Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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in vertice
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A,
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ut 3 ad 8; adeoQ.E.I. ea etiam ratione eſt linea
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GH
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ad lineam rectam quam corpus tempore motus ſui ab
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A
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ad
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P,
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ea
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cum velocitate quam habuit in vertice
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A,
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deſcribere poſſet. </
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DE MOTU
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CORPORUM</
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Corol.
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3. Hinc etiam vice verſa inveniri poteſt tempus quo cor
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pus deſcripſit arcum quemvis aſſignatum
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AP.
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Junge
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AP
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& ad
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medium ejus punctum erige perpendiculum rectæ
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GH
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occur
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rens in
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H.
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LEMMA XXVIII.
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Nulla extat Figura Ovalis cujus area, rectis pro lubitu abſciſſa, poſſit
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per æquationes numero terminorum ac dimenſionum finitas genera
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liter inveniri.
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>Intra Ovalem detur punctum quodvis, circa quod ceu polum re
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volvatur perpetuo linea recta, uniformi cum motu, & interea in rec
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ta illa exeat punctum mobile de polo, pergatque ſemper ea cum
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velocitate, quæ ſit ut rectæ illius intra Ovalem quadratum. </
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>Hoc
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motu punctum illud deſcribet Spiralem gyris infinitis. </
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>Jam ſi areæ
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Ovalis a recta illa abſciſſæ incrementum per finitam æquationem
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inveniri poteſt, invenietur etiam per eandem æquationem diſtantia
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puncti a polo, quæ huic areæ proportionalis eſt, adeoque om
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nia Spiralis puncta per æquationem finitam inveniri poſſunt: &
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propterea rectæ cujuſvis poſitione datæ interſectio cum Spirali in
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veniri etiam poteſt per æquationem finitam. </
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<
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>Atqui recta omnis
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infinite producta Spiralem ſecat in punctis numero infinitis, & æqua
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tio, qua interſectio aliqua duarum linearum invenitur, exhibet ea
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rum interſectiones omnes radicibus totidem, adeoque aſcendit ad
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rot dimenſiones quot ſunt interſectiones. </
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>Quoniam Circuli duo ſe
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mutuo ſecant in punctis duobus, interſectio una non invenietur
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niſi per æquationem duarum dimenſionum, qua interſectio altera
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etiam inveniatur. </
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>Quoniam duarum ſectionum Conicarum quatuor
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eſſe poſſunt interſectiones, non poteſt aliqua earum generaliter in
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veniri niſi per æquationem quatuor dimenſionum, qua omnes ſi
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mul inveniantur. </
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>Nam ſi interſectiones illæ ſeorſim quærantur, quo
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niam eadem eſt omnium lex & conditio, idem erit calculus in caſu
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unoquoque & propterea eadem ſemper concluſio, quæ igitur de
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bet omnes interſectiones ſimul complecti & indifferenter exhibere. </
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