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(1870 - 1883) (Volume 3)

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Bibliographic data

fullscreen: (1870 - 1883) (Volume 3)

Volume

Persistent identifier:: 89098929X

Author:: Crelle, August L.

Title:: Sammlung mathematischer Aufsätze und Bemerkungen

Sub title:: Mit 5 Steintafeln

Scope:: 1 Online-Ressource (VI, 309 Seiten, 5 Falttafeln)

Year of publication:: 1822

Place of publication:: Berlin

Identifier (digital):: 89098929X

Illustration:: Diagramme

Language:: German

Publisher of the original:: Mauersche Buchhandlung

Usage licence:: Public Domain Mark 1.0

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2017

Document type:: Volume

Collection:: Mathematics

Chapter

Title:: 9. Bemerkungen über einige Lehrsätze der Elementar-Geometrie.

Document type:: Volume

Structure type:: Chapter

The collected mathematical papers
(1870 - 1883) (Volume 3)
Cover
Title page
Title page
PREFATORY NOTE.
TABLE OF CONTENTS
1. ON THE ROTATION OF A RIGID BODY.
2. ON RECENT DISCOVERIES IN MECHANICAL CONVERSION OF MOTION.
3. ON THE PLAGIOGRAPH aliter THE SKEW PANTIGRAPH.
4. ON A LADY'S FAN, ON PARALLEL MOTION, AND ON AN ORTHOGONAL WEB OF JOINTED RODS.
5. NOTE ON SPHERICAL HARMONICS.
6. SUR LES INVARIANTS FONDAMENTAUX DE LA FORME BINAIRE DU HUITIÈME DEGRÉ.
7. SUR UNE MÉTHODE ALGEBRIQUE POUR OBTENIR L’ENSEMBLE DES INVARIANTS ET DES COVARIANTS FONDAMENTAUX D’UNE FORME BINAIRE ET D’UNE COMBINAISON QUELCONQUE DE FORMES BINAIRES.
8. SUR LE VRAI NOMBRE DES COVARIANTS ÉLÉMENTAIRES D'UN SYSTÈME DE DEUX FORMES BIQUADRATIQUES BINAIRES.
(9) THÉORIE POUR TROUVER LE NOMBRE DES COVARIANTS ET DES CONTREVARIANTS D'ORDRE ET DE DEGRÉ DONNÉS LINÉAIREMENT INDÉPENDANTS D'UN SYSTÈME QUELCONQUE DE FORMES SIMULTANÉES CONTENANT UN NOMBRE QUELCONQUE DE VARIABLES.
10. ADDRESS ON COMMEMORATION DAY AT JOHNS HOPKINS UNIVERSITY 22 FEBRUARY, 1877.
11. ON A GENERALIZATION OF TAYLOR'S THEOREM.
12. SUR LES INVARIANTS.
13. ON THE LIMITS TO THE ORDER AND DEGREE OF THE FUNDAMENTAL INVARIANTS OF BINARY QUANTICS.
14. CHEMISTRY AND ALGEBRA.
15. SUR LA LOI DE RÉCIPROCITÉ POUR LES INVARIANTS ET COVARIANTS DES QUANTICS BINAIRES.
16. SUR LA THÉORIE DES FORMES ASSOCIÉES DE MM. CLEBSCH ET GORDAN.
17. DÉTERMINATION D'UNE LIMITE SUPÉRIEURE AU NOMBRE TOTAL DES INVARIANTS ET COVARIANTS IRRÉDUCTIBLES DES FORMES BINAIRES.
18. PROOF OF THE HITHERTO UNDEMONSTRATED FUNDAMENTAL THEOREM OF INVARIANTS.
19. SUR LES COVARIANTS FONDAMENTAUX D’UN SYSTÈME CUBO-BIQUADRATIQUE BINAIRE.
20. SUR LE VRAI NOMBRE DES FORMES IRRÉDUCTIBLES DU SYSTÈME CUBO-BIQUADRATIQUE.
21. DÉTERMINATION DU NOMBRE EXACT DES COYARIANTS IRRÉDUCTIBLES DU SYSTÈME CUBO-BIQUADRATIQUE BINAIRE.
22. SUR LES COVARIANTS IRRÉDUCTIBLES DU QUANTIC DU SEPTIÈME ORDRE.
23. SUR LA FORME BINAIRE DU SEPTIÈME ORDRE.
24. ON AN APPLICATION OF THE NEW ATOMIC THEORY TO THE GRAPHICAL REPRESENTATION OF THE INVARIANTS AND COVARIANTS OF BINARY QUANTICS - WITH THREE APPENDICES.
25. NOTE ON THE THEOREM CONTAINED IN PROFESSOR LIPSCHITZ’S PAPER.
26. A SYNOPTICAL TABLE OF THE IRREDUCIBLE INVARIANTS AND COVARIANTS TO A BINARY QUINTIC, WITH A SCHOLIUM ON A THEOREM IN CONDITIONAL HYPERDETERMINANTS.
27. SUR LES ACTIONS MUTUELLES DES FORMES INVARIANTIVES DÉRIVÉES.
28. ON A RULE FOR ABBREVIATING THE CALCULATION OF THE NUMBER OF IN- OR CO-VARIANTS OF A GIVEN ORDER AND WEIGHT IN THE COEFFICIENTS OF A BINARY QUANTIC OF A GIVEN DEGREE.
29. NOTE ON CONTINUANTS.
30. SUR UNE PROPRIÉTÉ ARITHMÉTIQUE D'UNE CERTAINE SÉRIE DE NOMBRES ENTIERS.
