PHYSICI,
IN QVIBVS
De Motu Terræ Di&longs;putatur,
MARINI ÆSTVS NOVA
cau&longs;a proponitur,
libellam elevatio examinatur.
CARDINALEM FACCHINETTVM.
Sumptibus CHRISTOPHORI FOVRMY,
in vico Mercatorio, &longs;ub &longs;igno Occa&longs;ionis.
CVM PERMISSV SVPERIORVM.
PAGINATION
expono, Candidi&longs;&longs;ime Lector, elap&longs;o proxime Iu
nio ab Eminenti&longs;&longs;ime
NETTO,
in manibus habes, opu&longs;culum in lucem prodire volui, pro
&longs;umma illa, qua pollet humanitate, ad prandium invitatus
&longs;um, vt deinde pomeridianis horis, cum eruditi&longs;&longs;imis homini
bus, de nonnullis experimentis Phy&longs;icis di&longs;&longs;ertationem in&longs;ti
tuerem, cui Eminenti&longs;&longs;imus pro eo, quo e&longs;t in rem literariam
affectu, intere&longs;&longs;et. Aliquid fortè de me inaudierat
amici nunquam ferè de amico ni&longs;i hyperbolicè, illud, quod
in me &longs;entio, vel nullum, vel admodum tenue ingenium,
plus æquo efferre dignati &longs;uerant: parvi tamen, & hora
condicta adfui, quamvis alioquin tenuitatis meæ con&longs;cius, vt
morem Eminenti&longs;&longs;imo gererem; præ&longs;ertim; cùm opera pre
tium foret, Eminenti&longs;&longs;imum ab ea, quam per amicorum hy
perbolem, de me conceperat, opinione dimovere; quod mihi
&longs;anè pro votis &longs;ucce&longs;&longs;i&longs;&longs;e facilè crediderim, vbi me Emi
nenti&longs;&longs;imus vix balbutientem audivit. Vt vt &longs;it, de va
riis à nobis actum e&longs;t; &longs;ed præ&longs;ertim de motu Terræ, Maris
æ&longs;tu Aquarum & Mercurij in tubis erectis elevatione, alii&longs;
que huc pertinentibus. Cum autem is, quem &longs;ub Augu&longs;tini no
mine in &longs;cenam induxi, à me po&longs;t aliquot men&longs;es, efflagita&longs;&longs;et,
ta ip&longs;i con&longs;ignarem, &longs;atius fore putavi, &longs;i publicam in lucem
Typis mandata prodirent; cùm &longs;æpè accidat, vt ex amanuen
&longs;ium incuria, multi næ vi ac fœdi errores in ex&longs;cripta irre
pant. Cæterùm more Platonico & Tulliano Dialogi formam
adhibui, tum quia magis expedita e&longs;t, tum quia hoc ferè mo
do res ip&longs;aperact
facile intelliges, quam &longs;ub nomine Antimi vel doceo, vel
approbSihæc pauca tibi arri&longs;erint, dulci&longs;&longs;ime Lector, dabo
operam, vt alia quàm plurima iis &longs;uccedant; admi&longs;cui pau
ca Geometrica, non data opera &longs;ed ferè coastus, vt &longs;altem
inde videas, quantum Geometria, non modò vtilis, verùm
etiam nece&longs;&longs;aria &longs;it, ad res Phy&longs;icas pro dignitate pertractan
das. Vale.
hypothe&longs;i adducta, reijciuntur.
ILLA dies aibo &longs;ignata lapillo, qua me immerentem
&longs;anè, lauto &longs;imul & literatio convivio excepi&longs;ti,
CARDINALIS EMINENTISSIME, Nunquam mihi
venit in mentem, ni&longs;i & &longs;ingularis humanitatis tuæ, qua
tibi omnium animos arcti&longs;&longs;imè devinxi&longs;ti, & docti&longs;&longs;imo
rum illorum hominum, qui congre&longs;&longs;ui no&longs;tro interfue
runt, jucundi&longs;&longs;ima recordatio &longs;uavi&longs;&longs;imo voluptatis &longs;en
&longs;u animum meum perfundat : ita enim confabulando amœnus, promptus
arguendo, &longs;olvendo &longs;ubtilis, explicando elegans & limpidus omnibus no
bis vi&longs;us es, vt conjuncta eloquentiæ &longs;apientia, ad fundenda oracula, tua
voce, tuis verbis vti videretur. Vt autem perpetuum docti&longs;&longs;imi congre&longs;&longs;us
monumentum extet, cuius ego aliqua pars, licet exigua fui, literis illum &
typis con&longs;ignatum ad po&longs;teritatem tran&longs;mittere con&longs;titui; vt &longs;altem in
telligant homines, Eminenti&longs;&longs;imum Principem non politicis modò & gra
vioribus &longs;tudiis, verùm etiam amœnioribus literis plurimùm delectatum
fui&longs;&longs;e. Sed in &longs;cenam per&longs;onatos Actores induco, quos in arena literaria
di&longs;ceptantes audire priùs volui&longs;ti: &longs;ingulos facilè agno&longs;ces, quamvis enim,
vt fieri &longs;olet, nomina tantulùm mutata fuerint, eos tamen, in quos &longs;ingula
optimè quadrant, nullo negotio per&longs;picies Sed ad rem venio.
quod jamdudum à me de&longs;ideratam, hodierna die, abundè, vt &longs;pero, tui
copiam mihi facturus &longs;is; mirum enim, quanto eruditæ con&longs;uetudinis
&longs;tudio tenerime &longs;entiam, quæ grati&longs;&longs;imos, di&longs;cendi nova, & a&longs;&longs;equendi
hactenus incomperta, igniculos in me accendit, & quadam, vt &longs;ic loquar,
vellicatione. Ingenium &longs;timulat, ad ea nonnunquam expromenda, quæ lon
ga meditatione, & repetita cogitationum huc illuc ver&longs;atione, vix vnquam
elici potui&longs;&longs;ent. A te igitur illa audire percupio, quæ & &longs;itim meam ex
tinguant, & opinionem de te meam, quamvis alioquin maximam longè
&longs;uperent & po&longs;t &longs;e relinquant.
Hoc ip&longs;um tibi à me dictum e&longs;&longs;e puta; huc venis, Antimo,
vt doceas, non verò vt di&longs;cas; & &longs;i fortè identidem à me aliquid oppo-
lucem extorquendam. Eminenti&longs;&longs;imus Princeps, eo animo te invitavit,
vt cùm de te multa à nobis inaudii&longs;&longs;et, de rebus Philo&longs;ophicis di&longs;&longs;erentem
audiret; & non modico huiu&longs;ce rei de&longs;iderio teneri &longs;e, nobis &longs;emel atque
iterum &longs;ignificavit.
Quid tandem à me expromi queat, quod Eminenti&longs;&longs;imi auri
bus dignum &longs;it, profectò non liquet; quicquid enim, etiam cum aliquo
mentis ni&longs;u excogito, nugas inter & qui&longs;quilias mihi &longs;emper huc v&longs;que
reponendum e&longs;&longs;e vi&longs;um e&longs;t, qua&longs;i verò mea pluris faciam, quàm me?
Dic, vt voles, illud &longs;altem con&longs;tat, quidquid vel ex tuis lu
cubrationibus, vel ex tuo di&longs;&longs;erentis ore accepi, mihi &longs;ummoperè pla
cui&longs;&longs;e: vnum tamen e&longs;t, ne quid di&longs;&longs;imulem, quod in te aliqui de&longs;ide
ra&longs;&longs;ent, ne &longs;cilicet tanto adversùs Copernicanam hypothe&longs;im odio flagra
res, in quo nonnullis paululùm excedere mihi vi&longs;us es; poteras haud du
biè oppo&longs;itam &longs;equi, quam & ego demi&longs;&longs;a fronte o&longs;culor, cum iis præ&longs;er
tim, qui Eccle&longs;ia&longs;ticam vitam amplexi, Pontificiis &longs;tare debent decretis,
quibus in Galileum eiu&longs;dem &longs;ententiæ egregium & nunquam &longs;atis lauda
tum propugnatorem animadver&longs;um e&longs;t; &longs;ed non erat, quod tam alienum
animum o&longs;tentares.
Vix me teneo, Augu&longs;tine, dum hæc à te audio, præter omnem
expectationem meam: odium vocas contrarium &longs;en&longs;um, ab&longs;que vllo im
moderato affectu, in iis præ&longs;ertim, in quibus opinari, cuique liberum
e&longs;t. Nullo, crede mihi, odio, nullo contentionis &longs;tudio ducor; &longs;ed cùm
quædam in hypothe&longs;i Copernicana di&longs;pliceant, quæ in oppo&longs;ita nullum
mihi negotium face&longs;&longs;unt, facere non potui, quia hanc illi anteponerem;
nunquam tamen inficias iturus, præclarum inventum e&longs;&longs;e; Copernicum
A&longs;tronomorum &longs;ui temporis principem jure cen&longs;eri, eumque Galileum
fui&longs;&longs;e, qui nulli, quod &longs;ciam, impar ingenio æ&longs;timandus &longs;it, quique eo no
mine vel maximam gloriam &longs;ibi comparavit, quod argumenta, quibus
præfata hypothe&longs;is impugnabatur, ita diluerit, vt maximo inde plau&longs;u re
lato, ii&longs;dem illam potiùs confirma&longs;&longs;e videatur, cùm vero certum &longs;it, nec
ip&longs;e Galileus hoc inficietur, nullam demon&longs;trationem hucu&longs;que excogi
tatam fui&longs;&longs;e, qua hypothe&longs;is Copernicana probetur, ab antiqua illa, quæ
terram in mundi centro immobilem ad&longs;truit, di&longs;cedendum e&longs;&longs;e non puta
vi; præ&longs;ertim cùm hæc novis argumentis, &longs;i non demon&longs;trari, plurimùm
&longs;altem confirmari po&longs;&longs;it, quibus, vt liberè dicam, quod &longs;entio, mihi valdè
per&longs;ua&longs;um e&longs;t, hanc multis nominibus alteri e&longs;&longs;e anteponendam.
Docti&longs;&longs;imis illis, tui certè amantibus, & quos &longs;ingulari etiam
cultu per&longs;equeris, haud modicum ri&longs;um moveres,
rent, nec vllum mihi dubium e&longs;t, quin per jocum, vel ironiam hæc à te
dici putarent, vtpote qui apprimè &longs;cias, Copernicanam hypothe&longs;im iis
rationum momentis in&longs;tructam e&longs;&longs;e, quæ vt demon&longs;trationem Geometri
cam minimè adæquant, quod certè vltrò damus, ita proximè ad eam acce
dunt, atque adeò communi Doctorum omnium con&longs;en&longs;u longè aliâ pro
babiliorem jure cen&longs;eri.
