MOTIONIBVS
NATVRALIBVS
A GRAVITATE PENDENTIBVS
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MOTIONIBVS
NATVRALIBVS
A GRAVITATE PENDENTIBVS,
LIBER
IO: ALPHONSI BORRELLI
in Academia Pi&longs;ana Mathe&longs;eos profe&longs;&longs;oris.
In Officina Dominici Ferri. 1670.
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DOMINO
D. ANDREÆ
CONCVBLET
MARCHIONI ARENÆ. IO: ALPHONSVS BORRELLVS. S.
S
tur, id profectò non filijs &longs;ed progenitoribus tribuendum e&longs;&longs;e
Sapientes non nulli cen&longs;uere; proinde qui nobilitatem iactat, de
cus, ac bonum alienum non &longs;uum commendare dixerunt. Hoc &longs;a
nè verum e&longs;&longs;et, &longs;i Parentes alienæ, & minimè naturales e&longs;
&longs;ent liberorum cau&longs;æ, neque materiam, aut influxum in genera
tione præ&longs;tarent: at &longs;ecus res &longs;e habet, &longs;icut enim plantarum ger
mina, & fructus ip&longs;is Arboribus, ac Seminibus conformes e&longs;&longs;&etail;,
nec vnquam Ro&longs;am è papactere, aut dulcia Poma ex Quercu pro-
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AD LECTOREM.
HAbesiam, erudite Lector, in hoc Libro de Motionibus Natura
libus à grauitate pendentibus, vna cum præcedenti do Vi Per
cn&longs;&longs;ionis ea omnia, quæ præmitti debuerant ad perfectam intelligen
tiam doctrinæ de animalium motibus, exceptis quamplurimis mecha
nicis lemmatibus, quæ &longs;uis locis deincepsiuxta &longs;ubiecti exigentia&mtail;
exponentur. Debeo tamen nonnulla præfari de hoc, & præcedenti
Opere, in quibus multoties afferuntur &longs;ententiæ diuer&longs;æ ab Authorum
magni nominis opinionibus. Hoc tamen &longs;umma mode&longs;tia, & modera
tione exequutus &longs;um; quandoquidem &longs;ententias in&longs;ector, non autem
authorum nomina, aut famam attingo: quippe qui &longs;olummodo veri
tatem quæro, &longs;eruata interim dignitate, & fama clari&longs;&longs;imorum viro
rum: quod con&longs;tat ex eo, quod tunc &longs;olummodo viuentium autho
rum nomina recen&longs;eo, cum laudandi eos occa&longs;io offertur; cum vero
controuer&longs;iæ agitantur nomina authorum omnino teguntur, ac &longs;ilen
tur; quia verò hac tan religio&longs;a mederatione, & mode&longs;tia effugere non
potui contradicentium mordacitates, ideo vi&longs;um e&longs;t denuo pollicer&etail;
me ab in&longs;tituto incepto non dimoueri, nec di&longs;cedere velle, neque op
po&longs;it oribus, &longs;i qui for&longs;an extiterint, re&longs;pon&longs;um vllum apologeticum, &
contentio&longs;um edere velle, &longs;ed tantummodo &longs;i opus fuerit meam do
ctrinam melius, & apertius declarare, vel corrigere vbi for&longs;an huma
no more lap&longs;us fuero. Vale.
NATVRALIBVS
A Grauitate pendentibus.
de quibus hactenus nemo tract auit.
EVidenti&longs;&longs;imum e&longs;t motus corporum
lunarium
quod minimè impleri & occupari de
bet à corporibus duris, con&longs;i&longs;tentibus,
& omninò continuis, propterea quòd
duo corpora &longs;e mutuò penetrare nequeunt, igitur
nece&longs;&longs;e e&longs;t vt &longs;patium, in quo corpus aliquod moue
ri debet, aut &longs;it omninò vacuum, vel &longs;altem occupe
tur ab aliquo corpore di&longs;trahibili, & fluido, vel in
particulas &longs;ubdiui&longs;o, quod nimirum facilè expelli
po&longs;&longs;it è &longs;uo loco, vt &longs;ubintranti corpori, quod moue
ri debet locum cedat. ab hi&longs;ce fluidis corporibus re
gio i&longs;ta terram ambiens occupatur, vt ab aqua, aere,
& igne, in quibus fiunt motiones corporum &longs;ublu
narium.
De ip&longs;is porrò naturalibus motionibus corporum,
qu&ecedil; in medio fluido fiunt, &longs;cilicèt qua ratione, & qua-
re corpora varias magnitudines, pondera, & di
uer&longs;as figuras habentia, moueantur maiori, aut mi
nori velocìmte, certa quadam proportione in medio
fluido, nemo (quodl&longs;ciam) differuit. Igitur hanc
phy&longs;ico-mechanices partem hactenùs de&longs;iderata&mtail;
exponere, ac &longs;upplere animus e&longs;t; &longs;ed ne fa&longs;tidio&longs;&atail;
repetitione earum rerum, quæ ab alijs tradita &longs;unt,
lectores de tineam, &longs;upponam ea omnia, quæ in ele
mentis mechanicis tradita &longs;unt de natura libræ, vec
tis, trochleæ, & de reliquis ab hi&longs;ce in&longs;trumentis pen
dentibus, eorum que naturam participantibus.
tantummodò aliqua quæ præcipuum v&longs;um habent in
hac doctrina de naturalibus corporum motionibus,
non de omnibus, &longs;ed de ijs &longs;olum modò, quæ à vi mo
tiua grauitatis pendent.
porum mo
tus in medio
fluido fieri.
in ij&longs;dem fluidis innatantium.
SVbtili&longs;&longs;imè, & præclarè Archimedes egit de in&longs;i
dentibus humido, idip&longs;um po&longs;te a alia methodo
Galileus, & Steuinus demon&longs;tiatunt, cùm veritas in
numeris modis confirmari po&longs;&longs;it, ip&longs;e verò, non ge
nio variandi, nouas earumdem propo&longs;itionum de
mon&longs;trationes via longè diuer&longs;a procedendo, exco
gitaui, & attnli, &longs;ed quia hæ valdè conducunt ad ea
quæ po&longs;terius à nobis expliconda &longs;unt. at priùs ali
quæ hypothe&longs;es &longs;unt præmittendæ.
momentis
grauium in
fluido inna
tantium.
Suppono primò quòd quodlibet corpus, &longs;iuè den
&longs;um, &longs;iuè fluidum, ex ijs quæ globum terra-queu&mtail;
componunt, graue e&longs;t, exercetque vim &longs;eù conatum
fuæ grauitatis, etiam &longs;i in fluido &longs;ibi aut homogeneo,
aut non, con&longs;tituatur. hoc autem &longs;uo loco euidenti&longs;
&longs;imis rationibus, ac experimentis confirmabitur.
Secundo loco &longs;uppono vim, &longs;eù conatum, quo &longs;lui
da nituntur &longs;e&longs;e vnire &longs;phæræ terra queæ, effici per
lineas perpendiculares ad &longs;uperficiem horizontis. &
hoc patet quia quodlibet graue naturali in&longs;tinctuco
natur ad centrum terræ accedere via breui&longs;&longs;ima, igi
tur directio prædictimotus, &longs;eù conatus compre&longs;&longs;iuus
efficietur per &longs;emidiametros eiu&longs;dem terræ, hæ verò
perpendiculares &longs;unt ad &longs;uperficiem horizontalem,
quæ &longs;phæricè ip&longs;amterram comprehendit, igitur ma
nife&longs;tum e&longs;t quòd motus &longs;eù conatus compre&longs;&longs;iuus
omnium partium fluidi per lineas ad horizontem per
pendiculares efficitur.
Tertiò quod libet corpus graue e&longs;t impo&longs;&longs;ibile vt
moueatur motu &longs;pontaneo, & naturali, quando ad
trumhoc mani
fe&longs;tum e&longs;t quia cùm omnes partes terrenæ vt graues
naturali in&longs;tinctu ad terræ centrum accedere conen-
tur, hocque earum de&longs;iderium expleri minimè po&longs;&longs;it
ni&longs;i mediante motu, igitur ce&longs;&longs;ante fine nece&longs;&longs;ariò
medium quoque ce&longs;&longs;at, &longs;cilicet quando non pote&longs;t
graue aliquod magis, quàm prius ad terræ centrum
accedere, tunc nequa quam moue bitur. ex quo &longs;equi
tur vt prædicta corpora quie&longs;cant, quandoquidem &longs;i
mouerentur, aut deberent à centro telluris recedere
& remoueri, vel lateraliter circumferri, in primo ca
&longs;u &longs;equeretur operatio contraria naturali in&longs;tinctui
grauium, quod e&longs;t impo&longs;&longs;ibile; in &longs;ecundo verò ca&longs;u
efficeretur operatio vanæ, & &longs;i fru&longs;tratoria, nil enim
graue præterea acquireret cùm non amplius ad terræ
centru accedere po&longs;&longs;et ex hypothe&longs;i, ab&longs;urdum verò
e&longs;t atque repugnat naturam operari ca&longs;n, & ab&longs;que
fine; igitur e&longs;t impo&longs;&longs;ibile vt corpora, quæ ad
terræ accedere nequeunt, vllo pacto moueantur; qua
propter nece&longs;&longs;e e&longs;t vt in eodem &longs;itu fixè quie&longs;cant in
quo prius degebant.
momentis
grauium in
fluido inna
tantium.
&longs;suppositio.
Præterea Archimedes &longs;uppo&longs;uit vt primum prin
cipium per &longs;e notum, quod eiu&longs;dem fluidi con&longs;i&longs;ten
tis, partes quæ &longs;int continuat&ecedil; in eodem plano hori
zontaliminus pre&longs;&longs;æ debeant eijci expellique &longs;ur&longs;um
pre&longs;&longs;is
bet tamen aliquam ob&longs;curitatem, cùm minimè eui
dens &longs;it, quamobrem partes eiu&longs;dem fluidi po&longs;&longs;int
magis, aut minus comprimi; nec pariter euidenter
percipitur quomodo à naturali operatione, de&longs;cen
&longs;us nempè deor&longs;um, produci debeat operatio
contraria, a&longs;cen&longs;us nimirum alterius partis eiu&longs;dem
fluidi &longs;cilicet recedendo a centro telluris. erit igitur
operæpretium perfpicuè o&longs;tendere veritatem præ
dictæ operationis, eamque deducere ex principijs
magis notis, & euidentibus.
momentis
grauium in
fluido inna
tantium.
&longs;ur&longs;um a&longs;cendit quiæ integrum graue
SIt graue AB exten&longs;um, vel compo&longs;itum ex dua
bus partibus in extremitatibus eiu&longs;dem libræ
horizontalis AB di&longs;po&longs;itis, & commune centrum gra
uitatis earum &longs;it D. &longs;u&longs;ti
neatur po&longs;tea, fulciatur
que tota libra ex puncto
C remoto à centro graui
tatis D. dico quòd pars
eius oppo&longs;ita B &longs;ur&longs;u&mtail;
a&longs;cendet per arcum BF,
hac &longs;olummodo de cau&longs;&atail;
quia integrum graue AB magis, quàm prius ad cen
trum terræ accedit. quia duæ partes graues A & B
exercent &longs;uam grauitatem & conatum compre&longs;&longs;iuum
in centro communi earum grauitatum D; e&longs;t que
prædictum centrum D remotum à fulcimento &longs;tabili
C, igitur efformabitur veluti fune-pendulum CD
horizontaliter con&longs;titutum, &longs;u&longs;pen&longs;um, & alligatum
in centro C & pondus vniuer&longs;um applicatum eriti&ntail;
centro D extremo fili, vel lineæ CD: &longs;ed penduli na
tura talis e&longs;t vt conetur deor&longs;um ferri per arcum qua
drantis DE circa centrum eius &longs;ixum C v&longs;que ad lo
cum infimum E, quod magis ad centrum terræ appro
ximatur, quàm in &longs;itu horizontali D & patet quòd
vniuer&longs;a hæcoperatio nece&longs;&longs;aria, & naturalis e&longs;t de
pendens à de&longs;cen&longs;u totius grauis. & e&longs;t impo&longs;&longs;ibil&etail;
vt fune pendulum CD ad in fimum &longs;itum CE perduca
tur ab&longs;que eo quòd libra rigida &longs;itum perpendicula
rem ad horizontem acquirat, quale e&longs;t GCF, hoc ve
ro minimè acquiri pote&longs;t ni&longs;i pars minus grauis libræ
B &longs;ur&longs;um a&longs;cendat per arcum BF, igitur ca&longs;us, & de
&longs;cen&longs;us totius corporis grauis AB à &longs;itu eleuato D ad
infimum E e&longs;t vera & legitima cau&longs;a a&longs;cen&longs;us corpo
ris grauis B per arcum BF, quod fuerat o&longs;tendendum.
momentis
grauium in
fluido inna
tantium
Patet igitur quod &longs;im
plex ca&longs;us, aut de&longs;cen&longs;us
corporis grauis e&longs;t vera,
& legitima cau&longs;a motus,
& a&longs;cen&longs;us alicuius partis
eius &longs;ur&longs;um, & hoc planè
contingit quotie&longs;cumque
graue vniuer&longs;um &longs;u&longs;tine
tur ab aliquo eius puncto libræ realis, vel imagina
riæ, itaut efficiatur commotio omnium partium eius
non quidem per lineas rectas inter &longs;e parallelas, &
horizonti perpendiculares, &longs;ed vertigino&longs;as, & cir-
culares quales &longs;unt illæ quæ à fune-pendulis de&longs;cri
buntur, & in prædicto motu vertigino&longs;o e&longs;t tam ne
ce&longs;&longs;arius, & naturalis a&longs;cen&longs;us partis minus grauis B
per arcum BF quemadmodum nece&longs;&longs;arius e&longs;t lap&longs;us
& de&longs;cen&longs;us totius grauis per arcum DE v&longs;que ad lo
cum infimum E & licet a&longs;cen&longs;us prædictæ portionis
B vulgo cen&longs;eatur motus violentus, nihilominus &longs;i
perpendatur vertigo, & debita &longs;ituatio corporis gra
uis quatenus naturalis e&longs;t & naturali in&longs;tinctu acqui
&longs;ita, & producta; cùm &longs;it impo&longs;&longs;ibile vt prædicta &longs;itua
tio debita ab&longs;olute con&longs;equatur ab&longs;que a&longs;cen&longs;u por
tionis B &longs;itque verum quoque quod, qui vult fine&mtail;
velit quoque nece&longs;&longs;e e&longs;t media, quæ ad finem con&longs;e
quendum nece&longs;&longs;aria
à vi naturali verè impelli minus graue &longs;ur&longs;um ver&longs;us
F, ac proindè concedendum erit a&longs;cen&longs;um per BF
naturalem pror&longs;us e&longs;&longs;e vel potius in eadem naturali
operatione includi debere violentiam motus præ
dicti a&longs;cen&longs;us; &longs;ed vtcunque &longs;it &longs;ufficit nobis vt præ
dicta operatio &longs;it nece&longs;&longs;aria, &longs;it que pror&longs;us impo&longs;&longs;ibi
le vt aliter contingat; cæteriverò eam vocent &longs;iue na
tur alem, &longs;iue violentam ad eorum libitum.
momentis
grauium in
fluido inna
tantium
eodem &longs;iphone circulari.
PRærerea vt duo corpora in extremitatibus libræ
con&longs;tituantur non &longs;emper e&longs;t nece&longs;&longs;e vt corpora
grauia A & B affixa &longs;int virgæ alicui rigidæ & con&longs;i
&longs;tenti vt e&longs;t ACB pote&longs;t onim concipi canalis circu
laris AGBF qui &longs;i repleatur aqua vel quolibet alio
fluido liquore cuius pars dex
tera FAG grauior &longs;it quam re
liqua fluidi pars GBF &longs;cilicet
&longs;i fluidum FAG fuerit hydrar
girum, FBG verò aqua com
munis, tunc pariter efficietur
libra, & centrum grauitatis
amborum liquorum non iace
bit in diametro FCG perpendiculari ad horizontem,
&longs;ed vltra ip&longs;um inter C & A, &longs;cilicor in puncto aliquo
D tunc pariter erit centrum totius magnitudinis flui
di ip&longs;um C & in hoc præci&longs;e fiet &longs;u&longs;pen&longs;io totius flui
di, quia circa ip&longs;um efficiuntur duo motus contrarij,
nempe de&longs;cen&longs;us fluidi A & a&longs;oen&longs;us alterius oppo&longs;i
ti fluidi B cùm igitur centrum communis grauitatis D
duorum fluidorum di&longs;tet à centro &longs;u&longs;pen&longs;ionis C effi
cietur quoque pendulum, quod circulari motu ex
curret per arcum DE.
momentis
grauium in
fluido inna
tantium
po&longs;&longs;e exponitur, atque eius defectus,
& infufficientia detegitur.
ET hic breui & non omnino &longs;uperuacanea digre&longs;
&longs;ione indicabo impo&longs;&longs;ibilitatem motus perpetui
in machina quæ tantam veri&longs;imilitudinis apparenti
am habere videtur, vt quilibet iuraret tali organo
motum continuari facilè po&longs;&longs;e, huiu&longs;modi &longs;peculatio
nem & organi &longs;tructuram mihi olim communicauit
amicus optimus Clemens &longs;eptimius Galilei alumnus. is &longs;anè cum contemplaret tympana ver&longs;atilia &longs;eu ro
tas illas quibus nauiculæ trahuntur Pi&longs;is & in Belgio
ab vno canaliad alium à vi vnius hominis, qui inter
nam eius periphæriam, accliuem calcando ea&mtail;
reuoluit, vt quæ à canibus eodem tympano in coqui
nis verua rotantur, cogitauit eodem modo
efformari po&longs;&longs;e in quo
perpetuò medietas eius
&longs;ini&longs;tra à fluido corpor&etail;
grauiori quam medietas
dextra occupari po&longs;&longs;et. vt
in appo&longs;ito &longs;chemat&etail;. &longs;it tympanum æreum AF
BG comprehen&longs;um à &longs;u
perficie curua cylindrica ærea & à duabus laminis
planis circularibus inter &longs;e parallelis optimè læuiga
tis & cum illa coaptatis conglutinati&longs;que, verùm in
tra tympani cauitatem collocetur lamina plana FCG
quæ v&longs;um diaphragmatis præ&longs;tet & medietas cylin
dri FCGA aqua ver hydrargiro repleatur, reliqu&atail;
verò medictas BFCG oleo velaere oppleta &longs;it; lami
na verò FCG axi HC annexa & ferruminata intr&atail;
tympanum & circa axim fixum C manubrio aliquo
H fixè retineri & reuolui po&longs;&longs;it, hac lege vt exactè
tangat &longs;uperficies internas ambarum ba&longs;ium plana
rum & cauam &longs;uperficiem curuam eiu&longs;dem tympani:
oportet autem vt ad in&longs;tar epi&longs;tomij exacti&longs;&longs;imè dia
phragma illud reuolutum ab&longs;que vlla rima occludat
egre&longs;&longs;umque impediat aquæ vel mercurio in &longs;emicy
lindro FAG contento, remanente reliquo &longs;patio G
BF aere, vel oleo oppleto, &longs;itque præterea moles to
tius tympani &longs;u&longs;pen&longs;a in ip&longs;o axi C aflixo duobus ful
cris vt liberè circumuolui tympanum po&longs;&longs;it in plano
perpendiculari ad horizontem; tunc &longs;i vi manus ma
nubrium H eique annexum diaphragma FCG perpe
tuò in &longs;itu verticali ad horizontem retineretur, pro
culdubio (dicèbat amicus) haberemus in tali ca&longs;u li
bram radiorum æqualium perpetuam imaginariam
ACB quæ ab inæqualibus ponderibus premeretur,
&longs;cilicèt à pondere emi&longs;phærij mercurialis vel aquei
FAG radius CA grauaretur, dum oppo&longs;itus radius C
B à leuiori pondere olei, vel aeris deprimeretur. &
quia horum inæqualium ponderum centrum grauita
tis &longs;emper in aliquo puncto D intercepto inter C &
A caderet, igitur &longs;emper libra AB flecti deberet de
or&longs;um ad partes A, vel potius con&longs;titueretur pendu
lum horizontale CD &longs;u&longs;pen&longs;um in centro C & ideò
pendulum de&longs;cendere deberet per arcum DE; qui&atail;
verò fluidum grauius FAG de primi non po&longs;&longs;et ob im
pedimentum diaphragmatis FCG in &longs;itu verticali à
virtute manus retenti, &longs;equeretur vt vniuer&longs;um &longs;e
micylindricum mercurij comprimendo & calcando
curuam &longs;uper&longs;iciem tympani AG, quæ volubilis e&longs;t
eam impelleret, proindeque deor&longs;um conuerti debe
ret ab A ver&longs;us G cum à nullo retinaculo impediatur,
igitur &longs;emper reuolui po&longs;&longs;et tympanum ab A ver&longs;us
G quia &longs;emper per&longs;eueraret eadem cau&longs;a vertiginis
&longs;cilicet perpetuò con&longs;eruaretur pendulum CD in &longs;itu
horizontali, & ideò &longs;emper premeret & calcaret tym
pani &longs;uperficiem AG; quapropter tali artificio con
&longs;equi po&longs;&longs;e videtur motus perpetuus prædicti tym
pani.
momentis
grauium in
fluido inna
tantium
momentis
grauium in
fluido inna
tantium
momentis
grauium in
fluido inna
tantium
Hoc, vt dixi, tantam veri&longs;imilitudinem præ&longs;efer
re videtur vt nemo ex pluribus amicis quibus hoc ar
tificium communicaui fallaciamin eo latere &longs;u&longs;pica
tus fuerit, nihilominus licèt ego, nun quam ad praxim
hoc artificium reducere curauerim, non vereor tamen
ab&longs;olutè pronunciare motus perpetuitatem hac via
con&longs;e qui non po&longs;&longs;e, quia nimirum per&longs;uadere mihi
valeo grauia corpora moueri vnquam &longs;ponte debere,
quando nè pilum quidem magis, quàm prius
dere
unt: cum itaque centrum grauitatis communis D am
borum fluidorum &longs;emper
in eodem plano horizon
tali ABCD retineatur ac
&longs;i&longs;tatur mihi omninò im
po&longs;&longs;ibile videtur vt rot&atail;
&longs;iue tympanum AGBF
uertatur
&longs;us G. Itaque licet
grauitatis communis D di&longs;tet à centro &longs;ixo vertiginis
C & proinde pendulum horizontale con&longs;tituat; ta
men aio ip&longs;um retineri &longs;u&longs;pendique à vi manus, quæ
diaphragma FG retinet ne conuertatur à vi ponderis
in centro D operantis, non &longs;ecus ac &longs;i
aliquod CD à &longs;ubiecta manu &longs;u&longs;pen&longs;um deor&longs;um fer
ri non po&longs;&longs;et per arcum DE. & licèt fune-pendulum
CD in ca&longs;u no&longs;tro non &longs;it quid continuum &
centro C nihilominus perindè &longs;e habet, cumeius co
natus fiat per arcum DE eo modo præcisè, ac &longs;i cen
tro C alligatum fui&longs;&longs;et; ille verò qui prohibet de&longs;cen
&longs;um corporis grauis D, quod &longs;olummodo moueri per
arcum DE pote&longs;t, nece&longs;&longs;ariò impedit operatione&mtail;
eius loco motiuam, ideoque fluidum FAG cum omni
nò quie&longs;cat, non poterit impellere, & conuerter&etail;
tympanum; nullo enim modo capi pote&longs;t proiectum
impelli ab eo corpore quod omninò in quiete con&longs;i
&longs;tit, nam &longs;emper proijciens & impellens impetu &
motu locali affectum &longs;it oportet ad hoc, vt proyecto
gradum impetus imprimere valeat, cum igitur hy
drargyrum FAG omninò iners &longs;it & motu locali care
at, videtur omninò impo&longs;&longs;ibile vt proiecto &longs;cilicet
tympano gradum aliquem impetus imprimere queat,
proinde que tympanum non transferetur localimotu,
quare tali artificio motus vertiginis eius nedum con
tinuari perpetuò non poterit, &longs;ed neque motum in
coabit. Sed relicta digre&longs;&longs;ione ad rem no&longs;tram redeo.
momentis
grauium in
fluido inna
tantium
momentis
grauium in
fluido inna
tantium
perpendiculariter eleuata ad horizontem, fluidi
in eo de&longs;cendentis centrum grauitatis cur
uo itinere per lineam parabolicam
de&longs;cendit.
IN &longs;iphone TFGV &longs;int duo canales TF & GV pa
ralleli inter &longs;e, & erecti per pendiculariter ad ba
&longs;im FG, & ad horizontem, & quilibet eorum æquè
cra&longs;lus &longs;it; capacitas verò portionis cylindri TF &longs;u
pra horizontalem per V eductam vt e&longs;t TA in primo
ca&longs;u, & TC in &longs;ecundo, &longs;it æqualis
capacitati GV, quæ &longs;ecetur i&ntail;
quotcumque partes æquales à qua
ternario men&longs;uratas in X, Y, Z, I,
L, 2, & puncta A, B, C, D, E, &longs;int
centra grauitatum cylindrorum T
F, XF, YF, ZF, & AF, vel CF, pa
riterque H, I, K, L &longs;int centra gra
uitatum cylindrorum GI, GL, G2,
GV, & quia centra grauitatum A,
& B, bifariam &longs;ecant cylindros T
F, XF, ergo TF ad XF &longs;e habet vt
AF, ad BF, & per conuer&longs;ione&mtail;
rationis, & permutando TF ad AF
eamdem rationem habet, quàm TX ad AB, quar&etail;
AB &longs;emi&longs;&longs;is e&longs;t ip&longs;ius TX, non &longs;ecus ac HG mediatas
e&longs;t cylindri IG, intelligatur aqua primò eleuari i&ntail;
&longs;itu T & deprimi in dextro canali in G, & hinc eleua
ta aqua ad I de&longs;cendat à T ad X coniungantur qu&etail;
duæ rectæ lineæ AG, & BH &longs;e &longs;ecantes in M, eritque
punctum Min horizontali EL con&longs;titutum, propterea
quod duo cylindri aquæ AB, & HG æquales &longs;unt in
ter &longs;e, cum &longs;emi&longs;&longs;es &longs;int cylindrorum æqualium TX &
IG, ergo altitudo AB ad HG e&longs;t vt eiu&longs;dem cylindri
ba&longs;is H ad ba&longs;im A: eadem ratione AE ad LG erit vt
ba&longs;is H ad
ad HG,
res ad
lelæ, ergo ob &longs;imilitudinem triangulorum vt AM ad
MG ita erit BM ad MH, nec non EM ad ML, & ideo
rectæ AG, BH, & EL &longs;e mutuo &longs;ecabunt in eode&mtail;
puncto M. po&longs;tea vt moles aquæ XBF vnà cum GHI
ad molem aquæ IHG ita fiat di&longs;tantia HB ad BQ, &
diuidendo, vt moles aquæ XBF ad GHI ita erit di
&longs;tantia HQ ad QB, ideoque ex elementis mechanicis
punctum Q erit centrum grauitatis aquæ XBF vnà
cum GHI. quando verò aqua erat in &longs;ummitate T &
canalis GLV omninò exhau&longs;tus erat, tunc quide&mtail;
centrum grauitatis totius aquæ TAF per&longs;i&longs;tens i&ntail;
puncto A medio eiu&longs;dem canalis perindè operare
tur ac &longs;i &longs;u&longs;pen&longs;us fui&longs;&longs;et cylindrus èx puncto A: de
pre&longs;&longs;a po&longs;tmodum aqua v&longs;que ad Y & eleuata v&longs;que
ad L in oppo&longs;ito canali, denuo centrum grauitatis re
pertum prædictæ aquæ exi&longs;tet in puncto R & tandem
depre&longs;&longs;a aqua v&longs;que ad A in primo ca&longs;u & v&longs;que ad
Y in &longs;ecundo & &longs;ubleuata v&longs;que ad V; tunc quide&mtail;
centrum grauitatis prædictæ aquæ horizontaliter
&longs;titutæ
terea quòd vt ba&longs;is V ad ba&longs;im A &longs;eù vt cylindrus a
queus GLV ad equè altum cy
lindrum AEF in primo ca&longs;u vel
ad CEF in &longs;ecundo, ita fuit reci
procè di&longs;tantia EM ad ML. o
&longs;tendendum modò e&longs;t punct&atail;
A, Q, R, S, M in eadèm linea pa
rabolica e&longs;&longs;e. quia moles aquæ
TX æqualis e&longs;t æquæ moli GH
I, ergo, XBF vnà cum GHI æ
qualis e&longs;t moli aqueæ TAF; e
rat verò moles aquæ XBF vnà
cum GHI ad GHI vt linea HB
ad BQ &longs;eu (ducta QN parallel
là AE) vt LE ad EN, ergo FAT
ad TX atque &longs;emi&longs;&longs;is illius FA
ad huius &longs;emi&longs;&longs;em AB eamdem
proportionem habebit qua&mtail;
LE ad EN, e&longs;t verò EA ad AF vt MA ad AG, &longs;eù vt
ME ad EL, ergo ex æqualitate ordinata EA ad AB
eamdem proportionem habebit quam ME ad EN, &
per conuer&longs;ionem rationis EA ad EB erit vt EM ad
MN, &longs;eù vt EB ad NQ, erunt igitur tres continuæ pro
portionales EA, EB, & NQ in eadem ratione qua&mtail;
habet EM ad MN, quare quadratum ex EM ad qua
dratum ex MN eam proportionem habebit, qua&mtail;
AE ad NQ: ideoque puncta A & Q &longs;unt in parabol&atail;
cuius vertex M. quapropter aqua in prædicto &longs;iphone
dum ad æquilibrium de&longs;cendit mouetur eius centrum
grauitatis in linea parabolica; quod fuerat
momentis
grauium in
fluido inna
tantium.
momentis
grauium in
fluido inna
tantium
momentis
grauium in
fluido inna
tantium
tuentes æquè ad horizontem inclinati fuerint
idip&longs;um demon&longs;tratur.
SI po&longs;tea &longs;ipho inuer&longs;us eiu&longs;dem amplitudinis an
gularis fuerit, vt nimirum &longs;emi&longs;&longs;es brachiorum
AF & FL æquè &longs;int ad horizontem EL inclinata effi
ciatur què hi
&longs;c&longs;celium tri
angulum EF
L & brachij
&longs;upremi qua
drans EA æ
quale &longs;it FL,
&longs;iue FE. dico
denuò quòd
aqua totius
brachij F2.
cuius &longs;emi&longs;
&longs;is e&longs;t AF
fluit per canalem FL4 &longs;ur&longs;um & de&longs;cendit per 2 A;
tunc pariter eius centrum grauitatis per parabolam
deor&longs;um fertur. diui&longs;is æqualibus partibus in punctis
A, B, C, D, E, & F, H, I, K, L, quæ centra grauitatu&mtail;
partium aquæ e&longs;&longs;e intelligantur vt prius, & ductis ad
horizontalem perpendicularibus AG, BV, CN, DO,
FM, H3, &c. pariterque coniunctis rectis DK, CI,
BH. quia anguli ad L, E æquales &longs;unt in i&longs;o&longs;cele, &
&longs;unt quoque anguli recti O & T, & hypothenu&longs;æ DE,
KL &longs;unt inter &longs;e æquales, ergo in &longs;imilibus triangulis
DOE, & KTL latera DO, KT æqualia erunt & recta
OE æqualis erit TL, & addita communi TE erit LE
æqualis OT quæ
puncto Z, propter æquidi&longs;tantiam & æqualitatem la
terum DO, & TK. &longs;imiliter reliquæ rectæ lineæ NY
& CI æquales erunt prioribus, & bi&longs;&longs;ectæ in puncto
P, idemque de reliquis & quia canales,
& moles aqueæ in eis contentæ AB, & FH, æquales
&longs;unt, ergo BFH æqualis e&longs;t AF; fiat iam HB ad BQ,
vt BFH ad FH, vel potius vt FA ad AB: quare &longs;emi&longs;
&longs;es antecedentium ad ea&longs;dem con&longs;equentes in
ratione erunt, nempè vt EA ad AB, ita erit XB ad B
Q, & per conuer&longs;ionem rationis EA ad EB &longs;eu AG
ad BV, vel GE ad EV, & tandem vt duplum GM ad
duplum MN erit vt BX ad XQ, &longs;eu vt VX ad XN,
vel vt BV ad QN. igitur erunt tres continuæ propor
tionales AG, BV, & QN in eadem ratione quam ha
bet MG ad MN, quare vt quadratum MG ad quadra
tum MN, ita erit longitudine AG ad QN ideoqu&etail;
duo puncta A & Q in parabola erunt.
momentis
grauium in
fluido inna
tantium
Con&longs;tat ergo quòd &longs;i brachia &longs;iphonis perpendicu
laria fuerint ad horizontem, &longs;iuè ambo fuerint eiu&longs;-
dem latitudinis &longs;iuè non, &longs;emper centrum communis
grauitatis fluidi in de&longs;cen&longs;u parabolam de&longs;cribet; &longs;i
verò brachia &longs;iphonis æquè inclinata ad horizontem
fuerint, de&longs;cribet eius centrum in de&longs;cen&longs;u parabo
lam quotie&longs;cumque brachia æquè cra&longs;&longs;a fuerint.
momentis
grauium in
fluido inna
tantium
Siverò in eodem angulari &longs;iphone vnum brachium
dilatatum, alterum verò gracile fuerit, tunc eius
trum
&ecedil;mulantem.
Et tandem &longs;i vnum brachiorum perpendicular&etail;
fuerit ad horizontem, reliquum verò inclinatum in de
&longs;cen&longs;u de&longs;cribet commune centrum grauitatis
ellip&longs;im æmulantem.
His præmi&longs;&longs;is declarari debet altera libræ, &longs;eu &longs;i
phonis proprietas, in quo centrum grauitatis eius
mouetur non quidem motu obliquo, & curuo, &longs;ed per
lineam rectam ad horizontem perpendicularem, pro
cuius intelligentia præmittendum e&longs;t, quod.
luto &longs;u&longs;pen&longs;a, dum vnum eorum a&longs;cendit centrum gra
uitatis eorum per lineam
perpendicularem deprimitur.
momentis
grauium in
fluido inna
tantium
SIt pondus A maius, B verò minus alligata extre
mitatibus funis ADB, qui &longs;upponatur omninò
grauitate carere, & reuoluatur circa trochleam CDE
conuertibilem circa axim fixum F. patet quòd funes
AC, & BE perpendiculariter ad ho
rizontem CE prementes, & exten&longs;i
contingunt peripheriam rotæ in ter
minis oppo&longs;itis C, & E eiu&longs;dem dia
metri, &longs;eu libræ horizontalis, ergo
funes CA, & EB &longs;unt inter &longs;e paralle
li;
&longs;eceturque bifariam in G, & vt pon
dus A ad B ita fiat di&longs;tantia BI ad IA
tum I e&longs;&longs;e centrum grauitatis com
munis duorum colligatorum ponde
rum A & B, funis enim hanc propor
tionem non alterat, cùm nullius gra
uitatis &longs;upponatur: a&longs;cendat po&longs;tea
pondus minus B vbicumque ad L, & deprimatur ma
ius pondus A v&longs;que ad K. dico quod ambo in com
muni centro grauitatis de&longs;cendunt circa libræ cen
trum, &longs;eu fulcimentum &longs;tabile G motu directo, & per
pendiculari ad horizontem.
KL quia funis ADB æqualis, imò idem e&longs;t, quàm K
DL, igitur ablato communi ADL erit de&longs;cen&longs;us AK
æqualis a&longs;cen&longs;ui BL; quare in triangulis &longs;imilibus
ob æquidi&longs;tantiam laterum AK & BL homologorum
vt AK ad BL ita erit AG ad GB & ita pariter KML
ad M, &longs;untque latera AK & BL æqualia inter&longs;&etail;
ergo &longs;e mutuò bifariam &longs;ecabunt rectæ coniungentes
AB, & KL in eodem puncto G; idemque continget
translatis ponderibus in N, & O, & ideo punctum G
erit centrum, &longs;eu &longs;tabile
modolibet reuolutæ: ducatur tandem per I recta li
nea IP parallela funibus &longs;ecans libras KL, & NO i&ntail;
punctis M, & P patet libras in eadem proportione re
ciproca &longs;ecari in punctis I, M, P, quam habent oppo&longs;i
ta pondera proindeque eadem puncta erunt centr&atail;
grauitatum, earumdem librarum cum ponderibus ap
pen&longs;is; quapropter licet minus pondus B a&longs;cendat per
BLO, tamen ambo pondera A, & B in communi
tro
G, & in extremo fune-penduli GI de&longs;cendunt no&ntail;
circulari, &longs;ed directo motu perpendiculari ad hori
zontem ab I per M & P, quod fuerat o&longs;teudendum.
momentis
grauium in
fluido inna
tantium.
libus, & concentricis eiu&longs;dem trochleæ reuoluuntur.
SIt trochlea CDE circa axim F conuertibilis, & in
ea &longs;it alia concentrica circumferentia RSQ, &
funi SQB alligetur pondus B, alij verò funi DEA alli
getur pondus A
detur, vt in præcedenti, funes EA, & BQ e&longs;&longs;e inter&longs;e
parallelos; po&longs;tea
dus
punctum I e&longs;&longs;e centrum grauitatis communis ponde
rum A, & B (cum funes nullius ponderis
deinde reuoluta trochlea
oppo&longs;itum pondus A de&longs;cendat v&longs;que ad K
turque
in G. dico duo pondera A, & B i&ntail;
communi eorum centro grauitatis
I circa libræ centrum &longs;tabile G mo
tu directo, & perpendiculari ad
horizontem quia in tro
chleæ reuolutione
dit
plicatio funis è rota CDE, & pon
dus B a&longs;cendit quantum funis BQS
circumuoluitur circa rotam QSR
cùmque duæ rotæ concentricè con
nexæ &longs;imul tempore
ca &longs;ixum axim F, ergo de&longs;cen&longs;us AK
ad
nem habet, quam peripheria CDE ad peripheriam R
SQ, &longs;eu
FE ad radium
&longs;imilibus, ob æquidi&longs;tantiam laterum AK, & BL, erit
AG ad GB vt KG ad GL, &longs;eu vt AK ad BL;
in eodem puncto fixo G duæ libræ AB, & KL &longs;e mutuò
&longs;ecabunt in eadem proportione, quam habent motus
eorumdem terminorum, vnde, ex mechanicis, erit
punctum G centrum, & fulcimentum firmu&mtail;
vtriu&longs;que libræ AB, & KL po&longs;tremò ducatur per I
rectà IM parallela funibus, &longs;eu perpendicularis ad
horizontem &longs;ecans KL in M planè &longs;ectæ erunt duæ li
bræ prædictæ in I, & M in eadem proportione reci
proca ponderum &longs;u&longs;pen&longs;orum, ideoque puncta I, &
M erunt centra grauitatum vtriu&longs;que libræ: quare li
cet pondus B a&longs;cendat p BL, tamen verum e&longs;t duo
pondera AB in communi centro grauitatis I &longs;u&longs;pen&longs;a
circa centrum firmum G, & in termino fune-penduli
GI de&longs;cendere directo motu, & perpendiculari ad
horizontem per IM, & hoc erat o&longs;tendendum.
momentis
grauium in
fluido inna
tantium
momentis
grauium in
fluido inna
tantium
Huiu&longs;modi mechanicæ &longs;peculationes maximè
ferunt
pro cuius declaratione primò con&longs;iderari debet.
& in &longs;eip&longs;um reflexo.
SIt igitur &longs;ipho ABDG in &longs;e ip&longs;um reflexus cuius
brachia lateralia BN & GO directa &longs;int, in
ter &longs;e parallela, & ad horizontem perpendiculariter
erecta & æquè ampla. includatur po&longs;tea gutta aliqua
mercurij BC, quæ in fi&longs;tulis angu&longs;tis retinetur in eo
dem &longs;itu collecta, reliqua verò cauitas eiu&longs;dem fi&longs;tulæ
BAGDC repleatur aqua; tunc ductis à punctis B, &
C & à
neis rectis parall elis horizonti BG, HI, & CF, & &longs;ec
ta HI bifariàm in L; patet quòd duo grauia, mercu
rius nempe BC, & aqua GF &longs;u&longs;penduntur in eade&mtail;
libra imaginaria HI, quia hæc duo corpora motibus
contrarijs agitantur &longs;u&longs;pendunturque ab eadem li
bra horizontali: nec actionem eorumdem corporum
impediunt, vel adiuuant &longs;upremæ, vel infimæ aquæ
partes; quando quidem aqua AB,
æquilibratur collaterali AG cù&mtail;
&longs;int homogeneæ & æquè altæ, non
&longs;ecùs infimæ aquæ partes CD & F
E inter &longs;e æquilibrantur; quare ac
tioni compre&longs;&longs;iuæ mercurij CB,
tummodo
aquæ FG in eodem &longs;itu horizontali
con&longs;titutæ. fiatiam vt pondus mer
curij CB ad grauitatem aquæ FG
ita reciprocè di&longs;tantia IM ad MH,
quare punctum M erit centrum gra
uitatis duorum corporum BC, & GF, cùmque libr&atail;
imaginaria HI fulciatur in puncto L rectæ LK per
pendiculariter horizonti eductæ ex infimo &longs;itu fi&longs;tu
læ, vbi bifariam libra, & magnitudines fluidæ
tur
dè, iuxtà leges mechanices, libra flectetur
do
ficitur propterea quòd centrum communis grauita
tis M nece&longs;&longs;ariò labitur deor&longs;um iuxta penduli na
turam. &longs;ed prædictus motus centri grauitatis M non
e&longs;t circularis, &longs;ed e&longs;t directus ad horizontem
dicularis
tingit
&longs;us talis e&longs;t, cùm primum cvlindrus mercurij CB fer
tur deorsùm transferendo eius centrum H in N, de
nuò comparatur cum alio aquæ cylindro æquali ip&longs;i
FG è regione po&longs;ito, cuius centrum grauitatis erit
punctum O, & tunc denuò creatur noua libra
talis
in P & Q cuius centrum P, quia denuò partes aquæ
collaterales &longs;upernæ & infernæ &longs;ibi ip&longs;is æquilibratæ
non adiuuant, neque impediunt duo æqualia corpo
ra mercuriale ex N, & aqueum ex O, quæ ad inuicem
comparantur in eadem libra horizontali,
à parallelis lineis HN, MQ, & IO in ei&longs;dem rationi
bus diuidatur, perductum erit centrum grauitatis pr&ecedil;
dictorum corporum ad punctum Q, vnde patet de
&longs;cendi&longs;&longs;e per rectam lineam MQ perpendicularem ad
horizontem, perdurabitque eius de&longs;cen&longs;us,
corpus mercuriale CB ad &longs;itum infimum fi&longs;tulæ DE
perducatur, quando nimirum eius grauitatis
H præcisè infimum &longs;itum K fi&longs;tulæ attinget.
momentis
grauium in
fluido inna
tantium
momentis
grauium in
fluido inna
tantium
Nec dicas fictionem e&longs;&longs;e quòd ad&longs;it libra horizon
talis directa HI, quæ perpetuò renouetur, nam reue
rà fulciuntur, &longs;u&longs;tentanturque duo cylindri CB, & G
F à plano aquæ &longs;ubiectæ CF quod quidem, mobile e&longs;t,
cùm cedat de&longs;cen&longs;ui mercurij CB & &longs;uperficies F
eleuetur eodem tempore & pari velocitate circa eius
punctum intermedium, igitur prædicta duo corpora
BC, & GF dum ambo premunt libram fluidam &longs;ub
iectam &longs;uis ponderibus, & coguntur moueri &longs;imùl æ
què velociter contrarijs lationibus nece&longs;&longs;ariò libram
con&longs;tituunt, quæ in &longs;uo centro grauitatis energia&mtail;
vniuer&longs;æ &longs;uæ compre&longs;&longs;ionis exercent, verum tame&ntail;
e&longs;t quòd prædicta libra non flectitur, &longs;ed continentèr
renouatur in &longs;itu horizontali, quandoquidem aqu&atail;
eleuata iam non amplius agit contra pre&longs;&longs;ionem mer
curij CB vt dictum e&longs;t, propterea quòd æquilibratur
cum aqua collaterali &longs;upra mercurium CB eleuata.
momentis
grauium in
fluido inna
tantium
tuit cum æqualimole collateralis fluidi libram
radiorum, cuius centrum grauitatis continenter
de&longs;cendende eleuat leuiorem aquam col
lateralem, &longs;emperque renouatur
horizontalis libra.
HOc præmi&longs;&longs;o intelligatur iam vas aquà plenum
RSTX, & intra eius profunditatem appona
tur pri&longs;ma marmoreum ABCD, & producantur eius
ba&longs;es horizontales AB, & CD
v&longs;que ad G & H, atque planu&mtail;
AD producatur &longs;ur&longs;um, & deor
&longs;um v&longs;que ad M, & V perpendi
culariter ad horizontem. hic iam
habemus
ip&longs;um circumductum, vt in pr&ecedil;
cedenti propo&longs;itione expo&longs;itum fuit, quia aqua BM
GHVC ambit pri&longs;ma &longs;upernè, lateraliter, & infernè,
nec moueri pote&longs;t
&longs;ubiecta CID è &longs;uo loco expellatur, & lateralitèr fluat
ver&longs;us P, circumfera turque &longs;ur&longs;um v&longs;que ad locu&mtail;
relictum à pr&ecedil;dicto pri&longs;mate lapideo in E. &longs;unt igitur
duæ partes MT, & MS veluti duo canales laterales
&longs;iphonis, quitamen &longs;e&longs;e contingunt in communi la
tere MV; prætereà duæ portiones aquæ &longs;upremæ XA,
& MG cùm &longs;int homogeneæ, æquè graues &longs;pecie, &
æque altæ, &longs;e mutuò æquilibrantur, pariterque duæ
portiones aqueæ &longs;ubiectæ CV, & DS pariter æquili
brantur, vnde patet quòd tantummodo comparari
debent inter &longs;e duo corpora collateralia &longs;axum nimi
rum BD, & aqua AH, quæ ab ei&longs;dem planis horizon
talibus BG, & HC comprehenduntur, & hæc &longs;imiliter
fulciuntur &longs;u&longs;tentanturque à plano aquæ &longs;ubiectæ H
C
amouibili & cedenti. in&longs;i&longs;tunt igitur prædicta duo cor
pora BD, & AH non &longs;ecùs &longs;u&longs;pen&longs;a ac &longs;i &longs;uper libram
HC inniterentur; huius verò centrum mobile e&longs;&longs;et
punctum intermedium D, vbi nimirum libra HC bi
fariàm &longs;ecatur, & &longs;i à centro grauitatis O &longs;axi BD ad
centrum P grauitatis aquæ AH recta linea
tur
tionem grauitatum eorumdem corporum, patet Y e&longs;
&longs;e centrum grauitatis communis &longs;axi BD, & aquæ A
H, cùmque libra PO &longs;ecetur bifariàm à plano MV in
Q iam con&longs;urget fune-pendulum QY horizontaliter
excen&longs;um versùs O ob exce&longs;&longs;um grauitatis &longs;axi &longs;upra
aquæ pondus &longs;pecificum, igitur nece&longs;sè e&longs;t vt tot&atail;
libra flectatur Quia
verò in de&longs;cen&longs;u aqua &longs;ubiecta expul&longs;a ex I curuo iti
nere &longs;ur&longs;um fluit per ZF v&longs;que ad E denuò renouatur
libra horizontalis, comparanturque inter &longs;e &longs;axum B
D cum aqua collaterali in nouo &longs;itu horizontali de
pre&longs;&longs;iori exi&longs;tente, igitur denuò eadem proportione
di&longs;&longs;ecta libra imaginaria horizontali,
æquale priori eadem vi flectetur
centrum grauitatis eius motu perpendiculari ad hori
zontem quòu&longs;que ad fundum va&longs;is &longs;axum pertingat.
momentis
grauium in
fluido inna
tantium
momentis
grauium in
fluido inna
tantium
mer&longs;um minùs graue aqua collaterali fueris.
SI po&longs;tea pri&longs;ma BD fuerit ligneum, & minùs gra
ue &longs;pecie quam aqua AH, tunc ij&longs;dem manen
tibus &longs;olummodò centrum grauitatis communis Y
cadet ad partes aquæ inter Q & P, & proindè vniuer
&longs;um graue compo&longs;itum ex aqua, & ligno vim faciet
uitatis Y, & ideò vehementiùs
primetur
hæc verò ob eius continuitatem
& naturam
&longs;ioni non cedit, nece&longs;&longs;ariò impel
letur versùs I, & &longs;ic vim faciet &longs;ur
&longs;um exprimendo ligni &longs;uperficiem DC; at dum
a&longs;cendit, oportet vt expellat è &longs;uo loco
aquam E, quæ tran&longs;uer&longs;ali & obliquo motu perduce-
tur ab E per FZ versùs I, & &longs;ic à prædicto motu circu
lari aquæ ambiemis lignum expelletur &longs;ursùm; atta
men ratio mechanica huius actionis pendet ex eo,
quòd libra horizontalis imaginaria PO flectitur per
petuò deorsùm quidem ad partes centri grauitatis Y
circa centrum Q, & &longs;ursùm ad partes O. &longs;ed &longs;ummo
perè animaduertendum e&longs;t prædictam libram imagi
nariam horizontalem renouari &longs;ucce&longs;&longs;iuè prout
a&longs;cendit,
tibus aqueis, quæ &longs;ucce&longs;&longs;iuè offendit intercepta in
ter prædicta plana horizontalia GB, & HC: nece&longs;sè
ergo e&longs;t vt lignum prædictum numquàm quie&longs;cat in
tra aquam demer&longs;um quòu&longs;que ad &longs;upremam
aquæ RX perducatur; in&longs;uperque aliqua eius por
tio emineat.
momentis
grauium in
fluido inna
tantium.
Hinc patet veritas Archimedei a&longs;&longs;umpti, quòd
fluidi con&longs;i&longs;tentis natura requirit vt partium eius æ
què iacentium magis compre&longs;&longs;æ &longs;ursùm impellant
partes minus pre&longs;&longs;as perpendiculariter ad
Quia aqua &longs;ubiecta HCTS ob eius con&longs;i&longs;tentia&mtail;
non conden&longs;atur, & mobilis e&longs;t, quia fluida, ergo li
bram flexibilem con&longs;tituit,
magis compre&longs;&longs;a quàm DT (propterea quòd parsa
quea GD grauior e&longs;t ligno AC) igitur libra fluida
HDC flecti debet de&longs;cendendo HD & DC a&longs;cen
dendo, quare tota aqua HSVD deorsùm depre&longs;&longs;a im
pellet aquam DVTC &longs;ursùm.
momentis
grauium in
fluido inna
tantium.
tunc de&longs;cen&longs;us communis centri grauitatis non
efficietur per lineam perpendicularem ad
horizontem &longs;ed motu curuo per
parabolam.
IN progre&longs;&longs;u prædictæ operationis notabilis e&longs;t va
riatio &longs;itus centri grauitatis eius & mechanicæ eius
operationis.
Sit igitur in eodem va&longs;e pri&longs;ma ligneum ABCD
perductum ad &longs;upremam aquæ libellam RX, tunc &longs;i
militer inter &longs;e comparantur duo pri&longs;mata BD ligno
um, & AH aqueum in eodem plano horizontali &longs;u
biecto HC in&longs;i&longs;tentes, & proindè
efficitur-libra imaginaria PO mo
bilis circa eius fulcimentum Q, &
centrum grauitatis
porum cadit ad partes aquæ nem
pèin Y inter
ergo &longs;e quitur vt prædicta libra flecti debeat deorsùm
ad partes Y & &longs;ur&longs;um a&longs;cendatterminus O vnà cum li
gno versùs aquæ libellam fupremam RX, igitur por
tio aliqua ligni &longs;uprema eleuabitur &longs;upra prædictam
aquæ libellam, vt patet in po&longs;trema figura, & tunc
magis ligneum pri&longs;ma exurgit, eminetque &longs;upra aqu&ecedil;
libellam, & in prædicto a&longs;cen&longs;u dum collaterale pri&longs;-
ma aqueum imminuitur, pondus eius quòd prius &longs;u
perabat grauitatem ligni BD, tandem po&longs;t
ponderis aquæ
le ponderi cylindri lignei BD, & tunc coniunctis
centris grauitatum eorum à rect&atail;
PO hæc quidem bifariàm &longs;ecabi
tur in termino Q &
centrum, atque fulcimentum ha
bebitque pondus ligni BD ad
dus
proportionem, quam habet reciprocè PQ ad QO, &
proindè centrum grauitatis commune Y incidet præ
cisè in centro &longs;eù fulcimento libræ
bratis prædictis ponderibus libra quie&longs;cet, nec pri&longs;
ma ligneum BD vlteriùs
decidet ni&longs;i ex accidenti ratione impetus acqui&longs;iti.
momentis
grauium in
fluido inna
tantium.
Hinc patet quòd quando primò lignum BD exur
gere incipit &longs;upra aquæ libellam RX tunc continen
ter magis ac magis centrum communis grauitatis Y
motu obliquo, & curuo
tur cum fulcimento Q libræ PO &longs;ursùm tran&longs;lat&ecedil;,
non &longs;ecùs, ac in &longs;iphone aqua eleuata in vno eius bra
chio de&longs;cendendo perducit centrum grauitatis eius
per curuam lineam parabolicam, vt dictnm e&longs;t; con
cipi ergo debet &longs;ipho inæqualium brachiorum
primum ba&longs;is &longs;uprema AB ligni attingit aquæ libel
lam, & quia tunc exce&longs;&longs;us grauitatis &longs;pecificæ aquæ
AH &longs;upra pondus ligni BD perindè agit ac &longs;i aliud
fluidum æquè graue &longs;pecie ligno ip&longs;i BD & maioris
molis &longs;upra ba&longs;im HD in&longs;ifteret procul dubio ad ma
iorem &longs;ublimitatem eleuaretur prædictum fluidu&mtail;
minùs graue &longs;pecie, quàm aqua AH, cuius
pondus æquale e&longs;&longs;et ponderi eiu&longs;dem aquæ commu
nis AH, quare ab eleuatiori loco fluidum prædictum
deorsùm excurrendo eleuaret lignum depre&longs;&longs;um BD
præcisè vt in &longs;iphone &longs;uperiùs expo&longs;ito contingeret.
momentis
grauium in
fluido inna
tantium.
Ex hac theoria facili negotio re&longs;olui ac
ri
in primo de infidentibus humido demon&longs;trantur.
e&longs;t, neque habet centrum grauitatis in vno puncto
&longs;ed libra e&longs;&longs;e &longs;olet &longs;uperficialis, cuius fulci
mentum e&longs;t linea circa centrum figuræ,
& grauitas communis exercetur
quoque in linea aliqua.
SOllummodò indicabo
dicta mechanica operatione punctum, quod
mune
rea quòd libra compo&longs;ita ex &longs;olido & fluido ambien
te non &longs;emper linearis e&longs;t, &longs;ed &longs;uper ficiem aliquando
componit, in qua nedum fulcimentum, &longs;ed etiam lo
cus vbi exercetur communis grauitas linea e&longs;&longs;e &longs;olet
aliquando recta, aliquando curua, & multoties com
po&longs;ita ex pluribus rectis. &longs;i enim in medio aquæ im
mergatur directè & perpendiculariter ad
pri&longs;ma vel cylindrus &longs;olidus, tunc quidem dum pri&longs;
ma de&longs;cendit, vniuer&longs;a aqua illud ambiens &longs;ur&longs;u&mtail;
eleuatur. vel illo a&longs;cendente hæc deprimitur, com
parari ergo debet pri&longs;ma comprehen&longs;um cum anulo
&longs;eu potiùs cum fi&longs;tula fluida id ambiens, & &longs;ic effici
tur libra quædam plana cuius fulcimentum erit linea
in confinio cylindri demer&longs;i, & fluidi ambientis ex
ten&longs;a pariterque locus, vbi communis grauitas exer
cetur non erit punctum, &longs;ed erit quoque linea in eo
dem plano horizontali producta; &longs;ed facilitatis gra
tia concipi debet &longs;ector aliquis in prædicto plano ex
centro prædictæ libræ &longs;uperficialis in axe cylindri
con&longs;tituto v&longs;que ad &longs;uperficiem aquæ ambientis, qu&ecedil;
contrarijs motibus vnà cum cylindro mouetur; &longs;eù
potius concipi debet radius, &longs;eù &longs;emidiameter
diui&longs;ibilis, &longs;ed phy&longs;ica, & h&ecedil;c v&longs;urpari pote&longs;t vt libra
particularis cum &longs;uo fulcimento, & centro grauita
tis, vniuer&longs;a verò libra &longs;uperficialis compo&longs;ita erit ex
pluribus, & innumeris libris radio&longs;is, vt dictum e&longs;t,
& hæc innui&longs;&longs;e modò &longs;ufficiat in hac generali præpa
ratione, inferiùs enim accuratiùs exponentur.
momentis
grauium in
fluido inna
tantium.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
&longs;uperficiei Telluris graue e&longs;t, exercetque
vim &longs;uæ grauitatis etiam dum in
proprio loco, & in ip&longs;omet
fluido vniuer&longs;ali &longs;ui
generis con&longs;i&longs;tit,
ac quie&longs;cit.
SVppo&longs;uimus cum Archimede aquam, & reliqu&atail;
corpora fluida terram ambientia vi propriæ gra
uitatis compre&longs;&longs;ionem vniformem exercere ver&longs;us
centrum telluris, ex quo &longs;ubindè fit vt &longs;phæricè circa
terræ centrum di&longs;ponantur. præterea &longs;uppo&longs;uimus
cum eodem Archimede partes eiu&longs;dem fluidi minùs
pre&longs;&longs;as expelli ac &longs;ubleuari &longs;ur&longs;um à partibus
fluidi magis compre&longs;&longs;is, & grauatis; ex qua hypothe
&longs;i deducitur quodliber fluidum, veluti aqua e&longs;t, gra
uitatem habere eamque exercere etiam in proprio
loco, & naturali regione, &longs;cilicèt aquam ip&longs;am dum in
tota aqua quie&longs;cit tunc quoque grauitatem exercere
&longs;ubiecta corpora comprimendo.
mede dedu
cunt aquam
in ipsa aqua
non grauita
re, & id
Peripatetici
affirmaret.
Hoc autem à plurimis negatur qui putant Archi
medem oppo&longs;itum &longs;en&longs;i&longs;&longs;e. idip&longs;um quoque negant
aliqui peripatetici qui cen&longs;ent non &longs;emper veru&mtail;
e&longs;&longs;e quòd partes &longs;uperiores corporis grauis compri
mant, & vim inferant inferioribus, & contiguis, ni&longs;i
infimæ partes leues &longs;int ab&longs;olutè, vel re&longs;pectiuè, vnde
gr. &longs;uper
rem
pre&longs;&longs;ionis exercere, non itidem aquam &longs;upra ip&longs;a&mtail;
terram collocatam, nec aerem aquæ incumbentem,
imò nec aerem &longs;upra aerem con&longs;titutum, nec aquam
&longs;upra aquam po&longs;itam. huiu&longs;modi propo&longs;itionem tali
ratiocinio confirmare nituntur, cum Natura cau&longs;a, &
principium motus &longs;it, nec operetur fru&longs;tra &longs;ed ad cer
tum finem, & ad bonum, proculdubio ordinauit mo
tum naturalium corporum ad certum finem, & ad bo
num, &longs;cilicèt ad con&longs;eruationem, & quia actus, &longs;eù
perfectio quam appetunt, & quam acquirere nitun
tur corpora grauia, & leuia dum mouentur e&longs;t migra
tio, & debita con&longs;titutio in proprijs locis naturali
bus, grauium nempè de or&longs;um, & leuium &longs;ursùm, hine
&longs;equitur quòd po&longs;t
ducta &longs;unt, motus omninò ce&longs;&longs;at, vtpotè naturæ de&longs;i
derio, & fine expleto, eo quòd vt ait Ari&longs;toteles Na
tura non mouet corpus aliquod vt
cèt vt ip&longs;um perpetuò, & in
tummodo vt illud ad terminum, & finem perducat
vt ibidem quie&longs;cat; verùm facultates aut virtutes
quibus &longs;ublunaria corpora ad propria loca feruntur
nil aliud &longs;unt, quàm grauitas aut leuitas. igitur huiu&longs;
modi facultates ordinatæ &longs;unt ad perducenda
taria
nec vlteriùs v&longs;um aliquem habere po&longs;&longs;unt, quando
quidem &longs;i præterea motum pro&longs;e querentur in &longs;uis lo
cis perturbarent & confunderent naturalem fituatio-
nem eorumdem corporum. & profectò e&longs;t con&longs;enta
neum vt elementa non nitantur de&longs;erere propria lo
ca, & propterea careant illo naturali &longs;timulo &longs;eu prin
cipio motus quo impellebantur antequam ad &longs;ua na
turalia loca perueni&longs;&longs;ent; hinc deducitur nullum ele
mentum in proprio loco grauitatem, aut leuitatem
habere, &longs;ed aqua in ip&longs;a aqua po&longs;ita in propria, & na
turali regione degit & &longs;ic aer in aere, ergo neutrum
horum elementorum grauitatem in &longs;uo loco habet,
aut exercet. & primo quoad Archimedem pertinet
videntur aduer&longs;arij nequaquam tanti viri mente&mtail;
a&longs;&longs;equuti &longs;ui&longs;&longs;e vt ex eius verbis &longs;atis vt verò Peripateticis fiat &longs;atis, ne dum
tem po&longs;itiuam in natura dari o&longs;tendam, &longs;ed præterea
probabo fal&longs;um e&longs;&longs;e quòd po&longs;t quam corpora natura
lia ad &longs;ua loca perueniunt & ibidem quie&longs;cunt graui
tas v&longs;um non habet, ni&longs;i ad perturbandum pr&ecedil;clarum
ordinem vniuer&longs;i; nam è contra &longs;uadere conabor tunc
præcisè corpora grauitatem exercere cùm in &longs;uis lo
cis quie&longs;cunt, imò cau&longs;am, quare in &longs;uis locis quie
&longs;cunt, e&longs;&longs;e quia pondus exercent, &longs;ed prius
da
efficiat pondus dum comprimit; & profectò actio &
compre&longs;&longs;io corporis grauis non e&longs;t tran&longs;itus localis
pilæ ferreæ v.g. dum ver&longs;us terram de&longs;cendit, nec
præterea e&longs;t &longs;implex contactus quo coniungitur cum
&longs;uperficie telluris &longs;ubiectæ, &longs;ed e&longs;t vis, & energia, qua
impellitur deor&longs;um
terra; veluti cum pondus in trutina appenditur licet
quie&longs;cere videatur exercet actionem quamdam
pre&longs;&longs;iuam
autem facilè percipiemus &longs;i &longs;ingamus duos homines
æquè validos & robu&longs;tos qui totis viribus &longs;e mutuò
impellant, vbi manife&longs;tum e&longs;t quòd exi&longs;tentibus vi
ribus contrarijs inter &longs;e æqualibus, vt vna alteri no&ntail;
pr&ecedil;ualeat, tunc neuter luctantium dimouebitur è &longs;uo
loco, &longs;ed ibidem quie&longs;cet, licèr quilibet
&longs;am vim, & facultatem propriam exerceat impellen
do, & repellendo &longs;uum antagoni&longs;tam, non &longs;ecùs
do
ter, licèt minimè valeat eam è &longs;uo loco deijcere, ac
commouere, vt nimirum motus progre&longs;&longs;iuus hominis
impellentis, aut columnæ &longs;ub&longs;equatur; nihilominùs
negari non pote&longs;t motus impul&longs;iuus mu&longs;culorum, &
artuum hominis impellentis; nec pariter negari po
te&longs;t aliqua exigua & in&longs;en&longs;ibilis flexio eiu&longs;dem
næ
&longs;ui, & flexioni re&longs;i&longs;tit. &longs;imiliter cùm pila ferrea &longs;uper
ba&longs;im, vel laminam vitream innititur concedendum
omninò e&longs;t effici con&longs;tipationem quamdam partium
ferri prementis, & vitri compre&longs;&longs;i, vt nimirum ali
quanti&longs;per eorum poro&longs;itates
(vt o&longs;ten&longs;um e&longs;t cap.
26. de Vi percu&longs;&longs;ionis) reperiri
in rerum natura corpora compo&longs;ita
eò dura &longs;int vt compre&longs;&longs;ioni cuiuslibet corporis re&longs;i
&longs;tere valeant. quod verò prædicta compre&longs;&longs;io vitri ab
ingenti pondere &longs;iat patet ex eo quòd augendo ma
gis ac magis pondus comprimens, tandem ba&longs;is vi-
trea di&longs;rumpitur, di&longs;&longs;ilit, atque conteritur eo pr&ecedil;cisè
modo quo ab ictu mallei di&longs;rumpitur; & &longs;i quidem
hoc verum non e&longs;&longs;et &longs;cilicèt &longs;i à pondere vtcumqu&etail;
multiplicato & aucto ba&longs;is vitrea non &longs;tringeretur &
comprimeretur, quælibet exili&longs;&longs;ima ba&longs;is vitrea to
leraret vim compre&longs;&longs;iuam ponderis cuiu&longs;libet
va&longs;ti, quod procul dubio fal&longs;um e&longs;t.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
Hoc po&longs;ito nemo negabit quòd &longs;i pondus duplice
tur vt &longs;cilicèt vnum &longs;uper alterum &longs;uperponatur,
duplici vi, ac robore infima ba&longs;is vitrea comprime
tur ac con&longs;tipabitur, & proindè poro&longs;itates multò
magis imminuentur à duplici impul&longs;u, quando
concipi non pote&longs;t moles grauis aucta & multiplica
ta ab&longs;que eo quòd pondus, & proindè vis, & energia
compre&longs;&longs;iua versùs centrum telluris multiplicetur,
vnde fit vt partes &longs;olidæ & con&longs;i&longs;tentes
&
At &longs;i hoc contingit in corporibus duri&longs;&longs;imis, nega
ri certè non poterit in corporibus fluidis, quæ no&ntail;
minùs grauia &longs;unt &
continentur tanta vi, quanta e&longs;t energia ponderis
eorum, ita ut multiplicata fluidi mole centies, & mil
lies va&longs;is fundum centies, & millies maiori vi com
primatur, & licèt ibidem non ad&longs;it motus progre&longs;
&longs;iuus, numquam tamen deficiet motus tonicus, & re&longs;
trictio pororum fundi va&longs;is, & compre&longs;&longs;io pororum
eiu&longs;dem fluidi, &longs;i fortè poro&longs;itates habuerit, & &longs;icuti
fluidum grauitat atque con&longs;tringit poro&longs;itates fundi
va&longs;is, hac de cau&longs;a, quia ponderat, & grauitat, nulla
ratio vetat, quin pondere &longs;uo comprimat in fimam &longs;u
biectam laminulam eiu&longs;dem fluidi quæ fundo va&longs;is
contigua e&longs;t, quandoquidem minimè po&longs;&longs;unt &longs;upre
mæ fluidi partes fundum va&longs;is comprimere ab&longs;qu&etail;
eo quod impellant, & &longs;tringant in fimam eiu&longs;dem flui
di laminulam, cùm actio in di&longs;tanti fierinon po&longs;&longs;it, &longs;ed
contactu quodam remotiores impellendo eis conti
guas &longs;ubiectas partes, & hæ&longs;ub&longs;equentes &longs;erie qua
dam ordinata quou&longs;que fundum comprimant.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
SEd hoc euidentius &longs;ic patebit, &longs;it fi&longs;tula vitrea A
NO perpendiculariter ad horizontem erect&atail;,
repleaturquè aqua, &longs;eù quolibet alio fluido cor
pore, & ductis innumeris planis horizonti
tibus
laminas gracillimas &longs;eù membranas æquè
altas AB, BC, CD, DE, EF, FM, & MN. &
primò &longs;i verum e&longs;t, vt aduer&longs;arij credunt
aquam in ip&longs;amet aqua collocatam
uitare, igitur &longs;uprema laminula aquea AB
pror&longs;us
nam
cebit (hoc enim grauitatis nomen indicat) neque eam
deor&longs;um impellet perinde ac &longs;i aqua &longs;uprema AB non
ade&longs;&longs;et, proindeque hæc non augebit grauitatem in
ferioris laminæ BC, aliàs &longs;uprema aqua AB pondera-
ret, comprimeretque &longs;ubiectam aquam BC, quod e&longs;t
contra aduer&longs;arij hypothe&longs;im; eadem ratione vniuer
&longs;a aqua ABC nil ponderabit, ne que comprimet &longs;ub
iectam laminam aqueam CD, & tota aqua AD nec
etiam comprimet aut grauitatem inferet &longs;upra infe
riorem
bet de reliquis omnibus laminulis fluidis totam alti
tudinem aquæ componentibus, & hoc optima ratio
ne de duximus,
tium & nil pror&longs;us deor&longs;um impellentium nemo &longs;anæ
mentis affirmabit vim compre&longs;&longs;iuam deorsùm exer
cere, imò concedet æquè operari ac &longs;i e&longs;&longs;et vnica &longs;in
gularis laminula, vel dicet &longs;ubiectum corpus à nihilo
comprimi, & è contra &longs;eries corporum vim
poris, & hoc &longs;anè lumine naturæ
tur infimam laminam aqueam MN no&longs;tri va&longs;is nullam
compre&longs;&longs;ionem pati ab vniuer&longs;a aqua &longs;uperpo&longs;it&atail;
MA non &longs;ecùs ac &longs;i à nihilo premeretur vnde fit vt in
ferior pars aquea MN ablata qua MA tanta vi præ
cisè comprimat va&longs;is fundum NO ac &longs;i &longs;uper&longs;taret
immen&longs;a moles aquea NA, &longs;ed illa ob ponderis exi
guitatem haud &longs;en&longs;ibilem vim vitreo fundo infert,
nec ip&longs;um inflectit, aut di&longs;rumpit, igitur neque
inflectetur aut
quea NA ei &longs;uperponitur; quia verò hoc euidentiæ
&longs;en&longs;us repugnat affirmandum e&longs;t, aquam licèt in ip&longs;a
met aqua iners & quie&longs;cens videatur, nece&longs;&longs;ariò gra
uitatem exercere.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
dum in &longs;uo
toto quie
&longs;cens ponde
rat.
PRæterea v&longs;urpetur idip&longs;um vas vitreum, &longs;ed in
flexum, vt e&longs;t AMOP &longs;iphonis inuer&longs;i figuram
referens, atque portio ANO aqu&atail;
impleatur, reliqua verò fi&longs;tula OP o
leo. Et quia vt mox o&longs;ten&longs;um e&longs;t ex
aduer&longs;arij hypothe&longs;i tota aqua AM
vim non infert neque impellit infe
riorem aqueam laminam MN, cù&mtail;
nullam grauitatem &longs;uper eam exer
ceat; igitur tota moles aquea AM nil prorsùs impel
let terminum aquæ O & proindè ab hoc non impelle
tur &longs;ur&longs;um oleo&longs;us cylinder OP, igitur oleum OP
nulla ratione &longs;ubleuari &longs;ursùm deberet, &longs;ed hoc e&longs;t
fal&longs;um, igitur fal&longs;a e&longs;t quoque hypothe&longs;is a&longs;&longs;umpta,
quòd aqua in ip&longs;amet aqua po&longs;ita grauitatem no&ntail;
exerceat.
Et profectò methodus ac criterium digno&longs;cendi,
an corpus aliquod grauitet, atque impellat alterum,
erit huiu&longs;modi; con&longs;iderari nimirum debent effectus
ab eo producti, & quanta vis contraria requiritur,
vt vnum à con&longs;ortio, & contactu alterius diuellatur,
& &longs;eparetur, & quia &longs;i nauis natando lateraliter &longs;co
pulum contigeret, po&longs;&longs;et à quacumque exigua vi tra
hi, diuelli, & &longs;eparari ab eodem &longs;copulo, hinc in re
optimo inferemus nauim omninò carere vi motiua, &
impul&longs;iua tendendi ver&longs;us &longs;copulum, è contra, quia
videmus, quòd pila ferrea non pote&longs;t à contactu &longs;oli
&longs;eiungi, ac diuelli ni&longs;i æqualis facultas, & energi&atail;
contraria adhibeatur, &longs;cilicet ni&longs;i apponatur pondus
in altera extremitate libræ, quod æquale &longs;it grauita
ti prædictæ pilæ ferre&ecedil;, &longs;icuti cùm homo robu&longs;tus co
lumnam aliquam impellit, non pote&longs;t ab ea &longs;eiungi,
ni&longs;i adhibeatur vis motiua prorsùs æqualis ei, quam
homo exercet; hinc de ducemus pilam vim grauitatis,
& hominem vim mu&longs;culorum exercere.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
Porrò effectus producti ab illa ferrea pila à paui
mento &longs;ubnixa plures &longs;unt, ac varij, con&longs;tringuntur
nempè pori &longs;ubiecti corporis pilam &longs;u&longs;tinentis, in
flectitur paritèr idip&longs;um contunditurque, & multo
tiès diffringitur, ac di&longs;&longs;ilit in particulas minimas,
igitur &longs;i huiu&longs;modi effectus ip&longs;amet aqua operaretur,
ab&longs;que vlla hæ&longs;itatione aquam in ip&longs;amet aqua gra
uitare affirmaremus. Modò videmus, quòd aqua ad
ingentem altitudinem eleuata nedùm &longs;olum, ac fun
dum va&longs;is inflectit, &longs;ed ip&longs;um multoties diffringit, &
hoc magis patet &longs;i fundum va&longs;is flexibile fuerit, &longs;i ve
rò con&longs;tringi, ac conden&longs;ari poterit, illud con&longs;trin
git, atque ad minus &longs;patium redigit, non &longs;ecùs ac
homo robu&longs;tus comprimeret, & &longs;lecteret corpor&atail;
flexibilia, ac cedentia, dum ea impelleret.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
tium aquæ, & rerum in ea contentarum à pon
dere ip&longs;iu&longs;met aquæ.
SIt fi&longs;tula vitrea RVX vndique clau&longs;a
in &longs;upremo orificio R, hæc verò aqua repleatur,
& in ea ampullula vitrea AD immerga
tur &longs;itque ea plena aere, & eius pars ver
&longs;us infimum orificium a pertum D graui
or &longs;it, ad hoc vt ampullula AD &longs;emper
inuer&longs;o &longs;itu in ip&longs;a aqua per&longs;i&longs;tat. in hac
machina ob&longs;eruatur quòd vexica vitrea
AD quò magis deprimitur infra &longs;upre
mam aquæ libellam, vel potiùs ip&longs;amet
aqua altiùs infunditur, & eleuatur, tune
eò magis aer in ampulla contentus con
den&longs;atur,
gitur, & hoc fen&longs;u ip&longs;o patet dum aqu&atail;
ingreditur per orificium D atque colli
ampullæ particulam aliquam implet; quod verò hu
iu&longs;modi aeris re&longs;trictio &longs;it effectus ponderis aquæ &longs;u
premæ comprimentis &longs;en&longs;u ip&longs;o digno&longs;citur,
magis aquæ &longs;uprema &longs;uperficies S eleuatur versùs R
&longs;emper magis, ac magis &longs;ucce&longs;&longs;iuè aeris moles præ
dicti tubuli con&longs;tringitur &longs;ubintrando nimirùm aqua
magis à C versùs B. Quòd verò hoc dependeat à
pre&longs;&longs;ione
clariori experientia percipitur, &longs;i enim ab&longs;que noua
aquæ in fu&longs;ione in fi&longs;tula aliqua breui, vel pollice, vel
&longs;ubere comprimatur aqua orificium R attingens &longs;ta
tìm apparet effectus prædictæ compre&longs;&longs;ionis aquæ,
conden&longs;atur enim, ac&longs;tringitur aer in vitrea ampul
la AD eodem modo præcisè, ac maior mo
les altioris aquæ eleuatæ faciebat, e&longs;tqu&etail;
huiu&longs;modi compre&longs;&longs;io acris in prædict&atail;
ampullula tantæ energiæ vt exi&longs;tente eale
ui, &longs;cilicet quæ &longs;ponte &longs;ua &longs;ur&longs;um in aqu&atail;
SX a&longs;cendat po&longs;&longs;it è contrà
tere, atque acquirere grauitatem, moueri
que, ac de&longs;cendere deor&longs;um,
aqua in fi&longs;tula ad tantam altitudinem ele
uetur vt valdè comprimere ampullulæ aerem po&longs;&longs;it,
vt eam grauem reddat, nec vt hactenùs &longs;ursùm, &longs;ed
deorsùm vergat de&longs;cend atque.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
demon&longs;trare.
HOc deducitur ex eo quòd corpora, quæ ob ex
cedentem eorum grauitatem demerguntur in
fra aquam minùs grauitant in ip&longs;a aqua, quàm i&ntail;
aere, vt &longs;i fuerit pila AB ferrea &longs;pecie grauior quàm
&longs;it aqua ip&longs;a in va&longs;e RO contenta, & concipiatur IK
vt pondus ab&longs;olutum pilæ ferreæ AB, &longs;cilicèt expri
mat eam grauitatem quam in aere exercet, &longs;it que eius
portio K grauitas ab&longs;oluta pilæ aqueæ C quæ æqua
lis &longs;it ip&longs;i AB, &longs;it que pila C contenta intra eiu&longs;de&mtail;
aquæ RO profunditatem, vel in altera fi&longs;tula inuer&longs;i
&longs;iphonis, quæ cum reliqua continuetur, po&longs;tea eadem
pila AB filo DA ab aliqua potentia I &longs;u&longs;pen&longs;a in me
dio aquæ fixè retineatur. modò &longs;i po&longs;&longs;ibile e&longs;t pil&atail;
aquea C nil prorsùs ponderet in ip&longs;amet aqua, igitur
in &longs;iphone, vel in libra DE in eius puncto medio F
fulta pila aquea C &longs;u &longs;pen&longs;a à termino E, quæ
pror&longs;us granitatem exercere in aqua &longs;upponitur,
quam
gatætermino libræ D, propterea quòd nihilum ab
aliquo pondere &longs;ubtractum ip&longs;um nullo pacto immi
nuit; nec pariter denfitas, & tenacitas aquæ gradum
ponderis pilæ AB diminuere pote&longs;t, propterea quòd
illa re&longs;i&longs;tentia potis e&longs;t retardare, & impedire mo
tum, non autem vim, quam graue AB in quiete con
&longs;titutum exercet comprimendo; videmus enim, quòd
pila ferrea quie&longs;cens &longs;iue fulciatur à mollicera, &longs;iue
à rigido adamante, &longs;emper eadem vi comprimit, &longs;ci
licetmen&longs;urata à gradu eius
dum in &longs;uo
toto quie
&longs;cens pon
derat.
His po&longs;itis &longs;equitur, quòd pila fer
rea AB pendula intra aquam exerce
bit integram &longs;uam grauitatem IK,
&longs;cilicet eam, quam in aere exerce
bat, &longs;ed hoc e&longs;t fal&longs;um, imminuitar
enim præcisè pro men&longs;ura ponderis
K &longs;cilicet molis aqueæ C, & ei relin
quitur tantummodò pondus I, &longs;cili-
cet exce&longs;&longs;us quo pondus eius ab&longs;olutum &longs;uperat gra
uitatem aquæ eiu&longs;dem molis; quapropter verum
e&longs;t aquam C in ip&longs;amet aqua con&longs;titutam, nullam
pre&longs;&longs;ionem
dum in &longs;uo
toto quie
&longs;cens ponde
rat.
VAs RO repleatur aqua, in eaque immergatur
pila ferrea BA quæ filo aliquo DA &longs;u&longs;tineatur
ne ad fundum va&longs;is de&longs;cendat. Manife&longs;tum e&longs;t
tiam
tati quam ip&longs;a pila in aqua exercet, & quia in va&longs;e
aqueo RO deficit præcisè tanta aquæ quantitas,
tum
cupat, collocatur verò intra aquam ne dum grau&etail;
AB, &longs;ed etiam defectus molis aquæ æqualis eide&mtail;
AB quare &longs;umma po&longs;itiu&ecedil; grauitatis AB vnà cum de
fectiuo pondere molis aquæ expul&longs;æ à loco AB, &longs;ci
licet exce&longs;&longs;us ponderis AB &longs;upra pondus molis aquæ
æqualis pilæ AB æqualis erit ponderi quod exercet
pila AB in aqua ergò &longs;i huiu&longs;modi aquæ moles ex &longs;ui
natura nil in aqua ponderat quando tollitur a &longs;patio
AB moles aquea, quæ ip&longs;um replebat reuerà tollitur
res non grauis, & quæ nil omninò ponderat; igitur à
pondere ab&longs;oluto ip&longs;ius AB, & à &longs;patio ab ea occu
pato nihilum, &longs;eù nulla grauitas &longs;ubtrahitur, quando
verò ab ab&longs;oluta grauitate IK pilæ AB nil pror&longs;us
tollitur, remanet eiu&longs;dem gradus, ac proindè pon-
dus pilæ AB nil prorsùs imminutum erit, & æquali
energia &longs;u&longs;tineri debet à potentia D, ac &longs;i eadem pi
la extra aquam in aere libero penderet, &longs;ed hoc e&longs;t
fal&longs;um, cùm præcisè in ip&longs;a aqua grauitas pilæ æqua
lis &longs;it differentiæ ponderis eius ab&longs;oluti à grauitat&etail;
aquæ &longs;ibi æqualis mole, vt ex Archimede deducitur,
igitur nece&longs;&longs;ariò
collocatam ponderare, & grauitatem exercere.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
Contra hoc euidenti&longs;&longs;imum ratiocinium afferri
&longs;olet difficultas valdè &longs;pecio&longs;a, quam examinare, ac
di&longs;&longs;oluere erit operæ pretium, vtque ea ritè percipi
atur, con&longs;ideretur hæc figura. Sit vas cylindricu&mtail;
ABDC aqua plenum &longs;it que eius altitudo
di&longs;&longs;ecta in quotcumque partes æquales,
ductis nempè planis imaginarijs MO, &
HI, erit igitur moles aquea AI dupl&atail;
aque &ecedil; molis HD; igitur pondus aquæ AI
duplum e&longs;t ponderis aquæ HD. quia ve
rò corpus grauius minùs graue &longs;uperare
debet, hocque è &longs;uo loco expellere (cùm in eo con&longs;i
&longs;tat vis, & energìa grauitatis, vt tendat deorsùm,
& &longs;ic è loco infimo corpora minùs grauia expellat) &
po&longs;tquàm aqua AI translata e&longs;t ad locum HD, atque
aquam ibidem collocatam expulit denuò in &longs;itu &longs;u
periori fi&longs;tulæ AI aqua dupli ponderis, & molis ibi
dem re&longs;tituitur quæ pariter &longs;uperat grauitatem &longs;ub
duplam aquæ, quæ ad occupandum infimum locum
HD &longs;ucce&longs;&longs;it, igitur denuò aqua &longs;uprema vt grauior
in&longs;imam è &longs;uo loco extrudere, atque expellere de-
bet, & quia hoc &longs;emper repetitur, &longs;cilicèt perpetuò
re&longs;tituitur in &longs;uperioriloco AI aqua duplò grauior,
quàm ea, quæ in loco infimo HD reponitur, igitur
vt contingit in libra efficientur perpetuæ, & conti
nuatæ vibrationes, veluti in pendulo, & in aqua fie
ri&longs;olent plures vndulationes, &longs;ic in aqua perpetuo
motu agitarentur eius partes a&longs;cendendo, & de&longs;cen
dendo. hoc verò &longs;en&longs;us euidentia redarguit, igitur
fatendum e&longs;t &longs;upremam aquam AI &longs;u&longs;tentatam ab
inferiori aqua &longs;uper eam non exercere vim vlla&mtail;,
nec pre&longs;&longs;ionem, proinde que non grauitare, hac &longs;cili
cet de cau&longs;a, quia nimirùm in eius loco naturali col
locatare quie&longs;cit, ac &longs;i&longs;titur.
ctrinam &longs;u
periùs addu
ctam ade&longs;t
noua difficul
tas, quod ni
mirum mo
tu perpetuo
aqua agitari
deberet.
dum in &longs;uo
toto quie
&longs;cens ponde
rat.
vim compres&longs;iuam, quàm minor.
VT verò huiu&longs;modi paralogi&longs;mus detegatur, a
nima
quælibet aquæ moles maior alterà,
ceat quoque duplam vim grauitantem quotie&longs;cum
que maior &longs;upra minorem in&longs;i&longs;tat, & ab ea fulciatur,
&longs;ed tunc &longs;olummodò propo&longs;itio verificatur quando
earum ba&longs;es
eodem plano horizonti parallelo con&longs;titerint. Sup
ponatur vas cylindricum plenum aqua ABDC, &longs;it
que portio &longs;uprema, & ideò eius altitudo AH dupla
infimæ altitudinis HB, licèt ergo reuerà &longs;upremæ
aquæ AI pondus duplum &longs;it ponderis infimæ aquæ
HD, non hìnc tamen inferri licet &longs;ubiectam aquam
HD in tali &longs;itu vnicam libram tantummodò pendere
exi&longs;tente &longs;upremo pondere AI duarum librarum, &longs;ed
nece&longs;sè e&longs;t vt aqua HD comprimat va&longs;is fundum BD
ni&longs;u, ac vi non vnius libræ, &longs;ed æquali ei, quæ effi
citur à pondere trium librarum, & ratio e&longs;t quia ip
&longs;a aqua HD nedùm impellitur deor&longs;um à vi propriæ
grauitatis vnius libræ, &longs;ed in&longs;uper grauatur compri
miturque ab incumbente pondere aquæ AI, quæ
pre&longs;&longs;io
duabus libris effici pote&longs;t; nec profectò nouum e&longs;t &longs;i
quis centum laminas ferreas, vellapideas, æquè
derantes
teram imponat, quod in&longs;ima lamina non tantummo
dò &longs;uo pondere comprimet planum &longs;ubiectum, &longs;cili
cèt non efficiet vim æqualem cente&longs;imæ parti totius
prædicti aggregati, &longs;ed compre&longs;&longs;io infim&ecedil; laminæ ef
ficiet vim centuplo maiorem &longs;cilicèt impellet &longs;ubie
ctum planum vi æquali centum libris, & tunc
modò
gregati ponderabit, quando illa in vna lance, reli
quæ verò 100. in oppo&longs;ita lance eiu&longs;dem libræ ra
diorum æqualium &longs;u&longs;penderentur; &longs;ic paritèr &longs;i aqua
HD &longs;upra planum &longs;ubiectum &longs;iuè &longs;olidum, &longs;iuè flui
dum collocaretur iuxtà portionem aquæ AI, itaut &longs;e
&longs;e contingerent lateraliter, atque
les in eodem plano horizontali collocarentur, tunc
nece&longs;&longs;ariò dupla moles aquæ AI duplam vim com-
pre&longs;&longs;iuam, pro men&longs;ura duplæ grauitatis haberet. Verum tamen e&longs;t, quòd alia de cau&longs;a non e&longs;t nece&longs;
sè, vt &longs;emper ba&longs;es &longs;int æquales, neque grauitates
&longs;int in eadem proportione dupla, dummodò altitu
do AH dupla &longs;it altitudinis ip&longs;ius HB; & ratio huius
diuer&longs;itatis pendet ex alibi demon&longs;trandis.
dum in &longs;ue
toto quie
&longs;cens pon
derat.
dum in &longs;uo
toto quie
&longs;cens ponde
rat.
Ex &longs;uperiori igitur ratiocinio euinci
tur, fal&longs;um e&longs;&longs;e, quòd pronunciabatur,
nimirùm, duplam aquam AI vt grauio
rem, expellere de&longs;cendendo debere &longs;ub
duplam aquam &longs;ubiectam HD, cùm ècon
tra hæc vt grauior, grauitate nempe pro
pria, & ea, quæ ei &longs;uperadditur ab aqua
&longs;uperincumbente AI in eodem loco infimo perma
nere debeat, nec vnquam à debiliori compre&longs;&longs;ione
&longs;uper&longs;tantis aquæ expelli po&longs;&longs;it, ac proindè &longs;equitur
&longs;umma quies, ac tranquillitas, non verò motus per
petuus.
&longs;uperiùs tra
dita videtur
deduci po&longs;
&longs;e lignum
infra aquam
po&longs;itum &longs;ur
&longs;um
re
Sed dices, &longs;i vera e&longs;&longs;et adducta doctrina, lignum
deberet in fundo aquæ paritèr retineri, proptere&atail;
quòd nedum à propria grauitate comprimitur, &longs;ed
etiam à pondere totius aquæ &longs;uper&longs;tantis, & ideò
magis grauitaret quàm aqua ei&longs;uperpo&longs;ita, & proin
de lignum in fundo aquæ permanere deberet: hoc
autem fal&longs;um e&longs;t, cùm experientia con&longs;tet, lignum
&longs;ursùm ferri, nec quie&longs;cere, antequàm ad aquæ &longs;u
premam libellam perducatur.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
aquæ incumbentis exerceat, non proinde ibidem
quie&longs;cet.