31. SUR LA VALEUR MOYENNE DES COEFFICIENTS DANS LE DÉVELOPPEMENT D’UN DÉTERMINANT GAUCHE OU SYMÉTRIQUE D’UN ORDRE INFINIMENT GRAND ET SUR LES DÉTERMINANTS DOUBLEMENT GAUCHES.
32. TABLE DES NOMBRES DE DÉRIVÉES INVARIANTIVES D’ORDRE ET DE DEGRÉ DONNÉS, APPARTENANT À LA FORME BINAIRE DU DIXIÉME ORDRE.
33. SUR LA VALEUR MOYENNE DES COEFFICIENTS NUMÉRIQUES DANS UN DÉTERMINANT GAUCHE D'UN ORDRE INFINIMENT GRAND.
34. SUR LE VRAI NOMBRE DES COVARIANTS FONDAMENTAUX D’UN SYSTÈME DE DEUX CUBIQUES.
35. NOTE ON AN EQUATION IN FINITE DIFFERENCES.
36. NOTE ON DETERMINANTS AND DUADIC DISYNTHEMES.
37. ON THE COMPLETE SYSTEM OF THE "GRUNDFORMEN" OF THE BINARY QUANTIC OF THE NINTH ORDER.
38. TABLES OF THE GENERATING FUNCTIONS AND GROUNDFORMS FOR THE BINARY QUANTICS OF THE FIRST TEN ORDERS.
39. ON CERTAIN TERNARY CUBIC-FORM EQUATIONS.
40. TABLES OF THE GENERATING FUNCTIONS AND GROUNDFORMS FOR SIMULTANEOUS BINARY QUANTICS OF THE FIRST FOUR ORDERS, TAKEN TWO AND TWO TOGETHER.
41. NOTE SUR UNE PROPRIÉTÉ DES ÉQUATIONS DONT TOUTES LES RACINES SONT RÉELLES.
42. ON THE THEOREM CONNECTED WITH NEWTON’S RULE FOR THE DISCOVERY OF IMAGINARY ROOTS OF EQUATIONS.
43. ON THE EXACT RELATION WHICH RESULTANTS AND DISCRIMINANTS BEAR TO THE PRODUCT OF DIFFERENCES OF ROOTS OF EQUATIONS.
44. SUR LES DIVISEURS DES FONCTIONS CYCLOTOMIQUES.
45. SUR LA LOI DE RÉCIPROCITÉ DANS LA THÉORIE DES NOMBRES.
46. SUR LES ÉQUATIONS À 3 ET À 4 PÉRIODES DES RACINES DE L'UNITÉ.
47. ON A POINT IN THE THEORY OF VULGAR FRACTIONS.
48. INSTANTANEOUS PROOF OF A THEOREM OF LAGRANGE ON THE DIVISORS OF THE FORM Ax² + By² + Cz², WITH A POSTSCRIPT ON THE DIVISORS OF THE FUNCTIONS WHICH MULTISECT THE PRIMITIVE ROOTS OF UNITY.
49. SUR L'ENTRELACEMENT D’UNE FONCTION PAR RAPPORT À UNE AUTRE.
50. PREUVE INSTANTANÉE D’APRÈS LA MÉTHODE DE FOURIER, DE LA RÉALITÉ DES RACINES DE L’ÉQUATION SÉCULAIRE.
51. SUR UN DÉTERMINANT SYMÉTRIQUE QUI COMPREND COMME CAS PARTICULIER LA PREMIÈRE PARTIE DE L’ÉQUATION SÉCULAIRE.
52. SUR LES DÉTERMINANTS COMPOSÉS.
53. ON THE TRIANGLES IN- AND EX-SCRIBABLE TO A GENERAL CUBIC CURVE.
54. ON THE RESULTANT OF TWO CONGRUENCES.
55. ON THE PREROGATIVE OF A TERNARY DENOMINATIONAL SYSTEM OF COINAGE.
56. ON THE MULTISECTION OF THE ROOTS OF UNITY.
57. SUR LES DIVISEURS DES FONCTIONS DES PÉRIODES DES RACINES PRIMITIVES DE L’UNITÉ. .
58. SUR LES COVARIANTS IRRÉDUCTIBLES DU QUANTIC BINAIRE DU HUITIÈME ORDRE.
59. TABLES OF THE GENERATING FUNCTIONS AND GROUNDFORMS OF THE BINARY DUODECIMIC, WITH SOME GENERAL REMARKS, AND TABLES OF THE IRREDUCIBLE SYZYGIES OF CERTAIN QUANTICS.
60. A DEMONSTRATION OF THE IMPOSSIBILITY OF THE BINARY OCTAVIO POSSESSING ANY GROUNDFORM OF DEG-ORDER 10.4.
61. ON TCHEBYCHEFF'S THEORY OF THE TOTALITY OF THE PRIME NUMBERS COMPRISED WITHIN GIVEN LIMITS.
62. ON THE SOLUTION OF A CERTAIN CLASS OF DIFFERENCE OR DIFFERENTIAL EQUATIONS.
63. NOTE ON THE THEORY OF SIMULTANEOUS LINEAR DIFFERENTIAL OR DIFFERENCE EQUATIONS WITH CONSTANT COEFFICIENTS.
64. NOTE ON MECHANICAL INVOLUTION.
65. SUR LES PUISSANCES ET LES RACINES DE SUBSTITUTIONS LINÉAIRES.
66. SUR LES RACINES DES MATRICES UNITAIRES.
67. ON SUBINVARIANTS, THAT IS, SEMI-INVARIANTS TO BINARY QUANTICS OF AN UNLIMITED ORDER.
68. TABLES OF GENERATING FUNCTIONS, REDUCED AND REPRESENTATIVE, FOR CERTAIN TERNARY SYSTEMS OF BINARV FORMS.
69. ON A CERTAIN INTEGRABLE CLASS OF DIFFERENTIAL AND FINITE DIFFERENCE EQUATIONS.
70. ON A QUESTION IN PARTITIONS.
71. ON A GEOMETRICAL PROOF OF A THEOREM IN NUMBERS.
72. ON THE GEOMETRICAL FORMS CALLED TREES.
73. ON THE 8-SQUARE IMAGINARIES.
74. ON A GEOMETRICAL TREATMENT OF A THEOREM IN NUMBERS.
75. ON THE PROPERTIES OF A SPLIT MATRIX.

