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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 290, page id 1041163592:0324
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29c
PHILOSOPMLLE NATVRALIS
DEMOrV In experimento columnae quartae, morus equales oscillarionibus
Conronb 535 in aerc, ex 13 in aqua amisi PunE. Pranc quidem olcillationes
in aere paulo celeriores quam in aqua. AF E Oscillariones in aqua
in ca racione accelerarentur ut motus pendulorum in Medio utro-
que herent aequiveloces, maneret numerus idem olcillarionum 13
in aqua, quibus motus idem ac prius amieteretur; ob relistentiam
auctam ex simul quadrarum cemporis diminutum in eadem ratione
illa duplicata. Paribus igitur pendulorum relocieacibus mOcuS X
quales in aere oscillacionibus 535 ec in aqua oscillationibus 15 amissi
sunc; ideoque resictentia penduli in aqua est ad ejus resistentiam in
aere ut 535 2d 23. IIaeC est proportio resistentiarum cocarum in
CasU COLUINX QuarEX.
Delionet jam AV L CV disterentiam arcuum in descensu _e Tub.
sequenee ascensu descriptorum a G7lob0, in Aere cum velocitate maxi-
ma V moco; et cum relocitas maxima, in casu columnae quarex, siE
ad relocitatem maximam in casu columnae prime, ut 1 ad 8; ex disse-
rentia illa arcuum, in casu columnae quartae, ad differentiam in casu
columnae prima uc - 2d 8, 5) Scu ut 85= ad 4280: Scribamus in
his casbus = d 8 pro velocitacibus, aEque 853 dt 4280 pro dit-
ferenciis arcuum, _c Het A F C = 85 = dc 8A + 64 C = 4280 Peu
A = 8C = 535; indeque per reductionem aequationum proveniet
7C = 4497 d C = 644 _ A = 213: atque adeo relistentia, cum
SIE UE E AV + = CV, cric uE 13 E V + 48, V. Ouareincasu co-
Jumna quareae, ubi relocieas crat I, resistentia tora est ad parrem
suam quadraco relocitatis proportionalem, ut 13 = + 48,8 seu
6127 2d 48,7; _ idcirco relistentia penduli in aqua est ad resisten-
tixe partem illam in aere quae quadraro relocieatis proxortionalis
Cs. Quaeque Sola in mocibus relocioribus consideranda venic, ut 6123
2d 48,6_ 535 2d 23 conjunctim, id est, uE 57X ad T. Si penduli
in aqua oscillantis filum eocum fuissee immersum, resistentia ejus
fuisset adhuc major; adeo uc penduli in aere oscillantis resistentia
illa quae velocicatis quadraro proportionalis est, quaeque (0)2 in
corporibus relocioribus consideranda venic, sc ad resistenciam e
jusdem penduli rotius, eadem cum relocitare, in aqua oscillantiss
Ut 800 vel 000 ad T circiter, hoc cA, ue densitas aquae ad densica-
cacem aeris quamproxime.
In hoc calculo sumi quoque deberet pars illa resistentix penduli
in aquas quae esset ut quadracum relocitatis, sed (quod mirum FOr-
ce videatur) relistentia in aqua ausebatur in ratione relocitatis
DIUC.