VT autem huius argumenti falla cia pate&longs;iat, in
va&longs;e ARSE aqua pleno demergatur pri&longs;ma li
gneum, vel aereum HBDI &longs;itqu&etail;
pondus aquæ AI decem libraru&mtail;
v. g. lignum verò HD &longs;emilibra&mtail;
pendeat. Concedo, quòd lignu&mtail;
HD premit &longs;ubiectam aquam BV
non vi&longs;emilibræ, &longs;edrobore libra
rum decem, & &longs;emis, & ideo
HD magis comprimit, ac grauitat,
quàm &longs;ola aqua incumbens AI, &longs;ed non proindè &longs;e
quitur, lignum HD quatenùs magis comprimit, ac
grauitat in fundo aquæ per&longs;i&longs;tere debere, cùm ab
alia cau&longs;a &longs;ursùm exprimatur. Secto enim pri&longs;mat&etail;
aqueo CEFI æquali ip&longs;i AI, & aqueo pri&longs;mate IG
cuius moles æqualis &longs;it ligno HD, & eius pondus
duas libras &longs;uperet; patet quòd aqua &longs;ubiecta BV
premitur à pondere librarum decem, & &longs;emis, at
aqua DS comprimitur à pondere librarum duode
cim; ergo sipho, vellibra mobilis aquea BG flecti
debet eleuando lignum HD minus graue. Et hinc
patet, quòd ratio, quare lignum a&longs;cendit, non e&longs;t
pondus aquæ incumbentis AI, &longs;ed e&longs;t aqua collate-
ralis IG, & hoc con&longs;tat, quia &longs;i in &longs;tricta fi&longs;tula vitrea
ARVC ponatur in eius fundo aqua BV in loco me
dio lignum HD, vel exigua aeris ve&longs;ica, quæ va&longs;is
latera exactè tangat, & reliquum va&longs;is repleatur a
qua AI, tunc lignum non a&longs;cen det &longs;ur&longs;um, quia nem
pè &longs;ipho, vel libra mobilis
rinon pote&longs;t.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
de&longs;cendendo nullam grauitatem exercent.
SEd &longs;ublata prædicta difficultate deuenio ad
dendum
dum quie&longs;cunt in proprijs locis non grauitare, vt è
contra quando à locis naturalibus &longs;eparata mouen
tur
tes eiu&longs;dem corporis, quod licèt videatur parado
xum, o&longs;tendetur nihilominùs hac ratione. Conci
piantur primò facilitatis gratia duo lanæ inuolucra,
vnum &longs;uper alterum impo&longs;itum &longs;upra planum &longs;ubie
ctum, certum e&longs;t &longs;upremum comprimere, & grauita
tem exercere &longs;upra &longs;ubiectum inuolucrum, & hoc
&longs;tat
cumbentis, &longs;cilicèt ex inflexione, & compre&longs;&longs;ion&etail;
pilorum &longs;ubiectæ lanæ, & è contra con&longs;tat quando
eadem duo lanæ inuolucra collateralitèr &longs;e&longs;e contin
gunt fulciunturque à &longs;ubiecto plano, tunc neque pi
li lanei collaterales inflectuntur, nec comprimuntur,
propterea quòd ni&longs;us grauitatis non exercetur late
raliter, &longs;ed deorsùm.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
Hinc colligitur, quòd quotie&longs;cumque &longs;upremum
lanæ inuolucrum perpendicularitèt incumbens &longs;u
peralterum, &longs;i ip&longs;um non flecteret, nec &longs;tringeret,
tunc planè affirmandum e&longs;&longs;et lanam &longs;uperpo&longs;ita&mtail;
minimè &longs;uper &longs;ubiectam lanam grauitatem exercere.
His po&longs;itis, &longs;upremum lanæ inuolucrum applica
ri pote&longs;t &longs;uper infimum dum hoc actu per aerem mo
uetur de&longs;cendendo deor&longs;um, vel dum quie&longs;cit à pla
no &longs;tabili fultum; in primo ca&longs;u manife&longs;tum e&longs;t,
quòd inuolucra æqualia eiu&longs;dem lanæ æquales gra
dus velocitatum
dunt; igitur &longs;upremum inuolucrum non de&longs;cendet
tardiori, vel celeriori motu quàm &longs;ibi
indeque æquali velocitare &longs;uprema lana compri
mere conatur &longs;ubiectam lanam, ac i&longs;ta nititur effu
gere per&longs;equentem; proptereaque &longs;e mutuo placi
do contactu &longs;olummodò exo&longs;culantur, nec &longs;ubiecta
inflectetur, aut comprimetur à &longs;uper&longs;tante lana:
igitur, ex &longs;uperiùs dictis incumbens lana nequè
dus
lanam &longs;ubiectam. In &longs;ecundo verò ca&longs;u &longs;i po&longs;tquàm
in quiete &longs;ubiecta lana compre&longs;&longs;a e&longs;t à &longs;uperincum
bente ambas demittamus, & liberè deor&longs;um
dere
do iam re&longs;trictæ, & con&longs;tipatæ &longs;unt, & ideò in pro
gre&longs;&longs;u licèt paribus velocitatibus de&longs;cendant, reti
ne bunt tamen eandem con&longs;tipationem, quam prius
habebant; &longs;ed hinc non licet inferre, &longs;upremam la
nam dum mouetur grauitatem exercere, quia ill&atail;
con&longs;tipatio non dependet ab actione grauitatis in
cumbentis lanæ quæactio per&longs;eueret exerceaturque
tempore de&longs;cen&longs;us, &longs;ed illa con&longs;tipatio e&longs;t effectus
compre&longs;&longs;ionis in præcedenti quiete factæ, in actu e
nim de&longs;cen&longs;us nullo pacto impellere pote&longs;t &longs;uprema
lana &longs;u biectam pani velocitate ictum fugientem, &
ideo &longs;u per eam minimè pondus exercebit.
dum in &longs;uo
toto quie
&longs;cens ponde
rat.
&longs;olummodò eam exercet, quando quie&longs;cit &longs;uper
aquam.
SImili modo aqua non de&longs;cendit, quando fulci
tur à &longs;uper&longs;icie terræ, & maris, &longs;ed quando
extra &longs;uum locum peregrinatur, & mouetur, vt i&ntail;
aere, & tunc &longs;i con&longs;ideretur cylindrus aqueus per ae
rem de&longs;cendens, diuidaturque in partes æquales à
planis horizonti æquidi&longs;tantibus; quia partes æqua
les eiu&longs;dem aquæ &longs;unt æquè graues, habent impe
tus æquales à natura &longs;ibi a&longs;&longs;ignatos quibus de&longs;cen
dere deor&longs;um nituntur, igitur pars &longs;uprema ciu&longs;dem
cylindri aquei æquè velox erit, ac pars ei &longs;ubiecta,
igitur &longs;uprema non poterit impellere, vel compri
mere aquam ei &longs;ubiectam, cùm æquali velocitat&etail;
h&ecedil;c ictum, & percu&longs;&longs;ionem fugiat cum quanta à &longs;u
perincumbente in&longs;ectatur per&longs;equiturque, &longs;icuti
&longs;agitta explo&longs;a minimè percutiet &longs;ignum æquali ve
locitate ictum fugiens; igitur manife&longs;tum e&longs;t, aquam
minimè grauitatem exercere &longs;upra ei &longs;ubiectam a
quam, quando à proprio loco naturali exulat, & per
aerem mouetur.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
Secùs autem contingit in aqua quie&longs;cente, i&ntail;
puteo aliquo, vellacu, &longs;i enim diuidatur pariter in
laminas æque altas, patet quòd &longs;upremane dum
git
tra eam impellit tanta vi
uitatis, & patet quòd infima aqua pati cogitur com
pre&longs;&longs;ionem, cùm &longs;u&longs;tinere debeat pondus &longs;upremæ
aquæ incumbentis: & hoc accidit, quia &longs;ua quiete
impedit progre&longs;&longs;um, & conatum compre&longs;&longs;iuum
orsum
&longs;itates hæ nece&longs;&longs;ario con&longs;tringentur à vi ponderis
incumbentis aquæ. Modò quia impul&longs;us compre&longs;&longs;i
uus factus à &longs;uperiore aqua &longs;upra inferiorem nullo
alio vocabulo de&longs;ignatur, quàm grauitatis, vel
deris
quie&longs;centem grauitatem exercet non quando in mo
tu con&longs;tituitur, & extra &longs;uum naturalem locum, &longs;ed,
tantummodò, quando &longs;i&longs;titur, & quie&longs;cit in loco &longs;uo
naturali.
ctrinam &longs;u
p: riùs addu
ctam afferri
&longs;olet difficul
tas valdè
plau&longs;ibilis,
quod nimi
rum vrina
tores ingens
pondus aque
incumbentis
nec patian
tur, nec &longs;en
tiant.
Hi&longs;ce omnibus rationibus opponi&longs;olet
tia
profundo maris demer&longs;i non &longs;entiunt, neque
tur
multoties plures congios excedit; hinc inferunt, &longs;i
aqua in ip&longs;amet aqua pondus, & grauitatem habe
ret, nece&longs;&longs;ariò vrinatores comprimerentur à va&longs;to
pondere aquæ incumbentis &longs;uper eorum humeros,
immò nec po&longs;&longs;et pondus tam va&longs;tum à viribus huma
nis &longs;u&longs;tineri, quando videmus, ab homine robu&longs;to
minus pondus &longs;u&longs;tineri non po&longs;&longs;e; cùm ergo experi
entia doceat vrinatores in fundo aquæ grauitate&mtail;
nullam percipere, igitur verum non e&longs;t, aquam i&ntail;
ip&longs;a aqua collocatam grauitare, immò in proprio lo
co nil prorsùs ponderahit.
dum in &longs;uo
toto quie
&longs;cens ponde
rat.
Huic vulgari difficultati vt fiat &longs;atis
e&longs;t, quòd aqua in ip&longs;amet aqua con&longs;tituta,
quodlibet fluidum in &longs;uo homogeneo demer&longs;um non
alia de cau&longs;a quie&longs;cit, ni&longs;i quia vndique comprimi
tur pari vi à grauitate ambientis fluidi, cui propri&atail;
grauitate re&longs;i&longs;tit, vtque hoc clariùs percipiatur, o
&longs;tendemus, quod.
quia grauitatem exercent comprimunturque æquali
bus viribus ab ambientibus corporibus pariter
æquilibratis.
ESto libra AB radiorum æqualium in eius puncto
intermedio C &longs;u&longs;pen&longs;a, atque in eius extremi
tatibus, vtrinque quatuor laminas, vellateres æquè
ponderantes &longs;ibi mutuò incumbentes apponantur,
&longs;cilicet DE, EF,, FG, GH, &longs;u per A, & totidem IK,
KL, LM, MN &longs;uper Manife&longs;tum e&longs;t, ag
gregatum ex laminis DH ibidèm retineri indifferen
tia quadam, nec pelli &longs;ursùm, aut deorsùm, firmiter
que in tali &longs;itu quie&longs;cere, vt nimirùm &longs;i quis infr&atail;
laterem DE manum &longs;upponeret, minimè ab ip&longs;is
primeretur
autem non contingit ex eo, quòd lamin&ecedil; lateritiæ
grauitatem amittant, & deorsùm nil comprimant,
&longs;ed quia ab æquali vi contraria &longs;u&longs;tinentur, ac &longs;ursùm
in libra AB premente. Præterea quælibet lamina in
termedia FE &longs;imilitèr quie&longs;cit, &longs;i&longs;titurque iners, vt
ncque &longs;ursùm, neque deorsùm moueatur, nequ&etail;
&longs;ubiectam manum, quæ lateralitèr eam retinere co
naretur vllatenùs comprimit, aut impellit, & hoc
efficitur quia lamina
FE comprimitur de
or&longs;um ab incumben
te pondere FH, &longs;ur
sùm verò impellitur
à &longs;ubiecta lamina DE non virtute propria, &longs;ed eius,
quam exercet contra po&longs;itum pondus IN &longs;cilicet tan
ta vi, quanta
præterea lamina ip&longs;a FE exercet vim &longs;ui ponderis
contra pre&longs;&longs;ionem contrapo&longs;iti exce&longs;&longs;us KN fit vt vis
quæ impellit &longs;ursùm laminam FE æqualis &longs;it exce&longs;&longs;ui
ip&longs;ius KN &longs;upra FE, &longs;cilicet æqualis &longs;it NL; &longs;untque
FH, & LN inter &longs;e æquales; ergo viribus æqualibus
FE deprimitur ac &longs;ursùm impellitur. E contra lami-
na FE impellit deor&longs;um laminam DE, ne dum pro
prio pondere, &longs;ed etiam grauitate laminarum FH;
pariterque FE repellit laminas &longs;upremas FH no&ntail;
propria virtute, &longs;ed vi ponderis LN &longs;cilicet exce&longs;&longs;u
IN &longs;upra DF; Quaproptèr con&longs;tat, quòd lamina la
teritia FE comprimitur &longs;upernè, & infernè à duabus
viribus contrarijs quæ æqualibus momentis
tur
sùm, aut deorsùm moueri. Præterea colligitur, quòd
reuerà lamina lateritia FE non verè in quiete inerti
con&longs;tituitur, nec pondere priuatur, &longs;ed potiùs effi
citur lucta quædam contrariarum virtutum
virium, vndè æquatis momentis motus tonicus, &longs;eù
quies &longs;ub&longs;equitur, & hìnc deducitur quòd prædicta
corpora &longs;e mutuò comprimunt, & hìnc fit, vt neuter
proindeque cogantur fixè in eodem &longs;itu quie&longs;cere.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
dum in &longs;ue
toto quie
&longs;cens pon
derat.
EOdem ferè modo in aqua idem æquilibrium ef
fici manife&longs;tum e&longs;t, proindeque partes ip&longs;ius
aquæ partim &longs;upernè comprimi à &longs;uper&longs;tantibus a
quæ partibus, partim verò infernè &longs;ursùm expelli,
propria vi, &longs;ed pondere collateralis aquæ, quæ cum
illa libram imaginariam, vel &longs;iphonem con&longs;tituit. E&longs;to igitur, claritatis gratia, &longs;ipho HAB perpendi
cularitèr eleuatus &longs;upra horizontem, repletu&longs;qu&etail;
aqua v&longs;que ad &longs;uprema orificia H & N; &longs;ubdinida
tur tota eius altitudo in partes æquales ductis nimi
rum planis &longs;uperficiebus GM,
FL, EK, DI; hic profectò aquæ
portio FE, licèt nullum
grauitatis producere,
ter quie&longs;cere videatur, dùm in
differens e&longs;t ad motum fursùm,
& deorsùm, non hìnc deducere
licet, aquam ip&longs;am FE in tali &longs;i
tu vim propriæ grauitatis non exercere, nec
ab aqua &longs;uperna, & inferna:
FF, in parte &longs;uprema ab aqua FH comprimitur de
orsùm, è contrà à &longs;ubiecta aqua DE expellitur &longs;ur
sùm, non propria vi, &longs;ed pondere contrapo&longs;it&ecedil; aquæ
NL. Hinc colligitur, quòd aqua FE reuerà impelli
tur deorsùm à &longs;uperna aqua, & &longs;ursùm ab inferna;
ip&longs;a veròmet aqua FE è contrà vim exercet contr&atail;
vtramque compre&longs;&longs;ionem, &longs;cilicèt contra eam, quæ
efficitur ab aqua &longs;ubiecta, re&longs;i&longs;tit
prio vnà cum grauitate incumbentis aquæ FH, &longs;ed
contra vim, qua comprimitur &longs;upernè non re&longs;i&longs;tit, &
contranititur virtute propria, &longs;ed mediante impul
&longs;u de&longs;cen&longs;iuo collateralis aquæ NK, igitur huiu&longs;mo
di quies aquæ, quæ in &longs;itu FE indifferentèr retinetur,
nec pote&longs;t &longs;ursùm, aut deorsùm moueri, e&longs;t effectus,
qui nece&longs;&longs;ariò con&longs;equitur ad exercitium &longs;uæ natiuæ
grauitatis, & eius, quæ exercetur ab aqua &longs;iphonis,
velab aqua collaterali eiu&longs;dem va&longs;is, in quo paritèr
aqua operatur, veluti in &longs;iphone collocata fui&longs;&longs;et.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
ambiente aqua, & vtraque grauitatem exercet.
INtra vas ABCD aqua plenum intelligatur pri&longs;ma
aqueum FGHE, ducti&longs;que planis FL, & GM pa
rallelis horizonti. Dico, quòd aqua FH vndique pre
mitur ab ambiente aqua FILKG, & vtraque pondus
grauitatemque exercet. Quia aqua FH cum aqu&atail;
ambiente &longs;iphonem AKD con&longs;tituit, in quo fluidum
&longs;ibi homogeneum agitari pote&longs;t, & quie&longs;cit nihilo
minùs; ergo vna pars fluidi AK
æquilibratur, proindequè æquè
ponderat, ac pars reliqua latera
lis IC, portio verò aquæ FH licèt
motu careat, &longs;itque indifferens
ad motum &longs;ursùm, & deorsùm,
haud inferre licet eam non exer
cere vim &longs;uæ grauitatis vnà cum tota aqua ambi
ente, quia in &longs;iphonis brachio AK aquæ FH &longs;u
prema facies FE deor&longs;um impelli, & comprimi de
bet ab incumbente aqua AE, pariterque infim&atail;
illius facies GH &longs;ursùm impelletur à &longs;ubiecta a
qua GK non virtute propria, &longs;ed eius quam exercet
pondus aquæ collateralis IM; porrò nedum aqua FH
impellitur &longs;ur&longs;um ab aqua &longs;ubiecta BH, &longs;ed etiam, vt
experientia con&longs;tat, impul&longs;ionem, &
patietur facies eius FH ab aqua collaterali DH;
quod euidentius
go aqua FH vcluti prælo, nec tamen iners omninò
e&longs;t, repellit enim &longs;ursùm aquam
AE vi grauitatis aquæ lateralis
IL, aquam verò &longs;ubiectam repel
lit deorsùm vi grauitatis pro
priæ, & &longs;upremæ IE. quare quies
aquæ FH e&longs;t effectus dependens
à compre&longs;&longs;ione facta ab aqua am
biente, & ab exercitio &longs;uæ grauitatis, & eius quam
aqua ambiens &longs;iphonem con&longs;tituens exercet: quod
erat &c.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
primiturque
IN eadem figura quodlibet corpus durum, molle,
vel Dico ip&longs;um vndiquè &longs;tringi, ac
te fluido FILHB. Quia &longs;olidum FH intra aquam re
tentum vnà cum ambiente aqua con&longs;tituit &longs;iphonem
AKD in quo eius partes AK, & KD quie&longs;cunt, & æ
quilibrantur, ergò oportet vt aqua &longs;uprema AE
primat
pariterque debet aqua &longs;ubiecta GK impellere &longs;ur
&longs;um &longs;olidi &longs;uperficiem GH non virtute propria, &longs;ed
vi ponderis aquæ collateralis IM, &longs;imiliter &longs;olidi fa-
ciem EH &longs;tringet lateraliter eadem aqua IM. Igitur
vndique &longs;olidum FH &longs;tringitur comprimiturquè
quam
dum in &longs;uo
toto quie
&longs;cens pon
derat.
Et hìc notandum e&longs;t, quòd &longs;i corpus FH fuerit
ve&longs;ica flexilis repleta corpore fluido concipi pote&longs;t
con&longs;tans ex partibus non conden&longs;abilibus, vt e&longs;t a
qua, hydrargyrum, & aggregatum ex minimis &longs;ph&ecedil;
rulis cry&longs;tallinis; aut componatur ex partibus adeò
raris, atque poro&longs;is, vt ingentem conden&longs;atione&mtail;
pati po&longs;&longs;int, cuius natura Aer e&longs;t. In primo ca&longs;u li
cèt ve&longs;ica FH vndique æqualibus viribus compri
matur &longs;tringaturque, nihilominùs ob duritiem par
tium in ve&longs;ica contentarum, non poterit ip&longs;a ve&longs;ic&atail;
con&longs;tringi,
plere, quàm prius occupauerat, eò quòd particulæ
ip&longs;æ duri&longs;&longs;imæ fluidæ, vel den&longs;æ adinuicem fulciun
tur, veluti columnæ, aut fornices, quæ nullo pacto
po&longs;&longs;unt frangi, vel con&longs;tringi, cùm è contrà partes
aeris ob maximam earum raritatem facilè po&longs;&longs;int
&longs;tipari
redigi po&longs;&longs;it con&longs;trictis nempè eius poro&longs;itatibus.
His declaratis pro re&longs;olutione principalis proble
matis
pre&longs;&longs;ione ponderis incumbentis pa&longs;&longs;io dolorifica in
animali &longs;ub&longs;equatur.
cau&longs;a quare
à pondere in
cumbente
producitur
compre&longs;&longs;io,
&longs;ci&longs;&longs;io, diui
&longs;io continui,
& proinde
dolor.
Et primò experientia con&longs;tat, à pondere corporis
manum v. g. prementis aliquando effici &longs;ci&longs;&longs;ionem,
vt ab acie &longs;ecuris incumbentis, aliquando
multotiès luxari, & di&longs;rumpi articulos tractis nem-
pèviolentèr tendinibus articulos colligantibus, &
tandem fieri pote&longs;t contu&longs;io, & diffractio partiu&mtail;
&longs;olidarum. Et hi&longs;ce omnibus modis continuitatis
diui&longs;io in animali efficitur, à quà demum diui&longs;ion&etail;
pa&longs;&longs;ionem dolorificam exoriri vulgò credunt.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
Modò o&longs;tendendum e&longs;t, quòd diui&longs;io continui, &
dolor procreari pote&longs;t ab aliquo &longs;ingulari pondere,
quòd &longs;i pondus po&longs;tea comprimens augeatur, mul
tipliceturque, non proindè &longs;emper, & vniuersè ma
ior, &longs;ed minor, immò nulla &longs;ci&longs;&longs;ura, vel contu&longs;io,
aut fractio in animali &longs;ub &longs;equi pote&longs;t; quod quidem
licèt vid eatur paradoxum, poterit tamen facili ne
gotio demon&longs;trari.
flectitur, poterit à potentia duplicata dirigi.
SIt lamina chalybea AB parieti RS infixa,
cumbat pondus C à quo lamina ip&longs;a deorsù&mtail;
impul&longs;a curuitatem acquirat,
inflectaturque: adueniat po
&longs;tea vis motiua H æqualis pon
deri C, quæ contrario ni&longs;u &longs;ur
sùm impellat eamdem
manife&longs;tum e&longs;t, quòd à duplici
vi C, & H, non augetur curui
tas ip&longs;ius laminæ, &longs;ed ea potiùs dirigitur, quia ni
mirùm duæ vires contrari&ecedil; æqualibus
rantes &longs;ibi mutuò impellunt, & proindè vna alterius
vim, & actionem de&longs;truit, quantum ergo lamina in
flectitur deorsùm à
flectitur à contrario impul&longs;u ip&longs;ius H.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
verificatur.
APplicetur libra DE radio
rum æqualium &longs;uffult&atail;
in F, itaut terminus D infrà ex
tremitatem laminæ AB collo
cetur, & tunc po&longs;ito pondere
G æquale ip&longs;i C in altero extremo libræ E, impel
letur &longs;ursùm terminus libræ, vel vectis D à vi pon
deris G, & ab illo lamina AB in directum retine
bitur contra vim compre&longs;&longs;iuam ponderis C,
quidem
tuò impellunt, proindeque lamina intercepta AB,
neque deorsùm, neque &longs;ursùm flectetur.
SI nimirùm termino E im
ponatur pondus IG du
plumip&longs;ius C, atque in D ap
plicetur pondus M æqual&etail;
eidem C,
pondus IG æquale e&longs;t duo-
bus ponderibus C & M, & ideò æquilibrium efficie
tur, &longs;cilicèt intercepta lamina AB nil prorsùs flecte
tur, quia licèt à pondere &longs;upremo C deorsùm lami
na pellatur, repellitur infernè à corpore M non qui
dem propria vi, (cùm tendat deorsùm ob eius gra
uitatem) &longs;ed ab exce&longs;&longs;u ponderis IG &longs;upra M.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
eò quòd vndique contrarijs viribus à fluido com
primuntur.
IN &longs;uperiori diagrammate habemus exemplum &longs;i
mile omninò corpori animalis in aqua natantis,
nam licèt animalis brachium, ver. gra.
AB, compri
matur à &longs;uperpo&longs;ita aqua C, non tamen flectetur de
orsùm, aut di&longs;rumpetur, cùm præ&longs;tò &longs;it aqua &longs;ubie
cta M, quæ &longs;ursùm manum brachiumque repellat,
impediatque eius depre&longs;&longs;ionem, flexionemque,
&longs;iua
quæ in libra, vel &longs;iphone i
maginario, eo
excedit
eam &longs;ursùm impellit, & pro
pterea
ne à
Ethoc (dicet aliquis) &longs;ufficeret ad luxatione&mtail;
membrorum animalis euitandam, &longs;ed non proindè
dolor compre&longs;&longs;iuus animalis vitari po&longs;&longs;et, quando
quidem partes carno&longs;æ, & tendino&longs;æ contunderen
tur diffringerenturque, atque vniuersè &longs;ci&longs;&longs;ura&mtail;
aliquam paterentur.
dum in &longs;uo
toto quie
&longs;cens ponde
rat.
Vt verò fallacia huius ratiocinij detegatur.
xati
&longs;altem con
tu&longs;io, & dif
fractio par
tium anima
lis con&longs;equi
debere vi
detur.
declaratur.
EFfectus con&longs;equens ad actionem cunei, & aciei
&longs;ecuris, &longs;ci&longs;&longs;io nuncupari &longs;olet, quæ efficitur
propterea, quòd dum cuneus intra corpus &longs;ci&longs;&longs;il&etail;
in&longs;inuatur, huius partes hinc in de lateralitèr mouen
tur, & ab inuicem &longs;eparantur: hinc fit, quòd &longs;i par
tes&longs;ubiecti corporis minimè lateralitèr moueri po&longs;
&longs;ent, neque cuneus penetraret, nec &longs;ci&longs;&longs;io fieret:
triplici verò modo motus laterales &longs;ubiecti corporis
impediri po&longs;&longs;unt, primò, &longs;i gluten, quo partes &longs;ubie
cti corporis colligantur, fuerit immen&longs;æ virtutis, &
arcti&longs;&longs;imæ vnionis, & duritiei; &longs;ecundò, &longs;i prædictæ
partes inter &longs;e diui&longs;æ, vtarena,
duri&longs;&longs;imum, cuius parietes cuilibet impul&longs;ui re&longs;i&longs;te
rent, nec præterea partes contenti corporis &longs;uble
uari&longs;ursùm po&longs;&longs;ent, tunc profectò nec penetratio
cunei, nec &longs;ci&longs;&longs;io efficeretur; tertiò, &longs;i va&longs;e remoto
adhiberentur vires impul&longs;iuæ lateralitèr contrariæ
officium va&longs;is &longs;upplentes, tunc &longs;imilitèr &longs;ci&longs;&longs;io im
pediretur.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
ti, veluti e&longs;t malleus, paritèr ad cunei actionem
reducitur.
QVandoquidem particul&ecedil; corporis à malleo
pre&longs;&longs;æ
intra alias collaterales particulas, & quia in
&longs;inuatio prædictarum partium effici non pote&longs;t ni&longs;i
collaterales particulæ non contu&longs;æ locali motu late
rali tran&longs;portentur, hinc fit, quòd particulæ illæ
pre&longs;&longs;æ
verò &longs;it
tus impellens particulas compre&longs;&longs;as, cuneos refe
rentes.
bus partibus eius ab innumeris cuneis compre&longs;&longs;aneque
&longs;cindi, neque flecti, neque figuram commu
tare pote&longs;t.
SVpponatur modò ve&longs;ica ABCD, quæ repleatur
aqua, vel hydrargyro, aut arena, vel globulis
cry&longs;tallinis minuti&longs;&longs;imis, tunc &longs;i huiu&longs;modi ve&longs;ica à
pauimento RS fulciatur, atque ei &longs;uperponatur acies
&longs;ecuris, vel nouaculæ I, procùl dubio, aut ve&longs;ic&atail;
&longs;cindetur, aut &longs;altèm fluidum, &longs;iue arena content&atail;
cedet, & ver&longs;us latera ve&longs;i
cæ tran&longs;portabitur; at &longs;i in
telligantur innumeræ acies
&longs;ecurium, vndique compri
mentes ve&longs;icam, itaut null&atail;
eius pars intacta relinquatur:
primò manife&longs;tum e&longs;t, &longs;ci&longs;&longs;io
nem prohiberi, quandoquidem longa, & continua
ta &longs;eries acierum &longs;e&longs;e con&longs;equentium, & &longs;e mutuò
lateralitèr tangentium ab&longs;que vlla interruptione æ
quiualent corpori obtu&longs;o, proindeque acuties ill&atail;
omninò de&longs;truitur, & Proptereà non &longs;equetur &longs;ci&longs;&longs;io
quæ ab&longs;que acie acuta fieri nequit. Secundò non fi
et contritio, atque depre&longs;&longs;io alicuius partis prædi
ctæve&longs;icæ, quandoquidem non pote &longs;t &longs;uprema pars
eius A deprimi versùs C, quin aqua, vel arena ex
pul&longs;a recipiatur ad latera B, & D, &longs;ed hic quoqu&etail;
æqualibus viribus comprimitur lateralitèr ve&longs;ic&atail;,
igitur non pote&longs;t ibidem perduci fluidum, vel are
na
æqualibus compre&longs;sæ nulla particula cedet; & quia
aliundè materia ip&longs;a fluida, vel arena talis con&longs;i&longs;ten
tiæ e&longs;t, vt &longs;tringi, conden&longs;ari, & ad minus &longs;patiu&mtail;
redigi nequeat, fit vt ve&longs;ica illa, & aqua vel arena
in ea contenta, neque &longs;cindatur, neque flectatur,
neque vllo pacto figuram commutet quotie&longs;cumque
vndique circùmcirca ab æqualibus viribus compri
matur.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
aqua demergitur.
IBi enim nedùm à perpendiculariter incumbent&etail;
aqua comprimitur, &longs;ed etiam ab infima, & colla
terali, vndequaque, & vniuersè æqualibus viribus
impellitur, con&longs;tringitur que, vnde fit vt licèt ve&longs;i
ca &longs;it tenui&longs;&longs;ima, non po&longs;&longs;it tamen vnquam diffringi à
pondere licèt immen&longs;o &longs;uper&longs;tantis aquæ, vel hy
drargyri, nec contu&longs;ionem, aut diffractionem vllam
pati; & ratio e&longs;t quia licèt tota ma&longs;&longs;a contenta intra
ve&longs;icam &longs;it fluida, mollis, & cedens, nihilominus
quia minimæ particulæ fluidi, vel arenæ &longs;e mutuò
fulciunt, & natiua duritie compre&longs;&longs;ioni re&longs;i&longs;tunt, fit
vt conden&longs;ari, aut con&longs;tringi nequeant, & ab vni
uer&longs;ali circumambiente compre&longs;&longs;ione ne minimum
alteretur eius figura, neque &longs;itus partium.
pres&longs;ione aquæ incumbentis pati debeat.
NOn &longs;ecùs in corpore animalis continentur in
tra eius pellem partes aliæ quidem duræ, &
&longs;olidæ, vt &longs;unt o&longs;&longs;a, aliæ molles, vt &longs;unt tendines,
nerui, membranæ, & mu&longs;culi; aliæ verò &longs;unt fluidæ,
aqueæ, vel oleagino&longs;æ continentes innumeras alias
particulas &longs;alis, & aliorum corporum. Modò o&longs;&longs;a in
animali di&longs;rumpi, aut iuxari non po&longs;&longs;unt, vt o&longs;ten
&longs;um e&longs;t Prop. 29. ni&longs;i pondus incumbens ex vn&atail;
parte tantum comprimat, vt conting it in baiulis; at
&longs;i compre&longs;&longs;io &longs;ubdiuidatur, vt &longs;phæricè, &longs;ursùm, &
deorsùm, & lateraliter æqualibus viribus
ita vt nulla cutis particula libera à pre&longs;&longs;ione &longs;it, tunc
quidem e&longs;t impo&longs;&longs;ibile vt &longs;ci&longs;&longs;io, vel luxatio &longs;ub&longs;e
quatur; idip&longs;um dicendum e&longs;t de neruis, ac mu
&longs;culis, qui licèt &longs;int molles,
con&longs;i&longs;tentibus, & tenaci&longs;&longs;imis, fit vt vniuersè po&longs;&longs;int
&longs;e vici&longs;&longs;im fulcire, & re&longs;i&longs;tere vniuer&longs;ali, & &longs;phæri
cæ compre&longs;&longs;ioni: idem dicendum e&longs;t de &longs;anguine,
& alijs humoribus animalis, qui aquæ naturam par
ticipant, & &longs;icuti aqua manife&longs;tam conden&longs;ationem
non patitur, &longs;ic quoque animalis humores in cauita
tibus va&longs;orum eius contenti contritionem pati qui
dem po&longs;&longs;unt ab impul&longs;u facto ab vnico, vel paucis
locis peculiaribus; at ab vniuer&longs;ali, & circumqua
que facta compre&longs;&longs;ione minimè po&longs;&longs;unt è &longs;uis va&longs;is
expelli, ac diuelli. quotie&longs;cumque igitur partes &longs;o
lidæ, tendino&longs;æ, aut carno&longs;æ, aut humorales, &longs;ci&longs;&longs;i
onem, luxationem, contu&longs;ionem, aut aliam quam
libet &longs;itus mutationem non patiuntur e&longs;t impo&longs;&longs;ibi
le, vtdolor, aut pa&longs;&longs;io in animali &longs;ub&longs;equatur, quæ
à nulla alia cau&longs;a, quàm à continui diui&longs;ione creari
pote&longs;t. Quà propter cùm vrinatores in profundo ma
ris demer&longs;i ab aqua æquali vi vndique compriman
tur, &longs;upernè &longs;cilicèt, infernè, & lateralitèr circum-
circa à pondere ip&longs;ius aquæ, &longs;equitur ex demon&longs;tra
tis Prop. 29. & 32. nullam &longs;ci&longs;&longs;ionem, luxationem,
aut contu&longs;ionem in eis creari, &longs;cilicèt nullam conti
nui diui&longs;ionem à pondere aquæ incumbentis produ
ci, igitur nullam noxam, nec &longs;en&longs;um dolorificu&mtail;
patientur.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
Sed dices, e&longs;to nullam luxationem, fractionem, aut
contu&longs;ionem vrinatores &longs;ub aqua pati debere,
&longs;en&longs;u tactus perciperent compre&longs;&longs;ionem ponderis
illius va&longs;tæ molis aquæ incumbentis, quam non ne
gamus exercere &longs;uam grauitatem &longs;upra corpus ani
malis demer&longs;i. Hoc profectò e&longs;t, quod negamus, nam
ratio, quare &longs;en&longs;u pa&longs;&longs;ionem ab incumbente ponde
re illatam percipimus extra aquam po&longs;iti e&longs;t, qui&atail;
no&longs;træ partes ob articulorum flexilem
deorsùm pelluntur à premente graui, & idcò cogi
mur ingenti vi fibras mu&longs;culorum tendere, & con
trahere, vt lap&longs;um membrorum impediamus; at in
fra aquam ni&longs;u illo laborio&longs;o mu&longs;culorum non in
digemus, proptereà quòd aqua &longs;ubiecta vices mu
&longs;culorum &longs;upplet repellendo æquali vi &longs;ursùm
&longs;upremam vnà cum natante animali; & proinde &longs;u
prema aqua, &longs;nffulta à &longs;ubiecta virtute ponderis a
quæ collateralis cum qua æquilibratur, nullo pacto
animalis partes flectere, & deprimere pote&longs;t, & ideò
mu&longs;culi otio&longs;i &longs;unt, & propterea nullam aliam pa&longs;
&longs;ionem animal &longs;entiet pr&ecedil;ter vniuer&longs;alem
nem
molles, & fluidæ animalis compre&longs;&longs;ioni non cedunt
ob earum con&longs;i&longs;tentiam, hinc fit, vt nullam pa&longs;&longs;ionem
dolorificam &longs;entiant.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
ob acrem in eis contentum.
NOn tamen negari pote&longs;t ade&longs;&longs;e in animali par
tes aliquas aereas, & &longs;pirito&longs;as, quas
&longs;ari
cumambiente con&longs;tipatione, quam patiuntur vrina
tores in profundo maris con&longs;tituti, nece&longs;&longs;ariò aer in
pectoris cauitate contentus ob re&longs;pirationis ne
ce&longs;&longs;itatem, & particulæ illæ minimæ aereæ per cor
pus eius di&longs;per&longs;æ conden&longs;ationem aliquam patiun
tur; proindequè motiones internæ &longs;pirituum for&longs;an
impediuntur, & naturalis con&longs;titutio partium ani
malis perturbatur; & inde in&longs;en&longs;ibilis tran&longs;piratio
impedita laxitudinem, & pa&longs;&longs;ionem dolorifica&mtail;,
&longs;en&longs;umque &longs;uffocationis creat; & hoc quidem expe
rimur quotie&longs;cumque à ve&longs;te nimis angu&longs;ta
gimurSed notandum e&longs;t, compre&longs;&longs;ionem ve&longs;tis non
e&longs;&longs;e vniuer&longs;alem, & tunc quidem pote&longs;t &longs;anguis ex
pelli versùs faciem, & partes nudatas, & à ve&longs;ti
bus non con&longs;trictas, quod non contingeret &longs;i vni
uersènè minima cutis particula libera à compre&longs;&longs;io
ne e&longs;&longs;et. Sic cùm manus immergitur intra hydrar
gyrum, patimur quidem &longs;en&longs;ibilem compre&longs;&longs;ionem
dolorificam nedùm quia partes aereæ, & &longs;pirito&longs;æ
con&longs;tringuntur, & conden&longs;antur, &longs;ed præcipuè quia
compre&longs;&longs;io efficitur in peculiari loco, & non vni
uersè.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
Ex qua fit vt &longs;anguis à venis manus extrudatur ver
sùs brachium non demer&longs;um intra mercurium, & in
de duæ pa&longs;&longs;iones &longs;ub&longs;equantur, vna quidèm con&longs;tri
ctionis, altera verò e&longs;t ea, quæ ab impedita, & in
terrupta &longs;anguinis circulatione per totam manu&mtail;
oritur.
Sed obijciet forsàn qui&longs;piam exprædicta con&longs;tri
ctione partium aerearum in animali
quam dolorificam pa&longs;&longs;ionem oriri, quam vrinatores
in profundo maris con&longs;tituti percipere deberent. Hoc tamen vltrò conceditur, reuerà enim in profun
do maris pa&longs;&longs;io aliqua con&longs;trictiua in vniuer&longs;o cor
pore percipitur, pariterque aer in pectore animalis
contentus con&longs;tringitur, & conden&longs;atur, &longs;ed no&ntail;
proindè ingens pa&longs;&longs;io &longs;uffocatiua ob cra&longs;&longs;itiem con
den&longs;ati aeris in pectore contenti &longs;ub&longs;equetur,
doquidem
focatiuum percipi, quotie&longs;cumque aer in&longs;piratus
valdè attenuatur, rare&longs;cit, aut conden&longs;atur; &longs;ic enim
in hypocau&longs;to, atque in montis alti&longs;&longs;imi &longs;ummitate
aer valdè rarus attenuatu&longs;que e&longs;t, re&longs;pectu eius, qui
in profunda aliqua valle, vel in loco ceno&longs;o reperi
tur, qui valdè cra&longs;&longs;us, & conden&longs;atus e&longs;t, nihilomi
nùs, neque in ip&longs;a re&longs;piratione læ&longs;io, aut pa&longs;&longs;io ali
qua manife&longs;ta percipitur,
poris aer diuer&longs;imodè rarefactus differentiam nota-
tu dignam, & à nobis perceptibilem parit: igitur
vrinatores in profundo maris demerfi nullam pa&longs;&longs;io
nem dolorificam percipere po&longs;&longs;unt licèt &longs;upponatur
quòd ab aqua incumbente pondero&longs;a compriman
tur, & conden&longs;etur aliquo pacto aer in thorace eo
rum contentus. Quaproptèr ex hi&longs;ce omnibus con
cludere licèt
&longs;cit in &longs;uo naturali loco, nempè quando in ip&longs;amet
vniuer&longs;ali aqua fulcitur, & &longs;u&longs;tentatur.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
Non de&longs;unt po&longs;tea qui Renato Cartefio nimis
addicti velint partes minimas cuiuslibet fluidi, &
præcipuè aquæ
tari, accircumuolui per Hinc &longs;u
bindè inferunt partes aquæ in ip&longs;amet aqua con&longs;ti
tutas, nec grauitatem, nec leuitatem habere, cùm
po&longs;&longs;int qua qu an ersùm &longs;ursùm, atque deorsùm mo
ueri; nos è contrà.
cen&longs;ent par
tes aquæ in
ip&longs;a aqua,
nec grauita
re, nec leui
tare, quia
&longs;ursùm, &
deorsùm
tinentèr
uentur.
uoluatur, agiteturque, nihilominùs perpetuò retinet
propriam grauitatem, e amque perpetuò
exercet.
INtelligatur vas aqua plenum ABCD &longs;u&longs;pen&longs;u&mtail;
in extremo termino H libræ radiorum æqualium
HL, cuius centrum I, & pendeat pondus R ab alte
ro extremo libræ L, itaut libra quie&longs;cat, & æqueli
bretur vas aqueum AC cum corpore R, & hoc qui-
dem verificetur, dum aqua
in prædicto va&longs;e contenta
prorsùs quie&longs;cit, &longs;altè&mtail;
quoad &longs;en&longs;us
&longs;i po&longs;tea aqua agitetur, vt
nimitùm pars EF de&longs;cen
dat ver&longs;us va&longs;is fundum, reliqua verò pars FG, &longs;ur
sùm a&longs;cend at motu quodam vertigino&longs;o, fi veru&mtail;
e&longs;t, quòd motus a&longs;cen&longs;iuus ip&longs;ius aquæ indicat de
fectum grauitatis eius, tunc per&longs;euerante dicto mo
tu a&longs;cen&longs;us minui deberet pondns totius va&longs;is AC,
& propterea libra HL non quie&longs;ceret, &longs;ed deprime
retur pondns R, quod tamen repugnat &longs;en&longs;us eui
dentiæ; non igitur ex eo quòd aqua mouetur in ali
quo va&longs;e carebit propria, & natiua grauitate, &longs;icuti
homo a&longs;cend'ens per &longs;calam extremo termino libræ
alligatam æquali momento libram premeret, ac &longs;i
idem homo in &longs;cala quie&longs;ceret, quia nimirùm dum
a&longs;cendit non minus &longs;u&longs;tentatur quàm dum quie&longs;cit.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
Sed dices, cum motus vertigino&longs;us aquæ fieri
po&longs;&longs;it ab&longs;que eo quod vna pars de&longs;cendat, & reli
qua &longs;ubleuetur, e&longs;t valdè probabile, vt &longs;icut a&longs;cen&longs;us
aquæ FG indicat defectum grauitatis, cùm prædi
ctus motus &longs;upponat impetum à quo &longs;ursùm propel
latur &longs;icuti &longs;axum quod &longs;ursùm proijcitur in actu &longs;ui
a&longs;cen&longs;us, neque graue dici pote&longs;t, nec grauitatem
exercet, proptereà quòd ab impetu impre&longs;&longs;o con
trario grauitati, vel ip&longs;amet grauitas de&longs;truitur, vel
impeditur, & ce&longs;&longs;at eius operatio. Oppo&longs;itum con-
tinget in aqua de&longs;cendente EF quæ videtur habere
nedùm vim propriæ grauitatis, &longs;ed in&longs;uper
quo deorsùm fertur, &longs;icuti &longs;axum, quod deorsù&mtail;
proijcitur, vim, & percu&longs;&longs;ionem infert nedum men
&longs;uratam à gradu eius ponderis, &longs;ed etiam ab impe
tu eius de&longs;cen&longs;iuo; qua propter vis, quæ &longs;ubtrahitur
ab aqua
de&longs;cendenti EF, & &longs;ic duplicatur vis eiu&longs;dem aquæ
de&longs;cendentis qua fundum va&longs;is BC comprimitur;
igitur id, quod &longs;ubtrahitur ab aqua a&longs;cendente FG
&longs;uperaddatur ponderi aquæ de&longs;cendentis EF com
pen&longs;abitur defectus cum additamento impetus
pre&longs;&longs;iui
aquæ in va&longs;e AC contentæ, & hæc erit cau&longs;a, quare
etiam po&longs;t aquæ agitationem pondus eius in libr&atail;
non alteratur, nec imminuitur.
dum in &longs;uo
toto quit
&longs;cens ponde
rat.
adducta.
SEd facili negotio inefficacia huius ratioc inij
diQuoad primum, &longs;u&longs;pendatur vas aqueum AC duobus
filis AH, DL alligatis in extremitatibus eiu&longs;dem li
bræ HL radiorum æqualium, &longs;u&longs;pendaturque libra
cum va&longs;e ab illius centro I, manife&longs;tum e&longs;t, quando
aqua quie&longs;cit, nec agitatur, &longs;i eri æquilibrium, qui&atail;
&longs;cilicèt centrum grauitatis M totius va&longs;is, & aquæ in-
cidit præcisè in recta linea MI
perpendiculari ad horizontem,
quæ per centrum &longs;u&longs;pen&longs;ionis
ducitur. Modò agitetur aqua va
&longs;is, vt nimirùm pars EF de&longs;cen
dat, pars verò KG, &longs;ursùm ten
dat, & hoc per aliquod tempus
per&longs;eueret continuatis reuolu
tionibus, dummodò planities libellæ, AD non alte
retur; frigitur verum e&longs;t in tali ca&longs;u, quòd grauitas
a&longs;cendentis aquæ KG de&longs;truitur quatenus à virtute
impul&longs;iua proiectitia &longs;ursùm impellitur, & è contrà
&longs;i grauitas, & impetus aquæ de&longs;cendentis EF dupli
catur, quia eius ponderi &longs;uperadditur vis proiectiu&atail;
deorsùm, igitur medietas va&longs;is MAB, aut leuis effi
cietur, aut valdè eius grauitas pri&longs;tina imminut&atail;
erit, & è contrà reliqua va&longs;is medietas MDC
duplò grauior facta erit, proindeque terminus
libræ L deprimetur, eleuabiturque oppo&longs;itus ter
minus libræ H, quod tamen fal&longs;um e&longs;t, igitur quo
modocumque aqua agitetur, dum in ip&longs;amet aqua, &
in proprio loco continetur, neque amittit ob a&longs;cen
&longs;um, nec acquirit ob de&longs;cen&longs;um nouam grauitate&mtail;.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
Sed faciliùs hoc experieris, &longs;i intra vas ABCD in
&longs;eratur rota EGKF perpendicularitèr horizonti ere
cta, & parietibus oppo&longs;itis va&longs;is infixo axe eius i&ntail;
M vt facilè rota conuerti po&longs;&longs;it. Et &longs;iquidem centrum
grauitatis totius aggregati cadit in recta line&atail;
IM perpendiculari ad horizontem, tunc &longs;iue rot&atail;
quie&longs;cat, &longs;iue circa eius axim
M conuertatur libra &longs;emper
in &longs;itu horizontali æquilibra
ta perfi&longs;tet.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
Vt verò ratio huius effectus
percipiatur, recurrendum e&longs;t
ad centri grauitatis definitio
nem, ex qua habetur quòd corpus quodlibet &longs;u&longs;pen
&longs;um à centro grauitatis eius quomodocumque reuol
uatur circa centrum, &longs;emper æquilibrari, & haber&etail;
partes æqualium momentorum, vnde infertur, quòd
vniuer&longs;a vis, qua corpus aliquod
licet grauitas eius, exercetur in vnico illo puncto,
quod centrum grauitatis eius vocatur. Hinc deduci
tur, quod &longs;i rota, &longs;iuè pila &longs;u&longs;tineatur ex centro gra
uitatis eius &longs;iuè quie&longs;cat, &longs;iuè moueatur, numquam
centrum grauitatis &longs;itum commutabit, aliàs daretur
motus perpetuus, qui naturæ legibus repugnat.
Similitèr &longs;i concipiatur fi&longs;tula vitrea inflexa ad
modum anuli, vt e&longs;t EFGK, &longs;itque prædicta fi&longs;tul&atail;
plena aqua &longs;ituata perpendiculari
tèr &longs;uper planum &longs;ubiectum RS à
quo fulciatur; habebit profectò
trum
termedio N, dum quie&longs;cit aqua i&ntail;
prædicto anulo, at &longs;i reuoluatur vt
nimirùm pars EFG de&longs;cendat, reliqua verò GKE
&longs;ursùm
feretur
aquæ de&longs;cendentis, nam per&longs;euerante vertigine, &longs;ci
licèt translato centro grauitatis vltrà medium in O
&longs;emper &longs;emianulus EFG grauior e&longs;&longs;et, quàm GKE,
& propterea ille &longs;emper de&longs;cenderet, hìc verò &longs;em
per a&longs;cenderet, proindeque anulus excurreret mo
tu perpetuo progre&longs;&longs;iuo, quod e&longs;t fal&longs;um. per&longs;i&longs;tit
ergo centrum grauitatis &longs;emper in centro N anuli,
&longs;iue aqua in eo contenta quie&longs;cat, &longs;iuè circumduca
tur, nam ob contiguitatem partium aquæ non pote&longs;t
moueri vna pars aquæ F v. g. quin vniuer&longs;a aqu&atail;
EKG æquali velocitate reuoluatur, proindeque
vnica pars tantùm, &longs;ed aqua tota
tum acquirit, non &longs;ecùs ac rota lignea tota &longs;imul ic
tum recipit atque circa
libratur, pari modo aqua contenta in va&longs;e AC ante
præmi&longs;&longs;æ figuræ, licèt &longs;it fluida, habet tamen pun
ctum M circa quod partes habent æqualia momenta,
perinde ergo &longs;e habent ac &longs;i vniuer&longs;a aqua in prædi
cto va&longs;e contenta dura e&longs;&longs;et, & con&longs;i&longs;tens vt rota li
gnea, vel intra fi&longs;tulam anularem EFKG content&atail;
e&longs;&longs;et in qua reuoluta, &longs;iue quie&longs;cente rota, aut aqua
&longs;emper centrum grauitatis eius in eodem &longs;itu per&longs;e
uerare debet, & proinde libra HL quie&longs;cet in
&longs;itu horizontali. Igitur dubitandum non e&longs;t aqua&mtail;
in &longs;uo toto collocatam, grauitatem exercere, &longs;iuè illa
omninò ibidem quie&longs;cat, &longs;iuè quomodolibet agite
tur, & circumuoluatur.
dum in &longs;uo
toto quie
&longs;cens pon
derat.
tiuam leui
tatem no&ntail;
dari.
non dari.
HActenùs con&longs;iderauimus grauitatem non om
nium corporum fluidorum, &longs;ed tantummodò
aquæ, hydrargyri, & &longs;imilium, de quorum pondero
&longs;itate nemo dubitat, manife&longs;tè enim deorsùm ten
dunt, atque de&longs;cendunt. difficultas vertitur circ&atail;
reliqua corpora, quæ &longs;ursùm a&longs;cendere videntur, vt
&longs;unt ligna, & alia corpora, quæ in aqua &longs;ursùm
dunt
communem conceptum; nihilominùs cum melioris
notæ Philo&longs;ophis o&longs;tendere conabimur omnia cor
pora fluida elementaria grauitatem habere, leuita
tem verò po&longs;itiuam ab&longs;olutè in natura non dari, ita
que
bere vim &longs;e &longs;e vniendi ad efformandum no&longs;trum Sy
&longs;tema, &longs;cilicèt habere facultatem motiuam de&longs;cen
dendi versùs centrum globi terre&longs;tris, & huiu&longs;modi
vis vocatur grauitas. Et primo loco examinabimus
argumenta Ari&longs;totelis facta contra Platonem, & De
mocritum prædictæ &longs;ententiæ a&longs;&longs;ertores, po&longs;tea ad
examen reuocabimus rationes eiu&longs;dem Ari&longs;totelis,
quibus leuitatem po&longs;itiuam &longs;tatuere conatur. Tertio
loco afferam demon&longs;trationes, quibus euincitur non
dari leuitatem po&longs;itiuam; & tandem con&longs;idèrabo ea
omnia, quæ pa&longs;sìm à melioribus Peripateticis con-
tra Platonicam &longs;ententiam a fferuntur, quæ peruene
re ad meam notitiam.
tiuam leui
tatem no&ntail;
dari.
Quòad primum Ari&longs;toteles in&longs;ectatur Democriti,
Platoni&longs;que po&longs;itionem, &longs;ed more &longs;uo, non contr&atail;
&longs;ententias, at contra mera verba eorum argumenta
tur, &longs;cilicèt quod terræ grauitas maior, quàm aeris
pendeat à copia triangulorum, quæ maior in terra,
quàm in aere exi&longs;tit, a&longs;&longs;umitque prædicta triangula,
ac &longs;i e&longs;&longs;ent &longs;uperficies planæ omninò indiui&longs;ibiles,
quod patet fal&longs;um e&longs;&longs;e, cùm in Platonica po&longs;ition&etail;
atomi triangulares &longs;int corpora, non autem &longs;uperfi
cies indiui&longs;ibiles.
cap.2.
Præterea contra Democritum, ait, grandem aeris
ma&longs;&longs;am, veluti e&longs;&longs;et &longs;phæra aerea habens diametrum
decem cubitorum, habere maiorem copiam, &
dantiam
habens diametrum vnius digiti, & proindè pila ae
rea grauior e&longs;&longs;e deberet, & deor&longs;um de&longs;cendere, &
è Hoc,
inquam, argumentum non afficit Democritum, qui
numquam tantam ab&longs;urditatem &longs;omniauit,
enim con&longs;iderauit plenum &longs;olitarium, &longs;ed vnà cum
pleno ingentem vacui molem augmentatam in ill&atail;
grandi aerea pila, & &longs;emper maiori cum proportio
ne, quàm &longs;e habeat plenum aeris ad plenum aquæ. Quam exceptionem parùm &longs;incerè Ari&longs;toteles &longs;ub &longs;i
lentio inuoluit, quoniam exi&longs;tente aere rariore,
&longs;it ip&longs;a aqua, habebit pars vacua ad partem plena&mtail;
aeris maiorem proportionem, quàm habet pars va-
cua ad partem plenam ip&longs;ius aquæ, & permutando,
moles vacua aeris ad molem vacuam aquæ maiorem
proportionem habebit, quàm moles plena aeris ad
molem plenam aquæ, & proindè qu&ecedil;libet ampla ae
ris moles habebit
aqua, po&longs;ito quòd huiu&longs;modi cau&longs;a &longs;it vacuum, & è
contra in eodemmet aere debilior erit cau&longs;a graui
tatis, quæ ab ip&longs;o pleno, & ab eius men&longs;ura de&longs;u
mitur,
mento
aquea, &longs;uperadditur quoque cau&longs;a contraria, nemp è
alleuiationis, quæ e&longs;t vacuum plu&longs;quam milliès ma
ior, quàm &longs;it illud quod in ip&longs;a aqua continetur;
cùm igitur tàm enormiter excre&longs;cat, & &longs;uperet pro
portio vacuitatis reliquam proportionem plenitudi
nis in prædictis duobus elementis numquam poterit
ampla pila aerea grauior effici ob augmentum eius
plenitudinis, & partis materialis, quando ip&longs;a in &longs;e
quoque continet contrariam cau&longs;am, quæ eam
reddit multò magis multiplicatam, & hæc e&longs;t inani
tas, & vacuum. Eiu&longs;dem farinæ e&longs;t longa illa &longs;eries
argumentorum toties ab Ari&longs;totele contra antiquos
adductorum.
tiuam leui
tatem no&ntail;
dari.
Præterea verum non e&longs;t, a&longs;&longs;igna&longs;&longs;e antiquos &longs;pa
tio vacuo motum, aut virtutem operandi, &longs;ed
modò
bant, quod per&longs;picuè ex
refert enim antiquos po&longs;ui&longs;&longs;e omnia corpora
taria
prout plenum, & principium materiale deficeret,
aut abundaret in ip&longs;is; & in&longs;uper ait, quòd a&longs;cen&longs;us
&longs;ursùm aliquorum corporum, nempè ignis,
cipio aliquo po&longs;itiuo, &longs;cilicèt leuitate pendere an
tiquì cen&longs;ebant, &longs;ed effici huiu&longs;modi a&longs;cen&longs;um per
extru&longs;ionem factam à fluidis corporibus ambienti
bus pondero&longs;ioribus. Si igitur hæc fuit anti quoru&mtail;
&longs;ententia, quomodo eis tribui pote&longs;t tàm enormis
ab&longs;urditas, quòd nimirum vacuum moueatur, impel
lat, habeat &longs;itum, & regionem &longs;ursùm, versùs quam
tendit? quomodò, inquam, hæc affirmare poterant il
li, qui apertè aìe bant motus omnes naturales corpo
rum elementarium tendere deorsùm omne&longs;que pen
dere ab vnico principio po&longs;itiuo, &longs;cilicèt à pleno, &
materia corporea? nec quia aer &longs;ursùm impellitur,
extruditurque, inde &longs;equitur, quòd vacua in aere
tenta
cuum nil aliud e&longs;t, quàm &longs;patium, id erit immobile,
& proindè aer &longs;ecum non a&longs;portabit vacuum ip&longs;um
&longs;ursùm, &longs;ed in ip&longs;o a&longs;cen&longs;u &longs;ucce&longs;&longs;iuè acquiret noua
&longs;patia: relinquendo præcedentia, quæ &longs;unt omninò
immobilia. at &longs;i nomen vacui meram pleni priuatio
nem, ac nihilum &longs;ignificet, certum e&longs;t quòd nihilum
moueri non pote&longs;t, nec impellere, nec ab vno ad
alium locum migrare.
tiuam leui
tatem no&ntail;
dari.
Po&longs;tquam con&longs;iderauimus Ari&longs;totelis argumenta
contra Antiquos, qui leuitatem po&longs;itiuam omninò
negabant, re&longs;tat modò vt eiu&longs;dem Ari&longs;totelis ratio
nes pro leuitatis &longs;tabilimento, & po&longs;itione con&longs;ide-
remus. Præcipua eius ratio hæc e&longs;t, quia reperiun
tur duo loca contraria in natura &longs;ursùm, & deorsùm,
&longs;cilicèt circumferentia, & centrum mundi, &longs;eu ter
ræ; & euidentèr apparet, quòd terra infima e&longs;t, &
&longs;ubiacet omnibus alijs corporibus
gitur enìm de&longs;cendendo infrà aerem, & infra
quou&longs;que adlocum infimum perducatur, nempè ad
centrum, quando nimirum ea non impeditur; hinc
deducit, ergo terra e&longs;t ab&longs;olutè, & &longs;implicitèr gra
uis, & non relatiuè. E contrà videmus aerem pene
trare den&longs;itatem ip&longs;ius aquæ, & a&longs;cendere &longs;uper
& ignem perforare
ducique ad &longs;upremam, & extremam &longs;uperficiem ae
ris, veluti ad locum &longs;uum
tandèm quie&longs;cit, nec vlteriùs mouetur. Et quia, in
quit, ignis omnibus &longs;upereminet, igitur e&longs;t &longs;impli
citèr, & ab&longs;olutè leuis; terra omnibus &longs;ubijcitur, igi
tur e&longs;t ab&longs;olutè grauis.
tiuam leui
tatem no&ntail;
dari.
Vt verò vim, & energiam Ari&longs;totelici ratiocinij
percipiamus, & exactè perpendamus, oportet vt &longs;ta
tum controuer&longs;iæ memoremus, &longs;cilicèt the&longs;im Pla
tonis, atque Democriti, quam Ari&longs;toteles redargue
re profitetur, ante oculos ponamus, & po&longs;tea argu
mentum ab Ari&longs;totele adhibitum con&longs;ideremus. Et
primò ratum per&longs;pectumque e&longs;t duplici modo fieri
po&longs;&longs;e vtignis &longs;ursùm perducatur, & &longs;uper omnia e
lementa emineat, aut nempè quia ignis &longs;ponte &longs;u&atail;
mouetur &longs;ursùm à principio intrin&longs;eco, & naturali,
&longs;cilicèt à leuitate, vel potiùs, quia ibidem ignis ex-
pellatur, extrudaturque à maiori grauitate aliorum
corporum fluidorum, veluti e&longs;t aer, & aqua; & hæc
po&longs;trema erat Platonis, & Democriti &longs;ententia,
Ari&longs;toteles redarguere tenebatur: Argumentum ve
rò Ari&longs;totelis aliam longè diuer&longs;am propo&longs;itionem
à nemine in dubium reuocatam petit, atque in&longs;ecta
tur; nil enim aliud obijcit, quàm phenomenon, quod
&longs;en&longs;ibus patet, & quod aduer&longs;arij vltrò
&longs;cilicet quòd omnes videmus ignem &longs;upra
uari; at tenebatur potius Ari&longs;toteles demon&longs;trar&etail;
ignem a&longs;cendere non quia à medio fluido grauiori
extruditur
propria leuitatis mouetur, quod non præ&longs;titit, pote
rit ergò vocari Ari&longs;totelicum ratiocinium potiùs pe
titio, quàm demon&longs;tratio.
tiuam leui
tatem no&ntail;
dari.
Non de&longs;unt Peripatetici, qui vt
addant Ari&longs;totelico ratiocinio, aiunt ab&longs;urdum e&longs;&longs;e
omninò corpora naturalia moueri ad propria loc&atail;
non à principio intrin&longs;eco, & eis à natura in&longs;ito, &longs;ed
à violentia externi corporis per extru&longs;ionem, vnde
deducitur, quòd natura in operationibus tàm nece&longs;
&longs;arijs, & vtilibus fuerit deficiens, cùm nimirum in
digeat &longs;timulis, & impul&longs;u violento, & coactione,
quæ cùm re&longs;i&longs;tentiam, & violentiam includat, vide
tur operatio non naturalis, & propterea neque per
petua, neque vtilis ad ordinem, & con&longs;eruationem
vniuer&longs;i.
Huic &longs;pecio&longs;o ratiocinio re&longs;ponderi pote&longs;t, e&longs;&longs;&etail;
regulam fallacem, quòd vbicumque actiones, & o-
perationes non fiunt &longs;ponte, &longs;ed violentèr, tunc pro
tunciari debeat prædictas operationes à natura, at
que à principio naturali factas non e&longs;&longs;e.
tiuam leui
tatem no&ntail;
dari.
Vno verbo, erit quoque naturalis operatio ill&atail;,
quæ cum aliqua violentia efficitur.
cedat, nihilominùs operatio tota naturalis erit.
HOc autem pote&longs;t confirmari hac ratione; &longs;i
e&longs;&longs;et, quòd quælibet operatio in qua violentia
aliqua adhibetur reputari deberet non naturalis, &longs;e
queretur quòd alterationum corporum
pariterque omnium generationum vegetabilium, &
animalium nulla e&longs;&longs;et, neque vocari po&longs;&longs;et operatio
naturalis, eò quòd &longs;emper requiritur actio, & pa&longs;
&longs;io qualitatum, & corruptio præcedentis &longs;ub&longs;tantiæ. Nec tamen dubitandum e&longs;t pa&longs;&longs;iones prædictas, &
corruptiones, operationes e&longs;&longs;e violentas, non &longs;pon
te, &longs;ed cum di&longs;plicentia, & pa&longs;&longs;ione quadam factas,
igitur in omnibus prædictis operationibus natur&atail;
ip&longs;a violentiam exercet, & propterea confitendum
e&longs;t proprium in&longs;titutum naturæ e&longs;&longs;e violentiam exer
cere, ita vt &longs;ine ip&longs;a nil prorsùs efficere &longs;ciat, neque
&longs;uos fines con&longs;equi valeat.
Sed in&longs;tant,
cedentem formam, cùm &longs;ub &longs;equens minimè generari
po&longs;&longs;it per&longs;euerante prima, & proindè, inquiunt, pri-
mò, & per &longs;e naturam agere proptèr bonum, & prop
tèr finem, generationemque, & proindè
corruptio erit veluti quædam conditio &longs;ine qua &longs;ub
&longs;equens forma introduci, ac generari non pote&longs;t; fa
tentur ergo, quòd &longs;altèm per accidens, natura actio
nes violentas exercet, &longs;ed ea omnia quæ à natur&atail;
operantur, vocantur naturales actiones, igitur
tia
tur, erit
doquidem
quoque nece&longs;sè e&longs;t media illa, quæ ad finem condu
cunt, igitur naturalis in&longs;tinctus, quo formæ genera
tio qu&ecedil;ritur, con&longs;equiturquè, nece&longs;&longs;ariò inuoluit vio
lentiam, &longs;altem vt medium nece&longs;&longs;arium requi&longs;itum. Hinc deducere licèt non e&longs;&longs;e ab&longs;urdum, nec
quòd natura violentiam aliquam exerceat, vt ea me
diante alia maior ab ona con&longs;equatur. Si hoc,
verum e&longs;t in alterationibus, & corruptionibus, mul
tò magis hoc verificabitur in alijs &longs;uauioribus natu
ræ actionibus, quando corpora naturalia ad &longs;ua loca
perducuntur propter bonum, & commoditatem eo
rumdem corporum violenter agitatorum, non &longs;ecùs,
ac &longs;i quis curru, vel lectica è foro domum veheretur
ineptè quidem de coactione, & violentia quereretur,
cùm eiu&longs;modi violentia vtilitatem iucunditatemque
ei afferret. Eodem penè modo à grauibus naturaliter
de&longs;cendentibus perducerentur leuia ad debitu&mtail;
&longs;itum.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
naturalis, quia e&longs;t nece&longs;&longs;aria.
ET hæc quidem dicta &longs;untiuxtà vulgarem Peri
pateticam &longs;ententiam, &longs;ed qui&longs;quis hoc nego
tium attentè perpenderit, is planè percipiet, quòd
vox violen tiæ trahit originem metaphoricè ab illo
&longs;en&longs;u di&longs;plìcentiæ doloris, & amaritudinis, quam
patiuntur animantia, dum alterantur, & corrum
puntur. Hinc &longs;equitur, quòd vbi deficit &longs;en&longs;us, defi
ciat quoque dolor, & violentia nece&longs;sè e&longs;t, & proin
dè alia regula, & norma certiori, ac tutiori di&longs;tingui
deberent operationes naturales à non naturalibus,
&longs;eù violentis, e&longs;tque huiu&longs;modi: operationes omnes
quæ ab&longs;olutè, & omninò nece&longs;&longs;ariæ &longs;unt, neque vllo
pacto fieri pote&longs;t, vt Natura eas negligat, &longs;ed cogi
tur nece&longs;&longs;ariò eas exercere, iure naturales operatio
nes appellari, ac cen&longs;eri debent. Modò quia ope
ratio naturalis, qua corpora grauiora profundiùs
de&longs;cendunt, atque centro terræ propinquiora fiunt,
quàm minùs grauia nece&longs;&longs;ariò &longs;ecum inuoluit ordi
natam di&longs;po&longs;itionem corporum, vt nimirùm grauio
ra infimum locum po&longs;&longs;ideant; minùs grauia verò &longs;u
premum, & in&longs;uper vniuer&longs;a huiu&longs;modi recta di&longs;po
&longs;itio exigit vt ambo corpora moueantur tendendo
deorsùm in centro communi grauitatis eorum. Non
&longs;ecùs ac in libra pre&longs;&longs;a ab in æqualibus ponderibus,
a&longs;cen&longs;us minoris ponderis factus à de&longs;cen&longs;u corpo
ris grauioris alteram lancem prementis, ineptè qui
dem, & iniuria violentia appellatur; propterea quòd
huiu&longs;modi operatio, ac di&longs;po&longs;itio nece&longs;&longs;aria, ac na
turalis e&longs;t.
tiuam leui
tatem no&ntail;
dari.
Idip&longs;um, vel quid &longs;imile, dici debet de extru&longs;ione
cuiuslibet corporis minùs grauis facta à pre&longs;&longs;ion&etail;
ambientis fluidi grauioris, quia in tali ca&longs;u (vt &longs;uolo
co o&longs;tenditur) ade&longs;t libra quædam imaginaria per
petua, cuius centrum grauitatis &longs;ucce&longs;&longs;iuè deprimi
tur, &
tus &longs;ublimationis corporis minùs grauis, hocque
diù per&longs;euerat, quou&longs;que efficiatur æquilibrium.
igitur &longs;it effectus nece&longs;&longs;arius, & naturalis, extru&longs;io,
&longs;eù a&longs;cen&longs;us ligni quotie&longs;cumque circumdatur à flui
do grauiori, non pote&longs;t, nec debet prædictus a&longs;cen
&longs;us nuncupari, vel reputari violentus, quod erat
dendumHoc confirmari pote&longs;t ex Galilei pulcher
rimo ratiocinio.
de&longs;cen&longs;us eorundem.
FInge globum no&longs;træ terræ perforari puteo
trum
que in hoc demi&longs;&longs;a pila ferrea proculdubio natura
lis eius grauitas &longs;ucce&longs;&longs;iuè maiorem impetum acqui
ret, quòu&longs;que ad centrum terræ pertingat, & vniuer-
&longs;a hæc motionaturalis cen&longs;ebitur, eò quòd pendet à
&longs;uo intrin&longs;eco principio grauitatis; &longs;ed no&longs;tqua&mtail;
pila terræ centrum attingit profectò
nam impetus in præcedenti de&longs;cen&longs;u acqui&longs;itus pi
lam tran&longs;portabit vltra centrum, excurretque versùs
Antipodas. modò in hoc excur&longs;u cùm pila à centro
terræ recedat, procùl dubio &longs;ur&longs;um
que prædictus a&longs;cen&longs;us violentus motus, & contr&atail;
eius naturam, & tamen ab operatione naturali de
&longs;cen&longs;us dependet.
tiuam leui
tatem no&ntail;
dari.
Idip&longs;um alijs exemplis, quæ facilè po&longs;&longs;unt expe
riri, confirmari pote&longs;t.
Sit vas aqua plenum RSXV & ha
beatur quoque cylindrus ligneus
EF, qui in aqua demer&longs;us non de
mergetur integrè infra &longs;upremam li
bellam aquæ RS, &longs;ed remanebit ali
qua eius pars GE eminens &longs;upr&atail;
aquæ libellam, propterea quòd li
gnum minùs graue e&longs;t &longs;pecie, quàm
ip&longs;a aqua, (vt Archimedes ait.)
Si po&longs;tea eumdem ligneum cylindrum extra aqua&mtail;
&longs;ubleuauero v&longs;que ad &longs;itum AB, & hinc liberè eum
de&longs;cendere permittam, is profectò non con&longs;i&longs;tet, ne
què quie&longs;cet in &longs;itu EF,
&longs;cen&longs;u per aerem profundiùs infra aquæ libella&mtail;
motu violento cylindrum immittet v&longs;que ad &longs;itu&mtail;
CD & hinc denuò a&longs;cendendo tran&longs;gre&longs;&longs;o &longs;itu æqui
librij EF re&longs;iliet omninò extra aquam propè &longs;itu&mtail;
AB, & &longs;ic denuò quou&longs;que repetitis vibrationibus
&longs;en&longs;im languendo, tandèm quie&longs;cat in &longs;itu naturali
EF.
tiuam leui
tatem no&ntail;
dari.
Pari modo &longs;umpto
dulo
circa &longs;uum centrum firmum A,
remota pila plumbea. B à &longs;itu
&longs;uo naturali, &longs;eu perpendicu
lari ad horizontem, perducta
que ad &longs;itum eleuatum C, illa planè vt grauis excur
ret de&longs;cendendo arcum CB, & vniuer&longs;us is motus na
turalis erit, vtpotè dependens ab impetu grauitatis
intrin&longs;eco, non tamen in infimo &longs;itu B pila per&longs;i&longs;tet
po&longs;tquam ibidem perducta e&longs;t, &longs;ed vlteriùs excur
ret ferè æquali &longs;patio priori vltrà perpendiculum v&longs;
que ad &longs;itum D, a&longs;cendendo nimirùm ab infimo &longs;itu
B per integrum arcum BD, & quia motus ille qui gi
gnitur à principio intrin&longs;eco, & naturali non pote&longs;t
e&longs;&longs;e non naturalis, cùmque a&longs;cen&longs;us pilæ vltra cen
trum terræ, & de&longs;cen&longs;us cylindri EF infra aquæ li
bellam po&longs;t ca&longs;um, & a&longs;cen&longs;us pilæ plumbeæ per ar
cum BD pendeat, creeturque ab illa naturali virtu
te grauitatis nempè eiu&longs;dem corporis de&longs;cendentis
quatenùs de&longs;cendit: nulla enim alia cau&longs;a extrin&longs;e
ca &longs;uperueniens excogitari pote&longs;t, quæ violentia&mtail;
in&longs;erat, & &longs;ursùm impellat prædictum graue, quàm
impetus acqui&longs;itus, & conceptus in ip&longs;o ca&longs;u natura
litèr facto productoque à principio intrin&longs;eco graui
tatis eius, qui procùl dubio impetus à naturali prin-
cipio pendens naturalis, & intrin&longs;ecus quoque erit,
igitur etiam illa operatio a&longs;cen&longs;us erit naturalis qua
tenùs pendet creaturque à principio intrin&longs;eco, i&ntail;
eo enim &longs;olummodò ca&longs;u violenta
do
tiuam leui
tatem no&ntail;
dari.
Contra hoc ratiocinium in&longs;urgit in&longs;ignis Peripa
teticus, & ait, quod &longs;ub&longs;equens a&longs;cen&longs;us vltra cen
trum terræ, vel vltra perpendiculum per arcum BD
non pendet, nec procreatur à grauitate eiu&longs;dem cor
poris, &longs;ed ab impetu concepto per motum de&longs;cen&longs;us,
qui impetus, inquit ille, res e&longs;t, toto cœlo diuer&longs;a à
grauitate, imò prædictus impetus contra grauitatem
luctatur.
recentioris
authoris af
feruntur.
Patet ergò concedere aduer&longs;arium pilæ a&longs;cen&longs;um
po&longs;t excur&longs;um vltra centrum, vel vltra perpendicu
lum effici, ac produci à virtute impetus impre&longs;&longs;i, qui
nimirùm immediata cau&longs;a, & principium e&longs;t prædi
cti a&longs;cen&longs;us, &longs;eù operationis, quæ nomine leuitatis
in&longs;ignitur. At quia præter immediatam cau&longs;am illius
a&longs;cen&longs;us, &longs;cilicèt præter impetum, adnotari præte
rea debet cau&longs;a productrix prædicti impetus, quæ
e&longs;t grauitas naturalis, & intrin&longs;eca eiu&longs;dem corpo
ris, ergo hæc erit cau&longs;a &longs;altèm mediata illius po&longs;tre
mi a&longs;cen&longs;us, & hìc noto quod aduer&longs;arius non negat,
nec affirmat grauitatem fui&longs;&longs;e cau&longs;am, & principium
productiuum prædicti impetus, &longs;ed tantummodò ait
valdè differre grauitatem ab impetu, imò naturas
contrarias, & &longs;e mutuo de&longs;tructiuas habere, quia ni
mirùm non alia de cau&longs;a ce&longs;&longs;at
&longs;us tùm pilæ, tùm fune-penduli, ni&longs;i quia grauitas pi
læ contrario ni&longs;u vim impetus a&longs;cendentis de&longs;truit.
tiuam leui
tatem no&ntail;
dari.
Sed quid tandem hinc aduer&longs;arius deducere vel
let? an quia ex eo, quòd natura grauitatis diuer&longs;&atail;
&longs;it ab impetu dicemus impetum prædictæ pilæ de
&longs;cendentis v&longs;que ad centrum, vel perpendiculum ge
nitum non fui&longs;&longs;e à vi, & exercitio grauitatis? à qu&atail;
nam ergo virtute tamquam à principio immediato
genitus fuit? profectò &longs;i &longs;en&longs;us negare non velimus,
fatendum e&longs;t à nulla alia cau&longs;a, vel principio exter
no, &longs;ed tantummodò ab ip&longs;amet grauitate pilæ de
&longs;cendentis impetum prædictum genitum fui&longs;&longs;e, nec
certitudo &longs;en&longs;us relinqui debet propter difficulta
tem adductam ab aduer&longs;ario, vt præclarè Ari&longs;toteles
præcipit. Si igitur grauitas pilæ e&longs;t &longs;altem
& cau&longs;a mediata con&longs;equentis a&longs;cen&longs;us, nece&longs;&longs;ariò
actus, & operatio a&longs;cen&longs;us, quæ violenta, & præter
naturam &longs;axi exi&longs;timatur, efficietur procreabiturque
ab interno, & naturali principio grauitatis eius, &
proindè actus a&longs;cen&longs;us, &longs;eu motus violentus efficie
tur à principio interno, & naturali.
Et hìc obitèr mirari licèt horum philo&longs;ophoru&mtail;
fecuritatem; hìc negant impetum à grauitate pro
creari, & inculcant valdè inter &longs;e differre, & &longs;e mu
tuò de&longs;truere, & vnà
pertè fatentur impetum e&longs;&longs;e grauitatem fluentem e&longs;
&longs;eque pror&longs;us eiu&longs;dem naturæ, quia nimirum &longs;axum
impetu affectum comprimit, conterit aduer&longs;a cor
pora eodem modo, ac ingens pondus efficit.
tiuam leui
tatem no&ntail;
dari.
Sed in&longs;tat aduer&longs;arius quomodo pote&longs;t grauitas
efficere impetum quo pila a&longs;cendit &longs;i videmus
prædictum a&longs;cen&longs;us &longs;en&longs;im debilitari, & tandem ex
tingui &longs;olummodo propter renitentiam, & contra
riam actionem, quam efficit pondus eiu&longs;dem pilæ? Et hìc aio, quòd exercitium eiu&longs;dem ponderis, &longs;cili
cèt compre&longs;&longs;io eius producit duos effectus contra
rios, primò per de&longs;cen&longs;um creat, fouet, & auget im
petum eius, po&longs;teà per a&longs;cen&longs;um ei contranititur,
debilitat, atque de&longs;truit eum, & licèt hoc mirabil&etail;
videatur, nihilominùs idip&longs;um concedant nece&longs;sè
e&longs;t, velint, nolint, cùm &longs;en&longs;u con&longs;tet, &longs;ic eadem manus
impellendo &longs;axum dum deorsùm decidit, auget mul
tiplicatque eius impetum, at &longs;i &longs;axum &longs;ursùm a&longs;cen
deret eadem manus contrario motu impetum eius
debilitaret, atque de&longs;trueret. &longs;imilitèr idem calor
Solis generat, & auget plantas, & po&longs;tea eas exic
cat extinguitque. Ex his ergò patet in&longs;ufficienti&atail;
&longs;uperiùs adducti ratiocinij.
porum leuium effici pote&longs;t.
SEd redeo iam ad propo&longs;itum, & alia ratione
demVul
gati&longs;&longs;imum axioma omnium
natura &longs;emper producit &longs;uas operationes via bi eui&longs;
&longs;ima, &longs;ummo compendio, atque abhorret à prolixi-
tate, & multiplicitate cau&longs;arum quando &longs;uos effe
ctus producere pote&longs;t via illa breuiori, & faciliori. hinc deducitur, quod &longs;i po&longs;&longs;ibile e&longs;t
pora naturalia ad propria loca mediante vnica, & &longs;in
gulari motiua virtute grauitatis, vani&longs;&longs;imè, & &longs;tultè
natura ageret, &longs;i niteretur prædictum finem a&longs;&longs;e qui
adhibitis duobus principijs &longs;cilicèt grauitate, & al
tera oppo&longs;ita virtute, quæ leuitas nuncupatur. Quod
verò po&longs;&longs;int naturalia corpora ad &longs;ua naturalia loca
perduci à grauitate &longs;ola ab&longs;que leuitate patet ex &longs;u
periùs dictis, nam minor grauitas, quæ ve&longs;icæ aer&etail;
plenæ tribuitur, & maior aquæ, & omnium maxima
hydrargyro, &longs;ufficienti&longs;&longs;ima cau&longs;a e&longs;t apta ad produ
cendum
cipijs, & rationibus mechanicis. Quaproptèr pro
babili&longs;&longs;imè concedendum e&longs;t &longs;olo principio grauita
tis ab&longs;que vlla leuitate naturam &longs;uum finem a&longs;&longs;equi
collocandi corpora terrena in debitis locis, nempè
&longs;ursùm, & deorsùm.
tiuam leui
tatem no&ntail;
dari.
Et hactenùs adductæ &longs;unt rationes probabiles
tra
rectè o&longs;tendatur rationibus magis conuincentibus,
& efficacioribus.
tiuam leui
tatem no&ntail;
dari.
trin&longs;eco, & naturali&longs;ponte translatum faciliùs, &
celeriùs mouebitur in fluido rariori, & tenuio
ri, quàm in medio fluido cra&longs;&longs;o, &
tenaciori.
SInt duo va&longs;a GHIK, alterum KILM,
repleatur, &longs;ecundum verò hydrargyro, immer
gatur verò eadem pila lignea A in vtroque fluido, in
telliganturque duæ moles &longs;patiales ex prædictis flui
dis B, & C, quæ æquales &longs;int ip&longs;i A, eique
bant
&longs;i&longs;tentior, den&longs;ior, atque compactior e&longs;t, quàm &longs;it
moles aqu&ecedil; B. præterea pila lignea
A nullo pacto a&longs;cendere &longs;ursùm po
te&longs;t, ni&longs;i aquam B, ab eius loco ex
pellat vt ei locum cedat, atque mo
les ip&longs;ius ligni A
cupandum &longs;patium ei æquale B, &
hoc &longs;emper contingit, vbique enim
in
&longs;ursùm impellere incumbentem a
quæ molem ei æqualem, tenacita
temque eius penetrare, ponatur iam gradus natura
lis impetus leuitatis ip&longs;ius ligni e&longs;&longs;e D, quia verò cor
pus motiuum A impetu D affectum impellit corpus
B fluidum, quod in quiete con&longs;titutum &longs;ua naturali
inertia re&longs;i&longs;tit impul&longs;ui impellentis corporis leuis A;
ergò ex
vis motiua leuitatis ip&longs;ius A communicatur, &
ditur
dum B, igitur eius impetus D valdè debilitatur re
tardaturque, &longs;itque diminuta velocitas E, qua ni
mirùm lignum leue A, & fluidum B mouentur. pari
ratione &longs;it F velocitas retardata, qua idem lignu&mtail;
A nec non moles hydrargyri C &longs;ibi æquali agitatur. O&longs;tendendum e&longs;t quòd velocitas, E qua nimirum li
gnum a&longs;cendit per aquam maior &longs;it velocitate F quà
lignum per mercurium eleuatur, & habere veloci
tatem E ad F reciprocè ferè eamdem proportionem,
quam habet corporea &longs;ub&longs;tantia
AC ad corpulentiam AB. Quia ab
eadem virtute motiua impelluntur
duo corpora A, & B à qua priùs in
telligebatur moueri &longs;ingularis ma&longs;
&longs;a lignea A cui naturalis gradus
impetus D conueniebat, igitur mo
les corporea, & materialis duorum
corporum &longs;imul &longs;umptorum A & B
ad molem corpoream A reciprocè
eamdem proportionem habebit, quam eorum ve
locitates Simili ratio
cinio vt moles corporea A ad molem corpoream AC
ita e&longs;t velocitas F ad D, ergo ex æqualitate pertur
bata corporea &longs;ub&longs;tantia AB, ad AC eamdem pro
portionem habebit, quàm velocitas F ad E, e&longs;t qu&etail;
&longs;ub&longs;tantia corporea AB minor ea quæ continetur in
AC, ergò impetus F minor e&longs;t quàm E; quaproptèr
lignum A intrà mercurium C
dere
velocitas E, quæ
tiuam leui
tatem no&ntail;
dari.
cu&longs;&longs;ionis pro
po&longs;it. 15.
tiuam leui
tatem no&ntail;
dari.
Et profectò euidenti&longs;&longs;imum e&longs;t, quòd quodlibet
corpus à principio intrin&longs;eco motu &longs;pontaneo trans
latum, multò faciliùs gradietur excurretque per me
dium fluidum rarius, & cedens, quàm in medio flui
do tenaciori, & cra&longs;&longs;iori, vt pila aurea celeriùs per
aerem, quàm per aquam eiu&longs;dem &longs;patij de&longs;cendit, &
per aquam velociori motu, quàm per mercurium ex
currit; &longs;ic paritèr videmus animalia, quæ intrin&longs;ec&atail;
vi mouentur, difficiliùs gradi po&longs;&longs;e, &longs;i infra arena&mtail;
&longs;ub mergantur, & minùs difficilè infrà lutum, & fa
ciliùs in aqua, & multò faciliùs in aere, nec
contrarium contingere poterit, quòd nimirùm idem
animal eamdem vim motiuam exercendo difficiliùs
& tardiùs moueatur per aerem, quàm per aquam, &
difficiliùs per aquam, quàm per lutum, aut per hy
drargyrum.
intrin&longs;eca leuitatis.
HIs po&longs;itis con&longs;ideremus modò ceram, aut ve&longs;i
cam aere plenam
dia fluida, &longs;i
dit in aqua; authydrargyro motu &longs;pontaneo, nempè
ab intrin&longs;eca virtute motiua, quæ vocatur leuitas,
igitur nece&longs;sè e&longs;t vt in
da intermedia; atque eorum tenacitatem, & den&longs;i
tatem &longs;uperet, imò fluidum è &longs;uo loco expellat, vt
via, & tran&longs;itus paretur, qua &longs;ursùm a&longs;cendere, &
perduci po&longs;&longs;it, & quia hydrargyrum magis con&longs;ti
patum, den&longs;um, & graue e&longs;t,
libet corpus leue aere repletum, aut aeris natura&mtail;
participans, vt lignum, & cera, (quæ ex aduer&longs;ario
rum &longs;ententia mouentur ab intrin&longs;eca virtute leui
tatis) nece&longs;sè e&longs;t vt maiorem re&longs;i&longs;tentiam
in tran&longs;itu per hydragyrum, à cuius tenacitate, den
&longs;itate, & pondere gradus impetus eius nece&longs;&longs;ariò re
tunditur retardaturque multò magis, quàm in
&longs;u
dens &longs;it, minùs debilitat retardatque eamdem eius
vim motiuam, quaproptèr motus a&longs;cen&longs;us ligni, vel
ceræ per hydrargyrum multò magis retardabitur,
quàm ille, qui per aquam fit; quia verò hoc e&longs;t fal
&longs;um, & contra &longs;en&longs;us euidentiam, multò enim velo
ciòr e&longs;t motus ligni, vel ceræ factus per
rali principio &longs;ursùm moueri, & proindè cau&longs;a a&longs;cen
&longs;us non erit leuitas po&longs;itiua, ideoque nullum v&longs;u&mtail;
habebit in natura, nec propterea exi&longs;tet vlla leuitas.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
&longs;ursùm exprimitur, quàm à fluido minùs graui.
HViu&longs;modi difficultates omninò vitantur effu
giunturque, &longs;i certitudinem, & nece&longs;&longs;itatem
ex principijs mechanicis pendentem &longs;equamur, &longs;ci
licèt po&longs;ita &longs;olummodò grauitate in omnibus cor
poribus &longs;ublunaribus; nece&longs;sè e&longs;t vt
dum hydrargyri maiori impetu &longs;ursùm per extru&longs;io
nem impellat lignum, quàm aliud
ue, vt e&longs;t aqua, &longs;icuti in bilance pondus vnius vnciæ
maiori velocitate &longs;ursùm impellitur à maiori pre&longs;
&longs;ione contraria ponderis decem librarum, quàm à
minori compre&longs;&longs;ione ponderis vnius libræ. Demon
&longs;tratio verò huius rei &longs;uo loco exponetur, &longs;ed inte
rim &longs;i effectus omnes qui ob&longs;eruantur in hi&longs;ce corpo
ribus a&longs;cendentibus ijdem prorsùs &longs;unt, & ij&longs;de&mtail;
legibus mechanicis fiunt, ac &longs;i omnia corpora gra
uia fui&longs;&longs;ent, &longs;ed inæquali grauitate donarentur, &
præterea in ijs non apparet phenomena motus &longs;ieri
earatione, quæ requireretur &longs;i præter grauitate&mtail;
reperiretur quoque aliud principium contrarium le
uitatis: igitur concedendum e&longs;t &longs;ola grauitate natu
ram operari, neque leuitatem vllam exigere.
