DE MOTU CORPORUM IN GYRUM PDF

This reappears in Definition 5 of the Principia. Definition 3 of the Principia is to similar effect. 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. The context indicates that Newton was dealing here with infinitesimals or their limiting ratios. This reappears in Book 1, Lemma 10 in the Principia.

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Ea celeritate qua Cometa uniformiter percurrit rectam AD finge ipsum emitti de locorum suorum aliquo P et vi centripeta mox correptum deflectere a recto tramite et abire in Ellipsi Pbda. Sumatur angulus ECH tempori propor tionalis. Si corpus non cadit perpendiculariter describet id Ellipsin puta APB cujus umbilicus inferior puta S congruet cum centro. Id ex jam demonstratis constat. Exponatur tum corporis celeritas tum resistentia medij ipso motus initio per lineam AC elapso tempore aliquo per lineam DC et tempus exponi potest per aream ABGD atque spatium eo tempore descriptum per lineam AD.

Decrescit ergo celeritas in a[7] proportione Geometrica dum tempus crescit in Arithmetica. Prob 7. Corpore ascendente exponatur vis centripeta per datum quodvis rectangulum BC et resistentia medij initio ascensus per rectan gulum BD sumptum ad contrarias partes. Et similis est demonstratio motus expositi in ascensu. Nam si motus omnis obliquus cor poris projecti distinguatur in duos, unum ascensus vel descensus alterum progressus horizontalis: motus posterior determinabitur per Problema sextum, prior per septimum ut fit in hoc diagrammate.

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De motu corporum in gyrum

This reappears in Definition 5 of the Principia. Definition 3 of the Principia is to similar effect. 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. The context indicates that Newton was dealing here with infinitesimals or their limiting ratios. Newton uses for this derivation — as he does in later proofs in this De Motu, as well as in many parts of the later Principia — a limit argument of infinitesimal calculus in geometric form, [6] in which the area swept out by the radius vector is divided into triangle-sectors.

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