Hebetiori, quæ&longs;o, ingenio igno&longs;ce, optime Augu&longs;tine, quod
energiam illam rationum, quæ pro Copernico militant, nondum a&longs;&longs;equi
potuit; nec mirum profectò, lippos enim oculos &longs;ubtilia fallunt, ac &longs;e&longs;e
iis &longs;ubducunt; quate vt &longs;um inprimis veritatis amans, me tibi plurimùm
ob&longs;trinxeiis, &longs;i præfatas rationes ea mihi claritudine exponas, quâ, vt mi
rificè vales, ita & mihi opus e&longs;&longs;e fateor, ad debiliores mentis oculos re
creandos.
Non legi&longs;ti apud Galileum, ita limpidè ac per&longs;picuè explica
tas, vt nihil meo judicio, clarius aut liquidius legi po&longs;&longs;it?
Legi haud dubiè; Vt enim Authorem illum maximi facio, ita
nihil ab eo in publicam lucem editum fuit, quod &longs;tatim avidè &longs;æpè ac &longs;æ
piùs non legerim; hoc tamen tibi per&longs;uadeas, velim, prædictas rationes,
quamvis alioquin eleganti&longs;&longs;imè ab eo explicatas, illa vi & nervo, vt dicis,
pollere mihi non videri, &longs;ingulas accuratè perpendi & ponderavi, nec op
po&longs;itæ &longs;ententiæ &longs;tudium obfuit; nam crede mihi; vnius dumtaxat veri
tatis amore ducor, quam &longs;ive Copernicus porrigat, &longs;ive Ptolemæus, &longs;ive
Ari&longs;toteles, &longs;ive Democritus; illa æquè grata & chara mihi &longs;emper accidit. Sed quæ&longs;o te, periculum faciamus, vt &longs;altem dum no&longs;tri venerint, hoc mo
dicum tempus cum æ&longs;tu fallamus.
Per me licert &longs;ed cur&longs;im, iis tamen prætermi&longs;&longs;is, quæ inter
Academicos quidem, non tamen inter Philo&longs;ophos locum obtinent, quas
potiùs rationum vmbras, quàm veras rationes appellare &longs;oleo.
Optimè judicas, quid enim juvat, tantirem momenti levi&longs;&longs;imis
fulcire adminiculis: Nonnulla obiter indico. Sol, inquiunt, tes inter cor
poreas nobili&longs;&longs;imus, in nobili&longs;&longs;imo loco, &longs;cilicet in mundi centro, collo
cari debuit; qua&longs;i verò infimus locus &longs;upremo nobilior reputandus &longs;it, &
tenebro&longs;us orcus radianti præferendus Empyreo: &longs;ed pergunt, qui&longs;quis
alterius operâ indiget, ad illum accedere debet, neque hunc, &longs;ed illum
moveri par e&longs;t; cùm igitur reliqua corpora benigno Solis influxu indi
geant, hunc certè immotum con&longs;i&longs;tere, illa verò circa perennem illum
beneficæ naturæ fontem ite oportuit. Bellè profectò; Solem rerum crea
tarum Principem faciunt, qui tamen omnibus &longs;ervit, & non modò ani
mantibus, verùm etiam plantis dignitate cedit; Æquum igitur e&longs;t, vt circa
terram eat, cuius gratia conditus e&longs;t, non verò vt tellus eiu&longs;que incolæ
circa Solem ite cogantur. Denique ex culina ip&longs;a nova depromunt argu
menta; Videmus, inquiunt,
certè rationi con&longs;entaneum e&longs;&longs;e videtur; quidni ergo pariter terre&longs;tris
globus, qui calore Solis foveri & recreari debet, circa Solem, non Sol cir
ca terram volvatur? Hoc argumentum culinam olet, vnde profectum e&longs;t.
Sed hæc omittamus, quæ no&longs;tri per jocum potiùs, quàm &longs;eriò
dixerunt; ad &longs;eria igitur & gravia, quæ nobis non de&longs;unt, veniendum e&longs;t:
illud inprimis maximi ponderis e&longs;&longs;e videtur, quod in hypothe&longs;i no&longs;tra
(&longs;ic eam di&longs;putan di gratia deinceps appellabo) per &longs;implici&longs;&longs;imum eum
que proprium motum omnia explicemus, ablegatis alienis motibus,
illoque præ&longs;ertim, quem raptus vocant, primi &longs;cilicet mobilis, quo ab Ortu
fixa &longs;ub Æquatore, vnico temporis minuto leucarum miriadas conficiat,
quod certè non fidem modo, verùm etiam cogitationem ip&longs;am &longs;uperat. Hunc porrò motum ablegamus, & &longs;implici ac diurna telluris globi circa
&longs;uum centrum turbinatione, &longs;eu revolutione præfatum motum &longs;up
plemus.
Ab hoc vltimo incipio; quia nonnulli multam vim in eo fa
ciunt; cum tamen me parum, aut nihil pro&longs;us afficiat; nempe diver&longs;as
motuum velocitates per comparationem quamdam optimè intelligimus;
Sit enim quodlibet terræ punctum in æquatore, &longs;uppo&longs;ita ve&longs;tra hypo
the&longs;i, illud, vt probè no&longs;ti, in turbinatione præfati globi, præ&longs;cindendo
a motu centri, ita movetur, a&longs;&longs;umpto &longs;cilicet, quodam medio motu, vt vo
cant, vt &longs;ingulis horis 900. circiter miliaria Italica conficiat, 15.verò &longs;in
gulis minutis primis, vno denique &longs;ecundo minuto, 250. pa&longs;&longs;us geome
tricos, hoc e&longs;t 1250. pedes; vt autem comparationem in&longs;tituam, con&longs;ide
ro motum glandis plumbeæ ex maiore catapulta explo&longs;æ, quæ vno &longs;ecun
do minuto 1000. pedes circiter conficit; vnde vides punctum illud paulò
dumtaxat velociùs moveri.
Su&longs;tine tanti&longs;per; ne&longs;cio quid intelligas per illum medium
motum.
Intelligo motum æquabilem, ita vt &longs;ingulis horis punctum
illud æquale &longs;patium decurrere cen&longs;eatur, cùm tamen &longs;ecus ac
cidat.
Non capio, exi&longs;timo enim rem ita e&longs;&longs;è, & æqualibus tempo
ribus, æqualia &longs;patia decurri.
Ita &longs;anè nobis apparet, id tamen haud dubiè per errorem;
nempe punctum illud motu quodam mixto movetur, ex motibus orbis
& centri, &longs;ic enim vocare &longs;oles; Vnde fit, vt pro diver&longs;o ad &longs;olem a&longs;pectu,
modò tardiùs, modò velociùs moveatur; quia motus orbis ab hora &longs;exta
ve&longs;pertina ad &longs;extam oppo&longs;itam matutinam additur motui centri, ab hac
verò ad illam detrahitur; ac proinde punctum illud in meridie collocatum
tardi&longs;&longs;imè in a&longs;pectu oppo&longs;ito, &longs;cilicet, mediænoctis, veloci&longs;&longs;imè movetur
quod vt ad rudiores calculos reducam, &longs;uppono, exempligratia, diametrum
magni orbis, quem Sol&longs;ecundùm meam, & terra &longs;ecundùm ve&longs;tram hypo
the&longs;im decurrit, continere diametros terræ 2000. hoc po&longs;ito, motu centri,
vno &longs;ecundo minuto, decurruntur pedes circiter 6942. & motu orbis pe
des 1250. adde vnum alteri, venient pedes 8192.hoc e&longs;t &longs;patium, quod di
ctum punctum decurritin media nocte, tempore vnius &longs;ecundi minuti
detrahe verò, erunt pedes 5692. hoc e&longs;t, &longs;patium, quod eodem tempore,
decurrit in meridie; Vides inæqualitatem. Semoto igitur illo inæquali
motu, ex motibus orbis & centri re&longs;ultante, æqualem tantummodò con&longs;i
dero motum orbis, quo punctum terre&longs;tris globi in Æquatore, &longs;ingulis mi
nutis &longs;ecundis, pedes circiter 1250.decurrit.
Quid tum?
Non video, quid tibi velis, ad infirmandum
illud argumentum, quod ab incredibili velocitate motus raptus, &longs;eu
Jam iam videbis.
Suppone terre&longs;tem globum in mundi centro,
eo motu orbis torqueri, de quo &longs;upra; &longs;uppone radium à centro terræ
in Æquatoris plano ductum indefinitè, vt aiunt, id e&longs;t, ad quamcumque
longitudinem productum, eatque per centra Lunæ, Solis, lovis, Satur
ni, & cuiu&longs;piam &longs;tellæ fixæ, ac &longs;imul totus radius, eo, quo dixi orbis mo
tu, moveatur circa immobile centrum; certè po&longs;ito quod Luna di&longs;tet a
terra 50. &longs;emidiametris terre&longs;tris globi, velocitas motus Lunæ ad veloci
tatem puncti Æquatoris in quo dictus radius terræ &longs;uperficiem &longs;ecat e&longs;t
in ratione
centro terræ 2000. &longs;emidiametris e&longs;t in ratione
Iovis motum, erit in rationne
nique ad &longs;tellæ fixæ motum in ratione, &longs;tatue, vt voles, an fortè
vt fixarum di&longs;tantia à mundi centro &longs;it dupla di&longs;tantia Saturnij, tibi non
&longs;ufficit? Ponamus
an verò cogitationem omnem &longs;uperat, vnum motum e&longs;&longs;e ad alium in ra
tione quater decupla, immò centupla & millecupla? Crede mihi, hi &longs;unt
effectus imaginationis in fraudem inductæ; Vbi enim &longs;emel &longs;tatuitur vnus
motus, & huius cum aliis comparatio, huiu&longs;modi terricula illicò eva
ne&longs;cunt.
Rem probè intelligo; & &longs;anè miror, nonnullos in hoc argu
mento tantam vim & energiam agnovi&longs;&longs;e, vt præ cæteris ad illam hypo
the&longs;im confirmandam adhibendum e&longs;&longs;e putarint: non erat etiam
quod aliqui antiqui &longs;y&longs;tematis a&longs;&longs;ertores, & acerrimini propugnato
res ad divinam potentiam confugerent, licèt illa in tanta motuum
velocitate mirificè &longs;plende&longs;cere nec non &longs;uas partes agere vi
deatur.