Contra euidentiam harum rationum non de&longs;unt,
qui difficultates, & &longs;ubterfugia afferant pro
da
gnum tardiùs in hydrargyro a&longs;cendere debui&longs;&longs;e;
quàm per aquam ob maiorem illius re&longs;i&longs;tentiam; &longs;ed
propter contrarietatem, & inimicitiam, quam habet
lignum cum Mercurio, &longs;uum cur&longs;um accelerat vt ex
peditè mercurium fugiat, & aquam aeremque a&longs;&longs;e
quatur; quod symbolum elementum, atque
e&longs;t; & propterea ce&longs;&longs;ante odio non cogitur celerri
mè ab eo di&longs;cedere. Sed vide quàm faciles &longs;int præ
dicti philo&longs;ophi; qui occa&longs;ione exigente non
tur
uitas, quæ cortè ine&longs;t in hi&longs;ce terrenis corporibus,
celeriùs transfert &longs;axum, quò magis ad terram acce
dit, atque ei approximatur; re&longs;pondent quia vicinia
terræ velutiroboratur vis motiua &longs;axi cadentis; &longs;ic
paritèr leuitas ve&longs;ic&ecedil; aere&ecedil; cre&longs;cere deberet in aqu&ecedil;
&longs;ummitate, quia nempè aeri approximatur, & ideò
virtus eius motiua roborari quoque deberet. Sed
his omi&longs;&longs;is &longs;ummi po&longs;&longs;unt diuer&longs;a corpora, quæ na
turam, & temperiem diuer&longs;am, & contrariam aquæ
habeant, &longs;imillimam verò mercurio, & talis forta&longs;&longs;e
erit am pulla vitrea, vel ve&longs;ica, quæ repleatur mercu
rio &longs;ublimato, vel pr&ecedil;cipitato; &longs;ic quoque vas &longs;ieri
po&longs;&longs;et ex metallo, vel alio corpore &longs;rmillimo hy
drargyro, vt nimirùm efficiatur compo&longs;itum cuius
natura valdè diuer&longs;a &longs;it ab aqua, & &longs;imillima hydrar
gyro, & &longs;ic omninò tolleretur inimicitia, & antipa
thia inter vas, & fluidum cra&longs;&longs;ius mercuriale, nihi
lominùs ob&longs;eruabitur prædictum vas velociùs a&longs;cen
dere per hydrargyrum, tardo verò motu per aquam,
igitur illa &longs;omniata inimicitia non erit cau&longs;a prædi
ctæ inæqualitatis motus, &longs;ed mechanica, & naturalis
nece&longs;&longs;itas, qua maximum pondus hydrargyrj impe
tuo&longs;iore motu exprimit, & impellit &longs;ursùm conten
tum vas vitreum, vel ve&longs;ica, quàm impellere aqu&atail;
queat &longs;uo minori pondere.
tiuam leui
tatem no&ntail;
dari.
aduer&longs;arij ad
maiorem ini
habet
&longs;eu aer cum
hydrargyro,
quàm cum
aqua, vt de
ducant cele
riùs lignum
fugere mer
curium,
tur.
tiuam leui
tatem no&ntail;
dari.
Id ip&longs;um alijs exemplis confirmari po&longs;&longs;et, &longs;i nimi
rum &longs;umatur oleum à frigore conden&longs;atum, & gla
ciatum, cuius temperies, & natura potiùs grauiori
mercurio, vel oleo tartari a&longs;&longs;imilatur, & è contr&atail;
contrariam naturam, & diuer&longs;am haberet ab ip&longs;&atail;
aqua, & &longs;ic oleum prædictum ob amicitiam lento
motu a&longs;cendere deberet per hydrargyrum, aut per
oleum tartari. Sed celerrimè in aqua currere debe
ret, vtpotè oleo contraria. Similitèr calx in ve&longs;ica
tenta
nem ambarum, & è contrà &longs;ummè contraria erit
muni
dit, in hac tardè. Similitèr &longs;umi po&longs;&longs;ent va&longs;cula ex
cera, aut bitumine, quæ repleri po&longs;&longs;ent puluere, &longs;pi
ritu, oleo, velvino, vel alijs innumeris rebus, quæ
&longs;emper a&longs;cendent veloci&longs;&longs;imè in fluidis grauioribus,
vt &longs;unt aquæ regiæ, licèt in &longs;umma caliditate, & acre
dine &longs;alina conueniant, & è contra languido, & tar
do motu in fluidis
modò minùs grauia &longs;int. Quaproptèr verum non e&longs;t
ob inimicitiam, & contrarietatem ve&longs;icam aerea&mtail;
veloci&longs;&longs;imè à mercurio fugere, & languido motu ex
currere per aquam ei &longs;imilem, &longs;ed potiùs ob mecha-
nicam rationem
uitate, quæ deducitur ex Archimedis doctrina, quòd
&longs;cilicèt fluidum grauius per extru&longs;ionem impeller&etail;
quare ab&longs;que po&longs;itiua leuitate corpora &longs;ursùm
dere
tiuam leui
tatem no&ntail;
dari.
primò, quòd
runtur deorsùm tanta vi, quæ &longs;it æqualis differentiæ gra
uitatis mobilis &longs;upra grauitatem medij, constat euidentèr
euenturum proportion alitèr in leuioribus intra minùs leuia
&longs;ecundùm men&longs;uram exce&longs;&longs;us &longs;upra minùs leue &longs;ursùm ni
&longs;ura, vt &longs;imilis ratio per&longs;uadet. Hoc &longs;uppo&longs;ito veluti cer
tum, & euidens re&longs;pondet argumento &longs;uperius addu
cto, aitque
uem &longs;ecundùm men&longs;uram totius &longs;uæ leuitatis &longs;ursùm niti
intra aquam, ac proindè valere ad re&longs;i&longs;tentiam illius cele
ricèr &longs;uperandam, at verò valdè exiguum exce&longs;&longs;um &longs;upra
aerem obtinentem in leuitate &longs;ursùm niti præcisè &longs;ecundum
men&longs;uram talis exce&longs;&longs;us, ac proindè non e&longs;&longs;e mirum &longs;i lentè
per aerem a&longs;cendat etiam&longs;i dicatur à leuitate po&longs;itiua in
trin&longs;eca moueri.
mi&longs;&longs;a leuita
te colligunt
ignem cele
riùs per a
quam, quam
per aere&mtail;
bere.
Itaque &longs;icuti nos ex Archimedis doctrina deduci
mus rationem de&longs;cen&longs;us grauium, & a&longs;cen&longs;us
ex hac &longs;uppo&longs;itione, quòd corpora omnia &longs;ubluna
ria &longs;int grauia, &longs;ibi per&longs;uadent demon&longs;trare po&longs;&longs;e ea
dem symptomata &longs;upponendo nedùm corpora a&longs;cen
dentia, &longs;ed etiam medium fluidum, in quo
e&longs;&longs;e leuia; quaproptèr quotie&longs;cumque agitur de cor
poribus grauibus de&longs;cendentibus comparari debent
grauitates tum corporis mobilis, tùm medij fluidi in
quo de&longs;cendit; at è contrà cum agitur de corporibus
a&longs;cendentibus, debent paritèr intèr &longs;e comparari le
uitates eorum vnà cum leuitate medij fluidi in quo
a&longs;cendunt.
tiuam leui
tatem no&ntail;
dari.
Modò vt fallacia huius ratiocinij detegatur,
pe&longs;tea adhibitis hypothe&longs;ibus &longs;upradictis demon
&longs;trabo impo&longs;&longs;ibile omninò e&longs;&longs;e vt impetus velocita
tis quo &longs;ursùm a&longs;cendunt corpora illa, quæ leuia ap
pellantur, produci po&longs;&longs;it atque dependeat à princi
pio aliquo intrin&longs;eco à quo &longs;ursùm impellantur re
moueanturque à centro terræ.
Et primo loco ob&longs;eruo cum Ari&longs;totele in mecha
nicis, quòd.
motibus circa centrum agitari
debent.
SIt libra radiorum æqualium, vel rota AIBH con
uertibilis circa &longs;uum centrum C, hic
e&longs;t, quòd &longs;i libram, aut rotam re uoluere velimus, ita
vt terminus eius A de&longs;cendat
deorsùm percurrendo arcum
AI nece&longs;sè e&longs;t vt eius oppo&longs;i
tus terminus B motu contrario
&longs;ursùm a&longs;cendat percurrendo
arcum BH æqualem contrapo
&longs;ito AI. Et
dicti motus
ri nequeunt, tunc nece&longs;sè e&longs;t
vt libra, vel rota quie&longs;cati&ntail;
eodem &longs;itu, nec agitetur.
tiuam leui
tatem no&ntail;
dari.
partes
præualebit, libram
ferentiæ potentiarum.
APponatur poftea pondus DE termino libræ A;
hoc profectò vim efficit, conaturque traher&etail;
terminum libræ A per directionem AD versùs cen
trum telluris, at quia &longs;emidiameter AC in
figitur immobiliter, hinc con&longs;e quetur reuolutio libr&ecedil;
fereturque terminus A non per lineam rectam AD,
&longs;ed per arcum AI excurrendo integrum
& quia libra AB &longs;upponitur continua, & rigida
tempore quo terminus A arcum AI pertran&longs;it oppo
&longs;itus eius terminus B de&longs;cribet contrapo&longs;itum arcum
BH. Modò motum eiu&longs;dem libræ, & de&longs;cen&longs;um pon-
deris DE impedire po&longs;&longs;umus, &longs;i eidem termino A ap
plicaretur vis contraria G, qu&ecedil; traheret &longs;ursùm
&longs;um terminum A per eamdem rectam lineam
ti
& &longs;iquidem vis, & facultas motiua G æqualis e&longs;&longs;et vi
ponderis DE, nulla ratio &longs;uadet quòd vna earu&mtail;
virtutum reliquam &longs;uperet, aut vincat, proindequ&etail;
terminus libræ A non de&longs;cendet versùs I, nec a&longs;cen
det versùs H, &longs;ed omninò quie&longs;cetin eodem &longs;itu. Si
verò
&longs;us e&longs;&longs;et pondus E, tunc procùl dubio
ualeret &longs;uperaretque vim motiuam G, & impetus,
atque vis, à qua prædicta libra flecteretur deorsù&mtail;
versùs I men&longs;uraretur à vi ponderis E, quæ e&longs;t diffe
rentia, &longs;eù exce&longs;&longs;us, quo pondus premens DE &longs;upe
rat vim eleuantem G.
tiuam leui
tatem no&ntail;
dari.
ambæ deorsùm tendendo, &longs;e mutuò impedient, &
maior potentia præualebit, &longs;ed vi æquali
differentiæ earum.
POte&longs;t deindè alia ratione prohiberi, & impediri
de&longs;cen&longs;us ponderis DE ab&longs;que eò, quòd termi
no A applicetur vis aliqua animata contraria G, &
hoc con&longs;equitur &longs;i applicetur termino oppo&longs;ito B
aliud pondus F, quod dùm deorsùm impellit ad ea&longs;
dem partesad quas dirigitur pondus DE prohibetur
quoque de&longs;cen&longs;us termini A eiu&longs;dem libræ, vt
e&longs;t; & &longs;iquidem pondus F æquale fuerit ponderi
DE, tunc efficietur æquilibrium, quia dùm ambo
dera
duos terminos libræ versùs infimum &longs;ignum
tis I, & hoc efficitur æquali vi, & impetu, procùl du
bio vna vis, & conatus impedit motum, &
alterius, & ex hoc mutuo
totius libræ in &longs;itu horizontali; at &longs;i pondus F æqua
Ie fuerit vni portioni D totius ponderis DE, tune
præua lente maiori pondere deprimetter minum libr&ecedil;
A versùs I, a&longs;cendetque oppo&longs;itus terminus B versùs
H tanta vi quæ &longs;it æqualis exce&longs;&longs;ui ponderis E. Hinc
colligitur quod in libra, vel rota duo æquales im
petus ad ea&longs;dem partes
tes
&longs;imiles inter &longs;e, &longs;e mutuo impe
diunt, & de&longs;truunt, itaut quies
con&longs;equatur, &longs;i verò eorumdem
&longs;imilium motuum
vires inæquales fuerint, præua
lebit maius pondus, libramque
reuoluet non integra &longs;ua vi, &longs;ed tantummodò illa dif
ferentia, vel exce&longs;&longs;u, quo maius pondus &longs;uperat
minus.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
idem &longs;equetur.
ID ip&longs;um verum quoque e&longs;t,
&longs;i applicentur terminis op
po&longs;itis eiu&longs;dem libræ A, B duæ
vires inæquales, DE maior, &
F minor, quæ ambæ &longs;ursùmter
minos libræ trahant a&longs;cenden
do. & hìc eodem modo o&longs;ten
detur, quòd libra flectetur &longs;ur
sùm ab A versùs H, & reliqua
visminor F &longs;uperabitur ab ex
ce&longs;&longs;u virtutis DE &longs;upra F, de&longs;cendetque terminus B
versùs I.
sùm, altera deorsùm, &longs;e mutuò iuuabunt, & vis li
bram flectens æqualis erit &longs;ummæ ambarum
potentiarum.
TErtio loco in eadem rota, &longs;eù libra AB termi
nus A deorsùm trahatur à
oppo&longs;itus terminus B &longs;ursùm trahatur à vi a&longs;cenden
te F, quæ minor &longs;it vi ponderis D, dico, quòd libra
non quie&longs;cet, &longs;ed reuoluetur eius terminus A
dendo versùs I, eleuabiturque terminus oppo&longs;itus
B versùs H, & conatus, &longs;eù vis, quo libra reuoluitur
æqualis erit non differentiæ, & exce&longs;&longs;ui ponderis D
&longs;upra vim F, &longs;ed æquabitur aggregato ambarum vir
tutum D, & F. Applicetur termi
no B pondus E æquale vi &longs;ursùm
impellenti F, pariterque ibidem
le oppo&longs;ito ponderi D, manife
&longs;tum e&longs;t (amotis, vel coercitis vi
ribus F, & E) quòd
lia D, & G pendentia à terminis
radiorum æqualium eiu&longs;dem li
bræ efficient æquilibrium, & ideò
libra quie&longs;cet. Præterea quia pondus E æquatur vi
contrariæ &longs;ursùm trahenti F, & ambæ applicantur
eidem termino B libræ AB (ab æqualibus ponderi
ribus D, & G æquilibratæ) igitur duo pondera &longs;imùl
&longs;umpta G, & E libram impellunt contrario ni&longs;u, &longs;ci
licet à B ver&longs;us I, & præcisè adæquant conatum pon
deris D, & vim trahentem F, quæ ambo deprimere
po&longs;&longs;unt terminum libræ A versùs I &longs;ubleuando ter
minum B versùs H. Ergo duævires D, & F &longs;imùl
tæ
&longs;eù conatum, quo libra reuoluide bet ab A, versùs I.
tiuam leui
tatem no&ntail;
dari.
Et hìc animaduertendum e&longs;t, quòd duæ vires D,
& F, quæ reuerà contrariæ &longs;unt inter &longs;e (
sùm comprimat, hæc verò &longs;ursùm trahat) non &longs;ibi
mutuò opponuntur, nec vna earum alteriùs motu&mtail;
impedit, &longs;ed vna promouet, adiuuat, & auget cona
tum, vim, & impetum alterius; & hoc accidit
applicantur ambæ eidem termino A libræ, &longs;ed ter
minis oppo&longs;itis A, & B, qui iuxtà libræ, & rotæ pro
prietatem, & naturam debent moueri motibus con
trarijs, &longs;cilicèt A per arcum AI, & B per arcum BH.
igitur impulfus ponderis D deorsùm, & tractio facta
àvi F &longs;ursùm conueniunt, & &longs;e mutuò adiuuant, &
augent, vt ab vtri&longs;que reuolutio libræ efficiatur, quæ
ad ea&longs;dem partes impellitur ab ei&longs;dem viribus con
trarijs. ce&longs;&longs;et igitur admiratio quare duæ vires con
trariæ in libra &longs;e mutuò non
tuo &longs;e adiuuent, ita vt ex vtri&longs;que re&longs;ultet vna vis
po&longs;ita
tiuam leui
tatem no&ntail;
dari.
&longs;ursùm, & duæ deorsùm, conatus &longs;eù vis libram fle
ctens men&longs;uratur à &longs;umma differentiæ a&longs;cen
dentium, cum differentia de&longs;cendentium
potentiarum.
SI tandem eadem libra à quatuor viribus impel
latur trahaturque, quarum duæ D, & G graues
&longs;int deorsùmque tendant, duæ verò M, & F &longs;ursù&mtail;
eo&longs;dem terminos libræ trahant, &longs;itque energia virtu
tis M maior quàm F, pondus verò D minus &longs;it quàm
G,
A eleuari &longs;ursùm versùs Hab ex
ce&longs;&longs;u quo vis M &longs;uperat faculta
temmotiuam F, & è contrà op
po&longs;itus libræ terminus B depri
metur deorsùm versùs I ab ex
ce&longs;&longs;u quo pondus G &longs;uperat vim
grauitatis D; & quia prædicti
duo impul&longs;us differentiales con
trarij &longs;unt, vnus quidèm &longs;ursù&mtail;,
alter verò deorsùm,
tis eiu&longs;dem libræ; igitur &longs;e mutuo adiuuant promo
uenturque, & proindè conatus, vis, atque impetus,
quo vniuer&longs;a libra reuoluitur, æqualis erit aggrega
to prædict arum differentiarum.
tiuam leui
tatem no&ntail;
dari.
&longs;cendit, æqualis est differentiæ ponderis &longs;olidi &longs;upra
pondus fluidi ei æqualis mole.
HIs declaratis intelligatur
vas RGS aqua plenum, in
graue durum, ac con&longs;i&longs;tens DE,
quod grauius &longs;it aqua collaterali
F patet ex dictis prop.
9. & ex
Archimede, duo pondera DE, & F collocari in libra
quadam imaginaria, & perpetua AB in qua exce&longs;&longs;us
ponderis &longs;olidi DE &longs;upra grauitatem aquæ F quæ &longs;it
æqualis mole ip&longs;i DE, &longs;emper idem e&longs;t in quacumque
aquæ profunditate &longs;olidum collocetur, &longs;itque pon
dus E exce&longs;&longs;us quo pondus DE &longs;uperat grauitate&mtail;
aquæ F, igitur conatus, vis, & impetus, quo &longs;olidum
DE de&longs;cendit infra
tiuam leui
tatem no&ntail;
dari.
dit æqualis est exce&longs;&longs;ui leuitatis &longs;olidi &longs;upra leuita
tem fiuidi ei æqualis mole.
E Contrà, &longs;i &longs;upponamus, quod lignum DE pari
terque aqua F careant grauitate, &longs;ed
dò
impetum faciant &longs;ursùm conenturque a&longs;cendere,
&longs;ecùs o&longs;tendetur, quòd in libra, &longs;eù rota perpetua
ligni DE maior leuitas præualebit &longs;uperabitque mi
norem leuitatem fluidi collateralis F, proindeque
libra inflectetur ab A versùs R a&longs;cendendo tanta vi,
quanta e&longs;t differentia, &longs;eù exce&longs;&longs;us E, quo leuitas li
gni &longs;uperat aquæ leuitatem.
e&longs;&longs;e debet &longs;ummæ lenitatis &longs;olidi, & grauitatis
fluidi.
SI verò variata hypote &longs;i ponamus
& &longs;ursùm ab intrin&longs;eco principio impelli, & mo-
ueri, at ffuidum collaterale D, quòd &longs;it hydrargyrum
&longs;upponatur deorsùm tantummodò vim exercere, vt
exigit maxima eins grauitas, nec prorsùs &longs;ursùm im
pellere, tunc quoque libra, &longs;eù
rota perpetua efformabitur i&ntail;
qua &longs;emperterminus B trahetur
&longs;ursùm à po&longs;itiua leuitate ip&longs;ius
ligni F a&longs;cendetque versùs R,
terminus verò oppo&longs;itus depri
metur ab A versùs H vt natur&atail;
grauitatis exigit, & quia hi duo motus, & conatus in
oppo&longs;itis terminis libræ
&longs;e non de&longs;truunt, nec contrariantur, &longs;ed &longs;e mutuò fa
uent, & adiuuant. igitur conatus, & impetus quo re
uoluitur iam dictalibra, &longs;cilicèt quo lignum F a&longs;cen
dit à fundo mercurij æqualis erit non differentiæ, &longs;ed
aggregato ex vileuitatis F, & ex facultate ponderis
mercurij D.
tiuam leui
tatem no&ntail;
dari.
atque grauitatem, vis motiua, qua vnum eorum ele
uatur æqualis e&longs;t aggregato ex differentia leui
tatum vnà cum differentia grauitatum
earum.
TAndèm &longs;i &longs;upponamus, quod lignum vim faciat
&longs;ursùm vt leue, & etiam eodem tempore gra
uitatem eius natiuam exerceat, pariterque aqua D
in va&longs;e nedùm deorsùm comprimat, vt grauis, &longs;ed
etiamnon omninò priuetur gradu aliquo leuitatis,
tunc &longs;imilitèr libra perpetua imaginaria efformabi
tur in qua terminus I deorsùm impellitur ab exce&longs;&longs;u
quo grauitas aquæ D &longs;uperat
minus
ce&longs;&longs;u quo leuitas ligni &longs;uperat
leuitatem ip&longs;ius aquæ. Et quia
prædicti impul&longs;us &longs;unt contra
rij, applicanturque eidem li
bræ imaginariæ, igitur vnus impul&longs;us alteri non op
ponitur, & proindè vniuer&longs;alis conatus, & impetus
prædictæ libræ, &longs;cilicèt vis, & impetus, quo lignum
F a&longs;cendit in aqua men&longs;uratur ab vtroque exce&longs;&longs;u,
&longs;cilicèt ab aggregato differentiæ ponderum aquæ,
& ligni, vnà cum exce&longs;&longs;u leuitatis ligni &longs;upra aqueam
leuitatem.
tiuam leui
tatem no&ntail;
dari.
HIs præmi&longs;&longs;is &longs;upponamus cum aduer&longs;arijs pri
mo loco, quòd reuerà præter corpora graui&atail;
etiam leuia in natura exi&longs;tant, quorum aliqua, vt ait
Ari&longs;toteles, &longs;int &longs;implicitèr talia, alia verò re&longs;pectiuè,
veluti ignis dicitur ab&longs;olutè leuis, & terra, &longs;eù hy
drargyrum, vel aliud fluidum æquè graue, ac ip&longs;&atail;
terra e&longs;t appellabitur ab&longs;olutè graue
&longs;tea alia corpora intermedia &longs;implicia, vel mixt&atail;,
quæ vocantur grauia &longs;imùl, & leuia re&longs;pectiuè, &longs;cili-
cèt aqua demer&longs;a intra mercurium dicitur leuis, &
moueri &longs;ursùm à principio intrin&longs;eco, at &longs;i eade&mtail;
aqua intra oleum mergatur, dicetur iam grauis, no&ntail;
leuis, & moueri deorsùm à principio interno. Hoc
verò duplicem &longs;en&longs;um habere pote&longs;t, aut dictæ duæ
contrariæ qualitates &longs;emper in eodem corpore aquæ
exi&longs;tunt, & vigent, aut &longs;ucce&longs;&longs;iuè modò vna, modò
altera in ea reperitur, ita vt aqua in fundo hydrar
gyri po&longs;ita &longs;it reuera leuis, & nullo pacto grauis, &
è contià, quando eadem aqua in oleo demergitur,
hìc grauitatem habeat, & nullam prorsùs
itaut remaneat &longs;opita, & extincta leuitas illa, quæ
tanta efficacia
curij, igitur in primo &longs;en&longs;u retinere aqua deberet
perpetuò duas contrarias qualitates, &longs;cilicèt leuita
tem, & grauitatem eodem modo, ac dicuntur mixta
participare ex qualitatibus extremis, calido nempè,
& frigido, & veluti colores medij nigre dinem, at
que albedinem participare
beret, quod in igne prorsùs, & ab&longs;olutè leui qua
tuor integri gradus leuitatis reperiuntur, & &longs;imili
tèr in ip&longs;a terra exi&longs;tunt quatuor gradus grauitatis,
at aer habebit tres gradus leuitatis, & vnicum gra
dum pondero&longs;itatis, &longs;ic aqua vnicum gradum lèui
tatis, & tres grauitatis haberet, &
pus medium inter aerem, & aquam, veluti for&longs;an
e&longs;t &longs;piritus vini, habere po&longs;&longs;et duos gradus leuitatis,
& duos alios gradus grauitatis.
[missing]
53.) conatus, & impetus totalis, quo ignis per mer
curium a&longs;cendit, velterra per ignem de&longs;cendit, men
&longs;urari debet ab aggregato virium extremarum, &longs;ei
licet à tota vi leuitatis cum tota vi grauitatis, quar&etail;
totalis impetus erit octo graduum. Sed hoe e&longs;t fal
&longs;um, contra aduer&longs;arij a&longs;&longs;ertionem, & contra Archi
medem, ea enim, quæ in fluido cleuantur, tanta vi
a&longs;cendunt, quanta e&longs;t grauitas qua moles flaidimer
curialis æqualis corpori igneo intra ip&longs;um demer&longs;o
&longs;uperat huius grauitatem, quænulla e&longs;t, & proindè
ignis impetu quatuor graduum per mercurium
dit
uitatis, & ideò leuis non erit, quod erat &c.
nes aliqu
peripatetic
recen
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
de men&longs;ura
gradus præ
dicti impe
mus.
Sed in&longs;tabit denuò peripateticus, dicetque, quòd
eavelocitas, quæ exercetur ab igne a&longs;cendente per
mercurium, aut à terra de&longs;cendente perignem po
terit cen&longs;eri octo graduum, vel quatuor ad libitum,
quia non habemus certam men&longs;uram vnius gradus
impetus, & &longs;ic mediante &longs;enfu, & experientia non
pote&longs;t eius &longs;ententia redargui.
&longs;cerni valeat an impetus de&longs;cen&longs;us terræ per ignem,
vel a&longs;cen&longs;us ignis per mercurium &longs;it octo, vel
quatuor graduum.
SEd prædictùm effugium &longs;ic refellemus: Fiat ex
perimentum non in mercurio &longs;implicitèr graui,
&longs;ed in aqua, vel in aere, illa enim habebittres gradus
grauitatis, & vnicum lcuitatis, ergo ignis per
a&longs;cendet velocitate trium graduum; in mercurio ve
rò impetu octo graduum, & terra per ignem octies
velociùs de&longs;cendet, quàm per aquam. Præterea aer
habet vnicum gradum grauitatis, & tres gradus le
uitatis, igitur ignis octies velociùs per mercurium
a&longs;cendet, quàm per aerem, vnde hac ratione habe
bimus men&longs;uram vnius gradus impetus tàm in
&longs;u
petu ignis per mercurium a&longs;cendentis, & terræ per
ignem de&longs;cendentis; & proindè facilè conijci po
terit, an prædictæ velocitates extremorum elemen
torum reuerà &longs;int octuplæ, vel non, comparatæ ad
velocitates quas exercent in intermedijs elementis.
& licèt experimentum non det exactam
nihilominùs &longs;ufficienti&longs;&longs;imè euincit fal&longs;itatem peri
pateticæ hypothe&longs;is, &longs;edlicèt reuerà vis, & energia,
qua corpora a&longs;cendunt, vel de&longs;cendunt, minimè de
d
sùm, vt &longs;uo loco apertè o&longs;tendemus, tamen a&longs;&longs;umi
pote&longs;t cum aduer&longs;ario ad eum redarguendum.
tiuam leui
tatem no&ntail;
dari.
Con&longs;iderentur deindè elementa intermedia, vt
&longs;unt aer, & aqua, &longs;eù alia corpora mixta, quæ
gradibus leuitatis, & grauitatis afficiantur. Demon
&longs;trandum e&longs;t, nullum eorum corporum, quæ
&longs;ursùm po&longs;itiuam leuitatem habere.
tiuam leui
tatem no&ntail;
dari.
a&longs;cenderet à leuitate eius po&longs;itiua impul&longs;us.
ET primò &longs;upponamus prædicta elementa no&ntail;
retincre &longs;imùl eodemque tempore duas oppo
&longs;itas facultates grauitatis, & leuitatis, &longs;ed &longs;ucce&longs;&longs;i
uè modò vnam, modò alteram po&longs;&longs;ideant, prout in
diuer&longs;is medijs fluidis collocantur, &longs;cilic èt aqua i&ntail;
aere pendula &longs;olummodò grauis cen&longs;eri debeat, non
autem leuis, &longs;i po&longs;tmodum aqua infrà hydrargyrum
mergatur, tunc aqua leuis &longs;it, non autem grauis, po
natur etiam, quod aer, &longs;eù
&longs;ub aqua demer&longs;um leue &longs;it, nec
grauitatem vllam habeat. Con
cipiatur po&longs;tea vas RGHS a
qua D plenum, & in eo merga
tur ma&longs;&longs;a aeris, velligni F, pa
tet ergò ex &longs;upradicta hypo
the&longs;i, quod aqua D
dò grauitatem habebit, eò quòd prædicta aqua non
&longs;upponitur demer&longs;a intra aliud corpus fluidum den
&longs;ius, & pondero&longs;ius ip&longs;a, &longs;ed contigua e&longs;t aeri. Mo
dò quiaaer, vel lignum F &longs;upponitur ab aduer&longs;arijs
&longs;ursùm a&longs;cendere à G, versùs R impul&longs;a à po&longs;itiua
leuitate eius naturali, aqua verò circumfu&longs;a D cona
tum, atque impetum exercet deorsùm ab A versùs
H veluti natura eius grauitatis exigit, habebimus
leuitatis aeris F grad. 3. & grauitatis gra. 3. aquæ
circumfu&longs;æ D, & hæ duæ virtutes motiuæ &longs;imùl &longs;um
ptæ gr.6. component men&longs;uram conatus, & impetus,
quo lignum F per aquam a&longs;cendit, hoc tamen e&longs;t fal
&longs;um, & contra conce&longs;&longs;ionem eiu&longs;dem aduer&longs;arij, &
contra demon&longs;trationem Archimedis, & tande&mtail;
contra experientiam, quia ea, quæ feruntur &longs;ursùm
in aqua, tanta vi a&longs;cendunt, quanta e&longs;t grauitas,
qua moles aquæ æqualis corpori demer&longs;o &longs;uperat
huiusmet grauitatem, quod perindè e&longs;t, ac &longs;i dica
tur impetum &longs;ursùm men&longs;urari à differentia grauita
tum aeris, & aquæ gr. 2. non autem ab aggregato
gr. 6. leuitatis illius, & grauitatis huius. Quaprop
ter non poterit aer, vel
leuitate po&longs;itiua.
tiuam leui
tatem no&ntail;
dari.
leuitatis, & grauitatis exerceat.
SVpponamus &longs;ecundo loco tam
&longs;emper retinere ambas oppo&longs;itas qualitates,
&longs;cilicèt perpetuò afficiantur ij&longs;dem gradibus graui
tatis, atque leuitatis &longs;itque leuitas aeris F trium gra
duum, & maior leuitate ip&longs;ius aquæ D vnius gradus;
at è contrà gradus grauitatis eiu&longs;dem aeris F gra
dus vnius minor &longs;it pondere graduum 3. molis aquæ
D, quæ æqualis &longs;it ip&longs;i F, habebimus profectò qua-
tuor vires motiuas, quæ &longs;ibi mutuò aduer&longs;antur, &
in libra imaginaria BI operantur, vt nimirùm nulla
earum otiari queat, &longs;ed omnes &longs;imùl agant, & im
pellant, igitur ex propo&longs;itionibus 50. & 54. conatus,
&longs;eù impetus quo aer F impellitur &longs;ursùm in aqua à G
versùs R ratione leuitatis men&longs;urari debet ab ex
ce&longs;&longs;u 2. graduum quo leuitas eiu&longs;dem aeris &longs;uperat
leuitatem aquæ circumfu&longs;æ, & è
contra aerem efficitur ab exce&longs;&longs;u grauitatis aquæ D,
&longs;upra grauitatem aeris F paritèr gr. 2. & proindè
aqua deorsùm de&longs;cendere conatur nece&longs;&longs;ariò aerem
F exprimit, ac
ferentiæ, &longs;eù exce&longs;&longs;us virium contrariæ inter &longs;e, &longs;ci
licèt vna in libra imaginaria &longs;ursùm impellit, altera
verò deorsùm igitur vniuer&longs;alis conatus, & impetus
totalis quo aer F a&longs;cendit in aqua, men&longs;urari debet
ab aggregato eorumdem duorum exce&longs;&longs;uum, quod
e&longs;t gr. 4. non verò à differentia leuitatum, &longs;olummo
dò gr. 2. Sed hoc e&longs;t fal&longs;um contra experientiam,
tra
mede demon&longs;trata &longs;unt, quia nimirùm conatus, &
impetus quo fertur aerea pila &longs;ursùm in aqua æqua
lis e&longs;t differentiæ ponderum aeris, & aqu&ecedil;, igitur
verum
one concurrere.
tiuam leui
tatem no&ntail;
dari.
V&longs;que adhùc non con&longs;iderauimus difficultatem,
aut impedimentum, quod affert medium fluidu&mtail;
motui a&longs;cen&longs;us, vel de&longs;cen&longs;us corporum, quæ in ip
&longs;o feruntur, erit igitur operæpretium perpender&etail;
a&longs;mpto &longs;ub&longs;equatur.
tiuam leui
tatem no&ntail;
dari.
diuer&longs;a media fluida a&longs;cendat.
SIt igitur idem mobile B, quod &longs;it lignum leui&longs;&longs;i
mum, vel ve&longs;ica aere plena, impellaturque v&longs;que
ad fundum va&longs;is DCFE cuius medietas infima reple
atur aqua A, reliqua medietas &longs;uprema O repleatur
oleo, vel &longs;piritu vini, & ponamus leuitatem aereæ
ve&longs;icæ B e&longs;&longs;e trium graduum, & leuitatem &longs;piritus
vini duorum graduum, at leuitatem aquæ magis
&longs;æManife&longs;tum e&longs;t, quòd re&longs;i&longs;ten
tia aquæ A, & partium tenacitas, quæ penetrari de
bet à ligno, vel ve&longs;ica B dùm &longs;ursùm a&longs;cendit, erit
tò
ni O quantùm illa e&longs;t magis
&longs;a
licèt &longs;i
eorumdem fluidorum, quantò
maior e&longs;t corpulentia, & mate
ria, quæ pr&ecedil;dictum aqueum &longs;pa
tium replet ea materia quæ molem &longs;piritus vini oc
cupat, & quia
eamdem proportionem habere aiunt, quam illius
raritas ad huius raritatem, igitur tantò magis di&longs;tra
hibilis, & minùs re&longs;i&longs;tens erit &longs;piritus vini, quà&mtail;
aqua communis; quantò ille leuior e&longs;t aqua commu
ni, ergò re&longs;i&longs;tentia quam aqua in fert ve&longs;icæ
ti
reciprocè habet, quam &longs;piritus vini leuitas ad aquæ
communis leuitatem. Quapropter aqua communis
duplò re&longs;i&longs;tentior erit quàm &longs;piritus vini, veluti i&longs;te
&longs;upponitur duplò leuior illo. Modò, quia aduer&longs;arius
&longs;upponit
aerea ve&longs;ica per prædicta duo fluida men&longs;urari de
beat ab exce&longs;&longs;u, &longs;eu differentia leuitatum
corporum, igitur aerea ve&longs;ica B, quætres gradùs le
uitatis habebat, a&longs;cendet per
leuitatis habentem conatu, &longs;eu impetu men&longs;urato à
differentia prædictarum leuitatum, quæ erit
graduum, &longs;ed in &longs;piritu vini O qui duos gradus leui
tatis habebat, a&longs;cendet, eadem pila B impetu æquali
differentiæ leuitatum
vnius &longs;olummodò gradus, & hæc quidem con&longs;e
tur
tione differentiarum inter leuitatem corporis B, &
leuitates prædictorum fluidorum ve&longs;ica B per aquam
a&longs;cende
ritum vini eleuatur; nihilominùs velocitas qua præ
dicta ve&longs;ica B a&longs;cendit in aqua, non poterit e&longs;&longs;e du
pla eius, qua &longs;ublimatur in &longs;piritu vini, licèt virtus, &
energia, qua impellitur per aquam dupla &longs;it eius,
quæ in &longs;piritu vini exercetur, proptereà quod &longs;uper
uenit noua cau&longs;a, à qua prædicti impetus
& valdè alterantur, hæc verò e&longs;t maior
ritus vini; quæ, iuxtà Ari&longs;totelis a&longs;&longs;umptum,
tarditatem a&longs;cendenti corpori affert den&longs;itas aquæ,
&longs;cilicèt duplò maior, quàm &longs;it ea difficultas, qua à
&longs;piritu vini a&longs;cen&longs;us eiu&longs;dem pilæ impeditur. Hinc
&longs;equitur, quòd velocitas eiu&longs;dem pilæ B per aquam
ad eam quam habere pote&longs;t per &longs;piritum vini com
po&longs;ita &longs;it ex duabus proportionibus, &longs;cilicèt ex pro
portione differentiarum leuitatum eorumdem cor
porum, quæ erit vt duo ad vnum, & ex propo&longs;itio
ne reciproca re&longs;i&longs;tentiarum eorumdem medioru&mtail;,
quæ &longs;e habet vt vnum ad duo, &longs;ed proportio dupla,
& &longs;ubdupla componunt proportionem æqualitatis,
igitur æquali velocitate a&longs;cendet eadem ve&longs;ica B
per aquam A, & per
tèr
riorum, ergo ve&longs;ica aere piena non mouetur &longs;ursùm
in fluido vi leuitatis po&longs;itiuæ, quod erat o&longs;tenden
dum.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
Sed antequam vlterius procedamus,
men quoque reuocari aliæ obiectiones, quæ ab au
thoribus clari&longs;&longs;imis afferuntur contra no&longs;tram &longs;en
tentiam. Et primò quidem con&longs;iderabo argumenta,
quæ de&longs;umuntur à pyramidali figura flammæ lucer
næ, a qua, inquam, figura putant euidens
deduci, quòd flamma ip&longs;a &longs;ursùm impellatur ab in
terno principio leuitatis, &longs;icque ratiocinantur:
demus quieto, & tranquillo aere flammum ferri &longs;ursùm
pyramidalitèr, cùm
minùs quàm &longs;uperio
ris quando per expres&longs;ionem &longs;ursùm iaciuntur.
ta e&longs;&longs;entia vini in lapide accen&longs;a &longs;ursùm fertur non per ex
pres&longs;ionem, &longs;ed in&longs;ita leuitate, aer enim exprimens, vel
e&longs;&longs;et &longs;ub ba&longs;i ignis auolantis, & illum protruderet, quod e&longs;t
fal&longs;um; vel &longs;uperincumbens grauitando hanc
efficeret; neque hoc, quia &longs;ic aer vertici ignis incumbens eum
deprimeret potiùs, ac reuerberaret deorsùm, quàm &longs;ursùm.
menta pro
leuitate po
&longs;itiua
tur
tiuam leui
tatem no&ntail;
dari.
&longs;ursùm impelli.
PRimæ difficultati, quòd nimirum flamma lucer
næ in aere quieto, & tranquillo moueatur &longs;ur
sùm &longs;ponte, non verò per extru&longs;ionem factam ab ae
re ambiente, &longs;atisfacere nitemur adducendo experi
menta aliqua. Videmus enim maiores, & ampliores
flammas in caminis accen&longs;as non vigere, nec diutiùs
per&longs;euerare ni&longs;i ad&longs;it aditus aeri de foris aduenienti,
per quem ingrediatur ventus perpetuus, qui inter
crura, & fœmora ignem
sùs flammam, e&longs;tque euidentèr &longs;en&longs;ibilis, nam &longs;i cu
biculi o&longs;tium claudatur exten&longs;o panno, vel cortina,
vt fieri &longs;olet, h&ecedil;c inflatur ver&longs;us ignem camini, vt ve
lum nauis; imò in cubiculis vndiquè diligentèr clau
&longs;is, in quibus aer externus &longs;ubingredi nequeat non
poterit flamma &longs;ursùm impelli ab aere, quin cubi-
cto accendi pote&longs;t, nec in flammam verti, aut per
durare, ni&longs;i o&longs;tiolum, vel foramen aliquod in ip&longs;o ca
mino aperiatur, & tunc facilè flamma accenditur, &
per&longs;euerat. Ratio huius effectus pendet nedùm ab
impul&longs;u flammæ &longs;ursùm, &longs;ed etiam à rarefactione ae
ris propè ignem exi&longs;tentis, eumque
tam camini longitudinem, quia nempe aer prædictus
ab igne calefactus minùs grauis &longs;pecie redditur,
aer cubiculi, & externus, qui à camino di&longs;tat; Hoc
autem nece&longs;&longs;ariò aduenit ex legibus mechanicis, &
ex Archimedis
vt aerrarior, & minùs grauitans &longs;ursùm expellatur
exprimaturque à grauiore aere
fit vt po&longs;t a&longs;cen&longs;um illius aeris rarefacti per
diminuatur moles aeris ip&longs;ius cubiculi propè, & cir
ca caminum. Non ergo mirum e&longs;t, nouum aerem pro
fluere ad replendum cubiculi
&longs;a, quare percipitur ventus ille, & effluuium per
petuum dum flamma camini viget.
tiuam leui
tatem no&ntail;
dari.
Prædictum ratiocinium confirmari pote&longs;t à pul
cherrimo experimento à D. Candido Buono Floren
tiæ mihi communicato.
extru&longs;a à pondere aeris, reliquam lancem ambientis.
ERat enim trutina, &longs;eù bilanx tantæ perfectionis,
vt à quinquage&longs;ima parte vnius grani hordei,
imò à multo leuiori fe&longs;tuca flecti facilè po&longs;&longs;et. hæc
quidem &longs;u&longs;pen&longs;a intra arm ariolum vitreum, vt à &longs;or
dibus, & venti agitatione tueretur
cisè &longs;eruabat, vt e&longs;t DE, cuius centrum C, tunc
ta
ta in eius extrema parte
F lanci A approximaba
tur, ab&longs;que contactu,
libra ab æquilibrio remo
uebatur, depre&longs;&longs;a nimi
rum lance B, & eleuata A,
lato ignito ferro infra
parte ob&longs;eruabatur:
municaui
& Eminenti&longs;s. Cardinali Leopoldo Mediceo
quam deinceps more Italico
talem Mediceam vocabo. Concipiantur duæ &longs;phæ
rulæ aeris inter &longs;e æquales LG, & HK lances
tesApproximato po&longs;tea ferro ignito IF procùldubio à
profluuio ignearum exhalationum à feruente ferro
emanantium, calefit nedum lanx illa metallica A, &longs;ed
etiam &longs;phæra proximi aeris LG, quæ proindè ingen
tem raritatem acquirit, cùmque aer ambiens LG ar
ctè adhæreat
colligatus componat veluti lanuginem vnitam ip&longs;i
lanci, itaut nequeat moueri lanx A ni&longs;i &longs;ecum deferat
nexam LG, verùm lanci oppo&longs;itæ B, adhæret &longs;phæ
ra aerea HK den&longs;ior, vt potè non excalefacta à ferro
feruente; hinc fit vt &longs;umma lancis B vnà cum adnexa
cru&longs;ta ambientis aeris HK grauior &longs;it ærea lamina A
vnà cum rariori lanugine aeris adhærentis LG.
igitur non e&longs;t, quòd a maiori pondere libræ extremi
tas E deprimatur, & ei oppo&longs;ita D eleuetur. Eodem
ferè modo, vt dicebam priùs, aer cubiculi circ&atail;,
caminum cùm &longs;it valdè den&longs;us, comparatus cum
ma
ideò valdè rarefacto, mirum non e&longs;t &longs;i proptèr illius
grauitatem excedentem &longs;ursùm exprimat leuiorem
flammam, acremque adhærentem paritèr rarum. E&longs;t
igitur euidenti&longs;&longs;imum in hi&longs;ce experimentis, quòd
aer
partem aeris
que &longs;ursùm. Sed dicet aliquis, cur circa flamma&mtail;
lucernæ non ob&longs;eruatur prædictus ventus? re&longs;pon
detur non e&longs;&longs;e æquè &longs;en&longs;ibilem, quia nimirum lucer
næ flamma non in&longs;inuatur intra fi&longs;tulam aliquam, vt
e&longs;t canalis camini, qui exitum habet extra
cùm ergo lucernæ flamma vndique ambiatur abaere
aperto ab&longs;que euidenti con motione eam impellere
&longs;ursùm pote&longs;t exprimendo, nimirùm facto breui cir
cuitu à vertice flammæ v&longs;que ad eius ba&longs;im, & ob
flamm&ecedil; exiguitatem parua quoque e&longs;t moles aerisei
contigua, qu&ecedil; agitatur, & conuoluitur, & hæc e&longs;t
ratio, quare circa lucernæ flammam ventus non ob-
&longs;eruatur &longs;imilis ei, qui propè caminum percipitur.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
entia, & ra
tio eius ap
plicatur
mæ
a&longs;cend ntis.
circa lucer
næ flamma
non percipi
tur ventus
&longs;icuti in ca
mino.
tiuam leui
tatem no&ntail;
dari.
dere
Torricelliano.
SEd quòd reuerà ignis mo
ueatur
onem ambientis aeris,
a&longs;cendat &longs;ponte propria vir
tute euidenti&longs;&longs;imè percipitur
ex hoc meo
do Cardinali Mediceo
nicaui
it in Academia Experimentali
Medicea, & demum Exteris
per Epiftolas diuulgatum fuit.
Sit vas vitreum AFG, cuius
longitudo EF duobus cubitis
maior &longs;it, habeatque
ampullam vitream CEM, &longs;it
que incuruata eius extremitas HFG, atque duæ eius
extremitates A, & G &longs;int perforatæ, & apertæ, & pri
ùs &longs;trictè ob&longs;erato, duplici ve&longs;ica &longs;uilla, infimo orificio
G repleatur vas vniuer&longs;um hydrargyro infu&longs;o per &longs;u
premum os AB, po&longs;tea pilula aliqua D ex bitumine
aliquo atri coloris operculo ex bractea ferrea filo
colligeturque &longs;trictè: tandèm &longs;ublata ve&longs;ica infima
G concedatur egre&longs;&longs;us hydrargyro, vt nimirùm facta
&longs;olita vacuitate aeris remaneat hydrargyrum
&longs;um
cubiti, & quadrantis. His præparatis &longs;umatur lens
aliqua cry&longs;tallina KL, & directè Soli S exponatur in
ea di&longs;tantia, & &longs;itu in quo præcisè vertex coni radio
&longs;i à radijs Solis refractis conuergentibus formati ad
contactum pilæ bitumino&longs;æ D pertingat. Idip&longs;u&mtail;
fieri pote&longs;t ope &longs;peculi concaui v&longs;torij radios Solis
reflectentis, tunc lique&longs;cere incipit pila D, & fumum
emittit, in quo apparet mirabilis operatio, non enim
fumus, veluti in aere aperto accidit, &longs;ursùm a&longs;cen
dit, &longs;ed incuruatur flectiturque deorsùm per DMN
non &longs;ecùs ac virgulæ illæ aquæ cadentis è fontibus,
inflexas, & deorsùm tendentes lineas de&longs;cribunt.
tiuam leui
tatem no&ntail;
dari.
Porrò quia fumum non minùs quàm flammam
e&longs;&longs;e, atque &longs;ursùm moueri &longs;ponte &longs;ua à naturali prin
cipio impul&longs;a,
igitur nece&longs;&longs;ario in &longs;patio illo vacuo CEN, vel &longs;al
tèm in quo aer non degit ni&longs;i valdè expan&longs;us, & rare
factus, fumus maiori vi &longs;ursùm a&longs;cendere deberet,
quàm in aere aperto, quia nimirùm ab aeris cor
pulentia aliquo pacto impeditur ip&longs;ius progre&longs;
&longs;us (videmus enim in aere aperto fumum ampliari,
di&longs;&longs;ipari, ac di&longs;pergi à prædicta aeris re&longs;i&longs;tentia,)
que
fumus naturali leuitate non impeditus liberiùs, & fa-
ciliùs eleuari, igitur omninò nece&longs;sè e&longs;&longs;et vt fumus
in prædicto vacuo &longs;patio a&longs;cenderet &longs;ursùm, veluti
eius natura exigit, & è contrà e&longs;&longs;et impo&longs;&longs;ibile vt
deorsùm deprimeretur, & caderet, vt virgulæ deci
dentes aquæ fontium flectuntur deorsùm; quia verò
hoc experientiæ repugnat non poterit dici, quòd fu
mus &longs;it leuis, &longs;ed è contrà grauis erit. Cùm verò i&ntail;
aere idem fumus &longs;ursùm a&longs;cendat,
ab aere ambiente grauiori in &longs;pecie, quàm &longs;it fumus
iuxtà leges mechanicas libræ aer
&longs;ionem &longs;ursùm fumum minùs grauem expellit.
tiuam leui
tatem no&ntail;
dari.
vi leuitatis &longs;ursùm impelli.
VErùm, quod ad formam pyramidalem flammæ
lucernæ pertinet, non videtur, quòd eius figu
ra conica nece&longs;&longs;ariò per&longs;uadeat, & conuincat flam
mam &longs;ursùm &longs;ponte &longs;ua, & propria virtute leuitatis
a&longs;cendere, nam &longs;iue per extru&longs;ionem ambientis &longs;lui
di violenter, &longs;iuè &longs;ponte à vi leuitatis &longs;ursùm moue
ri &longs;upponamus, retinere æquè benè po&longs;&longs;et eamde&mtail;
conicam Præterea &longs;i
vera cau&longs;a figuræ pyramidalis flammæ lucernæ e&longs;&longs;et
eius leuitas po&longs;itiua, debereteadem leuitas po&longs;itiua
eumdem effectum producere in reliquis omnibus
corporibus fluidis paritèr ab ip&longs;a impul&longs;is, &longs;i tamen
reliqua &longs;int paria, &longs;cilicèt fumus non &longs;ecùs ac flam-
vna pars po&longs;t aliam generatur, & eructatur à po
ris eiu&longs;dem titionis, pariterque fumum leuitate&mtail;
po&longs;itiuam habere, & exercere
quàm flamma habet, igitur nece&longs;&longs;ariò fumus a&longs;cen
dens, & digrediens à titione deberet formam pyra
midalem acquirere &longs;imilem ei, quam flamma lucer
næ habet, deberetque paritèr in acumen &longs;ubtile &longs;u
periùs definere, quod profectò e&longs;t fal&longs;um, & contra
&longs;en&longs;us euidentiam, pro&longs;equitur enim fumus &longs;uu&mtail;
iter longo tractu &longs;ursùm ab&longs;que eo quòd in acumen
reducatur.
tiuam leui
tatem no&ntail;
dari.
Id ip&longs;um continget, &longs;i fi&longs;tula aliqua aer in fundo
aquæ in&longs;uflletur,
ræ ampullæ aere&ecedil;, quæ ab inuicem &longs;eparantur ab&longs;
que eo quòd pyramidalem figuram acquirant, licèt
aer non minùs quàm flamma leuis reputetur, & ab in
trin&longs;eco principio &longs;ursùm moueri credatur, cùmque
vna, & eadem cau&longs;a non po&longs;&longs;it diuer&longs;os effectus pro
ducere, concedant nece&longs;sè e&longs;t, figuram, quam in
ma
aquam a&longs;cendentis ab alia caufa longè diuer&longs;a de
pendere, non autem à prædicto principio intrin&longs;eco
leuitatis.
Et profectò &longs;i attentè perpendamus fumi, & flam
mæ con&longs;i&longs;tentias, valdè inter &longs;e differre reperiemus,
licèt ambo &longs;int corpora rara, & fluida.
tiuam leui
tatem no&ntail;
dari.
COn&longs;tat fumum e&longs;&longs;e ma&longs;&longs;am copio&longs;am particula
rum exiguarum olei, terræ, & aquæ, quæ par
ticulæ ab inuicem di&longs;cretæ, & &longs;eparatæ nondù&mtail;
accen&longs;æ &longs;unt, licèt valdè excalefactæ &longs;int. hoc planè
confirmatur ab operatione chymica, po&longs;&longs;unt eni&mtail;
recolligi ex fumo partes aqueæ &longs;egregatæ, & di&longs;cre
tæ à partibus vnctuo&longs;is, & &longs;ulphureis, nec non à
particulis terreis, & fuligino&longs;is, & vici&longs;&longs;im quæli
bet ex prædictis &longs;ub&longs;tantijs recuperari pote&longs;t &longs;epa
rata à reliquis; præterea con&longs;tat &longs;en&longs;u, fumum no&ntail;
e&longs;&longs;e corpus continuum, &longs;ed aggregatum ex particu
lis minimis ab inuicem &longs;eparatis, & di&longs;cretis, vt præ
clarè in nebula ob&longs;eruatur, & in alijs aqueis vapo
ribus, qui&longs;i attentè con&longs;piciantur in loco commodo,
ide&longs;t &longs;i interpo&longs;ita nebula vi&longs;us dirigatur in&longs;piciat
que ob&longs;curum, & tenebro&longs;um aliquem locum, & in
terim Sol transuer&longs;alitèr eamdem nebulam illu&longs;tret;
tunc illa nebula, quæ repre&longs;entabatur continua ap
paret e&longs;&longs;e con&longs;lata ex immen&longs;a multitudine exiguo
rum granulorum aquæ, quæ lento quodam motu per
aerem agitantur, vt contingit in ijs fragmentis ter
reis minuti&longs;&longs;imis, quæ con&longs;piciuntur in radijs Solis
intra cubicula. Iam prædicta granula aquea copio
&longs;i&longs;&longs;ima vagantia per aerem non facile vi&longs;ibilia &longs;unt
&longs;igillatim ob eorum exiguitatem, &longs;ed po&longs;&longs;unt tran-
lam vnius &longs;ub&longs;tantiæ raræ, & expan&longs;æ, vti pariter
multoties accidit in tempore pluuiæ, quo guttæ
aquæ decidentes ab inuicem &longs;eparat&ecedil;, &longs;i à loco aliquo
di&longs;tanti, & remoto in&longs;piciantur, &longs;imillimæ videntur
nebulis, & fumo.
tiuam leui
tatem no&ntail;
dari.
re &longs;ursùm exprimi pote&longs;t.
QVòd po&longs;tea partes minimæ fumum componen
tes non &longs;int adhùc accen&longs;æ, experientia
quia videmus multoties fumum accendi, atque in
flammari
delæ, prætereà videtur quoque impo&longs;&longs;ibile fumum
e&longs;&longs;e rem accen&longs;am, quia nimirùm fumus gignitur in
cauitatibus, atque poro&longs;itatibus internis &longs;igni, vel
cuiuslibet alterius corporis fumum eructantis, &longs;ed
in hi&longs;ce locis angu&longs;tis re&longs;tricti&longs;que nedum fumus ac
cendi non pote&longs;t, vt è contrà flammæ ip&longs;æ iam
&longs;æ
extinguantur, &longs;uffocenturque; imò licet concauita
tes cauerno&longs;æ &longs;int ampl&ecedil;, vt e&longs;t cauitas alicuius later
næ vndique occlu&longs;æ, &longs;ubitò
tò
&longs;itates &longs;unt re&longs;trictæ, & angu&longs;ti&longs;&longs;imæ, vt &longs;unt pori li
gni, vel alterius con&longs;imilis corporis. Licèt ergo præ
dicta fragmenta exigua fumum componentia
actu accen&longs;a, vel
lefacta, & rara e&longs;&longs;e &longs;olent, & hæc quidem raritas, &
agitatio
lationibus igneis, à quibus priùs euul&longs;æ, & &longs;egre
gatæ fuerunt à ma&longs;&longs;a lignea, vel alterius corporis, e&longs;t
in cau&longs;a vt non po&longs;&longs;int am pliùs in angu&longs;tis illis poro
&longs;itatibus retineri, & proindè coguntur ingenti impe
tu eructari, effluere que per orificia patentia earum
dem poro&longs;itatum, quæ orificia cùm vndique pateant,
fit vt fumus exeat nedùm è parte &longs;uprema ligni, &longs;ed
etiam à parte infima, & laterali. Diffractis itaque re
pagulis carcerum, egre&longs;&longs;i&longs;que fumi partibus in aere
aperto non &longs;ine &longs;ocietate ignearum exhalationu&mtail;
ma&longs;&longs;am componunt minùs grauem ip&longs;o aere
te
tu impelli &longs;ursùm atque tàm diù a&longs;cen&longs;us per&longs;euera
bit, quou&longs;que exhalationes igneæ ab ip&longs;is particulis
fumi non di&longs;cedant
deficiat impetus præconceptus ab ip&longs;o impul&longs;u præ
cedenti, à quo lento quidem motu per aerem
do
præterea exiguitas particularum eiu&longs;dem fumi cau
&longs;a &longs;ufficiens &longs;it, vt diù à qualibet minima aeris agita
tione
terre&longs;trem graui&longs;&longs;imum per aerem di&longs;pergi, ibiqu&etail;
diù retineri, vt experientia docet.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
perduci po&longs;&longs;unt, &longs;ed minùs graues redditi ab igniculo
rum commixtione exprimi ab ambiente aere
po&longs;&longs;unt.
ET notandum e&longs;t, quòd ab&longs;que exhalationibus
igneis non po&longs;&longs;ent ad in&longs;ignem altitudine&mtail;
fumi particulæ eleuari, quia licèt impetus ex &longs;ui na
tura, quo à ligni poro&longs;itatibus eructantur, vim per &longs;e
haberet ad eas longiùs eleuandas, nihilominùs, quia
huiu&longs;modi impetus facillimè debilitatur extingui
turque à particulis aeris quie&longs;centibus, vel prædicto
motu priuatis, quibus occurrunt fumi, non po&longs;&longs;et eius
a&longs;cen&longs;us longiùs propagari, &longs;ed citò extingueretur. Vlteriùs &longs;i re vera fumi à ligno eructati virtute im
petus
tem
a&longs;cenderet, is enim qui per poros laterales ligni e
greditur, impetum proiectitium tran&longs;uer&longs;alem acqui
reret, & ideò pro&longs;equi &longs;uum motum deberet per pla
num horizontalem, neque ab incepto itinere tanto
pere deuiaret: &longs;imiliter fumus ille, qui ab infima par
te titionis in aere &longs;u&longs;pen&longs;i exit, impetum acquirit ten
dendi deorsùm, non &longs;ursùm, proindeque deberet di
rectè profluere v&longs;que ad pauimentum, & deinceps
non po&longs;&longs;et ad &longs;u premam aeris regionem perduci,
quæ omnia fal&longs;a &longs;unt, & contra &longs;en&longs;us euidentiam;
Fatendum igitur e&longs;t, ab igneis particulis fumum ra
refactum eleuari ab impul&longs;u grauioris aeris ambien
tis per expre&longs;&longs;ionem.
tiuam leui
tatem no&ntail;
dari.
ambiente velocis&longs;imè &longs;ursùm exprimitur.
PErcepta iam & declarata fumi
pendere modò iuuat metamorpho&longs;im, qua&mtail;
patitur quando inflammatur. Debemus igitur con
cipere minimas particulas &longs;ulphureas in fumo con
tentas, cùm inflammantur, maximè dilatari, rarefieri,
& vehementi&longs;&longs;imè agitari, & in hoc con&longs;i&longs;tere eius
accen&longs;ionem, &longs;ed granula illa aquea, & terrea eiu&longs;
dem fumi, quæ ex &longs;ua natura accen&longs;ibilia non &longs;unt,
poterunt tantummodò rarefieri multò magis, quàm
priùs. iam à prædicta ferè
agitatione, & accen&longs;ione &longs;ub&longs;equitur con&longs;equen
tèr &longs;plendida, & lumino&longs;a apparentia flammæ. Ad
hæc aeris ambientis grauitas, licèt exigua &longs;it, &longs;upe
rabit nihilominùs notabili exce&longs;&longs;u minimum, & in
&longs;en&longs;ibile pondus ip&longs;ius flammæ multò, & multò ma
gis, quàm &longs;uperauerat pondus
nece&longs;&longs;ariò flamma ab ip&longs;o aere per extru&longs;ionem &longs;ur
sùm impelletur ineffabili velocitate. Et hìc plurima
aduertenda &longs;unt.
tiuam leui
tatem no&ntail;
dari.
eius velocitatem, redditurque po&longs;tea inui&longs;ibilis noua
de cau&longs;a, & tactui languida ob eius
di&longs;per&longs;ionem.
OB&longs;eruatur profectò titionem fumi copiam
tem
ui&longs;cat, h&ecedil;c mirabili velocitate fumi illius va&longs;tam mo
lem ab&longs;umere videtur, eumque in exiguum &longs;patium
flammæ concludere, cùm reuera non &longs;it re&longs;trictio,
flamma enim maiorem raritatem habet, quàm fumus,
pendet ergo hoc ab ineffabili velocitate partiu&mtail;
flammæ. aliundè enim notum e&longs;t per re&longs;trictum flu
minis canalem molem ampli&longs;&longs;imam aquæ totius flu
minis pertran&longs;ire, non quia in exiguo, & re&longs;tricto illo
&longs;patio canalis conden&longs;etur tota aqua fluuij,
veloci&longs;&longs;imo motu per eum excurrit; cùm è contrà in
parte ampla fluuij aqua lenti&longs;&longs;imo cur&longs;u progredia
tur, &longs;ic paritèr in fumo particulæ eius lento, & tardo
gradu excurrentes amplum, & grande &longs;patium oc
cupabant, in flamma verò
&longs;tricti&longs;&longs;imum canalem mirabili, & ineffabili veloci
tate currunt, & &longs;ic po&longs;&longs;unt exiguum &longs;patium comple
re. Sed quare flamma vltra verticem eius non exten
ditur, neque vi&longs;ibilis redditur? hìc primò
quòd reuerà flamma producitur vltra eius verticem
per notabile &longs;patium, & hoc quidem percipitur non
vi&longs;u, &longs;ed tactu, po&longs;&longs;um enim ab&longs;que noxa manum ad
latus flammæ approximare, vt ferè eam contingam,
non verò po&longs;&longs;um manum &longs;upra flammæ verticem i&ntail;
notabili di&longs;tantia vnius palmi ab&longs;que dolore, & v
&longs;tione retinere, igitur dicendum e&longs;t, quòd &longs;ub&longs;tan
tia illa ignita vltra verticem flammæ redditur tran&longs;
parens, & ideò inui&longs;ibilis alia noua de cau&longs;a efficitur. Sed tamen negari non pote&longs;t productio, & exten&longs;i
&longs;ub &longs;tantiæ igneæ vltra flammam productæ, cùm hoc
ab ip&longs;o tactu conuincatur. Sed dices, quare &longs;upra
mæ
tactu percipitur effluuium calidi&longs;&longs;imum eius, vt pro
pè eius verticem percipie batur? At for&longs;an hoc acci
dit, quia ignea &longs;ub&longs;tantia fluidi&longs;&longs;ima ab occur&longs;u aeris
di&longs;pergitur, & &longs;ubdiuiditur in alias partes minores
ab inuicem diui&longs;as, & di&longs;cretas, vt videmus aquæ
copiam è &longs;umma turri delap&longs;am in progre&longs;&longs;u de&longs;cen
&longs;us &longs;ubdiuidi in innumeras guttulas inter &longs;e di&longs;cre
tas, & &longs;icuti non æquè humectat, & madefacit pluuia
illa, ac ma&longs;&longs;a integra aquæ vnita, quia nimirùm nul
la pars &longs;ubiecti corporis à ma&longs;&longs;a continua aquæ tacta
relinquitur arida, cùm in pluuia non omnes partes &longs;o
li
mæ
è
dè di&longs;creta plagas exiguas, & inter &longs;e di&longs;tantes i&ntail;
ip&longs;a manu inferant, & hinc minori noxa, minorique
dolore incur&longs;us ignis tolerari poterit.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
&longs;us, & ideò velociùs a&longs;cendit, quàm ba&longs;is eius.
PRæterea
habere con&longs;i&longs;tentiam homogeneam, & &longs;imila
rem, pars enim infima flammulæ non e&longs;t omninò ac
cen&longs;a, quod con&longs;tat ex eius colore &longs;ubliuido, qui&atail;
nimirùm fumi oleo&longs;i eructati ab elicnio, velligno
in in&longs;tanti, &longs;ed in
&longs;imile e&longs;t, quòd
gre&longs;&longs;um in ip&longs;o contactu ba&longs;is flammæ &longs;imùl, & inte
grè accendantur, & propterea rarefactio, & accen
&longs;io continuatur dùm actu excurrunt illæ particulæ à
ba&longs;i versùs verticem flammæ. Modò &longs;i in ba&longs;i flam
mulæ fumi non &longs;unt omninò, & integrè accen&longs;i, non
habebunt veloci&longs;&longs;imum illum motum, cuius capax
e&longs;t flammæ puræ natura, igitur in ip&longs;a flamma conci
pi debet pars infima tardior, quàm &longs;uprema, & ver
ticalis, &longs;ed &longs;icuti in fluuio nulla alia de cau&longs;a tant&atail;
copia aquæ in angu&longs;ti&longs;&longs;imum &longs;patium aluei re&longs;trin
gitur coangu&longs;taturque, ni&longs;i quia veloci&longs;&longs;imè excur
rit, cùm è contrà in locis dilatatis, & amplis eadem
aquæ fiuminis moles amplius &longs;patium aluei ob eius
tarditatem occupet, ita in flamma lucernæ, quæ vt
fluuius ignis excurrentis concipi pote&longs;t, mirum
e&longs;t, quòd in ba&longs;i propè elicnium ob tarditatem eius
fluxus ampliorem &longs;itum occupet, quàm in eius ver-
tice, vbi velociori cur&longs;u fugit.
tiuam leui
tatem no&ntail;
dari.
Hinc colligitur, quòd ex figura pyramidali, & a
cuminata flammæ lucernæ non euincitur eam à vi
intrin&longs;eca leuitatis &longs;ursùm impelli. Cùm è contrà de
claratum &longs;it, qua ratione ab&longs;que po&longs;itiua leuitate ab
expre&longs;&longs;ione aeris grauioris ambientis &longs;ursùm expel
latur, pariterque o&longs;ten&longs;a e&longs;t cau&longs;a prædictæ eius fi
guræ acuminatæ & in verticem de&longs;inentis, quæ non
pendet à leuitate propria, &longs;ed ab expre&longs;&longs;ione aeris
maxima velocitate facta in eius acumine magis
&longs;o
candelarum non &longs;unt pvramidales, &longs;ed rotundæ, aut
oblongæ, & ouales, & hoc clarè con&longs;picitur quandò
virga illa fumo&longs;a, quæ eructatur ab infima lucern&atail;
nupèr extincta, denuò accenditur à contactu alte
rius flammæ in notabili di&longs;tantia ab inferiori cande
la, & tunc fumus inflammatus per longitudinem to
tius fumi &longs;ubiecti deorsùm labitur v&longs;que ad
&longs;ubiectæ lucernæ, con&longs;piciturque euidentèr figura
illius fumi
cerna accenditur, eius flamma rotunda e&longs;t, & po&longs;tea
verticem conicum acquirit. in flammis verò camini
non ob&longs;eruantur formæ pyramydales, &longs;ed multipli
citèr diui&longs;æ multotiès radios, &longs;eù linguas referunt,
& aliquando rotundæ con&longs;piciuntur, & &longs;ic eleuan
tur per aliquod &longs;patium. Sed de his &longs;atis.
quod ex &longs;i
gura acumi
nata flammæ
lucernæ non
euincitur
hanc à vi le
uitatis
dere
quæ flammæ
candelæ &longs;unt
rotundæ, &
flammæ ca
mini &longs;unt al
terius figu
ræ.
tiuam leui
tatem no&ntail;
dari.
&longs;piritu, & ideò pote&longs;t exprimi &longs;ursùm
ab ambiente aere.
VIdeamus modò an ex accen&longs;ione vini &longs;piritus
deducatur a&longs;&longs;ertio leuitatis po&longs;itiuæ. Et hic
denuò dico, quòd flamma &longs;piritus vini non e&longs;t actu
accen&longs;a in poris internis prædicti liquoris, &longs;ed &longs;icuti
de fumis lignorum dictum e&longs;t, educitur è &longs;piritus vi
ni fiuore fumo&longs;a quædam ma&longs;&longs;a rari&longs;&longs;ima, quæ in po
ro&longs;itatibus fluoris cùm retineri nequeat, ruptis car
cerum repagulis ingenti impetu per orificia poro&longs;a
vndique fluorem ambientia eructat, & po&longs;tmodu&mtail;
flammam concipit, accenditurque in aliqua &longs;en&longs;ibi
li di&longs;tantia à dicto fluore: hoc confirmatur exemplo
illius effluuij fumo&longs;i, egredientis ab aliqua titionis
poro&longs;itate, quod po&longs;tmodum accenditur in di&longs;tan
tia vnius digiti ab ip&longs;o ligno, & &longs;peciem præbet flu
oris bitumino &longs;i lateralitèr defluentis, qui in aer&etail;
ignem concipiat. Cùm igitur ab omnibus poro&longs;ita
tibus &longs;piritus vini, & cuiuslibet materiei accen&longs;ibi
lis vndequaque &longs;ursùm, deorsùm, & lateralitèr fu
mo&longs;æ exhalationes egrediantur, quæ po&longs;tea in ip&longs;o
aere aperto inflammentur, & accendantur, non vi
detur difficile vt aer po&longs;&longs;it infra flammam accen&longs;am,
& lateralitèr eam comprimere, & proinde expre&longs;&longs;io
ne facta eam &longs;ursùm impellere: &
expre&longs;&longs;io, quæ ab aere efficitur, non &longs;emper a&longs;&longs;imila
tur ei, quæ ex compre&longs;&longs;ione po&longs;tica digitorum crea
tur, veluti prunorum nucleos à digitis po&longs;ticè com
pre&longs;&longs;is pueri proijcere longè &longs;olent, vtque aduer&longs;a
rius exi&longs;timabat, &longs;ed expul&longs;io, & expre&longs;&longs;io flammæ
facta ab aere circumfu&longs;o fit, vt exigit ratio mechani
ca &longs;iphonis &longs;ursùm inuer&longs;i vt ex elementis hidro&longs;ta
ticis con&longs;tat, vtque meliùs inferiùs declarabitur vn
de malè infertur, quòd &longs;i flamma expul&longs;a e&longs;&longs;et ab am
biente aere, deberet fieri acuminata in eius ba&longs;i, &
rotunda in eius vertice.
tiuam leui
tatem no&ntail;
dari.
bente contundi, cùm ab eius pondere non exprimatur
&longs;ursùm, &longs;ed ab aere collater ali infernè reflexo.
PO&longs;trema in&longs;tantia, quòd aer flammæ
bens
tare, & deorsùm eam diuerberare,
tiem &longs;ublimare, facilè &longs;oluitur, quia aer fluidus non
&longs;olùm &longs;upremus, & flammæ incumbens, &longs;ed etia&mtail;
lateralis, & infimus ob eius grauitatem ad modu&mtail;
&longs;iphonis, vellibræ non pote&longs;t contundere
&longs;ed eam &longs;ursùm exprimere, & impellere debet, at
que aer &longs;upernus nece&longs;&longs;ariò ad latera excurrere de
bet, & tran&longs;itum minùs pondero&longs;æ flammæ
ti
terquàm contu&longs;ionem &longs;upremæ aciei flammæ, vt ni-
mirùm efficiatur vertex eius aliquo pacto rotundus,
& contornatus, ni&longs;i adfuerit noua alia cau&longs;a motum
eius accelerans, à qua proindè eius vertex acumi
nari pote&longs;t, vt &longs;uperiùs dictum e&longs;t.
tiuam leui
tatem no&ntail;
dari.
Pergamus modò ad po&longs;tremam difficultatem ab
eodem authore allatam. inquit enim:
ta inclu&longs;o aere, hæ&longs;ine dubio a&longs;cendit &longs;uper aquam, non
item minor, &longs;i ergo aqua deorsùm tendens exprimit
pilam, cur non reliquam? non igitur pila mouetur &longs;ursùm,
quia exprimitur, &longs;ed quia in &longs;e habet aerem natura &longs;ua le
uem. Et huic profectò argumento nil aliud re&longs;ponde
re po&longs;&longs;um, &longs;ed tantùm monere authorem eius &longs;e no&ntail;
e&longs;&longs;e &longs;atis memorem doctrinæ Archimedis, ex qu&atail;
deducitur ingentem pilam æneam excauatam, & ae
re plenam minùs ponderare, quàm moles aquæ ei æ
qualis, & ideò grauitas aquæ maior velut in libr&atail;
&longs;ursùm eleuare debet minus pondus prædictæ pilæ
æne-aereæ, cum verò comparatur ænea pila &longs;olida
licèt paruula &longs;it, illa tamen grauior e&longs;t multò magis,
quàm &longs;it moles aquæ huic pilulæ æqualis, cùmque
comparatio fieri debeat inter duas moles æquales
&longs;olidi nempè demer&longs;æ pilæ æneæ
bientis ei æquali, quia exce&longs;&longs;us ponderis penès pi
lam
ualebit, ideòque mergetur, & ad fundum de&longs;cendet,
ex quo patet prædictum argumentum non probar&etail;
pilam &ecedil;ne-aeream vim leuitatis in &longs;e habere.
authoris no
ua difficul
tas.
tur.
Tandem oper&ecedil;pretium erit di&longs;&longs;oluere nouas diffi-
cultates à pr&ecedil;claro authore euulgatas, qu&ecedil; ab hac ex
perientia de&longs;umuntur; &longs;it fi&longs;tula vitrea RSVX cuius
latitudo &longs;it duorum, vel trium digitorum, altitudo
verò &longs;it vnius, vel alterius cubiti, repleaturque aqua,
&longs;ed remaneat in eius vertice portio aliqua aeris vni
us, vel alterius digiti, po&longs;tea foramine RX perfectè
occlu&longs;o, vel palma manus, vel operculo aliquo re
uoluatur fi&longs;tula vt eius infima ba&longs;is SV in &longs;upremolo
co emineat, videbimus aerem è fundo RX &longs;ursù&mtail;
a&longs;cendere, atque incuruari ad modum arcus, ex par
te &longs;uperiori ABC, & è contrà ex parte infima AGC,
aut explanari, vel etiam cauitatem aliquam ad mo
dum &longs;cutellæ acquirere. Hinc prædictus Author in
fert certè deduci aerem &longs;ursùm in præ
dicta fi&longs;tula a&longs;cendere propria virtut&etail;
intrin&longs;eca leuitatis non per
factam ab aqua ambiente; quia, inquit
ip&longs;e,
&longs;culi, vt faciliùs peruadat aquam, & qua&longs;i
perforet illam, quia aer est, qui turge&longs;cendo
&longs;ursùm aquam introit, & cedere &longs;ibi cogit
qua&longs;i cuneo in illius medio adacto, alio quin
&longs;i idcircò aer &longs;ursùm tendit quia ab aqua de
orsùm tendente extruditur in &longs;uperiora, aqua
potiùs peruaderet cuneatim aerem; vt con
tingit in pluuia, vel &longs;altem retunderet &longs;uper
nè illius tumorem, & infernè illum qua&longs;i forcipe
constringeret ad figuram conoidem eius partem infimam.
tiuam leui
tatem no&ntail;
dari.
menta pro
leuicate po
&longs;itiua
ta à pulcher
rimo expe
rimento.
Pro re&longs;olutione harum difficultatum priùs metho-
do generali demon&longs;trabimus &longs;uppo&longs;ito quòd aer i&ntail;
aqua a&longs;cendat
extru&longs;ionem medij fluidi tunc figura aeris
tis
feriùs excauata, & è contrà &longs;uppo&longs;ito quòd aer inter
no principio leuitatis per aquam a&longs;cenderet, deberet
figura aeris a&longs;cendentis tumorem, & rotunditate&mtail;
habere tùm ex parte &longs;uprema, tùm ex parte &longs;ubiecta.
tiuam leui
tatem no&ntail;
dari.
aliud fluidum tran&longs;latum &longs;iuè virtute propria, &longs;iuè alie
na violentia impul&longs;um, dummodò eius partes non di&longs;
&longs;ipentur in ip&longs;o fluido in quo mouetur, &longs;ed &longs;e
mutuò contingant, & vniantur, nece&longs;&longs;ariò
tumorem, & rotundam figuram acqui
ret in parte anteriori mo
tus eius.
QVodlibet fluidum
ctu videtur &longs;ponte coale&longs;cere, ac &longs;imul in &longs;uo
toto partes &longs;uas conglutinare, vt videmus partes ae
ris libentèr, & auidè vici&longs;&longs;im vniri, & difficiliùs ab
inuicem di&longs;trahi &longs;epararique, &longs;ic quoque partes aqu&ecedil;
vniuntur, conglobanturque &longs;phæricè
&longs;ibi mutuò approximantur, itaut ex duabus guttulis
vna &longs;uper aliam excurrendo, & &longs;e mutuò
do
tenax huiu&longs;modi vnio, & vinculum partium aquæ, vt
&longs;i contingat aquæ guttam pendentem di&longs;trahi ab ali
qua violentia, illa attenuatur, & gracile&longs;cit elonga
turque, & denuò ce&longs;&longs;ante violentia re&longs;tringitur re
colligitur, conglobaturque, &longs;ic paritèr videmus a
quam ad membranæ &longs;ubtili&longs;&longs;imæ
circa aerem &longs;pumam componentem, vnde con&longs;tat
partes aquæ inter &longs;e vici&longs;&longs;im colligari vinculo
id ip&longs;um ob&longs;eruamus in vitro, & metallis fu&longs;is. Qua
li&longs;cumque igitur &longs;it cau&longs;a huius vinculi, & tenacita
tis partium homogenearum eiu&longs;dem fluidi, vel quia
ab aliquo glutine, &longs;eù vi&longs;co&longs;itate vniantur, aut ab
ali qua alia cau&longs;a partes
plexentur
prædictam vnionem, quotie&longs;cumque fluidum intr&atail;
aliud fluidum alterius naturæ collocatur, vt oleu&mtail;
intra aquam, vel aer intra quodlibet aliud fluidum,
non di&longs;&longs;ipabitur, &longs;ed tenaci quadam vnione conglo
babitur, licet in motu poterit aliquo pacto eius figu
ra rotunda alterari. hoc autem non contingit in om
nibus fluidis cuiu&longs;cumque naturæ &longs;int, nam aqu&atail;
intra vinum, & metalla fu&longs;a inter &longs;e commixta no&ntail;
&longs;egregantur; &longs;ed facilè commi&longs;centur, confundun
turque inter &longs;e. Et in hi&longs;ce aduertendum e&longs;t
ex perientiam locum non habere, &longs;ed tantummodò
in fluidis priùs expo&longs;itis non homogeneis inter &longs;e.
tiuam leui
tatem no&ntail;
dari.
Supponamus igitur fluidum ABC, verbi gratia ae
rem, vel hydrargyrum, moueri vi intrin&longs;eca, velvio
lenter impul&longs;um in aqua intra fi&longs;tulàm
contenta à termino B versùs E: & quia &longs;patium DN
LF vbi fluidum ABC tran&longs;portari de
bet, iam repletum, & occupatum e&longs;t
à medio fluido aqueo, hoc autem vt lo
cum cedat &longs;ubintranti fluido ABC, ne
ce&longs;sè e&longs;t vt hinc di&longs;cedat transferatur
que ad
derelinquitur à fluido ABC, cùmqu&etail;
corpus ABC vnionem &longs;eruet, nec di&longs;&longs;i
petur, igitur anterius medium fluidum
debet per eius latera obliquè excur
rere ad occupandas partes po&longs;ticas derelictas à flui
do ABC, &longs;cilicèt fluidum ENDB mouebitur ad
&longs;ini&longs;tram versùs A, & medium fluidum BFLE moue
bitur ad partem dexteram versùs C, eruntque prædi
cti motus non æquidi&longs;tantes axi EB, &longs;ed erunt incli
nati per lineas obliquas vt &longs;unt EA, & EC, & hoc
nece&longs;&longs;itate quadam contingit, quia fluidum è loco
ampliori SEBD
AO, & reliqua fluidi medietas VEBF pariter ab am
plo &longs;patio perduci, ac pertran&longs;ire debet per &longs;trictum
locum CP, & huiu&longs;modi viæ angu&longs;tæ cùm &longs;int lateri
va&longs;is adhærentes, nece&longs;sè e&longs;t vt motus, & fluxus aqua
à &longs;itu B versùs O, & P obliquo itinere fiat impellen
do, contundendo, & confricando &longs;uperficiem cor
poris ABC, quod compre&longs;&longs;ioni cedit ob eius fluidi
tatem, igitur ABC accommodari debet &longs;ituationi
obliquæ pre&longs;&longs;ionis corporum excurrentium à &longs;upre
mo loco B versùs O, & P, quapropter nece&longs;&longs;itat&etail;
quadam acquirit fluidum ABC tumorem, & conuc-
xitarem cuins vertex in parte eius anteriori B exi&longs;tit. Et quia fluidum ABC, vt dictume&longs;t, diuer&longs;æ natur&ecedil;, ac
con&longs;i&longs;tentiæ e&longs;t ab ip&longs;o fluido ambiente in quo mo
uetur, ideò non commi&longs;centur, neque vici&longs;&longs;im
duntur
nem, & connexionem &longs;uarum partium homogenea
rum. Hinc con&longs;tat quòd fluidum ABC dum fertur à
B versùs E, nece&longs;&longs;ariò acquirit figuram tumidam, &
acuminatam versùs anteriorem partem motus eius,
& hoc &longs;emperverificari debet, à quacumque virtute
motiua transferatur, &longs;iue ab intrin&longs;eca, & naturali,
&longs;iuè ab externa: & hoc propo&longs;itum fuerat.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
amibente grauiori, diuer&longs;æque con&longs;istentiæ, infima a
&longs;cendentis fluidi &longs;uperficies explanata, vel
concaua erit.
DEinde fluidum ABC, oleum v. g.
demer&longs;um in fundo alterius flui
di grauioris, & diuer&longs;æ con&longs;i&longs;tentiæ, vt
e&longs;t aqua intra fi&longs;tulam &longs;trictam SX con
tenta, & &longs;uppo&longs;ito, quòd idip&longs;um flui
dum ABC non a&longs;cendat in ip&longs;a aqua à
vi natiuæ eius leuitatis translatum, &longs;ed
expul&longs;um per
uitate fluidi aquæ ambientis.
dum
AGC eiu&longs;dem olei a&longs;cendentis nece&longs;&longs;ariò explana
tam, imò excauatam fore; quia ex hypothe&longs;i pondus
&longs;pecificum aquæ ambientis &longs;uperat &longs;pecificam gra
uitatem olei ABC; iam &longs;i e&longs;t moles aquæ collateralis
FQPC æqualis medietati olei BGC, proculdubio
aqua FQPC grauior erit oleo BGC, vel &longs;i moles in&ecedil;
quales &longs;unt, aquæ momentum &longs;uperat olei
hi&longs;ce verò inæqualibus ponderibus ineumbunt, &
&longs;ubijciuntur moles aquæ æque ponderantes, vel æ
qualium momentorum, ergo in &longs;iphone compo&longs;ito
ex cylindri portione aquea VXKL, & ex cylindri
portione EIKL compo&longs;ita ex aqua, & oleo inæqua
liter premuntur partes aquæ &longs;ubiectæ GPXI. quæ li
bram con&longs;tituunt, nempè aqua CPXK maiori ni&longs;u
comprimitur ab aqua FQPC, quam aqua GCKI pre
matur ab oleo BGC minus graui, & ideò ex coroll pr.
10. oleum BGC &longs;ursùm impelletur ab aqua &longs;ubiecta
GIKC, & talis expre&longs;&longs;io fiet (ex prop.
51.) tanta vi,
quanta e&longs;t grauitas exce&longs;&longs;us ponderis aquæ FQPC
&longs;upra grauitatem olei BGC. præterea quia aqua in
ter EB, & LC dum fertur deor&longs;um ad occupandu&mtail;
&longs;patium ab a&longs;cendente oleo derelictum, nece&longs;&longs;ariò
comprimit contunditque &longs;uper&longs;iciem collaterale&mtail;
olei BC non duri, &longs;ed cedentis, e&longs;tque motus obli
quus per &longs;u perficiem decliuem BC, ergo &longs;patiu&mtail;,
&longs;eù alueus, per quod incumbens aqua pertran&longs;ir&etail;
debet comprehen&longs;um à &longs;uperficie aquæ FCK dire
cto, & non impedito motu fluentis, & inclinatam de
cliuemque olei BC &longs;uperficiem, continentèr magis
con&longs;tringatur angu&longs;teturque, & proinde incumbens
aqua velociori motu, & ideò impetu, & vi maiori
fluere cogatur per angu&longs;tias C, quàm per amplu&mtail;
alueum
iori impetu, & vi pars olei versùs C deorsùm com
primatur, contundaturque quàm reliquæ partes olei
propinquiores vertici eius B, è contra aqua &longs;ubiecta
CKIG reflectitur &longs;ursùm, impellit, atque contundit
infimam ba&longs;im olei GC ea vi, & impetu quo collate
ralis aqua FCPQ exce&longs;&longs;u &longs;uæ grauitatis &longs;uperat &longs;pe
cificam olei pondero&longs;itatem. Patet ergo quod à dua
bus viribus
BCG &longs;upernè ab impetu aquæ obliquè de&longs;cenden
tis per BC, & infernè à vi aquæ reflexæ oleum
impellentis, cùmque vis, & compre&longs;&longs;io, quæ &longs;upernè
infertur, inæqualis &longs;it, vehementiori, & validiori vi
facta propè terminum C, & debiliori, ver&longs;us
B, impul&longs;us verò &longs;ubiectæ aquæ IKCG licèt vnifor
mis &longs;it vbique, nihilominùs propter minorem
dentis
vt vehementiùs oleum impellatur contundaturque à
&longs;ubiecta aqua reflexa versùs axem IG vbi ni&longs;um
trarium
C, & propterea &longs;uperficies &longs;ubiecta olei AGC exca
uata erit ad modum &longs;cutellæ, & hoc quidem nece&longs;
&longs;ariò efficietur non à vi intrin&longs;eca, & naturali leuita
tis ip&longs;ius olei, &longs;ed à &longs;uppo&longs;ita energia grauitatis
fluidi ambientis, quod fuerat demon&longs;trandum.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
diuer&longs;æ con&longs;istentiæ moueatur, in parte po&longs;teriori, &longs;eù
termino à quo, &longs;ui motus, non erit excauatum,
&longs;ed tumidam, & conuexam figuram
acquiret.
SVpponamus &longs;ecundo loco fluidum
ABC, quod &longs;it aqua, grauius e&longs;&longs;&etail;
ambiente fluido (quod &longs;it v. g. oleum)
manife&longs;tum e&longs;t aquam ABCH deorsùm
in oleo de&longs;cendere ab I versùs E ab in
trin&longs;eco principio &longs;uæ grauitatis impnl
&longs;um. Dico iam quod eadem aqua in par
te po&longs;tica &longs;ui motus H, &longs;cilicèt versùs
terminum à quo &longs;ui motus, non erit ex
cauata ad modum &longs;cutellæ, &longs;ed tumida, & conuexa
erit. Quia cum primo aqua ABCH demergitur in
fra olei
loco continenter recedat, & recurrat ad replen
dum locum po&longs;ticum AMKC ab aqua derelictum; er
go aqua AHCB, & oleum ambiens motibus contra
rijs agitari debent, nempe aqua de&longs;cendet dum am
biens oleum a&longs;cendit, igitur ratione motus, oleu&mtail;
po&longs;ticè recurrens non impellet aquam ictum fugien
tem, nec proinde eius figuram AHC contundere, &
explanare poterit. præterea aqua ABCH habet vim
&longs;e mouendi deorsùm in oleo, hoc verò nullam facul
tatem &longs;e mouendi deorsùm in
fluido &longs;ui generis iners æquilibretur, ergo hoc nomi
ne pariter aqua ictum fugiens, immò non impul&longs;&atail;,
nec percu&longs;&longs;a ab oleo po&longs;ticè recurrente non poterit
contundi, nec explanari, & hoc experientia patet,
nam &longs;i pila dura capillitium è filis &longs;ericis tenui&longs;&longs;imis
&longs;ibi annexum habuerit, & intra aquam filo deorsùm,
&longs;ursùm, vellateraliter trahatur nunquam po&longs;ticum
capillitium contundetur explanabiturque, dum vni
formi, non verò retardata velocitate pila in aqu&atail;
mouetur. & ab hac experientia|luculenter euinci
tur &longs;omnium illorum, qui aiunt ad vitandum
rapidi&longs;&longs;imo motu oleum po&longs;ticè recurrere, & &longs;ic po&longs;
&longs;e aquæ &longs;uperficiem contundere, & explanare. Qua
propter aqua excepto &longs;implici contactu in &longs;uperficie
AHC nullam contu&longs;ionem, aut percu&longs;&longs;ionem patie
tur ab oleo &longs;uperincumbente MACK, igitur nece&longs;sè
e&longs;t vt aqua in AHC retineat eamdem figuram, quam
priùs habebat, &longs;ed eius figura intra oleum vnita, &
contornata e&longs;&longs;e &longs;olet ob naturalem partum eius con
nexionem, & vinculum, & ob compre&longs;&longs;ionem vn
dequaque factam à fluido ambiente, vt dictum e&longs;t. igitur dum aqua ABC de&longs;cendit intra oleum po&longs;tre
ma eius ba&longs;is AHC, &longs;cilicèt versùs terminum à quo
motus inchoat, eius figura debet e&longs;&longs;e tumida con
uexa, & contornata, cum è contra eadem aqua
dens
ente nece&longs;&longs;ariò eius po&longs;tica ba&longs;is versùs principium
motus non tumida, &longs;ed excauata e&longs;&longs;e debuerat, &
hæc omnia o&longs;tendenda fuerant.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
dum diuer&longs;æ con&longs;istentiæ, quod valdè rarefieri, & co
den&longs;ari queat, tunc multò magis tumida efficie
tur pars postica fluidi decurrentis.
