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The collected mathematical papers of Arthur Cayley, Sc.D., F.R.S., late sadlerian professor of pure mathematics in the University of Cambridge (Vol. 12)

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fullscreen: The collected mathematical papers of Arthur Cayley, Sc.D., F.R.S., late sadlerian professor of pure mathematics in the University of Cambridge (Vol. 12)

Multivolume work

Persistent identifier:: 166358480X

Title:: Encyklopædie der Naturwissenschaften

Type of content:: Aufsatzsammlung

Year of publication:: 1879

Place of publication:: Breslau

Publisher of the original:: Verlag von Eduard Trewendt

Identifier (digital):: 166358480X

Language:: German

Editor:: Jaeger, Gustav; Kenngott, Johann Gustav Adolf

Document type:: Multivolume work

Volume

Persistent identifier:: 1663612013

Title:: Handbuch der Botanik

Scope:: VIII, 781 Seiten

Year of publication:: 1890

Place of publication:: Breslau

Publisher of the original:: Verlag von Eduard Trewendt

Identifier (digital):: 1663612013

Illustration:: Illustrationen

Signature of the source:: a 245(1,1,4)

Language:: German

Other Title:: 1. Abtheilung, 1. Theil: Handbuch der Botanik

Usage licence:: Public Domain Mark 1.0

Contributor:: Detmer, Wilhelm; Drude, Oscar

Editor:: Schenk, Joseph August; Ladenburg, Albert; Kenngott, Johann Gustav Adolf

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2019

Document type:: Volume

Collection:: Biology; Natural sciences

Chapter

Title:: [I.] Die fossilen Pflanzenreste von Prof. Dr. Schenk.

Write comment:: Zur weiteren Unterteilung wurden die Überschriften herangezogen.

Document type:: Multivolume work

Structure type:: Chapter

Chapter

Title:: Einleitung.