Rectè mones, Augu&longs;tine, huc divina potentia accer&longs;enda
non e&longs;t, cùm ex mera motus naturalis acceleratione, hæc eadem pe&longs;picua
e&longs;&longs;e con&longs;tet; &longs;ic enim v. g. motus glandis ex catapulta explo&longs;æ, vt dictum
e&longs;t &longs;upra, quo &longs;cilicet vno &longs;ecundo minuto, glans pedes circiter 1000.
decurrit, æquabilis e&longs;&longs;e &longs;upponitur; iam verò &longs;i eadem catapulta &longs;ursùm
rectà explodatur, de 500.dumtaxat pedes motu retardato glans perveniet,
& in de&longs;cen&longs;u eundem velocitatis gradum motu accelerato acquiret;
cùm igitur quælibet altitudo a&longs;&longs;umi queat ad libitum, ex qua corpus
grave de&longs;cendat motu accelerato, quilibet etiam velocitatis gradus ob
tineri pote&longs;t; quo dato tempore, datum quodlibet &longs;patium, motu æqua
bili decurratur, igitur prædicta motuum velocitas inter præcipua divi
næ potentiæ miracula minimè reponenda e&longs;&longs;e videtur; quamquam, ne
que hîc dee&longs;t, vnde divinam potentiam homines laudent, cùm id in &longs;a
cris literis nobis innuatur, laudet que P&longs;almi&longs;ta Dominum, ex pernici&longs;&longs;i
mo Solis motu, nec e&longs;t, quod Heterodoxi, qui &longs;acræ Scripturæ ita &longs;e ad
hærere patant, a literali eiu&longs;dem &longs;en&longs;u, vnius Copernici gratia di&longs;cedant,
ea&longs;que laudes ex eo capite &longs;upremo cœlorum Conditori atque motori
Deo, gratis, vt aiunt, recu&longs;ent.
Benè e&longs;t, in hoc vterque convenimus, &longs;ecùs fortè in alio
puncto, à me propo&longs;ito, quod à facilitate & &longs;implicitate &longs;y&longs;thematis peti
tur; vno enim, vel altero terre&longs;tis globi motu no&longs;tra hypothe&longs;is con&longs;tat,
cùm tamen ve&longs;tra motus ita multiplicet, etiam &longs;ibi invicem contrarios, vt
res illa, vel omnino impo&longs;&longs;ibilis, vel &longs;altem maximè difficilis e&longs;&longs;e videa
tur.
Primo &longs;anè a&longs;pectu, rem i&longs;tam minùs &longs;edulò con&longs;ideranti, ita
e&longs;&longs;e videtur; &longs;i tamen penitiùs illam in&longs;piciamus; primum errorem faci
lè ca&longs;tigabimus: & verò vt in vno Solis &longs;y&longs;temate periculum facia
mus, quotuplice motus opus e&longs;&longs;e putas ad &longs;alvanda omnia phæno
mena?
Duo motus, ni fallor, omnia &longs;alvant, orbis &longs;cilicet & centri,
terre&longs;tris globi, quie&longs;cente Sole in mundi centro.
Tibi omnino impo&longs;itum fuit, vel vt verius puto, tibi excidit,
Primò enim, motu
&longs;ignorum, nec qui&longs;quam hoc negat: Secundò, motu orbis diurno, quo
terra ita rotatur, vt pars &longs;uperior globi tendat in ortum; hîc autem mo
tus fit circa axem mundi, vel plani Æquatoris. Terrius motus nece&longs;&longs;a
rius e&longs;t, annuus &longs;cilicet, quo terra ita &longs;emel voluitur circa Axem Eclipticæ,
vt pars inferior, quæ Solem &longs;pectat, tendát in ortum; hoc enim motu obti
netur, vt Axis Æquatoris &longs;ibi ip&longs;i &longs;emper maneat parallelus; aliquis fortè
per incogitantiam quartum motum etiam adhiberet, quo &longs;cilicet Axis
Æquatoris vtrimque de&longs;cribit circulos polares, circa polos Eclipticæ, &longs;ed
hic motus à tertio diver&longs;us non e&longs;t, vt con&longs;ideranti patebit, & licèt aliqui
etiam ex iis, qui terram mobilem ad&longs;truunt, hunc diver&longs;um motum &longs;ta
tuant, ego tamen, vt &longs;incerè tecum ago, diver&longs;um à motu orbis annuo mi
nimè &longs;tatuo. Addo denique quartum motum Solis, circa proprium cen
trum, axemque immobilem, & inclinatum ad planum Eclipticæ, &longs;ine quo
macularum motus 27. circiter dierum explicari nequit: hunc etiam ne
mo ve&longs;trum inficiatur.
Cuncta hæc et&longs;i vltro damus, nihil tamen ob&longs;tat, quin adhuc
&longs;y&longs;tema no&longs;trum &longs;implicius e&longs;&longs;e dicamus, & ex paucioribus motibus,
quàm ve&longs;trum componi. Ve&longs;trum enim, &longs;i rectè memini, in vno Solo 7.
vel 8. motus po&longs;tulat. Primus e&longs;t motus raptus, &longs;eu primi Mobilis ab or
tu ad occa&longs;um, &longs;cilicet diurnus: &longs;ecundus, motus in Ecliptica annuus;
tertius, motus Solis circa proprium axem inclinatum, ferè men&longs;truus:
quartus motus eju&longs;dem circa axem erectum ad planum Eclipticæ, an
nuus: quintus motus prioris axis inclinati, de&longs;cribentis vtrinque circellos
circa Solarem axem erectum ad planum Eclipticæ, item annuus: &longs;extus,
motus Apogæi Solis iuxta &longs;eriem &longs;ignorum: &longs;eptimus motus præce&longs;&longs;io
nis Æquinoctiorum; octavus motus obliquitatis Zodiaci, vt vocant: et&longs;i
fortè mutetur excentricitas, de quo nonnulli dubitarunt: nonus motus
adjiciendus e&longs;&longs;et; vides, quantam motuum farraginem &longs;y&longs;tema ve&longs;trum
po&longs;tulet: quorum aliqui, cùm &longs;int oppo&longs;iti, vt annuus & men&longs;truus &longs;olaris
globi, quantumvis circa diver&longs;os axes, nec aliunde in &longs;olarem &longs;phæram
ture cuipiam impo&longs;&longs;ibiles videbuntur.
& dubito, an &longs;eriò, an verò per iocum hæc dicas; tu quoque imponere
mihi cogitabas; Apage igitur prefatam motuum farraginem; ego enim
vnum dumtaxat, cumque &longs;implici&longs;&longs;imum motum admitto in &longs;olari &longs;y&longs;te
mate, quod ne&longs;cio, an mirum tibi accidat.
Mirum pror&longs;us, immò fal&longs;um, neque id, opinor mihi vn
quam per&longs;uadebis; cum per&longs;picuum &longs;it (neque ve&longs;tri hoc negant) ad Sal
vanda cuncta phænomena, prædictos omnes motus, &longs;i fortè vltimum ex
cipias, quem non ita omnes a&longs;&longs;everanter ad&longs;truunt, nece&longs;&longs;arios e&longs;&longs;e.
Ne quæ&longs;o dubites, vbi rem a me intellexetis, tibi fortè per
&longs;uaderi &longs;ines; ea quippe dicam quæ, ni fallor, luce meridiana clariora &longs;int. Sol vno Eodemque motu &longs;implici&longs;&longs;imo movetur ab ortu ad occa&longs;um, &longs;ub
Ecliptica
deor&longs;um, &longs;ini&longs;tro&longs;um; & rotatione, &longs;eu turbinatione, circa axem æquè in
clinatum ad planum Eclipticæ, ac &longs;ibi &longs;emper parallelum. En tibi mo
tum &longs;implicidimum, quo &longs;uppo&longs;ito, cuncta facile ac planè explicantur.
Non intelligo; immò hæc mihi ab&longs;urda & repugnantia e&longs;&longs;e
videntur; nec capere po&longs;&longs;um, quî fiat vt omnia facile & plané hoc modò
explice utur.
Cuncta &longs;eor&longs;im explico, Cogita, &longs;i vis, Solem à puncto Æqui
noctij verni ab ortu ad occa&longs;um ita ferri, vt po&longs;t 24. horarum motum,
orbem &longs;uum nondum ab&longs;olverit, &longs;uper&longs;itque vnus ferè gradus, paulò
minùs; fing
&longs;igna vtriu&longs;que loci in cœlo ve&longs;tigia, atque ita deinceps moveri Solem
puta, &longs;ignatis &longs;ingulorum locorum ve&longs;tigiis; vbi verò Sol ad Tropicum
Cancri pervenerit, &longs;uppone qua&longs;i repercu&longs;&longs;um versùs Au&longs;trum eodem
modo deflectere, multiplicatis revolutionibus, donec ad Tropicum Ca
pricorni perveniat, a quo eodem modo versùs Boream deflectat donec
tandem ad Æquatorem denuò redeat; per &longs;ignata ve&longs;tigia &longs;i ducas circu
lum,, erit Ecliptica, quam circa mundi Axem finges moveri, & ab eius
polis circulos polares de&longs;cribi; ita autem &longs;ol attemperat reciprocam il
lam inclinationem, &longs;eu declinationem versùs Au&longs;trum & Boream, vt
nunquam à prædicto Eclipticæ circulo di&longs;cedat, quod quomodò obtineat,
paulò po&longs;t dicam.
Sed i&longs;ti &longs;unt duo motus, alter cuiu&longs;dam qua&longs;i librationis, al
ter circularis.
Vnicus e&longs;t motus, augu&longs;tine, &longs;ed per modum &longs;piræ; quis enim
negat turbinem proiectum &longs;implici motu moveri, id e&longs;t, eodem impetu
ad talem lineam determinato; nempe hoc &longs;uppono cerrum, ex alibi firma
ta motuum doctrina, eundem impetum ad diver&longs;as lineas determinati po&longs;
&longs;e, &longs;ic pila repercu&longs;&longs;a &longs;implici motu movetur, licet linea motus per quam
feretur, duplicem determinationem &longs;upponat &longs;cilicet à linea motus
directi, & à plano reflectente; Non e&longs;t igitur dubium, quin prædictus Pati modo cogita Solem &longs;imul inclinari
ab Apogeo ad Perigeum, & vici&longs;&longs;im, hæc &longs;ecunda determinatio, vel in
clinatio &longs;implici motui non obe&longs;t, vt patet: In hoc porrò motu, Ecliptica
etiam mo
Solari globo eadem &longs;emper e&longs;t; denique, finge, Solem circa &longs;uum cen
trum ita revolvi 27. circiter dierum &longs;patio, ab ortu in occa&longs;um, ratione il
lius hemi&longs;phærij, quod ad terram &longs;pectat, vt axis, circa quem voluitur, in
clinatus &longs;it ad Eclipticæ planum, & &longs;ibi &longs;emper parallelus; quod &longs;anè &longs;im
plicitatem motus non de&longs;truit; &longs;ic enim &longs;æpè ac &longs;æpiùs globos projicimus;
imò hic naturalis e&longs;t globorum motus.