ET hoc quidem verum e&longs;t quando fluidum am
biens, in quo aliud fluidum mouetur &longs;ursùm,
vel deorsùm, non patitur &longs;en&longs;ibilem
vel rarefactionem, veluti e&longs;t oleum, aut aqua; at &longs;i
valdè rarefiat conden&longs;eturque, vt aer propter velo
ci&longs;&longs;imum ca&longs;um aquæ AHCB remanet aer po&longs;ticus
MACK valdè rarefactus, ideoque inhabilis vt in&longs;e
qui po&longs;&longs;it aquam cadentem, & proindè nedùm aer
incumbens guttam aquæ de&longs;cendentem in H no&ntail;
percutiet, cùm è contrà, ne ibidem, (vt vulgò credi
tur) vacuum remaneat eius vertex tumidus H valdè
eleuabitur
uiales &longs;ecum trahere veluti caudam aqueam
tantùm abe&longs;t vt po&longs;ticè contu&longs;ionem patiantur, aut
excauentur, & hoc clariùs percipitur &longs;i pila aliqu&atail;
lignea, & dura, quæ habeat comam ex filamentis, &longs;eù
pilis exili&longs;&longs;imis, & nullius ferè ponderis compo&longs;itam
cadat deorsùm in aere, tunc enim pili &longs;upremi a&longs;&longs;ur
gunt efficiuntque veluti caudam fluctuantem, non
autem comprimuntur contundunturque versùs &longs;u-
premam partem ip&longs;ius pilæ, quod e&longs;t &longs;ignum euidens
nullam vim compre&longs;&longs;iuam pati ab aere &longs;uperincum
bente.
tiuam leui
tatem no&ntail;
dari.
tatis impul&longs;us non po&longs;&longs;et eius ba&longs;is excauari ad in&longs;tar
&longs;cutellæ.
TAndem demon&longs;trandum e&longs;t po
&longs;ito, quòd aer, vel oleum ABCH
a&longs;cenderet in ip&longs;a aqua à propria, &
intrin&longs;eca virtute leuitatis impul&longs;um,
quod e&longs;&longs;et ab&longs;olutè impo&longs;&longs;ibile, vt e
ius ba&longs;is infima excauata e&longs;&longs;et ad mo
dum &longs;cutellæ; quia ex aduer&longs;arij hypo
the&longs;i oleum ABCH a&longs;cendit in aqua contenta in fi
&longs;tula &longs;tricta RSVX propria virtute leuitatis ab Iver
sùs E, nec ab aqua infima impellitur exprimiturque
fursùm, ergò aqua MACK, quæ currit ad
&longs;patium derelictum ab oleo cum &longs;it ex &longs;ui natura gra
uis exercet vim &longs;ui ponderis ab H ver&longs;us I premen
do præcisè &longs;uper
exercere pote&longs;t &longs;ursùm abl versùs H, hoc enim e&longs;&longs;et
contra grauium naturam, & contra ip&longs;am aduer&longs;arij
hypothe&longs;im. Præterea quia oleum ABCH, & aqua
ambiens motibus contrarijs agitari debent, nempè
oleum, vt leue, a&longs;cendet dum aqua ambiens
det
inuicem conantur recedere; quare ratione motus
aqua inferiùs, & po&longs;ticè recurrens non impellet
ictum fugiens, nec proindè eius figuram AHC
tundereIgitur in hoc ca&longs;u duo
impetus inter &longs;e contrarij, & ab inuicem receden
tes reperiuntur leuitatis olei, nimirùm, &longs;ursùm ab H
versùs E, aquæ verò conatus inferiùs tendentis ab
H versùs I, igitur hæc duo corpora oleum AHCB,
& aqua &longs;ubiecta MACK &longs;e mutuò tantummodò tan
gent placidi&longs;&longs;imo amplexu ab&longs;que vlla pugna, & re
pul&longs;u, vt nimirùm aqua oleum non impellat, neque
hoc illam repellat, igitur oleum ABCH multò minùs
comprimi, ac contundi debetin H ab aqua &longs;ubie
cta deorsùm premente, quàm contundebatur po&longs;ticè
ab oleo incumbente, quando nimirum intra oleu&mtail;
de&longs;cendebat, & pondus eiu&longs;dem olei incumbentis
patiebatur (in vtroque enim ca&longs;urecur&longs;us fluidi ad
&longs;patium replendum æquè reperitur, & proindè ne
que nocet, neque adiuuat prædictum effectum) &longs;ed
ex antepræmi&longs;&longs;a propo&longs;itione aqua per oleum deci
dens à vi natiua grauitatis impul&longs;a retinet tumorem
eleuationemque
tus, igitur multò magis eleuari deberet tumor i&ntail;
oleo per aquam a&longs;cendente in parte po&longs;teriore mo
tus eius &longs;i ab intrin&longs;eca leuitate eleuaretur, qua pro
ptèr erit omninò impo&longs;&longs;ibile, vt oleum, vel aer dum
a&longs;cendit per aquam, excauetur in parte infima eius
ba&longs;is,
cipio leuitatis, quod demon&longs;trandum fuerat.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
His præmi&longs;&longs;is examinari modò debent &longs;igillati&mtail;
oppo&longs;itiones &longs;uperiùs adductæ.
nata quam aer acquirit in fi&longs;tula aqua plena in parte an
teriori eius motus dum &longs;ursùm a&longs;cendit, non e&longs;t argu
mentum efficax, & euincens aerem &longs;ursùm
moueri à principio intrin&longs;eco &longs;uæ
leuitatis.
QVia demon&longs;tratum e&longs;t corpora fluida
& homogenea &longs;i moueantur intra aliud cor
pus Huidum &longs;iue propria, & intrin&longs;eca virtute moti
ua, &longs;iue ab impul&longs;u facto à cau&longs;a extrin&longs;eca, aut ab
ip&longs;o medio, nece&longs;&longs;ariò in anteriori parte motus il
lius tume fieri, contornari, & aliquanti&longs;per acumina
ri debere, quaproptèr tumor, qui in aere a&longs;cenden
te peraquam ob&longs;eruatur, neque inuat, neque nocet,
nec &longs;uadet, neque di&longs;&longs;uadet leuitatem po&longs;itiua&mtail;. Mirum tamen e&longs;t non animaduer&longs;am fui&longs;&longs;e cau&longs;a&mtail;
cauitatis eiu&longs;dem aeris in parte po&longs;tica eius motus,
à qua cauitate, &longs;i
tur impo&longs;&longs;ibile e&longs;&longs;e aerem ab intrinfeco principio le
uitatis &longs;ursùm ferri, &longs;ed potiùs per
dij fluidi &longs;ursùm eleuari.
Cùm po&longs;tea in&longs;tat aduer&longs;arius aerem, dum per a
quam a&longs;cendit, acumen eius &longs;ursùm porrigere, vt fa
ciliùs terebrare, & perforare aquam vi &longs;uæ leuitatis
po&longs;&longs;it. Hoc profectò negatur, quia licèt aer non &longs;it
leuis, &longs;ed per extru&longs;ionem à medio fluido &longs;ursù&mtail;
expellatur, efformare debet quoque eminentiam il
lam contornatam, & acuminatam, vt demon&longs;tratum
e&longs;t.
tiuam leui
tatem no&ntail;
dari.
Sed vtile erit parumpèr circum&longs;tantias huius ex
perienti&ecedil; accuratiùs perpendere, inquit enim,
tem fistulæ &longs;uperiorem conuerte deorsùm, & erige fi&longs;tulam
perpendicularitèr ad horizontem, videbis enim aerem, qui in
fundo fi&longs;tulæ habuerat formam cylindri occupantem totam
cauitatem fistulæ in latum mox a&longs;cendere, & &longs;ic a&longs;cendere,
vt &longs;e coarctans extendat in longum, & &longs;uperiorem cylindri
illius &longs;uperficiem, quæ plana erat ad modum di&longs;culi, iam
conoidem factam e&longs;&longs;e. Itaque hic author
cen&longs;et quòd
dicularitèr
rem ROPX, quidum &longs;upernè con&longs;i&longs;te
bat cylindricam formam habebat,
in hoc &longs;itu infimo per&longs;euerare po&longs;&longs;&etail;
per aliquod tempus in eadem figur&atail;
cylindrica, quod profectò &longs;i verum e&longs;
&longs;et non facilè reddi ratio po&longs;&longs;et quare, & quemad
modum à compre&longs;&longs;ione aquæ
na aeris &longs;uperficies OP efficiatur tumida, & conue
xa, veluti e&longs;t ABC. Alia igitur longè diuer&longs;a ratione
res &longs;e habet.
tia notatu di
gna in tali
experimen
to affertur
ab ad
rio.
tiuam leui
tatem no&ntail;
dari.
aquæ ambientis.
INtelligatur denuò fi&longs;tula RV plena aqua, in qu&atail;
exi&longs;tat aereus cylindrus PORX in parte eius &longs;u
prema operculo XR
clau&longs;a, po&longs;tea circa
ctum
tur
ferendo
VX in locis VF, VG,
VH, & VK,
e&longs;t, quod in &longs;itu VF pro
pter va&longs;is
&longs;uperficies PO aquæ
POSV non per&longs;euera
bit in eodem &longs;itu incli
nato, cùm aqua natura
li in&longs;tinctu æquabili &longs;i
tu ad horizontem parallelo di&longs;poni, redigique de
beat, quaproptèr à &longs;itu decliui PO de&longs;cendet inferiùs
versùs &longs;uperficiem BDA horizonti parallelam, veluti
exigit &longs;itus, & pendentia fi&longs;tulæ VFR. Hinc &longs;equi
tur, vt aqua excurrat ad occupandum
à quo aer expul&longs;us deueniet ad replendum &longs;patium
&longs;upremum ab aqua derelictum, &longs;cilicèt PEBD. Pro
grediamur modò ad &longs;ituationem fi&longs;tulæ
VG multò magis aqua in&longs;inuabitur infra aerem dila
tando &longs;inum ampliorem ODAIR, & multò magis
incuruabitur aeris &longs;uperficies EBD, tum à vi qua flui
da &longs;e &longs;e connectunt conglobanturque, quotie&longs;cum
que in fluido ip&longs;is hetherogeneo
acce&longs;&longs;u noui aeris expul&longs;i à cauitate infima DAIRO. Poftquàm verò magis fi&longs;tula deprimitur in &longs;itu val
dè inclinato VH eadem ratione profluet aqua versùs
partem infimam, & omninò aerem &longs;eparabit, diuel
letque à fundo va&longs;is, & proindè &longs;ubintrabit ad oc
cupandum &longs;patium ODAICHR. Po&longs;tremò perdu
cta fi&longs;tula ad inclinationem omnium maximam i&ntail;
&longs;itu VK perpendiculari ad
in&longs;inuata fuerat circa, & infra aerem tumefactum, &
contornatum EBDC,
& lateribus va&longs;is diuellet, & proindè multò magis
de&longs;cen&longs;us, & compre&longs;&longs;io aquæ ambientis per latera
va&longs;is, & aeris continuari pote&longs;t; & vniuer&longs;a hæc o
peratio pendet, vt dictum e&longs;t, non ab aere &longs;pont&etail;
a&longs;cendente, neque ab eius leuitate, &longs;ed ab exce&longs;&longs;u
grauitatis fluidæ aquæ ambientis, quæ in vertigine
fi&longs;tulæ nece&longs;&longs;ariò &longs;eparat, atque diuellit aerem à la
teribus, & fundo va&longs;is, & &longs;ic via &longs;ternitur commodi&longs;
&longs;ima, vt continuari, & pro&longs;equi pre&longs;&longs;io aquæ po&longs;&longs;it,
vnde aer &longs;ursùm expul&longs;us continuare pote&longs;t eius cur
&longs;um, &longs;i, inquam, hoc ob&longs;eruatum, & adnotatum fui&longs;
&longs;et, proculdubiò ex mutatione figuræ planæ in tumi
dam in aere a&longs;cendente per aquam non deduxi&longs;&longs;et
prædictus author aeris leuitatem po&longs;itiuam.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
Sed po&longs;ito quòd in vehementi&longs;&longs;ima turbinatione
retineretur pauli&longs;pèr aqua adhærens fundo &longs;u premo
fi&longs;tulæ, & proinde aer infimus &longs;altem per
&longs;patium cylindricam formam ORXP retineret, mani
fe&longs;tum e&longs;t, quòd &longs;ubito ce&longs;&longs;ante impetu aqua vt gra
uior aere deorsùm de&longs;cenderet, labereturque, aut
in loco intermedio fi&longs;tulæ, aut ad latera, prout vndu
latio partium aquæ eam promoueret, & &longs;ic &longs;emper à
de&longs;cen&longs;u grauioris aqu&ecedil; figura tumida, & conuexa
aeris a&longs;cendentis crearetur, numquam verò &longs;pont&etail;
ab ip&longs;a leuitate aeris.
tur &longs;ingulis
oppo&longs;itioni
bus aduer
&longs;arij.
Cùm verò in&longs;tat:
aqua deorsùm tendente extruditur in &longs;uperiora aqua potiùs
peruaderet cuneatim aerem, quem admodum aqua
extra fistulam &longs;ubiectum aerem perrumpit, non verò illum
ambiens intra &longs;e recipit. Hic primò noto, quòd non
per
penetratur ab ip&longs;o aere quando nimirùm &longs;cinditur
in plures partes, vt contingit in plunia, vel potiùs
quando è fene&longs;tra catino aqua proijcitur.
Sic paritèr ma&longs;&longs;a pulueris terre&longs;tris è turris verti
ce proiecta licèt in principio &longs;it vnita, nihilominùs
ab aere di&longs;&longs;ipatur, di&longs;pergiturque, idemque accidit
in fumo a&longs;cendente per aerem. Secundò noto, quòd
partes aeris, vt dictum e&longs;t, &longs;ponte &longs;ua connectuntur
colliganturque inter &longs;e, & proinde intra aquam po
&longs;itæ omnes vniri debent, atque &longs;imùl, conglobatæ
per aquam a&longs;cendent, non &longs;ecùs, ac partes aquæ in
tra aerem, vel oleum vici&longs;&longs;im vniuntur, congloban-
turque. Et tunc &longs;olummodò ab inuicem &longs;egregantur
&longs;ubdiuidunturque, quando medium fluidum vehe
menti, & irregulari motu fluidum per ip&longs;um a&longs;cen
dens, vel de&longs;cendens perrumpit diuiditque, &longs;eù quia
non omnes partes prædicti fluidi excurrentis æquali
impetu mouentur, vel quia laterales partes fluidi ab
a&longs;peritatibus, & contactibus laterum fi&longs;tulæ retar
dantur, &longs;eù ab aliqua alia cau&longs;a detinentur: nil igitur
ex hoc pro leuitate po&longs;itiua acquiritur.
tiuam leui
tatem no&ntail;
dari.
Subdit po&longs;tea idem author, quòd
tunderet aeris tumorem, & infernè illum, qua&longs;i forcipe
comprimens, con&longs;tringeret ad figuram conoidem eius partem
infimam. Re&longs;pondetur hoc fal&longs;um e&longs;&longs;e, quia vt ia&mtail;
demon&longs;tratum e&longs;t nunquam figura aeris per aquam
a&longs;cendentis acuminata in eius infima parte effici po&longs;
&longs;et, &longs;ed nece&longs;sè e&longs;t, vt ab impul&longs;u facto ab aqua gra
uiori ibidem excauetur ad modum &longs;cutellæ, & prop
ter occur&longs;um, & ob&longs;taculum aquæ &longs;upremæ dum aer
fluidus a&longs;cendit tumorem, & conuexitatem &longs;uper
nè acquirat.
Cùm verò idem author &longs;ubdit, quod
tur particula aliqua aeris cum oleo per aquam a&longs;cendente,
con&longs;tat quòd huiu&longs;modi aggregatum velociùs a&longs;cendit per
aquam.
leuitate po&longs;itiua, imò nego quod
&longs;ica, & &longs;olidaratio cur velociùs moueatur coniunctum il
lud ex oleo, & aere, quàm oleum &longs;olum. Et po&longs;tea:
aquam citiùs de&longs;cendendo expellere quoque citiùs oleum
&longs;ursùm cum nec maior moles &longs;it aquæ &longs;upra Primò aio nil referre an moles aquæ &longs;it maior,
aut minor re&longs;pectu olei, & aeris, &longs;ed &longs;ufficit vt gra
uitas &longs;pecifica aquæ, multò maior &longs;it re&longs;pectu aggre
gatiex aere, & oleo, quàm re&longs;pectu &longs;olius olei, ita
que in ca&longs;u no&longs;tro moles aquæ, &longs;iue magna, &longs;iue exi
gua, in fi&longs;tula pote&longs;t comparari cum oleo tantùm, vel
cum aggregato ex oleo, & aere; modò ex Archime
dis doctrina eadem aqua grauior e&longs;t &longs;pecie aggre
gato ex oleo & aere, quàm oleo &longs;olitario, & quò ma
ior fuerit differentia grauitatum &longs;pecificarum, tantò
maior, c&ecedil;teris paribus, e&longs;t velocitas mobilis in fluido,
& hinc
ab&longs;urda
nece&longs;&longs;itate mechanica contingere debent. Po&longs;tremæ
oppo&longs;itioni, vbi ait:
ex oleo, & aere e&longs;&longs;e aliquid leuius, quàm aquæ alterum
tum
te excedere, quàm oleum &longs;eorsùm &longs;umptum, & proindè ci
tiùs illius locum occupare velle; nam &longs;i non datur leuitas,
& particula aeris habet aliquid grauitatis potiùs ex illa, &
oleo factum estcorpus grauius, quàm est &longs;olum oleum. Et
hic nil aliud re&longs;pondere po&longs;&longs;um, ni&longs;i quòd huiu&longs;mo
di ratiocinia condonari po&longs;&longs;untijs, qui in doctrin&atail;
Archimedis minimè ver&longs;ati &longs;unt. Affertur enim, vt
ab&longs;urdum, quòd aggregatum ex oleo, & aere grauius
&longs;it abfolutè &longs;olo oleo, quod profectò non negatur, e&longs;t
enim veri&longs;&longs;imum, &longs;ed tamen animaduertendum e&longs;t,
quod licèt prædictum aggregatum ex oleo, & aer&etail;
grauitate ab&longs;oluta magis ponderet, quàm oleum per
&longs;e &longs;umptum, tamen &longs;i grauitas &longs;pecifica con&longs;idere
tur, erit aggregatum ex oleo, & aere minùs graue,
quàm oleum &longs;olum, quia nempè pondus aggregati
ex oleo & aere, minorem proportionem habet ad
grauitatem molis aqueæ ei æqualis, quàm pondus
&longs;olius olei habeat ad
oleo æqualis, &longs;cilicèt &longs;i aggregati ex oleo, & aere
grauitas &longs;ubdupla fuerit pondere molis aquæ &longs;ibi æ
qualis, pondus olei &longs;olius maius erit medietate
deris
impetu &longs;ursùm per expre&longs;&longs;ionem impellatur aggre
gatum ex oleo & aere à &longs;uperabundanti grauitate
aquæ circumfu&longs;æ, quæmaiori differentia &longs;pecificam
grauitatem eius &longs;uperat, quàm moueatur oleum &longs;ur
sùm extru&longs;um à pondere minùs excedenti eiu&longs;de&mtail;
aquæ ambientis. Et hoc quidem &longs;i ritè percipiatur,
tollentur, & euane&longs;cent omnes difficultates, quæ
contra prædictam doctrinam afferri po&longs;&longs;unt.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
Præter ea, quæ iam dicta &longs;unt affert idem author
alia experimenta ex quibus putat euidentèr deduci
po&longs;&longs;e exi&longs;tentiam leuitatis po&longs;itiuæ, quia inquit:
vt multotiès exiliat totus &longs;upra aquam ille igitur &longs;altus in
dicium e&longs;t impetus ab intrin&longs;eca leuitate facti, quia aqua
non pote&longs;t illud vltrà trudere quam &longs;it ip&longs;i opus vt locum
inferiorem occupet ni&longs;i ip&longs;a &longs;ursùm priùs feratur, quod e&longs;t
contra ip&longs;ius grauitatem.
menta
Au
pro leuitate
po&longs;itiua.
tiuam leui
tatem no&ntail;
dari.
ob impetum acqui&longs;itum in præcedenti motu, licèt per
extru&longs;ionem fiat.
PRo re&longs;pon&longs;ione ponamus cylindrum ligneum in
fundo aquæ. Dico quòd &longs;i id moueatur &longs;ursùm
ab intrinfeca vilenitatis, vel ab extru&longs;ione medij flui
di aquei, nece&longs;&longs;ariò velocitas eius dum a&longs;cendit
tinentèr
libet temporis in&longs;tanti, eadem virtus motiua, aut le
uitatis, aut externi impul&longs;us, quæ &longs;emper eadem, &
eiu&longs;dem energiæ e&longs;t, pariterque extru&longs;io à medio
fluido paritèr efficitur ab eadem virtute impul&longs;iua,
quæ e&longs;t differentia, vel exce&longs;&longs;us ponderis aquæ &longs;u
pra pondus ligni a&longs;cendentis, cùmque gradus velo
citatum à ligno acqui&longs;iti ob impul&longs;iones ei illatas
&longs;ubitò extinguantur, &longs;ed per&longs;euerent, vt dictum e&longs;t,
igitur &longs;ub&longs;equentes impul&longs;iones imprimuntur ei mo
bili non inerti, &longs;ed iam agitati à præcedentibus im
pre&longs;&longs;is velocitatibus, & proindè &longs;ucce&longs;&longs;iuo incre
mento augebitur gradus impetus eiu&longs;dem ligni
dentisIgitur mirum non e&longs;t, cylindrum ligneu&mtail;,
quando iam acqui&longs;iuit in&longs;ignem gradum impetus à
continuato impul&longs;u, & pre&longs;&longs;ione aquæ circumfu&longs;æ,
&longs;iuè ab interna eius leuitate po&longs;itiua, mirum,
non e&longs;t &longs;i ab aqua pro&longs;iliat, & &longs;ursùm extra aquæ &longs;u
perficiem propellatur: non igitur &longs;ignum
e&longs;t &longs;altus, & pro&longs;ilitio ligni ab aqua leuitatis eius
po&longs;itiuæ, quandoquidem prædictus &longs;altus effici po
te&longs;t in vtraque hypothe&longs;i, &longs;cilicèt &longs;iuè admittatur,
&longs;iuè negetur leuitas po&longs;itiua.
tiuam leui
tatem no&ntail;
dari.
Sed vt apertè inefficacia huius argumenti perci
piatur, po&longs;&longs;umus ij&longs;dem ferè verbis o&longs;tendere fal&longs;um
e&longs;&longs;e, quòd à leuitate po&longs;itiua lignum &longs;ursùm impel
latur, ait enim
aquæ ambientis, quia aqua non potest illud vltrà trude
re, quàm &longs;it ip&longs;i opus, vt locum inferiorem occupet. Di
cam ego eodem modo contra leuitatem po&longs;itiuam,
quod non deberet eius leuitas propellere
quàm requiritrecta di&longs;po&longs;itio, & con&longs;titutio natura
lis, quia nempè (&longs;ubijciam) non pote&longs;t leuitas
vltrà &longs;ubleuare, quàm &longs;it ip&longs;i opus vt locum &longs;uperi
orem in aqua occupet, cùm &longs;it nempè leuitas null&atail;
alia de cau&longs;a ligno communicata ab ip&longs;a natura, ni&longs;i
vt vna pars ligni demer&longs;a &longs;ub&longs;idat, altera verò &longs;upra
eam in aere emineat, non verò vt lignum integru&mtail;
extra aquam collocetin ip&longs;o nempè aere. igitur con
cedat aduer&longs;arius nece&longs;sè e&longs;t non expul&longs;um fui&longs;&longs;e li
gnum &longs;ursùm à leuitate po&longs;itiua &longs;upra
libellam, & hinc planè conijciet &longs;ui argumenti inef
ficaciam.
idip&longs;um ar
gumentum
contra ad
uer&longs;arium.
Pro&longs;equitur deindè:
pote&longs;t inueniri, quæ pars aquæ illum &longs;ursùm trudat non illa,
quæ in fundo, &longs;uppono enim perfectum cylindrum phy&longs;icè,
& fundum va&longs;is exactè
aquæ interlabi pos&longs;it quamdiù cylinder vi detinetur ibi.
tiuam leui
tatem no&ntail;
dari.
Et hinc apertè conijcio non benè perceptum fui&longs;
&longs;e modum quomodò medium fluidum &longs;ursùm impel
lat
operæpretium erit apertè, & di&longs;tinctè hoc declarare.
rijs &longs;ursùm, & deorsùm &longs;imul tempore moueri que
ant, numquam lignum in aqua a&longs;cendet.
SIt vas ABCD aqua plenum i&ntail;
cuius fundo apponatur pri&longs;ma
ligneum EFGB hìc ade&longs;t aqua li
gno incumbens AEFH, atque aqua
collateralis HFID, quæ comprimit
&longs;ubiectum aqueum pri&longs;ma FICG,
Dico primò, quod &longs;uperincumbens
aqua AEFH nequaquàm &longs;ursùm impellit &longs;ubiectum
lignum, imò id comprimit: neque præterea &longs;uperna
collateralis aqua HFID prædictum lignum eleuat,
&longs;ed tantummodò æquilibratur cum collaterali aqua
AEFH. Tantummodò ad rem no&longs;tram facit aqu&atail;,
quæ ad latus ip&longs;ius ligni apponitur, FGCI, & hæc
&longs;emper &longs;ubleuare pote&longs;t lignum BF, ni&longs;i habuerit
duas conditiones, primò vt aqua FC de&longs;cender&etail;
deorsùm valeat, &longs;ecundò vt eodem tempore eadem
aqua lignum GE impellere &longs;ursùm po&longs;&longs;it. At quan
dò huiu&longs;modi motus contrarij ob aliquod impedi
mentum fieri &longs;imùl
&longs;cet in fundo ip&longs;ius aquæ, quia nimirum locum non
habet libræ, aut &longs;iphonis operatio. Hoc autem &longs;ic
per&longs;picuum fiet: &longs;upponamus ba&longs;im lignei pri&longs;matis
BG perfectè, & exqui&longs;itè tangere fundum va&longs;is BC,
&longs;cilicèt &longs;i amb&ecedil; &longs;uperficies fuerint explanatæ, & læ
uigatæ, tunc profectò aqua FC, licèt grauior &longs;it ip&longs;o
ligno minimè excurrere poterit deorsùm cùm no&ntail;
ad&longs;it aditus inter ligni ba&longs;im BG, &
nititur igitur atque &longs;u&longs;tentatur maius pondus aqu&ecedil;
FC à &longs;oliditate fundi GC eiu&longs;dem putei, quare ne
ce&longs;sè e&longs;t vt
&longs;cat, & proindè lignum EG non a&longs;cendet &longs;ursùm, nec
expelletur ab aqua collaterali quie&longs;cente, quaprop
ter habebimus libram BC non quidem
circa centrum G, &longs;ed &longs;tabilem, & firmam, cum in ea
minimè contrarij motus
&longs;us
demirum non e&longs;t lignum GE è fundo va&longs;is non
dere
tiuam leui
tatem no&ntail;
dari.
ter alis aquæ, quæ de&longs;cendere pos&longs;it, & præterea mo
tu reflexo infimam ligni ba&longs;im &longs;ursùm
impellat.
PRæterea dico, quòd non &longs;ufficit vt aqua collate
ralis FC &longs;olummodò moueri deorsùm po&longs;&longs;it,
&longs;ed oportet pr&ecedil;tere a vt reflectatur &longs;ursùm infrà
GE ad hoc vtlignum è fundo va&longs;is a&longs;cendat, quod
con&longs;tat hac experientia: Perforetur
tunc profectò aqua FG, & ei &longs;uperincumbens FD
profluet
proindè
turato foramine GC, vt aqua fluere, & in&longs;inuari po&longs;
&longs;it inter pri&longs;matis ba&longs;im BG, & fundum putei, & tune
a&longs;cendet lignum, &longs;i nimirùm concipiatur putei fun
dum magis depre&longs;&longs;um vt e&longs;t MK, & aqua FC proflu
ens repleuerit &longs;patium BMLG ef
ficietur &longs;ipho DKMA cuius vn&atail;
parsaquea HK grauìor e&longs;t reliqua
parte AL, & proindè
compre&longs;&longs;iuam habebit aqua HK,
quàm aqua, &
terea deprimetur de&longs;cendendo a
qua FGK eleuabiturque motu
cum ligno incumbente, nece&longs;&longs;ariò igitur requiruntur
hi duo motus contrarij de&longs;cen&longs;us aquæ grauioris FK,
& a&longs;cen&longs;us aquæ LB vt lignum eleuari po&longs;&longs;it. Hinc
colligitur, quod vis motiua, quæ impellit ligneu&mtail;
pri&longs;ma GE &longs;ursùm e&longs;t profectò grauitas aquæ colla
teralis FC, &longs;ed quatenùs moueri, atque de&longs;cendere
pote&longs;t, & præterea quatenus &longs;ursùm impellere va
let aquam BL, & huic impul&longs;ui cedere debet minor
vis deficientis grauitatis ligni EG, & hæc e&longs;t legiti
ma, & adæquata cau&longs;a, quare lignum à maiori im
pul&longs;u aquæ collateralis prementis &longs;ursùm impelli
tur ab aqua, quæ infra eius ba&longs;im in&longs;inuatur.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
His declaratis accedamus iam ad difficultates ad
ner&longs;arij, in quibus &longs;upponit, quòd dum ligneus cy
lindrus GE exqui&longs;ito, & immediato contactu fundo
va&longs;is adhæret, ip&longs;umque veluti exo&longs;culatur, licèt vas
repletum aqua fuerit, lignum &longs;ponte &longs;ua, & vi eius
leuitatis &longs;ursùm a&longs;cendere deberet. Sed quid facies,
&longs;i experimentum huic a&longs;&longs;ertioni refragatur? Et pro
cùl dubio &longs;i experimentum ita &longs;e haberet, vt ab ip&longs;o
refertur, &longs;cilicèt &longs;i cylindrus ligneus GE exqui&longs;itè
tangens &longs;uperficiem fundi va&longs;is BG complanatam,
& l&ecedil;uigatam, e&longs;&longs;etque vas aqua repletum, & nihilo
minus lignum &longs;ursùm a&longs;cenderet, nece&longs;&longs;ariò a&longs;&longs;erere
teneremur, & confiteri, lignum, non à principio ex
trin&longs;eco per extru&longs;ionem, &longs;ed à vinaturali leuitatis
eius a&longs;cendere.
tum fal&longs;um
aduer&longs;arij
pro leuitate
po&longs;itiua.
&longs;ed quia extru&longs;io à medio fluido grauiori fieri non po
test, lignum in aquæ fundo quie&longs;cere.
VErùm quia lignum EG in aqua demer&longs;um non
a&longs;cendit è fundo va&longs;is cui adhæret, imò ibidem
&longs;i&longs;titur, & quie&longs;cit, igitur
ginata, quæ leuitas po&longs;itiua vocatur. E contrà quo
tie&longs;cumque fieri, & exerceri pote&longs;t extru&longs;io medij
fluidi, ide&longs;t quotie&longs;cumque fluidum grauius fluer&etail;
pote&longs;t, & in&longs;inuari infra cylindrum ligneum, &longs;emper
&longs;ub&longs;equitur effectus a&longs;cen&longs;us illius, at quando (vt
in no&longs;tro ca&longs;u accidit) aqua &longs;ubingredi inter duas
&longs;uperficies ligni, & fundi va&longs;is non pote&longs;t ob exqui
&longs;itum contactum, & congruentiam, tunc non &longs;equi
tur effectus a&longs;cen&longs;us eiu&longs;dem ligni, veluti in bilance
pondus centum librarum non &longs;ubleuabit contrapo&longs;i
tum pondus vnciale quotie&longs;cumque illud impeditur,
vt ne queat deorsùm deprimi, igitur vera cau&longs;a
&longs;us
autem leuitas po&longs;itiua in ligno inexi&longs;tens.
tiuam leui
tatem non
dari.
Porrò hoc experti &longs;umus in Academia Experimen
tali Medicea. Po&longs;uimus pilam li
gneam G in fundo va&longs;is ABCD,
quæ tangebat
uitatis he mi&longs;phæricæ EIF in fun
do va&longs;is excauatæ, po&longs;teà reple
uimus vas hydrargyro v&longs;que ad
&longs;ummitatem AD, nec tamen li
gnea pila G fundum reliquit a
&longs;cendendo &longs;ursùm; &
quòd prædicta pila non arctè orificio va&longs;is adhære
bat, & colligabatur, &longs;ed potiùs facillimè digitis di
moueri contorquerique poterat, vnde conijcitur,
quàm debili nexu fundum, aut orificium acumi
natum EF quia po&longs;te à in&longs;ignis Peripateticus
&longs;u&longs;picabatur, quòd præcipua cau&longs;a detinens
pilam demer&longs;am infra hydrargyrum in fundo va&longs;is
erat timor, & abominium vacui, quod effici debui&longs;
&longs;et in illo &longs;patio quotie&longs;cumque pila &longs;ursùm a&longs;cen
deret; proptereà, vt petijt prædictus Philo&longs;ophus
perforauimus fundum va&longs;is IH, vt nimirùm è part&etail;
&longs;ubiecta aer &longs;uccedere po&longs;&longs;et ad replendum
& &longs;ie leuitas po&longs;itiua ligni G ab&longs;que vacui periculo
commodè &longs;ursùm a&longs;cendere po&longs;&longs;et; hac præparatione
facta, illa lignea pila fundum non dereliquit, nec &longs;ur
sùm a&longs;cendit; nec paritèr a&longs;cendit po&longs;tquam
Hocclu&longs;um denuò fuit, & cauitas &longs;ubiecta EIF, &
&longs;uprema AED repleta hydrargyro fuit. Vnde dedu
cere po&longs;&longs;umus pilam non à po&longs;itiua leuitate eleuari,
&longs;ed potiùs ab expre&longs;&longs;ione ambientis fluidi quotie&longs;
cumque excurrere pote&longs;t ab&longs;que impedimento in
fra &longs;uperficiem eiu&longs;dem pilæ.
tiuam leui
tatem no&ntail;
dari.
Perpendamus tandem po&longs;trema verba eiu&longs;de&mtail;
Authoris, qui ait:
va&longs;is e&longs;&longs;et foramen amplum, angu&longs;tius tamen cylindro, &
occlu&longs;um, quod eodem momento aperiretur quo manuseleuat
virgam? certè enim aqua efflueret deorsùm, & tamen cy
lindraceum lignum illud tenderet &longs;ursùm. Agno&longs;cant ergò
in ligno illo leuitatem aliquam, quæ impetum producendo
&longs;ursùm versùs priùs natura mouet, ac pellit
&longs;aest vt aqua corpus fluidum it a illi cedat, vt &longs;ubintret in
illius locum, ne detur vacuum, eamque non exercere gra
uitatem actu, &longs;ed &longs;uperiores quidem aquæ partes impelli à
cylindro ligneo, & cedere illi locum digrediendo ad latera,
vt locum illarum partium impleant, quæ infernè
in locum cylindri. Et hic nil aliud re&longs;pondere po&longs;&longs;u&mtail;
ni&longs;i mirari confidentiam, &longs;ecuritatemque qua a&longs;&longs;eri
tur experientia non &longs;icuti reuera &longs;e habet, vtque à
quolibet comprobari pote&longs;t, &longs;ed veluti præiudica
ta opinio eis per&longs;ua&longs;erat.
ab eodé au
thore allat
tiuam leui
taem no&ntail;
dari.
Sit igitur vas ABCD in cuius
do
&longs;it po&longs;tea ligneus cylindrus FE,
cuius ba&longs;is HE paulò amplior &longs;it
foramine va&longs;is, vt nimirum po&longs;&longs;it
ip&longs;um præcisè occludere, ob&longs;true
reque &longs;implici contactu; repleatur
po&longs;tea vas aqua
ponit aduer&longs;arius, quòd cylindrus
FE non po&longs;&longs;it in fundo va&longs;is deti
neri, ni&longs;i
ga quadam ferrea ML præterea
ait, quòd &longs;i occlu&longs;o infimo foramine BC,
mento temporis recludatur os infimum, remoueatur
que virga ML, fore vt aqua exeat per infimum os
BC, & lignum FE a&longs;cendat &longs;ursùm,
&longs;e,
ligni. Et hic primò ob&longs;eruo contra aduer&longs;arij a&longs;&longs;er
tionem, quòd &longs;i ba&longs;is cylindri HE zona circularis
præcisè tangat, & exo&longs;culetur perimetrum orificij
putei BC, tunc non requiritur epi&longs;tomium vt aqu&atail;
è va&longs;e non effluat, neque requiritur impul&longs;us virgæ
LM, vt prohibeatur a&longs;cen&longs;us cylindri FE è fundo va
&longs;is, &longs;ed ibidem quie&longs;cet, veluti &longs;i tenacitèr colliga
tus e&longs;&longs;et ab illo contactu &longs;implici. Imò, quod magis
mirere, &longs;i infima zona ba&longs;is HE ip&longs;ius cylindri lignei
non perfectè congrueret; neque compleret vndique
tangendo orificium infimum BC, &longs;ed per rimulas,
vel angulos aliquos aqua deor&longs;um efflueret, tunc
neque opus haberemus virga impellente ML vt li
gnum prædictum in fundo va&longs;is retineretur, &longs;ed
te
sùm trahere prædictum
tunc nedùm vt eius ba&longs;im diuelleret à contactu orifi
cij BC, &longs;ed etiam po&longs;t eius &longs;eparationem à fundo per
aliquod exiguum interuallum, aliqua renitentia per
&longs;entiretur, et vis aliqua trahens requireretur, aliàs
&longs;ponte &longs;ua lignum ip&longs;um decideret denuò ad occlu
dendum va&longs;is orificium BC, Hinc videat aduer&longs;arius
quàm iure exclamet, cùm ait:
leuitatem aliquam, &c.
oppo&longs;itum o&longs;tendat, iurè po&longs;&longs;emus ei reddere verba
&longs;ua: Agno&longs;catergo in ligno nullam leuitatem ine&longs;&longs;e.
tiuam leui
tatem no&ntail;
dari.
ponderis columnæ aqueæ v&longs;que ad &longs;upremam eius li
bellam exten&longs;æ.
ET profectò ij, qui ver&longs;ati
&longs;unt in hac doctrina hydro
&longs;tatica Archimedea optimè
runt
dicto va&longs;e aqua pleno aperitur
os in eius fundo BC, tunc ade&longs;t
cylindrus aqueus IBCK, qui
primit
dere &longs;upra quodlibet corpus im-
pediens exitum, ac fluxum prædictæ aquæ, quod
libet
infimum va&longs;is orificium BC, percipiet enim
&longs;ionem
uitas cylindri aquei prædicti, & hoc experitur ne
dùm quando palma manus vetat omninò effluxu&mtail;
aquæ, quam &longs;i aliquanti&longs;per manus &longs;ubleuetur, vt
po&longs;&longs;it aqua effluere. Hoc præmi&longs;&longs;o.
tiuam leui
tatem no&ntail;
dari.
aqua nullam po&longs;itiuam leuitatem exercere.
SVpponamus cum Aduer
&longs;ario (&longs;i po&longs;&longs;ibile e&longs;t) cy
lindrum ligneum FE &longs;ub a
qua
ac tendere &longs;ursùm intrin&longs;eca
vi &longs;u&ecedil; leuitatis
lateralis per rimulas infimas
H & E effluit è va&longs;e: Sit ve
rò energia leuitatis ligni (vt
æquum e&longs;t) certæ, & deter
minatæ men&longs;uræ, quæ expri
mi poterit à pondere corporis P
radiorum æqualium; Huic vi leuitatis aduer&longs;atur
trario
IFGK, quod paritèr intelligatur termino M eiu&longs;dem
libræ &longs;u&longs;pen&longs;um. Quoniam vis leuitatis cylindri li-
gnei FE in aqua demer&longs;i &longs;emper eadem e&longs;t, nec po
te&longs;t vnquam diminui, cùm &longs;it æqualis vi illius ponde
ris, quod &longs;ufficit ad prohibendum
ligno FE (vt con&longs;tat ex Archimede) & è contrà pon
dus incumbentis cylindri aquei IKGF pote&longs;t &longs;ucce&longs;
&longs;iuè diminui in infinitum prout eius altitudo IF dimi
nuta fuerit, &longs;ublata nimirum aqna è va&longs;e ABD. fiat
igitur vis ponderis aquæ IG minor energia leuitatis
ligni FE, &longs;cilicèt minor &longs;it pondere P, quia verò mi
nor vis &longs;uperari à maiori debet, igitur nece&longs;&longs;ariò
pondus P de primet radium libræ NO, &longs;uperabitque
re&longs;i&longs;tentiam diminutæ aquæ IG &longs;u&longs;pen&longs;æ in altera li
bræ extremitate M, &longs;cilicèt lignum FE (quod tange
re orificium va&longs;is HE &longs;upponebatur) &longs;ursùm a&longs;cen
det in ip&longs;a aqua vi maioris &longs;uæ leuitatis, &longs;ed hoc e&longs;t
fal&longs;um, & contra &longs;en&longs;us euidentiam, numquam enim
prædictus cylindius ligneus fundum de&longs;erit, nec &longs;ur
sùm a&longs;cendit; &longs;i tamen &longs;emper orificio BC in&longs;i&longs;tat,
nec incutiatur vt ad latus fundi ba&longs;is transferatur, vbi
maior eius ba&longs;is pars in&longs;i&longs;tit fundo &longs;tabili putei, vel
cylindrus ip&longs;e tran&longs;uersè fle ctatur. Igitur verum
e&longs;t lignum FE exercere nè minimum gradum impe
tus leuitatis.
tiuam leui
tatem no&ntail;
dari.
fluido lib.
1.
prop.
6.
II&longs;dem po&longs;itis intelligatur præterea quòd vis leui
tatis prædicti ligni, &longs;cilicèt pondus P æqualis &longs;it
energi&ecedil; ponderis incumbentis cylindri aquei IG:
tunc quælibet minima vis addita ponderi P deberet
eleuare v&longs;que ad &longs;upremæ aquæ libellam cylindrum
FE, quod &longs;imilitèr e&longs;t fal&longs;um, debet enim &longs;uperad
di ponderi P aliud pondus R æquale ponderi lignei
cylindri FE.
tiuam leui
tatem no&ntail;
dari.
TAndem (in eadem hypothe&longs;i) &longs;it vis leuitatis
po&longs;itiuæ ligni FE minor vi ponderis &longs;uperin
cumbentis cylindri aquei IG. (& maioris claritatis
gratia) &longs;upponamus pondus P æquale exce&longs;&longs;ui gra
uitatis aqueæ molis cylindro FE æqualis &longs;upra pon
dus cylindri lignei prædicti;
quia ex Archimede lignu&mtail;
FE tanto impetu in aqua
dit
uitatis pr&ecedil;dicti exce&longs;&longs;us. Mo
dò
maius e&longs;t pondere P, &longs;cilicèt
vi leuitatis ligni FE, igitur
prædicta leuitas à pondere
aquæ incumbentis &longs;uperabi
tur vtpotè à maiori virtut&etail;,
& proindè lignum detinebitur in fundo va&longs;is, nec a
&longs;cendet. Si po&longs;tea eidem termino libræ O &longs;u&longs;penda
tur aliud pondus Q æquale exce&longs;&longs;ui ponderis aquæ
IG &longs;upra grauitatem P, patet quod vt &longs;uperetur im
pedimentum, quod reperit lignum FE ip&longs;umque
&longs;cendere
rentia ponderis aquæ prementis IG, & leuitatis li
gni FE. Sed hoc e&longs;t fal&longs;um, quandoquidem pr&ecedil;ter
pondus Q requiritur etiam pondus R æquale pon
deri ab&longs;oluto cylindri lignei FE, & in&longs;uper requiri
tur pondus P quod vnà cum Q æquantur ponderi a
quæ IG. Quapropter adeò fal&longs;um e&longs;t ligneum cylin
drum FE virtute propriæ leuitatis vim &longs;ursùm exer
cere in aqua, vt potiùs deorsùm premat, vt corpus
graue.
tiuam leui
tatem no&ntail;
dari.
Et hactenùs comparauimus vires comprimentes
grauitatis &longs;uperincumbentis cylindri aquei IG & le
uitatis cylindri lignei FE, re&longs;tat modò vt paritèr
paremus
videndum qua velocitate lignum FE &longs;ursùm à vile
uitatis impellatur re&longs;pectu contrariæ celeritatis, qua
aqua ABD per infimum foramen BC effluit: eo pro
pemodum modo, quo pi&longs;ces contra cur&longs;um alicuius
fluentis fluminis mouentur, &longs;i enim pi&longs;cis velociùs
natat, quàm aqua contrario cur&longs;u currat, procùl du
bio pi&longs;cis re&longs;pectu fundi, & ripæ, & &longs;patij mundani
contra a quæ cur&longs;um reuera excurret aliquanti&longs;per,
quòd &longs;i prædictæ duæ contrariæ velocitates æquales
fuerint, licèt reuera pi&longs;cis agitetur, commoueatur
que &longs;emper in eodem &longs;itu mundani &longs;patij per&longs;i&longs;tet, &longs;i
tandèm velocitas pi&longs;cis minor fuerit celeritate con
traria fluentis, licèt pi&longs;cis natet, & verè anterius ex-
currat in aqua, nihilominùs retrocedet re&longs;pectu &longs;pa
tij mundani, &longs;ed cur&longs;u magis tardo, & lento, quà&mtail;
flumen mouetur.
tiuam leui
tatem no&ntail;
dari.
o&longs;tenditur.
IT aque eodem modo in va&longs;e ABC aqua pleno, &
infernè perforato in B intelligantur demer&longs;i glo
buli aerei, &longs;ed perpendiculariter imminentes &longs;uper
infimum foramen B, &longs;cilicèt intra cylindrum a queum
DBE, qui ad modum fluminis intra
aquam va&longs;is repleti defluit egre
diturque per foramen B. Et &longs;uppo
namus maiori celeritate, &longs;cilicèt
dupla, aquam fluere à D v&longs;que ad
B, quàm globus aereus G mouea
tur &longs;ur sùm translatus à naturali eius
leuitate, itaut, quando aqua prædi
cti cylindri fluentis
GI debeat aereus globus G &longs;ursùm impelli, &
&longs;igere
quod medium fluidum in quo globus aereus G
dit
flumen, igitur quando aqua &longs;patium GI tran&longs;egerit,
globus aereus contrario cur&longs;u medietatem itineris
IH perficiet, qua proptèr ex hi&longs;ce duabus contrarijs
velocitatibus re&longs;ultabit tertia qu&ecedil; dam celeritas, quæ
æqualis erit differentiæ prædictarum oppo&longs;itarum
celeritatum, & ideò aer G de&longs;cendet duplo tardiùs
aqua ambiente; Quòd verò hoc &longs;it fal&longs;um, experien
tia ip&longs;a docet &longs;inimitùm aqua DE atro colore tinga
tur, vel di&longs;per&longs;o puluere terre&longs;tri pauli&longs;per turbida
reddatur, tunc procùl dubio particulæ illæ areno&longs;æ
graues, aut ob exiguitatem in ip&longs;a aqua dum quie&longs;cit
non de&longs;cendunt, vellento motu deorsùm feruntur a
vi maioris grauitatis igitur quando aqua deor
sùm fluit, videtur impo&longs;&longs;ibile vt grauiores particulæ
areno&longs;æ minori velocitate transferantur deorsù&mtail;,
quàm aqua ip&longs;a in qua degunt, quare bulla aerea G
quæ vt leuis &longs;ursùm a&longs;cendere &longs;upponitur, non po&longs;&longs;et
pari velocitate &longs;imul
bidæ deorsùm de&longs;cendere, &longs;ed hoc e&longs;t fal&longs;um, cum
ab&longs;que vlla differentia velocitatis deorsùm feran
tur vnà cum aqua turbida cylindri fluentis, igitur ve
rum non e&longs;t, quòd aer G moueatur &longs;ursùm à vi natu
ralis leuitatis eius translatus, cùm
uera aer G principium motiuum leuitatis in &longs;e habe
ret non po&longs;&longs;et vllo pacto in aqua ip&longs;um
tiuam leui
tatem no&ntail;
dari.
sùm impelli.
EContrà quandò globus aereus G nullam pror
sùs leuitatem haberet, & &longs;olummodò per ex
tru&longs;ionem factam à grauitate fluidi ambientis eleua-
retur, nullo pacto in tali ca&longs;u po&longs;&longs;et aqua ab inferiori
&longs;itu H &longs;ursùm impellere aerem G, propterea quod
aqua DB cogitur excurrere deorsùm per va&longs;is aper
tum foramen B, & ideò non pote&longs;t motu reflexo &longs;ur
sùm impellere aerem G. igitur nece&longs;sè e&longs;t vt globus
aereus G deferatur à vi fluentis aquæ, vt ip&longs;a experi
entia o&longs;tendit. Vnde colligitur, quod nullum ex ad
ductis, & excogitatis
cere per&longs;uadereque pote&longs;t exi&longs;tentiam leuitatis po
&longs;itiuæ, & è contrà &longs;emper multò magis confirmatur,
demon&longs;traturque eius non exi&longs;tentia, quaproptèr fa
tendum e&longs;t corpora, quæ leuia appellantur, &longs;ursùm
impelli per extru&longs;ionem à fluidis ambientibus gra
uioribus.
tiuam leui
tatem no&ntail;
dari.
Sed coronidis loco afferam demon&longs;trationem à
me excogitatam, ab&longs;olutè non dari in natura
leuitatem, vtque commodiùs hoc efficiam primò
nonnullas &longs;uppo&longs;itiones &longs;en&longs;ui manife&longs;tas
& deinceps aliqua lemmata ex principijs mechani
cis de&longs;umpta demon&longs;trabo.
ET primò noto, quòd corpus &longs;iue &longs;imilare, & ho
mogeneum, &longs;iue heterogeneum, tunc vocatur
exi&longs;timaturque rarius &longs;pecie, quàm aliud, quando
&longs;nmptis æqualibus molibus eorumdem illud
copiam materialis &longs;ub&longs;tantiæ corporeæ, & &longs;en&longs;ibi
lis comprehendit in eodem &longs;patio, quàm i&longs;tud, quòd
profectò concipi pote&longs;t, &longs;i intelligatur mino: copia
materiei &longs;en&longs;ibilis in maiori &longs;patio corporis rarioris
exten&longs;a per interpo&longs;itionem inanium &longs;patiolorum.
tiuam leui
tatem no&ntail;
dari.
SI verò moles æquales, &longs;iuè inæquales non con
&longs;iderentur, & raritas in vna earum
ior fuerit raritate alterius, tunc dicetur illa raritas
ab&longs;olutè maior reliqua, &longs;iuè exce&longs;&longs;us raritatis exten
&longs;iuè in maiori mole multiplicetur, &longs;iuè inten&longs;iuè i&ntail;
minori mole augeatur.
PRæterea &longs;uppono ex Ari&longs;totele raritatem alicu
ius corporis multiplicari, & augeri in infinitum
po&longs;&longs;e prout &longs;ub&longs;tantialis moles corporea, quæ in eo
dem &longs;patio contine batur, &longs;ucce&longs;&longs;iuè imminuitur, &
po&longs;t diminutionem extenditur expanditurque vt re
pleat idip&longs;um &longs;patium, quod prius à non imminuto
corpore occupabatur.
SVppono præterea, quòd vis quæ requiritur ad
&longs;eparanda duo corpora &longs;e mutuò tangentia im
mediato, & exqui&longs;ito contactu, (quod accidit
do
l&ecedil;uigatæ) non e&longs;t infinita, &longs;ed determinata, quia ni
mirùm &longs;en&longs;us euidentia o&longs;tendit, quod &longs;i potenti&atail;
motiua augeatur &longs;emper magis, ac magisne dùm cor
pora &longs;e mutuò tangentia &longs;eparantur, & ab inuicem
diuelluntur, &longs;ed etiam corpora illa, quæ continu&atail;
cen&longs;entur, vt e&longs;t columna marmorea, vel virga me
tallica, tandèm à vi trahente di&longs;trahitur, euelliturque
directo motu vna pars ab altera, quæ tenaciori glu
tine vinculoque vniuntur, quàm illa duo corpora &longs;e
mutuò tangentia, & &longs;implici contactu vnita.
tiuam leui
tatem no&ntail;
dari.
pora &longs;e mutuò tangentia, pos&longs;ibile e&longs;t mediante libra
men&longs;urari hac ratione.
SIt cylindrus CAB cuius ba&longs;is
AB perfecti&longs;&longs;imè explanata,
& l&ecedil;uigata congruat exo&longs;cule
turque
pari diligentia complanatam, &
l&ecedil;uigatam, & cautionis grati&atail;,
vttuti omninò &longs;imus aerem am
bientem penetrare, ac ingredi non po&longs;&longs;e inter præ
dictas duas complanatas &longs;uperficies po&longs;&longs;ent colliga
ri tùm cylindro, tùm pauimento duæ laminæ vitreæ
AB, & DE, aut alterius &longs;ub&longs;tantiæ duri&longs;&longs;imæ, quæ in
&longs;tar &longs;peculi explanatæ, & l&ecedil;uigatæ &longs;int; po&longs;teà com
primantur, vna, &longs;uper alteram intrà aliquod fluidum
vi&longs;ibile veluti e&longs;t aqua, vel hydrargyrum, vt nimi
rùm vi&longs;u con&longs;tet nihil omninò intercipi inter prædi
ctas duas &longs;uperficies, dum nimirùm vna earum trahi
tur, vt ab altera diuellatur. Colligetur po&longs;tea cylin-
dri extremitas C termino H trochleæ, vel libræ HK
radiorum æqualium, cuius centrum I, & reliquo ex
tremo K &longs;u&longs;pendatur pondus N æquale grauitati ab
&longs;olutæ cylindri AC. profectò manife&longs;tum e&longs;t &longs;en&longs;ui
non &longs;ufficere pondus N ad &longs;eparandum, & diuellen
dum cylindrum AC à pauimento DE, &longs;ed requiritur
aliqua vis multò maior illa, quæ reperiri
poterit, non enim e&longs;t infinita, igitur &longs;i addatur con
tinentèr pondus ponderi termino K
mus ad pondus aliquod, vt e&longs;t O à quo cvlindrus CA
directa tractione diuelli à pauimento poterit. Quia
verò duo pondera N, & O directè diuellunt
AC, & hic re&longs;i&longs;tit &longs;eparationi duabus viribus, pro
prij &longs;cilicèt ponderis æqualis nempè ip&longs;i N, & vi
contactus, & repugnantiæ ad vacuum igitur remanens vis ponderis O æqualis erit, & aucta
&longs;uperabit vim connexionis duarum &longs;uperficierum &longs;e
mutuò exqui&longs;itè tangentium.
tiuam leui
tatem no&ntail;
dari.
Non defuit tamen qui hunc progre&longs;&longs;um in
reuocare au&longs;us &longs;it, & &longs;ic inutilem, ac inefficacem vni
uer&longs;am demon&longs;trationem &longs;ub&longs;equentem redder&etail;,
qu&ecedil; in prædicta experimentali operatione fundatur. Nucleus difficultatis talis e&longs;t, non videri po&longs;&longs;ibil&etail;
columnam AC vnquam po&longs;&longs;e motu tàm directo &longs;ur
sùm trahi, nec libra, nec trochlea itaut non flectatur
inclineturque, & hoc (inquiunt) nullo pacto huma
na diligentia a&longs;&longs;e qui po&longs;&longs;e; imò a&longs;&longs;erere au&longs;i &longs;unt,
quòd &longs;i funis HC directè traheretur perpendiculari
tèr nimirùm ad planum horizontis, & ad ba&longs;im DE
nunquam à quacumque vi diuelli columna po&longs;
&longs;et, nec&longs;uperari re&longs;i&longs;tentia ad vacuum, quod profe
ctò &longs;ub&longs;equeretur in actu violento &longs;eparationis &longs;u
perficierum AB, & DE. Si verò (aiunt) applicetur
vis tran&longs;uer&longs;alitèr, itaut latus BC columnæ angulum
con&longs;tituat cum linea tractionis, tunc facilè &longs;eparari,
ac diuelli ab inuicem poteruut prædict&ecedil; &longs;uperficies.
tiuam leui
tatem no&ntail;
dari.
Huiu&longs;modi cauillo&longs;a re&longs;pon&longs;io condonari pote&longs;t
ijs Philo&longs;ophis, qui mathematices imperiti &longs;unt.
ta, & totalis, quæ requiritur ad &longs;eparationem illam di
rectam, & ad korizontem perpendicularem efficien
dam ip&longs;ius columnæ à fundo va&longs;is, quotie&longs;cum
que constet quanta vis requiritur adeam
&longs;eparandam impetu obliquo ab
eodem &longs;olo.
SIt denuò cylindrus AC
cuius ba&longs;is AB l&ecedil;uigati&longs;
&longs;ima,
ficiem pauimenti DE paritèr
l&ecedil;uigatam tangat, & vis M
tran&longs;uer&longs;ali directione CM
perpendiculariad CB trahat
terminum columnæ C, & va
leat huiu&longs;modi potentia diuellere &longs;uperficiem AB
ab ip&longs;o
ponderi R, &
metri AB ba&longs;is prædictæ columnæ ad &longs;uam altitudi
nem BC, eamdem habeat pondus R ad aliud pondus
S. oftendendum modò e&longs;t vim ponderis S æqualem
e&longs;&longs;e totali re&longs;i&longs;tentiæ contactus duarum
&longs;uperficierum, &longs;eù potiùs æqualem e&longs;&longs;e vi, qua vacui
re&longs;i&longs;tentia &longs;uperatur, vel potiùs pondus S &longs;ufficer&etail;
ad diuellendam columnam à pauimento directa tra
ctione, &longs;cilicèt detinendo, &
&longs;emper æquidi&longs;tantem plano ba&longs;is DE. Quia in actu
&longs;eparationis &longs;uperficiei AB à pauimento debet pun
ctum eius B contingere, & inniti ip&longs;i pauimento, &
angularitèr &longs;ubleuari terminus oppo&longs;itus A, vnà cum
tota ba&longs;is &longs;uperficie AB, efficiendo nimirùm
cum pauimenti plano DE; & hic ob&longs;eruari debent
loca vbi duæ vires applicantur, &longs;cilicèt re&longs;i&longs;tentia, &
eius, quæ eam &longs;uperat, & per quam directionem tra
hunt & vim exercent; & pater, quòd re&longs;i&longs;tentia i&ntail;
omnibus
que
planum &longs;ubiectum, quæ cum eo coniunguntur colli
ganturque; è contrà vis mouens M vectem CB adhi
bet circa centrum firmum B, & quia vniuer&longs;a re&longs;i
&longs;tentia vniformiter di&longs;tribuitur per totam ba&longs;is &longs;u
perficiem AB, reducitur, & perindè re&longs;i&longs;tit ac &longs;i i&ntail;
centro aggregati prædictarum fibrarum collocat&atail;
e&longs;&longs;et, centrum verò omnium fibrarum prædictarum
idem e&longs;t ac centrum I, quod e&longs;t centrum eiu&longs;dem ba
&longs;is; quaproptèr maximus conatus vniuer&longs;æ re&longs;i&longs;ten-
tiæ ad diuul&longs;ionem exercetur in centro I circuli AB. Habebimus igitur vectem inflexum CBI in quo vis
in I, & fulcimentum, &longs;eù centrum reuolutionis vectis
CBI e&longs;t punctum B quod fixum per&longs;euerat dum cir
ca ip&longs;um motus, & reuolutiones partium vectis
Quaproptèr, iuxtà leges Mechanices, re&longs;i&longs;tentia to
talis ad diuul&longs;ionem, & &longs;eparationem &longs;uperficiei AB
ab ip&longs;o pauimento ad vim
portionem habebit, quam vectis longitudo CB ad
oppo&longs;itam eius portionem BI, &longs;cilicèt habebit eam
dem proportionem. quam pondus S habet ad pondus
R. Verùm pondus R æquale erat potentiæ M. igitur
pondus S æquale erit re&longs;i&longs;tenti&ecedil; ab&longs;olutæ, & totali,
quam exercet &longs;uperficies AB quando diuelli, & &longs;e
parari debet à &longs;uperficie paui Hinc deducitur quòd &longs;i
dus O propo&longs;itionis 89. di
uellit columnam à pauimento
directione, & impetu tran&longs;
uer&longs;ali, & perpendiculari ad
latus column&ecedil;, poterit nihilo
minùs indagari
&longs;oluta, & totalis contiguita
tis, vel repugnantiæ ad vacuum earumdem &longs;uperfi
cierum, eritque talis vis ab&longs;oluta tantomaior pon
dere O, quantò altitudo columnæ CB maior e&longs;t &longs;e
mi&longs;&longs;e diametri AB, & &longs;ic &longs;ivis transuer&longs;alitèr colum
nam diuellens æqualis e&longs;&longs;et ponderi trium librarum
v. g. & altitudo columnæ CB decies maior radio ba
&longs;is, tunc totalis re&longs;i&longs;tentia prædictæ contiguitatis, &longs;eù
repugnantia ad vacuuum admittendum, æqualis erit
potentiæ ponderis triginta librarum. Quaproptèr
con&longs;tat, quòd vis, quæ requiritur ad re&longs;i&longs;tentiam
tactus
&longs;it, quàm ea quæ actu exercetur, nihilominùs finita,
& determinata e&longs;t, & facili negotio indagari, men
&longs;urarique pote&longs;t. His declaratis pergo ad
dum
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
riri pote&longs;t, cuius raritas ab&longs;oluta ad illius raritatem
maiorem proportionem qualibet dataratione
maioris inæqualitatis habeat.
SIt cylindrus &longs;olidus ABC, &
quælibet data ratio maioris
inæqualitatis T ad V, & fiat RS
maior quàm T. reperiri debetcy
linder æqualis ABC cuius rari
tas ab&longs;oluta ad raritatem ABC
&longs;it vt RS ad V. Secetur portio cy
lindrica AD, & RX proximè maior quam V, & fiat
cylindrus &longs;olidus EF æqualis AD, cuiu&longs; raritas in
&longs;pecie ad raritatem ip&longs;ius AC &longs;it vt RX ad V; po&longs;tea
fiat alius cylindrus, &longs;iue fluidus, &longs;iue &longs;olidus FG æ
qualis DB, ita vt illius raritas in &longs;pecie ad raritatem
eiu&longs;dem AC &longs;it vt XS ad V. igitur duæ antecedentes
RX, & XS ad V, &longs;cilicet RS ad V eamdem propor
tionem habebit quam raritas &longs;pecifica aggregati ex
EF, & FG ad raritatem AC, &longs;untquè moles EH, &
AC æquales, ergo eorum raritates ab&longs;olutæ &longs;unt pro
portionales &longs;pecificis, &longs;cilicèt &longs;e habent vt RS ad V.
quod erat, &c.
tiuam leui
tatem no&ntail;
dari.
ris transformare in cylindrum &longs;imilitèr excauatum,
cuius pars continens homogenea, & æqualis &longs;it. vni illorum, pars verò excauata homo
genea, & æqualis &longs;it reliquo.
SIt datus cylindrus &longs;oli
dus AC, compo&longs;itus ex
duobus cylindris AD, & DB
inæqualitèr raris alium cy
lindrum &longs;imilitèr
æqualem, & &longs;imilem illi de
&longs;cribere, cuius pars continens æqualis, & homoge
nea &longs;it ip&longs;i AD, contenta verò æqualis, & homoge
nea &longs;it ip&longs;i DB. reperto centro
AC coniungantur rectæ AQ, BQ ad terminos lateris
cylindri AB, & fiat triangulum ENF &longs;imile, & æqua
le ip&longs;i AQB. po&longs;tea inter AB, & MB reperiantur duæ
mediæ proportionales, quarum maior &longs;it PB (vt do
cuimus lib.
5. conic. Apoll.lemm. 7.) deinde in
gulo ENF du
PB, & ducta RNS parallela ip&longs;is EF, & IK reuolua
tur figura circa axim RS vt fiant duo cylindri
trici
internum IKLO repletum &longs;ub&longs;tantia homogenea ip
&longs;i cylindro DB, & re&longs;iduum ambiens EFGH explea
tur ex eadem &longs;ub&longs;tantia corporea ip&longs;ius AD; & quia
AB ad MB, &longs;iuè cylinder AC ad cylindrum MC, vel
cylinder EG ad cylindrum IL triplicatam propor
tionem habet lateris AB ad PB, vel EF ad IK; ergo
cylinder AC ad MC eamdem proportionem habet,
quam integer cylindrus EG ad cauitatem cylindri
cam IL, & per conuer&longs;ionem rationis cylinder AC
ad. cylindrum AD &longs;e habet vt totus cylindrus EG
ad partem continentem EKGO. Suntque cylindri
AC, & EG æquales, cùm &longs;int &longs;imiles, & &longs;imilitèr po
&longs;iti circa latera æqualia AB, & EF, igitur cylinder
excauatus EKGO æqualis e&longs;t &longs;ibi homogenco cylin
dro AD, proindeque cylinder IL æqualis, & homo
geneus erit ip&longs;i MC, quod fuerat.
tiuam leui
tatem no&ntail;
dari.
His præhabitis noto, quòd cùm agitur de faculta
te, &longs;eù principio quo corpora vim faciunt tendendo
deorsùm, qu&ecedil;rimus tantummodò gradum virtutis
pre&longs;&longs;iuæ
pondere eorum men&longs;uratur, hoc verò duplici modo
augeri po&longs;&longs;e con&longs;tat, aut per multiplicationem eiu&longs;
dem corporis, vt cum lignea columna augetur mole,
aut cum
di&longs;&longs;eminata, & contenta magis &longs;tringitur, conden-
&longs;atur, con&longs;tipaturque, & primum vocatur augmen
tum grauitatis exten&longs;iuum, reliquum verò Regula verò, qua men&longs;urari pote&longs;t gradus prædictæ
grauitatis commodè de&longs;umitur à vi contraria, quæ
depre&longs;&longs;ionem eius prohibere pote&longs;t, & hic
e&longs;t minimè nos &longs;ollicitos e&longs;&longs;e de velocitate motus,
qua deorsùm eadem grauia feruntur, &longs;ed tantummo
dò con&longs;iderare vim, & conatum ponderis eius, qui
in libra à vi oppo&longs;iti
mens exten
&longs;iuè augetur
multiplicata
mole corpo
ris.
rò con&longs;tip
ta, & condi
&longs;ata mate
ria.
tiuam leui
tatem no&ntail;
dari.
dictæ grau
tatis men&longs;u
ratur à vi
traria, quæ
eius prohi
bere pote&longs;t.
tur de velo
citate
&longs;us
leuitas voca
tur augeri po
te&longs;t exten&longs;i
uè multipli
cato eodem
corpore le
ui.
NOn &longs;ecùs quando agitur de vi, & energia, qu&atail;
corpora, quæ leuia appellantur &longs;ursùm moue
ri nituntur, quæritur non velocitas, &longs;ed vis, quæ
&longs;ursùm impellit, quæ leuitas appellari &longs;olet, & hæc
quoque duplici modo augeri pote&longs;t, aut exten&longs;iuè,
aut
corporis leuis, vt &longs;phæra aeris palmaris octies
rem
maris, propterea quod vis illa leuitatis tantumdem
multiplicatur, quantum ma&longs;&longs;a eius corporea exten
ditur, cùm omnes partes eiu&longs;dem aeris æquè leues
&longs;int, & æquè raræ, requiraturque vis contraria pro
hibens illius a&longs;cen&longs;um octiès maior quam in huius
aeris minori mole requiratur. Secundo modo auge
ri pote&longs;t leuitas expandendo, & rarefaciendo
tiam corpoream, & plenam, vt nimirum maius
&longs;patium occupet, & in hoc ca&longs;u comparari debent
&longs;patia occupata, &longs;iuè moles æquales inter &longs;e, &
medio fluido in quo leuitant, vt &longs;i fuerint duæ pilæ
æquales, vna aquea, altera aerea intra
mer&longs;&ecedil;, dicetur maior leuitas inten&longs;iuè aeris re&longs;pectu
leuitatis aquæ, & leuitates eamdem proportionem
habebunt, quàm raritates molium æquallum aeris,
& aqu&ecedil; in mercurio con&longs;ideratæ habent. Et hoc eui
dentia &longs;en&longs;us &longs;uadet, &longs;i enim intra hydrargyrum de
mergatur ampulla vitrea plumbo repleta, huius qui
dem gradus leuitatis men&longs;uratur à vi
a&longs;cen&longs;um eius in mercurio prohibere pote&longs;t, &longs;itque
talis vis contraria pondus duarum vnciarum &longs;uper
po&longs;itum, & intra mercutium fixè detinens
ampullam. Si po&longs;tea plumbi vncia è cauitate ampul
læ &longs;ubtrahatur, patet quod
pullæ raritas aucta erit, quantum diminuta fuit &longs;ub
&longs;tantia corporea pondero&longs;a intra ampullam eiu&longs;dem
molis, & figuræ contenta, & tunc gradus leuitatis
præcisè augebitur vna vncia, nam &longs;i velimus
eiu&longs;dem ampullæ prohibere &longs;uperponi debent non
duæ vt priùs, &longs;ed tres vnciæ, po&longs;tea &longs;i ampullæ rari
tas denuò augeatur detracta altera
dus quoque leuitatis eadem men&longs;ura cre&longs;cet vt ni
mirùm requirantur quatuor vnciæ ad prohibendum
eius a&longs;cen&longs;um è mercurio, idemque verificatur &longs;i
vlterius pondus internum ampullæ diminuatur; qua
re incrementa leuitatis proportionalia &longs;unt incre-
mentis raritatis eiu&longs;dem corporis.
verò rarefa
ciendo id in
corpus.
tiuam leui
tatem no&ntail;
dari.
leu
portionalia
tis
eiu&longs;dem cor
poris
denque
&
tur
rum prohi
b
tiones.
tiuam leui
tatem no&ntail;
dari.
Hinc inferri licet, quòd &longs;i raritas non e&longs;t cau&longs;a ef
fectiua, motus &longs;ursùm, &longs;eù leuitatis, requiritur
raritas tamquam affectio nece&longs;&longs;aria, &longs;ine qua leuitas
minimè augeri pote&longs;t, &longs;ed oportet vt raritates in ali
quo medio fluido con&longs;iderentur, non autem ab&longs;olu
tè, & in vacuo.
e&longs;t causa a&longs;
cen&longs;us
requiritur
&longs;eriò
tanta vi &longs;ursùm, quæ &longs;uperet quamcumque finitam
vim.
SIt vas ABC
do M quod &longs;it aqua, vel hy
drargyrum, & &longs;it quælibet va
&longs;ta vis motiua R. debet reperiri
corpus, quod in prædicto fluido
innatet, atque ab eius
sum a&longs;cendat tanta vi, & energia
vt &longs;uperet vim datam R. &longs;uma
tur cylindrus DE cuiu&longs;cumque
&longs;olidæ materiei con&longs;i&longs;tenti&longs;que,
earum tamen, quæ in prædicto fluido M innatant,
et vis qua corpus DE a&longs;cendit è fundo fluidi M &longs;it S:
po&longs;tea (ex duabus præcedentibus propo&longs;itionibus)
reperiatur cylindrus excauatus FG, cuius extern&atail;
figura &longs;it æqualis, & &longs;imilis ip&longs;i DE, itaut raritas ab
&longs;oluta ip&longs;ius FG ad
portionem habeat,
tione) impetus, & energia, qua cylindrus FG &longs;ur
sùm fertur in dato fluido M ad eam vim, qua cylin
drus DE priori æqualis &longs;ursùm fertur in eodem flui
do eamdem proportionem habet, quam raritas cor
poris FG ad raritatem alterius DE, habentque præ
dictæ raritates ne dum ab&longs;olutè, &longs;ed etiam in medio
fluido mercuriali con&longs;ideratæ, maiorem proportio
nem, quam R ad S, igitur vis, & robur, quo cylindrus
FG &longs;ursùm a&longs;cendit in fluido M ad eam vim, qua ele
uatur ibidem cylindrus DE maiorem proportionem
habebit, quam R ad S, erat verò S vis, qua &longs;olidum
DE &longs;ursùm transfere batur in fluido M, ergò validi
tas, & energia, qua a&longs;cendit cylindrus FG in
fluido maior erit, quàm R, & hoc propo&longs;itum fuerat.
tiuam leui
tatem no&ntail;
dari.
Sed po&longs;&longs;umus faciliùs, & breuiori apparatu pro
blema ab&longs;oluere, &longs;i modò moles corporis innatantis
intra aliud fluidum &longs;impliciter augeatur multiplice
turque.
VT
præmitti debet, quòd quando agitur de vi, &
energia leuitatis, &longs;en&longs;u con&longs;tat duas æquales moles e
iu&longs;dem corporis homogenei v.g. eiu&longs;dem ligni æquè
leues e&longs;&longs;e, &longs;cilicèt exercere conatus impul&longs;iuos
inter &longs;e æquales in eodem fluido, in aqua nempè, ita
utimpelli deorsùm debeant ab æqualibus ponderi
bus ad hoc vt vetentur eorum a&longs;cen&longs;us, & fixè infra
&longs;upremam aquæ libellam detineantur. paritèr
e&longs;t inæquales moles eiu&longs;dem ligni inæquales vires
leuitatum in aqua habere, & inæqualibus conatibus,
& viribus &longs;ursùm impellere; nam &longs;i ex ligno maiori
&longs;ecetur auferaturque vna pars æqualis moliligni mi
noris, hæ cùm &longs;int æquè leues, mole&longs;que æquales ha
beant, vt nimirùm prohiberi eorum a&longs;cen&longs;us no&ntail;
po&longs;&longs;int, ni&longs;i ab æqualibus ponderibus
videtur impo&longs;&longs;ibile vt exce&longs;&longs;us ille ligni maioris &longs;u
pra minorem (cùm &longs;it eiu&longs;dem naturæ ligneæ proin
de que leuis) vim &longs;ursùm non exerceat pro men&longs;ura
&longs;uæ quantitaris, & proinde requiratvim contrariam
alicuius ponderis incumbentis, vt eius a&longs;cen &longs;us pro
hibeatur.
tiuam leui
tatem no&ntail;
dari.
corporis &longs;ursùm impellendo in eodem fluido exercent
vires, quæ eamdem proportionem habent, quam
moles ip&longs;æ.
IN va&longs;e FDE aqua pleno, vel alio
fluido demergantur duæ inæqua
les moles eiu&longs;demligni, quæ &longs;cilicèt
æquè rar&ecedil; &longs;int &longs;pecie, vt &longs;unt ABC, &
HIK, &longs;it que S leuitas, &longs;eù vis qua li
gnum ABC
&longs;it leuitas alterius HIK. Dico quòd
leuitas S ad R eamdem
habet, quam lignea moles ABC ad molem HIK. po
natur leuitas, aut vis
libet
quæ proponi po&longs;&longs;unt pariterque fiat moles BM ex
eodem ligno con&longs;tans quæ ad HIK &longs;e habeat vt N
ad R. mani fe&longs;tum e&longs;t, quòd quotie&longs;cumque lignum
BM æquatur ligno ABC, runc paritèr vis leuitatis N
æqualis erit ip&longs;i S (eò quòd moles æquales eiu&longs;de&mtail;
ligni &longs;ursùm æquali vi leuitatis impellunt) &
tie&longs;cunque
&longs;emper leuitas N maior eritleuitate S, & quando li
gnum BM minus fuerit, quàm ABC, erit quoque le
uitas N minor, quàm S, & habent BM, HIK, & N &
R quamcumque proportion alitatem commen&longs;urabi
lem, igitur (ex no&longs;tro Euclide re&longs;tituto) moles li
gnea ABC ad molem HIK eamdem proportione&mtail;
habebit quam vis leuitatis S, qua nimirùm ABC in
aqua a&longs;cendit, ad leuitatem R qua corpus HIK ele
uatur in eodem fluido, quòd fuerat &c.
tiuam leui
tatem no&ntail;
dari.
24.
Si quis fortè &longs;u&longs;picaretur ex figurarum diuer&longs;itate
prædictorum corporum leuium licèt eiu&longs;dem con&longs;i
&longs;tentiæ homogeneæ &longs;int, & eumdem gradum rarita
tis habeant, alterari po&longs;&longs;eiam dictam proportionali
tatem, monendus profectò e&longs;t, quod præter Ari&longs;tote
lis a&longs;&longs;ertum, vbiait, quod
tèr a&longs;cen&longs;us, vel de&longs;cen&longs;us corporum in fluido, &longs;ed tantum
modò tardioris, vel celerioris motus
mon&longs;tratum fuit ex Mechanicis principijs à Ghetal
do, & Galilæo. attamen inca&longs;u no&longs;tro non requirun-
tur figuræ corporum a&longs;cendentium omninò diuer
&longs;æ, & di&longs;&longs;imiles inter &longs;e, quia æquè benè no&longs;træ de
mon&longs;trationi aptari po&longs;&longs;unt cylindri æquè alti, & in
æqualium ba&longs;ium, &longs;iuè contra &longs;i ba&longs;es æquales &longs;int,
altitudines &longs;int inæquales. hoc præmi&longs;&longs;o libet
problema alia ratione re&longs;oluere.
alterat præ
dictam pro
portionali
tatem.
cap.
6.
tiuam leui
tatem no&ntail;
dari.
tare valeat, reperiri debet moles quam habere debet,
vt in eadem fluido a&longs;cendere pos&longs;it tanta vi, vt
&longs;uperet quamcumque finitam virtutem
motiuam.
SIt vas FDE, impleaturqu&etail;
fluido M, aqua nimirùm, aut
quolibet alio con&longs;i&longs;tenti fluido. Sumatur po&longs;tea ligneus cylinder
ABC, vel quælibet alia materia,
quæ in pr&ecedil;dicto fluido innatet, &longs;it
que quælibet immen&longs;a, &longs;ed
finita vis R, debet reperiri mo
les, & amplitudo quam haber&etail;
debet corpus aliud homogeneum
ip&longs;i ABC, vt tanta vi in fluido M a&longs;cendat quæ maior
&longs;it virtute motiua R. Immergatur in eodem fluido
cylindrus ABC, eiu&longs;que leuitas in fluido, &longs;eu vis, qua
nititur in eo Po&longs;teà fiat cylindrus HIK
&longs;imilis homogeneus, & eiu&longs;dem materiæ ac e&longs;t ABC,
& tantæ va&longs;titatis, vt ad eum moles ABC minorem
proportionem habeat, quam S ad R, &longs;cilicèt &longs;it vt S
ad V, quæ maior erit quam R, & quia eiu&longs;dem &longs;ub
&longs;tantiæ nempè ligni factæ &longs;unt duæ moles ABC, &
HIK; igitur (ex præcedenti) vt cylindrus ABC ad
HIK, ita &longs;e habet ab&longs;oluta leuitas illius S ad huius le
uitatem, quæ erit V, & habet S ad R
tionem, quàm moles ABC ad HIK, igitur leuitas V,
&longs;eù vis, qua &longs;olidum HIK a&longs;cendit in flui do M maior
e&longs;t quacumque data vi finita R.
tiuam
tatem
ostendemus.
SVmatur lignum L, vel aliud
corpus &longs;ibi homogeneum,
quod innatare po&longs;&longs;it intra flui
dum M, ponaturque quælibet
vis finita ponderis P, atque vt
pondus ab&longs;olutum molis fluidi
M, quæ æqualis &longs;it ip&longs;i L, ad
pondus ab&longs;olutum ligni L, &longs;ci
licèt vt grauitas &longs;pecifica flui
di M ad L, it a &longs;e habeat R ad S,
po&longs;tea fiat cylindr us ACB
grauitatem ab&longs;ol utam
nem habeat, quàm differentia ip&longs;arum R, & S ad S. Tandem immergatur cylindrus AC intra fluidum M
contentum in va&longs;e FDE tantæ profunditatis, vt cy
lindrus AC vniuersè, & perpendicularitèr ad Hori
zontem mergi po&longs;&longs;it, vt eius ba&longs;is non contingat
dum
bellam contingat. Præterea applicari debet pondus
P &longs;upra verticem cylindri CA, itaut pondus P immi
neat &longs;upra fluidi libellam, neque aliqua eius portio
demergatur. His præparatis
quia exce&longs;&longs;us
S ad ip&longs;um pondus S maiorem
uitas P ad pondus cylindri
ACB, ergò componendo, gra
uitas R ad S
nem habebit quàm duo
ra
pondus CAB; verùm grauitas
molis fluidi M æqualis &longs;olido AC ad pondus ab&longs;olu
tum eiu&longs;dem &longs;olidi AC habet eamdem
quam R ad S, ergò moles fluidi M æqualis &longs;olido AC
ad &longs;olidum idip&longs;um AC, &longs;eù illius pondus ad graui
tatemhuius habebit maiorem proportionem quàm
pondera P, & CAB &longs;imùl &longs;umpta ad pondus AC, &
proindè pondus ab&longs;olutum molis fluidi M æqualis
AC maius erit grauitate ip&longs;ius P vnà cum ponder&etail;
cylindri AC. Verumtamen Archimedes demon&longs;tra
uit &longs;olidum innatans tunc &longs;olummodò in fluido quie
&longs;cere quando eius pondus ab&longs;olutum æquale fuerit
grauitati molis fluidi ambientis, quæ &longs;it æqualis por-
tioni eiu&longs;dem &longs;olidi intra eiu&longs;dem fluidi libellam de
mer&longs;i. Qua proptèr quando pondus ab&longs;olutum præ
dicti &longs;olidi minus fuerit pondere prædicti fluidi am
bientis æqualis portioni eius demer&longs;æ nece&longs;&longs;ariò
&longs;olidum ip&longs;um in fluido eleuabitur vlteriu&longs;que
det
te pondere P eique coniuncto, & continuato no&ntail;
quie&longs;cet, &longs;ed &longs;ursùm a&longs;cendet, quaproptèr vis pre
mens ponderis P non &longs;ufficit, nec habet tanta&mtail;
vim vt retineat &longs;olidum AC integrè infra fluidi
M libellam demer&longs;um. Cùmque, vt Archimedes de
mon&longs;trauit, energia, & vis, qua &longs;olidum AC cona
tur, & vim facit vt &longs;ursùm a&longs;cendat in fluido M &ecedil;qua
lis &longs;it vi illius ponderis, quod &longs;i &longs;uper id imponatur,
pote&longs;t id retinere infra fluidi libellam prohibereque
cius a&longs;cen&longs;um, igitur vis, qua cylindrus AC conatur
&longs;ursùm a&longs;cendere in fluido M maior e&longs;t quacumque
vi finita ponderis P, & hoc propo&longs;itum fuerat.
tiuam leui
tatem no&ntail;
dari.
1. prop.
4.
tiuam
tatem
prop.
6.
nimirùm quodlibet corpus &longs;ursùm a&longs;cendens in date
aliquo fluido non eleuatur &longs;ponte &longs;ua à principio
nempè intrin&longs;ecoleuitatis impul&longs;um.
SIt L quodlibet corpus eorum, quæ à Peripateti
cis vocantur à prædominio aerea, vt &longs;unt ferè
omnia ligna, & alia innumera, & fluidum M in va&longs;e
FDI
aut hydrargyrum; procùl dubio corpus L intra flui
dum M demer&longs;um &longs;ursùm a&longs;cendet.
modò e&longs;t idip&longs;um non &longs;pontaneo motu ab intrin&longs;eco
principio leuitatis a&longs;cendere. Si hoc enim veru&mtail;
non e&longs;t, &longs;it, &longs;i fieri pote&longs;t leuitas
corporis L naturalis cau&longs;a, &
virtus à qua &longs;pontaneo motu
&longs;ursùm impellatur in fluido M. Et primò pr&ecedil;paretur infima ba
&longs;is AB cylindri homogenei ip&longs;i
L, vt nimirùm ei vniatur ferru
mineturque lamina aliqua vi
trea, vel metallica, quæ &longs;it op
timè explanata, & læuigata, & eiu&longs;dem materiæ, at
que figuræ, & læuitatis &longs;it pauimentum, vel fundum
putei DE. Secundo loco reperta iam &longs;it
ta, & determinata illius virtutis, quæ requiritur ad
&longs;eparandam, & diuellendam &longs;uperficiem vitri AB ab
immediato contactu cum fundo putei DE, &longs;iuè vis
illa, quæ &longs;uperare valet re&longs;i&longs;tentiam prædictaru&mtail;
&longs;uperficierum &longs;e tangentium ad vacuum admitten
dum; &longs;upponamu&longs;que huiu&longs;modivim e&longs;&longs;e æquale&mtail;
ponderi G, atque reperiatur cylindrus AC eiu&longs;dem
materiei L itaut vis leuitatis qua conatur &longs;ursùm mo
ueri in fluido M vna cum vitrea lamina AB maior &longs;it
vi, & energia ponderis G, &longs;itque vis illa leuitatis æ
qualis potenti&ecedil; H. quapropter vis qua &longs;olidum AC
conatur, & impetum facit vt &longs;ursùm in dato fluido
a&longs;cendat, maior e&longs;t illa vi, & facultate, quæ requi-
ritur ad &longs;eparandam, & diuellendam ba&longs;im AB à fun
do putei DE horizonti æquidi&longs;tante. dum igitur ba
&longs;is AB immediatè, & exqui&longs;itè tangit fundum putei
DE, vt &longs;ibi mutuò congruant, exo&longs;culenturque, re
pleatur vniuer&longs;um vas FE prædicto fluido M quou&longs;
que &longs;uprema fluidi libella ad &longs;ummitatem C cylindri
AC demer&longs;i pertingat. Et quia hìc iam exi&longs;tunt, &
operantur duæ vires contrariæ, vna quidem H im
pellit &longs;ursùm, e&longs;tque virtus eius leuitatis, alia verò
G, quæ huic re&longs;i&longs;tit, & vim deorsùm tendendo facit,
e&longs;tque energia contactus &longs;uperficierum AB & DE,
&longs;eù repugnantia ad vacuum admittendum qua con
trario ni&longs;ui a&longs;cen&longs;us cylindri AC re&longs;i&longs;tit: E&longs;tque
traria
te G tenacitatis, vel repugnantiæ ad vacuum, quæ
impetum contrarium deorsùm facit; igitur maior vis
leuitatis H nece&longs;&longs;ariò &longs;uperare debet vim minorem
G, & proinde di&longs;trahet diuelletque cylindrum AC à
fundo putei DE, atque po&longs;t &longs;eparationem idip&longs;u&mtail;
&longs;ursùm ad &longs;uperficiem fluidi M impellet, transferet
que; &longs;ed hoc e&longs;t fal&longs;um, & contra &longs;en&longs;us
proptereà quòd numquam contingit vt ba&longs;is colum
næ AB &longs;eparetur à
ponatur vim leuitatis quocumque exce&longs;&longs;u vim con
tactus &longs;uperare, igitur verum non e&longs;t cylindrum AC
&longs;ursùm impelli ab intrin&longs;eca, & po&longs;itiua facultat&etail;
leuitatis eius, quod fuerat demon&longs;trandum.
tiuam leui
tatem no&ntail;
dari.
89.
& 96.
tiuam leui
tatem no&ntail;
dari.
tiuam leui
tatem no&ntail;
dari.
ET procùl dubio cen&longs;eri non debet vera cau&longs;&atail;
alicuius effectus illa qua po&longs;ita, & non impe
dita ab excedente vi contraria, non ponitur nihilo
minùs, nec &longs;ub&longs;equitur effectus, &longs;ed po&longs;ita leuitat&etail;
po&longs;itiua in prædicta lignea columna AC infra
M demer&longs;a, & non impedita à virtute contraria con
tactus, aut à timore vacui (eò quòd ex con&longs;tructio
ne hæc multò minor fuerat virtute, & energia leui
tatis) non &longs;ub&longs;equitur nihilominùs effectus a&longs;cen&longs;us
columnæ in prædicto fluido, igitur leuitas po&longs;itiu&atail;
non e&longs;t cau&longs;a
Po&longs;tquam o&longs;ten&longs;a fuit pr&ecedil;dicta negatiua propo&longs;i
tio.
tone, & Archimede, quòd corporaomnia, quæ leuia
appellantur &longs;ursùm a&longs;cendunt ab extru&longs;ione
fluidorum in quibus innatant ob exce&longs;&longs;um
grauitatis eorumdem.