Document type:: Multivolume work

Structure type:: Chapter

Contents

Table of contents

The collected mathematical papers of Arthur Cayley, Sc.D., F.R.S., sadlerian professor of pure mathematics in the University of Cambridge
The collected mathematical papers of Arthur Cayley, Sc.D., F.R.S., late sadlerian professor of pure mathematics in the University of Cambridge (Vol. 12)
Cover
Title page
Title page
ADVERTISEMENT.
CONTENTS.
CLASSIFICATION.
799. ON CURVILINEAR COORDINATES.
800. NOTE ON THE STANDARD SOLUTIONS OF A SYSTEM OF LINEAR EQUATIONS.
801. ON SEMINVARIANTS.
802. NOTE ON CAPTAIN MACMAHON'S PAPER "ON THE DIFFERENTIAL EQUATION [...]"
803. ON MR ANGLIN'S FORMULA FOR THE SUCCESSIVE POWERS OF THE ROOT OF AN ALGEBRAICAL EQUATION.
804. ON THE ELLIPTIC-FUNCTION SOLUTION OF THE EQUATION x³+y³-1=0.
805. NOTE ON ABEL'S THEOREM.
806. DETERMINATION OF THE ORDER OF A SURFACE.
807. A PROOF OF WILSON'S THEOREM.
808. NOTE ON A FORM OF THE MODULAR EQUATION IN THE TRANSFORMATION OF THE THIRD ORDER.
809. SCHRÖTER'S CONSTRUCTION OF THE REGULAR PENTAGON.
810. NOTE ON A SYSTEM OF EQUATIONS.
811. ON THE LINEAR TRANSFORMATION OF THE THETA FUNCTIONS.
812. ON ARCHIMEDES' THEOREM FOR THE SURFACE OF A CYLINDER.
813. NOTE ON MR GRIFFITHS' PAPER "ON A DEDUCTION FROM THE ELLIPTIC-INTEGRAL FORMULA y=sin (A+B+C+...)".
814. ON DOUBLE ALGEBRA.
815. THE BINOMIAL EQUATION xp-1=0 ; QUINQUISECTION. SECOND PART.
816. ON THE BITANGENTS OF A PLANE QUARTIC.
817. ON THE SIXTEEN-NODAL QUARTIC SURFACE.
818. NOTE IN CONNEXION WITH THE HYPERELLIPTIC INTEGRALS OF THE FIRST ORDER.
819. ON TWO CASES OF THE QUADRIC TRANSFORMATION BETWEEN TWO PLANES.
820. ON A PROBLEM OF ANALYTICAL GEOMETRY.
821. ON THE GEOMETRICAL REPRESENTATION OF AN EQUATION BETWEEN TO VARIABLES.
822. ON ASSOCIATIVE IMAGINARIES.
823. ON THE GEOMETRICAL INTERPRETATION OF CERTAIN FORMULAE ON ELLIPTIC FUNCTIONS.
824. NOTE ON THE FORMULAE OF TRIGONOMETRY.
825. A MEMOIR ON THE ABELIAN AND THETA FUNCTIONS.
826. NOTE ON A PARTITION-SERIES.
827. ON THE NON EUCLIDIAN PLANE GEOMETRY.
828. A MEMOIR ON SEMINVARIANTS.
829. TABLES OF THE SYMMETRIC FUNCTIONS OF THE ROOTS, TO THE DEGREE 10 FOR THE FORM [...]
830. NON-UNITARY PARTITION TABLES.
831. SEMINVARIANTS TABLES.
832. NOTE ON AN APPARENT DIFFICULTY IN THE THEORY OF CURVES WHEN THE COORDINATES OF A POINT ARE GIVEN AS FUNCTIONS OF A VARIABLE PARAMETER.
833. ON A FORMULA IN ELLIPTIC FUNCTIONS.
834. ON THE ADDITION OF THE ELLIPTIC FUNCTIONS.
835. ON CARDAN'S SOLUTION OF A CUBIC EQUATION.
836. ON THE QUATERNION EQUATION qQ-Qq'=0.
837. ON THE SO-CALLED D'ALEMBERT CARNOT GEOMETRICAL PARADOX.
838. ON THE TWISTED CUBICS UPON A QUADRIC SURFACE.
839. ON THE MATRICAL EQUATIONS qQ-Qq'=0.
840. ON MASCHERONTS GEOMETRY OF THE COMPASS.
841. ON A DIFFERENTIAL OPERATOR.
842. ON THE VALUE OF tan (sin 0) - sin (tan 0).
843. ON THE QUADRIQUADRIC CURVE IN CONNEXION WITH THE THEORY OF ELLIPTIC FUNCTIONS.
844. ON A THEOREM RELATING TO SEMINVARIANTS.
845. ON THE ORTHOMORPHOSIS OF THE CIRCLE INTO THE PARABOLA.
846. A VERIFICATION IN REGARD TO THE LINEAR TRANSFORMATION ON THE THETA-FUNCTIONS.
847. ON THE THEORY OF SEMINVARIANTS.
848. ON THE TRANSFORMATION OF THE DOUBLE-THETA FUNCTIONS.
849. ON THE INVARIANTS OF A LINEAR DIFFERANTIAL EQUATIONS.
