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''De motu corporum in gyrum'' ("On the motion of bodies in an orbit") is the presumed title of a manuscript by Isaac Newton sent to Edmond Halley in November 1684. It followed a visit by Halley earlier in that year, when Halley had questioned Newton about problems then exercising the minds of Halley and his scientific circle in London, including Sir Christopher Wren and Robert Hooke. The title of the document is only presumed because the original is now lost. Its contents are inferred from surviving documents, which are two contemporary copies and a draft. Only the draft has the title now used; both copies are without title.〔D T Whiteside (ed.), Mathematical Papers of Isaac newton, vol.6 (1684–1691), (Cambridge University Press, 1974), (at pages 30 )-91.〕 This manuscript (''De Motu'' for short, but not to be confused with several other Newtonian papers carrying titles that start with these words) gave important mathematical derivations relating to the three relations now known as "Kepler's laws" (before Newton's work, these had not been generally regarded as laws).〔Curtis Wilson: "From Kepler's Laws, so-called, to Universal Gravitation: Empirical Factors", in ''Archives for History of the Exact Sciences'', 6 (1970), pp.89–170.〕 Halley reported the communication from Newton to the Royal Society on 10 December 1684 (Old Style). After further encouragement from Halley, Newton went on to develop and write his book ''Philosophiæ Naturalis Principia Mathematica'' (commonly known as the ''Principia'') from a nucleus that can be seen in 'De Motu' – of which nearly all of the content also reappears in the ''Principia''. ==Contents== One of the surviving copies of ''De Motu'' was made by being entered in the Royal Society's register book, and its (Latin) text is available online.〔The surviving copy in the Royal Society's register book was printed in S P Rigaud's 'Historical Essay' of 1838 (in the original Latin), but note that the title was added by Rigaud, and the original copy had no title: online, it is (available here as 'Isaaci Newtoni Propositiones De Motu' ).〕 For ease of cross-reference to the contents of ''De Motu'' that appeared again in the ''Principia'', there are online sources for the 'Principia' in English translation,〔English translations are based on the third (1726) edition, and the first English translation, of 1729, as far as Book 1, (is available here ).〕 as well as in Latin.〔Newton's 'Principia' in its original 1687 edition is online in text-searchable form (in the original Latin) (here ).〕 ''De motu corporum in gyrum'' is short enough to set out here the contents of its different sections. It contains 11 propositions, labelled as 'theorems' and 'problems', some with corollaries. Before reaching this core subject-matter, Newton begins with some preliminaries: *3 Definitions: :1: 'Centripetal force' (Newton originated this term, and its first occurrence is in this document) impels or attracts a body to some point regarded as a center. (This reappears in Definition 5 of the ''Principia''.) :2: 'Inherent force' of a body is defined in a way that prepares for the idea of inertia and of Newton's first law; (in the absence of external force, a body continues in its state of motion either at rest or in uniform motion along a straight line). (Definition 3 of the ''Principia'' is to similar effect.) :3: 'Resistance': the property of a medium that regularly impedes motion. *4 Hypotheses: :1: Newton indicates that in the first 9 propositions below, resistance is assumed nil, then for the remaining (2) propositions, resistance is assumed proportional both to the speed of the body and to the density of the medium. :2: By its intrinsic force (alone) every body would progress uniformly in a straight line to infinity unless something external hinders that. (Newton's later first law of motion is to similar effect, Law 1 in the ''Principia''.) :3: Forces combine by a parallelogram rule. Newton treats them in effect as we now treat vectors. This point reappears in Corollaries 1 and 2 to the third law of motion, Law 3 in the ''Principia''. :4: In the initial moments of effect of a centripetal force, the distance is proportional to the square of the time. (The context indicates that Newton was dealing here with infinitesimals or their limiting ratios.) This reappears in Book 1, Lemma 10 in the 'Principia'. Then follow two more preliminary points: *2 Lemmas: :1: Newton briefly sets out continued products of proportions involving differences: :if A/(A-B) = B/(B-C) = C/(C-D) etc, then A/B = B/C = C/D etc. :2: All parallelograms touching a given ellipse (to be understood: at the end-points of conjugate diameters) are equal in area. Then follows Newton's main subject-matter, labelled as theorems, problems, corollaries and scholia: 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「De motu corporum in gyrum」の詳細全文を読む スポンサード リンク
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