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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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90
PHLEOSODETLAE NATDRALIS
DE Moro Tohe distancia. Fingatur quod ris comprimens sit in duplicata
oronm patione densitatis, et graritas reciproce in ratione duplicata distan-
tixe, e densitas erit reciproce ut distantia. Casus omnes percurre
re lonsum cHet.
PROPOSITIO XXIII. THEOREMA XVII.
Si Fluidi ex parriculis se mutuo furientibus compositi densitas sit
ut compressio, vires centrifurae particularum sunt reciproce pro-
portionales distantiis centrorum suorum. Et vice versa, par-
ticulae viribus quae sunt reciproce proportionales distantiis cen
trorum suorum se mutuo fusientes componunt Pluidum Elasti-
cum, cujus densitas est compressioni proportionalis.
Includi incelligatur Fluidum in spatio cubico AC L, dein com.
prectione redigi in spacium cubicum minus ace; et particularum,
similem sicum inter sc in uero-
que spatio obcinentium, dictan-
tix erune ut cuborum latera
AB, ab; e Medii densitates
reciproce uc spatia continencia
ABcub. _ ab cub. In latere
cubi majoris ABC D capiatur
quadratum D P equale lateri
cubi minoris ab; _c Cx FI7pO-
chesi, prestio qua quadratum D P urget Fluidum inctuum, crit a
prestionem qua lacus illud quadratum ab urset Fluidune Mclusum
ut Medii densitares ad invicem, hoc CR, uE ab cub. 2d A BCMb. Sed
presio qua quadratum D B urset Fluidum inclusum, est ad pressi-
onem qua quadrarum D P urgec idem Fluidum, ut quadratum DB
ad quadratum D P, hoc cA, uc AB quad. 2d a b quad. FrsO, ex
aequos pressio qua lacus D B urset Fluidum, est ad prectionem qua
latus ab uroee Fluidum, uc ab ad AB. Planis FG FL, fCB, Per
media cuborum ductis, distinguatur Fluidum in duas partes, de hx
Se muruo prement iisdem riribus, quibus premuntur a planis AC, ac,
hoces, in proportione ab ad AB: adeoque rires centritueae, qui-
bus hae prectiones sustinentur, sunc in eadem ratione. Ob cundem
particularum numerum similemque licum in utroque cubo, vires
quasparticulae omnes secundum plana FEFF, fsh exercent in om-
L1C53