850. ON LINEAR DIFFERNTIAL EQUATIONS.
851. ON LINEAR DIFFERANTIAL EQUATIONS (THE THEORY OF DECOMPOSITION).
852. NOTE SUR LE MÉMOIRE DE M. PICARD "SUR LES INTÈGRALES DE DIFFÉRENTIELLES TOTALES ALGÉBRIQUES DE PREMIÈRE ESPÈCE."
853. NOTE ON A FORMULA FOR [...] WHEN n, i ARE VERY LARGE NUMBERS.
854. AN ALGEBRAICAL TRANSFORMATION.
855. SOLUTION OF (a, b, c, d)=(a², b², c², d²).
856. NOTE ON A CUBIC EQUATION.
857. ANALYTICAL GEOMETRICAL NOTE ON THE CONIC.
858. COMPARSION OF THE WEIERSTRASSIAN AND JACOBIAN ELLIPTIC FUNCTIONS.
859. ON THE COMPLEX OF LINES WICH MEET A UNICURSAL QUARTIC CURVE.
860. ON BRIOT AND BOUQUETS THEORY OF THE DIFFERENTIAL EQUATIONS [...]
861. NOTE ON A FORMULA RELATING TO THE ZERO-VALUE OF A THETA-FUNCTION.
862. NOTE ON THE THEORY OF LINEAR DIFFERNTIAL EQUATIONS.
863. NOTE ON THE THEORY OF LINEAR DIFFERENTIAL EQUATIONS.
864. ON RUDIO'S INVERSE CENTRO-SURFACE.
865. ON MULTIPLE ALGEBRA.
866. NOTE ON KIEPERTS L-EQUATIONS; IN THE TRANSFORMATION OF ELLIPTIC FUNCTIONS.
867. NOTE ON THE JACOBIAN SEXTIC EQUATION.
868. ON THE INTERSECTION OF CURVES.
869. ON THE TRANSFORMATION OF ELLIPTIC FUNCTIONS.
870. ON THE TRANSFORMATION OF ELLIPTIC FUNCTIONS (SEQUEL).
871. A CASE OF COMPLEX MULTUPLICATION WITH IMAGINARY MODULUS ARISING OUT OF THE CUBIC TRANSFORMATION IN ELLIPTIC FUNCTIONS.
872. ON THE FINITE NUMBER OF THE COVARIANTS OF A BINARY QUANTIC.
873. SYSTEM OF EQUATIONS FOR THREE CIRCLES WHICH CUT EACHT ODER AT GIVEN ANGLES.
874. NOTE ON THE LEGENDRIAN COEFFICIENTS OF THE SECOND KIND.
875. ON THE SYSTEM OF THREE CIRCLES WHICH CUT ECHT OTHER AT GIVEN ANGLES AND HAVE THEIRS VENTRES IN A LINE.
876. ON SYSTEMS OF RAYS.
877. NOTE ON THE TWO RELATIONS CONNECTING THE DISTANCES OF FOUR POINTS ON A CIRCLE.
878. NOTE ON THE ANHARMONIC RATIO EQUATION.
879. NOTE ON THE DIFFERENTIAL EQUATION [...].
880. NOTE ON THE RELATION BETWEEN THE DISTANCE OF FIVE POINTS IN SPACE.
881. ON HERMITE'S H-PRODUCT THEOREM.
882. A CORRESPONDENCE OF CONFOCAL CARTESIANS WITH THE BRIGHT LINES OF A HYPERBOLOID.
883. ANALYTICAL FORMULAE IN REGARD TO AN OCTAD OF POINTS.
884. NOTE SUR LES SUFACES MINIMA ET LE THÉORÈME DE JOACHIMSTHAL.
885. ON THE DIOPHANTINE RELATION. y²+y'²=SQUARE.
886. ON THE SURFACE WITH PLANE OR SPHERICAL CURVES OF CURVATURE.
887. ON THE THEORY OF GROUPS.
Cover

Full text

556 
[871 
871. 
A CASE OF COMPLEX MULTIPLICATION WITH IMAGINARY 
MODULUS ARISING OUT OF THE CUBIC TRANSFORMATION 
IN ELLIPTIC FUNCTIONS. 
[From the Proceedings of the London Mathematical Society, vol. xix. (1888), pp. 300, 301.] 
The case in question is referred to in my “Note on the Theory of Elliptic 
Integrals,” Math. Ann., t. xii. (1877), pp. 143—146, [657]; but I here work it out 
directly. 
y 1 + vu 2 (y + 2 u 3 ) x 2 5 
giving 
dy V v 
Vl — y 2 . 1 — v 8 y 2 V1 — X 2 . 1 
We thus have a case of complex multiplication if v 8 = u 8 , or say v = <yu, where 
7 8 = 1, or 7 denotes an eighth root of unity. Substituting in the modular equation, 
this becomes 
id (1 — y 4 ) + 2y u 2 (1 — fid) — 0, 
or, throwing out the factor u 2 and reducing, 
id — \u 2 (y 5 — 7) — y 6 = 0, 
U‘ 
7 
that is, 
| (y 4 — 1 + Vy 8 + 14y 4 + 1),

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