# Chasles' theorem

Several results in mathematics have been attributed to Michel Chasles (1793–1880) and named Chasles' theorem:

The proof that a spatial displacement can be decomposed into a rotation and slide around and along a line in space is attributed to Michel Chasles in 1830.[3] Recently the work of Gulio Mozzi has been identified as presenting a similar result in 1763.[4][5]

• In gravitation, the Newtonian gravitational attraction of a spherical shell, outside of that shell, is equivalent mathematically to the attraction of a point mass.[6]
• In algebraic geometry, if two pencils of curves have no curves in common, then the intersections of those curves forms another pencil of curves the degree of which can be calculated from the degrees of the initial two pencils.[7]

## References

1. ^
2. ^ William B. Heard (2006) Rigid Body Mechanics, page 42, Wiley-VCH ISBN 3-527-40620-4
3. ^ M. Chasles, Note sur les Proprietes Generales du Systeme de Deux Corps Semblables entr'eux, Bullettin de Sciences Mathematiques, Astronomiques Physiques et Chimiques, Baron de Ferussac, Paris, 1830, pp. 321±326
4. ^ G. Mozzi, Discorso matematico sopra il rotamento momentaneo dei corpi, Stamperia di Donato Campo, Napoli, 1763
5. ^ M. Ceccarelli, Screw axis defined by Giulio Mozzi in 1763 and early studies on helicoidal motion, Mechanism and Machine Theory 35 (2000) 761-770
6. ^ Peirce, Benjamin (1855). A System of Analytic Mechanics. p. 104.
7. ^
• M. Chasles. (1830). "Note sur les propriétés générales du système de deux corps semblables entr'eux et placés d'une manière quelconque dans l'espace; et sur le déplacement ﬁni ou inﬁniment petit d'un corps solide libre.". Bulletin des Sciences Mathematiques, Astronomiques, Physiques et Chimiques 14: 321–326. (Notes on the general properties of a system of 2 identical bodies randomly located in space; and on the finite or infinitesimal motion of a free solid body.)