Duo &longs;unt motus, ni fallor, orbis, &longs;cilicet, & centri &longs;implex
igitur motus non e&longs;t.
Igitur motus naturalis, quo corpus grave, v.g. globus fertur
deor&longs;um non e&longs;t motus &longs;implex, &longs;ed mixtus, quod nemo dixerit, cum &longs;im
plici&longs;&longs;imus &longs;it, vtpote ab eodem principio, &longs;cilicet à gravitate: &longs;i enim de
mittas globum, primò quidem per planum inclinatum, ex quo inde per li
berum aëra perpendiculariter de&longs;cendat, videbis illicò duos illos motus
quos dicis, centri & orbis; qui tamen reverà duo motus non &longs;unt, &longs;ed vnus
ab vna eademque gravitate profectus.
Nonnulli ex ve&longs;tris, vt &longs;alvent paralleli&longs;mum illius axis, cir
ca quem Sol revolvitur, adhibent alium motum revolutionis annuum cir
ca Solis axem, axi Eclipticæ parallelum.
Ita pror&longs;us.
Sed e&longs;t motus fictus, eo fine, vt meliùs res illa in
telligatur: vt enim terra circa axem axi Elipticæ parallelum revolui dici
tur annuo motu, in ve&longs;tra hypothe&longs;i ab occa&longs;u ad ortum, ratione hemi
&longs;phærij ad Solem ver&longs;i, vt axem, circa quem fit motus diurnus, &longs;emper pa
rallelum &longs;ervet, ita pror&longs;us &longs;olaris globus revolui dicendus e&longs;t annuo mo
tu, ad prædictum phœnomenum Axis paralleli &longs;alvandum; &longs;ed vtrimque
hic motus fictitius e&longs;t, cùm &longs;implex turbinationis motus &longs;ufficiat, circa
Axem inclinatum ad planum Eclipticæ, &longs;emper &longs;ibi ip&longs;i parallelum. Ana
logiam habes in acu magnetica, quæ cum pixide &longs;ua ita movetur, vt &longs;ine
novo motu, &longs;ibi parallela &longs;emper maneat.
Igitur non tres, aut quatuor motus in
tuendi &longs;unt, vt &longs;upra dicebas; cum vnus duntaxat, eo quo explicas modo
&longs;ufficiat: cur ergo quatuor nece&longs;&longs;arios e&longs;&longs;e fingis?
Iuxta morem ve&longs;trorum, & aliorum locutus &longs;um, qui prædictos
motus di&longs;tingunt; fateor tamen, in ve&longs;tra hypothe&longs;i, duos motus &longs;uffice
re, alterum turbinationis in terre&longs;tri globo, &longs;ervato, vt dixi, paralleli&longs;mo
Axis; alterum &longs;implicis revolutionis in Sole, circa Axem pariter inclina
tum, vt dixi, ad planum Eclipticæ. In no&longs;tra verò vnus duntaxat motus
&longs;ufficit turbinationis, circa axem pariter inclinatum ad planum Eclipticæ,
& &longs;ibi &longs;emper parallelum, cum gemina illa inclination ereciproca, in Bo
ream, & Au&longs;trum, & &longs;ur&longs;um atque deor&longs;um; &longs;ic turbo actus, orbes &longs;uos
ita de&longs;cribit, vt aliquando majores, aliquando minores &longs;int; quod certè,
vt dixi, &longs;implicitati motus turbinationis non ob&longs;tat: Ex his autem, vt
hoc &longs;altem primo capite, ve&longs;træ anteponenda.
Omittis duos alios motus, quos adhibent, &longs;cilicet obli
quitatis Zodiaci, præce&longs;&longs;ionis Æquinoctiorum, & fortè mutationem
excentricitatis.
Vobis æquè atque nobis prædicti motus explicandi e&longs;&longs;ent; &longs;ed
negotium neutri parti face&longs;&longs;unt, cùm &longs;emper eadem maneat Zodiaci
obliquitas, &longs;emper eadem excentricitas; quod verò &longs;pectat ad Æquino
ctorium præce&longs;&longs;ionem, tu illam explicare potes, adhibito tardi&longs;&longs;imo &longs;tel
larum motu, ortum versùs, ego verò, &longs;i dicam, paulò tardiùs &longs;tellas move
ri ab Ortu ad Occa&longs;um, quàm
tum versùs recedere à punctis Æquinoctiorum, id e&longs;t à &longs;ectionibus Æqua
toris & Æclipticæ; neque in hoc alia re&longs;tat difficultas, atque adeò, tuum
illud primum argumentum &longs;olutum manet; iam propone alia, &longs;i quæ
habes.
Vt vt &longs;it, Negari non pote&longs;t, quin no&longs;tra hypothe&longs;is ad
calculos A&longs;tronomicos magis accommodata &longs;it.
vtrinque &longs;imiles ferè calculi adhibendi &longs;int, ad quem finem, non realibus
& veris, &longs;ed fictitiis orbibus vtimur; omi&longs;&longs;o diurno Solis motu, fingimus
Solem moveri in Ecliptica motu annuo, item Apogæi motum, cum fictitio
circulo, &longs;eu circello ad calculos reducimus; &longs;ic calculis vtimur ad rationes
dati & accepti firmandas; cuncta igitur hæc ad calculationem adhiben
tur, cùm res perinde &longs;e habeat. atque &longs;i ita e&longs;&longs;et.
In quo, vt vides, nulla e&longs;t
difficultas. Sed de hoc argumento plura infra, &longs;i hoc tibi gratum accidat:
iam verò reliqua exprome, &longs;i quæ habes adversùm nos.
Crede mihi, Antime, abundè &longs;uppetunt, illudque in
primis, quod in hac mea hypothe&longs;i planetarum pa&longs;&longs;iones ea facilitate ex
plicantur. quá ne&longs;cio an major ex cogitari po&longs;&longs;it; puta &longs;tationes, retrogre&longs;
fiones, accelerationes &c.
Hic profectò Achilles ve&longs;ter e&longs;t; &longs;ed non invictus, meo iudi
cio; faveor explicari po&longs;&longs;e alicuius planetæ, puta Saturni, retrogre&longs;&longs;ionem
v.g. (figuram tecum non adhibeo, qui res i&longs;tas facilè intelligis) &longs;i enim ter
ram colloces in eo Eclipticæ gradu, qui ab alio di&longs;tet, in quo e&longs;t Saturnus
vno quadrante integro circuli, Saturnus in eo loco, in quo e&longs;t, non videbi
tur &longs;ed in alio remotiore.
intelligatur.
Schemate opus e&longs;&longs;e non putarem, quia tamen ita iubes, tibi
morem geram. Sit A. centrum vniver&longs;i, &longs;itque BCDE magnus Orbis,
vt vocant, in quo, primo loco, iuxta tuam hypothe&longs;im, terre&longs;trem globum
moveri &longs;uppono; &longs;it orbita Martis FRPS. Terra moveatur ex C. per B.
in con&longs;equentia, vt vocant, id e&longs;t, iuxta&longs;eriem Signorum; Item Mars ex F
per R. &longs;upponatur Mars in F, & terra in B; Supponamus lineam AF pro
ductam ad &longs;tellas, terminari ad principium Cancri, ac proinde AB. pro
ductam ad initium Libræ; ex puncto B, Mars videbitur per lineam BFL. Igitur in eo Zodiaci puncto, quod, a principio Cancri versùs Occa&longs;um di
&longs;tat, toto angulo BFA, vel quod idem e&longs;t, FAM. Item &longs;i &longs;tatuamus initio
Terram in D, Martem in S. erit Mars in Perigæo, & in oppo&longs;itione; &longs;patio
vorò &longs;ex men&longs;ium, circiter, Mars ab S. pervenit ad F, & Terra à D.ad IB;
tunc autem Mars e&longs;t in mediocri di&longs;tantia, & videtur retrogredi à puncto
in, quo non videtur ex B, &longs;ed in quo e&longs;t, ad punctum L, vel K, in quo non e&longs;t,
&longs;ed in quo videtur ex B.
In no&longs;tra comnunique hypothe&longs;i, hæc æquè facilè explicantur, &longs;it enim
Terra in Centro A &longs;it BCDE orbita Solis, &longs;it FRPS, deferens centrum
Epicych Marris; &longs;it demum ONCM, Epicyclus Martis, cuius motus, cir-
partem &longs;uperiorem, nec non eodem cum centro motu; Sit igitur centrum
Epicycli in S. planeta in D, id e&longs;t in Perigæo ;
ta in M ; igitur ex A videtur in K ; ergo videtur retrogredi: &longs;upponamus au
tem motum Martis e&longs;&longs;e duorum annorum; in ve&longs;tra hypothe&longs;i ; Terra ex
D prefecta, redit in idem punctum D. decur&longs;o orbe, eo tempore, quo
Mars ex S. profectus pervenit in R ; in S autem erat in Perigæo ; in R verò
e&longs;t in Apogæo ; videtur denique Mars retrogradus, quando e&longs;t in S. &
acceleratus quando e&longs;t in R. Pari modo in no&longs;tra hypothe&longs;i, eodem tem
pore, centrum Epicycli ex S pervenit in R, & planeta pervenit in I, & vt
in D e&longs;t Perigæus, ita in T e&longs;t Apogæus, di&longs;tantiis verinque ferè æquali
bus. Mars item in D. e&longs;t retrogradus, in I verò acceleratus.
Vtrùm verò
hæc ob&longs;ervationibus con&longs;entiant, hoc loco minimè di&longs;puto; hoc tantùm
demon&longs;tra&longs;&longs;e contentus, vtrimque fore &longs;imilia pa&longs;&longs;ionum phænomena,
accelerationum; &longs;cilicet, &longs;tationum, repre&longs;&longs;ionum &c. Vter verò explican
di modus magis aptus &longs;it, magi&longs;que naturæ ip&longs;i congruat, demon&longs;trandum
re&longs;tat.
