Theoria Attractionis Corporum Sphaeroidicorum Ellipticorum Homogeneorum

Carolo Friderico Gauss

A chapter in Werke, 1877, pp 3-22 from Springer

Abstract: Abstrahere Satis quidem constat, problema de attractione corporis sphaeroidici elliptici homogenei in punctum quodvis exacte determinanda ad quaestiones difficillimas astronomiae physicae referri, pluresque geometras, inde a Newton temporibus, acriter iteratisque vicibus illi incubuisse. Primo quidem, investigatione ad sphaeroidem per revolutionem semiellipsis circa alterutrum axem ortam restricta , ipse summus Newton attractionem quam patitur punctum in axi situm invenire docuit, simulque nexum inter attractiones , quas patiuntur puncta intra sphaeroidem in eadem diametro sita, assignavit (Princip. Lib. I Prop. XCI). Dein sagax Mac Laurin , synthesi perelegante usus, attractionem punctorum in sphaeroidis superficie vel in prolongatione plani aequatoris positorum determinavit , quo pacto simul theoria attractionis punctorum intra sphaeroidem sitorum, quae per NEWTON! theorema ad attractionem punctorum in superficie facile referebatur, complete absoluta erat (De caussa physica fluxus et refluxus maris, in Recueil des pièces qui ont remporté les prix de l’acad. roi. des sc. T. IV; Treatise of fluxions B. I. Ch. 14). Quae Mac Laurin per synthesin enucleaverat , postea per analysin (cui antes huiusmodi quaestiones inaccessibiles visae erant) haud minus eleganter eruere docuit ill. LAGRANGE , atque sic viam ad ulteriores progressus patefecit (Noun. Mém. de l’Acad. de Berlin 1773). Scilicet adhuc desiderabatur attractio punctorum extra sphaeroidem neque vero in axis nec in aequatoris prolongatione sitorum enodanda, quam difficillimam problematis partem absolvere contigit ill. Legendre (Recherches sur l’attraction des sphéroides homogènes , Mémoires présentés à l’acad. roi. des sc. T. X).

Date: 1877
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DOI: 10.1007/978-3-642-49319-5_1

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