Julius Plückers gesammelte wissenschaftliche Abhandlungen in zwei Bänden: Mathematische Abhandlungen

Plücker, Julius; Schoenflies, Arthur

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Multivolume work

Persistent identifier:: 870649760

Author:: Abel, Niels Henrik

Title:: Œuvres complètes

Edition title:: Nouvelle édition

Year of publication:: 1881

Place of publication:: Christiania

Identifier (digital):: 870649760

Language:: French

Publisher of the original:: Imprimerie de Grøndahl & Søn

Translator:: Sylow, Ludwig; Lie, Sophus

Document type:: Multivolume work

Volume

Persistent identifier:: 870653059

Author:: Abel, Niels Henrik

Title:: Contenant les mémoires

Scope:: VIII, 621 Seiten

Edition title:: Nouvelle édition

Year of publication:: 1881

Place of publication:: Christiania

Identifier (digital):: 870653059

Signature of the source:: Mr.I 57(1)

Language:: French

Publisher of the original:: Imprimerie de Grøndahl & Søn

Usage licence:: Public Domain Mark 1.0

Translator:: Sylow, Ludwig; Lie, Sophus

Document type:: Volume

Collection:: Mathematics

Chapter

Title:: XVI. RECHERCHES SUR LES FONCTIONS ELLIPTIQUES.

Document type:: Multivolume work

Structure type:: Chapter

Section

Title:: § VI. Expressions diverses des fonctions [...]([...]), [...]([...]). F([...]).

Document type:: Multivolume work

Structure type:: Section

Fundamental Views regarding Mechanics. (Philosophical Transactions of the Royal Society of London, Bd. 156, S. 361—380.1866.) Being encouraged by the friendly interest expressed by English geometricians, I have resumed my former researches, which have been entirely abandoned by me since 1846. While the details had escaped from my memory, two leading questions have remained dormant in my mind. The first question was to introduce right lines as elements of space, instead of points and planes, hitherto employed; the second question to connect, in mechanics, translator}' and rotatory movements with each other by a principle in geometry analogous to that of reciprocity. I proposed a solution of the first question in the geo metrical paper presented to the Royal Society. I met a solution of the second question, which in vain I sought for in Poiusot’s inge nious theory of coupled forces, by pursuing the geometrical way. The indications regarding complexes of forces, given at the end of the „Additional Notes“, involve it. I now take the liberty of presenting a new paper, intended to give to these indications the developments they demand, reserving for another communication a succinct abstract of the curious properties of complexes of right lines represented by equations of the second degree, and the simple analytical way of de riving them. I. 1. We usually represent a force geometrically by a limited line, i. c. by means of two points {x', y', s') and (a*, y, z), one of which {x , y', z ) is the point acted upon by the force, while the right liue passing through both points indicates its direction, and the distance between the two points its intensity. We may regard the six quantities (1) X — x, y — y', z — s', ye'—y'z, zx'—zx, xy'—x'y as the six coordinates of the force. The six coordinates of a force represent its three projections on the three axes of coordinates OX,

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