75. ON THE PROPERTIES OF A SPLIT MATRIX.
76. A WORD ON NONIONS.
77. ON MECHANICAL INVOLUTION.
78. ON CROCCHI’S THEOREM.
79. ON CERTAIN SUCCESSIONS OF INTEGERS THAT CANNOT BE INDEFINITELY CONTINUED.
80. ON THE FUNDAMENTAL THEOREM IN THE NEW METHOD OF PARTITIONS.
81. NOTE ON THE PAPER OF MR DURFEE'S.
82. ON DR F. FRANKLIN'S PROOF OF EULER'S THEOREM CONCERNING THE FORM OF THE INFINITE PRODUCT (1 - x) (1 - x²) (1 - x³)....
83. ON THE USE OF CROSS-GRATINGS TO OBTAIN CERTAIN DEVELOPMENTS CONNECTED WITH THE THEORY OF ELLIPTIC FUNCTIONS.
84. ON THE NUMBER OF FRACTIONS IN THEIR LOWEST TERMS WHOSE NUMERATORS AND DENOMINATORS ARE LIMITED NOT TO EXCEED A CERTAIN NUMBER.
85. PROOF OF A WELL-KNOWN DEVELOPMENT OF A CONTINUED PRODUCT IN A SERIES.
86. ON A NEW THEOREM IN PARTITIONS.
87. NOTE ON THE GRAPHICAL METHOD IN PARTITIONS.
88. AN INSTANTANEOUS GRAPHICAL PROOF OF EULER'S THEOREM ON THE PARTITIONS OF PENTAGONAL AND NON-PENTAGONAL NUMBERS.
89. ON FAREY SERIES.
Cover