QVia illa e&longs;t vera cau&longs;a alicuius effectus natura
lis, qua|po&longs;ita &longs;ub&longs;equitur effectus, & ablata
pariter effectus tollitur, &longs;ed po&longs;ita extru&longs;ione facta
à corpore fluido grauiori &longs;ub&longs;equitur effectus a&longs;cen-
&longs;us nimirùm &longs;olidi minùs grauis in eo demer&longs;i, &
quotie&longs;cumque prædicta extru&longs;io tollitur, aut im
peditur, aufertur quoque vetaturque a&longs;cen&longs;us præ
dicti corporis &longs;olidi, igitur nece&longs;&longs;ariò prædicta ex
tru&longs;io grauioris fluidi ambientis e&longs;t vera, & legitima
cau&longs;a a&longs;cen&longs;us eorum corporum, quæ leuia
tur
ta extru&longs;io aquæ, vel hydrargyri tollitur, & impedi
tur, cùm fluidum M interlabi,
aut excurrere non po&longs;&longs;it infra
ba&longs;im AB prædictæ column&ecedil; ob
arctam connexionem contactus
ba&longs;is AB cum fundo putei DE,
licèt ambiens
uius &longs;it prædicta
& in tali ca&longs;u columna &longs;ursùm
in fluido E contrà
quotie&longs;cumque extru&longs;io fieri pote&longs;t, &longs;cilicèt quoties
fluidum M excurrere pote&longs;t infra ba&longs;im AB ob con
cu&longs;&longs;ionem, vel minimam dilatationem
&longs;e tangentium, &longs;eù ob tran&longs;itum per fi&longs;&longs;uram, aut fo
ramen aliquod collaterale, tunc &longs;ub&longs;equitur effectus
a&longs;cen&longs;us prædictæ columnæ, igitur nece&longs;&longs;ariò extru
&longs;io facta à grauiori fluido M e&longs;t vera cau&longs;a &longs;ublima
tionis, & a&longs;cen&longs;us prædictiligni in fluido, quod fue
rat o&longs;tendendum.
tiuam leui
tatem no&ntail;
dari.
Et hìc &longs;ummopere
tionem pendere ex eo quòd tribuitur effectus no&ntail;
veræ cau&longs;æ, &longs;ed alij imaginatæ, quoniam
que lignum &longs;ursùm a&longs;cendit in aqua &longs;emper verifi
catur id minùs grauitare, quàm moles aquæ
tis
te&longs;t infra eius ba&longs;im, &longs;cilicèt &longs;i exercere pote&longs;t ex
ce&longs;&longs;um &longs;ui ponderis, mirum non e&longs;t eleuare corpus
minoris grauitatis, &longs;icuti in libra videmus minus
dus
dus maius liberè vim &longs;uam exercere pote&longs;t, at &longs;i fue
rit &longs;ub&longs;tentatum, vel fulciatur à pauimento pondus
minus eleuare non poterit. Huiu&longs;modi cau&longs;a, quæ
certa e&longs;t, & nece&longs;&longs;ariò operari debet iuxtà leges me
chanices,
ceptetur imaginata cau&longs;a leuitatis po&longs;itiuæ, quæ &longs;i
ade&longs;&longs;et, &longs;uum
po&longs;itionis 97. vbi nil prorsùs operari o&longs;ten&longs;um e&longs;t,
tamquàm &longs;cilicèt &longs;i non e&longs;&longs;et.
cination
tegitur.
tiuam leui
tatem no&ntail;
dari.
Po&longs;tquam igitur examinauimus, & reiecimus ra
tiones omnes Peripateticas
antiquos pro a&longs;&longs;ertione leuitatis po&longs;itiuæ, pariter
que inefficaces repertæ &longs;unt omnes aliæ rationes,
quæ pro confirmatione prædictæ
runtur, cùmque tandem methodo demon&longs;tratiua
ritatem
ab&longs;que iactantia, affirmare euici&longs;&longs;e nullam leuitatem
po&longs;itiuam in natura dari virtute cuius naturalia cor
pora conentur di&longs;cedere à no&longs;tra terra versùs &longs;upe
riores partes, &longs;ed è contra pronunciare po&longs;&longs;umus re
periri in omnibus corporibus &longs;ublunaribus vim
dam
terreno adhærendi mediante facultate de&longs;cen&longs;iu&atail;,
quæ grauitas appellatur, hæc, inquam, grauitas di
uer&longs;imodè participata à corporibus terram ambien
tibus efficit vt minùs grauia expul&longs;a ex inferioribus
locis à grauioribus illa &longs;ursùm eleuentur, & &longs;ic cor
pora elementaria optima
librentur
dem quie&longs;cant.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
& Vi Elateria Aeris.
IAm &longs;uperiùs &longs;atis &longs;uperque o&longs;ten&longs;um e&longs;t aqua&mtail;
grauitare etiam in propria regione, & in &longs;uo toto:
præterea o&longs;tendimus nullam leuitatem po&longs;itiuam re
periri in corporibus mixtis, in ijs nempè, quæ à præ
dominio aerea vulgò appellantur, quod verò peculi
ariter aer grauis &longs;it, ne dum Ari&longs;tot. apertè fatetur,
cùm ait: Hinc in
fert:
grauitatem habere e&longs;t nece&longs;&longs;arium. Aquam autem vbique,
prætèr quàm in terra, aerem verò præterquam in aqua, &
terra. In &longs;ua enim regione omnia grauitatem habent prætèr
ignem, etiam aer ip&longs;e. Signum autem est quia trahit plùs in
flatus vter, quàm vacaus. Sed etiam demon&longs;trari po
te&longs;t eodem modo, ij&longs;demque rationibus, quas in pr&ecedil;
cedenti capitulo adduximus, &longs;icuti enim ibi con&longs;ide-
rauimus ligna, ampullas vitreas|, & ve&longs;icas aere ple
nas per aquam a&longs;cendentes, demon&longs;trauimu&longs;que eas
non vi leuitatis, &longs;ed ab extru&longs;ione medij fluidi &longs;ursùm
impelli, &longs;ic pariter &longs;i loco ligni, aut ve&longs;ic&ecedil; ponatur aer
in
te
&longs;ione grauioris medij fluidi violenter &longs;ursùm impel
lentis. licèt ergo negotium omninò confectum e&longs;&longs;&etail;
videatur, vtile tamen erit idip&longs;um confirmare ex æ
quilibrio aeris cum cæteris fluidis.
cap.
4.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
&longs;uadetur aerem, vt grauem, æquilibrium
efficere cum mercurio.
ET hac occa&longs;ione con&longs;iderabimus pulcherrimum
profectò experimentum eorum, quæ hoc &longs;eculo
adinuenta &longs;unt, hydrargyri nempè eleuatio in fi&longs;tula,
quam primus
ricellius, e&longs;tque experimentum huiu&longs;modi: Sit fi&longs;tu
la vitrea ABC perforata tantummodò in eius extre
mitate C, in A verò clau&longs;a, hæc verò hydrargyro
repleta v&longs;que ad &longs;ummitatem C pulpa indicis &longs;trictè
claudatur, inuertaturque contrario &longs;itu, vt nimirùm
os eius C inferiùs re&longs;piciat; &longs;itque po&longs;tea præparata
&longs;cutella DHE pariter hydrargyro plena demerga
tur infimum orificium C fi&longs;tulæ vnà
dente infrà &longs;upremam hy
drargyri libellam DE, tunc
&longs;ublato digito mercurius
profluet ab orificio C quo
u&longs;que altitudo FB extantis
hydrargyri&longs;upra libella&mtail;
DE &longs;it pedum duorum, &
quadrantis, vel vnius cubi
ti, & quadrantis, nec vlte
rius hydrargyrum graui&longs;&longs;i
mum de&longs;cendit &longs;emperque
ad eamdem altitudine&mtail;
per&longs;euerat, licèt inclinetur
fi&longs;tula, &longs;cilicèt ducta recta FG parallela horizonti
per
FG perueniet quomodocumque fi&longs;tula inclinetur. Ip&longs;e Torricellius experimenti inuentor &longs;agaci&longs;&longs;imè
cau&longs;am quoque huius effectus indagauit, animaduer
tit enim nos in infima profunditate oceani aerei de
mer&longs;os e&longs;&longs;e, & &longs;icuti maris aqua vndique fundu&mtail;
comprimit per lineas horizonti perpendiculares, &longs;eù
directas ver&longs;us centrum telluris, &longs;ic quoque in oceano
aereo ni&longs;us eius grauitatis exercetur perpendiculari
tèr &longs;upra horizontis planum, vnde concipi debent cy
lindri aerei perpendicularitèr &longs;uperficiem hydrargy
ri DE &longs;upremam comprimentes; quia verò eade&mtail;
libella mercurij DE comprimitur quoque in &longs;itu B à
&longs;uperficie ba&longs;is B mercurialis cylindri FB efforma
tur veluti libra, vel &longs;ipho, quæ numquam quie&longs;cit, ni-
&longs;i æquilibrium momentorum efficiatur, &longs;cilicèt ni&longs;i
momentum ponderis cylindri aerei &longs;uperficiem DE
comprimentis æquale fuerit momento ponderis cy
lindri mercurialis BF. Huiu&longs;modi &longs;peculatio magno
plau&longs;u à viris doctis excepta fuit, alij&longs;que
tis
gyri aquam adhibeamus, vel aliud fluidum, tunc aqua
pura eleuatur ad altitudinem pedum 32. vel cubito
rum 17. proximè cuius pondus præcisè æquatur gra
uitati prædicti cylindri mercurialis BF vnius cubiti,
& quadrantis (&longs;umptis nimirum ba&longs;ibus æqualibus)
& &longs;i fuerit oleum altius quàm aqua pura eleuatur, &longs;ed
præcisè quantum exigit aquæ grauitas ei æqualis;
idemque continget &longs;i fuerit aliquis &longs;piritus, vel qui
libet alius liquor. cùm igitur in hi&longs;ce omnibus fi&longs;tulis
eleuentur varij liquores, itaut eorum partes eleuatæ
&longs;uper infimam libellam &longs;emper eiu&longs;dem &longs;int grauita
tis, dicendum nece&longs;&longs;ariò e&longs;t ab vnica, & eadem vi
compre&longs;&longs;iua eleuari, qu&ecedil; &longs;emper eiu&longs;dem roboris &longs;it:
at nulla alia a&longs;&longs;ignari pote&longs;t præter pondus cylindri
aerei liquori in &longs;cutella contento igitur
pote&longs;t aer incumbens eleuare prædictos liquores, hoc
autem minimè effici po&longs;&longs;et ab&longs;que eo quod in aer&etail;
æquilibrium efficeretur; &longs;icuti in maris oceano ex eo
quod omnes partes aquæ æquali ni&longs;u deor&longs;um ferun
tur, & premunt, fit vt eius &longs;uprema libella &longs;phæricè
contornetur, &longs;ic paritèr &longs;uprema aeris &longs;uperficies
&longs;phæricè tornata erit, ex eo quod partes eius omnes
æquali ni&longs;u deor&longs;um
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
QVòd po&longs;tea prædicta mercurij eleuatio in fi &longs;tu
la producatur ab aeris compre&longs;&longs;ione &longs;upr&atail;
mercurium in &longs;cutella contentum, confirmatur ali&atail;
ratione, fed clariùs adhibito
to
Experimentali Medice&ecedil; communicaui,
eiu&longs;que ichon habetur figura 34. libri
experimentorum ciu&longs;dem Academiæ,
ab&longs;que enim &longs;cutella DE &longs;ufficit vt in
fima pars fi&longs;tulæ BC incuruetur, &longs;ur
&longs;umque inflectatur,
ta vt priùs vniuer&longs;a fi&longs;tula mercurio,
reuoluatur vt eius pars clau&longs;a A & lon
gitudo fi&longs;tulæ AFB perpendicularitèr
ad horizontem emineat, tunc quidem
ab orificio aperto G hydrargyru&mtail;
profluet, vel intra amplitudinem am
pullæ DG reducetur, quou&longs;que altitu
do mercurialis cylindri FB &longs;upra
nius cubiti & quadrantis, & tunc
drus aereus DS v&longs;que ad &longs;upremam aeris &longs;uperficiem
S exten&longs;us, cuius pondus æquetur grauitati cylindri
mercurialis FB. Quod verò à compre&longs;&longs;ione prædicti
cylindri aerei DS eleuetur graui&longs;&longs;imum
FB probatur ex eo quod &longs;i augeatur impul&longs;us, & com-
pre&longs;&longs;io &longs;upra &longs;uperficiem hydrargyri D altiùs ele
uatur mercurius in fi&longs;tula BFA. &longs;ic &longs;i noua fi&longs;tula, vel
in&longs;trumento pneumatico aer in&longs;uffletur, vt compri
mat &longs;uperficiem hydrargyri D eleuatur quoque &longs;u
prema &longs;uperficies F hydrargyri in fi&longs;tula clau&longs;a; & &longs;i
è contrà embolo retracto, velùti exugatur aer impe
diatur que compre&longs;&longs;io eius &longs;upra mercurium D &longs;pon
tè labetur mercurius de&longs;cendetque deorsùm versùs
B. præterea &longs;i &longs;upra mercurium in D infundatur aqua,
quæ propagetur vique ad libellam GI, tunc quidem
mercurius quoque eleuatur ab F v&longs;que ad H, & quod
mirum e&longs;t, eleuatur mercurius præcisè pro men&longs;ura
ponderis aquæ incumbentis GD, &longs;cilicèt altitudo G
D erit quatuordeciès maior, quàm FH, quia talis re
ciprocè e&longs;t proportio ponderis mercurij ad aquam. Si igitur in &longs;patio inani nulla alia cau&longs;a vlterioris ele
uationis hydrargyri FH a&longs;&longs;ignari pote&longs;t præter gra
uitatem aquæ collateralis GD cum qua mercurius F
H æquilibrium efficit, quare negabimus reliquum
mercurij FB eleuari à pondere aliquo premente &longs;u
perficiem D, quæ &longs;it &longs;emper eiu&longs;dem roboris? cùm
que nullum aliud corpus grauitans a&longs;&longs;ignari po&longs;&longs;it
prætèr aerem, igitur nece&longs;&longs;ariò ab hoc mercurius
eleuatur.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Prætermi&longs;&longs;is alijs experimentis excogitatis à viris
docti&longs;&longs;imis in Italia, Gallia, & Anglia, de quibus fusè
agitur in libro ex
perimentalis Mediceæ nè repetamus ea, quæ iam pa&longs;
&longs;im vulgata &longs;unt, tantummodò recen&longs;ebo, & ad exa-
men reuocabo difficultates contra ratiocinium Torri
cellianum, & no&longs;trum à docti&longs;&longs;imo viro allatas
eiu&longs;dem ba&longs;is, itaut perfectum &longs;it vtrinque æquilibrium. Contra hanc &longs;ententiam nonnulla militant &longs;i appendatur fi
stula BD po&longs;tquàm &longs;ubducto digito de&longs;cendit mercurius in
IC &longs;tatera fideli adhibita, & &longs;ignetur pon
deris ratio, ac deindè citr à mercurij de&longs;cen
&longs;um eadem fi&longs;tula cum æquali quantitate
mercurij appendatur, eadem ratio ponderis
inuenietur paulò maior, æqualem quantita
tem mercurij intelligo
lò infra &longs;ub&longs;equitur.
&longs;u&longs;tinetur à cylindro exterioris aeris, igitur
cum illo perfectum æquilibrium facit, igitur
cum alio æquali pondere ad libram appen&longs;o
aliud æquilibrium facere non potest. Supponemus enim mer
curium IC eße trium librarum, æquilibrium facit cum cy
lindro aeris etiam trium librarum. Si autem aliud pondus
trium librarum in alter a lance appendatur
us æquilibrium facere nequit, alioquin &longs;ex Libris mercurius
æquilibraret, quod legibus staticæ repugnat.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
tes contra
no&longs;tram do
ctrinam.
rius in fl&longs;tula ab æquipondio aquæ &longs;u&longs;tineatur, nihilo
minùs vis eleuans fi&longs;tulam &longs;ustinet præterea
aquæ incumbentis pondus æquale
mercurio.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
QVia verò ratiocinium hoc à viro docti&longs;&longs;imo af
fertur vt conuincens, &
re veritatis, luculentèr exponere eius defectum, &
claritatis gratia operationem euidentiorem in ip&longs;&atail;
aqua con&longs;iderabo &longs;imilem omninò ei quam præ ma
nibus habemus. Sit vas profundi&longs;&longs;imum RTVS aere
plenum in cuius fundo pona
tur &longs;cutella DF mercurio ple
na, &longs;itque po&longs;tea fi&longs;tula vitrea
AC
uia cuius in fima pars C demer
gatur infra mercurij libellam;
po&longs;tea repleatur puteus aqua
vt vitri &longs;ummitatem A non at
tingat, & remaneat fi&longs;tula exi
nanita vt prius tunc quidem
&longs;en&longs;u con&longs;tat eleuari hydrar
gyrum in fi&longs;tula à C v&longs;que ad
B quou&longs;que mercurialis altitudo CB decima quarta
pars &longs;it aquæ altitudinis HG. hic iam quia effectus
eleuationis mercurij v&longs;que ad B productus fuit ab a
qua de nouo impo&longs;ita dubitandum
uitate mercurium eleuatum fui&longs;&longs;e, quod præterea
confirmatur ex æquipondio ip&longs;ius cylindri aquæ HG
cum mercuriali cylindro CB eiu&longs;dem ba&longs;is; itaque in
libra CEG, vel in &longs;iphone tunc quie&longs;cunt duo fluida,
mercurius nempè & aqua, cùm præcisè efficitur
æquilibrium; claudatur po&longs;tea fi&longs;tula in B interpo&longs;ita
nimirùm laminula non di&longs;&longs;imili ei, quàm in arundini-
hus ob&longs;eruamus à qua præcisè prohibeatur tran&longs;itus
fluidi per rimas laterales, po&longs;tea impleatur reliqua
pars fi&longs;tulæ AB aqua, & tandèm eadem vitrea fi&longs;tu
la termino I libræ IL radiorum æqualium &longs;u&longs;penda
tur, atque ab oppo&longs;ito termino eius L pendeat pon
dus M æquale ponderi ip&longs;ius vitri AC. videndu&mtail;
modò e&longs;t an à &longs;implici pondere M &longs;u&longs;tineri po&longs;&longs;it vi
trea fi&longs;tula AC, & patet non &longs;ufficere, quia in &longs;ipho
ne ACGH pondus cylindri aquei HG æquatur præ
cisè ponderi mercurij BC, cumque pr&ecedil;terea aqua
tenta
ergò &longs;umma aquæ AB, & mercurij BC duplo grauior
e&longs;t, quam &longs;it cylindrus aqueus HG vt nimirùm &longs;i a
qua HG fuerit vnius libræ erunt mercurius CB, &
aqua AB ferè duarum librarum (non con&longs;iderato
dere
bet addi ponderi M aliud pondus O, quod &longs;it æqua
le ponderi aquæ AB, & tunc in infima libra CEG,
&longs;eu &longs;iphone e&longs;&longs;icitur æquilibrium inter cylindrum a
queum HG, & mercurium CB, in &longs;uprema verò li
bra IL efficitur æquilibrium inter fi&longs;tulam vitrea&mtail;
AC, vnà cum aqua AB ex vna parte, & ponderæ M,
O ex altera parte. Igitur quia reuera mercurius CB
non &longs;u&longs;tinetur à potentia O &longs;ubleuante
mam
e&longs;t impo&longs;&longs;ibile fi&longs;tulam vitream AC &longs;u&longs;tineri à &longs;o
litario pondere M æquale grauitati ip&longs;ius vitri, ni&longs;i
in&longs;uper addatur alia potentia O, quæ &longs;u&longs;tineat cy
lindrum aqueum AB æquè graue ferè, ac|e&longs;t mercu
rius CB.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Si po&longs;tea fi&longs;tula vitrea &longs;ecetur in B, eiu&longs;que &longs;upre
ma portio BA tollatur amoue aturque, at que pondus
M æquale &longs;it grauitati vitri decurtati CB, tunc
incumbit, ac innititur fi&longs;tul&ecedil; cylindrus aqueus BA
fi&longs;tulamque comprimit non &longs;ecus, ac priùs quando
intra cauitatem fi&longs;tulæ AB continebatur.
uetur, tamen manus cogitur &longs;u&longs;tinere pondus cylin
dri aerei fi&longs;tulæ incumbentis, quod æquatur
deriinclu&longs;i
IDip&longs;um no&longs;træ fi&longs;tulæ directæ in ae
re con&longs;titutæ adaptari pote&longs;t, &longs;it
que illa AC duorum cubitorum habe
atque orificium C in&longs;ignis exiguitatis,
repleaturque mercurio deor&longs;umqu&etail;
inuertatur in aere libero (non enim
nece&longs;sè e&longs;t, vt os C intra &longs;cutellam
mercurij plenam infundatur,
valdè &longs;trictum e&longs;t os eius C,) tunc
ab infimo orificio C mercurius in ae
re profluet quou&longs;que altitudo CB
fuerit vnius cubiti, & quadrantis pro
ximè. Hic concipi debet cylindrus
aereus SG v&longs;que ad &longs;upremam regio
nis aeris &longs;uperficiem exten&longs;us, quire
flexus per EC vim faciat contra pre&longs;&longs;ionem mercu
rij BC, eumque &longs;u&longs;pendat, & &longs;ic liberè concedo ad-
uer&longs;ario, quòd fi&longs;tula AC nil prorsùs ab inclu&longs;o mer
curio BC grauatur, & &longs;ic de facto experimur appli
cata digiti pulpa ori infimo fi&longs;tulæ; quod in part&etail;
intermedia pulpæ à mercurio tacta nulla compre&longs;&longs;io,
nec
cisè mercurij altitudo BC e&longs;t vnius cubiti, &
drantis
iecti
curij &longs;upra eum qui altitudinem vnius cubiti, & qua
drantis occupat, & &longs;i è contrà mercurius deprima
tur violentèr infra debitam altitudinem BC, tunc ne
dùm &longs;ubiecta pulpa digiti non comprimitur, &longs;ed è
contrà exugitur, vt efficiunt cucurbitæ medicæ, &
hyrudines. Sed dicet aduer&longs;arius &longs;i mercurius BC
nil grauitat, nec comprimit digitum, quare requi
ritur vis, aut libræ, aut digiti &longs;ubiecti, quæ nedu&mtail;
æquet pondus &longs;olias vitri AC, &longs;ed prætereà &longs;u&longs;tine
re valeat duas libras v. g. quas Re&longs;pondeo aereum cylindrum SA fi&longs;tulæ vitreæ in
cumbentem &longs;ua grauitate agere non minùs, quà&mtail;
collateralis cylindrus aereus SG, cumque vitru&mtail;
CA non repellatur æquali actione contraria &longs;ursùm
ab aere collaterali SG, quia huius vis exercetur, &
omninò expletur &longs;u&longs;tentando mercurium BC; igitur
nece&longs;&longs;ariò vitrum CA comprimitur deorsùm à gra
uitate aeris incumbentis SA, cuius pondus æqual&etail;
e&longs;t mercurio BC hinc fit vi ex præconcepta fal&longs;a opi
nione tribuamus compre&longs;&longs;ionem aeris SA nobis in-
compertam alij cau&longs;æ nempe grauitati ip&longs;ius mer
curij BC intra fi&longs;tulam contenti. Hoc profectò con
firmatur ex eo, quod prædicta fi&longs;tula à digito &longs;u&longs;ten
tata exercet &longs;uam compre&longs;&longs;ionem contra pulpæ di
giti extremitatem, quæ à perimetro orificij vitri
gitur
pæ digiti partem, quæ ab ingenti pondere trium li
brarum mercurij v. g. magis, & euidentius compri
mi deberet quàm grauentur ambientes pulpæ digi
ti partes à perimetro ori&longs;icij vitri trium vnciarum.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Hanc euidenti&longs;&longs;imam demon&longs;trationem conatur
aduer&longs;arius refellere, ait enim,
pè æqualis cylindrus aeris incumbit ba&longs;i &longs;upremæ obstructæ
fistulæ &longs;iuemercurio, &longs;iue aqua, &longs;iue aere fi
&longs;tula plena &longs;it, vt patet. Vnde &longs;i
effectum, eumdem &longs;emper haberet, &longs;ed hæc
in&longs;t antia futilis est, quare in ea diutiùs mi
nimè hærendum. Sit fi&longs;tula AC plena ae
re non mercurio &longs;u&longs;tenteturque infer
nè eius orificium C à &longs;ubiecta digiti
pulpa, concedo, quod &longs;upernè digi
tus premitur à columna aeris SAC, pa
riterque
quidnam ex hoc deducit aduer&longs;arius? dicet, quod tantumdem ponderis pa
teretur digitus &longs;ubiectus
fi&longs;tula exinanita e&longs;t, quàm &longs;i
BC contineret, &longs;cilicèt &longs;i fi&longs;tula pen
deret duas vncias, & aereus cylindrus SA
libras exinanita fi&longs;tula æquè comprimeretur &longs;ubie
ctus digitus à pondere totius cylindri aerei SA
librarum vnà cum duabus vncijs vitri AC, cùmque
hoc &longs;it fal&longs;um; fi&longs;tula enim exinanita duas vncias &longs;o
lummodò pendit, non ergo &longs;uprema
SA fi&longs;tulam, & proindè digitum &longs;ubiectum compri
mit.
rius
nuo aduer
&longs;arius in&longs;ur
g&longs;t,
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
te
debet tamen in primoca&longs;u &longs;ubiectus digitus vi
tri tantum pondus percipere, in &longs;ecundo ve
rò præterea à pondere æquali merourio
&longs;u&longs;pen&longs;o grauabitur.
HVic difficultati
in&longs;inuatum e&longs;t, nulla alia de cau&longs;a fluida cor
pora circa tellurem &longs;phæricè
tèr eorum æquilibrium, &longs;cilicet quia omnes eius par
tes æquali ni&longs;u vim faciunt tendendo deorsùm, &
po&longs;tquam à &longs;oliditate terræ &longs;ubiectæ eius progre&longs;
&longs;us deorsùm impeditur ni&longs;u reflexo veluti in &longs;iphone
vici&longs;&longs;im &longs;e mutuo
&longs;olidi eleuatæ &longs;ursùm, itaque in ca&longs;u no&longs;tro, concipi
debet nedùm columna aerea SAC, &longs;ed etiam alia ei
æqualis aerea columna SG, quæ infernè per EC re
flectatur, & &longs;ursùm impellat digitum &longs;u&longs;tentantem
vitrum æquali ni&longs;u, ac ip&longs;a &longs;upernè comprimitur à
cylindro aereo SAC. digitus ergo
primitur
inter &longs;e contrarijs veluti forcipe, de
orsùm quidem à pondere aereo SAC,
flexi per EC,
natores pondus incumbentis aquæ
percipiunt, quia nimirùm æquali vi
&longs;ursùm motu reflexo impelluntur ab a
qua &longs;ubiecta, ac grauantur ab aqu&atail;
&longs;uprema
sum
&longs;tinebit tantummodò grauitatem dua
rum vnciarum fi&longs;tulæ vitreæ exinani
tæ AC quia nimirùm hic e&longs;t exce&longs;&longs;us
ponderis totius columnæ aereæ, & vitreæ SAC &longs;upra
aeream
e&longs;t ca&longs;us fi&longs;tulæ vitreæ mercurio &longs;tagnante repletæ,
quia nimirùm vis compre&longs;&longs;iua
ninò expletur ab&longs;umiturque eleuando
mercurium BC, & &longs;ic remaneat aerea columna SA
(prætèr vitrum) non &longs;u&longs;tentata à repul&longs;ione
aeris SG, & proindè &longs;u&longs;tineri debèt à digito &longs;ubiecto
eo mode, quo &longs;upra expo&longs;uimus.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Quapropter conuincens non e&longs;t argumentum do
cti&longs;&longs;imi viri, ideoque remanent illibatæ rationes &longs;u
periùs adductæ quibus per&longs;uademur
&longs;tula &longs;u&longs;tineri à pre&longs;&longs;ione circumambientis aeris.
Tran&longs;eamus iam ad examen tertiæ rationis ab eo-
dem viro clari&longs;&longs;imo adductæ, inquit
enim:
ris exterioris cylindro &longs;u&longs;tinetur, igitur
cylindrus exterior eamdem vim &longs;emper
habeat æqualem &longs;egmentum IC &longs;emper
&longs;ustinet. Sed hoc experimento repugnat,
nam &longs;i tantulum aeris antequàm demit
tatur mercurius in fi&longs;tula relinquatur mer
curius de&longs;cendet infra C; in C autem &longs;u&longs;ti
neri deberet &longs;i à cylindro aeris exterioris
&longs;u&longs;tineretur vt patet &c.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
gumen um
eiu&longs;dem au
thoris.
Non latuit huius argumenti authorem re&longs;pon&longs;io à
fautoribus contrariæ &longs;ententiæ allata, nimirùm
tantulum aeris infra fi&longs;tulam relicti po&longs;t de&longs;cen&longs;um mer
curij liberiorem nanci&longs;ci campum, ac proindè cum ante com
pre&longs;&longs;us e&longs;&longs;et explicare &longs;e&longs;e, ac dilatare, & premere &longs;uperfi
ciem mercurij, vnde hic infra C de&longs;cendit. Sed in&longs;tat di
cendo;
cacitèr ab ip&longs;o refutatam fui&longs;&longs;e.
Sed an reuerà iure refutata fuerit, po&longs;teriùs
demus
ab eadem experientia deducto retinebimus;
interea erit operæpretium exponere quomodò, &
quando aer intra mercurium in fi&longs;tula relictus expli
cetur dilateturque.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
celliana altitudinem mercurij con&longs;uetam deprimere
debeat; & &longs;imul traditur modus men&longs;urandi
maximam aeris dilatationem.
EX Roberuallij pulcherrima ob&longs;eruatione illius
ve&longs;icæ cyprinæ, quæ in vacuo fi&longs;tulæ dilatatur
ego conieci reperiri facilè po&longs;&longs;e in eodem Torricel
liano in&longs;trumento maximam amplitudinem, ad
aer non compre&longs;&longs;us à vi externa, & in &longs;ua libertat&etail;
relictus dilatari queat, quæ dilatatio certum, ac de
terminatum &longs;patium in vacuo Torricelliano occupa
ret, quod nimirum &longs;ufficienter exciperet maximam
eiu&longs;dem aeris expan&longs;ionem. Hinc po&longs;tea
molem aeris, quæ præcisè &longs;patium vacuum in Tor
ricelliano in&longs;trumento occuparet (quam molem me
diocrem appellabimus) non po&longs;&longs;e deorsùm impelle
re, & magis
curij &longs;tagnantis, ac proindè omnes moles aeris mi
nores illa, & ideò minus &longs;patium po&longs;t totalem eo
rum dilatationem exigentes non po&longs;&longs;e prædictam
mercurij &longs;upremam &longs;uperficiem deprimere,
trà moles omnes acris excedentes &longs;upradictam me
diocrem molem, & ideò exigentes amplius &longs;pa
tium deprimere nece&longs;&longs;ariò
ficiem in fi&longs;tula infra con&longs;uetam altitudinem vnius
cubiti, & quadrantis.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Vtque hæc experientia commodè exequi po&longs;&longs;et
efformaui fi&longs;tulas vitreas &longs;extam, & feptimam deli
neatas folio 43. libri experimentorum no&longs;træ Aca
demiæ Experimentalis Mediceæ, &longs;ed po&longs;tea facilio
ri apparatu idip&longs;um con&longs;equi po&longs;&longs;e animaduerti me
diante hoc in&longs;trumento, e&longs;tque eius artificium hu
iu&longs;modi: ampullæ vitreæ AB cuius diameter proximè
quatuor digitos adæquet
la BC maiore duorum cubitorum, quæ in&longs;lexa &longs;it i&ntail;
eius infimo loco CEF, atque in &longs;upremo loco eius A
continuetur quoque &longs;tricta alia fi&longs;tula AD cuius ex
tremum &longs;upremum orificium apertum D claudi po&longs;
&longs;it po&longs;t mercurij infu&longs;ionem &longs;uilla ve&longs;ica; po&longs;tea ter
minus extremus alterius fi&longs;tulæ FG vniatur cum al
tero extremo fi&longs;tulæ incuruatæ appo&longs;itis colligati&longs;
que portionibus inte&longs;tini agnini, quæ ne rumpantur
diffringantur que à nimio mercurij pondere pariter
operiantur fi&longs;tula, vel digitali coriaceo, atque arctè
alligatis inte&longs;tinis, & corio vtri&longs;que extremitatibus
fi&longs;tularum, poterit facilè fi&longs;tula FG inflecti &longs;ursùm,
& deorsùm po&longs;t mercurij infu&longs;ionem, eriganturqu&etail;
perpendiculariter ad horizontem ambæ fi&longs;tulæ DB
C, & GF. His præparatis per orificium D infundatur
hydrargyrum quou&longs;que duæ fi&longs;tulæ BC, FG, & am
pulla AB, repleantur, relinquaturque &longs;patium &longs;upre
mæ fi&longs;tulæ ID aere plenum, arctè po&longs;teà claudatur
&longs;upremum orificium D &longs;uilla ve&longs;ica; tandèm flecta
tur deorsùm fi&longs;tula collateralis FG, ab eius &longs;upremo
ore G pro&longs;&longs;uens mercurius excipiatur va&longs;e MN,
quou&longs;que infima mercurij
libella &longs;it LO, & &longs;uprema
&longs;uperficies eiu&longs;dem mer
curij &longs;tagnantis &longs;it H reli
cto nempè &longs;patio vacuo
DABH, quia verò cylin
drus aereus DI dilatatur,
nio in &longs;patio vacuo
relicto, fit vt po&longs;&longs;it
quando
nem integrè, & totalitèr
occupare
& tunc cum
pliùs explicari &longs;ua virtute
elatere non impellet deorsùm &longs;uperficiem hydrar
gyri H, & ideò &longs;umma altitudo mercurij HO erit
inalterata, &longs;cilicèt omnium maxima earum, quæ fie
ri po&longs;&longs;unt vnius cubiti & quadrantis proximè, & tunc
experientia con&longs;tat aerem DI maximè dilatatum in
tra &longs;patium DABH occupare locum 180. maiore&mtail;
quam prius. &longs;uppo&longs;ita hac cognitione ab experientia
deducta denuò operatio repetatur, & con&longs;tat quod
omnes moles aeris non excedentes &longs;patium DI non
depriment mediocrem mercurij eleuationem OH; &
è contrà omnes aeris moles excedentes DI
mercurium efficientque altitudinem OK minore&mtail;
men&longs;ura con&longs;ueta vnius cubiti, & quadrantis proxi
mè, & hoc profectò non fui&longs;&longs;e à docti&longs;&longs;imo viro ani-
maduer&longs;um facilè con&longs;tat, non enim dixi&longs;&longs;et:
lum aeris antequam demittatur mercurius in fistula, relin
quatur mercurius de&longs;cendet infra H. vbi &longs;u&longs;tineri debuerat
&longs;i ab aeris cylindro &longs;u&longs;tinebatur.
portiones aeris minores &longs;patio ID fummam altitudi
nem mercurij in fi&longs;tula non deprimunt, quia nimirùm
aereus cylindrus eiu&longs;dem roboris æquali vi compri
mit mercurium &longs;ubiectum. At quando aeris moles
maior ID ibidem includitur, tunc virtute eius elate
ria, vt po&longs;tea dicemus, vim facit contra impul&longs;u&mtail;
aeris externi, nempè cylindrus mercurij HO æquili
bratus ab aere externo impellitur &longs;ursùm ab O ver
sùs H, ab aere verò inclu&longs;o intra ampullam AB, dum
conatur &longs;e dilatare repellitur deorsùm ab H versùs
O. Vis ergo aeris comprimentis mercurium &longs;tagnan
tem L agit contra duas re&longs;i&longs;tentias, &longs;cilicèt contra
dus
clu&longs;i &longs;e dilatare conantis; igitur in hoc ca&longs;u minor erit
altitudo mercurij OK quam HO, licet producatur ab
eadem aeris virtute premente; Niligitur ex hac ter
tia aduer&longs;arij ratione deducitur contra aeris pre&longs;&longs;io
nem, & æquilibrium cum mercurio inclu&longs;o intra fi
&longs;tulam.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Quarta ratio eadem ferè e&longs;t cum prima, ad eamque
reducitur. quinta verò pendet ex eo quod &longs;patiu&mtail;
&longs;upremum fi&longs;tulæ po&longs;t mercurij lap&longs;um non vacuum,
&longs;ed repletum e&longs;&longs;e ait ex materia quadam tenui&longs;&longs;ima,
&longs;ed valdè ten&longs;a de qua re &longs;uo loco di&longs;putabimus; in
terim incidenter noto eius verba dum ait,
derume&longs;cat ve&longs;ica, antequam &longs;uperficies mercurij ad illam
perueniat.
quinta ratio
eiu&longs;dem au
thoris.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ricellianæ
nem, & ratio huius effectus redditur.
HOc profectò non &longs;emper accidit, præcipuè
do
bet, in ea enim commodè aliqua aeris portio, quæ
per
ligitur reduciturque po&longs;tquàm &longs;egregatur à mercu
rij &longs;ub&longs;tantia, per quam a&longs;cendunt innumera granula
aerea partim vi&longs;ibilia, partim incon&longs;picua ob minu
tiem, & hæc quidem ad &longs;upremam mercurij &longs;uperfi
ciem a&longs;cendunt, & prout magis ad &longs;patium vacuum
appropinquantur, eo magis cre&longs;cunt bullæ aereæ, in
fianturque, & tandem expanduntur, di&longs;&longs;iliunt
turque
ter
ficies exigua aquæ portione cooperiatur, tunc gra
nula aerea à mercurio a&longs;cendentia videri po&longs;&longs;unt in
tran&longs;itu per aquam tran&longs;picuam, quæ &longs;peciem repre
&longs;entant ebullitionis cuiu&longs;dam compo&longs;itæ ex prædi
ctis particulis aereis inflatis, & veloci&longs;&longs;imè
currentibus. His po&longs;itis ve&longs;icula illa cyprina Rober
uallij inclinata fi&longs;tula &longs;olet detume&longs;cere antequa&mtail;
mercurius eam attingat, propterea quòd partes illæ
aereæ, quæ priùs &longs;ummè dilatatæ erant in amplo &longs;pa
tio inani in &longs;ummitate fi&longs;tulæ, po&longs;tea re&longs;tricto &longs;patio
ob mercurij a&longs;cen&longs;um denuò conden&longs;antur, & proin
dè mirum non e&longs;t ve&longs;icam cyprinam ab aere eam am
biente den&longs;iori, quàm &longs;it aerintra ve&longs;icam
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateria
eius.
Quando verò &longs;ubdit, quod aer intra fi&longs;tulam im
mi&longs;&longs;us dum mercurius eleuatus e&longs;t ad prædictam al
titudinem cubiti vnius, & quadrantis proximè,
fertur tanto impetu, vt &longs;upremum fi&longs;tulæ fundum, &
ba&longs;is diffringatur; di&longs;&longs;iliatque, & quia ab exce&longs;&longs;u exi
gui ponderis tantus impetus creari non pote&longs;t, hinc
deducit non po&longs;&longs;e à cylindro aeris ambiente, & ab
eius
que aer in prædicta fi&longs;tula.
vi ela&longs;tica, & impetu in motu acqui&longs;ito diffringere
fundum &longs;upremum fistulæ pote&longs;t.
HVic difficultati occurro
curius in fi&longs;tula &longs;ursùm impellitur ab aere ex
terno non vnica, &longs;ed triplicivi, ponderis nimirum,
virtutis ela&longs;ticæ ad modum machinæ, & impetus in
motu acqui&longs;iti: &longs;ed præcipua, & in&longs;ignis actio in ca
&longs;u no&longs;tro impetui tribui debet. Quia po&longs;tquam è
fi&longs;tula cum mercurio extante in aere pendula effluit
gutta aliqua mercurij &longs;ubito ce&longs;&longs;at æquilibrium, &
ideò maius pondus collateralis columnæ aereæ po
te&longs;t &longs;ursùm intra fi&longs;tulam impellere molem minus
derantis
curij &longs;ursùm &longs;it tardus, & debilis, tamen in progre&longs;
&longs;u, & continuatione prædicti motus dum repetitis
ictibus mercurius ab aeris pondere, & vi eius ela&longs;ti
ca continenter impellitur, nouos gradus impetus, &
velocitatis creat, qui impetus &longs;unt integri, &
energiæ, non enim à vacuo intra fi&longs;tulam inclu&longs;o de
bilitari po&longs;&longs;unt, veluti debilitantur impetus
per aerem excurrentium; prædicti verò gradus velo
citatum &longs;imul coaceruati, tandem vim illam
componunt, quæ diffringere fundum vitreæ fi&longs;tulæ
pote&longs;t; adde quod corpora graui&longs;&longs;ima; vt e&longs;t hydrar
gyrum validius fu&longs;cipiunt retinentque vim impetus
præconcepti, & hinc &longs;equitur percu&longs;&longs;io eius validi&longs;
&longs;ima in vitri fundum. Supradictum ratiocinium abip
&longs;a experientia
longa &longs;ubtili, & gracili fundo clau&longs;a, & mercurio ple
na inuer&longs;o ore infra mercurium in &longs;cutella
demer&longs;a, & inclinato &longs;itu detineatur vt mercurius
minus vno digito à &longs;upremo fundo di&longs;tet, tunc &longs;u
&longs;pen&longs;a fi&longs;tula aer adueniens fundum eius non diffrin
git, at perpendiculari &longs;itu erecta fi&longs;tula aer
ingenti impetu
lit vt eum diffringat, quia nimirum in prolixiori mo
tu plures gradus impetus creari, & &longs;imul coaceruari
po&longs;&longs;unt.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateria
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateria
eius.
Po&longs;tea &longs;ubdit:
nulli volunt) mercurij extantis &longs;egmentum &longs;u&longs;tinetur, ne
que plus, neque minus pote&longs;t &longs;ustinere, igitur &longs;i ferrum can
dens admoueatur &longs;egmento vacuo fi&longs;tulæ, nulla e&longs;t ratio cur
&longs;uperficies &longs;uprema mercurij &longs;ub&longs;idat. Sub&longs;idit tamen.
Si
tur.
gumenturn.
per &longs;e, cum variè impellendo, &
aeris in &longs;ummitate fistulæ Torricellianæ reli
ctas, facilè po&longs;&longs;unt &longs;ub&longs;identem mercu
rium æquilibratum deprimere.
RE&longs;pondeo, quòd igneæ particulæ nedùm &longs;e ip
&longs;as vehementèr agitant, commouentque, &longs;ed
præterea aereas quoque particulas in vitri &longs;ummita
te inclu&longs;as, vt dictum e&longs;t, vehementi&longs;&longs;imè impellunt;
porrò quia quodlibet corpus æquilibratum pote&longs;t à
quacumque exigua vi agitari, (vt demon&longs;trauimus
in no&longs;tro opere de vi percu&longs;&longs;ionis) &longs;itque prædictus
mercurius in fi&longs;tula æquilibratus cum
te
ftina illa agitatione ignearum, & aerearum particu
larum &longs;uper&longs;icies mercurij percu&longs;&longs;a propelli pote&longs;t,
& ideò deprimi infra con&longs;uetam eius altitudinem de
bet, è contrà adhibitaniue, vel trita glacie, &longs;patium
illud dumigne priuatur, & deficit quoque agitatio,
& reuolutio nedum particularum ignis, &longs;ed etia&mtail;
aeris contenti, propterea præualere pote&longs;t exce&longs;&longs;us
grauitatis aeris ambientis &longs;upra mercurium in fi&longs;tu
la eleuatum.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateria
eius.
Affert po&longs;tea &longs;eptimam rationem:
curius &longs;ub&longs;idit vas infimum claudatur vt nulla rima &longs;u-
&longs;ub&longs;idit, &longs;ed tunc non &longs;u&longs;tinetur à cylindro aeris, quia &longs;cili
cèt non est applicatus.
&longs;tantia.
Huic argumento primus omnium re&longs;pondit Cla
ri&longs;&longs;imus Torricellius in epi&longs;tola ad Clari&longs;&longs;imum Mi
chaelem Angelum Riccium mi&longs;&longs;a, quam humani&longs;&longs;i
mè mihi communicauit anno 1658. eamque Floren
tiæ po&longs;teà Sereni&longs;&longs;imo Principi Leopoldo tradidi, &
inter amicos euulgaui.
gnantem in &longs;cutella, tamen quia aer relictus ibidem
remanet eodem modo pre&longs;&longs;us, & con&longs;tipatus
ac prius pote&longs;t mercurium in fistula ad
eamdem altitudinem re
tinere.
IS habet, quod
commercium inter ambientem aerem, & eum, qui
immediatè &longs;uperficiem &longs;tagnantis mercurij tangit
po&longs;ito nimirùm operculo, vt v. g. quando in fi&longs;tul&atail;
inflexa ABG mercurius eleuatur v&longs;que ad
BF vnius cubiti, & quadrantis relicto &longs;patio inani
AF, & po&longs;ito quod prædicta mercurij &longs;ublimatio de
pendeat à compre&longs;&longs;ione, quam cylindrus aereus SD
v&longs;que ad &longs;upremam aeris &longs;uperficiem exten&longs;us &longs;u&atail;
grauitate efficiat &longs;upra
curium D, &longs;equitur, quod &longs;i occludatur
orificium G eiuldem fi&longs;tulæ remanebit
portio aerea intercepta GD
do
nimirùm digitus, vel operculum reti
net con&longs;eruatque aerem in eadem po
&longs;itione, & con&longs;trictione, quam prius ab
incumbente aere patiebatur. Eode&mtail;
ferè modo, ac &longs;iloco aeris &longs;uperpone
rentur mercurio plures cylindri lapidei
vnus &longs;uper alterum incumbens, tunc
profectò infimus cylindrus comprime
ret &longs;uperficiem &longs;ubiecti hydrargyri D
non tantùm energia ponderis proprij,
&longs;ed vi conflata ex grauitate omnium incumbentium
cylindrorum modò ablatis &longs;emoti&longs;que &longs;upremis om
nibus columnis &longs;i in fimus cylindrulus, tantummodò
tabula, vecte, aut quo cumque alio retinaculo
vi fixè in eodem &longs;itu retineretur, patet quòd æquali
energia comprimeret &longs;ubiectam mercurij
D ac priùs premebatur à prælonga illa &longs;erie colum
narum incumbentium; Et hic dicendum e&longs;&longs;et, quòd
cau&longs;a immediata impellens mercurium non e&longs;t longa
illa &longs;eries columnarum SD, &longs;ed o&longs;t infimus cylindru
lus GD qui tanta vi comprimit &longs;ubiectum
quanta e&longs;t grauitas omnium columnarum SD; itaque
grauitas omnium columnarum appellari pote&longs;t cau
&longs;a productiua illius compre&longs;&longs;ionis, quam facit infi
mus cylindrulus GD mercurio immediatè
quia verò huiu&longs;modi effectus remanet, quando clau
ditur orificium G, remouenturque columnæ &longs;upre
mæ, igitur æquali vi, & æquali men&longs;ura debet mer
curius BF &longs;ublimari. Id ip&longs;um dici debet de aere SD,
certum profectò e&longs;t dum orificium G e&longs;t apertum cy
lindrum aereum GS v&longs;que ad aeris &longs;upremam &longs;uper
ficiem exten&longs;um comprimere cylindrulum aereu&mtail;
GD tanta vi quanta exigit energia grauitatis aeris
SG, quando verò digito, vel operculo impeditur
tactus
lindrulus aereus GD eodem modo compre&longs;&longs;us re&longs;tri
ctu&longs;que, ac prius igitur nece&longs;&longs;ario eodem modo &longs;ub
iectum mercurium D premet proindeque ad
altitudinem BF eum &longs;ubleuabit.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
VEritas huius a&longs;&longs;erti alio experimento confirma
tur: Demergatur in aliquo puteo RV aqua ple
no eadem fi&longs;tula ABG cum mercurio extante FB, vi
demus quod aliquanti&longs;per mercurius infra libellam
D deprimitur à pondere
paritèr altiùs
tium BH, vt nimirùm exce&longs;&longs;us FH &longs;upra eam eleua-
tionem, quæ in libero aere efficiebatur, &longs;it pars de
cimaquarta altitudinis aquæ ND. in hoc rerum &longs;ta
tu digito, vel quolibet alio operculo claudatur fi
&longs;tulæ o&longs;tium G hic iamce&longs;&longs;at om
ninò actio, & compre&longs;&longs;io
cylindri aquei NG, & tamen mer
curius in eodem &longs;igno fi&longs;tulæ H
per&longs;euerat, igitur eodem modo
in aere occlu&longs;o o&longs;tio G per&longs;eue
rare, & retineri debet mercurius
&longs;ubleuatus
dem
bebat
re&longs;trictione, quam produxerat pondus incumbentis
aeris SG. vnde con&longs;tat quod mercurius in fi&longs;tula ele
uari pote&longs;t à pondere aeris ambientis, nec adduct&atail;
difficultas hanc &longs;ententiam debilitat aut de&longs;truit.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Subdit po&longs;tea pro confirmatione &longs;ui ratiocinij:
quod aer interceptus inter operculum, & &longs;uperficiem vlte
riori compre&longs;sioni re&longs;istat, nempè &longs;i admoto dicto operculo, &
extante mercurio in BF aperiatur foramen in A mercurius
illicò infra F de&longs;cendit, idque notabili &longs;egmento, &c.
cinium cona
tur refellere
aduer&longs;arius.
Sibi ip&longs;i po&longs;tea opponit dicendo, quòd mercurius
tis mercurij BF, &
rem vlteriùs comprimat, & mercurium infra F depri
mat. po&longs;tea huic argumento re&longs;pondet:
lum à mercurio FB, & cylindro aeris grauitantis per fora
men A, quam remoto operculo, & clau&longs;o foramine A ab eo
dem mercurio BF & eodem cylindro aeris exterioris, nam
perindè e&longs;t &longs;iue tota vis pre&longs;sionis per lineam vnicam inci
dat, vel applicetur; &longs;iue &longs;ubduplum per vnam, & &longs;ubdu
plum per oppo&longs;itam. Vnde (paucis interceptis conclu
dit)
extare mercurium BF, & minimè &longs;ub&longs;idere, quia &longs;cilicet
dictus aerinterceptus comprimi vltra non pote&longs;t, &longs;ed alia de
cau&longs;a, &c.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Sed pace tanti viri, aio, verum
tum, demon&longs;trabo enim quod clau&longs;o vitro in G, & a
perto in A vis, qua comprimitur aer FB duplò vali
dior e&longs;t ea, qua comprimitur clau&longs;o vitro in A, & a
perto in G, pro cuius intelligentia præmittenda e&longs;t
&longs;equens.
dupla potentia comprimitur con&longs;tringiturque,
quàm à dupla, &longs;eu à duabus potentijs illi
æqualibus vtrinque anulum, vel
ve&longs;icam constringentibus.
SIt ABC anulus calybeus, vel ve&longs;ica aere plena, &
primò
inter&longs;e æqualibus P, & E, &longs;eu G. Et quia vnaquæque
&longs;eu energiæ compre&longs;&longs;ionis, quam patitur pars B,
do
momentum
le e&longs;t
energiæ, compre&longs;&longs;ionis,
patitur B, & fiunt ni&longs;us per
eamdem rectam perpendi
cularem ad horizontem, igi
tur ab&longs;oluta potentia P æ
qualis| e&longs;t re&longs;i&longs;tentiæ ab&longs;olutæ, &longs;eu vi compre&longs;&longs;ionis,
quam patitur B. Pari ratione ab&longs;oluta potentia E, vel
G æquatur re&longs;i&longs;tentiæ, &longs;eu vi compre&longs;&longs;ionis partis op
po&longs;itæ C. vnde deducitur duas potentias P & E, &longs;eu
G &longs;imul &longs;umptas æquales e&longs;&longs;e re&longs;i&longs;tentiæ integræ, &longs;eu
vi totali compre&longs;&longs;ionis, quam patitur anulus, vel ve
&longs;ica ABC.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateria
eius.
Po&longs;tea &longs;ub&longs;tituatur pauimentum durum RS loco
potentiæ flectentis E, vel G, & &longs;olummodo &longs;upernè
anulus, vel ve&longs;ica aerea comprimatur à potentia P
&longs;cilicet à &longs;emi&longs;&longs;e potentiarum P, & E. Dico anulu&mtail;,
vel ve&longs;icam aeream æquè con&longs;tringi, ac priùs à dua
bus potentijs contrarijs contundebatur. Quia paui
mentum &longs;tabile RS perinde reagit impediendo mo
tum, & de&longs;cen&longs;um ponderis P, ip&longs;umque in eodem &longs;i
tu quiete &longs;tabili permanere cogit, ac operatur manus
&longs;ubiecta E, vel pondus G mediante libra FE, ergo
&longs;tabilitatis &longs;oli momentum æquatur momento, & po
tentiæ ab&longs;olutæ ip&longs;ius E, &longs;eu P. quare anulus, &longs;eu ae
rea ve&longs;ica BC comprimitur non à &longs;ingulari, & &longs;ubdu-
pla potentia P, &longs;ed a duplici
potentia, tanquam à forcipe,
vel prælo, nempè à P, & ab
huic æquali re&longs;i&longs;tentia paui
menti RS. Igitur æquè com
primetur anulus, vel ve&longs;ica
aerea &longs;olo innixa à &longs;ingulari
potentia P, ac &longs;i à duabus contrarijs potentijs P, &
E, vel G con&longs;tringeretur.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateria
eius.
HInc patet, quòd &longs;i duæ potentiæ æquales &longs;imul
coniunctæ comprimant eumdem &longs;upremu&mtail;
anuli terminum pauimento innixi, tunc momentu&mtail;
fiue energia, qua anulus contunditur &longs;tringiturqu&etail;
duplex e&longs;t eius, qua ab ij&longs;dem potentijs oppo&longs;itos
terminos &longs;tringentibus comprimitur.
Quia quotie&longs;cum que duæ potentiæ inter &longs;e æqua
les P & G premunt &longs;upremum terminum B anuli BC,
tunc &longs;olum &longs;tabile RS in E, cui innititur idem præ&longs;tat,
& tanta energia operatur, ac &longs;i in E ade&longs;&longs;et potenti&atail;
æqualis ambabus contrarijs potentijs G & P: quare
vis, qua &longs;tringitur anulus æqualis e&longs;t duplo potentia
rum G, & P. è contrà quando anulus &longs;tringitur ab ij&longs;
dem potentijs G, & P &longs;ubdiui&longs;is, &longs;cilicèt à potenti&atail;
P in &longs;itu B, atque à potentia G in oppo&longs;ito eius ter
mino C vt in præcedenti figura videre e&longs;t, tunc vis,
qua &longs;tringitur anulus, æqualis e&longs;t præcisè duabus po
tentijs oppo&longs;itis G, & P, igitur quando anulus &longs;olo
innixus&longs;tringitur ab ij&longs;dem potentijs G, & P in B du
plici energia con&longs;tringitur, contunditurque quam &longs;i
ab ij&longs;dem duabus potentijs G, & P &longs;ubdiui&longs;is
geretur
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateria
eius.
&longs;cutellæ, & aperta &longs;ummitate fi&longs;tulæ, aer in &longs;cu
tella interceptus inter mercurium, &
operculum à vi duplò validiori
comprimitur, quàm illo
aperto, & hoc clau&longs;o.
IN fi&longs;tula Torricelliana ACG aper
ta in G, & clau&longs;a in A, facto vacuo,
more &longs;olito, remanente mercurio BF
eleuato
&longs;iu&longs;met aduer&longs;arij hypothe&longs;i, quòd
aer in &longs;cutella, &longs;eu ampulla DG con
tentus &longs;tringitur, comprimiturque à
duabus potentijs contrarijs inter &longs;&etail;
æqualibus (eò quod æquilibrantur)
nempè à pondere mercurij
& à pondere columnæ aereæ GS. Si
po&longs;tea appo&longs;ito operculo exactè clau
datur orificium G, & aperiatur
in &longs;ummitate fi&longs;tulæ A aer interceptus
inter operculum G, & mercurium D
&longs;tringitur comprimiturque à mercuio BF, & à colum-
na aerea FS æquali ip&longs;i GS, tunc patet, quòd poten
tiæ comprimentes mercurij FB, & aeris FS æquales
&longs;unt potentiæ eiu&longs;dem mercurij FB, & aeris SG. Iam
dico, quod duplò validiori vi comprimitur aer DG
clau&longs;o orificio G, & aperta &longs;ummitate A, quàm illo
aperto, & hoc clau&longs;o. Quia obturato vitro in A, & a
perto in G ampulla aerea DG &longs;tringitur à duabus
oppo&longs;itis potentijs, à mercurio nempè FB, & ab aeris
columna SG, ergo vis, qua aerea ve&longs;ica DG &longs;tringitur
æqualis e&longs;t duabus potétijs mercurij BF, & aeris SG,
&longs;eu duplò ponderis mercurij BF. è contra clau&longs;o ori
&longs;icio G, & aperto vitro in A duæ potentiæ mercurij
BF, & aeris SF comprimunt
aer innititur fundo &longs;tabili, nempè operculo G, igitur,
ex corollario præcedentis, propo&longs;itionis vis, qua aer
DG &longs;tringitur æqualis e&longs;t duplò
rij BF, & aeris SF, nempèl quadruplò potentiæ mer
curij BF; igitur dupla vi, & energia
DG clau&longs;o orificio G, & aperto vitro in A, ac
mebatur
tur verò in G.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateria
eius.
top. III. 111.
Quod verò à maiori vi compre&longs;&longs;iua, nempè dupla
magis con&longs;tringi, conden&longs;arique debeat aer DG, &
proinde mercurius deprimatur infra &longs;upremam ele
uationem F mirum profectò non e&longs;t, imò iuxtà ordi
nem naturæ, & nece&longs;&longs;itatem, qua operatur debet
mercurius in prædicto ca&longs;u aliquantulum deprimi, vt
exigit aeris natura, quæ dilatationi, & con&longs;trictioni
obnoxia e&longs;t. Hinc con&longs;tat ab aere
hiberi de&longs;cen&longs;um mercurij BF, quæ compre&longs;&longs;io facta
fuit à cylindro aereo incumbente SG ope eius na
tiuæ grauitatis.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Non e&longs;t nece&longs;sè vt hìc repetam
mera, quæ pa&longs;&longs;im obuia
Mer&longs;ennus, Pecquetus, Boile, Ga&longs;&longs;endus, & plures
alij&longs;crip&longs;erunt, & tandem prodijt liber experimen
torum no&longs;træ Academiæ Experimentalis Mediceæ;
ex his enim euincitur, ab aere ambiente mercuriu&mtail;
in fi&longs;tula &longs;ubleuari, quandoquidem quotie&longs;cumque
aer ex&longs;ugitur, &longs;eu prohibetur eius compre&longs;&longs;io &longs;uper
&longs;tagnantem mercurium, tunc deprimitur mercurius
infra &longs;upremum &longs;ignum in fi&longs;tula, & &longs;i hoc fiat in &longs;pa
tio vacuo, &longs;cilicètin loco à quo aer exclu&longs;us &longs;it, tunc
quidem mercurius omninò deprimitur, & è contrà
adueniente aere &longs;ubitò mercurius in prædicta fi&longs;tula
eleuatur. idip&longs;um accidit in aqua.
uationein fi&longs;tula, prout altitudo aeris maior, aut mi
nor fuerit.
PRætere a euidenti&longs;&longs;imum e&longs;t, mercurium in prædi
ct a fi&longs;tula eò magis deprimi infra altitudine&mtail;
vnius cubiti, & quadrantis, quò magis
eleuatur à plano &longs;ubiecto, &longs;ic Dominus Pa&longs;chalius in
montibus Aruerniæ expertus e&longs;t in radice montis
mercurij altitudinem fui&longs;&longs;e pollicum 27. cum tribus
lineis:
900. &longs;upra montis radicem, mercurij altitudo fuit&longs;o
lummodò pollicum 25. in cacumine verò montis vbi
altitudo ab eius radice erat pedum 3000. eleuatio
mercurij fuit pollicum 24. lin. 2. con&longs;tat ergo nedùm
minui compre&longs;&longs;ionem quando minuitur aeris altitu
do, &longs;ed etiam euincitur difformitas grauitatis ip&longs;ius
aeris; conijcitur enim, quòd aer habeat con&longs;i&longs;tentiam
veluti &longs;pongio&longs;am
partes &longs;uperiores dum comprimunt infimas, reddunt
aeris regionem difformiter grauem pro varia earu&mtail;
compre&longs;&longs;ione, & con&longs;tipatione, & pro varia mi&longs;tu
ra particularum aquæ, & terræ.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Idip&longs;um po&longs;tea ob&longs;eruauimus Florentiæ in alti&longs;&longs;i
ma turri palatij, in qua a&longs;cen&longs;is &longs;olummodò cubitis
50. &longs;upra infimam plateam, & palatij atrium depre&longs;
&longs;us apparuit mercurius &longs;patio vnius gradus, &longs;cilicèt
decima parte vnius digiti, at po&longs;tea perducto in&longs;tru
mento ad altitudinem 100.
curij minor fuit altero gradu euidenti, & notabili
defectu. Idemque po&longs;tea ob&longs;eruatum fuit in monti
bus propè Florentiam, & ne &longs;u&longs;picio &longs;ubiret aeris &longs;u
premi frigiditatem depre&longs;&longs;i&longs;&longs;e mercurium in fi&longs;tul&atail;
elegimus loca, & tempora commoda, &longs;cilicèt calefa
cta à &longs;ole in turris cacumine, & vmbro&longs;a in eius ra
dicibus, vt eorum temperies eadem e&longs;&longs;et, & hoc in
dicabatur adhibitis perfecti&longs;&longs;imis termometris, quç
o&longs;tendebant aerem in &longs;ummitate turris, aut eade&mtail;
temperic, aut calidiori &longs;eruari quem in radice turris
aut montis. & ne &longs;u&longs;picio &longs;ubiret à concu&longs;&longs;ione mer
curij in fi&longs;tula dum transferebatur &longs;ursùm exclu&longs;is
particulis minimis aereis, debui&longs;&longs;e po&longs;tea mercurium
aliquanti&longs;per deprimi, curauimus etiam obturato in
fimo fi&longs;tulæ orificio, ne vlla concu&longs;&longs;io mercurij effice
retur, & po&longs;tea in ip&longs;o de&longs;cen&longs;u vidimus præcisè
mercurium in ij&longs;dem locis eleuatum fui&longs;&longs;e ad ea&longs;dem
altitudines, ad quas in a&longs;cen&longs;u
uenerat, vnde colligitur &longs;olummodò ab aeris vari&atail;
compre&longs;&longs;ione mercurium &longs;uas altitudines varia&longs;&longs;e.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
mercurij in
fi&longs;tula Torri
celliana non
&longs;emper eiu&longs;
dem men&longs;u
ræ e&longs;t.
Vltimo loco animaduertimus non &longs;emper mercu
rium ad eamdem præcisè altitudinem in fi&longs;tula ele
nari, quæ aliqua ex parte pendet à temperie aeris
calida, & frigida, &longs;ed hæc quidem exigua e&longs;t &longs;i vi
trea fi&longs;tula in vertice eius &longs;upremo annexam ampul
lam vacuam, amplam habeat; mirabilis profectò vi
&longs;a e&longs;t variatio illa altitudinis, quæ procùl dubio à
perie
de ob&longs;eruata &longs;it temporibus æ&longs;tiuis, & hyemalibus,
pariter que in cubiculo ab igne excalefacto, vel fri
gido, et habeo penès me ob&longs;eruationes
rum 1657. & 1658.
&longs;ingulis diebus
termometro, an dies fuerit ne bulo&longs;us, vel pluuius,
aut &longs;erenus, & quinam venti &longs;pirarint, quas feci mo
nitu, & iu&longs;&longs;u Sereni&longs;s. Ferdinandi Secundi M. Ducis
Ætruri&ecedil;, naturalium operationum &longs;agaci&longs;&longs;imi explo
ratoris: & tandem videtur ex pluribus ob&longs;eruatio
nibus &longs;imùl collectis deduci po&longs;&longs;e, quòd multoties
cùm imminet aliqua diuturna, & continuata pluuia
in illa regione, tunc mercurius in fi&longs;tula per aliquos
gradus &longs;upra con&longs;uetam altitudinem eleuatur, è con
trà pluuia iam actu cadente mercurius in prædicta &longs;i
&longs;tula deprimi &longs;olet, nec e&longs;t exigua prædicta differen
tia, multotiès enim Pi&longs;is ob&longs;eruaui in diuturnis plu
uio&longs;is tem pe&longs;tatibus varia&longs;&longs;e mercurij altitudine&mtail;
per duodecim gradus, &longs;cilicèt per latitudinem vnius
pollicis. Quia verò a&longs;&longs;eruo penès me exemplar epi
&longs;tolæ, quam Sereni&longs;&longs;imo Principi Leopoldo modò
Cardinali ampli&longs;&longs;imo anno 1657. &longs;crip&longs;i circa hanc
materiam, hìc afferam breuiter ea, quæ tunc &longs;pecu
latus &longs;um, quod nimirùm fieri pote&longs;t ob aeris pre&longs;
&longs;ionem &longs;upra mercurium &longs;tagnantem in fi&longs;tula, vt an
te pluuiam aer multò magis grauitet, & comprimat,
quam in ip&longs;o pluuiæ de&longs;cen&longs;u, quod vt clariùs o&longs;ten
dam, præmittendum e&longs;t.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
à grauiori &longs;uper addito fluido occupetur, mercu
rius in fistula altiùs &longs;ubleuatur, at post
illius delap&longs;um denuo mercurius
deprimitur.
SVmpta fi&longs;tula vitrea ABC flexa in B, & facto i&ntail;
ea vacuo, more &longs;olito, mercurius eleuetur v&longs;que
ad F, demittatur po&longs;tea fi&longs;tula intra vas vitreum cy
lindricum DE maxim&ecedil; altitudinis earum quæ exca-
uari efformarique po&longs;&longs;unt, atque in eius fundo E de
mittatur fi&longs;tula cum &longs;tagnante mercurio ABC; po&longs;tea
repleatur cylindrus vitreus oleo, vel alio liquore le
uiori v&longs;que ad G, con&longs;tat à nouo pondere olei &longs;upra
mercurium &longs;tagnantem C incumbentis eleuari præ
terea mercurium ab F ad H, vt nimirum fiat æquili
brium inter mercurium HF, &
CG; po&longs;tea &longs;i&longs;upra olei
G innatet vas NO, quod arena, a
qua, vel alio grauiori fluido
ninò impleatur, procùl dubio à no
uo pondere NO altiùs mercurius
eleuabitur in fi&longs;tula ab H v&longs;que ad
M. His peractis reuoluatur vas N
O, vt nimirum arena, vel a qua flue
re po&longs;&longs;it deorsùm ad modum pluui&ecedil;
per &longs;patium oleo&longs;um GC, & dùm
prædicta pluuia deorsùm de&longs;cendit
non de&longs;eret mercurius
fi&longs;tulæ M, at po&longs;tquam areno&longs;a, vel aquea pluuia
dum
libellam mercurij C de primitur, tunc mercurius non
ampliùs per&longs;i&longs;tet in &longs;ummitate &longs;i&longs;tulæ M, &longs;ed paula
tim de&longs;cendet versùs H, prout maiori copia pluui&atail;
aquea, vel areno&longs;a ad ra
tio huius rei e&longs;t quia licèt arena, vel aqua grauior o
leo &longs;it, & proindè comprimat mercurium &longs;tagnantem
in C, eumque eleuet v&longs;que ad M, nihilominùs quan
do arena, vel aqua
mit eius fundum, non verò
curij C, & &longs;ic mercurius comprimitur tantummodò à
cylindro oleo&longs;o GC.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
nebulis pluuio&longs;is impregnatur, at postquam pluuia
delap&longs;a e&longs;t, denuò mercurius in fistulæ
deprimitur.
AB hoc euidenti&longs;&longs;imo experimento problema no
&longs;trum &longs;olui po&longs;&longs;e cen&longs;eo, quandoquidem quid
aliud &longs;unt nebulæ pluuio&longs;æ, &longs;cilicèt aqua grauidæ,
quàm aggregatum ex innumeris granulis minuti&longs;&longs;i
mis aqueis? & cùm prædicta nebula in alti&longs;&longs;imis ae
ris partibus innatat, vellenti&longs;&longs;imo
motu aquæ particulæ eius
dunt
turali augent aeris
que maiori ni&longs;u globum
comprimunt, quam aer purus, &
aqueis guttulis omninò priuatus
con&longs;tringere eum po&longs;&longs;it: & ideò fi
&longs;tula mercurialis ABC in infimo
prædicto aere con&longs;tituta compri
mitur nedùm à pondere &longs;uper&longs;tan
tis aeris, &longs;ed præterea à ponder&etail;
totius aquæ nebulam &longs;uprema&mtail;
componentis: itaque per aliquod tempus
pluuia de&longs;cendat, fieri pote&longs;t vt mercurius in fi&longs;tula
&longs;upremam illam altitudinem M pertingat, in caque
permaneat, & hoc nedum à nebulis, &longs;ed à quacum
que alia cau&longs;a grauitante effici pote&longs;t, &longs;i enim terre
&longs;tris puluis à vento, vel alia commotion e &longs;ursùm im
pellatur, atque per aerem di&longs;&longs;ipetur &longs;pargaturque
tunc nemo dubitat aerem grauiori ni&longs;u &longs;uperficiem
orbis terraquei comprimere. Si po&longs;tea à qualibet
cau&longs;a nebula impellatur, vt nimirùm terram attin
gat, &longs;cilic èt pluuia paulatim terram a&longs;&longs;e quatur
que
terræ innici, neque amplius aeris grauitatem, &
compre&longs;&longs;ionem augere, & quia à terra &longs;ubiecta &longs;u
&longs;tentantur, non po&longs;&longs;unt vt priùs &longs;uo|naturali pondere
comprimere &longs;uperficiem infimam mercurij &longs;tagnan
tis, & propterea &longs;emper à minori pondere mercu
rius in C comprimitur prout magis pluuia ad terram
perducitur, & prout magis aer illo pondere alleuia
tur, & propterea &longs;uperficies eius in &longs;uprema fi&longs;tulæ
parte &longs;en&longs;im deprimitur v&longs;que ad infimum &longs;itum F.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
conuer&longs;a re
gula vera est
nam ab alijs
cau&longs;is eleua
tio mercurij
in fi&longs;tula va
riari pote&longs;t.
Licèt hoc verum &longs;it, non tamen indè elici pote&longs;t
conuer&longs;a regula generalis, vt nimirum quotie&longs;cum
que mercurius in fi&longs;tula eleuatur debeat pluuia ex
pectari, quando quidem pote&longs;t huiu&longs;modi
compre&longs;&longs;ionis produci ab aliqua ingenti agitatione
&longs;upremæ atmo&longs;phæræ; & &longs;i fortè à particulis aqueis,
& terreis &longs;ubleuatis maior grauitas aeris producitur
fieri pote&longs;t vt à violentia ventorum alibi tran&longs;por
tentur nebulæ, & &longs;ic pluuia alibi translata non deci-
dat in eo loco vbi originem habuit. Arque ex his om
nibus concludi pote&longs;t aeremreuera &longs;uo pondere, &
vi ela&longs;tica comprimere mercurium in fi&longs;tula conten
tum, eumque ad illam determinatam altitudinem ele
uare.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
lem e&longs;&longs;e.
SEd multò magis patebit veritas prædictæ propo
&longs;itionis adhibitis experimentis à quibus imme
diatè, & directè o&longs;tenditur aeris grauitas, & primò
con&longs;tat
inflatum maiorem grauitatem, & pre&longs;&longs;ionem exerce
re quàm hocque po&longs;tea diligenti&longs;&longs;imè ab alijs
comprobatum e&longs;t, & &longs;umma facilitate perfici pote&longs;t
non quidem follibus violenter
leni plenitudine vtre clau&longs;o, vel commodiùs pila lu
&longs;oria aerea ad trutinam examinata, & po&longs;tea funicu
lo circa vtrem, vel pilam reuoluto violenterque con
&longs;tricto, tune quidem ob aeris conden&longs;ationem pon
dus vtris, aut pilæ manife&longs;tè ad trutinam augetur;
præterea, vt docuit Galilæus, intra vitream lagenam
violentèr aer in&longs;ufflari pote&longs;t vt valdè conden&longs;etur,
& tunc pondus prædictæ lagenæ &longs;en&longs;ibilitèr augetur
tia
uareperit, quòd grauitas molis aeris, quæ æqualis
&longs;it cubo aqueo vnius libræ granum vnum pendet. at
Mer&longs;ennus in Ph&ecedil;nomenis pneumaticis opeignis
dem
eamque vehementi&longs;&longs;imo igne calefecit, vt prorsùs
cande&longs;ceret, & &longs;ic in bilance per&longs;ecti&longs;&longs;ima, quæ à &longs;e
migraro &longs;lecte batur, examinauit pondus eiu&longs;de&mtail;
&ecedil;olopilæ 6. & gran. 15. po&longs;tea refrigerata æolo pila eius pon
dus præcedentem &longs;uperauit gran. 4. & hinc elicit ae
rem inclu&longs;um in æolo pila grana 4. pondera&longs;&longs;e, porrò
pondus aeris illius ad æqualem aquæ molem ait re
peri&longs;&longs;e in proportione 1. ad 1356.
cap.
4.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Sed prædicta experientia multis nominibus infi
delis e&longs;t, primò quia corpora vehementer excalefacta
in bilance &longs;u&longs;pen&longs;a non o&longs;tendunt veram grauitatem
eorum, &longs;ed diminutam, quia vt &longs;uperiùs o&longs;ten&longs;u&mtail;
e&longs;t, ignis diffu&longs;us ab æolo pila candente valdè rare
facit aerem prædictam æolo pilam ambientem, cum
que aer ambiens fimul cum pila vnum corpus graue
componat intra den&longs;iorem aerem &longs;u&longs;pen&longs;um, fit vt
aggregatum prædictum minùs graue &longs;pecie &longs;it,
prius, & proinde imminuitur grauitas æreæ æolo pi
læ, non &longs;olùm ob de&longs;ectum aeris inclu&longs;i, &longs;ed etiam ob
eius &longs;eruenti&longs;&longs;imam caliditatem.
Rursùs aer in &ecedil;olopila à vehementi&longs;&longs;imo igne am
pliatus expan&longs;u&longs;que non pote&longs;t diciverè rarefactus,
quia nimirùm copia ignis vehementi&longs;&longs;imè agitati, &
circumuoluti intra æolo pilæ cauitatem di&longs;gregat, ac
&longs;e parat particulas aliquas aeris ibidem relictas, ita
que intercapedines, quæ &longs;eparant aeris particulas,
partim occupantur ab igne, partim ab inani &longs;patio,
dum igneæ particulæ motu veloci&longs;&longs;imo conuertun
tur, & vertigines complent, intercipiendo grandia
&longs;patia in ania; vndè malè hinc infertur raritas maxima
ad quam aer ampliari pote&longs;t.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
fact a dubia quoque e&longs;t.
MElior e&longs;t &longs;ecunda Mer&longs;enni experientia dù&mtail;
in bombarda, &longs;eu &longs;clopeto pneumatico ma
gno conatu immi&longs;it va&longs;tam aeris molem, quæ in exi
guo &longs;patio conden&longs;ata fuit, aitque pondus &longs;exagin
ta
ab 8. vncijs aquæ impleri poterat, hinc deducit ae
rem in &longs;clopeto immi&longs;&longs;um adeò conden&longs;ari vt quin
decies &longs;patium internum catapultæ expleat; proin
de que tres digitos cubicos aeris ferè
num vnum. Sed ex tanto apparatu tandem Mer&longs;en
nus nil certi colligit, cùm afferat innumeras difficul
tates, & ingenuè fateatur, &longs;emper dubitari po&longs;&longs;e an
intra catapultæ cauitatem vnà cum aere in&longs;uffletur
particula aliqua oleagino&longs;a, vel aquea, quandoqui
dem epi&longs;tomium emboli humectari debetin eius &longs;u
per&longs;icie coriacea, vt omninò rimæ claudantur, vt re
gre&longs;&longs;us aeris prohibeatur.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Hi&longs;ce omnibus difficultatibus perpen&longs;is plures
modi
mentali Medicea excogitati
ris, hìc tamen referam aliquos ex multis à me ibidem
propo&longs;itis.
exponitur.
PRimò &longs;umatur fi&longs;tula vitrea
ABCF inflexa propè eius
extremum C, in &longs;ummitate verò
annexam habeat
lam AB diametro 4. digitoru&mtail;,
habeatque duo orificia aperta in
M & F, longitudo verò eius BD
maior &longs;it &longs;e&longs;qui cubito. Vas
dictum
orificium M, obturato prius o&longs;tio
infimo F, & po&longs;teà denuò ve&longs;ica
&longs;uilla clau&longs;o &longs;upremo orificio M
ibidem alligari debet æneum fi
lum
to infimo o&longs;tio F, facto vacuo mo
re &longs;olito, de&longs;cendet mercurij &longs;u
perficies v&longs;que ad L, po&longs;t qua&mtail;
&longs;cilicèt maior pars eius fluxerit ab infimo orificio F,
reman&longs;erit que &longs;patium ABL exinanitum, & tunc de-
nuò duplici ve&longs;ica &longs;uilla &longs;trictè alligata claudatur
orificium F. Po&longs;teà præparari debet vas profundum
PQR aqua plenum v&longs;que ad &longs;ummitatem PR, &longs;itque
eius profunditas tanta vt mergi po&longs;&longs;it vniuer&longs;um in
&longs;trumentum MAC, vt tamen eius ba&longs;is C putei fun
dum non attingat; demergatur fi&longs;tula prædicta vitrea
vnà cum mercurio contento intra aquam; & &longs;i fortè
os &longs;upremum vitri M non demergitur infra aquæ &longs;u
per&longs;iciem PR, exigui anuli ænei
na pendentes in C, & in &longs;ummitate A apponantur,
quou&longs;que vniuer&longs;a machina vitrea fiat proximè mi
nùs grauis &longs;pecie quàm aqua, &longs;cilicèt innatet, & emi
neat &longs;upra aqu&ecedil; libellam PR pars aliqua SN prædi
cti fili ænei vitro annexi, & in S fiat æquilibrium, &
quies. Deinde in aere aperiatur &longs;upremum os vitri
M, vt &longs;patium inane ABL aere impleatur,
bitque
propterea quod operculum in F impedit
curio LCF. In hoc &longs;tatu denuò eadem &longs;uilla ve&longs;ic&atail;
claudatur arcteque ligetur vitri os &longs;upremum M; &
tandem denuò demergatur fi&longs;tula infra
PR. Et quia in hoc ca&longs;u demergitur infra aquæ libel
lam moles conflata ex ij&longs;dem corporibus, &longs;cilicèt ex
vitro ACF, ex hydrargyro LCF, & ex ij&longs;dem ve&longs;icis,
& filis M & F, & &longs;olummodò de nouo ade&longs;t aer ABL,
quo fi&longs;tula priùs care bat; igitur nece&longs;sè e&longs;t, vt
totius machinæ NACF maius &longs;it quàm in priori &longs;ta
tu quando &longs;patium ABL vacuum fuerat. Quaproptèr
non poterit denuò &longs;ubleuari fi&longs;tula ad eamdem alti-
tudinem S, ni&longs;i grauitas eius imminuatur; au&longs;erri igi
tur debent aliqua grana, &longs;eù anuli ænei è collo &longs;i&longs;tulæ
AM, vt machina ad æquilibrium
mergaturque denuò
na tolluntur à fi&longs;tulæ collo A, tot præcisè men&longs;ura
bunt pondus aeris ABL intra fi&longs;tulam inclu&longs;i.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Multis modis po&longs;tea indagari pote&longs;t proportio
ponderis aeris ad aquam, &longs;ed omnium facillimus, &
&longs;implex erit &longs;i in aere perfecti&longs;&longs;ima bilance pondere
tur moles aquæ æqualis &longs;patio ABL, & hic compa
retur cum pondere iam inuento aeris eiu&longs;dem molis
ABL.
afferam instrumentum quo pondus ab&longs;olutum aeris
in diuer&longs;is locis eleuatis, ac depres&longs;is, & variè
temperatis reperiri pote&longs;t.
FIant tres ampullæ, vel ve&longs;icæ vitreæ, vel æneæ,
qualis e&longs;t AB, habeantque collum
æneum perfecti&longs;&longs;imè contornatum, hoc autem vi&longs;co
&longs;a aliqua materia, ac tenaci vniatur ferrumineturque
cum &longs;uprema ampullæ parte; habeat po&longs;tea
&longs;eu colli cauitatem turbinatam conicè, & perfecti&longs;&longs;i
mè
operculum paritèr æneum, & turbinatum, & exqui
&longs;iti&longs;&longs;imè læuigatum, vt nimirùm nulla rimula rema
neat, & perfecti&longs;&longs;imè claudat orificium fi&longs;tulæ C, vt
prohibeat ingre&longs;&longs;um, aut exitum aquæ, vel aeri;
dem
in particulas æquales, &longs;eu gra
dus. Po&longs;tea in fundo va&longs;is D in
clud antur granula exigua plum
bi quou&longs;que vniuer&longs;am
CAB
lam PR, ita tamen vt ampull&atail;
CB
&longs;is Q, &longs;ed innatet, & &longs;ecetur fi
lum æneum CE à libella aquæ
PR in aliquo eius puncto inter
medio F. His præparatis
tres pr&ecedil;dictæ ampullæ tempera
ri in eodem loco, & eodem va&longs;e aqueo, impleantur
que aere eiu&longs;dem cubiculi ad
tis
quod aquæ &longs;uper&longs;iciem tangit, & adhibitis vulgari
bus termometris notetur gradus caliditatis tùm ae
ris cubiculi, tùm aquæ po&longs;tea duæ am
pullæ
ris vel montis, reliquare ponatur medio loco inter
mitatem
riantur, vt raritatem aeris montani acquirant (arti
ficiosè aere temperato &longs;i opus fuerit vt ad eumde&mtail;
caliditatis gradum reducantur, quem in cubiculo ha
buerat;) po&longs;tea denuò am pullæ claudantur, atqu&etail;
intra idip&longs;um cubiculum a&longs;portentur, & ibidem in
tra aquam deme
ampullarum demer&longs;ione, aer enim &longs;upremæ turris,
vt minùs grauis altiùs eleuabit &longs;ilum æneum CE, vt
nimirùm &longs;upra aquæ libellam emineat portio maior,
quàm EF, & ex prædicta comparatione facilè digno
&longs;ci pote&longs;t diuer&longs;itas ponderis aeris, quæ in diuer&longs;is
eleuationibus reperitur. Sic etiam reperiri poterunt
differentiæ grauitatum aeris diuer&longs;orum locorum, ac
Vrbium.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
aquæ ad aeris grauitatem &longs;e habere, vt
SEd præcipuus, ac pulcherrimus modus
di
diceæ experimentali anno 1660. communi caui, vnà
cum eius demon&longs;tratione,
eumque ibidem eiu&longs;de&mtail;
anni &ecedil;&longs;tate ad praxim re
degi: &longs;ump &longs;i plum beam pi
lam cauam BC aere
& vndique clau&longs;am, hanc
quidem perfecti&longs;&longs;ima bi
lance in aere ponderaui,
po&longs;tea addito pondere F,
à quo po&longs;&longs;et pila BC infra
aquæ libellam demergi, paritèr eius pondus pr
&longs;um in aqua reperi, alligata nimirùm pila non funi-
culis, &longs;ed pluribus &longs;etis equinis à quibus eius gra
uitas in aqua non alteratur &longs;altem differentia &longs;en&longs;ibi
li; poterit ergò &longs;umi additamentum ponderis F ac &longs;i
augeret cra&longs;&longs;itiem pilæ
dus totius pilæ BACL vnà cum pondere adiuncto F
in aere trutinato; GH verò &longs;it pondus eiu&longs;dem ag
gregati BALCF intra quia verò,
ex Archimede, pondus corporis intra aquam demer&longs;i
imminuitur pro quantitate
æqualis &longs;it integro corpori demer&longs;o, igitur differen
tia HE erit pondus molis aquæ PQ, quæ æqualis &longs;it
corpori demer&longs;o BALCF. po&longs;tea pilam plumbeam
BC eodem modo clau&longs;am violentèr malleo contudi,
vt ad minus &longs;patium BLC redigeretur;
e&longs;t con&longs;ti patum re&longs;trictumque &longs;ui&longs;&longs;e aerem inclu&longs;um
vt nimirùm portio aeris A inclu&longs;a &longs;it in eodem &longs;pa
tio, quod occupabat reliqua aeris portio L. denuò
igitur pilam plumbeam contu&longs;am BLCF ponderaui
in aere, & in aqua, atque in aere pondus eius fuit
GN maius, quàm GE, eius verò pondus in aqua fuit
GM, quaproptèr ponderum differentia MN erit gra
uitas molis aquæ RS quæ æqualis &longs;it corpori demer
&longs;o BLCF, & &longs;ecetur EO æqualis MN. Quia verò aer
AL in ip&longs;omet aere
æquilibrium, igitur pondus GE tribui debet plum
bo BCF, cùm verò pila contu&longs;a in aere magis graui
tet pro men&longs;ura nimirùm GN, tunc quoque tota gra
uitas GE plumbo eidem tribui debet, at exce&longs;&longs;us
grauitatis EN nullo pacto tribui pote&longs;t portioni ae-
reæ L, quæ priùs æquè rara erat cum &longs;uo ambient&etail;,
&longs;ed tribui de bet portioni aereæ A, quæ in&longs;inuata e&longs;t
in eodem &longs;patio L, in quo reliqua pars aeris contine
batur; Po&longs;tea quia HE e&longs;t pondus molis aquæ PQ,
quæ &ecedil;qualis e&longs;t moli BA
LCF, & EO e&longs;t
lis aquæ RS æqualis inte
græ pilæ contu&longs;æ BLCF; i
gitur differentiale pondus
HO pertinet ad
&longs;upra RS, qu&ecedil; æqualis e&longs;t
aeri A in&longs;inuato intra
tium
corpora inter &longs;e æqualia mole
A, horum autem pondera ab&longs;oluta, ex Archimed&etail;,
eamdem proportionem habent, quam eorum gra
uitates in &longs;pecie; igitur pondus HO ad OM &longs;iu&etail;
ad ei æquale EN, eamdem
grauitas in &longs;pecie ip&longs;ius aquæ ad grauitatem &longs;peci fi
cam aeris, reperta autem fuit EN grauitas molis ae
ris A ob contu&longs;ionem in&longs;inuati intra L, igitur nece&longs;
&longs;ariò pondus HO tribui debet aqueæ moli VX. &longs;i po
&longs;tea &longs;umatur moles aquæ Y ad quam aquæ moles VX
eamdem proportionem habeat, quam HO ad OM,
patet eamdem grauitatem habere aquam Y ac aer A. His demon&longs;tratis referam iam experimentum factum
in no&longs;tra Academia experimentali Medicea; pon
dus in aere totius pilæ, & aeris BALCF fuit GE gra-
norum 31616. pondus verò
gran. 4272, eorum differentia HE fuit gran. 27344.
Præterea pondus totius pilæ contu&longs;æ GN fuit gra
norum 31623. in aere, in aqua verò fuit GM gran.
12508, ergò eorum differentia &longs;cilicèt pondus MN,
vel EO fuit granorum 19115. pondus EN differen
tiale inter GE, & GN fuit gran. 7. pondus verò dif
ferentiale HO eritgranorum 8229. quare ex regula
aurea vt pondus aeris granor. 7. ad pondus molis a
quæ ei æqualis gran. 8229. ita &longs;e habet 1. ad 1175.
cum 4. &longs;ept. itaque vna particula aquæ æquè ponde
rabit, ac æ&longs;tiui aeris particulæ 1175. cum 4. &longs;ept. quarum &longs;ingulæ æquales &longs;int mole ip&longs;i aquæ.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ibus humi
do l. 1. pr. 7.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Et in hac operatione facillima, quæ fallacijs, ac
difficultatibus minimè obnoxia e&longs;&longs;e videtur, &longs;ummo
compendionedùm grauitas ip&longs;ius aeris, &longs;ed etia&mtail;
proportio, quam habet ad aquæ grauitatem vnic&atail;
operatione elicitur.
maximam dilatationem est vt
TAndem ex no&longs;tris experimentis deducitur ma
xima aeris dilatatio. Suppo&longs;ito enim quòd in
catapulta pneumatica aer ad
tem redigatur, quia &longs;upra, ex no&longs;tro experimento, de
duximus aerem rarefieri vt &longs;patium expleat centies,
& octuagies maius, quàm priùs, quia verò hic aer
communis &longs;tringi conden&longs;arique pote&longs;t violenter v&longs;
que ad decimam eius partem, vel decimam quintam. igitur di&longs;tantia inter
ampli&longs;&longs;imam eius expan&longs;ionem, aut erit 1800. aut
2700.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
raris&longs;imus e&longs;t, & &longs;patium occupat bis millies maius
quam in &longs;tatu maximæ eius violentæ constri
ctionis, quæ &longs;i remoueatur &longs;pontè, & in
genti vi ad
tatem redigitur.
