Full text: Gravesande, Willem Jacob: Physices elementa mathematica, experimentis confirmata, sive introductio ad philosophiam Newtonianam

MATHEMATIC A. LIB. II. CAP. X. titudo autem hujus fluidi prementis ſemper eſt duplum di-
ſtantiæ Ei, quæ ergo diſtantia cum hac vi motrice in ea-
dem ratione creſcit & minuitur. Diſtantia autem Ei eſt
ſpatium a fluido percurrendum, ut a ſitu EH perveniat
ad ſitum quietis; quod ergo ſpatium ſemper eſt ut vis quæ
continuo in fluidum agit: ſed tali ex cauſa demonſtravi-
mus penduli in cycloide oſcillati vibrationes omnes eſſe æ-
que diuturnas ; ideo & hîc quæcunque fuerit agitationum inæqualitas, æquali ſemper tempore fluidum it aut redit.

335.1.

252.
287.

Tempus in quo fluidum ſic agitatum adſcendit aut de-
ſcendit, eſt tempus in quo vibratur pendulum, cujus longi-
tudo, id eſt, diſtantia inter centra oſcillationis & ſuſpen-
ſionis, æqualis eſt ſemi-longitudini fluidi in tubo, ſive ſe-
mi-ſummæ linearum EE, FG, & GH: longitudo hæc
in axe tubi menſuranda eſt.

335.1.

885.

Vibretur hocce pendulum in cycloïde methodo ſuperius
explicata . Pendulum PC & arcus AD ejuſdem ſunt longitudinis ; in puncto A directio curvæ ad horizontem perpendicularis eſt, & corpus toto ſuo pondere juxta cur-
vam deſcendere conatur: hoc autem pondus eſt ad vim in
corpus agens, poſito hoc in P, ut AD, aut PC ad PD. Sit nunc fluidum in eo ſitu, ut iE (fig. 5.) æqualis ſit PD; pondus totius materiæ movendæ, id eſt, totius fluidi, eſt
ad pondus lE, quod eſt vis in hoc ſitu in fluidum agens
ut longitudo fluidi in tubo ad lineam lE, in qua ratione
etiam ſunt harum quantitatum ſemiſſes, id eſt PC ad PD
(fig. 6.) . In pendulo ergo pondus materiæ movendæ eſt
ad vim in hanc agentem in P, ut in tubo pondus materiæ mo-
vendæ ad vim in hanc agentem in ſitu EH. Æqualibus viribus
ideo corpus pendulum & fluidum in hac occaſione propel-
luntur, & hoc ubique obtinet ubi ſpatia, a fluido in agi-
tatione & a corpore in vibratione percurſa, ſunt æqualia; idcirco in hoc caſu agitatio & vibratio eodem tempore per-
aguntur, & non modo in hoc caſu, ſed ſemper . Cum vero vibrationes exiguæ in circulo a vibrationibus in cy-

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