Nemini profectò dubium &longs;it, quin res tota planior in no
&longs;tra hypothe&longs;i cen&longs;eatur, in qua &longs;implex & vnica Martis orbita &longs;tatui
tur, cùm tamen in tua, duos circulos ponas, deferentem &longs;cilicet,
& Epicyclum; ac proinde duos etiam motus; in mea vnicum dumtaxat
agno&longs;cis.
cùm tamen &longs;ecus &longs;it; nam in tua quoque hypothe&longs;i, gemin
totidem motus ponendi &longs;unt; ni&longs;i enim terræ motum &longs;imul cum Martis
motu ad calculos reducas, nunquam prædicta phænomena invenies; vn
de motum pro motu, circulum pro circulo reddimus; Orbitam Martis
eandem vterque ponimus, &longs;cilicet FRPS, diver&longs;imode tamen illa vti
mur; tu enim vis ab ea deferri planetam, ego verò centrum Epicycli. Tu
magnum orbem accer&longs;is, in quo terram moveri decernis, ego Epicyclum
Martis, eiu&longs;dem omnino &longs;emidiametri in quo planeta movetur; vterque
igitur geminos orbes & circulos ponimus.
Magnus orbis etiam a te ponendus e&longs;t, in quo Sol ip&longs;e mo
veatur; orbes igitur multiplicas.
Magnus orbis ad prædictarum pa&longs;&longs;ionum phænomena, mihi
nece&longs;&longs;arius non e&longs;t; &longs;tatuta terra immobili in centro A, cum orbita Mar
i, & Epicyclo, eo modo, quo dixi; nam etiam &longs;emoto magno illo orbe,
prædicta phænomena, regre&longs;&longs;ionum, accelerationum, &longs;tationum &c. nece&longs;
&longs;ariò con&longs;equentur.
Pace tua dixerim, Antime; ni&longs;i enim magnum orbem &longs;ta
tuas, & in eo Solem moveri, &longs;upponas, nunquam obtinebis, vt
Mars Perigæus, &longs;it &longs;emper oppo&longs;itus; Apogæus verò, Soli &longs;emper coniun
ctus &longs;it.
Equidem nunquam habemus Martem Soli coniunctum, vel
oppo&longs;itum, ni&longs;i Solem e&longs;&longs;e &longs;upponamus; nec etiam e&longs;&longs;e pote&longs;t, ni&longs;i alicu-
&longs;itus: moveatur autem tum centrum Epicicli S, tum ip&longs;e Epicyclus, eo
modo, quo diximus, quando centrum Epicycli erit in R, planeta erit in T;
igitur Apogæus & coniunctus; atque ita deinceps emen&longs;is revolutioni
bus iuxta præ&longs;criptum motum, Mars &longs;emper erit Perigæus in oppo&longs;itio
ne, Apogæus in coniunctiono; Iam &longs;umus ergo pares, & vtrinque par
numerus e&longs;t circulorum & motuum: vter verò modus rationi & naturæ
magis con&longs;entaneus &longs;it, videndum re&longs;tat.
Vtrique parti, &longs;uus videbitur in rem i&longs;tam magis quadrare;
quid enim pro tua cau&longs;a dici po&longs;&longs;it, non video, quod pro mea æquè non
militet.
Secus e&longs;&longs;e crediderim; nempe
naturæ magis con&longs;entaneus e&longs;t, qui nec &longs;en&longs;um, nec intellectum in erro
rem inducit, &longs;ed exhibet planetam in eo loco, in quo revera e&longs;t; is enim
poti&longs;&longs;imùm oculorum finis, vt objectum, & tale quale e&longs;t, & in loco in
quo e&longs;t, exhibeant. Atqui iuxta no&longs;trum modum, video ex A Martem in
M, per lineam rectam productam ad verum locum Eclipticæ, in quo e&longs;t,
cùm tamen iuxta tuum, ex B, videam Martem in eodem loco Eclipticæ, in
quo tamen non e&longs;t, &longs;ed in alio, ad quem terminatur recta AF. Igitur in
mea hypothe&longs;i, nec &longs;en&longs;us fallitur, nec intellectus; & provt terum natura
po&longs;tulat, videtur Planeta in eo loco, in quo e&longs;t; in tua verò, & &longs;en&longs;us fal
litur, & per &longs;en&longs;um intellectus; Licit hic deinde ex aliis notionibus &longs;en
&longs;um corrigat; & contra rerum naturam & rectæ rationis ordinem, plane
ta &longs;emper in eo loco videtur, in quo non e&longs;t, & nunquam in eo, in quo e&longs;t,
citra puncta oppo&longs;itionum & conjunctionum. Fateor vltrò, &longs;en&longs;us ali
quando falli, & multis &longs;ubjici fallaciis; &longs;ed profectò id accidit, vt aiunt, per
accidens; nam per &longs;e &longs;en&longs;us non fallit, nec fallitur; &longs;ed meo iudicio, ab
&longs;urdum dictu e&longs;t, naturam oculis &longs;emper illudere volui&longs;&longs;e, quod tamen
ex tua hypothe&longs;i nece&longs;&longs;ariò &longs;equitur; Video Solem moveri, ac Terram &longs;ta
re, turpiter erro, Sol enim quie&longs;cit, Terra movetur; terre&longs;trem globum in
centro Vniver&longs;i e&longs;&longs;e video, & Solem in ætherea regione extra medium;
&longs;ed oculi hallucinantur; nam Sol in centro e&longs;t, atque inter Sydera Tellus:
Video Martem in 20. gradu Geminorum, oculo minimè impedito,
centro ter
Cancri; &longs;ic nobis Natura gratis impo&longs;uit, & in perpetuo errore ver&longs;ari
voluit, quis hoc credat? Quis homini cordato per&longs;uadeat?
præ&longs;ertim vbi
nulla nece&longs;&longs;itas vrget, nulla ratio po&longs;tulat, nulla cogunt phænomena.
Illa facilitas Apogæi ac Perigæi, quæ in no&longs;tra hypothe&longs;i
mirabilis e&longs;t, negari profectò nequit.
Quæ major facilitas excogitari pote&longs;t, quàm illa, qua res Apo
gæi ac Perigæi per Epicyclum explicatur? Quis &longs;tatim non capiat, Mar
tem in O e&longs;&longs;e Apogæum, in C verò Perigæum ? Quis non videt, eodem
modo terram ab E, per EBC, accedere ad Martem F, quo Mars ab O
per ONC, accedit ad terram A, &longs;cilicet ab O in N, & ab E in B, iuxta
rationem &longs;inuum ver&longs;orum, ab N verò in C, & à B in C, iuxta rationem &longs;i-
cultas, &longs;ed par vtrinque facilitas; no&longs;ter tamen modus naturæ, veritati,
& rationi congruit, ve&longs;ter errori & fallaciis patrocinatur. Hic autem ac
curatas revolutionum men&longs;uras non definio, &longs;ed illud duntaxat intendo
æquè facilè in no&longs;tra hypothe&longs;i, atque in tua, explicari illa omnia, quæ ad
Planetarum pa&longs;&longs;iones &longs;pectant, licet no&longs;tra hypothe&longs;is naturæ ac rationi
magis congruat. Sed ne in hoc quidem pares e&longs;&longs;e videamur, per te mihi
liceat, quæro, rem i&longs;tam paulò minutiùs enucleare. Suppone, Martem,
cum eo velocitatis gradu, quo velociùs Sole movetur, moveri ab ortu in
occa&longs;um, haud dubiè Solem po&longs;t &longs;e relinquit, & po&longs;t aliquot revolutio
nes, modò e&longs;t in Quadraturis, modò in oppo&longs;itione, modò in Coniunctio
ne; &longs;it enim v.g. Sol in C, Mars in F, & vterque versùs occa&longs;um eat, &longs;ci
licet Sol à C, versùs D, Mars ab F, versùs S ; haud dubiè Mars Solem à
tergo relinquit versùs ortum, atque adeò po&longs;t aliquot revolutiones Mars
erit in F ; & Solem a&longs;piciet in B, tum in F ; po&longs;tea in D, ac demum
eum a&longs;&longs;equetur in C, redibitque Conjunctio; Vides, vtrumque moveri
&longs;implici&longs;&longs;imo motu; Cogita duos equos in duobus circulis currentes,
quorum alter velociùs &longs;uum orbem ab&longs;oluit; Hinc Mars &longs;emper a&longs;&longs;equi
tur partem ortivam di&longs;ci Solaris; hinc &longs;emper ve&longs;pertinus occidit He
liacè, id e&longs;t, immergitur in radios Solis, ac proinde de&longs;init videri; Matuti
nus verò Heliacè oritur; id e&longs;t, emergit ex radiis &longs;olaribus, Sole po&longs;t &longs;e
relicto versùs ortum; ac proinde incipit videri.
Optimè &longs;anè intelligo, quomodò ex diver&longs;o velocitatis gra
du, &longs;uppo&longs;ito etiam motu &longs;implici&longs;&longs;imo, vtriu&longs;que Planetæ diver&longs;i a&longs;pe
ctus &longs;equantur, & &longs;uppleatur vtriu&longs;que motus ortum versùs, motu illo
diurno; &longs;ed quæ&longs;o te, quomodò Apogæum & Perigæum explicabis?
Per&longs;picuè omninò; &longs;uppo&longs;ito enim illo velocitatis gradu,
quem Mars motu recto acqui&longs;ivit, eo temporis
in orbem, &longs;imul vna cum Sole, retinuit tantulam inclinationem primus
ille impetus deor&longs;um, ab Apogæo, &longs;cilicet, in quo tune erat, cum volui
cœpit, eamque ad in&longs;tar motus accelerati, v&longs;que ad mediocrem di&longs;tan
tiam, & ab hac v&longs;que ad Perigæum ad in&longs;tar motus retardati; atque ita
deinceps: Ita porrò hæc inclinatio, qua Planeta deor&longs;um &longs;ur&longs;umque vi
bratur, eo modo, quo dixi, attemperata e&longs;t, vt men&longs;ura illius periodi, qua
&longs;cilicet Planeta ab Apogæo ad Apagæum redit, &longs;it ferè æqualis, priori pe
riodo, quæ &longs;cilicet intercedit, ab vna Conjunctione ad aliam Conjunctio
nem, ac proinde, po&longs;ito quod, Mars initio, cum primùm cœpit moveri mo
tu circulari, e&longs;&longs;et in Apogæo & in conjunctione, nece&longs;&longs;atiò &longs;equitur oppo
&longs;itionem fieri, cùm e&longs;t in Perigæo, ac &longs;imul deinde ad Coniunctionem &
Apogæum redire. Cur autem prædictæ inclinationis &longs;it talis men&longs;ura, vel
periodus, facilè dictu e&longs;t; po&longs;ito &longs;cilicet, quod Naturæ Auctor ita di&longs;po
nere voluerit; nempe negari non pote&longs;t, quin res &longs;ecus e&longs;&longs;e potuerit, ac
diver&longs;us motuum & revolutionum modus; &longs;ed &longs;tatuto &longs;emel hoc ordi
ne, finis Planetæ fuit, ita volvi, & ad Solem componere &longs;e&longs;e; proportio
nata igitur fuit ad hunc finem prædicta inclinatio, imò & talis medio-
extrin&longs;eco, &longs;ive per motum acceleratum prævium.