QVia verò experientia con&longs;tat aerem dilatari
quidem
ritate maxima, & è contrà
gi conden&longs;arique videmus, &longs;ed &longs;emper hoc efficitur
ab aliqua violentia externa, hinc cogimur a&longs;&longs;erer&etail;
aerem habere virtutem quamdam ela&longs;ticam, qua ni
mirùm quotie&longs;cumque violentiam con&longs;trictiuam pa
titur, tunc quidem re&longs;ilire vehementerque vibrar&etail;
&longs;e&longs;e dilatando po&longs;&longs;e; hoc autem con&longs;tat
perimento in ip&longs;a catapulta pneumatica, in qua aer
magna vi inclu&longs;us in eius cauitatem po&longs;tea amot&atail;
valuula tanta violentia ruit, erumpitque, vt pila&mtail;
plumbeam, &longs;eù telum impellat proijciatque, vt i&ntail;
magna di&longs;tantia tabulam oppo&longs;itam &longs;atis cra&longs;&longs;a&mtail;
di&longs;rumpat, atque terebret: hoc autem nulla ration&etail;
fieri po&longs;&longs;et, ni&longs;i aer haberet vim, & facultate&mtail;
ingentem &longs;e&longs;e dilatandi, & amplius &longs;patiu&mtail;
occupandi. Cùm igitur iam ex &longs;uperiùs dictis inno
tuerit ad quamnam maximam amplitudinem aer ra
refieri, dilatarique po&longs;&longs;it, pariterque ad quem gra
dum con&longs;tipationis,
leat, & vidimus quòd eadem aeris moles, quæ in &longs;ua
maxima conden&longs;atione fuit redacta occupabat minus
quam bis mille&longs;imam partem &longs;patij, quod in maxima
&longs;ui dilatatione explebat, dicendum e&longs;t aerem in &longs;ua
naturali con&longs;titutione, ide&longs;t remota omni violenti&atail;
externa, ampli&longs;&longs;imum &longs;patium exigere, & in tali qui
dem
vel in &longs;patio vacuo, at in regione infima aeris propè
aquam, & terram tunc quidem varijs modis compri
mitur, cùm à pondere aeris incumbentis, tùm à pon
dere aquæ aut terræ in infimis cauitatibus, aut à qua
cumque alia vi motiua ad prædictam maximam con
&longs;tipationem redigitur. Sic videmus in in&longs;trumento
Torricelliano aeris granula ad latera mercurij po&longs;i
ta, dum &longs;ursùm a&longs;cendunt quò magis ad mercurij
&longs;ummitatem
nulorum augeri, quou&longs;que propè &longs;patium inane &longs;u
premum ingentes &longs;ph&ecedil;ras expleant: idip&longs;um immi&longs;&longs;a
ve&longs;ica cyprina propemodum exinanita intra mercu
rium ob&longs;eruatur, & clariùs mercurio &longs;uperpo&longs;ita a
quæ portione con&longs;picitur in eodem in&longs;trumento,
granula aerea intra aquam
&longs;ui exiguitatem inob&longs;eruabilia, & incon&longs;picua fue
rant, po&longs;tea facto vacuo, &longs;cilicèt &longs;ublata incumbentis
aeris compre&longs;&longs;ione, &longs;ubitò con&longs;piciuntur &longs;en&longs;im infla
ri, augerique, vt efficiant ampullas grandes per
a&longs;cendentes, quæ ad confinium &longs;upremum eius per
ductæ di&longs;&longs;iliunt, euomuntque aereas particulas intra
prædictum &longs;patium inane, cùm è contra &longs;i dum actu
eleuantur ampullæ amplæ illæ aereæ, denuò compri
mantur aere &longs;upemè introducto momento con&longs;pi
cies aerem denuò ad &longs;tricti&longs;&longs;imum, & incon&longs;picuum
&longs;patium redigi; Non pote&longs;t igitur negari, ni&longs;i negatis
&longs;titutio
præterea quòd quotie&longs;cumque à vi externa compri
mitur, con&longs;tringiturque nihilominùs habeat quoque
vim, & energiam naturalem &longs;e&longs;e celerrimè dilatandi,
facta nimirum re&longs;ilitione ad modum machinæ.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
quidem adhibita violentia po&longs;sint, &longs;ed postea
&longs;ponte re&longs;ilire ad in&longs;tar arcus valeant.
HIc iam quæri pote&longs;t, qualis nam e&longs;&longs;e oporteat
aeris &longs;tructura ac forma, vt prædictas opera
tiones efficere valeat. Et profectò &longs;i &longs;en&longs;u, non uerò
phanta&longs;ticis, & chimericis hypothe&longs;ibus philo&longs;o
phandum e&longs;t, confiteri tenemur aerem componi ex
machinis flexibilibus, & re&longs;ilientibus ad modum ar-
cus, quia nimirum in hi&longs;ce machinis prædictum &longs;ymp
toma ob&longs;eruatur, &longs;cilicèt arcus, vel machinæ exigunt
amplam illam exten&longs;ionem, & &longs;i ab externa vi con
&longs;tringantur, comprimanturque, tunc &longs;ponte &longs;ua re&longs;ili
unt prioremque amplam
aereæ particulæ non e&longs;&longs;ent machinæ profectò percipi
non po&longs;&longs;et quare, & quomodò po&longs;t compre&longs;&longs;ionem
&longs;ilirent
loca non minora, &longs;ed &longs;ibi ip&longs;is ad&ecedil;quata occupant,
non po&longs;&longs;int corpora &longs;e mutuò penetrare, igitur i&ntail;
pr&ecedil;dicta con&longs;trictione libenter per&longs;i&longs;tere deberent,
nec qu&ecedil;rerent loca ampliora, quæ ab ip&longs;is impleri oc
cupariquè non po&longs;&longs;ent: deberet igitur ip&longs;is a&longs;&longs;ignari
vis quædam motiua quæ di&longs;&longs;ociaret &longs;epararetque ae
ris particulas à &longs;e inuicem, hæc verò &longs;en&longs;u, & cogni
tione quadam anima&longs;tica percipere deberent
quod ad
perciperent, qua quæ&longs;o ratione &longs;e excitarent ad ope
randum? Quanto rationabilius e&longs;t eam &longs;tructuram ae
reis particulis a&longs;&longs;ignare, à qua nece&longs;&longs;itate cæca
tur
ralem exigentiam
mur &longs;i concipiamus aeream &longs;ub&longs;tantiam conflari ex
innumeris machinulis iuxtà &longs;e po&longs;itis, & tunc quidem
clarè percipiemus in prædicto aggregato virtute mil
lam elateriam reperiri po&longs;&longs;e, quia nimirùm machinu
læ illæ po&longs;t compre&longs;&longs;ionem &longs;e&longs;e conantur dilatare. vt
verò con&longs;tet, me non &longs;ubitò nec o&longs;citanter huic &longs;en
tentiæ a&longs;&longs;en&longs;um pr&ecedil;bui&longs;&longs;e, referam quicquid in
venit circa aeris &longs;tructuram.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
virtute affecti, &longs;aluari po&longs;&longs;ent symptomatæ conden&longs;a
tionis violentæ, & &longs;pontaneæ eius ingentis
rarefactionis.
PRimò enim excogitaui artificium, quo &longs;uppo&longs;i
tis aereis minimis particulis non flexibilibus,
po&longs;&longs;et nihilominùs fieri prædicta aeris &longs;pontanea di
latatio. Supponebam enim minimas aeris particulas
e&longs;&longs;e conicas, &longs;ed excauatas:
aerei coni po&longs;&longs;it intra
te&longs;t planè &longs;aluari illa compre&longs;&longs;io, quæ videtur
prehen&longs;ibilis
&longs;olida corporea, & plena prædictorum conorum po
te&longs;t e&longs;&longs;e nedùm pars bis mille&longs;ima, &longs;ed adhùc minor
&longs;patio inani intra prædictos conos
vetat corpus den&longs;um, ac durum in gracili&longs;&longs;imas lami
nas extendi po&longs;&longs;e, à quibus coni excauati efformen
tur. &longs;ed hic iam nodus difficillim&ecedil; &longs;olutionis &longs;e offert,
qua,
conus intrà
facit &longs;e ab eo
bio ijs vis qu&ecedil;dam motiua a&longs;&longs;igna
ri debet, & hæc diuer&longs;a
ea, quæ in alijs corporibus terre
nis reperitur:
ABC, DCE, FGH, IHL. & &longs;ic alij innumeri eodem
modo di&longs;po&longs;iti: animaduerti po&longs;tea, quòd in ma
gnete, & in omnibus magneticis corporibus dantur
duo poli, borealis nempè, & au&longs;tralis, & quotie&longs;
cumque duo corpora magnetica &longs;uper aquam inna
tantia ad &longs;e&longs;e propiùs accedunt, tunc quidem polo
vnius au&longs;trali vnitur, connectitur que alterius corpo
ris borealis polus, & &longs;i contingat vt alitèr di&longs;ponan
tur à violentia aliqua externa, fponte &longs;ua recedunt,
& indebita con&longs;titutione &longs;ituantur, tum re&longs;pectu &longs;ui,
cum re&longs;pectu poli au&longs;tralis Orbis Terræ. cogitaia&mtail;
conos excauatos ABC, FGH e&longs;&longs;e magneticos, vel
ferreos virtute tamen magnetica affectos, vt nimirùm
omnes vertices A, & F &longs;int poli boreales, partes ve
rò au&longs;trales &longs;int ba&longs;es BC, & GH, & quia ba&longs;es præ
dictæ &longs;unt cauæ poli au&longs;trales præcisè exi&longs;tent in cen
tris circulorum BC, & GH. his po&longs;itis innatent iam
pr&ecedil;dicti conuli, &longs;cilicèt mouerilateralitèr po&longs;&longs;int ab&longs;
que vllo impedimento, tunc quidem polus borealis
F coni FGH, &longs;i coniungi debet iuxtà magneticas le
ges cum polo au&longs;trali conuli ABC nece&longs;&longs;ariò vertex
F cum centro circuli ba&longs;is BC coniungetur naturali
in&longs;tinctu, & ideò re&longs;i&longs;tet externæ violentiæ, quæ
fituationem perturbare conaretur. A dueniat iam alia
vis externa, quæ violentèr in&longs;inuet verticem F intra
finuo&longs;am cauitatem alterius versùs A, tunc quide&mtail;
naturali ni&longs;u, ce&longs;&longs;ante
tex coni FGH ab interna illa po&longs;itione, & denuò re
trocedet
circuli ba&longs;is BC. Et hæc inquam e&longs;&longs;et vis ela&longs;tica, quæ
in aere reperitur, nec talis hypothe&longs;is vt impo&longs;&longs;ibilis
reprobari po&longs;&longs;et, cum reuera & terra, & corpora om
nia terrena magneticam vim habere manife&longs;tum &longs;it,
in quibus prædicta operatio nece&longs;&longs;ariò &longs;equeretur,
po&longs;ita
gneticis. Po&longs;&longs;ent aliunde omnia alia phænomen&atail;,
quæ in aere ob&longs;eruantur &longs;aluari ex prædicta hypo
the&longs;i, igitur concediea deberet &longs;altem vt po&longs;&longs;ibilis.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
læ &longs;int duræ flexibiles, & re&longs;ilientes ad modum ma
chinæ, habeantque figuram tubi, vel cylindri
excauaticompo&longs;iti ex laminis, vel filis
læuibus, aut ramo&longs;is obliquè in &longs;e
ip&longs;os circumductis.
HAnc tamen hypothe&longs;im po&longs;tea reiecire accura
tiùs con&longs;iderata; &longs;nppo&longs;ui enim tubulos ali
quos gracili&longs;&longs;imos multis modis componi po&longs;&longs;e ex
materia re&longs;iliente ad modum machinæ. Primò &longs;uppo
ni po&longs;&longs;unt tubuli conflati ex tenui&longs;&longs;ima laminula i&ntail;
&longs;e ip&longs;am circumducta, & continuata, quæ paritèr
machina &longs;it flexibilis, & po&longs;t compre&longs;&longs;ionem re&longs;ilire
valeat, vt contingit in arcu compre&longs;&longs;o. hinc &longs;aluari
pote&longs;t maxima illa aeris conden&longs;atio quam patitur à
vi externa comprimente, quia nimirùm perimetrum
internum fi&longs;tulæ licèt &longs;emper eiu&longs;dem men&longs;uræ &longs;it,
tamen minorem capacitatem continentèr acquirit,
quò magis comprimitur, &longs;cilicèt quò magis à circu
lo recedit eius ba&longs;is, & ad figuram longiorem ellip
ticam redigitur. Alio modo componi po&longs;&longs;unt tubuli
aerei, &longs;i nimirùm concipiatur inuolucrum factum ex
lamina tenui&longs;&longs;ima, quæ quidem paritèr flexibilis &longs;it,
& ad modum arcus re&longs;ilire valeat, hæc, inquam, mul
tò magis comprimi pote&longs;t, & ad minus &longs;patium redi
gi, quam &longs;implex tubus paulò ante expo&longs;itus, qui&atail;
nimirùm internus ambitus adhùc con&longs;tringi, & immi
nui pote&longs;t, vt nimirùm perimeter ba&longs;is minor fiat, re
petitis nimirum conuolutionibus prædicti inuolucri,
& præterea, non minùs, quam antea pote&longs;t laterali
tèr comprimi vt nimirùm ba&longs;is non circularis, &longs;ed el
liptica fiat, & &longs;ic duplicata cau&longs;a re&longs;trictionis mul
tò magis minui poterit moles aeris con&longs;tipati con
den&longs;atique; Tertiò &longs;i &longs;upponantur tubuli aerei com
po&longs;iti ex tenui&longs;&longs;ima virga ramo&longs;a, vel fa&longs;cia obliquè
reuoluta, & in &longs;e ip&longs;am circumducta ad modum &longs;pi
ræ, relictis nimirùm aliquibus inter&longs;titijs inter tran&longs;
uer&longs;ales &longs;piras, tunc quidem multò faciliùs tubulus
prædictus con&longs;tipari poterit tribus nominibus, &
quia ambitus internus imminuitur, pariterque decur
tatur altitudo fi&longs;tulæ, & tandem ad figuram compre&longs;
&longs;am ellipticam redigitur, quare &longs;i &longs;olida materia præ
dicti tubuli, &longs;eù &longs;piræ &longs;it dura quidem, &longs;ed flexibilis,
& apta ad re&longs;iliendum vt machina, vel arcus chali
beus, eique naturalitèr competat ampla, & dilatat&atail;
&longs;igura, poterunt profectò
ce&longs;&longs;ante violentia
&longs;tatum dilatatum, rarumque redigentur, vt videmus
in ijs &longs;erpentibus puerorum ex tenui&longs;&longs;imo æneo filo
confectis, &longs;cilicèt &longs;piralitèr reuolutis ad modum co
chleæ, in
ximè imminuitur, at po&longs;tmodum raritatem &longs;uam de
nuò repetunt. Et hac quidem figura a&longs;&longs;ignata aeri fa
cilè &longs;aluantur phænomena omnia, quæ in ip&longs;o aer&etail;
ob&longs;eruantur, de quibus &longs;igillatim &longs;uis in locis pecu
liaritèr agemus.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
ris grauitate
æquilibrio,
&longs;tructura, &
vi elateri&atail;
eius.
Natura dari.
NIl frequentiùs apud Medicos, & Philo&longs;ophos
reperitur, quàm nomen qualitatis, &longs;eu virtu
tis attractiuæ, quæ licèt magno fa&longs;tu, & &longs;upercilio
proferatur, nil profectò ab&longs;urdiùs reperies, &longs;i attentè
igitur manife&longs;tè con&longs;tare in natura attractionem da
ri, vt videre e&longs;t in magnete, qui ferrum ad &longs;e trahit,
pariterque electrica omnia corpora fe&longs;tucas exiguas
magno impetu ad &longs;e adducunt, &longs;ic paritèr calorem,
& dolorem in aliqua determinata parte animalis ex
citatum, vt in manu v. g. vel crure, attrahere à parti
bus longinquis nedùm &longs;anguinem, &longs;ed etiam humo
res cæteros aiunt; non &longs;ecùs cucurbitulæ medicæ fol
les, & alia in&longs;trumenta pneumatica dum aerem exu
gunt, attrahunt quoque humores adnexos; quia ve-
rò in hi&longs;ce omnibus operationibus nullum organum
corporeum apparet à quo tractio effici valeat; hinc
concludunt vim, & qualitatem attractiuam incor
poream e&longs;&longs;e, habereque facultatem ad &longs;e attrahendi
fluida corpora ambientia. Sed quis capiet à virtut&etail;
incorporea naturali vi, & immediatè, ab&longs;que organo
corporeo, corpus aliquod moueri, & trahi po&longs;&longs;e? quo
modo enim quod incorporeum, & proindè indiui&longs;i
bile e&longs;t applicare &longs;e pote&longs;t, apprehendere, con&longs;trin
gere, impellereque corpus exten&longs;ionem habens, cum
lumine naturæ con&longs;tet nullam motionem, aut actio
nem phy&longs;icam ab&longs;que contactu fieri po&longs;&longs;e, pariter
que con&longs;tet corpus ab incorporeo minimè tangi? Igi
tur nece&longs;sè e&longs;t vt attractio fiat mediante aliquo in
&longs;trumento corporeo.
dari attracti
onem.
corpus, quod præterea fune, vel vncino alligatum
transferri debet.
QVia
tiua trahit aliud corpus nece&longs;&longs;ariò agitari
& &longs;tabile agens &longs;upponatur, quomodò quæ&longs;o aliud
corpus contiguum agitabit, & è &longs;uo loco dimouebit? verùm quando agens motu locali agitatur, tunc com
prehendo, quòd corpus ei adnexum è regione po&longs;i
tum expelli è &longs;uo loco debet, aliàs agens corpus non
moueretur; & hoc
penetrare
dum fuerit, &longs;altem agitari debet lateralitèr vt
tran&longs;itum impellenti corpori concedat, & &longs;i fuerit
durum, ac con&longs;i&longs;tens, integrum corpus obiectum di
mouebit id expellendo. Si verò corpus ambiens
non anteriùs motui eius obijciatur nec ip&longs;um impe
diat, &longs;ed po&longs;ticè ei adhæreat, tunc quidem &longs;i allige
tur fune, vel vncino, alioque con&longs;imili corpore cur
uo, fieri pote&longs;t, vt ad motum agentis etiam
corpus &longs;ub&longs;equens transferatur. Et hoc quidem ea
dem ratione lumine naturæ deducta euincitur, quia
in&longs;trumenti tractorij pars curua, quæ anteriùs impel
litur ab agente, ob
teriùs impellitur, & ab eius duritie, & &longs;oliditate cor
pus po&longs;ticè apprehen&longs;um transfertur; at &longs;i funis, aut
vncinus, vel quodlibet aliud organum curuum re
moueatur, non video, neque percipio quomodo
mouetur corpus anticum trahere &longs;ecum debeat cor
pus
dari attracti
onem.
Sed non de&longs;unt Philo&longs;ophi, qui dicant:
lè concipi corpus ten&longs;um dum &longs;e&longs;e reducit, aliud corpus, cui
contiguum est &longs;ecum adducere, ac corpus compre&longs;&longs;um aliud
corpus à&longs;e amouere, nec alio fune opus e&longs;t ad hunc finem,
cùm enim iuxtà naturæ in&longs;titutum omnia corpora &longs;int par
tes vniuer&longs;i, & partes, quætotum aliquod componunt con
iunctæ eße debeant, alioquin partes non e&longs;&longs;ent &longs;i &longs;eor&longs;im e&longs;&longs;e
po&longs;&longs;ent, ideò vnum corpus adhæret alteri.
dari attracti
onem.
ducit aliud corpus cui contiguum e&longs;t &longs;ecum adducere,
ac corpus compre&longs;&longs;um aliud corpus à &longs;e
amouere.
QVia nece&longs;&longs;itas huius operationis patet ex eo
quòd corpus moueri non pote&longs;t ad locum al
terius corporis occupandum, ni&longs;i expellat illud ibi
degens, cùm duo corpora in eodem loco poni no&ntail;
po&longs;&longs;int; atquod corpus dum mouetur recedendo ab
alterius corporis locotrahere &longs;ecum adhærendo de
beat corpus po&longs;ticè &longs;ibi contiguum à cuius contactu
conatur recedere, & cui non colligatur glutine, fu
ne, aut alio vinculo, nedùm gratis a&longs;&longs;eritur,
ninò impo&longs;&longs;ibile videtur, & omnem captum &longs;uperat. Cùm verò ait
&longs;int partes vniuer&longs;i
quòd
& quod aliàs partes non e&longs;&longs;ent &longs;i &longs;eor&longs;im e&longs;&longs;e po&longs;&longs;ent;
partes exercitus di&longs;cretæ &longs;unt, & tamen totum exer
citum componunt. Similiter plures lineol&ecedil; di&longs;cretæ
totam longitudinem palmarem componere po&longs;&longs;ent,
non &longs;ecùs ac &longs;i Et noto, quòd nomine coniunctionis hìc non intelli
gitur vnio, & connexio omninò firma, &longs;ed &longs;implex
contactus partium, qualis e&longs;t ille quo aceruus arenæ,
& granorum tritici connectitur; nam aqua à
aere attracta, vel ab embolo eis non connectitur vni
turque, &longs;ed tantum adhæret &longs;implici contactu. Modò
nemo e&longs;t, &longs;i &longs;eriò, & bona fide loqui velit, qui no&ntail;
percipiat e&longs;&longs;e impo&longs;&longs;ibile vt grana tritici &longs;ub&longs;equen
tia trahantur ab antecedentibus granis, eorumqu&etail;
motum imitentur à vi &longs;implicis contactus ab&longs;que vl
lo vinculo, vel glutine, & procùl dubio talis motus
effici po&longs;&longs;et quando grana &longs;ub&longs;equentia ab aliqu&atail;
vimotiua impellerentur, qu&ecedil; aut &longs;pontaneo motu, co
gnitione præuia, vt animalia, aut cæca nece&longs;&longs;itate,
vt grauia, tran&longs;portarentur, quæ omnia in no&longs;tro ca
&longs;u locum non habent.
dari attracti
onem.
Sed ne gratis prolata verba diutiùs in&longs;ectemur,
noto quòd aduer&longs;arij numquam euincent dari in na
tura vim, &longs;eu qualitatem attractiuam, ni&longs;i euidentia
&longs;en&longs;us, aut demon&longs;tratione o&longs;tendant, quòd corpo
ra, quæ attrahi videntur non moueantur à vi intrin&longs;e
ca &longs;pontaneo motu, neque impellantur ab externo a
liquo corpore. Hoc autem cùm numquam præ&longs;tite
rint, profectò affirmare non po&longs;&longs;unt dari in natura ve
ram attractionem, proindeque licitum erit eorum a&longs;
&longs;ertionem negare.
E contrà &longs;i nos offenderimus, quòd aliqua corpo
ra eorum, quæ attrahi videntur vi naturali,
ueantur, & accedant ad alia corpora: reliqua verò vi
externa impellantur, planè profligata erit vis, & qua
litas attractiua è rerum natura.
dari attracti
onem.
terna impelluntur.
ET primò quoad ferrum, & magnetem pertinet,
iam o&longs;tendimus (lib.
de vi percu&longs;s.) ambo hæc
corpora naturali vi &longs;pontaneo motu vnum versùs al
terum moueri non &longs;ecùs, ac grania &longs;ponte ad terram
feruntur. In electricis verò iam ab alijs cau&longs;a attra
ctionis tradita e&longs;t; con&longs;tat enim experientia, quod
ni&longs;i electrica corpora incale&longs;cant ope confricationis
in aliquo panno factæ non attrahunt exiguas, & leues
ei&longs;que vicinas fe&longs;tucas, quæ proindè collocantur in
quadam veluti at mo&longs;phæra ex fumo&longs;is, & calidis ex
halationibus compo&longs;ita ambiente corpus
ex quo fit vt ma&longs;&longs;a illa ex prædictis vaporibus, & fe
&longs;tucis compo&longs;ita leuior &longs;it aere contiguo magis re
moto, ideoque ab hoc ma&longs;&longs;a illa fumo&longs;a exprimitur,
con&longs;tringiturque vndique versùs
ctricum, &
In tubis pneumaticis, & cte&longs;ibianis, nec non in cu
cur bitulis medicis, dicendum, quòd ad eas fluida, &
mollia corpora feruntur non &longs;pontaneo motu, &longs;ed à vi
externa impul&longs;a, & hæc profectò non e&longs;t alia quà&mtail;
&longs;implex grauitas oceani aerei
bientis, à quo aqua, & corpora mollia &longs;ubiecta
primuntur
hydro&longs;tatica &longs;uperiùs expo&longs;ita. Hinc fit vt &longs;ubleua-
to embolo in tubo, vel rarefacto aere interno cucur
bitulæ pars fluida, & mollis &longs;ubiecta minùs compre&longs;
&longs;a ab ambiente aere expelli &longs;ursùm debeat à part&etail;
magis pre&longs;&longs;a. Stultè ergo quis recurreret ad vim, &
qualitatem attractiuam emboli, vel cucurbitulæ, vt
aquam eleuet, cùm ad&longs;it vera, & nece&longs;&longs;aria cau&longs;a hu
ius effectus, quæ e&longs;t columna aerea aquam
comprimens, à qua vi impul&longs;iua aqua in&longs;inuatur, ex
primiturque intra tubum, vel cucurbitam.
dari attracti
onem.
Sed hoc clariùs &longs;uo loco declarabitur; interim tran
&longs;eo ad difficultatem &longs;atis plau&longs;ibilem, quæ contra
doctrinam afferri &longs;olet. Inquiunt enim, quando cu
curbitulæ carnem attrahunt, vel fi&longs;tula digiti
intra eam in&longs;inuat, manife&longs;tè percipitur &longs;en&longs;us dolo
rificus in parte illa carnis, aut digiti, quæ intra cucur
bitulam, vel fi&longs;tulam in&longs;inuatur, nulla verò pa&longs;&longs;io, aut
noxa percipitur in reliqua parte corporis animalis,
nec in po&longs;tica digiti parte, &longs;en&longs;us verò doloris à nihi
lo produci non pote&longs;t, & è contrà cau&longs;a actiua com
pre&longs;&longs;ionem efficiens &longs;en&longs;ationem dolorificam afferre
deberet, igitur &longs;en&longs;us doloris percipi deberet non in
pulpa digiti, &longs;ed in oppo&longs;ito vngue, pariterque dolor
non in &longs;capulis, vbicucurbita idhæret, &longs;ed in pecto
re percipi deberet, vbi reuerà efficitur compre&longs;&longs;io,
& contu&longs;io ab extremo aere ambiente, in ip&longs;a verò
pulpa carnis intra cucurbitam, vel fi&longs;tulam in&longs;inuata
nulla pa&longs;&longs;io percipi deberet, cùm ibi deficiat cau&longs;&atail;
illa, quæ &longs;ua violentia impellit, & comprimit
&longs;io animalis
carnem intra
cucurbitulas
impelleret
dolor in
pe&longs;ita corpo
ris parte
pre&longs;&longs;a
pi deberet,
non in pur
Pro huius difficultatis &longs;olutione repetenda &longs;unt
aliqua priùs declarata, vbi &longs;cilicèt quærebatur qua
re vrinatores in profundo maris ingentem
aquæ incumbentis non percipiunt, diximus hoc pro
uenire, ex eo, quòd partes aquæ fluidæ æquali ni&longs;u
grauitatis comprimunt vndequaque corpus anima
lis demer&longs;um, nempè è parte &longs;uprema infima, & col
laterali, quia ibidem o&longs;tendimus, quòd impul&longs;io, at
que compre&longs;&longs;io in vno peculiari loco facta luxatio
nem, rupturam, contu&longs;ionemque efficere pote&longs;t, &
è contra &longs;i eadem virtus compre&longs;&longs;iua multiplicetur,
vt vndique impellat,
tunc o&longs;tendimus nedùm noxam doloremque non au
geri, &longs;ed è contrà nullam luxationem, neque contu
&longs;ionem, & proinde nullam pa&longs;&longs;ionem dolorifica&mtail;
procreari po&longs;&longs;e. Et hoc euidenti&longs;&longs;imum e&longs;t ex &longs;upe
riùs demon&longs;tratis. Præterea diximus, quòd licèt in
&longs;ignis luxatio, & diui&longs;io continui ab vniuer&longs;ali ill&atail;
compre&longs;&longs;ione fluidi non &longs;ub&longs;equatur, nontamen ne
gari pote&longs;t con&longs;trictio quædam totius corporis, quæ
quidem in profundo oceani oportet vt &longs;entiatur, ob
nouitatem; at in aere nullo pacto animal ab vniuer
&longs;ali eius compre&longs;&longs;ione con&longs;trictioneque vllam pa&longs;
&longs;ionem percipere debet ob a&longs;&longs;uetudinem, ab ip&longs;o e
nim ortu animalia &longs;emper eadem ve&longs;te aerea
tur
nem in ip&longs;o animali aeris compre&longs;&longs;io producit, &
propterea cen&longs;et à nulla vi ambiente con&longs;tringi, aut
comprimi, igitur à prædicta vi compre&longs;&longs;iua carnes,
va&longs;a, & vi&longs;cera patiuntur con&longs;trictionem quamdam,
quæ profectò nullo pacto percipi pote&longs;t ab animali
bus. Imò etiam con&longs;trictiones non perpetuæ, vt
illæ quæ fiunt à no&longs;tris ve&longs;timentis ob
pa&longs;&longs;ionem dolorificam minimè afferre &longs;olent.
dari attracti
onem.
&longs;uperior dif
ficultas.
dari attracti
onem.
lis ea
HIs præmi&longs;&longs;is animaduertendum e&longs;t, quòd nouus
effectus flexionis, aut diui&longs;ionis continui, vel
contu&longs;ionis in animali duplici modo produci pote&longs;t,
aut quia &longs;uperuenit noua cau&longs;a
malis latus, aut quia deficit ibidem vis illa compre&longs;
&longs;iua fluidi ambientis, quæ reliquas omnes animalis
partes con&longs;tringit, comprimitque, & quæ hactenùs
ob con&longs;uetudinem non percipiebatur. In primo ca&longs;u
mirum non e&longs;t effectum contu&longs;ionis dolori&longs;que tribui
impellenti virtuti &longs;uperuenienti; at in &longs;ecundo ca&longs;u
fallacia oriri pote&longs;t ex phanta&longs;ia præiudicata, &longs;cili
cèt exi&longs;timabitur defectum comprimentis fluidi i&ntail;
vno latere tractionem, & &longs;uctionem procreare,
doquidem
pre&longs;&longs;io facta à fluido ambiente, cuius actionem num
quam percepit ob a&longs;&longs;uetudinem, contu&longs;ionem, aut
impul&longs;ionem fanguinis, & carnium efficere vnquam
potui&longs;&longs;et. Nec de&longs;unt exempla quibus hoc confirma
tur. ponatur Rana infra aquam, vel hydrargyrum de
mer&longs;a,
do ambiente; &longs;i po&longs;tea foramini collaterali va&longs;is ra
næ abdomen applicetur vt exactè perimetrum fora
minis contingat, tunc portio cutis eius comprehen
&longs;a à prædicto foramine inflari, & turgere con&longs;picie
tur, & veluti mammillam tumidam extra forame&ntail;
ad partes aeris exporrigere, non quidem quia attra
hitur ab aere externo, &longs;ed quia exprimitur à pre&longs;&longs;io
ne grauioris fluidi ambientis: verùm cùm prædict&atail;
extuberantia creari non po&longs;&longs;it ab&longs;que violenta tra&longs;
po&longs;itione, & di&longs;tractione partium in abdomine con
tentarum, &longs;cilicet inte&longs;tinorum, membranarum, va
&longs;orum, & cutis, igitur hinc &longs;ub&longs;equetur pa&longs;&longs;io dolo
rifica, quam rana iudicabit ab aeris externi attra
ctione factam fui&longs;&longs;e, nec vnquam per&longs;uaderi po&longs;&longs;et à
pondere aquæ, vel mercurij ambientis depender&etail;. Non &longs;ecùs vniuer&longs;alis illa aeris compre&longs;&longs;io continua
ta, & a&longs;&longs;idua quadam pre&longs;&longs;ione contu&longs;ioneque corpus
vniuer&longs;um animalis veluti prælum &longs;tringit, atque ob
con&longs;uetudinem nullam noxam, neque &longs;en&longs;atione&mtail;
creat; ce&longs;&longs;ante po&longs;tea in aliqua peculiari corporis
parte huiu&longs;modi compre&longs;&longs;ione mirum non e&longs;t &longs;i hu
mores, & carnes ob compre&longs;&longs;ionem factam in reliquis
locis animalis impellantur violentèr intra cucurbi
tulam, vbi actio compre&longs;&longs;iua aeris deficit, & ibidem
pa&longs;&longs;io dolorifica &longs;entiatur.
dari attracti
onem.
dari attracti
onem.
fluidi corpora mollia intra cucurbitulas, & fistulas
in&longs;inuari.
QVòd po&longs;tea reuerà caro intra cucurbitulam in
&longs;inuetur à compre&longs;&longs;ione externi aeris
tis&longs;uma
tur ve&longs;ica &longs;uilla aere plena, &longs;ed non valdè ten&longs;a, eique
applicetur orificium cucurbitulæ paritèr aere ple
næ, vt nimirùm perimetrum eius oris tangat ve&longs;icæ
pelliculam, pofteà ve&longs;ica cum annexa cucurbitula in
fra aquam demergatur, videbis quò magis ve&longs;ica ad
fundum aquæ perducitur, eò magis portionem ve&longs;i
cæ intra cucurbitam contentam turgere inflarique, &
intra cucurbitulæ cauitatem aliquantulum in&longs;inuari,
perindè, ac caro no&longs;tra turgens intra cucurbitulas
immitti &longs;olet. Et multò euidentiùs hoc continget fi
prædicta ve&longs;ica aqua impleatur, & po&longs;tmodum vnà
cum annexa cucurbitula infra
tur, videbis quòd tanta vi turgida pars ve&longs;icæ intrà
cucurbitulam immittitur, vt requiratur violentia ali
qua ad diuellendam cucucurbitulam ab ip&longs;a ve&longs;ica. Et hoc profectò tribui non pote&longs;t virtuti attractiuæ,
quam nec cucurbitula, neque aer inclu&longs;us habet, &longs;ed
manife&longs;tè hoc efficitur à pondere aquæ, vel mercurij
ambientis, à quo ve&longs;ica vndique comprimitur præ
terquàm in illo circello comprehen&longs;o à cucurbitulæ
orificio, ibi enim aer inclu&longs;us in cucurbitula
modò
veluti fornex impedit ne aqua, vel hydrargyrum am
biens &longs;ubiectam ve&longs;icæ particulam comprimat con
tundatque.
dari attracti
onem.
Idip&longs;um hoc alio opportuniori experimento com
probari pote&longs;t: in fi&longs;tula vitrea vtrinque aperta aere
plena infernè aptata digiti pulpa orificium eius om
ninò claudatur, po&longs;tea manus cum ei annexa, & in
cumbente fi&longs;tula immergatur intra
gyrum, itaut &longs;upremum fi&longs;tulæ orificium extet &longs;u
pra mercurij, aut aquæ libellam; tunc caro pulpæ di
giti inflatur tumoremque in&longs;inuat rubicundum intr&atail;
fi&longs;tulam, percipitur que &longs;en&longs;us quidam &longs;uctionis, &
hic con&longs;tat non ade&longs;&longs;e vim vllam attractiuam, cù&mtail;
aer intra
faciat, & proindè concedendum e&longs;t, à pondere am
bientis aquæ, vel mercurij, comprimi manum, atque
digitum, & &longs;ic
parte digiti, quæ non &longs;tringitur, nec comprimitur
à pondere ambientis fluidi.
aquæ demer&longs;us fi&longs;tulam làbijs comprehen&longs;am, & &longs;u
premo aeri communicantem &longs;ecum deferat, vel orifi
cium fi&longs;tulæ cuti manns, aut brachij applicet; is cer
tè videbitlinguam, vel cutim intra fi&longs;tulam parum
per in&longs;inuari, & &longs;en&longs;um &longs;uctionis patietur, ad in&longs;tar
eius qui in cucurbitulis fieri &longs;olet.
Idip&longs;um experieris &longs;i ingentem cucurbitulàm ab-
domini applicatam tecum deferas in Ex quibus omnibus
dij fluidi ambientis
malis, & proindè exprimi pote&longs;t
lis in ea cauitate cucurbitæ, in qua cutis caret com
pre&longs;&longs;ione cùm aer cucurbitæ rarefactus ab igne, vel
à &longs;uctione, aut emboli tractione &longs;it imminutus, fit vt
minimè comprimat cutim &longs;ubiectam, ea validitat&etail;,
qua reliquæ animalis partes ab ambiente aere con
tunduntur.
dari attracti
onem.
&longs;en&longs;u p
pi
in parte cor
poris centi
gua cucur
bitulæ, non
verò pæti im
pul&longs;um à flui
do in reli
quo corpo
factam.
Sed, dices, &longs;en&longs;u ip&longs;o percipitur tractio quæda&mtail;
in cucurbitulis, non verò percipimus impul&longs;ione&mtail;
factam à fluido externo
lis partes à cucurbitula non tactas.
&longs;en&longs;us falsò &longs;e percipere &longs;uadetur trahi cutim, & &longs;an
guinem, cum verè tumor fiat à pres&longs;ione am
bientis aeris.
NVllus alius effectus percipitur in cucurbitulis
medicis præter quàm violenta quædam ex
pre&longs;&longs;io, & intru&longs;io carnis, & &longs;anguinis intra cucur
bitulæ cauitatem, à qua nimirum pellis vehementer
inflatur, & tumet proindeque cutis di&longs;ten&longs;a &longs;en&longs;um
doloris patitur. Hoc autem triplici modo fieri po&longs;&longs;e
con&longs;tat, aut quia funibus, & vncinis incon&longs;picuis cu
tis, caro, & &longs;anguis
quia &longs;pontaneo motu ad replendum vacuum ibidem
accurrunt, vel quia ab extrin&longs;eca violentia pre&longs;&longs;io
nis aeris ibidem exprimuntur immittunturque. pri
mus modus videtur omninò ab&longs;urdus, &longs;ecundus reij
citur quoque, nam &longs;i reuerà caro, & &longs;anguis &longs;pont&etail;
&longs;ua intra cucurbitulam migrant, ergo ibidem no&ntail;
attrahuntur violentèr, proindeque e&longs;t impo&longs;&longs;ibile, vt
facultas animalis percipiat &longs;en&longs;um doloris ob
tiamEt licèt dici po&longs;&longs;et dolorem creari per accidens ob
cutis, & carnis di&longs;tractionem; ex hoc ip&longs;o infertur
&longs;itiuæ
iuraret fen&longs;u percipere tractionem violentam carnis,
non verò motum eius &longs;pontaneum intra
dari attracti
onem.
Fatendum ergo e&longs;t, tumorem carnis, & &longs;anguinis
intra cucurbitulas produci non po&longs;&longs;e ab alia cau&longs;&atail;
quàm à pre&longs;&longs;ione aeris ambientis, quæ ex præmi&longs;&longs;is
propo&longs;itionibus nece&longs;&longs;ariò prædictum effectum cre
are debet, quatenùs in particula illa carnis intra cu
curbitulam inclu&longs;a deficit vis compre&longs;&longs;iua ambientis
aeris, hæc verò cùm minimè percipiatur, nec ad
uertatur ob a&longs;&longs;uetudinem, mirum non e&longs;t, nouum effe
ctum tumoris non tribui cau&longs;æ ignotæ licèt veræ, &longs;ed
potiùs tribuatur ei cau&longs;æ licèt &longs;al&longs;æ, quæ
&longs;e &longs;en&longs;ibus con&longs;tat, &longs;cilicèt cucurbitulæ exinanitæ.
Neque nouum e&longs;t, intra vi&longs;cera, & partes animalis
fieri tumores ex affluxu humorum, cùm tamen
cipiamus an prædicti humores &longs;ponte, vel vi ibidem
deferantur.
dari attracti
onem.
Tran&longs;eo iam ad aliud argumentum adductum pro
confirmatione attractionis: Sit DEF vas oblongu&mtail;
mercurio plenum,
trea vtrinque aperta AB, & immerga
tur intra vas DF, quou&longs;que &longs;upremum
eius orificium A demergatur infra li
bellam mercurij E;
ti pulpa &longs;upremo orificio fi&longs;tulæ A, vt
arctè claudatur. Iam &longs;i &longs;ummitas fi&longs;tu
læ A vnà cum claudente digito eleue
tur, percipitur manife&longs;ta attractio di
giti pulpæ, quam &longs;uprema mercurij &longs;u
perficies tangit, hæc (inquiunt) vio
lentia procùl dubio efficitur à pondere
&longs;ubiecti mercurij,
manus &longs;uftentare debeat pondus prædicti mercurij,
non &longs;ecùs, ac &longs;i vncino aliquo digito annecteretur,
hinc deducitur quòd detur in rerum natura facultas,
& operatio attractiua, & &longs;i hoc verùm e&longs;t (inquiunt)
quare in cucurbitulis &longs;imilitèr ab&longs;que funibus, aut
vncinis non pote&longs;t &longs;imilis attractio fieri?
m
tra
adductam do
ctrin
turata, & infernè intra
mur percipere in digito &longs;en&longs;um &longs;uctionis, & ponderis
mercurij &longs;ustentati, tamen verè grauamur à cy
lindro aereo &longs;upra vnguem incumbente, & &longs;u
ctio pulpæ digiti à defectu pres&longs;ionis aeris
dependet.
dari attracti
onem.
REuera Mercurius pulpæ digiti connectitur in A,
non vi aliqua attractiua, &longs;ed à compre&longs;&longs;ion&etail;
aeris ambientis &longs;upra &longs;tagnans hydrargyrum E
va&longs;is &longs;ubiecti; hoc autem confirmatur ex eo, quòd &longs;i
altiùs eleuetur fi&longs;tula, vt nimirùm &longs;oli
tam altitudinem vnius cubiti, & qua
drantis excedat, tunc quidem &longs;uprema
mercurij &longs;uperficies leni&longs;&longs;imo motu
ab&longs;que vlla difficultate diuellitur, &longs;epa
raturque à digiti pulpa &longs;uprema A, non
igitur à vi attractiua mercurius digito
annectebatur. Sed quæres; vnde ergò
oritur &longs;en&longs;us ille &longs;uctionis, & tractio
nis, qui in prædicta pulpa digiti perci
pitur, & quomodò &longs;u&longs;tentat, atqu&etail;
percipit grauitatem mercurij &longs;ubiecti? Re&longs;pondeo, quòd à pondere aeris ma
nui, & digito incumbentis
tes digiti, excepta illa particula, quæ orificium vitri
A attingit, & ab hac compre&longs;&longs;ione exprimitur &longs;an
guis in tumore illo rubicundo pulpæ digiti, quæ in
orificio vitri A in&longs;inuatur, quando &longs;patium inane ibi
dem creatur. Præterea ade&longs;t pondus hydrargyri in
tra fi&longs;tulam contenti, quod &longs;u&longs;tinetur à pre&longs;&longs;ione cy
lindri aerei dum comprimit mercurij &longs;uperficiem &longs;ta
gnantis. Vnde ex vna parte habemus pondus cylin
dri aerei, orificium, & digitum in A comprimentis,
pariterque ade&longs;t pondus vitri AB, & mercurij in ip
&longs;o contenti, ex altera verò parte ade&longs;t grauitas alte-
rius aerei cylindri prementis &longs;tagnantem &longs;uperfici
em E, & ab hoc
virtute manus &longs;u&longs;tinetur re&longs;iduum ponderis vltra æ
quilibrium, &longs;cilicèt pondus vitri AB vnà cum ponde
re cylindri aerei orificio, & digito A incumbentis,
licèt falsò per&longs;uadeatur &longs;e &longs;u&longs;tinere mercurium &longs;ub
iectum, eique adnexum.
dari attracti
onem.
Et profectò ab hac experientia euincitur, quòd tra
ctio illa, quæ in digito percipitur, non &longs;it vera attra
ctio facta ob vacui timorem, quia dum fi&longs;tula minùs
cubito cum quadrante eleuatur, mercurius à digito
non diuellitur, & proindè &longs;patium inane ibidem non
intercipitur, vnde nulla attractio fieri deberet, cùm
è contrà maxima fieret quando ob mercurij de&longs;cen
&longs;um efficitur &longs;olita inanitas, & tamen hoc fal&longs;um e&longs;t,
cùm in vtroque ca&longs;u ferè æquali vi digiti pulpa de
or&longs;um attrahi &longs;entiatur.
&longs;i&longs;&longs;ima difficultas, quam cari&longs;&longs;imus amicus Diony
&longs;ius Guerrinus M.D. Ætrur.
fectus mihi di&longs;cutiendam propo&longs;uit. Dicebat enim &longs;i
in tubis pneumaticis, &longs;eu cte&longs;ibijs, quibus aqua&mtail;
haurire &longs;olemus è puteis, aqua eleuatur, non
vera attractione, quatenùs embolo eleuato hauritur,
vel exugitur aqua &longs;ubiecta, vt pueri calamo intr&atail;
aquam immi&longs;&longs;o re&longs;tricto ore, & anhelitu, & &longs;piritu
attracto aquam &longs;ursùm eleuant; &longs;ed hoc contingit,
quia dum embolus manu &longs;ursùm trahitur, impellitur
&longs;ursùm quoque cylindrus aereus embolo
& proindè prohibetur impeditur que actio compre&longs;
&longs;iua prædicti aerei cylindri &longs;upra aquam &longs;ubiectam. Vis ergo & conatus manus embolum eleuantis sem
per eidem re&longs;i&longs;tentiæ opponitur, nempè&longs;u&longs;pendit e
leuatque eumdem cylindrum aereum &longs;upra
incumbentem, igitur &longs;emper eadem vis, idemque co
natus manus requiritur ad
reum cylindrum, & ad prohibendam eius compre&longs;&longs;i
onem &longs;upra aquam &longs;ubiectam. Hinc inferebat, igitur
&longs;iue in tubo cte&longs;ibico &longs;upra libellam &longs;ubiecti putei a
qua magis, vel minùs eleuetur &longs;emper eadem vi, &
energia manus &longs;u&longs;pendere embolum, & con&longs;equen
ter aquam eleuare poterimus, &longs;ed hoc e&longs;t fal&longs;um, &
contra experientiam, cùm &longs;emper maior vis, & cona
tus requiratur, quo aqua ad maiorem altitudinem in
tubo pneumatico eleuatur, igitur fal&longs;um e&longs;t aqua&mtail;
eleuari, propterea quòd &longs;u&longs;penditur prohibeturque
&longs;trumenti. Cùm è contrà &longs;i reuera vi attractiua à ma
nu embolum trahente &longs;ubleuatur aqua, manife&longs;tu&mtail;
e&longs;t, quòd quò altiùs a&longs;cendit maior aquæ copia, pro
indè grauior moles &longs;upra putei libellam &longs;u&longs;penditur
eleuaturque, mirum non e&longs;t maius pondus aquæ à
maiori vi &longs;u&longs;tentari eleuarique debere, quam minor
aquæ copia.
pulchett
pro attracti
one.
dari attracti
onem.
dari attracti
onem.
vis ad trahendum embolum cum adhærente aqua ad
altitudinem maiorem, quàm ad minorem &longs;e
cundùm
&longs;ubleuatæ pondera, vel mo
menta.
VT verò huic difficultati per&longs;picuè &longs;atisfacia
mus, &longs;upponamus in puteo, cuius &longs;uperficies
aquea BC, demergi tubum pneumaticum RB, qui
facilitatis gratia continuari intelligatur cum &longs;ip ho
ne inuer&longs;o BIKD; intelligatur que libra radiorum æ
qualium GH, cuius centrum N, & vtrinque pendeant
ab extremitatibus æqualia
E, & F, & hæc contingant
aquæ BC, itaut ambograuia F, & E
comprimant, impellantque aquam
ip&longs;am deorsùm, E
tè, F verò mediante embolo QB, ha
beantque figuram cylindricam, &
ad modum emboli intra canales &longs;i
phonis &longs;trictè, & arctè moueri
ac deorsùm po&longs;&longs;int, & &longs;upponamus
embolum QB grauitate carere; ad
ueniat po&longs;tea externa vis, quæ &longs;u&longs;tentet pondus F ip
&longs;umque &longs;ursùm impellat, h&ecedil;c profectò non debet e&longs;&longs;e
æqualis integro ponderi va&longs;to ip&longs;ius F, proptere&atail;
quòd hoc æquilibratur ab æquipondio ip&longs;ius E, &
proinde F nullam compre&longs;&longs;ionem exercet, perinde,
ac &longs;i grauitate omninò careret, quare à quacumque
exili&longs;&longs;ima vi &longs;u&longs;pendi, & &longs;ursùm impelli poterit, &longs;it
que talis vis &longs;u&longs;pen&longs;iua, vna pars
quarta
dus
tæ partes totius ponderis E, igitur
non ampliùs fiet æquilibrium, &longs;ed
pondus E exercebit quadrantem
totius &longs;ui ponderis, & cum hoc
primet
dè eleuare poterit in oppo&longs;ito tu
bo &longs;iphonis aquæ molem BM, cu
ius pondus vna quarta pars &longs;it
ponderis E, vel F. Po&longs;teà denuò &longs;uperaddita cau
fa externa &longs;ursùm F impellente, & &longs;u&longs;tentante, vt
nimirùm remaneat vis comprimens ip&longs;ius E immi
nuta, & æqualis medietati ponderis E. Manife&longs;tu&mtail;
e&longs;t magis æquilibrium &longs;uperare graue E, &longs;cilicèt eius
momentum erit æquale dimidio totius eius ponderis
E, vel F, proindeque eleuabit duplam aquæ molem
in aduer&longs;o tubo v&longs;que ad O, vt nimirùm moles aquæ
BO dupla &longs;it ip&longs;ius BM, & &longs;ic vlteriùs adueniente no
ua vi &longs;u&longs;tentante pondus F &longs;emper magis diminuetur
ip&longs;ius F compre&longs;&longs;io, & tantumdèm præcisè cre&longs;cet
momentum ponderis E, & tantundem augebitur ele
uatio aquæ in tubo BR, quaproptèr con&longs;tat quod à
maiori vi &longs;ursùm
ior moles aquæ in tubo pneumatico eleuatur, & è
uer&longs;o
uata maiorem vim &longs;u&longs;tentantem, & eleuantem exi
git. Intelligatur modò corpus FV e&longs;&longs;e aereum cylin
drum embolo AB incumbens, eumque deprimens &longs;u
pra aquæ libellam B (neglecta facilitatis gratia gra
uitate ip&longs;ius emboli) pariterque &longs;it cor
pus EX alter cylindrus aereus &longs;uperfi
ciei aquæ C incumbens, igitur quotie&longs;
cumque duo pondera aerea FV, & EX
æqualia &longs;unt, æquali vi &longs;ubiectam
premunt, & in tali &longs;tatu aqua B nequ&etail;
eleuabitur, neque deprimetur, dum equè
comprimitur à
æquilibratis; at quando aduenit quæli
bet exigua vis poterit &longs;u&longs;tentare
cylindrum FV æquilibratum, & ideò
grauem, eumque &longs;ursùm impellere, &
proindè prohibere eius pre&longs;&longs;ionem &longs;upra aquam B,
& tunc tanta præcisè erit compre&longs;&longs;io facta à cylindro
aereo EX &longs;upra &longs;ubiectam aquam, quanta e&longs;t vis, à
qua cylindrus aereus FV &longs;u&longs;tinetur &longs;ubleuaturque,
& tanta præcisè erit aquæ moles BS eleuata in tubo
pneumatico, igitur quantum præcisè augetur graui
tasip&longs;ius aquæ BS &longs;ubleuatæ, tantum præcisè augeri
debet vis illa, qua cylindrus aereus FV &longs;ursùm im
pellitur, &longs;eù tantumdem augeri debet vis manus &longs;ur
sùm embolum trahentis, à quo paritèr aereus cylin
drus FV &longs;u&longs;tinetur impelliturque &longs;ursùm. Et hinc pa-
requiritur maior vis ad modò quia &longs;uperficies aquæ B premitur ab aqua BS
(non con&longs;iderato embolo) & ab aere FV, & &longs;uper&longs;i
cies aquæ C grauatur tantummodò à cylindro aereo
EX æquè graui ac FV (eò quòd in&longs;ignis atmo&longs;phær&ecedil;
&longs;ublimitas e&longs;t in cau&longs;a vt exce&longs;&longs;us altitudinis cylin
dri EX &longs;upra cylindri FV altitudinem &longs;it omninò in
&longs;en&longs;ibilis, proindeque cen&longs;eri po&longs;&longs;int aerei cylindri
EX, & FV æquè graues) ergo exce&longs;&longs;us grauitatis a
quæ BS compen&longs;ari debet à vi contraria manus A
embolum AI trahentis. Sed animaducrtendum e&longs;t
quòd vis manus embolum trahentis reuera non ele
uat aquam BS, quia hæc æquilibratur à &longs;ibi æquali
momento aeris EX, fed tantummodò manus &longs;u&longs;ten
tat prohibetque pre&longs;&longs;ionem incumbentis aeris FV,
æquilibrati cum EX, cuius pre&longs;&longs;ionis
tur ponderi aquæ &longs;ubienatæ BS. hinc fit vt præiudi
cio decepti putemus nos &longs;u&longs;tinere aquam &longs;ubiectam
quando reuerà &longs;u&longs;tentamus aerem incumbente&mtail;
FV æquilibratum ip&longs;i EX.
dari attracti
onem.
dari attracti
onem.
dari
vis. embolú
at tra
&longs;
que
tiùs &longs;
ben
Tandem cùm altitudo aquæ BS ad 18. cubitos fe
rè peruenerit, licèt deinceps embolus maiori vi alti
ùs trahatur nè minimum quidem aqua vlterius &longs;uble
uabitur, ex quo euincitur aquam non attrahi ab em
bolo, &longs;ed impelli à pondere cylindri aerei collatera
lis, qui cum prædicta aquæ altitudine æquilibratur. Et hæc modo &longs;ufficiant pro euer&longs;ione virtutis attrac
tiuæ.
natura flui
ditatis.
PO&longs;tquam euicimus aquam, & aerem, in eorum
metregionibus ponderare, & grauitatem exer
cere, in&longs;uperque attractionem in natura non dari; po
terit
Et primò more no &longs;tro de finitionem fluiditatis affe
remus de&longs;umptam ab aliqua in&longs;igni, & euidenti pa&longs;
&longs;ione eius corporis, quod fluidum appellatur. Et pro
fectò quotie&longs;cumque video, atque con&longs;idero diffe
rentiam inter glaciem, & aquam fluentem, ob&longs;eruo
in illa duritiem, & con&longs;i&longs;tentiam, qua ifta caret, video
enim immi&longs;&longs;o digito, quòd glacies non cedit, aqu&atail;
verò fluida facillimè locum præ&longs;tat &longs;ubmer&longs;ioni, &
ingre&longs;&longs;ui digiti, perfecteque circa ip&longs;um di&longs;poni
tur, & adaptatur, vt vndequaque Video
in&longs;uper non po&longs;&longs;e angulum glaciei impelli, aut quo
modolibet loco-moueri, quin tota ma&longs;&longs;a glacialis &longs;i
mùl moueatur, cum è contrà in aqua fluida po&longs;&longs;it qu&ecedil;
libet eius particula impelli, circumuolui, alij&longs;qu&etail;
modis agitari, quie&longs;centibus tamen reliquis partibus
eius, vel &longs;altem agitatis motu tardiori, vel non ad ea&longs;
dem partes facto. Po&longs;tremò ob&longs;eruo aquam fluidam
perfecti&longs;&longs;imè explanari, & ad libellam horizonti æ
quidi&longs;tantem reduci, quod minimè fieri po&longs;&longs;et, ni&longs;i
partes eius extremæ, &longs;uper ficiale &longs;que æquè à medio
puncto telluris recederent.
natura flui
ditatis.
Ex hi&longs;ce omnibus phenomenis colligi pote&longs;t pa&longs;&longs;io
præcipua ex qua reliquæ omnes dependent atqu&etail;
exprimuntur, eritque talis: corpus fluidum erit il
lud, cuius partium æquè ponderantium pote&longs;t vna à
vi externa moueri non motis reliquis, vel diuer&longs;o mo
do agitatis quàm duris corporibus competit. Quæ de
finitio parùm differt ab ea quæ traditur ab Ari&longs;tote
le, vbi ait humidum e&longs;&longs;e, quod facilè termino alieno
terminatur, & hoc accidit ex eo, quod po&longs;&longs;unt facil
limè aliquæ partes moueri, non motis teliquis, vel
diuer&longs;o motu. Et hoc quidem, vt euidenti&longs;&longs;imum,
indiget vlteriori declaratione.
fluiditatis.
corrup lib.
2.
cap.
3.
Re&longs;tat modò præcipua difficultas, an fluidum re
ucra &longs;it corpus continuum, an verò &longs;it di&longs;cretum, &longs;ci
licèt aggregatum ex innumeris particulis &longs;ubdiui&longs;is,
qualis e&longs;t aceruus granorum, vel arenæ, & hoc erit
oper&ecedil; pretium accuratè examinare, idque præ&longs;tabi
mus o&longs;tendendo quòd.
indiui&longs;ibilibus, licèt numero infinitis.
QVia puncta indiui&longs;ibilia non videntur exi&longs;tere,
neque in &longs;ub&longs;tantiali corpore a&longs;&longs;ignari po&longs;&longs;e,
ni&longs;i fictione, & mentis cogitatione, nec &longs;unt partes,
neque elementa
tia, quod patet ex eo, quod punctum additum puncto
bis, decies, millies &c. non facit maius, & nil puncta
plura differre videntur ab vnico puncto, quandoqui
dem, tàm &longs;ingulare punctum, quàm eorum multitudo
nullum &longs;patium quantum occupant, contra ac contin
git in vnitatibus, quæ &longs;imul coniunctæ creant magni
tudinem numericam, ex quo proinde fit, vt vnitates
meritò partes, & elementa numeri cen&longs;eantur, no&ntail;
verò puncta ip&longs;ius &longs;ub&longs;tantiæ quantæ. Hinc infertur,
quod &longs;icut ex infinitis cyfris numerus creari non po
re&longs;t, & ex infinitis non entibus nequit ens confici, &longs;ic
exinfinitis non quantis, quæ nec partes nec elementa
quantitatis &longs;unt, non pote&longs;t quantum componi; &longs;unt
que puncta indiui&longs;ibilia non quanta, nec &longs;unt partes
aut elementa
finitis punctis indiui&longs;ibilibus &longs;ub&longs;tantia corpore&atail;
quæ quanta e&longs;t componi, crearique non poterit.
natur
ditatis.
actu infinitæ, & eiu&longs;dem men&longs;uræ com
ponunt exten&longs;ionem infinitam;
SInt partes quantæ A, B, C, D, E, F, G, &c.
actu in
finitæ numero, & æquales inter &longs;e, dico eas ex
ten&longs;ionem infinitam compone
re. &longs;umatur quælibet quantitas
finita cuiu&longs;libet va&longs;titatis RS
eiufdem generis cum particulis
A, B, C, &c. profectò aut RS.
multiplex e&longs;t ip&longs;ius A, &longs;cilicèt
hæc illam metitur, vel non; & primò ponamus RS al
A
tionem, quam aliquis numerus finitus ad vnitatem
& ideò in infinita multitudine partium A, B, C, &c
&longs;umi pote&longs;t multitudo partium, quæ maior &longs;it numer
partium ip&longs;ius RS, & prædicta maior multitudo par
tium efficiat
ip&longs;a RS, at aggregatum ex infinitis particulis A, B, C
&c. maiorem exten&longs;ionem creat quam prædicta mul
titudo finita X, ergo multò magis aggregatum ex in
finitis particulis maiorem extenfionem efficit, quàn
habeat RS, illa verò exten&longs;io quæ maior e&longs;t
quantitate finita, nece&longs;&longs;ariò infinita erit, ergo aggre
gatum ex particulis quantis numerò infinitis inter &longs;
æqualibus efficit exten&longs;ionem infinitam.
natura flui
ditatis.
Secundò &longs;int A, & RS inte
&longs;e
RS addi po&longs;&longs;e portionem ali
quam SV ita vt RV multiple
&longs;it ip&longs;ius A, & tunc aggregat
ex infinitis particulis æqualibu
A, B, C, &c. maiorem exten&longs;ionem efficiet quà
RV, vt mox o&longs;ten&longs;um fuit, & ideò multò maiore
exten&longs;ionem, quàm RS, creabit, proptereaque inf
nitam e&longs;&longs;e concludemus.
natura flui
ditatis.
componunt exten&longs;ionem infinitam.
SInt partes AB, CD, EF, GH, IK, &c.
numero in
finitæ, & inter &longs;e inæquales. Dico exten&longs;ionem
infinitam conflare. Quia dantur omnes partes quan
tæ numero infinitæ, ergò datur earum minima, quæ
&longs;it AB, & ex reliquis maioribus &longs;ecentur portiones
CL, EM, GN, &c. &longs;ingulæ æquales minimæ AB; &
quia particulæ infinitæ inæquales
AB, CD, EF, &c. maiorem exten
&longs;ionem
finitæ diminutæ, inter &longs;e æquales
AB, CL, EM, &c. &, ex præcedenti,
infinitæ particulæ quantæ eiu&longs;dem generis AB, CL,
EM, &c. inter &longs;e æquales componunt exten&longs;ione&mtail;
infinitam, ergò multò magis in&longs;i initæ partes illis ma
iores inæquales AB, CD, EF, &c. exten&longs;ionem infi
nitam efficient, quod erat.
&longs;centibus, vel omnes inæqualibus motibus agitentur,
qui tamen non competant, nec aptari pos&longs;int
partibus corporis duri, & con&longs;istentis, ne
ce&longs;&longs;ariò illius aggregati partes erunt
actu diui&longs;æ.
natura flui
ditatis.
QVærimodo debet &longs;ignum ex quo lumine natu
ræ euidenti&longs;&longs;imè digno&longs;cere valeamus an ali
quod corpus actu diui&longs;um &longs;it implùres partes, vel &longs;it
vnum continuum, licèt prædictæ partes ob exiguita
tem, veltran&longs;parentiam earum &longs;int incon&longs;picuæ, &
inob&longs;eruabiles; hoc autem
&longs;cilicèt &longs;i con&longs;tat quòd vna pars A compo&longs;iti mouetur
varijs modis
&c. in eodem &longs;itu quie&longs;cunt, certum erit partem
agitatam A à reliquis di&longs;ci&longs;&longs;am, & di&longs;cretam e&longs;&longs;&etail;. at quando omnes partes eiu&longs;dem compo&longs;iti mouen
tur, videndum qua ratione
&longs;imus an prædictæ partes &longs;int continuatæ, & vnitæ,
vel ab inuicem diui&longs;æ, & profectò non &longs;emper inæ
qualitas motuum indicat diui&longs;ionem potiùs quà&mtail;
continuitatem, namin vertigine rotæ &longs;olidæ, & du
ræ earum particulæ licèt tenaciter ei affixæ, & con
nexæ &longs;int, uih lominùs mouentur inæqualibus veloci
tatibus &longs;ecundùm proportionem, quam habent di
&longs;tantiæ ab axi firmo eiu&longs;dem rotæ circumductæ, igi
tur in aliquo fluido reuoluto &longs;i orbes ab eius particu
lis eodem tempore de&longs;eripti maiores fuerint, quo
magis ab axe reuolutionis recedunt, & &longs;ecundù&mtail;
proportionem di&longs;tantiarum, dubitare profectò po&longs;
&longs;umus an particulæ prædicti fluidi &longs;int continuatæ, an
verò actu di&longs;cretæ.
Hinc deducitur, quòd &longs;i in rotæ vertigine vna eius
pars magis, vel minùs, quàm priùs à centro recedat,
vel celeriori, aut tardiorimotu ferat
petit di&longs;tantiæ eius ab axe, tunc nece&longs;&longs;ariò talis par
ticula erit à rota disiuncta, & &longs;egregata. Vt in rot&atail;
AEH reuoluta circa cen
trum D &longs;i eius particulæ
A, B, C eodem
&longs;cribunt
CGL,
nem habentes quam di
&longs;tantiæ à centro AD, BD,
& CD tunc di&longs;tingui non
pote&longs;t an pr&ecedil;dictæ parti
culæ &longs;int di&longs;ci&longs;&longs;æ vt arena,
vel &longs;int agglutinatæ rotæ &longs;olidæ, propterea quòd id
ip&longs;um &longs;ymptoma particulis duri&longs;&longs;imæ rotæ competit. Si verò
excurrit per tangentem rectam AM, aut curuam &longs;pi
ralem AN euidenti&longs;&longs;imum &longs;ignum erit particulam A
non e&longs;&longs;e annexam, & vnitam, &longs;ed diui&longs;am à rota &longs;o
lida, quia continentèr à centro D magis, & magis re
mouetur vt in N, vel M.
natura flui
ditatis.
Præterea &longs;i particulæ eamdem à centro
retinuerint, & eodem tempore, quo rota integra&mtail;
reuolutionem BFB ab&longs;oluit, alia particula A, vel
maius, vel minus &longs;patium, quàm circulum AEA per
&longs;icit, &longs;cilicèt percurrit arcum AEH, vel AEO, tunc
euidentèr con&longs;tat particulam A non e&longs;&longs;e agglutina
tam, &longs;ed diui&longs;am à rota &longs;olida.
Similitèr in motu directo aggregati AEH, &longs;i eius
particulæ inæqualibus velocitatibus feruntur, &longs;cili-
cèt dum A pertran&longs;it rectam lineam AB alia pars E
excurritrectam lineam EC minorem quàm AB, & alia
pars H excurrit &longs;patium HD minùs,
quàm EC euidenti&longs;&longs;imum
tales particulas A, E, H, diui&longs;as in
ter &longs;e e&longs;&longs;e.
natura flui
ditatis.
Hinc generali&longs;&longs;ima regula elici
pote&longs;t, quòd
gatum corporum mouetur motu di
recto, & eius partes inæqualibus ve
locitatibus feruntur, aut itinera non
&longs;unt æqui di&longs;tantia. Vel &longs;i motu circulari circa
D agitatur, omnes eius particulæ &longs;piras vt AN de
&longs;cribunt, vel &longs;i circulos pertran&longs;eant velocitates eo
rum proportionales non &longs;unt di&longs;tantijs à centro: vel
è contra &longs;emper tardiores &longs;nnt quò magis à
cedunt, vt &longs;i particula C verè tardiori motu feratur,
quàm D, & adhùc B tardiori, quàm C, & &longs;ic reliquæ
omnes, procùl dubio ex qualibet ex prædictis inæ
qualitatibus euincitur partic
gatum componentes omninò inter &longs;e di&longs;eretas, & di
ui&longs;as e&longs;&longs;e, propterea quod hi motus non competunt,
nec aptari po&longs;&longs;unt partibus corporis continui con&longs;i
&longs;tentis, & duri.
e&longs;&longs;e debent.
natura flui
ditatis.
HIs po&longs;itis animaduerto quòd quotie&longs;cumqu&etail;
corpus aliquod fluidum e&longs;&longs;e &longs;upponitur, nece&longs;
sè e&longs;t, vt eius partes actu diui&longs;æ inter &longs;e &longs;int; quia flui
dum habere debet naturalem conformationem di
&longs;po&longs;itionem, & omnia requi&longs;ita vt elicere po&longs;&longs;it
motum, quem fluxionem vocamus, &longs;cilicèt &longs;i vn&atail;
eius pars moueri queat cæteris quie&longs;centibus, vel &longs;i
omnes mouentur, percurrant motu directo inæqualia
&longs;patia, vel &longs;i circularitèr ferantur, maiorem, vel mi
norem proportionem vertigines habeant, quam di
&longs;tantiæ à centro reuolutionis; hæ enim motiones ef
fici nequeunt, ni&longs;i partes fluidi actu inter &longs;e diui&longs;æ
fint, vt mox
pus aliquod fluidum e&longs;&longs;e &longs;upponitur, nece&longs;&longs;ariò par
tes eius actu inter &longs;e diui&longs;æ erunt.
tinuum con&longs;tituentes.
PRæterea &longs;i partes fluidi non e&longs;&longs;ent diui&longs;æ actu,
&longs;cilicèt &longs;i aqua haberet omnes eius partes planè
connexas, & conglutinatas vnum continuum con&longs;ti
tuentes, atque hæ motu directo, vel circulari moue
rentur intra fluidum &longs;ui generis, &longs;cilicèt intrà aquam
&longs;tagnantem, cum eius particulæ minimæ eamdem in
uariabilem di&longs;po&longs;itionem, &longs;ituationem, ac texturam
retinere
velrotæ &longs;olidæ e&longs;&longs;ent, procùl dubio eodem tempore
les, & cre&longs;centes in eadem proportione, quam
tiæ
gere aliquando po&longs;&longs;et. At quia con&longs;tat non
aquam lacus directè æquali motu moueri, vel conuer
ti vnà cum interna illa portione translata, vel circum
ducta, &longs;ed videmus, quòd remoti&longs;&longs;imæ partes placi
dè omninò quie&longs;cunt, dum intermediæ excurrunt,
vel rotantur veloci&longs;&longs;imo motu, nec à maxima veloci
tate internarum partium prædicti corporis, vel fluid&ecedil;
rotæ immediatè tran&longs;itur ad partes fluidi remotiores
prorsùs quie&longs;centes, quæ officium va&longs;is &longs;uppleant,
&longs;ed vt videre e&longs;t in aqua turbida, & in aere fumo&longs;o
tran&longs;itur ordinato decremento ab aquæ partibus ve
loci&longs;&longs;imè directo motu agitatis, vel reuolutis per mi
nùs veloces gradatim, quou&longs;que ad extimas quie
&longs;centes perueniatur; non igitur aqua habere poterit
partes connexas vnum continuum con&longs;tituentes. His
præmi&longs;&longs;is deuenio ad propo&longs;itionem princip alem.
natura flui
ditatis.
fluidæ non &longs;unt.
SI enim hoc verum non e&longs;t, minimæ particulæ, ex
quibus fluidum con&longs;tat, &longs;int &longs;emper fluidæ, &longs;i fie
ri pote&longs;t, ergo diuidendo corpus fluidum inde&longs;inen
tèr, & infinitè numquam deueniemus ad minima&mtail;
eius particulam, quæ fluida non &longs;it, &longs;ed &longs;emper flui-
daEt quia fluidum catenùs motum, quem fluxio
nem vocamus, elicere pote&longs;t, &longs;cilicèt catenus fluidum
e&longs;t quatenùs eius aliquæ partes mouentur cæteris
quie&longs;centibus, vel diner&longs;is, & inæqualibus motibus
agitantur ab ijs, qui competunt duris, & continuis
corporibus; ergò ad hoc, vt nulla particula corporis
fluidi care at hac pa&longs;&longs;ione fluiditatis; oportet vt &longs;em
per ei conueniat fluiditatis definitio, &longs;cilicèt &longs;emper
quælib et eius pars moueri po&longs;&longs;it cæteris quie&longs;centi
bus, vel inæqualibus motibus agitentur, quàm &longs;int il
li, qui duris, & continuis corporibus competunt. Sed
partes contiguæ eiu&longs;dem ma&longs;&longs;æ non po&longs;&longs;unt partim
moueri, partim quie&longs;cere, vel inæqualibus motibus
agitari diuer&longs;o modo, ac continuis corporibus
petit, ni&longs;i inter &longs;e &longs;int diui&longs;æ, & di&longs;cretæ; igitur nul
la particula fluidi corporis quantumuis exigua a&longs;&longs;i
gnari pote&longs;t, quæ actu di&longs;&longs;ecta, & &longs;ubdiui&longs;a non &longs;it in
plures alias particulas; qua propter nunquam perue
niri poterit ad finem enumerationis multitudinis par
tium eius, & ideò talis multitudo maior erit
que
finita, ergo infinita erit; at infinitæ partes actu diui
&longs;æ &longs;i e&longs;&longs;ent quantæ &longs;iue inter &longs;e æquales, &longs;iue non, e&longs;li
cerent
maris e&longs;&longs;et infinitæ magnitudinis, quod e&longs;t fal&longs;u&mtail;,
igitur non quantæ, &longs;ed indiui&longs;ibilia puncta erunt; hoc
verò e&longs;t quoque impo&longs;&longs;ibile, cùm infinita puncta ex
ten&longs;ionem quantam nequeant componere: ergò fal
&longs;um e&longs;t, quòd minimæ particulæ ex quibus fluidu&mtail;
con&longs;tat, & in quas diuidi pote&longs;t, &longs;int &longs;emper fluidæ,
quod erat o&longs;tendendum.
natura flui
ditatis.
136.
natura flui
ditatis.
Hinc deducitur, quòd corpus fluidum componitur
ex minimis particulis non fluidis.
SI enim hoc verum non e&longs;t, &longs;cilicèt &longs;i particulæ a
quam fluidam componentes &longs;emper fluidæ &longs;unt,
igitur diuidi &longs;emper poterit aqua &longs;ucce&longs;&longs;iuè, & i&ntail;
infinitum in particulas, quæ &longs;emper fluidæ &longs;int, hoc
tamen primò repugnat ip&longs;imet Ari&longs;toteli, qui negat
contra Anaxagoram po&longs;&longs;e quodlibet corpus natura
le retinere eandem
per continuam diui&longs;ionem ad exiguas & minimas
particulas reducatur; &longs;ic diui&longs;a animalis carne deue
nietur tandem ad particulas, quæ non ampliùs carnes
&longs;int; &longs;ic paritèr, vt habent eius expo&longs;itores in elemen
tis facta con&longs;imili diui&longs;ione &longs;ucce&longs;&longs;iua, tandem minu
ti&longs;&longs;imæ particulæ non ampliùs elementarem naturam
retinebunt. Hinc igitur licet inferre quòd fluido a
queo in infinitum &longs;ucce&longs;&longs;iuè diui&longs;o deuenietur tan
dem ad particulas eius, quæ fluidæ non &longs;int, &longs;cilicèt
cuius vna particula non po&longs;&longs;it moueri quie&longs;centibus
reliquis, & propterea omnes &longs;imùl vnico motu agita
ri poterunt, &longs;cilicet con&longs;i&longs;tentiam &longs;olidam haber&etail;
neceisè e&longs;t.
cap.
4.
Sed relicta Ari&longs;totelis, & Peripateticorum autho-
ritate perpendamus rationis vim, & energiam. Si ve
rum e&longs;t aquam fluidam quomodocumque diui&longs;am, &
&longs;ubdiui&longs;am &longs;emper fluiditatem retinere, igitur &longs;em
per hi&longs;ce po&longs;tremis particulis fluidis definitio fluidi
tatis &longs;uperiùs tradita competet, &longs;cilicèt aliqua mi
nor particula
&longs;centibus collateralibus partibus. His po&longs;itis, qui&atail;
corpora omnia &longs;ublunaria innumeris poris, & forami
nulis peruia &longs;unt, &longs;equitur quòd aqua omnia corpora
concreta penetraret, nam concipiamus quemlibet
porum &longs;tricti&longs;&longs;imum in va&longs;e ligneo, vitreo, vel metal
lico, certum e&longs;t quòd portio aquea foraminulo præ
dicto &longs;uperpo&longs;ita cui adæquatur, dimen&longs;ionem, &
quantitatem habet æqualem amplitudini foraminis,
& iuxtà quantitatis naturam &longs;emper diui&longs;ibilem po
terunt concipi particulæ centrales, & &longs;trictiores,
&longs;it amplitudo eiu&longs;dem pori, quæ particulæ aquæ
trales
bus, vt &longs;uperiùs expo&longs;ita fluidi natura exigit, ergo ne
ce&longs;&longs;ariò pe
terunt, & proindè nullum vas reperietur, per quod
aqua penetrare queat: & aduertendum e&longs;t, quòd à
qualibet exigua vi motiua impelli, & in&longs;inuari po&longs;&longs;et
aqua per prædictas poro&longs;itates, &longs;cilicèt à vi &longs;uæ pro
priæ grauitatis, &longs;eù à quacumque alia vi eam
te
tem e&longs;t euidenter fal&longs;um, cùm aqua communis, aut
&longs;piritus vini &longs;ubtili&longs;&longs;imus vitri poro&longs;itates penetrare
non po&longs;&longs;it, licèt
fluidum diuidi po&longs;&longs;e in infinitum in partes &longs;emper
fluidas; qua propter nece&longs;sè e&longs;t, vt tandem diuiden
do perueniamus ad particulas aqu&ecedil;, qu&ecedil; non ampliùs
fluidæ &longs;int, &longs;cilicèt in quibus non vale at moueri vn&atail;
eius minima particula quie&longs;centibus collateralibus,
proindeque illæ po&longs;tremæ fluidi particulæ erunt
fi&longs;tentes
natura flui
ditatis.
natura flui
ditatis.
Quòd verò à valdè exigua vi impelli po&longs;&longs;it aqu&atail;
per vitri poro&longs;itates, patetex eo, quòd videmus præ
longam trabem &longs;uper aquam &longs;tagnantem
uersè
vis motiua &longs;uperare pore&longs;t re&longs;i&longs;tentiam tot partiu&mtail;
aquæ quot a&longs;&longs;ignari po&longs;&longs;unt in prædicta amplitudine
trabis. Vnde conijcitur, quòd vis, quæ requiritur ad
impellendam paruam, & acutam fe&longs;tucam natantem
debeat e&longs;&longs;e ferè in&longs;en&longs;ibilis
tiem, & tamen à tam minima vi mouetur vna aquæ
particula non motis collateralibus, & proptereà vis
huic æqualis &longs;ufficiens e&longs;t &longs;u perare tenacitatem, qua
aquæ particulæ colligantur, vniunturque, erit igitur
energia tenacitatis partium aquæ minimi, & exigui
roboris, & propterea &longs;uperari poterit à pu&longs;illa vi im
pul&longs;iua.
Nec ob&longs;tat, quòd aqua communis non &longs;it omninò
&longs;incera, & ab&longs;que mixtura partium terre &longs;trium, & &longs;o
lidarum, nam licèt hocverum &longs;it, nihilominùs negari
non po&longs;&longs;unt partes puræ aquæ, quæ inter minuti&longs;&longs;ima
fragmenta terre&longs;tria intercedunt, & ex &longs;ui natura
&longs;int fluid&ecedil;, po&longs;&longs;ent quidem penetrare inter&longs;titia inter
arenulas commixtas cum ip&longs;ametaqua, imò
arenularum poro&longs;itates pertran&longs;ire valerent.
natura flui
ditatis.
Nec præterea ob&longs;tat, quòd poro&longs;itates vitri, aut
metalli non &longs;int directæ, &longs;ed miris modis contortæ, &
anfractuo&longs;æ, nec &longs;emper eiu&longs;dem amplitudinis, nam
nihilominùs vetari, & impediri non po&longs;&longs;et tran&longs;itus
fluentis aquæ, &longs;altem tardiori motu, longiorique
pore
pertran&longs;ire debui&longs;&longs;et. Hoc autem cùm non contin
gat, &longs;cilicèt aqua intra vas vitre um diù inclu&longs;a num
quam exudet, concedendum e&longs;t, minimas eius parti
culas non fluidas, &longs;ed con&longs;i&longs;tentes e&longs;&longs;e.
tates cuius
lib
ris &longs;int tor
tuo&longs;æ tamen
à fluido p
mea
&longs;unt.
Quòd verò pori cuiuslibet va&longs;is permeabiles om
ninò &longs;int, nec viæ obturamentis impediantur, occlu
danturque, probari &longs;atis pote&longs;t ex eo quod per eos
aliqua fluida penetrant, vt hydrargyrum per poros
auri, aqua, oleum, & hydrargyrum quoque per po
ros ligni, & va&longs;is fictilis, quare per eo&longs;dem reliqua
omnia fluida nece&longs;&longs;ariò pertran&longs;ire, & fluere debe
rent, &longs;altèm tardiori motu, &longs;i verum e&longs;t, quòd nulla
fluidi pars a&longs;&longs;ignari pote&longs;t, quæ paritèr fluida non
&longs;it; deberet igitur aer effluere è va&longs;e fictili, & ligneo
quotie&longs;cumque violentèr
in minimas particulas, talis figuræ, vt vna &longs;uper alte
ram facilè &longs;luere pos&longs;it, & omnes æqualem vim
motiuam grauitatis habeant.
natura flui
ditatis.
SI modò philo&longs;ophari velimus non iuxtà homi
num placita, &longs;ed
conditiones nece&longs;&longs;ariæ e&longs;&longs;e videntur ad fluidi con&longs;ti
tutionem. Primùm vt &longs;it corpus diui&longs;um, & &longs;ub diui
&longs;um in exiguas, & minimas particulas. Secundò vt
eius figuræ ad orbicularem formam quam proximè
accedant. Tertiò vt harum &longs;uperficies, vel &longs;int per
fecti&longs;&longs;imè l&ecedil;uigatæ ad
mè vna &longs;uper Et
oportet vt omnes habeant
deorsùm tendant, &longs;cilicèt &longs;int æquè graues; Po&longs;&longs;ent
hæc omnia (licèt rudi exemplo) non ineptè confir
mari &longs;umptis pluribus globulis cry&longs;tallinis,
in aliquo va&longs;e, primò prædicti globuli ad &longs;igara&mtail;
va&longs;is adaptantur, & &longs;i manus v&longs;que ad &longs;undum va&longs;is
immittatur, tunc globuli prædicti locum cedunt, & ad
latera excurrunt, præterea poteritmoueri vna, vel al
tera pila cry&longs;tallina, quie&longs;centibus pilis collaterali
bus, vel parum motis; in&longs;uper po&longs;t agitationem ex
planarentur prædicti globuli, non enim aceruum, aut
montem efficerent, veluti grana frumenti, aut arenæ,
&longs;ed ob eorum læuitatem facilè excurrerent de&longs;cende
rentque versùs infima loca, & &longs;ic &longs;uprema &longs;uperficies
explanaretur, & proximè horizonti æquidi&longs;tantèr
di&longs;poneretur. Si po&longs;tea prædictæ &longs;phærulæ cry&longs;talli
næ magis exiguæ, & minutæ e&longs;&longs;ent, tunc multò faci
liùs prædictæ operationes efficerentur, & &longs;i tandèm
ad ineffabilem paruitatem redigerentur, non po&longs;&longs;ent
neque tactu neque vi&longs;u percipi, &longs;ed apparentem con-
tinuitatem repr&ecedil;&longs;entarent, vt contingit in minuti&longs;&longs;i
mo puluere; & tunc quidem haberi po&longs;&longs;ent effectus
omnes fluiditatis, &
innumeris globulis cry&longs;tallinis duris, &
natura flui
ditatis.
Sed audax quædam &longs;ententia, quæ hi&longs;ce tempori
bus viget, meretur vt aliquanti&longs;per in eius examin&etail;
immoremur; concedunt enim fluidum componi ex
particulis diui&longs;is, exiguis, l&ecedil;uigati&longs;que, &longs;ed aiunt pal
mariam eius conditionem e&longs;&longs;e, vt particulæ quibus
con&longs;tat, diuer&longs;imodè agitentur, &longs;iue motus ille &longs;it ijs
connatus, &longs;iue per &longs;ubtiliorem quamdam &longs;ub&longs;tantiam
&longs;uo tran&longs;itu ip&longs;as quaqua ver&longs;um
putat præci
puam fluidi
e&longs;&longs;e vt om
nes elus par
tes inte&longs;tino
motu
tur
Duæ præcipuæ rationes afferuntur ad huius
tiæ
tallorum fu&longs;ione ab ignis violentia minimas particu
las metallicas verè agitari, idemque ob&longs;eruatur i&ntail;
cera, & in reliquis alijs corporibus, quæ ab action&etail;
ignis fluida rediguntur, & profectò euidens e&longs;t i&ntail;
aqua feruente quod per lebetis poro&longs;itates igneæ
exhalationes penetrantes efficiunt innumeras &longs;ph&ecedil;
rulas veloci&longs;&longs;imo motu
hinc &longs;u&longs;picari licet ab illa vehementi ebullition&etail;
fluxilitatem pendere, & licèt aliquando huiu&longs;modi
bullæ intra fluidum non con&longs;piciantur, imòcorpus fu
&longs;um &longs;ummè tranquillum, & placidum con&longs;piciatur,
vt in plumbo fu&longs;o videre e&longs;t, nihilominùs quia moles
plumbi, à fu&longs;ione valdè augetur, & in&longs;uper ab eo fu
mi egredientes non paucas plumbi partes tran&longs;por
tant, manife&longs;tè euincitur fu&longs;um plumbum continuè
agitari, ciu&longs;demque partes varijs modis contorqueri
ac moueri.
probant ex
metallorum
fu&longs;ione.
natura flui
ditatis.
Secunda ratio de&longs;umitur ex fermentatione; &longs;i enim
grana aliqua &longs;alis in fundo aquæ demergantur, aut
quælibet alia materia di&longs;&longs;olubilis, & fermentabilis,
videmus, quòd citò vniuer &longs;am aquam &longs;apor, & tinctu
ra illius fermenti in &longs;icit, & alterat, hoc autem minimè
fieri po&longs;&longs;et, ni&longs;i particulæ &longs;alinæ
vniuer&longs;am aquam, quod ab&longs;que agitatione partium
eiu&longs;demmet aquæ nullo modo fieri po&longs;&longs;et.
&longs;alium fu&longs;i
one in aqua.
læues, & facilè amouibiles, licèt omninò
quie&longs;cant, duritiem creare non
po&longs;&longs;unt.
ET profectò po&longs;ito, quòd corpus diui&longs;um &longs;it i&ntail;
exiguas, & minimas particulas, &longs;i prædictæ par
tes diuer&longs;imodè reuolutæ, & agitatæ fuerint, negari
non pote&longs;t eas apparentiam fluidam repr&ecedil;&longs;entare;
&longs;ed non proinde oppo&longs;itum verificatur, &longs;cilicèt quòd
quotie&longs;cumque dee&longs;t agitatio, & motus minimarum
& con&longs;i&longs;tens (vt apertè fatentur aliqui recentiores)
præcipua, & propria pa&longs;&longs;io corporis duri non e&longs;t e&atail;
quam Carte&longs;ius affert, &longs;cilicet quòd omnes eius parti
culæ quie&longs;cant in eodem &longs;itu in quo degunt; & ratio
e&longs;t, quia talis pa&longs;&longs;io non conuenit &longs;olummodò corpo-
ribus duris, cum arenæ particulæ quie&longs;cant, nec
cumulum &longs;olidum, & durum efficiant. Ex eo igitur,
quod videmus in corpore duro vnam eius parte&mtail;
moueri non po&longs;&longs;e qu
deducitur, quòd non &longs;ufficit &longs;implex contactus par
tium immotarum, &longs;ed præterea nece&longs;&longs;e e&longs;t, vt &longs;int ad
inuicem connexæ, & agglutinatæ, vt firmitudinem, &
duritiem creare po&longs;&longs;int. & &longs;anè &longs;i reuerà corpus &longs;ub
diui&longs;um fuerit in minuti&longs;&longs;imas particulas rotundas,
aut ad rotunditatem proximè accedentes, & careant
omni &longs;cabritie, &longs;intque omnes æquè graues, & in qui
ete con&longs;titutæ, tunc e&longs;t impo&longs;&longs;ibile, vt prædictum ag
gregatum durum, & con&longs;i&longs;tens &longs;it, nec poterit &longs;u&longs;ti
neri, vt arena in accliui, &
terea quod particularum figuræ rotundæ, & l&ecedil;uigatæ
non po&longs;&longs;unt vetare excur&longs;um, atque de&longs;cen&longs;um par
tium earundem grauium, & proindè nece&longs;&longs;e e&longs;t vt ex
planentur, nec vna eius pars maiorem eleuatione&mtail;
&longs;upra planitiem horizontis habere poterit, quàm a
lia; præterea quodlibet corpus con&longs;i&longs;tens intra præ
dictum aggregatum demer&longs;um &longs;i vim compre&longs;&longs;iuam,
&longs;eù grauitatem maiorem habuerit, quàm particulæ
illæ &longs;ub diui&longs;æ, facilè poterunt impelli, ac eleuari &longs;u
pra eius libellam, & ob earum rotunditatem, & l&ecedil;ui
tatem nullo negotio excurrere circa corpus
po&longs;&longs;unt, idque omni ex parte contingere, atque ad
eius figuram accommodari.
natura flui
ditatis.
co
riorem do
c
Sed videamus qua ratione ingenio&longs;i&longs;&longs;imus Author
neotericus hanc &longs;ententiam confirmare nitatur, quòd
nimi
earum quietis fluiditatem amittant; ait ip&longs;e:
ciliùs moueri po&longs;&longs;e corpus quodlibet in motu constitutum,
&longs;i quie&longs;cens, & stabile e&longs;&longs;et, quia in primo ca&longs;u non est nece&longs;
sè, vt producatur, vel creetur motus, cui corpus quodlibet ob
natur alem &longs;uam inertiam re&longs;istit, &longs;ed
tus ip&longs;e hactenùs existens, & vigens in eodem corpore diri
gatur.
natura flui
ditatis.
tatum, quàm quie&longs;cens, &longs;i tamen eius quies
fuerit amouibilis.
