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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 265, page id 1041163592:0299
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PRINCIPLA MATHIEMATICA.
265
PrOP. ZIX, quod non mutabune sicum partium interNArUmM INEEF LIDEn
Sc: proindeque, si Animalia imMErSANEUE, _ Senlatio omnis a MO- SECDNDOS.
cu parcium oriatur; nec laedent corpora immerta, nec sensario-
nem ullam excitabunt, nisi quarenus lxc corpora a compressione
condenlari DoNunt. EC par est racio cujuscunque corporum Sy-
Rematis Auido comprimente circundaci. SyHematis DartES OMMCS
uldem agicabuntur motibus, ac E in racuo constituerentur, ac l0-
Jam recinerent gravitatem Cuam comparaciram, nili quatenus Aui
dum vel motibus carum nonnihil resictat, rel ad caldem comprelli.
one conslutinandas requiratur.
PROPOSITIO ZXI THEOREMA XVI
Sit Fluidi cujusdam densitas compressioni proportionalis, e partes
ejus a vi centripeta distantiis suis a centro reciproce proportio-
nali deorsum trahantur: dico quod si distantiae illae sumantur
continue proportionales, densitates Fluidi in iisdem distantiis e-
runt etiam continue proportionales.
Designet ATV Fundum Sphaericum cui Ruidum incumbie, S
CenErUM, SA, SB, SC, SD, SF. Ec. distaneias continue prODOr-
cionales. Frigantur perpendicula FI, BD CK, DL, F M, 8C.
quae sinc ue densitates Medii in locis , B, C, D, F; St specitica
graritates in isdem locis crunt ut 2FY BF CK
perinde cAt, ut ITY BT CK
AS BS C 5 ec. vel, quod
AB BC C.∞ dec. Pinse pri-
num has oravieaces uniformiter continuari ab
A 2d B, 2 B 2dC, a C ad D, _cc. Factis per
Eradus decrementis in punctis B, C, D, _EC. RF
hae gravitaces ducte in alcitudines AB, BC,
C D, Scc. consicient presiones AFI, BI, CK,
quibus Fundum ATV (jUXEA THCOrEMA XV.
ursecur. Suctinet ergo parricula A pressiones
omnes AIL, BI, CK, D L. pergendo in
intinicum; e particula B prestiones omnes
praecer primam AFI; e parcicula C omnes
praeter duas primas AII, BI; e Sic deinceps: adeoque parci-
culae primae A densitaS AH est ad parriculae secunde B densi-
Mtm
eacem