American Journal of Mathematics, Volume 1Johns Hopkins University Press, 1878 The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics. |
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Common terms and phrases
a₁ algebraical angle atomicules atoms axes axis bending moment binary bonds coefficients conjugate conséquent coordinates corresponding covariant curve déduit degree denote deux développement diameter distance divisible égal equilibrium polygon espèce exemple expression facteurs FERMAT fonctions numériques formes linéaires formules function geometry given graph Hence infinite intersection invariant J. J. SYLVESTER k₁ l'équation l'on linear linear functions multiplication nombres premiers obtained P₁ parabola parallel partitions peut polygon précédent principal forms puissances Q²r quadratique quadric quantic quantities quelconque racines reciprocal represented résidus roots série de FIBONACCI séries sextic SIMON NEWCOMB substitution suivant suppose syzygies tangent theorem théorème theory tion triangle trilinear coordinates U₁ U₂ V₁ V₂ valence valeurs values variables vector
Popular passages
Page 350 - Without offering any hypothesis regarding the cause of this symmetrical grouping of atoms, it is sufficiently evident, from the examples just given, that such a tendency or law prevails, and that, no matter what the character of the uniting atoms may be, the combining power of the attracting element, if I may be allowed the term, is always satisfied by the same number of these atoms.
Page 131 - ... Moon's co-ordinates being developed in series of sines and cosines of angles which vary uniformly with the time, the coefficients of the several terms of these series will depend on the eccentricities of the orbits of the Sun and Moon, the inclination of the Moon's orbit, to the plane of the ecliptic, the ratio of the mean motions of the Sun and Moon, and the ratio of their mean distances from the Earth.
Page 271 - Upon this supposition of a positive curvature, the whole of geometry is far more complete and interesting; the principle of duality, instead of half breaking down over metric relations, applies to all propositions without exception. In fact, I do not mind confessing that I personally have often found relief from the dreary infinities of homaloidal space in the consoling hope that, after all, this other may be the true state of things.
Page 265 - Raume zu beweisen: und da die Frage, ob zwey von der dritten geschnittene Geraden, wenn die Summe der inneren Winkel nicht ~ 2/?, sich schneiden oder nicht? niemand auf der Erde ohne ein Axiom (wie Euclid das XI) aufzustellen, beantworten wird; die davon unabhängige Geometrie abzusondern; und eine auf die...
Page 384 - ... that the locus of the foot of the perpendicular from the focus on the normal is...
Page 265 - Begriffe, von eingebildeten und unendlich-kleinen Grossen gereinigt, anschaulich und logisch-streng darzustellen. II. In der Geometrie, die Begriffe der geraden Linie, der Ebene, des Winkels allgemein, der winkellosen Formen, und der Krummen, der verschiedenen Arten der Gleichheit ud gl. nicht nur scharf zu...
Page 51 - A group is defined by means of the laws of combination of its symbols : for the statement of these we may either (by the introduction of powers and products) diminish as much as may be the number of...
Page 352 - Applications of Grassmann's Extensive Algebra" Clifford wrote: I propose to communicate in a brief form some applications of Grassmann's theory which it seems unlikely that I shall find time to set forth at proper length, though I have waited long for it. Until recently I was unacquainted with the Ausdehnungslehre, and knew only so much of it as is contained in the author's geometrical papers in Crelle's Journal and in Hankel's Lectures on Complex Numbers.
Page 278 - Elementary Theorems Relating to the Geometry of a Space of Three Dimensions and of Uniform Positive Curvature in the Fourth Dimension," published in Borchardt's Journal, Bd.
Page 278 - The addition of a fourth dimension to space not only extends the actual properties of geometrical figures, but it also adds new properties which are often useful for the purposes of transformation or of proof. Thus it has recently been shown that in four dimensions a closed material shell could be turned inside out by simple flexure, without either stretching or tearing ; and that in such a space it is impossible to tie a knot.