AT ip&longs;e in hoc ei a&longs;&longs;entiri nullo modo po&longs;&longs;um,
nam licèt verum e&longs;&longs;et, quòd faciliùs impelli
po&longs;&longs;et corpus in motu con&longs;titutum, quàm quie&longs;cens,
non in de &longs;equitur &longs;implicem quietem particularu&mtail;
fluidi duritiem eius creare. nam videmus arenæ cu
mulum &longs;olummodò acquirere con&longs;i&longs;tentiam, & duri
tiem, quando glutine, vel arcti&longs;&longs;ima vnione, & angu
lorum mutua in&longs;inuatione connectuntur cius grana,
vt in pauimento contingit, non verò quando arenæ
particul&ecedil; di&longs;&longs;olutæ placidi&longs;&longs;ima quiete &longs;e mutuò tan
gunt, igitur eodem modo aquæ particulæ læues, di&longs;
&longs;olutæ, tranquilli&longs;&longs;ima quiete &longs;e mutuò tangentes
efficient duram, & rigidam connexionem glacialem. Prætereà &longs;i corpus aliquod in quiete amouibili fuerit
con&longs;titutum, &longs;cilicèt &longs;i indifferens fuerit ad motu&mtail;
quemlibet, & ad quietem non difficiliùs nouus mo
tus ei imprimitur, quando quie&longs;cit, quàm quando
actu mouetur. hoc autem
re de Vi Percu&longs;&longs;ionis: Imò &longs;i velimus philo&longs;ophari
iuxtà &longs;en&longs;us euidentiam, multoties experimur, quòd
maiori difficultate imprimitur nouus motus in eo cor
pore, quod actualitèr mouetur,
uibili con&longs;titutum fui&longs;&longs;et, & hoc con&longs;tat hac ratione:
quia aut motus, qui de nouo imprimi debet, ab im
pellente vergit, ac tendit ad ea&longs;dem partes ad quas
corpus mobile fere batur, aut ad partes oppo&longs;itas, vel
tran&longs;uersè; & patet, quod in his multò difficiliùs im
primitur nouus motus, quia præter inertiam corpo
ris mobilis, debet quoque &longs;uperari re&longs;i&longs;tentia impe
tus motus contrarij, & &longs;ic videmus, quòd difficiliùs
reijcimus, & repercutimus pilam aduenientem, &
nobis occurrentem motu contrario, quàm &longs;i eade&mtail;
pila omninò motu careret, & pauimento innixa quie
&longs;ceret. Si po&longs;tea motus corporis mobilis, & mouen
tis fiunt versùs ea&longs;dem partes, atque velociori motu
mobile, quàm mouens fertur, tunc patet adeò fal&longs;um
e&longs;&longs;e faciliùs moueri po&longs;&longs;e corpus illud in motu velo
ciori con&longs;titutum, quàm &longs;i quie&longs;ceret, vt è contrà i&ntail;
quiete ab illo impelli po&longs;&longs;et, at in fuga non po&longs;&longs;et à
tardiore impul&longs;ore vrgeri; &longs;i verò gradus impetus
mouentis corporis maior fuerit illo quo mobile
fugit, tunc difficiliùs, &longs;eu tardiùs illud mouebitur,
quàm &longs;i in quiete amouibili con&longs;titutum fui&longs;&longs;et; nam
in hoc ca&longs;u percu&longs;&longs;io fieret ab integro gradu impetus
impellentis corporis, in illo verò ca&longs;u impul&longs;io fie
ret à diminuto gradu velocitatis eius, &longs;cilicèt ab ex
ce&longs;&longs;u &longs;upra velocitatem fugientis corporis. Prætereà
in corporibus concretis non omninò duris, nouus mo
tus imprimi non pote&longs;t in in&longs;tanti, &longs;ed in tempore, vt
alibi o&longs;ten&longs;um e&longs;t, non contactu &longs;implici, &longs;ed &longs;ociali
motu mouentis, & mobilis, hoc autem faciliùs con
&longs;equi pote&longs;t in corpore aliquo quie&longs;cente amouibi
litèr, quàm &longs;i agitetur directè, vel tran&longs;uersè. Hinc
colligitur fal&longs;um e&longs;&longs;e, quòd faciliùs impelli po&longs;&longs;et
corpus agitatum, quàm
rit amouibilis, vt dictum e&longs;t. Et profectò quies ill&atail;
particularum cuiuslibet corporis firmi, & duri no&ntail;
erit amouibilis, &longs;cilicèt illæ particulæ non &longs;unt indif
ferentes ad motum, cum non à qualibet exigua, & mi
nima vimotiua moueri, & diuelli ab integra ma&longs;&longs;&atail;
dura queant, &longs;ed requiritur in&longs;ignis
ticulæ aquæ glaciatæ à tota ma&longs;&longs;a &longs;eparentur; ex quo
proinde inferre licet, quòd vt plurimùm figuræ præ
dictarum particularum durum corpus
nec &longs;unt regulares, nec l&ecedil;uigatæ, &longs;ed miris modis an
gulo&longs;æ, ramo&longs;æ, contortæ, & vncinatæ, & proindè
partes eius a&longs;peræ, & angulo&longs;æ &longs;e&longs;e contingentes, &
vici&longs;&longs;im vna intra &longs;patium alterius in&longs;inuata, po&longs;&longs;unt
mutuò &longs;atis benè congruere,
uimentum, & opus te&longs;&longs;ellatum, & &longs;ic non pote&longs;t vna
particula ex toto aggregato diuelli extrahique, no&ntail;
quidem propter eius quietem, aut defectum motus,
&longs;ed tantummodò quia eius concatenata &longs;tructura dif
ficilè d
natura flui
ditatis.
natura flui
ditatis.
natura flui
ditatis.
cidens in eis fluiditatem creat, quatenùs &longs;cilicèt ea
rum figuræ angulo&longs;æ ab inuicem &longs;eparantur, &
ob ignis interpo&longs;itionem po&longs;&longs;unt vna &longs;uper
ET reuerà quotie&longs;cum que perpendo, quanta co
pia, & vehementia ignis requiritur, vt aren&atail;,
vitrum, ferrum, aut aliud durum metallum, in
minimas
ctam
rotunditatem accedentes, &longs;ed puto maximè angulo
&longs;as, a&longs;peras, & elongatas e&longs;&longs;e debere, & ideò difficil
limè po&longs;&longs;e contorqueri reuoluique inter contiguas
&longs;ui generis particulas. in hi&longs;ce duos effectus igne&mtail;
producere mihi veri&longs;imile videtur, primò, quòd
quamque
per aliquod &longs;en&longs;ibile interuallum, hocque efficitur à
tran&longs;itu multiplicium, & vehementi&longs;&longs;imarum exhala
tionum, & particularum ignearum inter&longs;luentiu&mtail;,
virtute cuius particulæ &longs;olidæ arenæ eodem modo
ab inuicem di&longs;gregatæ di&longs;ponuntur, ac puluis terreus
intra aquam infu&longs;us, & di&longs;per&longs;us, qui eam luto&longs;am, &
c&ecedil;no&longs;am reddit. Quòd verò arenæ, vel ferri fu&longs;i par
ticulæ reuerà per aliquod interuallum ab inuicem di
&longs;cretæ, & &longs;eparatæ &longs;int, euincitur ex eo, quòd moles
eiu&longs;dem ferri, vel vitri fluentis in&longs;ignitèr augetur &longs;u
pra molem, quam idem corpus durum, & con&longs;i&longs;tens
priùs habebat; ignis ergò copio&longs;i&longs;&longs;imè, & vehemen
ti&longs;&longs;imè fluens inter particulas ferri, vel vitri
pemodum præ&longs;tat, ac rotulæ, vel cylindri &longs;uper quo
rum rotunditatem lapides angulo&longs;i, & figuras irre
gulares habentes labuntur, vel v&longs;um præ&longs;tat &longs;ebi,
vel cuiuslibet alterius corporis vnctuo&longs;i, ope cuius a
renulæ a&longs;perrimæ
na particula &longs;uper aliam facili negotio circumuolui,
agitari, ac dilabi pote&longs;t, quod perindè e&longs;t, ac &longs;i præ
dictæ particulæ vitri, aut ferri acqui&longs;iui&longs;&longs;ent figuram
l&ecedil;uem, rotundam, vel orbicularem &ecedil;mulantem. Ve
rum tamen e&longs;t, quòd huiu&longs;modi operatio effici nullo
modo pote&longs;t ab&longs;que commotione, vertigine, &
po&longs;itione
non indè euincitur fluiditatem in tali ca&longs;u ab&longs;olutè
dependere à prædicta commotione partium, ni&longs;i ex
accidenti, quatenus non po&longs;&longs;unt &longs;egregari, & fluere
particulæ a&longs;peræ, & angulo&longs;æ ferri, vel vitri ab&longs;que
&longs;uperabundanti, & vehementi profluuio ignis, à quo
demùm particulæ ip&longs;æ &longs;olidæ lubricitatem, &
acquirunt. Hoc autem bellè confirmatur ab experi
mento adducto à docti&longs;&longs;imo Roberto Boile quando
alaba&longs;tri
qui&longs;iui&longs;&longs;e ait, at po&longs;tmodum quælibet particula eiu&longs;
dem fluoris &longs;upra papyrum refrigerata reperie batur
aggeries arenularum minuti&longs;&longs;imarum, neque concre
tum, & &longs;olidum corpus effieiebat, vt in vitro, & fer-
ro po&longs;t fu&longs;ionem refrigerato videre e&longs;t.
natura flui
ditatis.
rimento
probatur
natura flui
ditatis.
Sed ad maiorem huius doctrinæ euidentiam con
&longs;ideretur aggeries arenæ minuti&longs;&longs;imæ, & aridæ, hæ
quidem non excurrunt, neque lubricitatem habent,
&longs;i po&longs;tea immi&longs;&longs;a, & intercepta aqua luto&longs;am
acquirat,
tæ nedùm eas di&longs;&longs;ociant, &longs;ed velutirotæ, vel cylin
druli, aut materia aliqua vnctuo&longs;a commoditatem eis
præ&longs;tat, vt po&longs;&longs;int excurrere vna particula arenæ &longs;u
per aliam contorqueri, atque agitari, & tandem ob
natiuam grauitatem quælibet earum deorsùm ten
dendo explanantur, & ad &longs;uperficiem planam hori
zontalem rediguntur, quòd priùs ab&longs;que aqua ill&atail;
inter arenulas intercepta in cumulum &longs;atis accliuem
&longs;u&longs;tinebatur, acquirit ergò ma&longs;&longs;a illa areno&longs;a vnà
cum aqua con&longs;i&longs;tentiam fluidam, explanatur, & reci
pit figuram continentis va&longs;is, non &longs;ecùs, ac vitrum,
& &longs;errum fu&longs;um efformatur, & paritèr ad in&longs;tar glo
bulorum cry&longs;tallinorum, qui licèt &longs;int aridi ab &longs;que
vllo fluido admixto, & omninò quie&longs;cant in va&longs;e ali
quo, neque agitentur, omnes tameniam dictas flui
di proprietates retinere videntur.
tur
non vt fluiditatem constituat, &longs;ed vt ex plan are he
rizont aliter fluidum pos&longs;it.
VErum tamen e&longs;t, quòd illa præcipua conditio, &
proprietas fluidi, qua explanatur, & æqualitèr
iacet in plano horiz ontali, nullo pacto verificari po
te&longs;t, ni&longs;i in ip&longs;o fluido ponatur virtus aliqua motiua,
qua &longs;i omninò careat, nullo pacto poterit aqua fluida
explanari, & ad libellam horizontalem reduci. At
huiu&longs;modi virtus motiua longè diuer&longs;a e&longs;t ab ea, quæ
exigitur à Carte&longs;io, eiu&longs;que &longs;ectatoribus, non eni&mtail;
e&longs;t motiua virtus vaga, & irregularis, quæ inordina
tam agitationem &longs;ursùm, & deorsùm, & tran&longs;uersè
continuato fluxu efficiat, &longs;ed e&longs;t tantummodò vis, at
que impetus naturalis grauitatis, ope cuius particu
læ omnes fluidi æquali ni&longs;u
sùm; &longs;ic enim æquatis momentis efficitur
partium eiu&longs;dem fluidi, vnde &longs;ub&longs;equitur æqualis di
&longs;po&longs;itio earum
uitas in fluido deficeret, non po&longs;&longs;et virtute æquilibrij
æqualitèr di&longs;poni, &longs;ed vna eius pars depre&longs;&longs;a, alia ve
rò &longs;ublimis efficeret inæqualem, & a&longs;peram &longs;uperfi
ciem externam eius, compo&longs;itam ex vallibus, &
tibusNece&longs;&longs;ariò ergò fatendum e&longs;t in hi&longs;ce fluidis
no&longs;tratibus vim motiuam aliquam ade&longs;&longs;e vt omnes
æquali vi, & impetu, ad ea&longs;dem partes, &longs;cilicèt deor
sùm tendant. Et profectò &longs;i ponerentur motus vagi
irregulares, & contrarij in eodem corpore fluido, vt
aduer&longs;arij exi&longs;timant, &longs;equeretur de&longs;tructio
hypothe&longs;is, nam cùm in eadem aqua v. g. non po&longs;
&longs;int omnes particulæ eiu&longs;dem aquæ ex condicto &longs;i
mul ad ea&longs;dem partes ordinata &longs;eriè moueri, vt i&ntail;
progre&longs;&longs;u alicuius cohortis, vel vt in &longs;upplicationi
bus fieri &longs;olet, omninò nece&longs;sè e&longs;t, vt aliæ partes
&longs;ursùm a&longs;cendant, aliquæ verò deorsùm ferantur, &
proinde videtur impo&longs;&longs;ibile, atque incredibile, vt
aliquando prædictæ partes motibus contrarijs &longs;ibi
mutuò non occurrant, & proptereà &longs;e mutuò no&ntail;
impediant, & ad quiet em non redigantur. Cùmque
ab&longs;que illa vertigine, & agitatione partium fluidi
tatem exi&longs;tere negent; imò duritiem creari affirment. Sequitur ex eadem hypothe&longs;i (in qua commotiones
partium aquæ ad fluidi con&longs;titutionem requiruntur)
effici duritiem, & con&longs;i&longs;tentiam, &longs;altèm in illis parti
culis fluidi, in quibus quies creatur, quod præcisè
de&longs;truit eorum hypothe&longs;im.
natura flui
ditatis.
natura flui
ditatis.
In&longs;uper &longs;i vera e&longs;t prædicta vis motiua partiu&mtail;
fluidi &longs;ursùm, & deorsùm illa profectò quanta erit,
& certi, ac determinati gradus energiæ, quare no&ntail;
poterit &longs;uperari à minima, & exigua vi externa eam
pilli, quo nauim in aqua &longs;tagnante trahemus.
Re&longs;tat modò po&longs;trema difficultas, quomodò nimi
rùm aqua fluida, & quodlibet men&longs;truum ex vegeta
bilibus, &longs;alibus, & mineralibus tincturas extrahunt,
ac fermentatione quadam corpora illa di&longs;&longs;olunnt,
ac per vniuer&longs;um fluidum &longs;pargunt, diffunduntque;
& quia huiu&longs;modi operatio ab&longs;que agitatione a
& fluidi fermentantis percipi non pote&longs;t, hinc con
cludunt aquam, & fluidum quodlibet componi ex
particulis miris, & varijs modis agitatis, à qua tan
dem partium agitatione fluxibilitatem creari
natura flui
ditatis.
cèt non omnia vera &longs;int, non tamen euincunt fluidi
tatem &longs;emper à continua partium agitatione
pendere.
ET hìc primò non negabo exhalationes igneas,
& alia corpora &longs;e mouentia excurrere, atqu&etail;
penetrare corpora omnia concreta, & ide ò
partes commouere; &longs;ed non proindè confiteri cogi
mur fluiditatem à continua agitatione partium eius
pendere, quandoquidem
ab Aduer&longs;arijs afferuntur veræ &longs;unt, & illæ, quæ ve
ræ &longs;unt non euincunt partes omnes eiu&longs;dem corpo
ris fluidi perpetuò agitari, atque commoueri, itaut
ne minima particula in aliquo angulo fluidi remane
at quie&longs;cens, & ab&longs;que vlla agitatione, &longs;altem per
aliquod breue tempus. & primum &longs;i granum &longs;alis &longs;o
lidum in fundo aquæ immergatur, verùm
citò vniuer&longs;a aqua va&longs;is &longs;al&longs;edine imbibitur, ni&longs;i va&longs;a
&longs;int ampla, & aqua &longs;it agitata, &longs;i verò &longs;umatur fi&longs;tu
la vitrea &longs;atis angu&longs;ta, atque in eius fundo &longs;al appo
natur, aqua verò placidè, & &longs;olertèr &longs;ali &longs;uperpo
natur, euitata, quantum fieri pote&longs;t, agitatione, &
commotione eius, tunc aqua, quæ in &longs;ummitate fi&longs;tu
læ reperitur, &longs;al&longs;edine non afficitur, & hoc etiam à
Boile experimento comprobatum fuit: vnde conij
citur, quòd reuerà aqua ob eius æquilibrium facilè
pote&longs;t commoueri, & &longs;ic repetitis conuolutionibus
&longs;ursùm, & deorsùm &longs;ecum tran&longs;portare valet minu
ti&longs;&longs;imas &longs;alis particulas, & hoc citiùs con&longs;equitur &longs;i
agitatio
te externo, vel ab ignis vehementia per vitri poro&longs;i
tates penetrante, & per aquam a&longs;cendente; tame&ntail;
quando in fi&longs;tula angu&longs;ta, & alta non æquè commo
dè, & facilè aqua agitari, vel &longs;emèl incepta agitatio
ne promoueri non pote&longs;t, tunc &longs;alis particulæ non a
&longs;cendunt v&longs;que ad
nimirùm, licèt aqua æquilibrata à qualibet vimotiua
moueri, & impelli po&longs;&longs;it, nihilominùs quando agita
tio non e&longs;t vehemens, & copio&longs;a, citò extinguitur,
reliqua moles aquæ &longs;uprema non impul&longs;a ob &longs;ui na
turalem inertiam, & aliqualem vi&longs;co&longs;itatem violen
tiæ motus aliquo pacto re&longs;i&longs;tat, proindeque impre&longs;
&longs;us motus in infimis aquæ particulis citò retardatur,
extinguitur que à reliquis aqu&ecedil; partibus in quiete
&longs;titutis
propagari v&longs;que ad va&longs;is &longs;ummitatem non pote&longs;t.
natura flui
ditatis.
tiones, & ex
tractiones
chymicæ ab&longs;
que motu
fluidi men
&longs;trui fieri ne
queunt; at du
bitatu an
motus, qui in
f
ne ob&longs;erua
tur,
vel effectus
fermentatio
nis.
In&longs;uper, quòd prædictæ
ræ extractionum chymicarum
motu, & agitatione fluidi men&longs;trui,
tum, & euidens, &longs;ed dubitatur controuertiturque,
an motus, qui in fermentatione ob&longs;eruatur, &longs;it cau
&longs;a, vel effectus eiu&longs;dem fermentationis, &longs;cilicèt a&ntail;
motus ille antecedenter &longs;it proprius fluidi corporis,
& fluiditatem con&longs;tituat, &longs;itque cau&longs;a effectiua fer
mentationis, an è contrà di&longs;&longs;olutio &longs;alium, & reliquæ
fermentationes ab alia cau&longs;a longè diuer&longs;a depen
deant, à qua producatur veluti effectus motus ill&etail;,
qui in fermentatione ob&longs;eruatur. Modò &longs;i o&longs;tende
rimus, quòd &longs;implex grauitas fluidi ratione quadam
mechanica, & iuxtà leges æquilibrij in&longs;inuare, & im
pellere pote&longs;t fluidi particulas intra poro&longs;itates &longs;a
lium mineralium, & vegetabilium, vndè po&longs;tea con
&longs;equatur agitatio, & ebullitio, quam in fermentatio
ne con&longs;picimus, procùl dubio non licebit ex hoc ex
perimento inferre motum illum antecedenter fluido
competere, & fluiditatem con&longs;tituere.
Cap, 7. d
natura flui
ditatis.
non e&longs;t proprin ip&longs;ius aquæ, neque fluiditatem eius co
&longs;tituit, &longs;ed e&longs;t effectus dependens à grauitate
eiu&longs;dem fluidi.
IMmergamus priùs in aqua fru&longs;tum &longs;pongiæ, con
&longs;tat &longs;pongiæ &longs;ub &longs;tantiam
ro&longs;itates exiguas, & inter &longs;e communicantes ad in&longs;tar
fi&longs;tularum exiguarum, quæ aut aere replentur, aut
omninò inanes &longs;unt. Tunc nemo negabit aquam pro
prio, & naturali pondere in&longs;inuari debere intra
giæ
ab&longs;que motu, & agitatione ip&longs;ius aquæ, nece&longs;sè e&longs;t,
vt ambientes partes fluidi contiguæ, & proximæ
&longs;equutiuo
giæ
quales, & variæ e&longs;&longs;e debent, & ad diuer&longs;as plagas
tendentes, prout in &longs;pongiæ poro&longs;itatibus &longs;upremis
infimis, & lateralibus aqua ingreditur; at quia &longs;e
mel aqua commota nece&longs;&longs;ariò impetum concipit, er
gò nece&longs;sè e&longs;t, vt vis prædicti impetus impre&longs;&longs;i mini
mè otio&longs;a &longs;it, proindèque percu&longs;&longs;iones inferat tùm
particulis &longs;olidis ip&longs;ius &longs;pongiæ, cùm etiam particu
lis aquæ contiguæ, quare non poterit extingui om
ninò prædicta agitatio, ni&longs;i po&longs;t aliquod
quàm &longs;cilic èt ab impedimentis à glutine
demmet aquæ illatis, impetus præconceptus extin
guatur. Patet ergò, quòd agitatio aquæ, quæ in
giæ
quæ, neque fluiditatem eius con&longs;tituit, &longs;ed potiùs
e&longs;t effectus dependens à vigrauitatis eiu&longs;dem
quatenùs iuxtà naturæ in&longs;titutum, & hydro&longs;taticæ
leges in&longs;inuari debet intra &longs;pongiæ poro&longs;itates, vel
inanes, vel à leuiori corpore aereo occupatas.
Cap 7. d&etail;
natura flui
ditatis.
defactione ob&longs;eruatur, non e&longs;t propria, & con&longs;titu
tiua fluidatis eius, &longs;ed e&longs;t effectus dependens à
pondere eiu&longs;dem fluidi.
IMmittatur po&longs;tea intra aquam pumex loco &longs;pon
giæ, cuius poro&longs;itates aere refertæ &longs;unt,
vtpotè grauior aere intra prædictas poro&longs;itates con
tento &longs;en&longs;im in pumicis exterioribus foraminibus in-
&longs;inuari debet, & proindè aereæ particulæ, quæ poru
los occupabant, expelli debent, & hæ cùm in fundo
aquæ permanere nequeant, nece&longs;sè e&longs;t vt &longs;ursùm per
aquam a&longs;cendant expre&longs;sæ à maiori pondere ip&longs;ius
aquæ; dum verò granula, &longs;eu ampullæ aereæ &longs;ursùm
feruntur, & ebullitionem quamdam oculis repr&ecedil;&longs;en
tant, fieri non pote&longs;t, vt aqua per quam
quo pacto non agitetur commoueaturque tum expri
mendo aerem, cùm etiam cedendo locum aeri tran
&longs;ituro. Habemus iam nouam cau&longs;am agitationis, &
commotionis ip&longs;ius aquæ præter priùs
dò
&longs;pongiæ poros; nam præterea dum aerei globuli ex
pre&longs;&longs;i, & à pumice exclu&longs;i per aquam a&longs;cendunt, ne
ce&longs;&longs;ariò aqua agitari quoque debet, igitur vniuer&longs;a
illa commotio, & veluti ebullitio aquæ habet
efficientem, quæ e&longs;t &longs;implex aquæ grauitas, quar&etail;
non licèt inferre, quòd pr&ecedil;dictus motus ebullitionis,
qui in aqua po&longs;t immer&longs;ionem pumicis con&longs;picitur,
&longs;it &longs;ignum, & euincat motum illum proprium e&longs;&longs;e ip
&longs;ius aquæ, & fluiditatem eius con&longs;tituere.
Cap, 7. d
natura flui
ditatis.
eam non e&longs;t propria, & fluiditatis con&longs;titutiu
producitur àgrauitate fluidi.
SI po&longs;tea gleba arida intra aquam mergatur, quia
inter pumicem, & glebam hoc di&longs;criminis inter-
cedit, quòd parietes porulorum pumicis duri
&longs;i&longs;tentes
ba parietes pororum &longs;unt valdè fragiles, & di&longs;&longs;olubi
les; vnde &longs;equitur, quòd aquæ particulæ vi grauitatis
intra poros glebæ in&longs;inuatæ nedùm expellant aerem
ibi contentum, &longs;ed etiam arenulas glebam con&longs;titu
entes, quæ tantummodò &longs;e tangunt, & nullo alio vin
culo, nec glutine nectuntur, facilè ab inuicem di&longs;&longs;o
cient di&longs;pergantque. porrò cùm ad aquæ
& aeris expre&longs;&longs;ionem, atque a&longs;cen&longs;um nece&longs;&longs;ariò mo
tus, & agitatio ip&longs;ius aquæ
tus ab&longs;que impetu e&longs;&longs;e non po&longs;&longs;it, qui cùm vim cuiu&longs;
cumque ponderis finiti &longs;uperet, vt demon&longs;trauimus,
facilè poterit exiguas illas arenulas di&longs;&longs;olutas nedum
lateraliter, &longs;ed etiam &longs;ursùm aliquanti&longs;per impelle
re, & hinc oritur turbida quædam nebula, quæ pro
pè glebam demer&longs;am con&longs;picitur diù Ex
vniuer&longs;a hac naturali operatione nemo &longs;anæ mentis
eliciet aquæ particulas continuo, & vago motu agi
tarinaturali in&longs;tinctu, & ab hoc principio produci
glebæ di&longs;&longs;olutionem, di&longs;per&longs;ionemque arenularum
eius, & feruoris, qui in aqua tunc temporis con&longs;pici
tur, nam hæc omnia habent &longs;uam cau&longs;am
nempè aquæ grauitatem, quæ pote&longs;t, & debet
expellere &longs;ursùm leues aeris particulas intra glebæ
poro&longs;itates contentas, &longs;ed etiam di&longs;&longs;oluere, & di&longs;per
gere &longs;uo impetu puluerulentas glebæ particulas per
ip&longs;ammet aquam.
Cap.
7. d
natura flui
ditatis.
In li
p
Cap.
7. d&etail;
natura flui
ditatis.
tione ob&longs;eruatur, non pendet ab intrin&longs;ece, & natura
li motu aquæ, &longs;ed à fimplici eius gra
uitate.
COgitemus po&longs;tea &longs;alem e&longs;&longs;e
&longs;olubilem, qui con&longs;tatex &longs;uis minimis parti
culis figuratis non vndequaque &longs;e tangentibus, con
nexi&longs;que, & proindè &longs;alis gleba habet innumeros
porulos, & canaliculos inter&longs;per&longs;os, qui vt
non replentur, nec occupantur ab aere, cùm &longs;int val
dè exigui angu&longs;tique, &longs;ed aut à materia valdè tenui,
vel potiùs vacui omninò &longs;unt. Con&longs;tat aliundè, quod
aqua facillimè &longs;ali vnitur, connectitur, eiu&longs;que po
ro&longs;itates penetrat, contra, ac in pumice, ligno, & alijs
corporibus contingit, in quibus madefactio, & a
quæ penetratio non fit, ni&longs;i longo tempore, & diffi
cilè (&longs;iuè hoc pendeat ab aere contento in horu&mtail;
poro&longs;itatibus, &longs;iuè ab incongruentia pororum.) Ex
hac, inquam, maxima facilitate, qua aqua &longs;alibus in
&longs;inuatur, licet inferre, quòd motu velociori accurrat
ad occupanda illa &longs;alium foraminula, & ideò maio
ri, & vehementiori impetu diffoluat &longs;e paretque par
ticulas &longs;alium, ea&longs;que vehementius quoque impellat
vnà cumreliqua ambiente aqua, quæ ne dum con&longs;e
quutiuo motu celeriùs agitatur, &longs;ed etiam ab a&longs;cen&longs;u
leuiorum particularum, quæ in porulis &longs;alium conti-
nebantur, commouetur. Non e&longs;t po&longs;tea difficile à ve
hementiori impetu, & motu ip&longs;is aquæ minimas &longs;a
lis particulas ad loca remotiora di&longs;pergi, atque
ferri
&longs;is ampli inficiant. Et hic quoque con&longs;tat vniuer&longs;am
hanc operationem fermentatiuam non
te&longs;tina motione partium aquæ fluxibilitatis con&longs;titu
tiua, &longs;ed à &longs;implici aquæ grauitate legibus mechani
cis operante, vt dictum e&longs;t.
Cap.
7. d&etail;
natura flui
ditatis.
Ex &longs;
ctrina &longs;equ
videtur,
quod
ta
ne &longs;alis, eius
particulæ, vt
graues ad
dum va&longs;is
de
aqua dulcis
red
quod
&longs;um.
Sed hìc difficultas oritur, &longs;i verum e&longs;&longs;et; quòd à vi
grauitatis aqua intra poros &longs;alium in&longs;inuata
acquireret, & &longs;ic &longs;alia di&longs;&longs;olueret, & feruorem crea
ret, ergò po&longs;tquam &longs;emel completa e&longs;&longs;et di&longs;&longs;olutio
&longs;alis, & extinctus feruor ebullitioque, redacta e&longs;&longs;et
aqua &longs;apida ad exactam tran quillitatem, non po&longs;&longs;ent
&longs;alis particulæ grauiores &longs;pecie ip&longs;a aqua &longs;u&longs;pen&longs;æ
retineri in ip&longs;amet aqua, &longs;ed &longs;ponte &longs;ua &longs;altem tar
diori motu ad fundum va&longs;is deciderent, proindeque
aqua &longs;uprema dulcis omninò remaneret, quod e&longs;t
fal&longs;um, igitur dicendum quòd non ab impetu fer
mentationis dependente à vi grauitatis fluidi parti
culæ &longs;alis di&longs;perguntur, &longs;ed potiùs ab inte&longs;tina, & na
turali partium aquæ agitatione, fluiditatemque eius
&longs;alis partieulæ retinentur natantes intrà aquæ &longs;ub
&longs;tantiam.
Cap.
7. d&etail;
natura flui
ditatis.
&longs;penduntur ab intestina aquæ commotione, &longs;ed ab eius
naturali glutine validiùs operante in &longs;uperfi
cieculis particularum &longs;alium.
SEd huic difficultati re&longs;pondeo,
agitatæ, &longs;ed ab alia longè diuer&longs;a cau&longs;a grauio
res particulas innatantes &longs;u&longs;tineri po&longs;&longs;e. Certum e&longs;t
corporum particulas quò tenuiores, & minutiores
&longs;unt, eò tardiùs per fluida de&longs;cendere, vt contingit
in puluere terre&longs;tri in aere, vel aqua di&longs;per&longs;o, qui&atail;
nimirùm in hi&longs;ce corpu&longs;culis exiguis eorum &longs;uper&longs;i
cies externa &longs;emper magis, ac magis cre&longs;cit in re
&longs;pectu ad &longs;uam grauitatem, vt alibi declarauimus;
quia verò men&longs;ura impedimenti fluidi externi auge
tur, prout pr&ecedil;dicta &longs;uperficies cre&longs;cit
pus per fluidum moueri queat, quin &longs;ucce&longs;&longs;iuè è loco
anteriori fluidum ei contiguum expellat, quotie&longs;
cumque vis impul&longs;iua grauitatis minuitur pro molis
diminutione, &longs;uperficies verò in multo minori &longs;cili
cèt &longs;ubduplicata proportione diminuitur, &longs;equitur,
vt fluidi impedimentum minus decre&longs;cendo, du&mtail;
impetus grauitatis valdè minuitur,
litatem, & æquilibrium quamproximè accedant, &
proindè hoc nomine particulæ minimæ fluido graui
ores motu &longs;emper tardiori in ip&longs;o de&longs;cendent quo
magis eorum moles imminuitur.
Cap.
7. d&etail;
natura flui
ditatis.
Prætereà quia experientia con&longs;tat fluidi partes
glutine aliquo necti inter&longs;e debere, vt po&longs;tea fusè
declarabitur, atque vis, & energia prædicti glutinis
&longs;it certi ac determinati gradus, huic verò contrapo
nitur energia grauitatis, & velocitatis, quæ &longs;emper
magis, ac magis imminui pote&longs;t, prout moles eius
&longs;ubdiuiditur, hinc fit vt tandem ad eam exiguitatem
vis grauitatis, & impetus redigatur, vt æquari præ
cisè po&longs;&longs;it energiæ glutinis ip&longs;ius fluidi, proindeque
vna alteri præualere nequeat, vnde æquatis viribus,
factoque æquilibrio nece&longs;&longs;ariò particulæ illæ graues
in ip&longs;o fluido innatantes in eodem &longs;itu quie&longs;cere de
bent. Hac ratione fieri pote&longs;t, vt minim&ecedil; &longs;alis parti
culæ per aquam di&longs;per&longs;æ, & innatantes æquilibrari,
& quie&longs;cere in ip&longs;a aqua po&longs;&longs;int, proindeque aqu&atail;
&longs;emper &longs;al&longs;edinem retinere valet.
apparet, pendet non ab inte&longs;tino m
eius grauitate di&longs;&longs;oluente, & exprimente igneas
particulas, quæ in calce contine
bantur.
IN calce po&longs;tea intra
&longs;a feruoris oritur, quia in exiguis calcinati &longs;axi
poro&longs;itatibus, in eiu&longs;que anfractibus includuntur in
numeræ particulæ ignis ibidem in&longs;inuatæ à
&longs;imo
&longs;&longs;uxibilitate particulas calcis
illis corpu&longs;culis, quæ po&longs;tea expre&longs;&longs;a ab excedenti
aquæ pondere velociori motu &longs;ursùm per
dunt
aquæ partes laterales celeriùs, & vehementiùs agi
tantur.
Cap, 7. de
natura flui
ditatis.
ab aqua forti.
IDip&longs;um eadem ferè ratione producit aqua fortis,
vel regia in metallis, dum enim intra illius poro
&longs;itates vi ponderis eius in&longs;inuatur, &longs;alibus quibus a
qua fortis referta e&longs;t, veluti talis, ac &longs;calpris abradit
&longs;olidas aliquas metalli particulas, &longs;imulque relaxat
o&longs;tiola, egre&longs;&longs;umque concedit materiæ igneæ ibidem
tis veloci&longs;&longs;imo motu per eamdem
dit
ebullitionem feruentem producunt, vnà cum ingenti
aquæ agitatione; quæ omnia immeritò ab inte&longs;tin&atail;
partium aquæ fortis agitatione qui&longs;quam effici cen
&longs;eret, cùm ad&longs;it nece&longs;&longs;aria, & euidenti&longs;&longs;ima cau&longs;&atail;
nempè &longs;implex grauitas aquæ fortis, quæ e&longs;t impo&longs;
&longs;ibile vt intra poro&longs;itates inanes, aut à leuiori cor
pore oppletas, non in&longs;inuetur, & proinde in eius
motu impetum non concipiat, cuius virtute exiguæ
metalli particulæ corrodantur, exprimaturque ma
teria ignea in eo contenta, proindeque vehementiùs
aqua agitetur, & tandem à vi eiu&longs;dem impetus parti
cul&ecedil; minimæ metalli, licèt aqua grauiores &longs;int, po&longs;&longs;unt
hinc inde di&longs;pergi, tran&longs;portarique, & extincto fer
uore à naturali partium aquæ vi&longs;co&longs;itate retineri in
media aqua po&longs;&longs;unt, quotie&longs;cumque vis re&longs;i&longs;tentiæ
aquæ æqualis &longs;it exili&longs;&longs;imo ponderi earumdem par
ticularum metallicarum.
Cap.
7. d&etail;
natura flui
ditatis.
Aliquæ
peri&etilde;tiæ no
&longs;træ
riæ refragati
bus inf
&longs;atisfacie
mus.
Hic po&longs;&longs;ent innumera ph&ecedil;nomena afferri, quæ in
prædictis di&longs;&longs;olutionibus &longs;alium mineralium, & ve
getabilium ob&longs;eruantur, vt nimirùm cùm calx, aut
metallum non demergitur intra aquam, &longs;ed eminet,
tangitque dumtaxat &longs;uperficiem eius externam, &
nihilominùs aqua a&longs;cendit, &longs;ubleuaturque penetran
do &longs;alis, & metalli poro&longs;itates, & po&longs;tea denuò de
&longs;cendendo di&longs;perguntur &longs;olidæ particulæ efficiunt
que vniuer&longs;am aquam &longs;apidam, vel metallo impr&ecedil;
gnatam; non minùs videmus
&longs;imas, per &longs;pongias aquam contingentes &longs;upra eius
&longs;uperficiem, a&longs;cendere. Vnde qui&longs;piam dubitandi
an&longs;am arripere po&longs;&longs;et, non pendere has operationes
à vi grauitatis, quæ naturæ ductu non &longs;ursùm, &longs;ed
deorsùm impellere aquam fluidam pote&longs;t.
Sed interim
ex demon
f
ter reij
oppo&longs;ita
tentia
Sed hoc
in &longs;pongia, pumice, &longs;ale, calce &c. intra aquam de
mer&longs;is nece&longs;&longs;ariò vis grauitatis fluidi prædictas ope
rationes efficit, hæ verò diuer&longs;æ operationes paritèr
producuntur ab eodem principio grauitatis, vt in-
feriùs o&longs;tendemus, patebitque nece&longs;&longs;itate quadam
mechanica à grauitate, & momento aquæ fluidæ
in&longs;inuari intra eleuatas fi&longs;tulas, vel intra
& &longs;alium eminentes poro&longs;itates. Vnde elicere po&longs;
&longs;umus, quòd ex prædicto motu fermentationis dedu
cinon pote&longs;t, quòd in fluido partes cius perpetuò in
te&longs;tino motu agitentur, à qua commotione fluidi
tas efficiatur, & ab hac veluti à ca
&longs;alium metallorum, &c. non dependeant.
Cap.
8.
Cap.
7. d&etail;
natura flui
ditatis.
Deinde expendenda e&longs;t præcipua figura particu
larum aquam componentium iuxtà Carte&longs;ij
Putat enim prædictas particulas oblongas virgulas
flexibiles, & lubricas e&longs;&longs;e, vti &longs;unt anguillæ, quæ va
rijs modis contortæ &longs;e mutuò amplexentur, &
ponant
plicatæ excurrunt, varièque flectuntur, & &longs;ic flui
ditatem aquæ componere, atque efficere. Et hinc ra
tionem eliciunt, quare guttæ aquæ è &longs;upremis arbo
rum ramis, ac folijs pendentes non decidunt, &longs;ed te
naci quodam vinculo retinentur, hocque confirmare
nituntur tali exemplo; multotiès è ca&longs;ei fragmento
&longs;ursùm eleuato, & ab eius prona facie pendet agge
ries plurimorum vermium, qui nedùm non
deorsùm, &longs;ed componunt veluti quamdam gibbo&longs;i
tatem deorsùm pendentem,
mes miris modis agitantur, & inflectuntur.
Ex Carte
aquæ parti
culæ &longs;u
longæ, flexi
biles, vt an
guillæ, per
petuò agita
ræ, & hinc
gnttas aquæ
pendulas &longs;u
cen&longs;e
Cap.
7. d
natura flui
ditatis.
Carte&longs;ianæ.
AT &longs;i talis e&longs;t aquæ natura, &longs;equitur vt eius par
ticulæ &longs;int animatæ, oportet enim vt percipi
ant, & eligant motus, & inflexiones, quæ nece&longs;&longs;ari&ecedil;
&longs;unt ad prædictum effectum producendum. Nam &longs;i
cuti illi vermes nece&longs;sè e&longs;t vt partim in&longs;inuentur i&ntail;
&longs;upremas ca&longs;ei poro&longs;itates non directè, &longs;ed tortuosè
capita inflectendo, vt nimirùm efficiant hamos, vel
vncinos, & è contrà infimæ partes vermium
tes
in quibus &longs;ub&longs;equentes vermes adrepant, debent
que paritèr &longs;ub&longs;equentes vermes non &longs;ecùs incurua
ri, vt duplices vncinos
tibus. idip&longs;um efficere deberent anguillæ illæ
componentes. At quomodo per&longs;euerare po&longs;&longs;et ag
geries prædictarum aquæ anguillularum, ni&longs;i prædi
ctæ earum curuitates &longs;umma &longs;olertia, & prouidentia
fierent, & per&longs;euerarent, prout nece&longs;&longs;itas
nisEt &longs;i non prouiden
tia, &longs;ed ca&longs;u, vt con&longs;entaneum e&longs;t; monentur, quomo
do po&longs;&longs;ent perpetuò agitari, & inflecti quin
dovide
tur enim impo&longs;&longs;ibile vt vniuer&longs;a ma&longs;&longs;a virgularu&mtail;
aquæ aliquando, &longs;altem per breue tempus non diri
gatur, vel &longs;altem diuer&longs;o modo flectatur, quàm opus
e&longs;t, vt continuata &longs;eries hamorum, vel vncinorum &longs;e
vici&longs;&longs;im &longs;u&longs;tinentium non e&longs;formetur, & &longs;ic fieri po&longs;
&longs;et vt tota gutta aquæ pendens, aut aliqua eius por
tio &longs;olutis vinculis, directi&longs;que vncinis deorsùm la
beretur, quod tamen e&longs;t fal&longs;um. Tandem &longs;i attentè
con&longs;ideretur &longs;tructura animalium optimè percipitur
non po&longs;&longs;e vermem inflecti, ac con&longs;eruari in aliquo &longs;i
tu curuo ab&longs;que vi, & tractione mu&longs;culorum, vt ni
mirùm eorum fibræ decurtentur relaxatis fibris con
trapo&longs;iti mu&longs;culi. hoc autem quàm &longs;it durum, & in
comprehen&longs;rbile in particulis ip&longs;ius aquæ &longs;uppone
re vnu&longs;qui&longs;que per &longs;e videt. Si igitur &longs;aluari pote&longs;t
aquæ fluiditas, & tenacitas illa, qua guttæ penden
tes retinentur faciliori, & euidenti po&longs;itione, vt mox
patebit, quis quæ&longs;o præeliget hanc violentam, diffi
cilemque hypothe&longs;im? nulla igitur e&longs;t nece&longs;&longs;itas po
nendi formam, & motionem partium aquæ tam ab
&longs;urdam
menta
ra efformauit, ponantur.
Cap 7. d&etail;
natura flui
ditatis.
non pote&longs;t ab&longs;que machinulis flexibilibus, & re&longs;ilien
tibus, à quibus aquæ particulæ, veluti lanu
gine ambiuntur.
PO&longs;tremo loco dicendum e&longs;t de alia fluidi pa&longs;&longs;io
ne, quæ in exiguis eius partibus ob&longs;eruatur,
non autem in
aquam, & cætera fluida naturam quamdam glutino
&longs;am, & vi&longs;co&longs;am habere, quod quidem euincitur ex
eo quod guttæ fluidæ &longs;u&longs;pen&longs;æ pendent è &longs;upremis
ramis arborum, & &longs;i quis velit particulam eiu&longs;dem
guttæ à reliqua eius ma&longs;&longs;a diuellere, per&longs;entiet re&longs;i
&longs;tentiam aliquam, & ce&longs;&longs;ante viexterna denuò gutta
&longs;ponte recolligitur; quòd verò prædicta operatio
pendeat à glutine, con&longs;tat ex eo, quòd &longs;i aquæ puri&longs;
&longs;imæ addatur mi&longs;ceaturque &longs;uccus, vel ma&longs;&longs;a aliqua
glutino&longs;a, & vi&longs;co&longs;a, tunc quidem guttulæ penden
tes amp&longs;iores fiunt, in fila tenui&longs;&longs;ima &longs;atis longa ex
tenduntur, atque in membranas gracili&longs;&longs;imas attenu
antur quoties in&longs;ufflato aere efficiuntur bullæ
tesSic videmus
vi&longs;co&longs;am, vel aquam cum albugine oui, vel &longs;aponi
admixtam extendi in tenui&longs;&longs;ima fila, & denuò recol
ligi, qui effectus procùl dubio illi vi&longs;co&longs;itati admix
tæ tribui debet. Si igitur tam in&longs;ignis effectus pro
ducitur à grandi copia glutinis, vel humor is vi&longs;co&longs;i,
quis dubitabit eumdem effectum quando e&longs;t minùs
in&longs;ignis productum fui&longs;&longs;e à minori copia eiu&longs;de&mtail;
glutinis, & vi&longs;co&longs;i humoris? Sed nemo ferè dubitat
in aqua, & in reliquis fluidis vi&longs;co&longs;itatem, aut quid
analogum glutini in exi&longs;tere, dubitatur &longs;olummodò
de cau&longs;a prædicti glutinis, cùm hæc po&longs;&longs;it e&longs;&longs;e exter
na, & interna, duo enim corpora vniri po&longs;&longs;unt, & re
&longs;i&longs;tere &longs;eparationi, cùm à cau&longs;a externa impelluntur
vnum versùs aliud, vel potiùs ab aliqua vi motiua,
qualis e&longs;t illa, quæ in magnete, & magneticis corpo
ribus ob&longs;eruatur. Sed hæc inferiùs refellentur.
alij
po&longs;tea recurrunt ad figuras hamatas, & vncinatas
corporum gluten componentium. Sed meo iudicio
videntur huiu&longs;modi curuitates, & vncinos per &longs;&etail;
minimè vi&longs;co&longs;itatem efficere po&longs;&longs;e, quia po&longs;tqua&mtail;
actu vncini, & hami illi di&longs;&longs;oluti, & disiuncti &longs;unt,
nullam vim haberent &longs;e &longs;e denuò
endi; po&longs;&longs;et profectò hoc effici &longs;i prædict&ecedil; hamatæ fi
guræ e&longs;&longs;ent flexibiles, & re&longs;ilientes, vt machinæ, &
arcus, qui po&longs;tquam di&longs;tracti &longs;unt, vim habent &longs;e
trahendiQuod verò particulæ fluidi machinæ na
turam participent, confirmatur ex eo, quòd fluid&atail;,
quæ rigida, & dura reddi po&longs;&longs;unt, po&longs;t refrigeratio
nem flecti po&longs;tea, & re&longs;ilire, & dirigi
cum &longs;umuntur graciles laminæ prædicti corporis in
durati, vt patet inglacie, vitro, ferro, &c. Quòdque
præterea veri&longs;imilis &longs;it prædicta po&longs;itio machinula
rum in fluidis, patet exemplo aeris, qui reuerà com
ponitur ex particulis
næ, vt &longs;uperiùs o&longs;ten&longs;um e&longs;t, igitur non erit impo&longs;&longs;i
bile, vt eamdem naturam fluida den&longs;iora
&longs;cilicèt con&longs;tent ex ij&longs;dem machinulis, alitèr tame&ntail;
efformatis, quàm in aere. Verum tamen e&longs;t, quòd
prædictæ machinulæ in aqua, & &longs;imilibus fluidis de
bent e&longs;&longs;e valdè &longs;uperficiales, veluti lanugo quædam
tenuis, & debilis inue&longs;tiens quodlibet aquæ mini
mum, &longs;cilicèt concipi debet interna, & indiuidu&atail;
quælibet aquæ particula &longs;olida, & dura, cuius figura
&longs;it octacdra, vel alterius fimilis figuræ; hæc, inquam,
extrin&longs;ecè ambiri debet à tenui&longs;lima lanugine, quæ
flecti, & re&longs;ilire po&longs;&longs;it ad Sed opor
tet vt prædictæ machinulæ &longs;int breues, contortæ, &
exigui roboris, vt nimirùm minimam, &
vim habeant, nec po&longs;&longs;int impedimentum &longs;en&longs;ibil&etail;
a&longs;ferre fluxui interno earumdem partium aquæ.
Cap.
7. d
natura flui
ditatis.
In lib
percu
Cap.
7. d&etail;
natura flui
ditatis.
natura flui
ditatis.
Sed circa vim prædicti glutinis fluidi
ficultates occurrunt. prima quomodo, & quare par
tes fluidi facilè &longs;uper &longs;e ipfas excurrere po&longs;&longs;int, diffi
cilè verò à tota ma&longs;&longs;a fluida diuelli, &longs;egregariqu&etail;
valeant. &longs;ecunda, quare lamina &longs;olida, quæ in&longs;en&longs;ibi
litèr magis, vel minùs grauis fit, quàm fluidum, deor
sùm, aut fursùm a&longs;cendere po&longs;&longs;it in ip &longs;omet fluido, ex
quo deducunt nullam vi&longs;co&longs;itatem in ip&longs;o fluido re
periri. tertia quare aliqua fluida non mi&longs;centur, imò
fugiunt alia fluida, & &longs;olida corpora, vti aqua no&ntail;
mi&longs;cetur cum aere, neque cum oleo, neque cum hy
drargyro, & quodlibet ex prædictis corporibus
gitur
non &longs;int.
tur difficul
tates aliquæ
circa vim
glutinis flui
dorum.
difficilè verò à tota ma&longs;&longs;a fluida pen
dula diuelli, di&longs;iungique qucant,
rationem reddere.
QVoad primam videtur machina eius naturæ e&longs;
&longs;e, vt tantò maiorem energiam, autre&longs;i&longs;tenti-
am habeat, quantò à maiori violentia di&longs;trahatur, vt
con&longs;tat
mè &longs;lectatur, vel dilatetur, videmus quòd &longs;emper ma
gis, ac magis re&longs;i&longs;tit di&longs;tractioni maiori, & validiori
energia, quò magis ex plicatur, vel inflectitur machi
na; &longs;ed quia partes aquæ connectuntur ad inuice&mtail;
&longs;uperficietenùs ob iam dictam lanuginem, fit vt quo
tie&longs;cumque diuellere tentamus vnam aquæ parte&mtail;
ab alia, tunc prædictæ machinulæ lanuginem com
ponentes inter &longs;e connexæ violenter di&longs;trahantur; &
proindè maiorem re&longs;i&longs;tentiam habeant, quàm partes
eiu&longs;dem aquæ, quæ &longs;implici contactu &longs;olummodò vni
untur
patiantur; vnde fit vt minori tenacitate connectan
tur, & ideò ob flexilitatem extremarum partium di
ctæ lanuginis facilè vna aquæ pars &longs;uper alteram mo
ueri, & fluere po&longs;&longs;it: quia vero actus, & operatio ip&longs;a
diuul&longs;ionis aquæ ab aqua &longs;ecum inuoluit violenta&mtail;
machinularum aquæ di&longs;tractionem, non item fluxus
aquæ per aquam, hinc &longs;equitur vt in di&longs;tractione, &
diuul&longs;ione re&longs;i&longs;tentia percipiatur, non verò in fluxu e
iu&longs;dem aquæ &longs;uper reliquas eius partes. Similiter in
gutta pendente particulæ minimæ aquæ &longs;uperficiem
eius extrin&longs;ecam componentes, mutuò &longs;e
vinciunturque, connexis nempe machinulis à quibus
aquæ particulæ ambiuntur, veluti à lanugine
vt dictum e&longs;t; quia verò prædictæ partes externæ &longs;u
&longs;tinent, ne dùm pondus proprium, &longs;ed etiam grauita
tem omnium partium internarum eiu&longs;dem guttæ, &
proindè omnium maximè comprimuntur, fit vt præ
dictæ machinulæ externæ maximè di&longs;trahantur, ex
tendanturque, & &longs;ic efficiant veluti reticulum te
nax, & con&longs;i&longs;tens, internæ verò partes guttulæ
quia minus pondus &longs;u&longs;tinent immo &longs;u&longs;tinentur à
reticulari prædicta &longs;uperficie externa aquæ, & no&ntail;
vniuer&longs;am ponderis vim patiuntur, vti externæ par
tes, ideò minùs, quàm externæ machinulæ di&longs;trahun
tur, & propterea debiliori tenacitate &longs;e mutuò nec
tunt, & hinc fit vt altera &longs;uper alteram excurrere fa
c
ternas guttulæ partes vago motu agitari fluereque.
natura flui
ditatis.
natura flui
ditatis.
re&longs;istere penetrationi corporum &longs;oli
dorum per eam di&longs;currentiu
CIrca &longs;ecundam, dici pote&longs;t, quòd reuerà adfit pu
&longs;illa aliqua re&longs;i&longs;tentia cum dura lamina fluidum
penetrat, & confricat laterales partes eius, quæ re&longs;i
&longs;tentia ob &longs;ui exiguitatem conuincinon pote&longs;t ab ex
perimentis aliquorum. Et profectò &longs;i reuerà nulla&mtail;
vi&longs;co&longs;itatem fluidum haberet, nil omninò penetratio
ni alterius corporis refi&longs;teret, & ideò quodlibet cor
pus grauius &longs;pecie quàm aqua in ea de&longs;cenderet, &
quodlibet minus graue &longs;pecificè a&longs;cenderet &longs;ursùm,
neque exce&longs;&longs;us perimetri, aut &longs;uperficiei corporis de
mer&longs;i re&longs;pectu grauitatis eius po&longs;&longs;et omninò prohi-
bere de&longs;cen&longs;um, vel a&longs;cen&longs;um in aqua, &longs;ed &longs;olum
modò tarditatem afferret, non autem quietem ab&longs;o
lutam, vt fatentur Ghetaldus, Steuinus, & alij. Modò
minuti&longs;&longs;ima grana terrea, &longs;alium, metallorum, & non
minùs particulæ minimæ corporum leuiorum ligni,
aeris, &c. licèt habeant excedentem, & grandem &longs;u
perficiem re&longs;pectu pu&longs;illæ grauitatis eorum non ta
men po&longs;&longs;ent omninò quie&longs;cere in medio aquæ, &longs;ed
ti&longs;&longs;imo
exce&longs;&longs;us, vel defectus grauitatis &longs;pecificæ corpu&longs;cu
lorum demer&longs;orum à grauitate fluidi aquei; &longs;ed hoc
e&longs;t fal&longs;um, metalla enim, &longs;ales, & aer in minuti&longs;&longs;im&atail;
granula redacta immobilitèr in medio aqu&ecedil;
& ibidem per&longs;euerant, igitur falfum e&longs;t aquam gluti
ne omnino priuari, & nil prorsùs penetrationi re&longs;i&longs;te
re;erit igitur aliquanti&longs;per aqua glutino&longs;a,
&longs;altem aliquam pu&longs;illam; & &longs;uperficialem vi&longs;co&longs;ita
tem. Adde quòd partes intermediæ fluidi cùm &longs;int
æquilibratæ atque &longs;u&longs;tine antur exiguam compre&longs;&longs;io
nem creant, & proindè machinulæ &longs;uperficiales par
ticularum aquæ &longs;ubiectæ non po&longs;&longs;unt valde di&longs;trahi,
vel con&longs;tringi, & &longs;ic minimam vim re&longs;ilientem exer
cere po&longs;&longs;unt.
natura flui
ditatis.
Sed dices, &longs;r aquæ particulæ à prædicta lanugin&etail;
ambiuntur, ergo aqua non minùs quàm aer conden&longs;a
ri deberet quod repugnat experientiæ. Re&longs;pondeo
quòd prædicta lanugo valdè exigua e&longs;t re&longs;pectu in
ternæ &longs;oliditatis cuiu&longs;libet globuli aquei, & &longs;ic no&ntail;
negatur quòd aliquanti&longs;per aqua conden&longs;ari, con&longs;ti-
parique po&longs;&longs;it, tamen ob inperceptibilem paruitatem
&longs;en&longs;um fugit.
natura flui
ditatis.
cius experimento probatur.
ET hoc &longs;atis concinnè confirmari po&longs;&longs;e videtur à
præclaro experimento facto in aula Sereni&longs;&longs;imi
M. D. Hetruriæ is iu&longs;&longs;it (vt mihi
pilam
di, ac ferruminati, quæ po&longs;tea graui malleo contu&longs;&atail;
priorem &longs;phæricitatem ami&longs;it, proindeque internum
eius &longs;patium euidenti contractione diminutum fuit,
cùm con&longs;tet
omnium capaci&longs;&longs;imam, nece&longs;sè ergo fuit vt moles a
quæ, quæ priùs ingens &longs;patium &longs;phæricum replebat,
aliquo pacto &longs;tringeretur angu&longs;tareturque, tunc mi
rabile &longs;pectaculum &longs;e obtulit, nimirùm vndique pila
argentea ex&longs;udare cæpit effundendo exiguos globu
los aqueos &longs;imiles illis, qui in cute no&longs;tra dum &longs;uda
mus apparere &longs;olent. Ga&longs;&longs;endus po&longs;tea refert in &longs;imi
li pila contu&longs;a po&longs;tquam exiguum foramen aperui&longs;
&longs;et, longiùs aquam pro&longs;ilientem eieci&longs;&longs;e. Ex his om
nibus videtur elici po&longs;&longs;e aliquanti&longs;per aquam ant&etail;
ex&longs;udationem, aut eiectionem conden&longs;atam fui&longs;&longs;e.
Et licèt re&longs;ponderi po&longs;&longs;et, vas prædictum po&longs;t con
tu&longs;ionem violentèr &longs;e di&longs;tendi&longs;&longs;e, & dilata&longs;&longs;e laterali
tèr, & hac ratione capacitatem eius auctam &longs;upplere
potui&longs;&longs;e con&longs;trictionem factam à contu&longs;ione, & vio
lentam di&longs;tractionem illius laminæ argenteæ ad mo
dum machinæ &longs;e re&longs;tringendo facilè potui&longs;&longs;e
illud ad in&longs;tar fonticuli, vel ex&longs;udationem per poros
dilatatos efficere; nihilominùs videtur incredibil&etail;
in illa violenti&longs;&longs;ima compre&longs;&longs;ione facta in actu per
cu&longs;&longs;ionis aquam ne minimum conden&longs;atam fui&longs;&longs;e &longs;al
tem per breui&longs;&longs;imum
clarè &longs;aluatur in no&longs;tra po&longs;itione, quia &longs;cilicèt parti
culæ aquæ duri&longs;&longs;imæ ambiuntur veluti à lanugine ma
chinularum flexibilium, quæ parumper po&longs;&longs;unt com
primi, conden&longs;ationemque pati.
natura flui
ditatis.
EX eadem hypothe&longs;i texturæ partium aquæ, & ae
ris reddi pote&longs;t ratio alterius pulcherrimi ex
perimenti. Si enim
&longs;imum eius foramen aqua repleatur, tunc &longs;i ore infe
riùs inuer&longs;o ampulla reuoluatur in aere aqua non de
fluit, at &longs;i po&longs;tea ampullæ orificium vinum (rubru&mtail;
commoditatis gratia) contingat in &longs;ubiecto va&longs;&etail;
contentum, tunc videbis per idip&longs;um foramen aquam
eodem tempore de&longs;cendere, & &longs;imul vinum a&longs;cende
re in tenui&longs;&longs;ima fila extenuatum; & profectò mirabi
aquæ grauitas aerem &longs;uperet, quam grauitatem vi
ni. At hoc (ni fallor) contingit ex eo quod vinu&mtail;
aquæ naturam participat, cum non &longs;it vinum ni&longs;i pu
ra aqua cui immi&longs;centur plures &longs;piritus, &
hacde cau&longs;a facilè par
re, & fluere po&longs;&longs;unt; at non &longs;ic aer, qui ex grandiori
bus &longs;piris componitur, & propterea mixtionem cum
aqua refugit, eiu&longs;que effluuium impedit, quatenus
in fundo orificij guttula aquæ pendens qua&longs;r
&longs;uis villis violenter di&longs;tractis efformat; & &longs;ic non fa
cilè po&longs;&longs;unt di&longs;&longs;olui di&longs;gregariqueà grandi oribus ae
ris &longs;piris &longs;imùl pariter inter &longs;e adnexis, intricati&longs;que,
& hac de cau&longs;a non pote&longs;t aqua effluere eodem
pore
potè&longs;t.
natura flui
ditatis.
diuer&longs;ænaturæ, & con&longs;i&longs;tentiæ.
AD tertiam dico, quòd reuera ob defectum ana
logiæ non mifcentur aliqua fluida inter &longs;e, ne
que aliqua &longs;olida corpora madefaciunt; at prædict&atail;
analogia non con&longs;i&longs;tit in &longs;imilitudine, & &longs;ymmetri&atail;
pororum corporis fluidi, nam, vt deinceps dicemus,
aqua per aquam penetrare, & fluere pote&longs;t licèt eius
p
particularum; igitur vera cau&longs;a (vt puto) quare aqua
non mi&longs;cetur oleo, & aeri, e&longs;t quia lanugo extern&atail;
aquæ penetrare nequit oleum, velaerem, for&longs;an quia
machinulæ pilorum lanuginis aquæ offendunt facie
culas, & lanugines partium olei vel aeris à quibus
flectuntur incuruanturque, & &longs;ic à vi machinæ re&longs;ili
entis nedum prohibetur penetratio
particularum, &longs;ed in&longs;uper ab inuicem &longs;egregantur. In &longs;olidis verò corporibus &longs;i ad&longs;it incongruentia po
rorum, partes fluidi
vt hydrargyrum lignum non madefaciet, &longs;i verò pori
congruentes fuerint tamdiù retardatur mi&longs;cella, &
madefactio, quamdiùnon explicatur lanugo
larumCau
&longs;a verò, & vis impulfiua, quæ impellit prædictas flui
di particulas intra &longs;olidi poro&longs;itates, po&longs;tea a&longs;&longs;igna
bitur.
natura flui
ditatis.
aquæ particularum &longs;upra aquæ libellam
in ip&longs;o aere.
VEritatem Archimedeæ doctrinæ luculentèr &longs;u
periùs confirmauimus, quod &longs;cilicèt omni&atail;
elementaria corpora &longs;iue fluida, fiue
uitatem habent, eamque exercent etiam in proprijs
locis, vnde deducitur impo&longs;&longs;ibile e&longs;&longs;e vt aqua v. g.
leges æquilibrij tran&longs;grediatur, atque perturbet pul
cherrimum atque admirabilem ordinem, di&longs;po&longs;itio
nemque partium vniuer&longs;i; &longs;cilicèt alterando, atqu&etail;
deformando figuram &longs;phæricam, vnde infertur, quòd
aquanullo pacto po&longs;&longs;it
ris per aliquod tempus, neque poterit eleuari &longs;upra
&longs;uperficiem &longs;upremam totius aquæ &longs;ubiectæ,
do
&longs;cendendo per cauitates fi &longs;tularum &longs;upra aquæ infi
mam libellam eleuatarum. Et hoc nedùm ip&longs;a ratio
per&longs;uadet, &longs;ed etiam &longs;en&longs;us euidentia o&longs;tendit i&ntail;
grandioribus aquæ portionibus.
exiguæ aqu&ecedil;
guttæ &longs;upra
a&longs;cendunt.
E contrà videmus in paruis guttulis aquæ, & reli
quorum fluidorum vniuer&longs;alem regulam prædicta&mtail;
minimè verificari; aquæ enim guttæ in folijs
non intra earum cauitates &longs;tagnantes quie&longs;cunt, ex
plananturque, &longs;ed tumidæ eleuantur vt monticuli, &
&longs;phæricam figuram quod ammodò affectare Similiter aliæ guttæ pendulæ &longs;u&longs;tinentur è &longs;upremis
ramis arborum, neque à naturali earum grauitat&etail;
deorsùm impelluntur; imò &longs;i prædictæ guttulæ pen
dulæ à contactu digiti, vel fe&longs;tucæ deorsùm leuitèr
trahantur, ce&longs;&longs;ante vi externa &longs;ponte &longs;ua aquea ill&atail;
mammilla retrahitur
&longs;imis, in
teCùm
que doctrina illa vniuer&longs;alis æquilibrij in dubium re
uocari nequeat, nece&longs;sè e&longs;t vt aliæ nouæ cau&longs;æ, quæ
in hi&longs;ce guttulis fluidis operantur, efficiant
effectuum diuer&longs;itatem, quam digno&longs;cere èrit ope
ræpretium.
guis pertur
barur vni
uer&longs;alis re
gula, qu&atail;
fluida vt gra
uia expla
ri debeant.
Et primo loco inquirenda e&longs;t cau&longs;a, à qua guttæ
fluidi &longs;phæricè contornari, eleuari, &longs;u&longs;pendique po&longs;
funt ad &longs;imilitudinem monticuli. Et procùl dubio fa
tendum e&longs;t aquæ guttulas, aut vi naturali, & intrin
&longs;eca &longs;ponte &longs;ua vniri conglobarique, & &longs;ic efficer&etail;
&longs;phærulas illas aqueas, vel hoc à violentia aliqu&atail;
externa effici. non de&longs;unt vtriu&longs;que &longs;ententiæ fauto
res. Aliqui enim affirmant ab aere ambiente compri
mi aqueas guttulas, vel pondere, vel vi ela&longs;tica ae
ris, aut vtroque modo eas vndique con&longs;tringendo,
& con&longs;tipando. Quia verò numquam eædem guttæ
aqueæ naturalem grauitatem amittunt, &longs;ed &longs;emper
eam exercent; fit vt in exiguis guttulis minima earum
grauitas &longs;uperari po&longs;&longs;it à vi compre&longs;&longs;iua aeris. Cùm è
contrà in guttis amplioribus vis grauitatis &longs;uperet
eiu&longs;dem aeris vim compre&longs;&longs;iuam, & proindè depri
mantur explanenturque in cauitatibus terræ.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
guttularum fluidi.
HÆc profectò &longs;ententia pluribus difficultatibus
obnoxia e&longs;&longs;e videtur, quia vt animaduertit
ingenio&longs;i&longs;&longs;imus Portius amicus no&longs;ter, vis eiu&longs;de&mtail;
aeris compre&longs;&longs;iua vnius, & eiu&longs;dem roboris, & ener
gi&ecedil; e&longs;&longs;e debet, igitur &longs;emper eumdem effectum pro
ducere valet, & proindè quotie&longs;cumque eius actio
exercetur contra duas inæquales re&longs;i&longs;tentias, maior,
& in&longs;ignior operatio efficietur in &longs;ubiectum minùs
re&longs;i&longs;tens, quàm in aliud. Con&longs;iderentur modò duo
fluida inæqualitèr grauia &longs;pecie, &longs;cilicèt hydrargy
rum, & aqua communis, certum e&longs;t guttam mercu
rij quatuordecies pondero&longs;iorem e&longs;&longs;e gutta aque&atail;
eiu&longs;dem molis, quia verò vis aeris externa compri
menshæc duo fluida &longs;emper eiu&longs;dem roboris e&longs;t, igi
tur non poterit conglobare, & &longs;phæricè contornare
guttam mercurij æquè
cùm mercurius grauior, & ideò magis
rat maiorem vim compre&longs;&longs;iuam, quàm aqua minùs
grauis; ergo gutta mercurij, quæ ab eadem energia
aeris contornari debet vna pars decimaquarta opor
tet vt &longs;it amplitudinis guttæ aquæ paritèr &longs;phæricè
conglobatæ; igitur e&longs;t omninò impo&longs;&longs;ibile vt aer ef
ficiat &longs;phærulam mercurialem grandiorem, quàm a
queam; at quia hoc con&longs;tat experientia, guttæ eni
inercurij, quæ &longs;upra tabulam planam &longs;phæricè con
tornantur, agitanturque, non minores e&longs;&longs;e videntur,
quàm guttæ aqueæ, quæ &longs;upra bra&longs;&longs;icæ folia
bari
ra cau&longs;a turbinationis aquæ, vel mercurij.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
PRæterea &longs;i energia grauitatis, aut vis ela&longs;tica ae
ris e&longs;t illa, quæ guttas fluidi vndique
mendo
ab aere rari&longs;&longs;imo, aut infinitè expan&longs;o ambiuntur,
minùs comprimi deberent, quàm ab aere copio&longs;o, &
maximè conden&longs;ato, igitur in va&longs;e Torricelliano,
facto vacuo, vbi nullæ, aut &longs;altèm exili&longs;&longs;imæ aeris
particulæ reperiuntur, minùs eleuari, & magis
contu&longs;æ e&longs;&longs;e deberent, aut valdè diminutos, &
exiguos globulos efficere deberent prædict&ecedil; aqueæ
guttulæ à folijs bra&longs;&longs;icæ &longs;u&longs;tentatæ, quàm illæ, quæ
ab aere valdè conden&longs;ato ope follium, vel
ti
e&longs;t, &ecedil;què enim tumidæ &longs;phæricè &longs;u&longs;penduntur, & ad
eandem altitudinem, &
tæ aqueæ in vacuo Torricelliano ab aere rari&longs;&longs;imo,
quàm ab aere valdè den&longs;o, & con&longs;tipato, vt in Aca
demia experimentali Medicea experti &longs;umus.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
tornentur, oportet vt vires motiuæ earum versùs
trum
beant eamdem proportionem quam ea
rum diftantiæ à centro.
AD hæc poterit euidenti demon&longs;tratione (ni&longs;i
fallor) euinci aqueas guttas non conglobar
&longs;phæricè à vi externa aeris compre&longs;&longs;iua. Si enim per
pendamus, quare vniuer&longs;um aquæ elementum circ&atail;
centrum sy&longs;tematis elementaris &longs;phæricè congloba
tur, percipiemus hoc effici quia partes aquæ habent
vim &longs;emouendi directè versùs centrum terræ, e&longs;tque
talis vis motiua in eodem corpore homogeneo aquæ
non &longs;emper eiu&longs;dem gradus, ni&longs;i cùm partes exter
næ à centro terræ æquè recedunt.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
Sit ergo punctum E centrum globi terraquei, &
&longs;upponamus aquam ABCD inæqualitèr di&longs;tare à
tro
queus MAK &longs;upra reliquam eius &longs;uperficiem &longs;phæri
cam BCD. & &longs;iquidem vis
motiua deorsùm |impellens
versùs centrum E e&longs;&longs;et
dem
in B, non po&longs;&longs;et deprimi &longs;u
prema aqua A deorsùm, ex
pellendo, & &longs;uperando
&longs;tentiam
nimirùm potentia æqualis in Nece&longs;sè ergò e&longs;t vt aqua
eleuata MAK maiorem vim
aqua B: e&longs;tque hoc euidenti&longs;&longs;imum, quia moles aquæ
EA, quæ altior, copio&longs;ior, & ideò grauior e&longs;t, &longs;upera
bit re&longs;i&longs;tentiam minùs eleuatæ aquæ EB, & minoris
molis; Igitur vera cau&longs;a, quare elementum aquæ cir
ca centrum terræ &longs;phæricè contornatur, e&longs;t, quia par
tes aquæ cum reliquis continuatæ magis à centro
terræ eleuatæ, maiorem vim compre&longs;&longs;iuam habent,
quàm ali&ecedil; partes minùs à prædicto centro
exiguæ aqu&ecedil;
guttæ &longs;upra
a&longs;cendunt.
tricæ collocentur, quarumexterior grauis &longs;it, non verò
interior, quæ habeat montuo&longs;itatem aliquam,
compres&longs;io vniuer&longs;alis fluidi ambientis
non poterit montuo&longs;itatem
fluidi contundere.
SVpponamus modò mercurium ABCD non habe
re vim &longs;e &longs;e vniendi, &longs;cilicèt non habere graui
tatem, patet quòd &longs;i prædictum hydrargyrum pone
retur circa centrum E totius regionis elementaris
ricum, &longs;ed retineret
montuo&longs;itatem MAK. Sup
ponamus po&longs;tea mercurium
à &longs;phæra aeris FGHI circun
dari, & habeat prædictu&mtail;
fluidum ambiens
& principium motiuum ver
sùs centrum eius E, & proin
dè ma&longs;&longs;a mercurialis ABCD vndique comprimetur à
fluido ambiente FGHI; &longs;itque prædictum fluidu&mtail;
&longs;ibi homogeneum, &longs;cilicèt &longs;it vniformitèr graue. Dico
quod ambiens fluidum nulla ratione mercuriu&mtail;
ABCD &longs;phæricè contornabit; quia fluidum ambiens
comprimit comprehen&longs;um fluidum præcisè,
exigit men&longs;ura grauitatis eius; e&longs;t verò grauitas flui-
di FA ad grauitatem alterius partis BG vt altitudo,
&longs;eu moles illius ad huius molem (cum &longs;upponatur
fluidum &longs;ibi ip&longs;i homogeneum) & e&longs;t moles fluidi FA
minor, quàm GB, igitur fluidum FA minùs grauitat,
& ideò minùs comprimit &longs;ubiectum fluidum AE,
quàm fluidum GB comprimat &longs;ibi &longs;ubiectum fluidum
EB; &longs;ed e&longs;t impo&longs;&longs;ibile vt minor vis compre&longs;&longs;iua flui
di ambientis FA impellat deorsùm, &
tuo&longs;itatem
milior pars eiu&longs;dem fluidi EB; & hæc &longs;ursùm expelli
nequit ni&longs;i cædat vis compre&longs;&longs;iua grauitatis totius
fluidi GB, igitur deberet vis grauitatis maior totius
aquæ BG &longs;uperari à potentia minoris grauitatis FA,
quod e&longs;t impo&longs;&longs;ibile, ergò vis compre&longs;&longs;iua extern&atail;
aeris, vel cuiuslibet alterius fluidi, non pote&longs;t effice
re tumorem illum &longs;phæricum, quem in guttis mercu
rij, & aquæ ob&longs;eruamus, quotie&longs;cumque prædictæ
guttæ grauitate carerent, & in centro regionis ele
mentaris collocatæ e&longs;&longs;ent.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
ambientis aeris compres&longs;ione demonstratur.
RE&longs;tat modò vt idip&longs;um o&longs;tendamus in guttis a
queis in &longs;uperficie no&longs;træ telluris Gutta aquea ABCD &longs;u&longs;pen&longs;a &longs;it filo GA, vt pauimen
tum VX non attingat, & &longs;uppo&longs;ito, quòd ab oceano
aereo RS vndique gutta &longs;u&longs;pen&longs;a contundatur, & ve-
luti forcipe
aereis GA, lateralitèr à cylindris GH, & SD & infer
nè à Dico ab ae
reo oceano minimè gutta&mtail;
ABCD &longs;phæricè contornari. Quia guttæ aqueç partes AH
CD omninò
qua ferantur versùs centrum
eiu&longs;dem guttæ, eo quòd pars
eius &longs;uprema A trahitur
sum
tendit
du&ecedil; partes oppo&longs;itæ A & C
à &longs;e inuicem fugiunt, & proindè potius conantur
à centro ‘guttæ’ recedere, quàm ad ip&longs;um ferri, &
cum eo vniri; partes verò collaterales H, & D &longs;iu&etail;
vim grauitatis exerceant, &longs;iue non,
rizontali motu versùs guttæ centrum naturali in&longs;tin
ctu tendent, ergò &longs;iconcipiatur
ac &longs;i e&longs;&longs;et centrum &longs;y &longs;tematis
tæ cen&longs;eri po&longs;&longs;ent non graues. His po&longs;itis intelliga
tur &longs;uperaddita, vel eleuata eminentia, &longs;eu mammil
la aquea H in laterali loco guttæ, tunc aereus ocea
nus RS ne dum &longs;upernè &longs;uperficiem A, &longs;ed etiam la
tera eius H, D, & infimas facieculas B, C æquali ener
gia comprimet, tum ratione grauitatis, cum ratione
virtutis ela&longs;ticæ eius. Habemus igitur ca&longs;um &longs;imilem
ei qui in
cèt gutta ABCD cuius partes non nituntur vniri, nec
&longs;ponte ferri versùs centrum eiu&longs;dem guttæ, & ab ae
re æqualibus viribus vndique comprimitur; quar&etail;
e&longs;t impo&longs;&longs;ibile, vt mammilla H contundatur, hoc e
nim, vt dictum e&longs;t, exigit maiorem vim compre&longs;&longs;iuam
in H, quàm in D.
cisè contornari, & acquirere tumorem &longs;phæricum.
exiguæ aqu&ecedil;
guttæ &longs;upra
a&longs;cendunt.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
Idip&longs;um verificari in guttulis aqueis pauimento
innixis, patet ex eo, quòd &longs;altem collaterales partes
eius H, & D carent vi motiua horizontali qua feran
tur versùs guttæ centrum, & tunc mammilla H no&ntail;
poterit contundi ab aere GH cum eius vis
ior vi compre&longs;&longs;iua aeris SD. Vnde colligitur, quòd
compre&longs;&longs;io fluidi aerei RSXV nullo pacto globo&longs;ita
tem guttularum aquæ creat, quare fatendum e&longs;t ab
alia longè diuer&longs;a cau&longs;a hoc prouenire.
Videndum modò o&longs;t, an à vi intrin&longs;eca, & natu
rali mercurij, vel aquæ prædictæ guttulæ
tur
ralitumorem, & &longs;phæricitatem acquirere.
QVia guttæ fluidæ diuer&longs;is in locis collocari ef
formarique po&longs;&longs;unt, hinc &longs;equitur vt eius par
ticulæ componentes cogantur modò versùs vna&mtail;
plagam, modò versùs alteram tendere, ac promoue
ri, prout centrum, aut &longs;u&longs;pen&longs;io guttulæ varijs in lo
cis transferri, ac &longs;ituari pote&longs;t, & tunc &longs;i &longs;en&longs;u carent
mirari profectò &longs;ubit à quo N
o&longs;tenditur, vbi gentium guttæ centrum exi&longs;tat, tran&longs;
portatumque &longs;it, & quo &longs;en&longs;u id a&longs;&longs;equi valeant, &
quo appetitu afficiantur, vt eum amplecti velint; po
ni ergo debet vis aliqua, quæ cæca nece&longs;&longs;itate tran&longs;
ferat, retineat, conglutinetque aqueas particulas
circa centrum guttulæ &longs;u&longs;pen&longs;æ, hæc autem vis mo
tiua cùm non &longs;it determinata ad aliquam plagam, erit
profectò vaga, & incerta, quæ nihilominùs certu&mtail;
gradum impetus, & proindè æqualem vim &longs;&etail;
mouendi &longs;ursùm, deorsùm, & ad latera habebit,
ergo hi&longs;ce omnibus motionibus agitari deberent a
quæ, vel mercurij particulæ in ip&longs;is guttis pendenti
bus, & contornatis, & hoc quidem audactèr aliqui
recentiores pronundiant, quorum &longs;ententia (ni fal
lor) non &longs;ecùs, ac præcedens, facilè refelli pote&longs;t,
quia &longs;i qu&ecedil;libet pars fluidi in gutta æquali vi, & ener
gia mouetur, &longs;emel alterata, & perturbata eiu&longs;de&mtail;
guttærotunditate, &longs;cilicèt exporrecta aliqua mam
milla ex eodem fluido guttam componente, non po&longs;
&longs;et pri&longs;tinam &longs;pli&ecedil;ricitatem denuò acquirere, prop
terea quod pars illa magis à centro remota non po&longs;
&longs;et centro guttæ approximari, ni&longs;i expelleret longiùs
à centro reliquas partes in vallibus guttæ exi&longs;tentes,
nec hæ cedere locum po&longs;&longs;ent, cùm æqualem
ac vim habeant, ac illæ, quæ in &longs;ummitate mammil
læ degunt. Si verò con&longs;iderentur motus contrarij, &
diuer&longs;i quatenùs vna portio ad infimum &longs;itum guttæ
deprimitur, altera verò eleuatur, ali&ecedil; lateraliter
tur, tunc quidem quis capiet globo&longs;am, &
figuram fluidi partes irregularitèr &longs;e mouentes com
ponere po&longs;&longs;e? Finge in hac aula pluuiam copio&longs;a&mtail;
granulorum frumenti cadentium, & &longs;imùl infernè ab
aliqua violentia grana delap&longs;a repelli &longs;ursùm, & la
teraliter; in hac (inquam) perpetua, & confu&longs;a agi
tatione, quomodò po&longs;&longs;ent prædicta grana deciden
tia, & a&longs;cendentia &longs;ph&ecedil;ricam figuram conflare, &
potiùs quamlibet aliam figuram irregularem, vt ex
perientia con&longs;tat?
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
Recurrere ad inflexionem particularum mercurij,
vel aquæ, qu&ecedil; ad in&longs;tar anguillarum conglobentur, &
vniantur, & &longs;ic guttulas pendentes, & &longs;phæricas effi
ciant, videtur omninò ab&longs;urdum, vt &longs;uperiùs in&longs;inua
uimus.
fectum
giæ
tra aer
&longs;inuar
po&longs;&longs;e, & i
deò motu re
flaxo in &longs;&etail;
ip&longs;is cooglo
bati.
Tantummodò con&longs;ider abimus ea, quæ ab alijs af
feruntur, qui aiunt ob defectum analogiæ mercurij,
vel aquæ cum aere ambiente fieri, vt hydrargyrum,
vel aqua aerem effugiat, & aer aquam, & potiùs i&ntail;
&longs;e ip&longs;am &longs;pontaneo motu conglobetur, vniaturqu&etail;
non quidem à perceptione vtilis electione &longs;ponta
nea, &longs;ed nece&longs;&longs;itate quadam, quæ cogat vt partes
fluidæ &longs;e mouentes, & perpetuò agitatæ, dum in ae
re moueri nequeunt, reflectantur intra &longs;e ip&longs;as, & &longs;ic
guttulas illas &longs;phæricas efforment. A&longs;&longs;ignant po&longs;tea
duas cau&longs;as à quibus fluidorum diuer&longs;a, & heteroge
nea natura pendet: prima e&longs;t motuum diuer&longs;itas, &longs;ci
licèt quia pariculæ minimæ aquæ diuer&longs;o modo agi
tantur, ac mouentur particulæ aeris
pendere aiunt quod aquæ particulæ nequeant &longs;ua&mtail;
vim motiuam exercere intra aerem, & propterea co
gantur motu reflexo excurrere intra profunditatem
eiu&longs;dem aqueæ guttulæ, & ex hi&longs;ce motibus reflexis
&longs;phæricam figuram guttæ efformari aiunt. Secund&atail;
cau&longs;a e&longs;t pororum a&longs;&longs;imetria, inquiunt enim poro&longs;i
tates aeris eius figuræ e&longs;&longs;e, vt particulæ aquæ nequa
quam po&longs;&longs;int per incongruentes poro&longs;itates aeris in
&longs;inuari, & excurrere. Vndè guttula aquæ perindè ab
aere coercetur, ac &longs;i e&longs;&longs;et fornix marmoreus.
analogiæ flui
dornm, aut a
diuet&longs;it ai&etail;
motunm aut
ab
tia poroium
pendere c
&longs;cut.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
guttulæ &longs;phæricè conglobari.
ET quoad motuum diuer&longs;itatem pertinet,
dum
poris omninò impediatur à motu diuer&longs;o alterius,
hoc enim contingit quando prædicti motus &longs;unt in
ter &longs;e contrarij per eamdem rectam lineam, & æqua
libus viribus, & velocitatibus facti; &longs;i enim non &longs;int
inter &longs;e contrarij, &longs;ed ambo ad ea&longs;dem partes
tunc non omninò impeditur motus alterius corporis,
&longs;ed tantummodò alteratur quoad directionem, vel
circa velocitatem; quia verò aduer&longs;arij &longs;upponunt
motiones partium tum aquæ cùm aeris, vagas, & di
uer&longs;imodas &longs;ursùm, deorsùm, & lateraliter, erit om
ninò impo&longs;&longs;ibile, vt &longs;em per motus
opponantur motionibus, quibus partes aeris
tur, & &longs;i hoc verum e&longs;t, oportet vt ex parte, &
do
biente, &longs;ed frequentiùs, & vt plurimùm nullum im
pedimentum motioni aquæ afferent, & tunc &longs;e mu
tuo penetrabunt, & ideò non vnientur &longs;phæricè gut
tæ aqueæ, quod e&longs;t fal&longs;um.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
Præterea &longs;i aer valdè expan&longs;us, & rarior e&longs;t, quàm
aqua, & tam infirmæ, & de bilis con&longs;i&longs;tentiæ vt faci
lè à quacumque exigua vi di&longs;&longs;ipari, & è &longs;uo loco di
moueri po&longs;&longs;it, veri&longs;imile e&longs;t vt partes aquæ den&longs;io
res, & con&longs;i&longs;tentes po&longs;&longs;int, dùm mouentur, facilè ae
reas particulas è &longs;uis locis expellere, & &longs;ic per eius
&longs;ub&longs;tantiam penetrare; quod profectò ab ip&longs;a expe
rientia confirmari videtur, nam videmus vapores a
queos è mari, & lacubus exhalantes &longs;umma facilita
te per aerem penetrare, cùm
e&longs;&longs;e, quàm congeriem exili&longs;&longs;imarum aquæ particula
rum, quæ motu placido, & tranquillo ab aqua
tur
alterius rapidæ violentiæ. Et profectò numquam aer
reperiri pote&longs;t &longs;incerus ab&longs;que admi&longs;tione minima
rum aquæ partium, vt con&longs;tat ex experimentis i&ntail;
no&longs;tra Academia experimentali Medicea factis; igi
tur &longs;icuti illæ minimæ aquæ particulæ vaporem com
ponentes à diuer&longs;a aeris agitatione non
nec impediuntur quin liberè, & impunè aerem pe
netrare po&longs;&longs;int, &longs;ic paritèr particulæ illæ guttæ pen
dulæ terebrare poterunt aeris ambientis
& proindè aerearum partium diuer&longs;æ motiones non
impedient effluuium, & motionem vagam partium
aquæ. Imò &longs;i quis hoc negotium attentè perpendat,
percipiet ab ij&longs;dem partibus aqueis potius impediri
motiones eius, quàm ab aere externo; primò qui&atail;
&longs;unt æquè con&longs;i&longs;tentes, & corpulentæ, & &longs;ic non po&longs;
&longs;unt vici&longs;&longs;im è &longs;uis locis dimoueri, ac expelli: in&longs;upèr
cum earum motus &longs;int vagi, & inordinati, non
omnes ad ea&longs;dem partes dirigi, & ideò vna pars &longs;u
per aliam incidens motu contrario, vici&longs;&longs;im &longs;e &longs;e i&ntail;
progre&longs;&longs;u impedient. Ad hæc, vbi dee&longs;t aer, deficiet
pror&longs;us cau&longs;a impediens motiones particularum a
quæ, proptereà quòd vbi aer non ade&longs;t, neque eius
motus impedimentum afferre poterit agitationi par
tium aquæ. hoc autem contingit in vacuo Torricel
liano, vbi nullo pacto impedirentur motiones
dem
rè vacuum &longs;pargi di&longs;&longs;iparique po&longs;&longs;ent, & proindè non
cogerentur motu re&longs;lexo intra ea&longs;dem guttas regre
di, agitari, con&longs;tiparique, & ideò ce&longs;&longs;aret cau&longs;a, &
nece&longs;&longs;itas ob quam guttulæ aquæ in vacuo, vel in ae
re rari&longs;&longs;imo &longs;ph&ecedil;ricum tumorem acquirere
& tamen hoc repugnat experientiæ, cùm in prædicto
vacuo guttulæ non minùs rotundæ, quàm in aere a
perto, tornentur.
exiguæ aqu&ecedil;
guttæ &longs;upra
a&longs;cendunt.
re diffu&longs;ionem particularam aquæ per
aerem.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
SI po&longs;tea con&longs;ideremus
patet verum non e&longs;&longs;e aduer&longs;ariorum a&longs;&longs;ertum
aiunt, ideò ab aere impediri motiones partium aqu&ecedil;,
quia orificia pororum aeris &longs;trictiora &longs;unt,
ea aquæ particulæ ingredi, & fluere po&longs;&longs;int, nam hinc
inferre liceret neque aqueas particulas per
aquam cieri, & excurrere po&longs;&longs;e; facilè enim percipi
tur, quòd in aqua poro&longs;itates non po&longs;&longs;unt e&longs;&longs;e adeò
amplæ, vt per eas intromitti po&longs;&longs;int particulæ eiu&longs;
demmet aquæ, &longs;ed debent e&longs;&longs;e multò minores, &longs;icuti
inter&longs;titia, quæ in aceruo granorum tritici, vel milij
intercipiuntur, &longs;emper minora &longs;unt,
dem tritici, vel milij, aliàs facta acerui concu&longs;&longs;ione
&longs;e mutuò magis con&longs;tringerent amplexarentur qu&etail;
granula prædicta, intromi&longs;&longs;is nempè granulis in ei&longs;
dem amplis inter&longs;titijs. Hinc &longs;equitur vt æquè diffi
cilè aquæ particulæ per ip&longs;am aquam moueri, agita
rique po&longs;&longs;int, quàm per aerem, quia nempè æquè in
commodus e&longs;t progre&longs;&longs;us aquæ per aquam, ac per ae
rem; &longs;i verum e&longs;t requiri poro&longs;itates in fluido tantæ
amplitudinis vt capaces &longs;int particularum aquæ ad
lioc vt per prædictum fluidum moueri queant. cùm
que aquæ angu&longs;tæ poro&longs;itates non impediant motum
particularum aquæ per ip&longs;am aquam. ergò pariter
angu&longs;tia pororum aeris non impediet motum
aquæ per aerem.
exiguæ aqu&ecedil;
guttæ &longs;upra
a&longs;cendunt.
eius poro&longs;itates in&longs;inuantur, &longs;ed quia aereas particu
las &longs;olutas, & amouibiles expellere è &longs;uis
locis poßunt.