&longs;emper e&longs;&longs;et oppo&longs;itus, & Apogæus &longs;emper coniunctus, quod tamen cum
veritate
gæus extra coniunctionem; quod certè in hac tua hypothe&longs;i ab&longs;urdi&longs;&longs;imum
e&longs;&longs;et; &longs;upponamus enim Martis Apogæum in O, Perigæum in E, & con
iunctionem citiùs fieri, quàm Mars perveniat ad Apogæum ; haud dubiè
coniunctio non fiet in O, &longs;ed versùs ortum, id e&longs;t, versùs R. Igitur po&longs;t
alteram revolutionem punctum coniunctionis promovebitur vltra, versùs
ortum, atque ita deinceps; igitur po&longs;t multas revolutiones, eveniet tan
dem, vt coniunctio fiat in Perigæo, & Mars in Solem fortè impingat.
Nodus i&longs;te nullo negotio &longs;olvitur; &longs;i enim Sol &longs;emper e&longs;&longs;et in
mediocri di&longs;tantia, haud dubiè coniunctio &longs;emper fieret in Apogæo, &
oppo&longs;itio in Perigæo ; &longs;i autem Sol &longs;emper e&longs;&longs;et in Perigæo, oppo&longs;itio fie
ret vltra Perigæum, citrà verò &longs;i Sol &longs;emper e&longs;&longs;et in Apogæo ; nempe Sol
circa &longs;uum Apogæum ver&longs;ans, maiores orbes decurrit, igitur tardiùs
ab&longs;olvit; Quid mirum igitur, &longs;i Mars citiùs illum a&longs;&longs;equatur? cùm ta
men Sol Perigæus paulò minores circulos de&longs;cribat, citiùs igitur illos ab
&longs;oluit, Mais igitur tardiùs illum a&longs;&longs;equitur: At cùm Sol &longs;emper recurrat
ab Apogæo ad Perigæum per mediocrem di&longs;tantiam, & vici&longs;&longs;im, iu&longs;ta fit
compen&longs;atio breviorum & maiorum orbium, & pro diver&longs;a coniuga
tione vtriu&longs;que Apogæi & Perigæi, e&longs;t enim diver&longs;a vtrinque revolutio
num periodus modò præit Coniunctio Apogæum, modò &longs;ub&longs;equitur,
v. g. &longs;i Sol circa Apogæum ver&longs;etur cum tardiùs orbes &longs;uos, vtpote ma
iores decurrat, citiùs illum Mars a&longs;&longs;equitur; ac proinde coniunctio præit
Apogæum ; &longs;i verò circa Perigæum, citiùs &longs;uos orbes conficit, ac pro
inde tardiùs illum Mars a&longs;&longs;equitur, ac proinde &longs;equitur po&longs;t Apogæum
coniunctio. Hæc ni&longs;i facilia &longs;int & ex &longs;implici&longs;&longs;imis principiis deducta,
quid &longs;implex &longs;it & facile, nequit intelligi. Suppono hoc loco Solem in
Apogæo po&longs;itum, maiorem orbem de&longs;cribere, &longs;cilicet diurnum, mi
nimum verò in Perigæo, licèt &longs;ecus aliquando accidat, de quo infra;
Sed ad rem hanc &longs;ufficit, Solem aliquando maiores, aliquando mino
res, aliàs mediocres orbes per annum decurrere; exempli autem gra
tia, &longs;uppono, maiores e&longs;&longs;e in Apogæo, minores in Perigæo, medio
cres in mediocri di&longs;tantia.
Negari non pote&longs;t, quin hæc &longs;int facillima; at vnum &longs;cire
averem, cur Mars aliquando matutinus bis emergat, & &longs;emel occul
tetur.
Vnus Keplerus, &longs;altem quod &longs;ciam, hoc a&longs;&longs;erit, cui tamen
parum fidei habendum e&longs;&longs;e puto; Vt vt &longs;it, hoc etiam facilè explicari
pote&longs;t; nam &longs;i Coniunctio præcedat Apogæum, cùm Mars &longs;uos orbes
citiùs ab&longs;oluat, quàm Sol &longs;uos, Solem po&longs;t &longs;erelinquit versùs ortum, at
que adeò emergit; quia verò paulò po&longs;t proximè accedit ad Apogæum, &
Sol ad Perigæum, Mars tardiùs, Sol citiùs &longs;uum orbem decurrit, hinc
po&longs;t aliquod tempus, Sol à Perigæo, & Mars ab Apogæo recedunt, Mars
citiùs &longs;uos orbes decurrit; hinc Solem po&longs;t &longs;e relinquit; hinc demum
emergit. Si hoc phænomenum verum e&longs;t, vix puto aliam illius cau&longs;am
a&longs;&longs;ignari po&longs;&longs;e; &longs;ed vt iam indicavi, Kepleri dictis parum fidei haben
dum e&longs;&longs;e putarem; præterquàm quòd fieri potuit, vt cra&longs;&longs;iores vapores
Martem circa horizontem ortivum oculis &longs;ubduxerint per aliquot dies,
quibus deinde di&longs;cu&longs;&longs;is, &longs;e&longs;e iterum Planeta videndum præbuerit, ac
proinde non fuerit vera immer&longs;io, vel emer&longs;io; Vt vt &longs;it, nec enim de
hoc laboramus, &longs;i phænomenum verum e&longs;t, in no&longs;tra etiam hypothe&longs;i
&longs;ua cau&longs;a & ratione non caret, & vix &longs;cio, quonam pacto in ve&longs;tra ex
plicari po&longs;&longs;it.
Rectè omnia explicas,
ablegato etiam ve&longs;tro Epicyclo, retardationem, accelerationem, retro
gradationem, &longs;tationem Martis explices; &longs;upponamus enim, Martei
motu &longs;emper æquabili &longs;uos agere orbes, cum maiorem circulum de&longs;cri
bat in Apogæo, & minorem in Perigæo, hunc citiùs, tardiùs illum per
ficit; Supponamus autem, versùs Apogæum &longs;uum orbem decurrere tar
diùs, quàm &longs;tellas, citiùs verò ver&longs;us Perigæum; haud dubiè versùs Apo
gæum, longè retro à &longs;tellis relinquitur versùs ortum, vnde progredi vi
detur in con&longs;equentia &longs;ignorum, idque maiore intervallo, quò propiùs
ad Apogæum accedit; minore verò, quo longiùs ab eo recedit; at verò
versùs Perigæum &longs;tellas ver&longs;us ortum po&longs;t &longs;e relinquit; igitur versùs oc
ca&longs;um progredi videtur, id e&longs;t, à &longs;tella recedere, quod retrogredi vocant;
vbi demum &longs;uum orbem æquè citò conficit atque &longs;tella, &longs;tare dicitur: Hæc
&longs;atis bene intelligo, etiam, ex principiis Phy&longs;icis, quæ per optica tan
tùm in no&longs;tra hypothe&longs;i, explicantur; nonnulla tamen à te &longs;cire de&longs;ide
ro, v. g. vtrùm Mars in mediocri di&longs;tantia citiùs &longs;uum orbem decurrat,
quàm &longs;tellæ, an verò tardiùs; deinde, cur Mars &longs;it retrogradus breuiori
tempore, & longiore directus; cur ab Apogæo ad Quadraturam plus
temporis ponat, quàm ab i&longs;ta ad Perigæum.
Mars haud dubiè in mediocri di&longs;tantia tardiùs &longs;uum orbem
quàm &longs;tellæ, & non procul à Perigæo æquè citò illum decurrit; vnde
non mirum e&longs;t, &longs;i cum ab vna coniunctione ad aliam dies circiter 780. &longs;eu
revolutiones &longs;pirales intercurrant, &longs;it directus in 705. retrogradus in 73.
in 2. demum &longs;tationarius. Si autem in mediocri di&longs;tantia &longs;uum orbem
æquè citò ac &longs;tella conficeret, æque diu e&longs;&longs;et retrogradus, ac directus;
ac proinde nunquam ad oppo&longs;itionem pervenire po&longs;&longs;et, & in Perigæo
e&longs;&longs;et etiam Soli coniunctus, vt Venus; vnde parum omnino regreditur,
&longs;i ob&longs;ervationes con&longs;ulamus, quibus haud dubiè &longs;tandum e&longs;t, non verò
fictitio Sy&longs;temati.
Sy&longs;tema ex ob&longs;eruationibus &longs;tatuitur, ac proinde his &longs;tan
tibus, &longs;y&longs;tema etiam &longs;tare nece&longs;&longs;e e&longs;t.
Vis liberè dicam, quod &longs;entio; cum ex multis ob&longs;ervationi
bu: &longs;y&longs;tema &longs;tatuatur, eo &longs;emel &longs;tatuto, reliquas ad illud vt plurimùm
Martis, nonnulli cum Ptolemæo Epicyclum po&longs;uerunt, alij cum Tycone
circulum cuius centrum in Sole &longs;emper fixum e&longs;&longs;et; alij cum Copernico
orbem excentricum circa Solem immobilem in centro mundi; his autem
&longs;tatutis, ac definitis circulorum diametris; periodis, &longs;itu, &c. omnes ob
&longs;ervationes ad prædicta &longs;y&longs;temata, vt dixi, accommodant, licèt vt pluri
mum, aliquæ parum congruant. Hinc non mirum, &longs;i fortè &longs;upponant, Mar
tem pluribus gradibus retrogredi, quam re ip&longs;a retrogrediatur. Sed iam ad
alia tua po&longs;tulata gradum fac
Su&longs;tine parumper, vnum exciderat, quod jam in mentem
venit; dixi&longs;ti enim paulò ante, ni fallor, Solem in Perigæo &longs;uum orbem
citiùs, in Apogæo tardiùs conficere; dies igitur no&longs;tri &longs;unt inæquales.
