a theorem in definite integration
- 487 On the quartic surfaces (*)(U, V, W)2 = 0
- 488 Note on a relation between two circles
- 489 On the porism of the in-and-circumscribed polygon, and the (2, 2) correspondence of points on a conic
- 490 On a problem of elimination
- 491 On the quartic surfaces (*)(U, V, W)2 = 0
- 492 Note on a system of algebraical equations
- 493 On evolutes and parallel curves
- 494 Example of a special discriminant
- 495 On the envelope of a certain quadric surface
- 496 Tables of the binary cubic forms for the negative determinants ≡ 0 (mod. 4) from –4 to –400; and ≡ 1 (mod. 4) from – 3 to – 99; and for five irregular negative determinants.
- 497 Note on the calculus of logic
- 498 On the inversion of a quadric surface
- 499 On the theory of the curve and torse
- 500 On a theorem relating to eight points on a conic
- 501 Review. Pineto's tables of logarithms
- 502 On the surfaces divisible into squares by their curves of curvature
- 503 On the surfaces each the locus of the vertex of a cone which passes through m given points and touches 6 – m given lines
- 504 On the mechanical description of certain sextic curves
- 505 On the surfaces divisible into squares by their curves of curvature
- 506 On the mechanical description of a cubic curve
- 507 On the mechanical description of certain quartic curves by a modified oval chuck
- 508 On geodesic lines, in particular those of a quadric surface
- 509 Plan of a curve-tracing apparatus
- 510 On bicursal curves
- 511 Addition to the memoir on geodesic lines, in particular those of a quadric surface
- 512 On a correspondence of points in relation to two tetrahedra
- 513 On a bicyclic chuck
- 514 On the problem of the in-and-circumscribed triangle
- 515 Sur les courbes aplaties
- 516 Sur une surface quartique aplatie
- 517 Sur les surfaces divisibles en carrés par leurs courbes de courbure et sur la théorie de Dupin
- 518 Sur la condition pour qu'une famille de surfaces données puisse faire partie d'un système orthogonal
- 519 On curvature and orthogonal surfaces
- 520 On the centro-surface of an ellipsoid
- 521 On Dr. Wiener's model of a cubic surface with 27 real lines; and on the construction of a double-sixer
- 522 Note on the theory of in variants
- 523 On the transformation of unicursal surfaces
- 524 On the deficiency of certain surfaces
- 525 An example of the higher transformation of a binary form
- 526 On a surface of the eighth order
- 527 On a theorem in covariants
- 528 On the non-Euclidian geometry
- 529 A “Smith's Prize” paper [1868]; solutions by Prof Cayley
- 530 Solution of a Senate-House problem
- 531 A “Smith's Prize” paper [1869]; solutions by Prof Cayley
- 532 Note on the integration of certain differential equations by series
- 533 On the binomial theorem, factorials, and derivations
- 534 A “Smith's Prize” paper [1870]; solutions by Prof Cayley
- 535 Note on the problem of envelopes
- 536 Note on Lagrange's demonstration of Taylor's theorem
- 537 Solutions of a Smith's Prize paper for 1871
- 538 Extract from a letter from Prof. Cayley to Mr. C. W. Merrifield
- 539 Further note on Lagrange's demonstration of Taylor's theorem
- 540 On a property of the torse circumscribed about two quadric surfaces
- 541 On the reciprocal of a certain equation of a conic
- 542 Further note on Taylor's theorem
- 543 On an identity in spherical trigonometry
- 544 On a penultimate quartic curve
- 545 On the theory of the singular solutions of differential equations of the first order
- 546 Theorems in relation to certain sign-symbols
- 547 On the representation of a spherical or other surface on a plane: a Smith's Prize dissertation
- 548 On Listing's theorem
- 549 Note on the maxima of certain factorial functions
- 550 Problem and hypothetical theorems in regard to two quadric surfaces
- 551 Two Smith's Prize dissertations [1872]
- 552 On a differential formula connected with the theory of confocal conics
- 553 Two Smith's Prize dissertations [1873]
- 554 An elliptic-transcendent identity
- 555 Notices of Communications to the British Association for the Advancement of Science
- NOTES AND REFERENCES
- SELECT SCIENTIFIC PUBLICATIONS OF THE CAMBRIDGE UNIVERSITY PRESS
534 - A “Smith's Prize” paper [1870]; solutions by Prof Cayley
Published online by Cambridge University Press: 03 May 2011
Book contents
- Frontmatter
- PREFATORY NOTE
- ARTHUR CAYLEY
- COUESES OF LECTURES DELIVERED BY PROFESSOR CAYLEY
- Contents
- CLASSIFICATION
- 486 Note on Dr. Glaisher's paper on a theorem in definite integration
- 487 On the quartic surfaces (*)(U, V, W)2 = 0
- 488 Note on a relation between two circles
- 489 On the porism of the in-and-circumscribed polygon, and the (2, 2) correspondence of points on a conic
- 490 On a problem of elimination
- 491 On the quartic surfaces (*)(U, V, W)2 = 0
- 492 Note on a system of algebraical equations
- 493 On evolutes and parallel curves
- 494 Example of a special discriminant
- 495 On the envelope of a certain quadric surface
- 496 Tables of the binary cubic forms for the negative determinants ≡ 0 (mod. 4) from –4 to –400; and ≡ 1 (mod. 4) from – 3 to – 99; and for five irregular negative determinants.
