Philosophiæ naturalis principia mathematica autore Js. Newton ...

About this Item

Title
Philosophiæ naturalis principia mathematica autore Js. Newton ...
Author
Newton, Isaac, Sir, 1642-1727.
Publication
Londini :: Jussu Societatis Regiae ac Typis Josephi Streater ...,
1687.
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Subject terms
Mechanics -- Early works to 1800.
Celestial mechanics -- Early works to 1800.
Link to this Item
http://name.umdl.umich.edu/A52251.0001.001
Cite this Item
"Philosophiæ naturalis principia mathematica autore Js. Newton ..." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A52251.0001.001. University of Michigan Library Digital Collections. Accessed June 11, 2024.

Pages

Prop. XLI. Theor. XXXI.
Pressio non propagatur per Fluidum secundum lineas rectas, nisi ubi particulae Fluidi in directum jacent.

Si jaceant particulae a, b, c, d, e in linea recta, potest quidem pressio directe propagari ab a ad e; at

[illustration]
particula e urgebit particulas oblique po∣sitas f & g oblique, & particulae illae f & g non sustinebunt pressionem illatam, nisi ful∣ciantur a particulis ulterioribus h & k; quatenus autem fulciuntur, premunt par∣ticulas fulcientes; & hae non sustinebunt pressionem nisi fulcian∣tur

Page 355

ab ulterioribus l & m easque premant, & sic deinceps in in∣finitum. Pressio igitur, quam primum propagatur ad particulas quae non in directum jacent, divaricare incipiet & oblique pro∣pagabitur in infinitum; & postquam incipit oblique propagari, si inciderit in particulas ulteriores, quae non in directum jacent, ite∣rum divaricabit; idque toties, quoties in particulas non accurate in directum jacentes inciderit. Q.E.D.

Corol. Si pressionis a dato puncto per Fluidum propagatae pars aliqua obstaculo intercipiatur, pars reliqua quae non intercipi∣tur divaricabit in spatia pone obstaculum. Id quod sic etiam

[illustration]
demonstrari potest. A puncto A propagetur pressio quaqua∣versum, idque si fieri potest secundum lineas rectas, & obstacu∣lo NBCK perforato in BC, intercipiatur ea omnis, praeter par∣tem Coniformem APQ, quae per foramen circulare BC transit. Planis transversis de, fg, hi distinguatur conus APQ in frusta

Page 356

& interea dum conus ABC, pressionem propagando, urget frustum conicum ulterius degf in superficie de, & hoc frustum urget frustum proximum fgih in superficie fg, & frustum il∣lud urget frustum tertium, & sic deinceps in infinitum; mani∣festum est (per motus Legem tertiam) quod frustum primum defg, reactione frusti secundi fghi, tantum urgebitur & pre∣metur in superficie fg, quantum urget & premit frustum illud secundum. Frustum igitur degf inter Conum Ade & frustum fhig comprimitur utrinque, & propterea (per Corol. 6. Prop. XIX.) figuram suam servare nequit, nisi vi eadem comprimatur undique. Eodem igitur impetu quo premitur in superficiebus de, fg conabitur cedere ad latera df, eg; ibique (cum ri∣gidum non sit, sed omnimodo Fluidum) excurret ac di∣latabitur, nisi Fluidum ambiens adsit, quo conatus iste co∣hibeatur. Proinde conatu excurrendi premet tam Fluidum ambiens ad latera df, eg quam frustum fghi eodem impetu; & propterea pressio non minus propagabitur a lateribus df, eg in spatia NO, KL hinc inde, quam propagatur a superficie fg versus PQ.Q.E.D.

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