Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Globi inverſe, & ſubduplicata ratione Vis abſolutæ Globi etiam
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inverſe.
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E. I.
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DE MOTU
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CORPORUM</
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Corol.
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1. Hinc etiam Oſcillantium, Cadentium & Revolventium
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corporum tempora poſſunt inter ſe conferri. </
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>Nam ſi Rotæ, qua Cy
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clois intra globum deſcribitur, diameter conſtituatur æqualis ſemi
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diametro globi, Cyclois evadet Linea recta per centrum globi tran
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ſiens, & Oſcillatio jam erit deſcenſus & ſubſequens aſcenſus in hac
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recta. </
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>Unde datur tum tempus deſcenſus de loco quovis ad
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centrum, tum tempus huic æquale quo corpus uniformiter cir
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ca centrum globi ad diſtantiam quamvis revolvendo arcum qua
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drantalem deſcribit. </
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>Eſt enim hoc tempus (per Caſum ſecun
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dum) ad tempus ſemioſcillationis in Cycloide quavis
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QRS
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ut
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1 ad √(
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AR/AC
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). </
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Corol.
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2. Hinc etiam conſectantur quæ
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Wrennus
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&
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Hugenius
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de
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Cycloide vulgari adinvenerunt. </
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>Nam ſi Globi diameter augeatur
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in infinitum: mutabitur ejus ſuperficies ſphærica in planum, Viſque
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centripeta aget uniformiter ſecundum lineas huic plano perpendi
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culares, & Cyclois noſtra abibit in Cycloidem vulgi. </
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>Iſto autem
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in caſu longitudo arcus Cycloidis, inter planum illud & punctum
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deſcribens, æqualis evadet quadruplicato ſinui verſo dimidii arcus
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Rotæ inter idem planum & punctum deſcribens; ut invenit
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Wren
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nus:
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Et Pendulum inter duas ejuſmodi Cycloides in ſimili & æ
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quali Cycloide temporibus æqualibus Oſcillabitur, ut demonſtravit
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Hugenius.
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Sed & Deſcenſus gravium, tempore Oſcillationis unius,
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is erit quem
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Hugenius
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indicavit. </
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<
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>Aptantur autem Propoſitiones a nobis demonſtratæ ad veram
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conſtitutionem Terræ, quatenus Rotæ eundo in ejus circulis maxi
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mis deſcribunt motu Clavorum, perimetris ſuis infixorum, Cycloi
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des extra globum; & Pendula inferius in fodinis & cavernis Terra
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ſuſpenſa, in Cycloidibus intra globos Oſcillari debent, ut Oſcilla
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tiones omnes evadant Iſochronæ. </
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<
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>Nam Gravitas (ut in Libro
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tertio docebitur) decreſcit in progreſſu a ſuperficie Terræ, ſur
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ſum quidem in duplicata ratione diſtantiarum a centro ejus, de
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orſum vero in ratione ſimplici. </
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