Novum profectò dictu non e&longs;t; nempe in antiqua etiam hypo
the&longs;i Ptolemaica, ex duplici capite illa dierum inæqualitas petitur; primò
ex eo quod Sol in Apogæo excentrici in con&longs;equentia versùs ortum videa
tur tardiùs promoveri, contra verò velociùs in Perigæo ; igitur in Apogæo
citiùs orbem &longs;uum ab&longs;olvit, diurnum &longs;cilicet, ab ortu ad occa&longs;um, tardiùs
verò in Perigæo: Igitur circa Sol&longs;titium æ&longs;tivum, ex hoc capite &longs;unt bre
viores, & circa brumale, longiores. Secundò ex a&longs;cen&longs;ione recta & obli
qua Eclipticæ, nempe æquali tempore major arcus a&longs;cendit obliquæ, quàm
rectæ; Igitur Sol in Sol&longs;titiis in quibus e&longs;t a&longs;cen&longs;io recta, tardiùs, in Æqui
noctiis, in quibus e&longs;t obliqua velociùs orbem diurnum ab&longs;olvit. Sed his
rejectis, ex alio capite, prædictam inæqualitatem etiam duci po&longs;&longs;e dicimus;
&longs;cilicet ex inæqualibus circulis, &longs;eu &longs;piris à Sole decur&longs;is, cum eodem &longs;ci
licet velocitatis gradu; vnde reverà fit, vt Apogæus majorem, & tardiùs,
Perigæus verò breviorem & citiùs orbem decurrat; Vellem, vt fideli fune
pendulo inæqualitatem illam probares, numerato &longs;cilicet vibrationum nu
mero, idque &longs;ub initium Iulij & Ianuarij: Tunc enim e&longs;t aliqua, etiam for
tè &longs;en&longs;ibilis circulorum in æqualitas, igitur & dierum; & plures vibratio
nes numerantur intra &longs;patium &longs;emihoræ &longs;ub initium Iulij, Sole in Apogæo
exi&longs;tente, quàm &longs;ub initium Ianuarij, quo tempore Sol in Perigæo ver
&longs;atur; & his vibrationibus, crede mihi, aliquam differentiam invenires,
minimam certè, at, ni&longs;i &longs;allor, &longs;en&longs;ibilem.
Si hæc cum veritate con&longs;entiant, nullus dubitat, quin A&longs;tro
nomos plurimùm tibi ob&longs;trinxeris, &longs;ed antequam meis po&longs;tulatis facias
&longs;atis, &longs;i tibi grave non e&longs;&longs;et, vellem, vt rude &longs;altem tui &longs;y&longs;tematis Solaris
&longs;chema mihi exhiberes.
Prolixior reverà e&longs;&longs;em, &longs;i rem hanc, vt par e&longs;t, explicandam
&longs;u&longs;ciperem; &longs;ed quandoquidem rudiorem dumtaxat delineationem fla
gitas, eò libentiùs tibi morem geram.
Sit igitur centrum mundi A, Axis
mundi BC, diameter Æquatoris KF,
diameter Tropici Cancri ID, Capri
corni LH, Apogæum D, Perigæum L,
mediocris di&longs;tantia AQ, quæ di&longs;po
&longs;itio fortè fuit anno mundi 5400. Sit
angulus obliquitatis Zodiaci DAF,
item HAF, &longs;upponamus Solem in
Apogæo cum tali velocitatis gradu,
quo circa Axem mundi æquabili mo
tu &longs;uum orbem diurnum decurrit ab
Ortu ad Occa&longs;um, cum duplici in
clinatione, altera &longs;cilicet versùs
centrum A, ad in&longs;tar motus accelerati,
v&longs;que ad mediocrem di&longs;tantiam, &
retardati ab hac ad Perigæum, atque
ita deinceps; altera verò versùs E, ad
in&longs;tar pariter motus accelerati v&longs;que
ad Æquatorem, & retardati ab Æqua
tore ad Tropicum, atque ita deinceps;
cùm autem circuli &longs;int, vt diametri,
vel &longs;emidiametri, erunt orbes decur
&longs;i, &longs;i tamen decurruntur orbes, vt B
D, AQ, CH; & cùm AQ, &longs;it haud
dubiè major, quàm BD, maximus
circulus decurritur circa Æquatorem
quod certè in hac hypothe&longs;i &longs;ingulare non e&longs;t, cùm etiam in Ptolemaica,
& Tyconica locum habeat Dixi, cautè, &longs;i tamen decurrantur orbes, quia
orbes non decurruntur, &longs;ed &longs;piræ, quæ ita componuntur, per majorem aut
minorem di&longs;tractionem, vt &longs;ingulæ æquales ferè &longs;ingulis evadant, dico
ferè, quia non nego, aliquam ine&longs;&longs;e inæqualitatem, vt &longs;upra dictum e&longs;t. Finge igitur, &longs;epo&longs;ito motu circulari, Solem duplici inclinatione, eo modo,
quo &longs;uprà dictum e&longs;t, in&longs;tructum, ite, ac redire, tum versùs centrum mun
di A, tum à D ad E per arcum DE, & vtraque &longs;uo gaudeat acce&longs;&longs;u &
rece&longs;&longs;u; hoc quidem motum retardatum, illo verò acceleratum imitante,
&longs;itque men&longs;ura acce&longs;&longs;us primæ inclinationis FQ, vel EV, & rece&longs;&longs;us VH;
Secundæ verò, acce&longs;&longs;us DF, & rece&longs;&longs;us FE, atque ita vici&longs;&longs;im; finge igi
tur, inquam, Solem ita moveri, &longs;epo&longs;ito motu circulari diurno; ibit haud
dubiè per lineam curvam DQH.
Quis amabo &longs;ciat, lineam illam curvam e&longs;&longs;e?
quid &longs;i dixe
rim e&longs;&longs;e rectam in latere cylindri, vel coni? Deinde &longs;i curva e&longs;t, quis de
finiat, quæ & qualis &longs;it? vide, quàm ab&longs;tru&longs;a & ob&longs;cura nobis obtru
das.
Recta e&longs;&longs;e non pote&longs;t in latere cylindri: &longs;it enim DE recta, &longs;i
fieri pote&longs;t; erit AE æqualis, AD; igitur Perigæum æquè di&longs;tabit a Sit enim DH re
cta; &longs;itque exempli gratia HE
brevior AH vt con&longs;tat ex Trigonometria; accedit enim propiùs ad per
pendicularem; omitto calculos, quia res e&longs;t per&longs;picua, etiam tyronibus
Geometris; dixi
Quæ&longs;o te, Antime, tibi per&longs;picuum e&longs;t, aliis fortè non
item, memini aliquando à magno Geometra, tibi haud ignoto, audii&longs;&longs;e,
cum de te, tua que hypothe&longs;i &longs;ermo incidi&longs;&longs;et, DH, e&longs;&longs;e latus coni.
Scio, quem intelligas, hoc etiam mihi primùm, ne quid tibi di&longs;
&longs;imulem in mentem venerat, & maximè in votis hoc erat; &longs;i enim DH &longs;it
latus coni, volvaturque BDEC, circa Axem BC,
jus coni, quod &longs;i &longs;ecetur per Axem DL, erit &longs;ectio elliptica &longs;imul, &
ecliptica, vnde Kepleri & aliorum ellip&longs;is ex Phy&longs;icis principiis demon
&longs;trata maneret; &longs;ed, vt iam dixi, DH non e&longs;t linea recta; &longs;i enim, &longs;i
fieri pote&longs;t, ducatur recta DGE; igitur AX e&longs;t minor AH, quod re
pugnat, vt dixi; cùm enim angulus DAF &longs;it gradus 23.30. min. erit. DG
illius &longs;inus rectus; igitur AG &longs;inus complementi; iam verò in hoc libel
lo tabularum &longs;inuum, invenio, vt vides, GA e&longs;&longs;e æqualem &longs;inui recto
anguli grad 66.30 minut. qui e&longs;t ad
tur GF erit vt 8794.Igitur fere Sed HE &longs;upponitur
tur AH e&longs;t maior AG, & potiori iure maior AX, quæ minor e&longs;t AG:
quanquam, vt dixi, fortè E e&longs;t minor
Satis e&longs;t; igno&longs;ce, hæc Geometrica pene mihi exciderunt;
&longs;ed &longs;i linea DQH curva e&longs;t, vix &longs;ciri pote&longs;t, quænam & qualis
&longs;it.
Hoc etiam &longs;ciri pote&longs;t; e&longs;t enim linea quædam motus mix
ti, à magno Archimede iam olim inuenta; fac enim radium DA volui in
hoc plano circa A, motu quidem accelerato, donec perveniat ad AF,
retardato verò donec veniat ad AE, & &longs;imul vna punctum D ire versùs A
in radio AD mobili, motu quidem accelerato, donec decurrerit &longs;egmen
tum radij æquale VE, retardato verò, tantundem; dictum punctum D
ibit per curvam DQH modò acce&longs;&longs;us & rece&longs;&longs;us vtriu&longs;que motus &longs;int
æquè diuturni; vnde vides curvam DQH e&longs;&longs;e veram &longs;piralem Archi
medis; ac proinde Sectio per axem DL, in &longs;olido genito à plano BDQ
HC circa axem BC revoluto, quæ munere Eclipticæ defungitur, non
e&longs;t vera ellip&longs;is, cuius tractatio ad præ&longs;entem quæ&longs;tionem non pertinet.
Iam vtcumque tuam Solarem hypothe&longs;im concipio, vis
enim Solem &longs;implici motu æquabili diurno ferri ab Ortu ad Occa&longs;um,
gemina inclinatione, eo modo, quo dixi&longs;ti; & cum vno ferè gradu &longs;in
gulis diebus à &longs;tellis retroagatur, videtur &longs;emper inhærere prædictæ el
lipticæ mobili circa eundem Mundi Axem; ita tamen vt &longs;patio 24. hora
rum quodlibet illius punctum &longs;uum integrum orbem decurrat, itemque
in ea moveri ab Occa&longs;u ad Ortum, ita vt &longs;patio vnius anni totam decur
rat; &longs;ed hic motus non e&longs;t realis, vt vocant, &longs;ed tantùm apparens, ita
que hæc &longs;atis bene intelligo; &longs;ed non levis difficultas mihi e&longs;&longs;e videtur,
maliæ Solis; Sol enim, vt nemo ne&longs;cit, &longs;tatuto Apogæo in D, plures dies
ponit à Tropico Cancri ad Æquatorem, quàm ab Æquatore ad Tropicum
Capricorni.