- 497 Note on the calculus of logic
- 498 On the inversion of a quadric surface
- 499 On the theory of the curve and torse
- 500 On a theorem relating to eight points on a conic
- 501 Review. Pineto's tables of logarithms
- 502 On the surfaces divisible into squares by their curves of curvature
- 503 On the surfaces each the locus of the vertex of a cone which passes through m given points and touches 6 – m given lines
- 504 On the mechanical description of certain sextic curves
- 505 On the surfaces divisible into squares by their curves of curvature
- 506 On the mechanical description of a cubic curve
- 507 On the mechanical description of certain quartic curves by a modified oval chuck
- 508 On geodesic lines, in particular those of a quadric surface
- 509 Plan of a curve-tracing apparatus
- 510 On bicursal curves
- 511 Addition to the memoir on geodesic lines, in particular those of a quadric surface
- 512 On a correspondence of points in relation to two tetrahedra
- 513 On a bicyclic chuck
- 514 On the problem of the in-and-circumscribed triangle
- 515 Sur les courbes aplaties
- 516 Sur une surface quartique aplatie
- 517 Sur les surfaces divisibles en carrés par leurs courbes de courbure et sur la théorie de Dupin
- 518 Sur la condition pour qu'une famille de surfaces données puisse faire partie d'un système orthogonal
- 519 On curvature and orthogonal surfaces
- 520 On the centro-surface of an ellipsoid
- 521 On Dr. Wiener's model of a cubic surface with 27 real lines; and on the construction of a double-sixer
- 522 Note on the theory of in variants
- 523 On the transformation of unicursal surfaces
- 524 On the deficiency of certain surfaces
- 525 An example of the higher transformation of a binary form
- 526 On a surface of the eighth order
- 527 On a theorem in covariants
- 528 On the non-Euclidian geometry
- 529 A “Smith's Prize” paper [1868]; solutions by Prof Cayley
- 530 Solution of a Senate-House problem
- 531 A “Smith's Prize” paper [1869]; solutions by Prof Cayley
- 532 Note on the integration of certain differential equations by series
- 533 On the binomial theorem, factorials, and derivations
- 534 A “Smith's Prize” paper [1870]; solutions by Prof Cayley
- 535 Note on the problem of envelopes
- 536 Note on Lagrange's demonstration of Taylor's theorem
- 537 Solutions of a Smith's Prize paper for 1871
- 538 Extract from a letter from Prof. Cayley to Mr. C. W. Merrifield
- 539 Further note on Lagrange's demonstration of Taylor's theorem
- 540 On a property of the torse circumscribed about two quadric surfaces
- 541 On the reciprocal of a certain equation of a conic
- 542 Further note on Taylor's theorem
- 543 On an identity in spherical trigonometry
- 544 On a penultimate quartic curve
- 545 On the theory of the singular solutions of differential equations of the first order
- 546 Theorems in relation to certain sign-symbols
- 547 On the representation of a spherical or other surface on a plane: a Smith's Prize dissertation
- 548 On Listing's theorem
- 549 Note on the maxima of certain factorial functions
- 550 Problem and hypothetical theorems in regard to two quadric surfaces
- 551 Two Smith's Prize dissertations [1872]
- 552 On a differential formula connected with the theory of confocal conics
- 553 Two Smith's Prize dissertations [1873]
- 554 An elliptic-transcendent identity
- 555 Notices of Communications to the British Association for the Advancement of Science
- NOTES AND REFERENCES
- SELECT SCIENTIFIC PUBLICATIONS OF THE CAMBRIDGE UNIVERSITY PRESS
Summary
1. Mention what form, of given relation ϕ (a, b, c, …) = 0 between the roots of a given equation will in general serve for the rational determination of the roots; explain the case of failure; and state what information as to the roots is furnished by a given relation not of the form in question.
In the given relation, φ (a, b, c,…) must be a wholly unsymmetrical function of the roots; that is, a function altered by any permutation whatever of the roots; or, what is the same thing, by any interchange whatever of two roots.
For this being so, if α, β, γ, … be the values of the roots, then for some one order, say α, β, γ, …, of these values the given relation φ (a, b, c,…) = 0 will be satisfied by writing therein a = α, b = β, c = γ, &c.; but it will in general be satisfied for this order only, and not for any other order whatever (viz. it will not be satisfied by writing a = β, b = α, c=γ, &c, or by any other such system).
- Type
- Chapter
- Information
- The Collected Mathematical Papers , pp. 474 - 490Publisher: Cambridge University PressPrint publication year: 2009First published in: 1895