HInc deducitur, quòd vera cau&longs;a, quare aqua fa
cilè per aquam penetrare, & fluere pote&longs;t,
&longs;it amplitudo pororum eius, &longs;ed quia partes ip&longs;ius
aquæ facilè expelli po&longs;&longs;unt è &longs;uis locis vt locum ce
dant particulis aqueis, quæ ibidem in&longs;inuari
& ni&longs;i anteriores aquæ particulæ è &longs;uis locis expelle
rentur, nequaquàm aliæ partes ibidem &longs;uccedere, &
fluere po&longs;&longs;ent. Si igitur hoc verum e&longs;t, percipimus,
quòd particulæ aqueæ po&longs;&longs;unt quoque aerem pene
trare, & per eius profunditatem fluere, licèt aer po
rostàm re&longs;trictos, & angu&longs;tos habeat, vt aquæ parti
culæ per eos ingredi nequeant, &longs;ufficit enim vt aereæ
particulæ po&longs;&longs;int è &longs;uis loculis expelli, vt ibidem a
queæ partes in&longs;inuari po&longs;&longs;int, eodem modo, ac con
tingit in ip&longs;amet aqua. Quod autem hoc faciliùs i&ntail;
aere effici valeat, quàm in aqua, patet ex eo, quòd ae
reæ particulæ magisraræ, & expan&longs;æ, & ideò minus
re&longs;i&longs;tentes &longs;unt, quàm partes aqueæ; non erit igitur
difficile vt partes aquæ ip&longs;o aere &longs;olidiores è &longs;uis lo
cis expellant particulas aeris, & &longs;ic facilè per eas a
qua moueatur. Adde quòd experientia
as particulas perpetuò intra aerem in&longs;inuari, vt &longs;upra
dictum e&longs;t de vaporibus; & reuerà nunquam reperiri
pote&longs;t aer omninò aridus, & ab&longs;que vlla admixtione
aquæ, &longs;ed e&longs;t veluti &longs;pongia quædam.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
tur ab ambiente aere, non proindè &longs;phæricè
conglobari po&longs;&longs;et.
TAndèm dato quòd aquæ particulæ ob defectum
analogiæ fugerent ab aere ambiente, & impe
direntur tamquam à fornice, & proindè motu refle
ro excurrerent intrà eamdem aquam, non indè&longs;equi
tur quòd &longs;phæricè guttæ ip&longs;æ efformari po&longs;&longs;ent. Fin
ge enim in aliquo lacu innumeros pi&longs;ciculos, vel an
guillulas intra vtrem, vel &longs;accum raræ, & cedentis
&longs;i&longs;tentiæ
cocedente, & di&longs;trahibili, ac aquæ particulæ ab ip
&longs;o aere, quia videmus pi&longs;ciculos minimè &longs;phæricè
conglobari, &longs;ed in prædicta cauitate vtris oblong&atail;
expatiari. idip&longs;um
ticulis coercitis à reti aereo, quæ licèt miris modis
agitarentur, nihilominùs &longs;phæricam rotunditate&mtail;
acquirere non po&longs;&longs;ent; & ratio e&longs;t quia vt plura cor
pora fluida &longs;pontè contornentur oportet vt omnes
tendant directè versùs vnum punctum intermedium,
& præterea oportet vt vires motiuæ non &longs;int &longs;emper
inter &longs;e æquales, &longs;ed maiorem vim impul&longs;iuam ha
beant, quò magis à prædicto centro di&longs;tant. igitur
ex his omnibus licèt concludere, quòd neque defe
ctus analogiæ, nec diuer&longs;itas motuum, neque incon
gruentia pororum aeris cau&longs;a e&longs;&longs;e pote&longs;t rotundita
tis guttularum fluidarum.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
Po&longs;tquam reiecimus aliorum fal&longs;as &longs;ententias, re
&longs;tat modò vt veram cau&longs;am huius effectus pro viribus
detegamus. & primò debet præmitti &longs;equens propo
&longs;itio mechanica.
tibus &longs;u&longs;tineatur à potentia termino oppo&longs;ito, & horizon
tali eiu&longs;dem corporis applicata; potentia ad corporis
pondus &longs;e habebit, vt di&longs;tantia centri grauitatis
eius à fulcimento ad di&longs;tantiam poten
tiæ ab eodem fulcimento.
SIt corpus D à pluribus angulis comprehen&longs;um,
& paries verticalis AB, cuius &longs;uperficies &longs;it a
&longs;pera, & denticulata, in huius lo
co B innitatur &longs;u&longs;tineaturque ex
tremitas angulo&longs;a corporis D, vt
nimirum minimè excurrere po&longs;&longs;it
deor&longs;um; &longs;u&longs;pendatur po&longs;teà op
po&longs;ita eius extremitas E ab aliqua
potentia, tunc vis eleuans in E mi
nor erit pondere corporis D, & ad
eius grauitatem ab&longs;olutam
proportionem habebit, quam di&longs;tantia BD à centro
grauitatis prædicti &longs;olidi v&longs;que ad parietem habet
adlongitudinem EB totius &longs;axi; quia corpus graue
D &longs;u&longs;penditur in medio vectis
bus potentijs, ab illa quam exercet potentia &longs;u&longs;ten
tans E, & ab a&longs;peritate parietis denticulati in B, er
gò ex mechanicis potentia E ad
Deandem rationem habet quam di&longs;tantia DB ad to
tam vectis EB longitudinem.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
tendo, & rotando corpus polihedrum regulari &longs;imile
innixum a&longs;peritatibus eiu&longs;dem verticalis
parietis.
SIt corpus D angulo&longs;um, & regulari &longs;imile, ita vt
centrum grauitatis eius &longs;it quoque centrum ma
gnitudinis eiu&longs;dem. Dico quòd eadem potentia &longs;ub
dupla E poterit eleuare corpus graue D ad
altitudinem parietis AC; quia cùm &longs;olidum D &longs;it re
gulare, & habeat figuram angulo&longs;am, & denticula
tam, vt in quolibet &longs;itu &longs;uæ &longs;uperficiei po&longs;&longs;it adnecti,
& &longs;u&longs;tineri in &longs;ub &longs;equentibus a&longs;peritatibus parietis
denticulati CA, &longs;equitur vt quo modolibet reuolua
tur corpus D, &longs;emper in &longs;ub &longs;equentibus eminentijs
parietis a&longs;peris AB paritèr &longs;u&longs;tineatur fulciaturque,
atque in eodem &longs;itu horizontali ab ij&longs;dem duabus
potentijs corpus D &longs;u&longs;tinebitur, &longs;cilicèt à potenti&atail;
E, & ab aliqua denticulari eminentia parietis AC;
cùmque &longs;emper eadem proportio remaneat inter eo
rum di&longs;tantias à contactu, &longs;cilicèt inter DB ad BE,
igitur &longs;emper eadem vis E &longs;u&longs;tinere, & impeller&etail;
&longs;ursùm poterit eamdem
propter fiet continua vertigo &longs;olidi D nedùm circ&atail;
eius centrum, &longs;ed etiam rotando, adh&ecedil;rendoque
gitudini
cum
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
parieti va&longs;is adhærendo à vi ponderis aqua collate
ralis impul&longs;æ.
PO&longs;tea con&longs;idero in va&longs;e XRSV in aquæ &longs;uprem&atail;
parte laminam horizontalem conflatam ex mi
nimis aquæ particulis A, B, D,
exiguum corpus A parietem &longs;ir
mum contingat in L, ob huius a
&longs;peritatem fulcietur, &longs;u&longs;tentabi
tur que terminus L granuli aquei
A, reliqua verò portio eius ver
sùs C cùm non adhæreat nequ&etail;
&longs;u&longs;tentetur ab vllo pariete, fulcietur, &longs;u&longs;tinebiturque
à &longs;ubiecta aqua FI, quæ non grauatur ab integro
dere
propterea quòd concurrit ad id &longs;u&longs;tentandum parie
tis &longs;cabrities L. Con&longs;ideretur po&longs;tea con&longs;equens mi
nimum granulum aqueum B, quod à pariete
integram &longs;uam grauitatem exercet
iectam a quam IE, & quia partium aquæ EIF, æquali
tèr &longs;cilicèt horizontalitèr iacentium, IE magis pre
mitur quàm FI, cùm illa duplum pondus, &longs;cilicèt in
tegrum ip&longs;ius B &longs;u&longs;tineat, hæc verò &longs;emi&longs;&longs;em ponde
ris ip&longs;ius A, ergo pars FI minus pre&longs;&longs;a &longs;ursùm impel
letur ab EI magis pre&longs;&longs;a, proindeque pars aquæ FI
vim faciet &longs;ursùm impellendo terminum C granuli
aquei A; quia verò eius extremitas L foueolis a&longs;pe
ris parietis adhæret, impeditur retineturque nè dire
cto motu &longs;ursùm ferriqueat, ergò nece&longs;sè e&longs;t, vt gra
nulum A flectatur ad modum vectis circa firmum ter
minum L, cùmque tactus, & adhæ&longs;io in pariete reno
uetur
&longs;ecùs, ac in rotis dentatis contingit, pariterque re
nouetur &longs;emper cau&longs;a vlterioris &longs;u&longs;pen&longs;ionis granuli
A, quæ e&longs;t minor compre&longs;&longs;io &longs;ubiectæ aquæ FI quam
EI; igitur &longs;em per renouatur flexio vectis CL &longs;ursù&mtail;
proindeque minuti&longs;&longs;imum granulum aquæ A motu
vertigino&longs;o, & reptitio a&longs;peritatibus parietis LK
adhærendo eo v&longs;que eleuabitur, quou&longs;que fiat æqui
librium cum aqua collaterali.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
Pr. 10.
Videndum modò qua ratione po&longs;&longs;int &longs;aluari effe
ctus omnes, qui in guttis exiguis ob&longs;eruantur.
&longs;olidi corporis &longs;ustineantur.
exiguæ aqu¸
guttæ &longs;upra
a&longs;cendunt.
ET primò con&longs;ideretur gutta pendula ex &longs;uperfi
cie prona rami alicuius arboris, cuius figur&atail;
videtur conoidalis parabolica: reddi debet hìc cau&longs;a
efficiens, & formalis huius &longs;u&longs;pen&longs;ionis; concipian
tur externæ &longs;uperficiales particulæ huiu&longs;modi gutt&ecedil;,
quæ vici&longs;&longs;im connexæ à &longs;uis machinulis aliquo pacto
incuruatis ad modum arcus efficiant veluti linteum,
vel &longs;accum in eius perimetro annexum &longs;ummitati li
gni duri, & con&longs;i&longs;tentis; partes verò intermediæ gut
tulæ &longs;ua grauitate naturali premunt, &
teum, vel rete &longs;uperficiale, at quia energia machi
nularum non cedit vi pu&longs;illæ grauitatis guttulæ pen
dentis, fit vt æquatis momentistota gutta &longs;u&longs;pen&longs;&atail;
hæreat.
&longs;u&longs;tineantur.
SEcundo loco &longs;it pila fluida pendula ex filo pari
tèr fluido, vt euidentiùs contingit in Saliua, &
in alijs humoribus glutino&longs;is; hìc iam concipi
hinc inde à filo in orbem particulæ fluidi, quæ
rendo
glutinatis
machinularum earum efformant veluti &longs;acculum
cularem
vt eius pondus non &longs;uperet robur machinularu&mtail;
glutinis.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
&longs;u&longs;tineatur.
TErtiò pila fluida innixa pauimento paritèr &longs;u&longs;ti
netur veluti à filo, &longs;eù virga
planum &longs;ubiectum à quo &longs;u&longs;tentatur; à prædicta vir
ga in orbem colligantur aliæ particulæ eiu&longs;dem flui
di, quæ in èxigua ba&longs;i fulciuntur à plano &longs;ubiecto,
quando ob ariditatem eius, & incongruitatem po
rorum aqua non diffluit, nec ip&longs;um humectat; in tali
ca&longs;u filum fluidum perpendiculare perinde agit, ac
filum pendulum; &longs;ed guttæ figura differt aliquo pa
cto à præcedenti, non enim e&longs;t &longs;phærica, nec oblon
ga oualis, &longs;ed inferiùs dilatatur, & &longs;upernè acumen
veluti conoidale acquirit.
augentur, & quare po&longs;t violentam fluidi tractionem
denuò &longs;ponte &longs;ua recolliguntur.
IN primo, & &longs;ecundo ca&longs;u ex affluxu noui fluidi
augeri pote&longs;t moles guttæ pendulæ, vt eius pon
dus maius &longs;it, quàm vt à vi glutinis &longs;u&longs;tineri queat, &
tunc elongatur infernè, & tandem di&longs;rumpitur, &
decidit, at pars re&longs;idua oblonga recolligitur &longs;ursùm,
efficitque nouam exiguam globo&longs;itatem; cau&longs;a verò
huius recollectionis, & a&longs;cen&longs;us &longs;ursùm hæc e&longs;t, quia
à pondere, & à motu ingentis guttulæ
chinulæ re&longs;iduarum partium fluidi violentèr di&longs;tra
ctæ &longs;pontè &longs;ua apt&ecedil; natæ &longs;unt, denuò &longs;e &longs;e recollige
re, reducique ad naturalem &longs;itum, &longs;icut contingit in
arcu, & in qualibet machina, quæ po&longs;t violenta&mtail;
di&longs;tractionem, exten&longs;ionemque, denuò &longs;e flectit re
duciturque ad pri&longs;tinum &longs;itum, cùmque in hac vni
uer&longs;ali actione machinularum filum fluidum compo
nentium &longs;ub&longs;equatur motus regre&longs;&longs;us &longs;ursùm, nec
motus fieri po&longs;&longs;it ab&longs;que impetu, igitur ab hoc præ
dictæ fluidi particulæ impelluntur altiùs quàm exi
gat naturalis earum grauitas, & hinc &longs;equitur vt de
nuò po&longs;tea affluentibus circumcirca fluidi particulis,
denuò gutta rotunda efformetur.
exiguæ aqu&ecedil;
guttæ &longs;upra
a&longs;cendunt.
In tertio ca&longs;u Propo&longs;it. præcedentis augeri pote&longs;t
gutta duplici modo, & ex concur&longs;u noui fluidi &longs;u
pernè &longs;en&longs;im additi, quou&longs;que vis glutinis &longs;ufficiat,
vt pondus guttæ &longs;u&longs;tinere valeat, nè decidat, &longs;ed
augetur, lateralitèr cre&longs;cit, ampliaturque, & &longs;ic gut
ta amittit pri&longs;tinam globo&longs;itatem.
vniunturque.
SEd dignior inqui&longs;itione e&longs;t recollectio duarum
guttularum quoties lateralitèr &longs;e mutuò
ex quibus componitur vnica gutta rotunda. Ratio
e&longs;t, quia partes eiu&longs;dem fluidi homogenei facillimè
excurrunt &longs;upra, & intra &longs;e ip&longs;as, dum propter &longs;oli
ariditatem, quando ip&longs;um humectare, & madeface
re non po&longs;&longs;unt ob pororum incongruentiam, oportet
vt omnes &longs;imul
axim perpendicularitèr plano &longs;ubiecto in&longs;i&longs;tentem,
& &longs;ic in orbem, vt priùs dictum e&longs;t, axi connectuntur,
& globum integrum efformant magis tamen contu
&longs;um, & depre&longs;&longs;um, quàm antea.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
Sed dices, quænam e&longs;t vis motiua, quæ impellit
partes duarum guttularum &longs;e tangentium vt &longs;ursùm
a&longs;cendant in &longs;ummitate guttulæ amplioris ex eis
po&longs;itæRe&longs;pondeo, quòd hoc
&longs;iua collateralium partium, quæ cùm
no &longs;ubiecto vniri, & à vi glutinis &longs;uperatur pondus
partium eiu&longs;dem fluidi, &longs;equitur vt ratione vectis
particulæ intermediæ eleuentur. Vniuer&longs;a hæc ope
ratio &longs;ic perficitur: pri
mò duo globi mercurij A
BCD, & EBFG innixi
pauimento VX in locis
C, & F &longs;e tangant latera
liter in B. hinc patet,
quòd partes fluid&ecedil; BC, &
BF facilè intra &longs;e ip&longs;as excurrendo &longs;e mutuò ample
cti po&longs;&longs;unt, & excludere aerem
tio facto à contactu B versùs C, & F. Idip&longs;um accidit
in&longs;upremis partibus AB, & EB, vnde efformabitur
figura qua&longs;i &longs;phæroidalis, & oualis HIKL, qu&ecedil; po&longs;tea
magis rotunda reddetur, &longs;ed aliquo pacto contu&longs;a, &
compre&longs;&longs;a remanebit, propterea quòd circa axi&mtail;
HK ad planum
VX perpendicularem al
ligantur in orbem partes
in&ecedil;qualium
quia nempè inæqualitèr,
&longs;cilicèt magis diftant ab
axi HK partes laterales
I, & L quàm anterior, & po&longs;terior, & ideò iuxtà le
ges mechanices partes minùs pre&longs;sæ à magis com
pre&longs;&longs;is expelli debent longiùs ab axi.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
Præterea ex dictis, ratione vectis partes fluidi I, &
L remotiores ab axe HK &longs;ursùm impellent eas, quæ
eidemaxi proximæ&longs;unt, ac proindè eleuabitur flui
da eminentia OMN, & con&longs;equentèr latera I, & L
con&longs;tringentur vt in P, & R.
flamma candelæ in&longs;ufflatæ ope fistulæ dum lique&longs;cit
recolligitur pilam rotundam efformans,
& augons.
RAtio huius effectus e&longs;t quia dum à copio&longs;o, &
vehementi igne particulæ vitri di&longs;gregantur,
non tamen omninò, neque &longs;ecundùm totum, nam vni
cam ma&longs;&longs;am inflatam, & fluidam componunt, & ideò
ex parte &longs;e &longs;e tangunt, ergo cùm habeant glute&ntail;,
&longs;cilicèt habeant machinas flexiles, & re&longs;ilientes, &longs;it
vt à prædicta ignis penetratione violentèr di&longs;trahan
tur machinulæ illæ, vt totidem arcus, & ideò pro eo
rum ingenio vim habent &longs;e recolligendi, & &longs;e vnien
di cum reliquis partibus fili liquefacti, à quibus di
&longs;tractæ fuerant: cùmque adueniant duæ aliæ cau&longs;æ
accidentales, quarum vna e&longs;t durities, aut minor flu
xibilitas perimetri, aut &longs;uperficiei eius externæ re
&longs;pectu partium intermediarum magis fluidarum, vn
de efficitur veluti epidermis, & &longs;acculus con&longs;i&longs;ten
tior; altera cau&longs;a e&longs;t inflatio, quam efficit ignis
hementi&longs;&longs;imè
quæ cùm circumdentur ambianturque à perimetro,
& &longs;uperficie duriori, & tenaciori, veluti à &longs;acculo,
&longs;it vt à vi glutinis dum conantur &longs;e recolligere par
tes prædicti fluidi tota ma&longs;&longs;a fu&longs;a, & in&longs;lata retraha
tur, recolligaturque versùs filum, & &longs;ic efformetur
globulus, & eadem ratione augeatur eius diameter,
at dum augetur pila cre&longs;cente pondere amittit prio
rem illam formam orbicularem, & efficitur gutta ob
longa deorsùm tendens. modò quia vis glutinis, &longs;eù
energia machinularum e&longs;t cau&longs;a retractionis particu
larum fu&longs;arum, hoc dum &longs;uperat vim exigui ponde
ris prædictæ guttulæ facilè poterit ip&longs;am mouere,
& retrahere &longs;iuè &longs;ursùm, &longs;iuè lateralitèr.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
&longs;pecie foueam efficit in aqua dum innatat, & quare
monticuli illi aquei non decidant.
PRo clariori eiu&longs;dem problematis intelligenti&atail;
inquirenda e&longs;t ratio alterius effectus, qui in flui
dis ob&longs;eruatur: in va&longs;e BCEI
aqua pleno applicetur graci
li&longs;&longs;ima lamina ænea FG ho
rizontalitèr, hæc quidem &longs;i
arida fuerit licèt grauior &longs;pe
cie &longs;it ip&longs;a aqua, non omninò
demergetur, nec ad fundum va&longs;is feretur, &longs;ed
det
tabit efficiendo argines aqueos tumidos, & eleuatos
GAB, & IF, qui non &longs;ecus, ac &longs;i e&longs;&longs;ent parietes im
pediunt effluxum &longs;upremæ aquæ AB vt nequeat
&longs;cendere
ne eiu&longs;dem laminæ: & hìc anima duertendum e&longs;t ca
uitatem, &longs;eu puteum IFGA effici tunc &longs;olummodò,
quando excurrit ad prædictum &longs;patium replendu&mtail;
aliquod fluidum leuius, &longs;ed non homogeneum ip&longs;i
aquæ veluti e&longs;t aer, vel vacuum Torricellianum: at
adueniente aqua, vel fluido aquæ
te, vt e&longs;t vinum, tunc margines aquei GAB, & IF
per&longs;i&longs;tent, &longs;ed di&longs;rumpentur, & deorsùm dilap&longs;i fo
ueam replebunt. Præterea notandum e&longs;t fieri no&ntail;
po&longs;&longs;e vt argines prædicti aquei cuiu&longs;cumque altitu
dinis per&longs;i&longs;tant, &longs;i enim quartam partem latitudinis
digiti auricularis &longs;uperauerint, &longs;ubitò deorsùm præ
cipitantur. Ratio quæ a&longs;&longs;ignari &longs;olet, huius effectus,
aut e&longs;t compre&longs;&longs;io aeris multoties à nobisreiecta, aut
quia veluti in aceruo granorum tritici, vel arenæ
tingit
nimirùm &longs;upremæ partes fulciuntur ab inferioribus,
vt arginem inclinatum efforment, qui non pote&longs;t e
leuari vltra angulum &longs;emirectum, aliàs &longs;ubitò grana
ip&longs;a deciderent deorsùm; concipiunt ergo minim&atail;
aquam componentia e&longs;&longs;e minuti&longs;&longs;ima quædam gra
nula, & proindè ad in&longs;tar arenæ efformare po&longs;&longs;e ar
ginem prædictum. Sed hoc non videtur &longs;ufficiens
duplici de cau&longs;a, primò quia argines aquei non ele
uantur ad quamlibet altitudinem, vt contingit in a
ceruo granorum tritici, licèt enim angulus inclina
tionis arginis aquei, &longs;cilicèt complementum anguli
AGF, minor &longs;it &longs;emi&longs;&longs;e vnius anguli recti, non pote&longs;t
altitudo prædicti arginis eleuari vltra altitudine&mtail;
quadrantis latitudinis digiti auricularis, cùm oppo
&longs;itum ob&longs;eruetur in aceruo granorum tritici. Præte
rea argines aquei BAG, & FI &longs;unt curui, & gibbi, &
in infima eius parte G angulus inclinationis maior e&longs;
&longs;e &longs;olet &longs;emirecto, igitur requiritur aliqua alia cau&longs;a
præter fulcimentum particularum minimarum, quod
in arena, & in aceruo granorum tritici Hoc
egregiè ex no&longs;tra hypothe&longs;i &longs;aluatur, dum enim la
mina FG de&longs;cendit infra &longs;upremam aquæ
particulæ extimæ &longs;uperficiei aquæ CAG, & IF quæ
mutuò inter &longs;e connectebantur, ob iam dictam lanu
ginem flexibilem, &
entem, po&longs;tea di&longs;trahun
tur machinul&ecedil;, & ideò fortiùs
ad
indè efformant veluti pleu
ram, &longs;eù reticulum à quo re
tineri, & impediri po&longs;&longs;unt partes aquæ prædicti
ticuli
ad
re&longs;i&longs;tentia machinularum ip&longs;ius aquæ exigui roboris
e&longs;t, & proindè tamdiù per&longs;euerabit, quamdiù pu&longs;il
lam vim grauitatis &longs;uperat, quæ naturali in&longs;tinctu
deorsùm tendere debet obliquo, & inclinato itine
re, & ideò eius momentum men&longs;uratur à perpendi
culari altitudine &longs;upra planum FG, quæ valdè exi
gua e&longs;t vt diximus.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
exiguæ aqu&ecedil;
guttæ &longs;upra
a&longs;cendunt.
aquæ libellam non e&longs;t propria ip&longs;ius aquæ, neque aeris,
&longs;ed e&longs;t grauitas eiu&longs;dem aquæ collateralis legi
bus mechanicis operando.
DEbemus modò rationem afferre alterius phœ
nomeni difficilioris. &longs;it vas aqua
in quo immergatur quodlibet corpus &longs;olidum, & du
rum FGK, quod &longs;it aridum, & non vngatur &longs;ebo, vel
alia &longs;imili vnctuo&longs;a materia, huius verò corporis re
maneat vna pars FK eminens &longs;upra aquæ libella&mtail;,
vel emineat paries eiu&longs;de&mtail;
va&longs;is, tunc con&longs;tat experientia,
quòd aqua non per&longs;i&longs;tit in in
fima eius libella horizontali
AK, &longs;ed repit, a&longs;cenditque per &longs;uperficiem
KG efformando pri&longs;ma aqueum triangulare, cuius
&longs;ectio e&longs;t BGK, ibidemque retinetur &longs;u&longs;penditurque
mons prædictus aqucus,
uo BG impediretur eius fluxus deor&longs;um ver&longs;us
&longs;ubiectam AB. Quia verò aqua non amittit
eius grauitatem, a&longs;&longs;ignari debet cau&longs;a à qua &longs;u&longs;pen&longs;a
retinetur, & quæ vis ip&longs;am &longs;ursùm prius impulit. Hæc profectò aut propria, & naturalis e&longs;t ip&longs;ius aqu&ecedil;,
vt nimirùm &longs;ponte &longs;ua &longs;ursùm a&longs;cendat, ibidemqu&etail;
retineatur, aut hoc &longs;it ab aliqua cau&longs;a violenta ex
terna. Quòd verò non &longs;it vis propria, & natiua ip&longs;ius
aquæ, patet ex &longs;uperiùs dictis, quia nimirùm &longs;emper
aqua grauis e&longs;t, exercetque &longs;uam vim compre&longs;&longs;iuam
versùs centrum telluris, vt &longs;en&longs;us euidentia con&longs;tat.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
Alij po&longs;tea recurrunt ad aeris vim compre&longs;&longs;iuam,
aiunt enim aerem
minori energia &longs;ubiectam aquam K comprimere,
aer HB à pariete remotus premat &longs;ubiectam aquam
B, propterea quòd illa quodammodo ab a&longs;perita
tibus parietis retinetur, ac impeditur ne libero co
natu, & fluxu premere queat aquam &longs;ubiectam K
hæc vniuer&longs;am &longs;uam grauitatis, & virtutis ela&longs;ticæ
energiam liberè exercere po&longs;&longs;it; hoc autem fal&longs;u&mtail;
e&longs;&longs;e &longs;ic
gyro, quia ex hypothe&longs;i aduer
&longs;arij, aer FKG parieti va&longs;is
tiguus
iectum mercurium K, quàm aer
HB ab
tus premat
rius K, vel &ecedil;quilibratur
mento
le à parietis a&longs;peritatibus impeditur, hic verò libe
rè premit. igitur hìc
curialis versùs parietem, vt in aqua contingit, quod
e&longs;t fal&longs;um, & repugnat experientiæ, potiùs enim de
primitur in foueam BGK, non ergo ab illa inæquali
aeris pre&longs;&longs;ione aqueus monticulus versùs pariete&mtail;
va&longs;is eleuatur. Et licèt re&longs;ponderi po&longs;&longs;et quòd cau&longs;a
huius diuer&longs;æ operationis pendeat à defectu analo
giæ mercurij, & parietis va&longs;is, ob quem ille refugit
huius contactum, non tamen in dubium reuocatur ab
aduer&longs;arijs inæqualis illa aeris pre&longs;&longs;io &longs;upra mercu
rium, quare in rali ca&longs;u operatur vis illa, qua mercu
rius a va&longs;is &longs;uperficie interna &longs;eparatur vnà cum inæ
quali vicompre&longs;&longs;iua aeris, ideò in duobus va&longs;is cy
lindricis angu&longs;tis RST, & VXZ &longs;it amplitudo, &longs;eu
ba&longs;is ST maior, quàm XZ in ei&longs;que hydrargyrum in
fundatur v&longs;que ad B, & E.
exiguæ aqu&ecedil;
guttæ &longs;upra
a&longs;cendunt.
Et
ficie interna fi&longs;tulæ &longs;eparari, ni&longs;i &longs;u&longs;pendatur
do tumidum Verùm minus grauis mercu
rij moles in &longs;trictiori fi&longs;tula contenti faciliùs &longs;u&longs;pen
ditur, quàm grauior moles eiu&longs;dem latiorem
ris fi&longs;tulæ &longs;uperficie &longs;eparatur,
ris fi&longs;tulæ &longs;uperficie, & proinde altius, vel &longs;altem
minùs altè &longs;eparari deberet mercurij monticulus GF
quàm CA. po&longs;tea aer perimetris in
ternis vtriu&longs;que fi&longs;tulæ adhærens æ
què impeditur, & propterea æquè
aeris pre&longs;&longs;iones debilitat&ecedil; viribus æ
qualibus &longs;ubiectum mercurium
primere
tes aeris versùs axes cylindrorum
les vires compre&longs;&longs;iuas habebunt, eò quòd inæquali
tèr à &longs;uperficiebus internis va&longs;orum recedunt, quare
aer incumbens mercurio in A maiori vi eum compri
met, ac contundet, quàm aer incumbens mercurio
in G, igitur validiori vi retundetur monticulus tumi
dus BAD quàm EGL, & ideo altior erit monticulus
mercurij EGL, quàm BAD; &longs;ed hoc e&longs;t fal&longs;um, multò
enim maior e&longs;t altitudo CA quàm FG, ergo aeris vis
compre&longs;&longs;iua nullam inæqualitatem &longs;ortitur, vel non
talis e&longs;t vt tàm in&longs;ignes varietates producere valeat,
&longs;cilicèt non eleuarentur argines illi aquei &ecedil;què ab ae
re compre&longs;&longs;i, ac reliqua aquæ &longs;uperficies horiz onta
lis. Præterea in vacuo Torricelliano aer ibi non exi
&longs;tens
&longs;tulæ adh&ecedil;rentes; vel &longs;i ibidem remanet minima aeris
portio valdè expan&longs;a, & rara erit, & ideò (ex Prop.
105.) eius pondus, & vis compre&longs;&longs;iua minor erit
pè
terni eiu&longs;dem molis: igitur illa non poterit &longs;upra a
quæ libellam eleuare
in aere aperto ab huius ingenti pondere
tur
in prædicto vacuo &longs;ublimantur, ac in aere aperto, igi
tur non ab aere ibidem non exi&longs;tente, vel rari&longs;&longs;imo
argines prædicti &longs;u&longs;penduntur.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
Alij po&longs;tea recurrunt ad &longs;cabritiem, &
parietis à qua impeditur de&longs;cen&longs;us, &longs;u&longs;pendunturque
particulæ aqueæ; &longs;ed hoc minimè &longs;ufficere videtur,
nam ad &longs;ummum dicta &longs;cabrities commoda e&longs;&longs;et, &
apta ad retinendam aquam po&longs;tquam &longs;emèl eleuata
fui&longs;&longs;et ad illam altitudinem, quatenùs ab a&longs;peritati
bus, veluti vncinis impediretur defluxus aquæ deor
sùm, at non po&longs;&longs;ent aquam &longs;ubleuare, cùm &longs;cabrities
vim motiuam non habeat; & &longs;anè a&longs;peritates nedum
non adiuuarent, &longs;ed potiùs impedirent aquæ eleua
tionem in prædictis arginibus duplici nomine, primò
quia eædem parietis &longs;cabro&longs;itates, quæ vim habent
prohibendi defcen&longs;um aquæ,
a&longs;cen&longs;um; præterea multò magis, & maiori vi a&longs;cen
&longs;us aquæ impediri deberet quàm eius
in a&longs;cen&longs;u aqua præter re&longs;i&longs;tentiam a&longs;peritatis parie
tis &longs;uperare debet impedimentum, & reluctantiam
propriæ grauitatis, cum è contra in de&longs;cen&longs;u ab hac
adiuuetur. igitur &longs;cabrities parietis non pote&longs;t e&longs;&longs;&etail;
cau&longs;a eleuationis aquæ in prædictis arginibus.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
Debet modo a&longs;&longs;ignari virtus motiua, quæ eleuat,
& &longs;u&longs;tinet aquam &longs;upra propriam libellam v&longs;que ad
&longs;ummitatem arginis, & hanc demon&longs;trabo e&longs;&longs;e &longs;im
plicem aquæ grauitatem. Quia aquæ particulæ ad
hærentes parieti va&longs;is in&longs;inuant ramos &longs;uarum machi
nularum intra poro&longs;itates, & foueolas parietis, à cu
ius eminentijs, & a&longs;peritatibus fulciuntur extremi
tates particularum aquæ, quarum oppo&longs;iti termini
&longs;u&longs;tinentur, à &longs;ubiecta collaterali aqua, proptereà
efficientur veluti totidem vectes conuertibiles circa
eorum fulcimenta parieti annexa. Hinc fit vt prædi
ctæ aquæ particulæ exiguam vim compre&longs;&longs;iuam exer
ceant, & minori momento &longs;ubiectam aquam com
primant, cùm partes aquæ collateralis liberè
do
momentum exerceant, igitur ex prop.
174. partes
minùs pre&longs;&longs;æ &longs;ursùm impelli debent à partibus ma
gis compre&longs;&longs;is: & licèt illæ retineantur, & impedian
tur ne motu &longs;ibi ip&longs;i æquidi&longs;tanti ferri &longs;ursùm
tamen eadem impedimenta
clarè adiuuant flexionem, & turbinationem earun
dem aquæ particularum, igitur à vi motiua grauita
tis maioris aquæ collateralis &longs;lecti, rotari, & impelli
&longs;ursùm po&longs;&longs;unt parieti adh&ecedil;rendo eædem aquæ par
ticulæ; dum verò efficitur prædicta eleuatio, &longs;ummi
tates guttularum reuolutarum eminentiores reddun
tur quàm aliæ particulæ parieti adhærentes, igitur
tunc prædictæ particulæ iam eleuatæ naturali in&longs;tin-
ctu excurrent versùs parietem, cui &longs;uis villis adhæ
rebunt, ex qua adhæ&longs;ione momentum eius grauitatis
denuò imminuetur, & ideò renouabitur cau&longs;a vlte
rioris eius eleuationis à compre&longs;&longs;ione laterali aquæ
&longs;uo momento non imminuto comprimentis, & hinc
&longs;equitur continuatio prædicti a&longs;cen&longs;us rotando, &
adhærendo parieti, quou&longs;que efficiatur æquilibrium
cum prædicta aqua collaterali liberè premente.
exiguæ aqu&ecedil;
guttæ &longs;upra
a&longs;cendunt.
Et hìc notandum e&longs;t, quòd vis prædictæ adhæ&longs;io
nis aquæ non e&longs;t æqualis in omnibus partibus prædi
ctæ montuo&longs;itatis, &longs;ed omnium maxima e&longs;t illa, quæ
retinet mini nas aquæ particulas immediatè
tangentes, quæ non &longs;ecùs, ac &longs;i e&longs;&longs;ent claui, vel vn
cini tenaci nexu ibidem in&longs;inuantur, & minima erit
vis illa, quæ retinet remoti&longs;&longs;imas, & po&longs;tremas par
ticulas dictæ montuo&longs;itatis aquæ, aliarum verò par
tium illæ, quæ parieti viciniores &longs;unt, maiori tena
citate &longs;u&longs;pendentur, quam aliæ partes aquæ a præ
dicto pariete magis remotæ. Et hinc oritur decliuitas
illa montis aquæ pendentis.
prædicti a
quei montis
pendet ex in
æqualitate
virtutis mo
tiuæ.
Hic iam re&longs;oluere po&longs;&longs;umus aliud problema val
dè agitatum, vnde nimirùm proueniat, quòd aqu&atail;
in fi&longs;tulis tenui&longs;&longs;imis vtrinque apertis &longs;ursùm a&longs;cen
dat. Et primo loco phænomena, quæ in hac opera
tione ob&longs;eruantur, recen&longs;eri debent.
tur ob&longs;erua
tiones
&longs;us
f
cili&longs;&longs;imis.
Po&longs;tquam gracili&longs;&longs;ima fi&longs;tula EH contingit aquæ
&longs;im a&longs;cendere incipit ad notabilem altitudinem HK
eiu&longs;dem cauitatis &longs;upra aquæ &longs;ubiectæ libellam RV.
Siverò prædicta cauitas priùs humectata, & made
facta fuerit, & denuò exinanita &longs;ubitò po&longs;t
multò altiùs, & celeriùs v&longs;que ad G aqua perpendi
cularitèr eleuatur, ac a&longs;cendebat
in priori ca&longs;u quando interna fi
&longs;tulæ cauitas arida erat. Præterea
&longs;i po&longs;t aquæ exuctionem transfe
ratur fi&longs;tula AB ab aqua ad
non &longs;ecùs in ea perpendiculari
ter erecta fixè retinetur eade&mtail;
aquæ moles in eodem &longs;itu, & al
titudine CD, quàm priùs habe
bat. In&longs;uper &longs;i eadem exigua fi
&longs;tula interiùs madida, &longs;ed exina
nita contingat paruulam guttulam aquæ F in palm&atail;
manus eleuatam, &longs;i immediatè po&longs;t guttæ contactum
fi&longs;tula citò eleuetur, tunc videmus aquam exucta&mtail;
non quie&longs;cere in infimo fi&longs;tulæ &longs;itu B, &longs;ed vlteriùs
pauli&longs;per &longs;ursùm promoueri, excurrereque &longs;ucce
dente aere in eius infima parte.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
larum eius impul&longs;a, neque in&longs;inuatur, retineturque
ibidem ab æquilibrio aeris, aut ab internis ca
naliculi a&longs;peritatibus.
RElatis ob&longs;eruationibus
dicta phænomena &longs;aluari po&longs;&longs;int ex no&longs;tris, vel
ex aliorum Authorum principijs. Et primò &longs;i aqu&atail;
&longs;ponte &longs;ua a&longs;cenditintra fi&longs;tulæ cauitatem à vi parti
cularum eius &longs;e mouentium, igitur aut grauitate om
ninò carent, aut in tali ca&longs;u eam non exercent (quod
vltrò aliqui Authores concedunt) &longs;i inquam hoc ve
rum e&longs;t, impo&longs;&longs;ibile e&longs;&longs;et vt aqua in fi&longs;tula immi&longs;&longs;&atail;
perpendiculariter erecta exerceret vllam vim com
pre&longs;&longs;iuam deorsùm, & ideò &longs;i fi&longs;tula infernè prolon
garetur, nullo pacto aqua ibidem deorsùm de&longs;cende
ret, quod tamen experientiæ refragatur, nam
fi&longs;tula cum aqua contenta in aere translata, & per
pendiculariter ad horizontem erecta &longs;i inuer&longs;o &longs;itu
di&longs;ponatur vt pars eius &longs;upina A fiat prona, aut ei alia
fi&longs;tula infernè adnectatur, aqua in ea contenta celeri
motu de&longs;cendit, &longs;i madida fuerit, quou&longs;que prope
infimum orificium perducatur; igitur fal&longs;um e&longs;t a
quæ in fi&longs;tula contentæ particulas grauitate priuari,
proindeque &longs;ponte &longs;ua intra fi&longs;tulam a&longs;cendere.
verò aiunt cau&longs;am prædicti a&longs;cen&longs;us aquæ pender&etail;
ex eo quòd eius particulæ naturali in&longs;tinctu feruntur
versùs fluidum aqueum, vel aquæ analogum
tum
quam negant, impediri po&longs;&longs;unt: &longs;i hoc, inquam, ve
rum e&longs;&longs;et, madefacta vniuer&longs;a fi&longs;tulæ interna cauita
te, & po&longs;tea exinanita, atque immer&longs;o orificio infra
aquæ &longs;ubiectæ
aqua v&longs;que ad fi&longs;tulæ &longs;upremum orificium, quod ta
men e&longs;t fal&longs;um, non ergo &longs;ponte &longs;ua aqua intra fi&longs;tu
lam eleuatur.
exiguæ aqu&ecedil;
guttæ &longs;upra
a&longs;cendunt.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
Alijj po&longs;tea aiunt quòd dum fi&longs;tula AB
va&longs;is RSV, vel guttulam &longs;u&longs;pen&longs;am F, tunc aer
&longs;uo pondere, & vi ela&longs;tica com
primit infernè partem aqu&ecedil; F ex
tra fi&longs;tulam exi&longs;tentem, eamque
impellit versùs orific
nè verò aer penetrando cauita
tem fi&longs;tulæ, AB contrario ni&longs;u re
pellit &longs;ummitatem aquæ F intr&atail;
orificium B in&longs;inuatam: quia ve
rò fieri non pote&longs;t vt contactus,
& a&longs;peritates internæ fi&longs;tulæ non
impediant de&longs;cen&longs;um, & ni&longs;um
compre&longs;&longs;iuum aeris, fit vt minori momento aer per
fi&longs;tulæ canaliculum pertran&longs;iens premat aquæ &longs;um
mitatem F, quàm liber aer externus à nullo impedi
mento debilitatus; igitur aqua F à validiori vi impul
&longs;iua aeris externi impelli &longs;ursùm debet, & in&longs;inuari
intra fi&longs;tulam à B ad C. quou&longs;que minor vis aeris per
AC tranfeuntis vnà cum pondere aquæ CB æquili
brentur momento totali aeris externi, quapropter
exce&longs;&longs;us momenti totalis aeris non impediti &longs;upr&atail;
momentum aeris debilitati æqualis e&longs;t ponderi aquæ
CD.
Debemus modò fal&longs;itatem huius &longs;ententiæ o&longs;ten
dere. Reuoluatur fi&longs;tula AB vnà cum aqua contenta
CD inuer&longs;o &longs;itu, vt &longs;upina eius pars A fiat prona,
aer infernè per prolixum canaliculum AC immi&longs;&longs;us
non &longs;ecùs ac priùs impeditur à contactibus, & a&longs;pe-
ritatibus internis vitri, & ideò eodem debiliori, &
imminuto momento pellit aquam CD &longs;ursùm, impe
ditque eius de&longs;cen&longs;um. E contrà aer &longs;upernè nil fe
rè impeditus premit deorsùm aquam D orificio B pe
nè contiguam, igitur non &longs;ecùs, ac priùs aer totali
momento eius deorsùm impellit aquam DC: ab hoc
verò momento non &longs;ubtrahitur, immò ei additur
dus
pellitur deorsùm maiori exce&longs;&longs;u, nempè duplò &longs;upe
rat vim, qua &longs;ursùm repellitur, &longs;cilicèt æqualis e&longs;t
duplo ponderis aquæ DC, &longs;ed priùs medietas pr&ecedil;di
cti exce&longs;&longs;us, non ob&longs;tante fi&longs;tulæ interna ariditate, a
quam &longs;ursùm celeri motu eleuauerat, igitur multò ce
leriùs, & faciliùs in
tutis motiu&ecedil; deprimi aqua DC deorsùm deberet per
aridum canalem CA, &longs;ed hoc e&longs;t fal&longs;um, nam aqu&atail;
DC quie&longs;cit, aut tardi&longs;&longs;imo motu de&longs;cendit versùs
A, ergò non eleuatur aqua in fi&longs;tula ob inæquales ae
ris impul&longs;iones.
exiguæ aqu&ecedil;
guttæ &longs;upra
a&longs;cendunt.
Tandem quod interna vitri &longs;cabrities non impel
lat illam aquæ exiguam molem, &longs;atis a pertè con&longs;irma
tur ij&longs;dem rationibus adductis in fine propo&longs;itionis
183. Igitur & c.
de&longs;luat rationem reddere.
MOdò remanet difficultas, quare &longs;cilicèt in infi
mo fi&longs;tulæ confinio in aere con&longs;titutæ impe-
ditur aquæ defluxus; & licet videatur hoc à contactu
aeris fieri, nihilominùs ex no&longs;tris principijs dici po
te&longs;t, quod in infimo fi&longs;tul&ecedil; orificio machinulæ lanugi
nis particularum aquæ inter &longs;e connexæ
& ideo tenaciori re&longs;i&longs;tentia vinciuntur, & efficiunt
veluti rete adhærens extremo fi&longs;tulæ, & quia vis pr&ecedil;
dictarum machinularum violenter di&longs;tractarum ma
ior e&longs;t vi ponderis exigui aquæ intra fi&longs;tulam
tæ
ac &longs;u&longs;tinentur guttæ aqueæ è ramis arborum pen
dentes.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
impellitur aqua in fi&longs;tulis.
QVæ meo iudicio ex theoria nuper expo&longs;ita
det
larum internus aquæ contactus grandis e&longs;t, & amplus
re&longs;pectu illius aquæ moleculæ ibidem exi&longs;tentis, er
go &longs;ubitò ac infimum fi&longs;tulæ orificium attingit
efficitur in eius interno, & cauo perimetro efficaci&longs;
&longs;imus contactus à cuius adhæ&longs;ione fulciri &longs;u&longs;tineri
què pote&longs;t maius pondus, quàm habet pu&longs;illa aquæ
particula in&longs;inuata, & ideo gradus prædictæ virtutis
&longs;u&longs;pen&longs;iuæ, & adhæ&longs;ionis exercetur in aqua &longs;ubicta,
& proinde ea reddetur aliquo pacto leuis, &longs;eu minùs
pondero&longs;a, quàm &longs;it aqua collateralis liberè Et quia minimæ aquæ particulæ poro&longs;itatibus, & a&longs;-
peritaribus internis fi&longs;tulæ innixæ efficiuntur
turque
rotari, nece&longs;sè e&longs;t vt partes aquæ collaterales magis
compre&longs;&longs;æ à totali energia &longs;ui ponderis vim faciant
impellendo &longs;ursùm particulas illas aquæ, quæ minùs
comprimuntur à vectibus &longs;upradictis, & ideo rotando
excurrere po&longs;&longs;unt interiùs efformando tumorem, vel
monticulum aqueum, qui excurrendo lateralitèr al
tioribus fi&longs;tulæ poro&longs;itatibus in&longs;inuabitur, adhære
bitque, & ideò denuò imminuetur|eius vis
ua
proindè altiùs aqua intra fi&longs;tulam impelletur, & &longs;ic
de nouo eminentioribus lateribus adhærendo &longs;uc
ce&longs;&longs;iuè altius impelletur, quou&longs;que ad &longs;upremam, &
maximam illam altitudinem aqua perducta, in qu&atail;
æquilibrium cum aqua collaterali liberè premente
efficiatur, tunc quidem quies eius &longs;ub&longs;equetur, nec
vlteriùs eleuari poterit.
174.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
reijcitur vis aeris ab hac operatione.
SEd pro clariori huius rei intelligentia ph&ecedil;menon
nupèr à me ob&longs;eruatum in medium adduca&mtail;,
Sit fi&longs;tula &longs;tricta vitrea AB hæc quidem arida
dicularitèr
BF; &longs;i verò internè fi&longs;tula priùs humectata fuerit, &
deindè exinanita, in contactu aquæ &longs;ubiectæ altiùs
eleuatur per &longs;patium BE; &longs;i po&longs;teà eadem fi&longs;tul&atail;
pro&longs;undiùs demergatur infra aquam, vel inclinetur,
aqua exucta maius &longs;patium BC occupa
bit. His po&longs;itis tran&longs;portetur integra fi&longs;tu
la vnà cum aqua
perpendicularitèr tamen erecta ad planum
horizontis tunc effluere cunctanter con&longs;pi
citur ab infimo orificio B guttula quædam,
quæ &longs;en&longs;im colligitur, tume&longs;citque; & hoc
contingit quando valdè excedens e&longs;t alti
tudo aqu&ecedil; BC, at &longs;i
in &longs;itu perpendiculari ab&longs;que eo quòd ex
orificio B defluat noua aquæ gutta. Modò
fi&longs;tulæ B contingat aquam va&longs;is, vel guttulam D &longs;u
&longs;pen&longs;am à palma manus, vel adhærentem externæ,
& extremæ parti ip&longs;ius fi&longs;tulæ B, videbis aquam BC
deprimi deorsùm v&longs;que ad E, vbi nimirùm con&longs;i&longs;te
bat aqua exucta è va&longs;e, quando interna cauitas hu
mectata fuerat; è contrà &longs;i altitudo aqu&ecedil; internæ val
de diminuta fuerit, vt BG, tunc quidem in contactu
guttulæ inferioris augetur eius altitudo exugendo
nimirùm aquam ip&longs;ius guttulæ D.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
Ratio huius admirandi effectus videtur pendere
ex legibus æquilibrij aquæ externæ, & internæ. pri
mò quando gutta pendula D adhæret in&longs;imo fi&longs;tulæ
orificio, concipere debemus &longs;uperficiem externa&mtail;
prædictæ guttulæ pendentis e&longs;&longs;e veluti &longs;acculum, vel
bur&longs;am compo&longs;itam ex machinulis aqueis variè con-
textis, incuruatis, & di&longs;tractis à pondere totius aquæ
prementis, vt alibi dictum e&longs;t, internæ verò partes
eiu&longs;dem guttulæ, ob earum lubricitatem, liberè &longs;lue
re po&longs;&longs;unt intra alias aquæ particulas, orificium va&longs;is
explentes. Hinc fit vt illæ exercendo liberè earu&mtail;
momentum grauitatis, præualeant energiæ compre&longs;
&longs;iuæ diminutæ, ac debilitat&ecedil; particularum aquæ GB
intra cauitatem vitri adhærentium, & &longs;ic &longs;ursùm im
pellantur à G v&longs;que ad F, vel &longs;i cauitas madida fue
rit v&longs;que ad E, nempè quou&longs;que fiat momentorum
æquilibrium. è contrà
ius erit eo, quo aqua va&longs;is &longs;ubiecta, vel intra guttu
lam D contenta liberè premit, proindeque illa de
&longs;cendet in fi&longs;tula à &longs;ummitate C v&longs;que ad E, vbi ni
mirùm eorum momenta adæquantur. Sed in priori
ca&longs;u for&longs;an facilè &longs;u&longs;picabitur à compre&longs;&longs;ione aeris
&longs;ursùm impelli guttulam infimam à G v&longs;que ad E, cu
ius inditium e&longs;&longs;e pote&longs;t, quòd tota guttula D exugi
tur à fi&longs;tula, imò vlteriùs promouetur aere
te
dem non exi&longs;tit, & proinde operari nequit, &longs;ed ab
aere impellitur. &longs;ed re&longs;ponderi pote&longs;t quod à vi im
petus, quo aqua in fi&longs;tula a&longs;cendit pro&longs;equi, &
tinuari
ticulæ guttæ ip&longs;ius D, quatenus à glutine machinu
larum aquæ connectuntur po&longs;trem&ecedil; illæ guttulæ par
tes, cum præcedentibus, & ab impetu earum
quæ actu in fi&longs;tula mouentur &longs;ursùm, trahantur vlte
riùs, & con&longs;equentèr aer po&longs;tea &longs;uccedat in &longs;patio
infimo fi&longs;tulæ inani ab aqua derelicto.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
quàm in ca quæ aquam, aut aerem tangit.
SEd procedamus ad præcipuam difficultatem, ex
cuius &longs;olutione reliquis omnibus &longs;atisfiet. Sit
vas RSV aqua plenum, &longs;umanturque duæ fi&longs;tulæ æ
quales, & æquè amplis cauitatibus perforatæ, vtrin
que apertæ, vna quidem AB profundiùs demergatur
infra aquæ libellam RV; reliqua verò EH tantum
modò &longs;uperficiem aquæ RV contingat, & ambo per
pendicularitèr in&longs;i&longs;tant &longs;upremo
plano aquæ RV. Si ergo veru&mtail;
e&longs;t, quòd aqua collateralis magis
compre&longs;&longs;a à totali eius momento
qualis e&longs;t cylindrus aqueus FI
comparatus cum aqua BC, quæ
minus comprimit
eò quòd &longs;u&longs;penditur, &longs;u&longs;tentatur
que ab internis vitri a&longs;peritati
bus, redditurque aqua CB veluti
virga lignea re&longs;pectu aquæ colla
teralis FI; ergo quò profundiùs demergitur fi&longs;tul&atail;
longior e&longs;t virgula minùs grauis aquea BC, & ideò,
ex demon&longs;tratis, validiori vi &longs;ursùm impelletur ab a
qua collaterali FI, quàm impellatur &longs;ursùm exiguus
cynndrulus aquæ H, qui fu&longs;tinetur, &
aqua &longs;uperficiali RV.
exiguæ aqu&ecedil;
guttæ &longs;upra
a&longs;cendunt.
Sed re&longs;pondetur, quòd aqua CB non redditur le
uior ob internum contactum fi&longs;tulæ, nam intern&atail;
fi&longs;tulæ &longs;uperficies cùm &longs;it madida, nihil, aut paru&mtail;
impedit vim grauitatis aquæ contentæ intra fi&longs;tulam
BC, & hoc experitur cùm in aere trans&longs;ertur fi&longs;tula,
tunc enim aqua intra cauitatem eius madidam libe
rè mouetur de&longs;cend it que; præcipuum verò impedi
mentum in extremo orificio fi&longs;tulæ B experitur, non
intra aquam, &longs;ed po&longs;tquam aerem attingit; non qui
dem à vi ela&longs;tica, vel ponder&etail;
eiu&longs;dem aeris, &longs;ed quia tunc i&ntail;
aqua ad
citur rete &longs;uperiùs
tenùs particul&ecedil; infernæ illius aqu&ecedil;
vici&longs;&longs;im connexæ dum pendent à
vi propri&ecedil; grauitatis di&longs;tract&ecedil; ea
rum machinulæ paritèr maiorem
violentiam patiuntur, & ideò ma
iori vi vici&longs;&longs;im connectuntur, &
&longs;ic re&longs;i&longs;tere violentiæ pre&longs;&longs;ionis
demer&longs;o infra aquam non pote&longs;t effici rete illud ro
bu&longs;tum aptum ad &longs;u&longs;tinendam aquam
quia non di&longs;trahuntur machinulæ aquæ B exi&longs;tentes,
& contingentes internam aquam va&longs;is RSV: hinc fit
vt facilè vna aquæ pars &longs;uper aliam &longs;ibi contigua&mtail;
excurrere valeat, & hinc deducitur ratio quare i&ntail;
fi&longs;tula EH vnà cum aqua HK excedente con&longs;uetam
altitudinem, &longs;i tota in aere con&longs;tituta fuerit, altiùs
prædictam aquam &longs;u&longs;tinebit, quàm &longs;i aquæ libellam
RV tetigerit, tunc enim de&longs;cendit à K ad G, & HG
altior erit quàm DC, &longs;cilicèt quando fi&longs;tula profun
diùs mergitur, vt in B; quia nimirum dum in aere ex
tabat, efficiebatar rete prædictum, cùm verò aquam
&longs;ubiectam contingit, tum connexio illa tenax facilè
&longs;oluitur diffluitque, & &longs;ic non ampliùs &longs;u&longs;tinere tan
tum pondus incumbens pote&longs;t.
exiguæ aquæ
guttæ &longs;upra
a&longs;cendunt.
Id ip&longs;um præterea confirmatur, quia in contactu
aquæ in H &longs;u&longs;penditur circa fi&longs;tulam externè monti
culus quidam aqueus &longs;upra libellam RV, quod con
&longs;equenter &longs;uadet aquam a vi contactus vitri externi
&longs;u&longs;pendi ni&longs;u contrario eius, qui à grauitate aquæ
exercetur, & proindè aqua prædicto monticulo &longs;ub
iecta, & annexa leuior redditur, igitur aqua infr&atail;
orificium &longs;ubiectum fi&longs;tulæ ob prædictam &longs;u&longs;pen&longs;io
nem minùs grauis facta, nece&longs;sè e&longs;t, vt eleuetur ab
integro momento collateralis aquæ liberè premen
tis, & &longs;ic in&longs;inuetur intra cauitatem fi&longs;tulæ &longs;upra a
quæ &longs;ubiectæ libellam quou&longs;que fiat momentorum
æquilibrium.
Ex hac theoria facilè re&longs;oluuntur circum&longs;tantiæ,
quæ in operationibus prædictarum fi&longs;tularum ob&longs;er
uantur, & &longs;imul magis confirmatur doctrina &longs;uperiùs
expo&longs;ita.
exiguæ aqu&ecedil;
guttæ &longs;upra
a&longs;cendunt.
latioribus, & in fistulis æqualibus, &longs;ed in æqualiter ad
aquæ &longs;uperficiem inclinatis aqua ad eamdem
altitudinem eleuatur.
ET primo loco percipitur quare in fi&longs;tulis latio
ribus aqua ad minorem altitudinem eleuatur,
quàm in &longs;ubtili&longs;&longs;imis, & angu&longs;ti&longs;&longs;imis canalibus: &
e&longs;t, quia adhærentia, & connexio aquæ parietibus
internis canalium maiorem proportionem ad molem
aquæ in&longs;inuatæ exten&longs;iuè, & inten&longs;iuè in canaliculis
&longs;ubtili&longs;&longs;imis, habet quàm in amplis, & capacioribus. Et quoad exten&longs;ionem pertinet, quia vis adhæ&longs;ionis
men&longs;uratur à contactibus, & ideò à &longs;uperficie inter
na canaliculorum, è contrà re&longs;i&longs;tentia men&longs;uratur à
pondere cylindri aquei contenti in ij&longs;dem canalicu
lis, e&longs;tque proportio cylindrorum aqueorum
altitudiais duplicata eius rationis, quam habent eo
rum perimetri |interni, igitur quanto magis cre&longs;cit
interna canalis amplitudo, tantò magis minuitur ad
hæ&longs;io, & augetur re&longs;i&longs;tentia ponderis ip&longs;ius aquæ
tentæImminuitur po&longs;teà gradus inten&longs;iuus internæ
adhæ&longs;ionis, proptereà quod, vt dictum e&longs;t &longs;upra,
e&longs;t æquè valida facultas, & energia adhæ&longs;ionis aqu&ecedil;,
& connexionis|cum parietibus internis |in |vniuer&longs;o
illo argine montuo&longs;o, &longs;ed e&longs;t minus efficax, quantò
magis ab internis parietibus remouetur. Modò i&ntail;
fi&longs;tulis amplioribus aqua contenta versùs axim caui
tatis eius magis recedit à &longs;uperficie interna fi&longs;tulæ
dilatatæ, quàm in fi&longs;tula &longs;trictiori, & ideò in illa de
biliùs aqua &longs;u&longs;tinebitur &longs;u&longs;pendeturque, & quantò
minor e&longs;t vis &longs;u&longs;tinens, & eleuans re&longs;pectu ponderis
fluidi contenti, tantò debet imminui &longs;ublimitas eius
eleuationis, vbi præcisè efficitur æquilibrium &longs;upe
riùs expo&longs;itum.
182.
exiguæ aqu&ecedil;
guttæ &longs;upra
a&longs;cendunt.
Similitèr in eodem canaliculo ad horizontem in
clinato longiori &longs;patio eleuabitur aqua, quàm &longs;i per
pendicularitèr horizonti in&longs;i&longs;teret, quia nimirùm &longs;u
blimitas verticalis in
cùm in &longs;itu inclinato momentum aqu&ecedil; prementis
&longs;uretur
ab&longs;oluto cylindri aquei &longs;ubleuati, &longs;ed ab eius verti
cali eleuatione, & propterea
pelletur ab eadem cau&longs;a eleuante non alterata, &longs;cili
cèt à pondere ab&longs;oluto aquæ collateralis liberè pre
mentis.
dictæ opera
tiones non
contingant
ni&longs;i fi&longs;tulæ
&longs;int vtrinque
apertæ.
Et hæc omnia contingere debent quotie&longs;cumque
canaliculus &longs;upernè non clauditur; Si enim ob&longs;tru
ctus fui&longs;&longs;et aer idem internè comprehen&longs;us impediret
aqu&ecedil; a&longs;cen&longs;um, quia non po&longs;&longs;et aqua in&longs;inuari ab&longs;que
eo quod contentus aer &longs;tringeretur conden&longs;aretur
que, cumque aer conden&longs;ari
ni&longs;i à noua cau&longs;a violentèr eum conden&longs;ante, cui aer
&longs;ua vi ela&longs;tica re&longs;i&longs;tit, igitur &longs;i aqua intra prædictam
fi&longs;tulam ingrederetur, con&longs;tringere
deberet, & propterea idem aer &longs;ua vi ela&longs;tica impe
dict
corpn&longs;culo
rum
tium
amplexu at
que fuga.
atque fuga.
SVnt ferè triginta duo anni, cùm ego experiri vo
lui an filamenta ferrea &longs;uper aquam innatanti&atail;
in diuer&longs;is ad meridianam inclinationibus elongata
retinerent eandem po&longs;ituram, ad
nem, directionemque redigerentur in qua fabrefacta
fuerant, vt Guglielmus Gilbertus ait, & dum hoc at
tentiùs ob&longs;eruarem, mirabile &longs;pectaculum &longs;e&longs;e obtu
lit hactenùs non animaduer&longs;um, quod nimirùm ali
quæ extremitates natantium corporum auido cur&longs;u
&longs;e vniebant, amplectebanturque, aliæ verò &longs;egrega
bantur non &longs;ecùs, ac in magnete, & ferro contingit:
igitur ab hac nouitate excitatus idip&longs;um comproba
ui adhibitis alijs corpu&longs;culis, fe&longs;tucis, folijs
& innumeris alijs corporibus; cùmque ego &longs;ummo
perè optarem cau&longs;am prædicti effectus perciper&etail;,
po&longs;t innumera experimenta, animaduerti huiu&longs;modi
operationes contrarias de
pendere ab aqueis arginibus
circa corpora natantia adia
centia, aliquando eminenti
bus,
duas laminulas æreas papyro
graciliores, quales &longs;unt V, &
X, & in earum punctis intermedijs C, & L appo&longs;ui
duas fe&longs;tucas CD, & LM, ibidemque cera eas ferru
minaui perpendicularitèr erectas ad plana laminula
rum. appo&longs;ui po&longs;tea laminas &longs;upra
horizontali applicatione, quæ infra aquæ libella&mtail;
innatando deprimebantur, efficiebantquè circumcir
cà argines aqueos EA,
GB, nec non IN, KO;
po&longs;teà efformaui duas
a&longs;&longs;ulas ligneas Y, & Z,
quarum altitudines
midigitum
tur
ues, vt EA, GB &longs;upra His præparatis &longs;olertèr digitis impuli &longs;ummitate&mtail;
D fe&longs;tucæ approximando laminulam V versùs X,
que
teriùs laminæ V perueniret, eratque di&longs;tantia inter
laminas minor latitudine vnius digiti, tunc primò vi
di &longs;ponte &longs;ua duas laminas V, & X &longs;e&longs;e mouere vn&atail;
versùs alteram, & licèt mediocri violentia digitis re
tinerentur, impedireturque acce&longs;&longs;us earum, po&longs;te&atail;
non minùs, quàm priùs veloci cur&longs;u &longs;e mutuò ample
ctebantur, &longs;ed in ip&longs;o actu coniunctionis earum om
ninò explanabatur
&longs;egregabantur, po&longs;tea me
Y, & Z quæ paritèr immobiles, & inertes erant
do
li, &longs;ed magis appropinquata vna versùs alteram, &longs;u
bitò a&longs;&longs;ulæ excurrebant ad &longs;e &longs;e amplectendum, &
hìc accidit operatio diuer&longs;a à præcedenti, nam duæ
montuo&longs;itates eleuatæ GB, & IN nedùm non &longs;e ex
planarunt, nec redegerunt ad aquæ &longs;ubiectæ libellam
FH de&longs;cendendo, &longs;ed è contrà &longs;patium
& cauitas BHI omninò repleta e&longs;t v&longs;que ad
culmen BI. Tandem
a&longs;&longs;icula Z, & vidi, quod
quotie&longs;cumque approxi
mabantur ad di&longs;tantia&mtail;
digito minorem, nedùm &longs;e
mutuò non amplecteban
tur, &longs;ed è contra vna rapi
dè ab altera effugiebat,
fegregabaturque, qua&longs;i a
bominaretur Quaprop
ter experientia con&longs;tat, quòd acce&longs;&longs;io, approximatio,
& amplexus laminularum, tunc &longs;olummodò accidit,
quando argines aquei &longs;imiles &longs;unt inter &longs;e, &longs;cilicèt
tra aquæ va&longs;is libellam; &longs;ed quando argines aquei
contrario ordine di&longs;po&longs;iti, vnus quidem depre&longs;&longs;us,
alter verò eleuatus &longs;upra aquæ libellam, tunc effici
tur a&longs;&longs;ularum &longs;eparatio, & fuga. Et in omnibus præ
dictis operationibus experitur, quod &longs;i vna prædi
ctarum laminularum fixè, & in quiete retineatur, &longs;eù
potiùs in ori&longs;icio va&longs;is exi&longs;tat, reliqua laminula li
bera, & non retenta, aut accedet, aut fugiet conta-
ctum alterius laminæ immobilis; cùm verò ambo li
berè in fluido innatant, tunc motus e&longs;t communis in
vtroque corpore, cum hac tamen differentia, quòd
corpus minùs amplum, & minùs pondero&longs;um veloci
orimotu, aut accedit, aut refugit à reliquo, cum è
contrà agitatio amplioris laminæ tardi&longs;&longs;imo, & lan
guido motu fiat. Et hæc e&longs;t vera, & accurata hi&longs;toria
huius admirandi effectus. non igitur miror
&longs;am huius effectus adductam non fui&longs;&longs;e, cùm non
ftabat
rationis, quæ tantummodò clarè, & euidentèr ob&longs;er
uari pote&longs;t mediantibus &longs;upradictis laminulis à m&etail;
excogitatis.
acce&longs;&longs;us, &
rece&longs;&longs;us cor
porum
rantium
omnibus &longs;u
is
tijs
tu
corpu&longs;culo
rnm
tium
amplexu |at
que fuga.
corpu&longs;culo
rum
tium
amplexu at
que fuga.
corpu&longs;culo
rum
tium
amplexu at
que fuga.
Hanc experientiam Amicis communicaui, quorum
quamplurimi adhùc po&longs;te à anno 1655 Florentiæ Sereni&longs;&longs;imo Ferdinando
Magno Duci, & Principi Co&longs;mo Hetruriæ, ac Mæ
c
nali Mediceo, qui humani&longs;&longs;imè nuperis &longs;uis literis
huius meæ o&longs;ten&longs;ionis, & ratiocinij à me tunc tem
poris adducti &longs;e optimè recordari &longs;crip&longs;it. In&longs;titut&atail;
po&longs;tea
cijs illis docti&longs;&longs;imis eamdem experientiam o&longs;tendi,
& innumeris præclaris viris variarum nationum, qui
bus præcipiente Sereni&longs;&longs;imo Cardinali offe
&longs;pectaculum &longs;electiorum experimentorum prædictæ
Academiæ.
Præter iam dictas nouitates
àcau&longs;a longè diuer&longs;a pendentem pro cuius intelli-
gentia recen&longs;eri priùs debet effectus &longs;atis vulgatus
duarum laminularum ex vitro exqui&longs;itè explanato, &
l
lantur, ampl
ma horizonti parallela &longs;ursùm eleuetur, pariter &longs;uc
cedit, trahiturque alia lamina contigua inferior, &longs;u
&longs;tineturque pendula, non &longs;ecùs, ac &longs;i e&longs;&longs;et &longs;uperiori
connexa conglutinataque, quod &longs;i &longs;uperna vitrea la
minula pauli&longs;pèr ad planum horizontis inclinetur,
tunc &longs;ubitò inferior laminula excurret versùs partem
decliuem plani &longs;uperioris ab&longs;que eo quod à &longs;uprema
lamina diuellatur, &longs;ed &longs;emper illi adhærendo de&longs;cen
det impul&longs;a ab in&longs;tinctu naturali, quo grauia conan
modo, quo po&longs;&longs;unt, &longs;cilicèt via inclinata, cum directa,
& perpendicularis fuerit impedita.
corpu&longs;culo
rum
tium
amplexu at
que fuga.
non quie&longs;cent, &longs;ed lateralitèr excurrent quou&longs;que ver
tices earum in eadem recta perpendiculari ad
horizontem extiterint.
HOc &longs;uppo&longs;ito &longs;int duæ guttulæ aquæ ABC, vna
DE, & alia FGH eleuata &longs;upra a&longs;&longs;ulam LM
&longs;uper aquam RS, tunc &longs;i vertex B &longs;uperioris guttulæ
tularum &longs;uperficies horizonti æquidi&longs;tantes G, & B
&longs;ibi mutuò congruent, & proindè nulla ratio &longs;uadet
vt guttulæ ip&longs;æ, & con&longs;equen tèr a&longs;&longs;iculæ lateralitèr
moueantur, cùm earum neutra
vim motiuam habeat
talem
uerentur horizonti
ter
tro grauium
neque mos e&longs;t naturæ fru&longs;trà
operari.
corpu&longs;culo
rum
tium
amplexu at
que fuga.
Fiat deindè contactus guttularum lateralis, &longs;cili
cèt &longs;uperficies &longs;ini&longs;tra AB, &longs;upremæ pendulæ guttu
læ tangat &longs;uperficiem dextram GH inferioris guttu
læ, tunc efficietur contactus, & &longs;uperficierum con
gruentia, non in vnico puncto &longs;icuti configuratio ea
rum tumida, & conuexa requireret, &longs;ed in &longs;atis &longs;en
&longs;ibili &longs;patio veluti e&longs;t IK, & hìc efficitur adhæ&longs;io, &
congruentia inter duas aque as partes non minori te
nacitate, quam duæ laminæ vitreæ &longs;uperiùs expo&longs;itæ
&longs;e &longs;e mutuò necte bantur, itaque difficile diuelluntur
prædictæ aquæ vna ab altera, &longs;ed facillimè pote&longs;t v
na &longs;uper&longs;icies &longs;uper alteram excurrere, vt aquæ &longs;lu
xibilitas requirit, igitur quia prædictæ guttulæ effi
ciunt contactum IK obliquum, & decliuem versùs
centrum telluris, nece&longs;sè e&longs;t vt guttula inferior gra
uis FGH exerceat natiuam &longs;uam vim de&longs;cen&longs;iua&mtail;
eo modo quo pote&longs;t, & ideò dilabetur, fluetque de
orsùm &longs;emper tamen &longs;uperiori guttulæ adhærendo,
& hoc eò v&longs;que fiet, quou&longs;que ad infimum &longs;itum de-
cliuitatis AB peru eniatur: non pote&longs;t verò deorsù&mtail;
illa fluere dilabique ab&longs;que eo quod eius vertex G
versùs culmen B approximetur; neque huiu&longs;modi
approximatio fieri pote&longs;t ab&longs;que eo quod lamin&atail;
&longs;ubiecta LM innatando lateralitèr moueatur versùs
S, & &longs;uprema lamina AC excurrat aliquanti&longs;pèr ver
sùs R, igitur nece&longs;sè e&longs;t, vt ambæ laminæ moueantur
lateralitèr, & propriùs ad &longs;e &longs;e accedant, & tunc præ
cisè quie&longs;cent, nec vlteriùs &longs;e promouebunt, quan
do præcisè obliquitas de&longs;cen&longs;us terminatur, &longs;cilicèt
adhæretque extremitati B guttulæ &longs;upremæ, & tunc
pr&ecedil;dicti vertices aliquo pacto explanantur, efficiun
turque horizonti æquidi&longs;tantes, quod efficitur me
diante vnione notabilis &longs;uperficiei in vtraque gut
tula, vnde &longs;equitur effectus quietis &longs;uperiùs expo
&longs;itus,
corpu&longs;culo
rum
tium
amplexu at
que fuga.
Tran&longs;eo iam ad alia experimenta difficiliora, pro
quorum declaratione præmitti debent aliqua lem
mata tum ex hydro&longs;taticis, cùm ex mechanicis.
mer&longs;um ne dum ab hoc &longs;ursùm exprimitur, &longs;ed etiam
later ali motu eius partes &longs;tringuntur.
COn&longs;tat ex coroll.
prop.
10. fluidi naturam con
&longs;i&longs;tentis talem e&longs;&longs;e vt partium eius inferiorum
æquabilitèr di&longs;po&longs;itarum, &longs;cilicèt horizontalitèr in-
ter &longs;e connexarum partes illæ, quæ &longs;unt magis pre&longs;
&longs;æ, impellant, ac&longs;ubleuent alias partes collaterales
&longs;ursùm, &longs;i fuerint minùs compre&longs;&longs;æ. Sed oporter&etail;
ait, Archimedes, vt conatus, & impul&longs;us fluidi pre
mentis fiant per lineas ad horizontem perpendicu
lares. Hoc profectò veri&longs;&longs;imum e&longs;t quotie&longs;cumqu&etail;
innatet intra aquam pri&longs;ma aliquod con&longs;i&longs;tens, &
durum; At &longs;i in va&longs;e BCEI aqua pleno intra &longs;patium
AIFG collocatur
um, &longs;ed aliud corpus molle, vel flui
dum cedens minùs graue &longs;peci&etail;,
quàm &longs;it aqua collateralis, tunc ne
dùm fluidi IG &longs;ursùm perpendicu
laritèr impelletur &longs;uperficies FG
versùs IA, &longs;ed præterea latus eius
AG propelletur
dem tempore, fluidum minùs graue IG &longs;imùl a&longs;cen
dat perpendicularitèr versùs IA, & lateralitèr quo
que ab AG versùs IF tran&longs;portetur. Hinc colligitur,
quod aqua, &longs;eù quodlibet fluidum BG grauius &longs;pe
cie, quàm corpus IG
pendicularitèr, &longs;ed etiam vim exercet lateralitèr
quidem per horizontales lineas BA, & HG, &longs;ed per
lineas inclinatas BK, & LG, & hoc &longs;uppleri Archime
deo a&longs;&longs;umpto debere cen&longs;eo, cùm in&longs;tinctu naturæ
corpora omnia grauia de&longs;cendere conentur versùs
terræ centrum, qulbu&longs;cumque modis hoc ab eis con
&longs;equi po&longs;&longs;it, nedum itinere perpendiculari ad hori
zontem, &longs;ed etiam inclinato.
corpu&longs;culo
rum
tium
amplexu at
que fuga.
bus
lib.
1.
corpu&longs;culo
rum
tium
amplexu at
que fuga.
Hoc po&longs;ito, &longs;i in
tio ABHG intelligatur collaterale pri&longs;ma AGFI ab
aere repleri, vel à quolibet alio fluido minùs graui
&longs;pecie, quàm &longs;it ip&longs;a aqua, tunc paries aqueus AG
nullo pacto &longs;u&longs;tine bitur in eodem &longs;itu erectus, &longs;ed
dilabetur &longs;&longs;uetque è &longs;upremo loco A versùs
F, neque oppo&longs;itum vnquàm contingere po&longs;&longs;et, vt
&longs;cilicèt
deret
&longs;ursùm perpendicularitèr aquæ infimam libellam FG
versùs IA propelleret perpendiculari motu, profe
ctò hoc contigeret &longs;i inter aquam, & aerem ade&longs;&longs;et
paries ligneus, à quo impediretur effluuium aquæ in
tra foueam AF; atnullo pariete interpo&longs;ito videtur
omninò impo&longs;&longs;ibile vt aqua non defluat motu incli
nato ad replendam cauitatem aHocqu&etail;
confirmatur euidenti experientia; fiat bur&longs;a coria
cea parallele pipeda &longs;ursùm aperta ad in&longs;tar putei,
& dilatatis quatuor eius angulis digitis, vel virgis,
immergatur bur&longs;a aere plena intra aquam; videbis,
quod nedùm ba&longs;is, & fundum, &longs;ed etiam quatuor fa
cies collaterales bur&longs;æ incuruantur conuexè versùs
intermedium axim eiu&longs;dem putei, & &longs;i &longs;imùl digiti,
aut virgulæ educantur, nec ampliùs vim exerceant,
nedùm bafis, & fundum putei a&longs;cendet &longs;ursùm, &longs;ed
etiam eius parietes collaterales &longs;e &longs;e con&longs;tringent, &
ad &longs;e &longs;e inuicem accedent, quod e&longs;t euidenti&longs;&longs;imum
&longs;ignum, aquam nedùm vim facere &longs;ursùm perpendi
cularitèr aerem expellendo, &longs;ed etiam lateralitèr
conari excurrere per lineas obliquas con&longs;tringendo
laterales parietes prædicti putei coriacei. Hinc in
ferre licèt, quòd &longs;i magis flexibiles, & cedentes fiant
parietes prædicti putei, &longs;emperque magis
tur
paries di&longs;tinguens aquam ab aere, tunc idip&longs;um
tinget
quo intra cauitatem aeream AF.
corpu&longs;culo
rum
tium
amplexu at
que fuga.
Si po&longs;tea loco aeris repleatur eadem fouea AIFG
alio fluido minùs graui &longs;pecie, quàm &longs;it ip&longs;a aqu&atail;
BG, v.g. repleatur oleo, dubitandum non e&longs;t
contingere, &longs;cilicèt nedùm ba&longs;is FG perpendicula
ritèr &longs;ursùm eleuabitur, &longs;ed etiam paries AG, &longs;eù
finium
pelletur versùs IF.
dum compre&longs;&longs;erit, quàm alia eius pars collateralis, hæc
do
ET hìc notandum e&longs;t non debere &longs;emper fluidum
in &longs;patio AF contentum rarius, & di&longs;trahibilius
e&longs;&longs;e, quàm &longs;it fluidum AH. Sed etiam &longs;i fuerit ma&longs;&longs;a
aquea eiu&longs;dem con&longs;i&longs;tentiæ, ac e&longs;t BG, dummodò
pondus, &longs;eù momentum fluidi BG maius &longs;it grauita
te alterius fluidi AF, impelletur quoque &longs;uperficies
AG (à qua fluida &longs;eparantur) tran&longs;uer&longs;ali motu ver-
nus erit momento &longs;ectoris a&longs;&longs;ulæ ligneæ 4 CD, & am
bo comprimunt partes aquæ &longs;ubiectæ C6, & CZ æ
què di&longs;po&longs;itas, & in directum continuatas, &longs;cilicèt &longs;u
pra eamdem libellam horizontalem BCY, igitur la
mina innatans AC approximabitur termino Y. eadem
ratione reliqua a&longs;&longs;ula lignea EH tran&longs;portabitur ver
sùs YT ab aqua &longs;ubiecta RF magis pre&longs;&longs;a, quàm col
lateralis aqua FZ, quaproptèr duæ a&longs;&longs;ulæ ligneæ AC,
& EG nece&longs;&longs;ariò ad &longs;e &longs;e accedent, & &longs;emper maiori,
& celeriori impetu, quò magis &longs;tringuntur coniun
gunturque, quia &longs;emper magis momentum aquæ in
terceptæ imminuitur; quod erat demon&longs;trandum.
corpu&longs;culo
rum
tium
amplexu at
que fuga.
aqueos conterminales, alter depre&longs;&longs;us, reliquus vero &longs;u
pra ciu&longs;dem libellam cleuatus: hæc &longs;ibi ip&longs;is approxima
tanon vnientur, &longs;ed motibus contrarijs vnum ab altero
fugiet.
IN eodem va&longs;e KVNL innatent duæ laminæ AC
ænea, & EH lignea quarum centra grauitatum 4
& 7, illa deprimetur efficietque argines depre&longs;&longs;os K
A, DG, hæc verò &longs;u&longs;tinebit argines eleuatos EG, &
IL &longs;upra eamdem aquæ libellam KL. & &longs;iquide&mtail;
prædicta duo innatantia corpora in tanta di&longs;tantia in
ter&longs;e remoueantur, vt terminus G conterminaliu&mtail;
arginum DG, & GE, &longs;cilicèt &longs;ummitas illius, & alte
rius infimus terminus pertingant præcisè vniantur-
que in eadem libella aquæ KL vt nimirùm figuræ cur
uæ earum in G planitiem horizontalem con&longs;tituant,
tunc con&longs;tat expe
rientia, quod in hac
di&longs;tantia, & in reli
quis omnibus maio
ribus ip&longs;a DF omni
nò quie&longs;cunt prædi
cta duo corpora innatantia in eodem &longs;itu æquilibra
ta, facta eadem con&longs;tructione o&longs;tendetur vt prius
(ex pr. 196.) quod momentum &longs;ectoris 4CE æqua
le e&longs;t momento portionis anuli aquei DCQG.
corpu&longs;culo
rum
tium
amplexu at
que fuga.
Accedant po&longs;tea ad &longs;e &longs;e lamina AC, & a&longs;&longs;ula EH,
procùl dubio terminus communis duorum contermi
nalium arginum non habebit figuram planam hori
zonti parallelam con&longs;titutam in eadem aqu&ecedil; libella
KL, vt priùs, quando nullam decliuitatem in puncto
G habebant, &longs;ed nece&longs;sè e&longs;t vt efficiant montuo&longs;am
eleuationem ETD valdè decliuem, quæ &longs;ecabit pla
num KL in T; & hoc patet, quia po&longs;t laminarum ap
proximationem oportet, vt &longs;upremus terminus G in
fimæ decliuitatis DG in&longs;inuetur versùs E, & recedat
ab infimo termino S &longs;upremæ accliuitatis SE, in quo
coniungebantur, & S, G in eodem plano libellæ KL,
exi&longs;tunt; ergo G infra ES penetrando termino E, at
que S termino D approximantur, & ideò tota &longs;uper
&longs;icies 3G cadet infra &longs;uperficiem S2E, & punctum 3
cadet infra T, & punctum 2 &longs;upra idip&longs;um,
decliuitas aquæ E2 in aere
nece&longs;sè e&longs;t vt aucta decliuitate vniatur cum infim&atail;
accliuitate D3, & ideò nece&longs;sè e&longs;t vt &longs;uperficies
po&longs;ita
quam priùs; & ducta perpendiculari TY &longs;upra MN,
eam &longs;ecet in Y & va&longs;is fundum in Z: & quia momen
tum portionis aquei anuli CDTY maius e&longs;t momen
to eiu&longs;dem &longs;ectoris aquei anuli
(non
negotio, nec noceat, vt dictum e&longs;t, &longs;ed quia eius
tuo&longs;a
ad perpendicularem
momentum integræ portionis anuli aquei CDGQ æ
qual emomento &longs;ectoris laminæ 4CD, igitur momen
tum portionis anuli aquei magis decliuis CDTY erit
maius momento &longs;e
ctoris laminæ 4CD,
& premunt ambo
partes aquæ &longs;ubie
ctas 4P, & CZ
tinuatas
ter di&longs;po&longs;itas &longs;upra idip&longs;um planum horizontale MB
CY, quapropter (ex demon&longs;tratis) prædicta lamina
AC di&longs;cedet, remouebiturque ab YZ. eadem ratio
ne reliqua a&longs;&longs;ula EH remoueri debet, fugereque à vi
cinia YZ, cum expelli debeat lateralitèr aqua &longs;ubie
cta RF vnà cum in&longs;i&longs;tente lamina, propterea quod à
magis pre&longs;&longs;a aqua FZ expelli debet; Patet igitur duo
corpora AC, & EH &longs;egregari debere, & vnum ab al
tero &longs;ugere quotie&longs;cumque duo eorum argines con-
trarij aquei mutuò connectuntur, quod erat demon
&longs;trandum.
corpu&longs;culo
rum
tium
amplexu at
que fuga.
corpu&longs;culo
rum
tium
amplexu at
que fuga.
Licèt ob facilitatem, & per&longs;picuitatem
tionis
gines eiu&longs;dem figuræ &longs;int in ambitu eiu&longs;dem corpo
ris innatantis, nihilominùs fieri pote&longs;t, vt circa vnum
latus eiu&longs;dem laminæ aqua eleuetur &longs;upra eius com
munem libellam, in altera verò parte deprimatur ef
ficiendo cauam montuo &longs;itatem, hocque in lamin&atail;
metallica fieri pote&longs;t inflectendo pauli&longs;pèr angulum
eius: idip&longs;um in quolibet alio corpore innatante
&longs;equi
factus, reliquus verò aridus, quod etiam effici pote&longs;t
&longs;i vngatur &longs;ebo, vel aliqua alia &longs;imili pinguedine vna
eius facies, & tunc prohiberi &longs;olet
rentia aquæ &longs;upra eius libellam; & in tali ca&longs;u contin
git vt idem corpus ex vna parte trahatur, ex alter&atail;
verò expellatur ab alio corpore innatante, &longs;cilicèt
quando argines &longs;imiles &longs;unt, aut ambo depre&longs;&longs;i, au
ambo eleuati, tunc efficitur acce&longs;&longs;us, &longs;ed quando ar
gines &longs;unt
& fuga vnius ab altero, & hæc omnia pendent ex ea
dem demon&longs;tratione.
denque
re innatante
fieri po&longs;&longs;une
argines con
trarij.
to altitudinem foueæ in aqua genitæ à de&longs;cen&longs;u laminæ
grauioris &longs;pecie ip&longs;a aqua, ad cra&longs;sitiem laminæ demer&longs;æ
proportionem minorem habere quàm grauitas &longs;pecifica ip
&longs;ius laminæ habet ad grauitatem aquæ in &longs;pecie.
corpu&longs;culo
rum
tium
amplexu at
que fuga.
IN va&longs;e KVZG aqua pleno innatet lamina æne&atail;
æquè cra&longs;&longs;a ABCD, quæ efficiat in aqua fouea&mtail;
KBCG, cuius altitudo SC & RB. dico SC ad DC mi
norem proportionem habere quam grauitas in &longs;pecie
ip&longs;ius laminæ AC habet ad aquæ grauitatem. quia
hydro&longs;taticis moles aquæ æqua
lis &longs;patio GKBC æquè ponde
rat, ac lamina AC vnà cum ae
re GKAD (qui ob in&longs;en&longs;ibilem
eius grauitatem negligi pote&longs;t)
& pondus ab&longs;olutum laminæ AC ad ab&longs;olutam gra
uitatem aquæ eiu&longs;dem molis AC eamdem proportio
nem habet quam grauitas &longs;pecifica laminæ AC ad
&longs;pecificam grauitatem aquæ, ergo grauitas laminæ ad
aquæ grauitatem in &longs;pecie eamdem proportione&mtail;
habet, quam pondus molis aquæ GKBC ab&longs;olutæ ad
pondus molis aquæ AC, &longs;eù proportionem, quam ha
bet moles GKBC ad molem AC: e&longs;t verò pri&longs;ma RB
CS minus &longs;olido inæqualium ba&longs;ium GKBC, ergo
pri&longs;ma RBCS ad AC &longs;eù altitudo SC ad DC minorem
proportionem habet, quàm laminæ AC grauitas in
&longs;pecie ad aquæ grauitatem. Itaque vulgata propo&longs;i
tio vera e&longs;&longs;et &longs;i &longs;patium cauitatis ab aere repletum
haberet parietes AK, & DG directos, & perpen
diculares ad horizontem, &longs;cilicèt &longs;i ba&longs;is KG æqua
lis foret ip&longs;i AD; at quia ob curuitatem in&longs;ignem &longs;u
perficierum AK & DG, &longs;emper altitudo CS ad cra&longs;&longs;i
tiem laminæ DC minorem proportionem habet
grauitas &longs;pecifica &longs;olidi AC ad eam,
& huiu&longs;modi proportio &longs;emper magis, ac magis im
minuitur, quò magis con&longs;tringitur ba&longs;is laminæ AC,
itaut po&longs;ito quòd lamina aurea AC &longs;it vige&longs;ies graui
or &longs;pecie ip&longs;a aqua, pote&longs;t adeò imminui ba&longs;is eius
AD vt altitudo arginum SD minor &longs;it quàm CD, cùm
tamen debuerat e&longs;&longs;e SD ad DC vt 19 ad 1, propterea
quod anuli triangularis SDG cra&longs;&longs;ities SG &longs;emper
e&longs;t eiu&longs;dem men&longs;uræ pote&longs;t adeo con&longs;tringi circulus
ba&longs;is AD interceptus vt valdè excedat prædictu&mtail;
circulum, & cylindrum interceptum, vt facilè o&longs;tendi
po&longs;&longs;et.
corpu&longs;culo
rum
tium
amplexu at
que fuga.
aquæ libellam demer&longs;i non e&longs;t præcisè æquale ponderi to
tius inn at antis corporis.
SEcundo loco operæpretium erit innuere quod ex
prædictis
pre&longs;&longs;is miris modis alterantur propo&longs;itiones illæ, quæ
in hydro&longs;taticis demon&longs;tratæ &longs;unt; quando enim effi
ciuntur argines eleuati; tunc moles aquæ æqualis &longs;pa
tio corporis
e&longs;t eiu&longs;dem ponderis, ac e&longs;t corpus ip&longs;um innatans,
quando quidem argines illi aquei
ues quoque &longs;unt, & &longs;u&longs;penduntur ob adhærentiam, &
connexionem cum a&longs;peritatibus externis eiu&longs;dem in
natantis corporis, at quia à prædicto pondere adiun
cto arginum grauius ab&longs;olutè redditur corpus præ di-
ctum, & ideò multò magis deprimitur, quàm &longs;i à præ
dicto anulo montuo&longs;o aquæ non grauaretur. huiu&longs;mo
di verò exce&longs;&longs;us in&longs;ignis e&longs;&longs;e pote&longs;t, &longs;i enim tabul&atail;
grandis metallica &longs;upra hydrargy rum innataret,
tuo&longs;itates
&longs;ed etiam aliquarum librarum excederet. Et hìc ani
maduertendum e&longs;t, quòd men&longs;ura demer&longs;ionis &longs;umi
non debet ab illis &longs;upremis terminis, quos
argines aquei eleuati, cùm hoc &longs;it manife&longs;tè fal&longs;um.