Full text

'h [B 
V PQ. PR 
a with pr 
each other 
'raph, so is 
3o not let 
the limbo 
;ely indeed 
o subserve 
Philistine 
>f the four 
¡■ate points, 
lateral formed 
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node is seen 
! figure in its 
[led kite-form, 
did not quite 
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paper inserted 
ity established 
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osed from one 
e are indebted 
iree-bar sextic 
no other such 
Mathematical 
illy little more 
'ollege), to the 
ar societies on 
rently founded 
t, are destined 
er young, ever 
awhile, in the 
ience, a young 
f a movement 
i where, in the 
to reflect some 
gine the bitter 
se, “the bigots 
low not what 
3] On the Plagiograph aliter the Shew Pantigraph 33 
say r, is attached to the end of a radius so centred and of such a length that 
the path of r is a circle which, geometrically completed, would pass through 
p, the remaining conjugate point q will be forced to describe a straight line 
perpendicular to the line joining the two fixed points—so by means of our 
Quadruplane, when P is fixed and R made to move in the arc of a circle 
passing through P, the point Q may be made to describe a straight line 
having any desired obliquity to the line of centres, the amount of such obliquity 
depending on the magnitude of the supplemental equal angles P, Q, R, S. 
Thus the Plagiograph (and in the first instance Mr Kempe’s notice of the 
homceographic commutability of the lengths of the connecting rod and the 
radial bars in ordinary three-bar motion) has led by a devious path to the 
construction of a three-piece-work giving the most general and available 
solution of the problem of exact parallel motion that has been discovered 
or that can exist—I say the most available, for it is evident, in general, that 
piece-work must possess the advantage of greater firmness and steadiness 
from the more equal distribution of its strain over ordinary link-work. 
The Peaucellier and Hart cells, duly mounted, afford the means by obvious 
methods of adjustment to cut straight lines at any distance from either of 
the fixed centres, but confined to lying perpendicular to the line of centres; 
whereas the Quadruplane puts it into our power with one and the same 
instrument affected with simple means of adjustment to make straight cuts 
(and, if desired, two parallel ones simultaneously) in all directions as well 
as at all distances in the plane of motion. So again the Plagiograph enables 
us to apply the principle of angular repetition (as, for instance, in making an 
ellipse with dimensions either fixed or varying at will, successively turn its 
axis to all points of the compass) to produce designs of complicated and 
captivating symmetry from any simple pattern or natural form, such as a 
flower or sprig; and as the head of a house at Oxford in the good old port- 
wine days was heard to complain about the electro-magnetic machine, that 
“he feared it would place a new weapon in the hands of the incendiary” (the 
power of Swing being then rampant in the land), so, but with better reason 
and upon the highest authority, it maybe predicted that this simple invention 
will be found to place a new and powerful experimentative and executory 
implement in the hand of the engine-turner, the pattern-designer, and the 
architectural decorator. 
parsimonious 
i appropriating 
idem Aristotle, 
at Berlin! If 
land a frantic 
funds on mere 
P.S.—I rejoice to be able to state that the Institute of France has quite 
recently adjudged its great mechanical prize, the “Prix Monty on,” to Col. 
Peaucellier for his discovery of an exact parallel motion when a lieutenant 
in 1864. The first practical application of this discovery, made by Mr Prim 
under the sanction of Dr Percy, may be seen daity at work in the Ventilating 
3 
s. HI.

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