Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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Corollarium.
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<
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>Hinc area Ellipſeos, quæ radio ab umbilico ad corpus mobile
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ducto deſcribitur, non prodit ex dato tempore, per æquationem
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finitam; & propterea per deſcriptionem Curvarum Geometrice ra
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tionalium determinari nequit. </
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<
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>Curvas Geometrice rationales ap
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pello quarum puncta omnia per longitudines æquationibus defiNI
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tas, id eſt, per longitudinum rationes complicatas, determinari
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poſſunt; cæteraſque (ut Spirales, Quadratrices, Trochoides) Geo
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metrice irrationales. </
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>Nam longitudines quæ ſunt vel non ſunt ut
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numerus ad numerum (quemadmodum in decimo Elementorum)
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ſunt Arithmetice rationales vel irrationales. </
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>Aream igitur Ellipſeos
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tempori proportionalem abſcindo per Curvam Geometrice irratio
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nalem ut ſequitur. </
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PROPOSITIO XXXI. PROBLEMA XXIII.
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Corporis in data Trajectoria Elliptica moti invenire locum ad
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tempus aſſignatum.
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>Ellipſeos
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APB
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ſit
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A
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vertex principalis,
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S
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umbilicus, &
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O
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centrum, ſitque
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P
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corporis locus inveniendus. </
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>Produc
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OA
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ad
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G,
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ut ſit
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OG
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ad
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OA
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ut
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OA
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ad
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OS.
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Erige perpendiculum
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GH,
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centroque
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O
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& intervallo
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OG
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deſcribe circulum
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EFG,
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& ſuper regula
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GH,
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ceu fundo, progrediatur Rota
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GEF
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revolvendo circa axem
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ſuum, & interea puncto ſuo
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A
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deſcribendo Trochoidem
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ALI.
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