Rectè omninò: Hinc vides, ni fallor, duo triangula ABD,
ACH e&longs;&longs;e proportionalia, quia æquiangula; ac proinde, vt AD ad AH,
ita BA ad AC; igitur AC e&longs;t minor AB; igitur breviore tempore de
curritur: &longs;epo&longs;ito enim motu circulari, cum prima inclinatione, &longs;it mo
tus acceleratus à B ad A, & retardatus ab A versùs C, &longs;i &longs;patia &longs;int, vt
lineæ BA, AC, &longs;itque inter BA, AC media proportionalis BY, erunt
tempora vt YB, AB; &longs;unt enim &longs;patia in duplicata ratione tempo
rum. Hoc autem ex duplici analogia facilè intelligitur; Prima e&longs;t;
Sit corda ten&longs;a BC, tendatur vltrà in BAC, affixo
gemino clavo in FG, redit in BC motu accelerato; hic
e&longs;t acce&longs;&longs;us; per rece&longs;&longs;um verò pervenit in FEG; ita vt
DE &longs;it ad DA, vt DF ad DB; tempus autem acce&longs;&longs;us
e&longs;t ad tempus rece&longs;&longs;us, vt AD ad DE. Alia verò &longs;it
hæc; &longs;it BI funependulum in perpendiculo, pendens ex
B, &longs;itque affixus clavus in F, ita prima &longs;emivibratio fiat per
arcum AI, altera verò per IE, &longs;it inter AD, DE, media
proportionalis AO, tempus vibrationis AI erit ad tem
pus vibrationis IE, vt AD ad AO; &longs;unt enim tempora in
&longs;ubduplicata ratione &longs;patiorum, vt con&longs;tat ex doctrina mo
tuum. Vtraque analogia facilè applicatur.
Quod verò &longs;pe
ctat ad rationem motus accelerati, vt ad calculos reduca
tur, fortè po&longs;&longs;et accipi quadrans circuli BZ, qui repræ&longs;en
tet tempus acce&longs;&longs;us divi&longs;um in quotcunque partes æqua
les. v. g. accipiatur (
graduum demittatur NM perpendicularis, acce&longs;&longs;us pro
motus e&longs;t illo tempore &longs;egmento BM, vel vt ad Phy&longs;icas
cau&longs;as propiùs accedatur, acciperet aliquis &longs;emiparabo
lam ABZ, cuius Axis &longs;it BA, applicata quælibet, &longs;eu
&longs;emiba&longs;is AZ, hæc &longs;i dividatur in quotcumque partes
æquales, puta in 90. repræ&longs;entat tempus acce&longs;&longs;us, v.g. ab initio acce&longs;&longs;us
&longs;it tempus AO 45.graduum; ducatur ON parallela Axi AB, tum appli
cata NM, applicatæ AZ parallela, BM erit men&longs;ura &longs;patij decur&longs;i in
acce&longs;&longs;u, nec fortè vna progre&longs;&longs;io multùm differt ab alia, vt patet ex
calculatione; vix enim a&longs;&longs;umptis quotcunque partibus temporis, diffe
rentia &longs;patiorum acce&longs;&longs;us vnum gradum integrum adæquat; &longs;ed profectò,
vt A&longs;tronomicè vtramque probo, ita neutram phy&longs;ice admitto; germa
nam dabimus &longs;uo loco & Phy&longs;icam. Hæc enim obiter quatenus ad rem
no&longs;tram facit, hîc tantùm indico; &longs;ed alibi ju&longs;tum cúmque integrum tra
ctatum edemus
Acce&longs;&longs;us ab Apogæo ad Perigæum, & vici&longs;&longs;im, eodem
modo ad calculos reducitur, a&longs;lumpta &longs;emiparabola &longs;ub Axe EV; item-
cunque divi&longs;a repræ&longs;entat tempus, tum acce&longs;&longs;us, tum rece&longs;&longs;us.
Optimè; vnum tamen ob&longs;erva, in acce&longs;&longs;u ita dividi tempus,
quod repræ&longs;entatur per lineam AZ, vt incipiat ab A & terminetur in Z;
in rece&longs;&longs;u verò incipiat à Z, & de&longs;inat in A: idem dico de acce&longs;&longs;u & re
ce&longs;&longs;u Apogæi. Iam verò ad id, quod de motu Apogæi quæ&longs;iveras re&longs;pon
deo, periodum inclinationis, &longs;eu motus Apogæi, æqualem non e&longs;&longs;e perio
do alterius inclinationis; ita vt, Sol citiùs redeat ad Tropicum Cancri,
vnde di&longs;ce&longs;&longs;erat, ab&longs;oluto totius Eclipticæ motu, quàm ad Apogæum,
quod tantùm attingit paulo pò&longs;t: igitur interea Sol tantulùm promove
tur in Ecliptica, hinc Apogæum videtur moveri &longs;ecundùm &longs;eriem Signo
rum, &longs;ed adeò lentè, vt vix &longs;ingulis annis 1. minutum conficiat; & hic
motus e&longs;t tantùm apparens. Hæc dixi ad reducendum ad calculos Ano
maliæ motum; nam re ip&longs;a AD habet minorem proportionem ad AH.
&longs;eu BD ad CH, quàm tempus, quo Sol Apogæus in Cancro decurrit
arcum Eclipticæ æ&longs;tivum, à principio &longs;cilicet Cancri ad Libram, ad tem
pus quo arcum autumnalem de&longs;cribit, &longs;unt enim &longs;piræ paulò laxiores in
hoc arcu; ac proinde pauciores; igitur pauciores dies; quod ideò fit, vt
vna &longs;pira diurna Solis &longs;it ferè æqualis alteri diurnæ; &longs;ic enim &longs;upplet natu
ra æqualitatem motuum; quod &longs;anè multis aliis exemplis comprobare
po&longs;&longs;em, &longs;i fortè ita iuberes. Ex his reliqua, ni fallor, quæ ad Solare
no&longs;trum &longs;y&longs;tema pertinent, facilè intelliges.
Ita e&longs;t: quare ad prima illa po&longs;tulata de Marte redeo; vnum,
ni fallor, &longs;upererat, cur &longs;cilicet Mars à coniunctione, vel Apogæo
ad Quadraturam, plus temporis ponat, quàm à Quadratura, &longs;cilicet re&longs;
pectu Solis, ad Oppo&longs;itionem, vel Perigæum.
Miror à te, qui adeò per&longs;picax es, non videri; cùm enim
Mars ab Apogæo & Coniunctione ad mediocrem di&longs;tantiam orbes &longs;uos
tardiùs conficiat; haud dubiè minoribus intervallis Solem po&longs;t &longs;e relin
quit, quàm dum à mediocri di&longs;tantia tendit ad Perigæum; quia orbes
&longs;uos citiùs decurrit; igitur maioribus intervallis Solem po&longs;t &longs;e relinquit;
igitur cum æqualibus temporibus, ab Apogæo ad mediocrem di&longs;tantiam,
& ab hac ad Perigæum perveniat, & cum eo tempore, quo ab Apogæo
pervenit ad mediocrem di&longs;tantiam, minore arcu Solem po&longs;t &longs;e relinquat,
maiore verò æquali tempore, quo à mediocri di&longs;tantia pervenit ad Pe
rigæum; inde &longs;equitur, vt arcus hinc inde &longs;int æquales, provt reverà
æquales apparent, à Coniunctione ad Quadraturam, & ab hac ad Oppo&longs;i
tionem, a&longs;&longs;umenda e&longs;&longs;e inæqualia temporum intervalla, maius &longs;cilicet
ab Apogæo ad Quadraturam, minus verò ab hac ad Perigæum.
tio detrahere videatur; iam verò mihi facilè per&longs;uadeo, reliqua omnia,
quæ ad alias pa&longs;&longs;iones &longs;uperiorum Planetarum pertinent, pari facilitate ex
iactis à te principiis explicari
Ita e&longs;t pror&longs;us; nam res eodem modo explicatur in Iove &
Saturno; ni&longs;i quod cùm Iupiter maioribus intervallis Solem po&longs;t &longs;e relin-
ctione ad Oppo&longs;itionem minus temporis excurrat; atque adeò, cùm il
lud temporis intervallum, æquè dividatur à mediocris di&longs;tantiæ momen
to, ad eundem finem obtinendum, Iovis &longs;cilicet Apogæi, in Coniunctio
ne, & Perigæi in Oppo&longs;i
Iove quàm in Marte; vnde frequentiùs recurrunt Coniunctiones in Iove,
gatur, cur plus temporis ponat à Coniunctione ad Quadraturam, quàm
ab hac ad Perigæum; cur aliquando retrogredi, & &longs;tare aliquando vi
deatur, eodem modo in Iove explicamus, quo iam in Marte explicuimus;
item cur Iupiter citiùs in con&longs;equentia moveri videatur circa Apogæum ;
hic porro Planeta dies ponit in &longs;ua revolutione integra, nimirum à Con
iunctione ad Coniunctionem 399. ita vt diebus 283. directo motu feratur,
&longs;cilicet apparenter; diebus 118. retrogrado; 4. verò &longs;it &longs;tationarius. In
Saturno cuncta hæc locum habent; ni&longs;i quod maioribus adhuc intervallis
Solem po&longs;t &longs;e relinquit versus Ortum; ac proinde pariodus revolutionis
à Coniunctione ad Coniunctionem brevior e&longs;t, illa autem e&longs;t dierum 378.
ita vt &longs;it directus diebus 244. retrogradus 136. &longs;tationarius fere 8. Hæc
omnia ex ii&longs;dem no&longs;tris principiis nece&longs;&longs;ariò con&longs;equuntur.
Inaudij non nihil de motu Apogæi; trium &longs;uperiorum Plane
tarum; ne&longs;cio, vtrùm in tua hypothe&longs;i rectè illud explicare po&longs;&longs;is.
Recti&longs;&longs;ime Nam &longs;upponamus, Apogæum Marris coniuncti
e&longs;&longs;e in primo Arietis gradu; cùm illius revolutio ab Apogæo ad Apogæum,
duret diebus 780. Sol bis redit ad idem punctum diebus fere 731. quibus
detractis ex 780. re&longs;tant adhuc 49. ac proinde po&longs;t 49. ferè dies, Mars tan
tùm a&longs;&longs;equitur Solem, quibus per totidem ferè gradus Eclipticæ Sol pro
gredi videtur; Igitur Apogæum Martis tunc erit circa gradus 19. Tauri. Igitur &longs;ingulis annis & diebus 25. Apogæum Martis 25. circiter gradi
bus in con&longs;equentia moveri videtur. In Iove autem, cum illius revolutio
fiat diebus 399. detractis 365. &longs;uper&longs;unt adhuc 34. quibus Sol totidem
decurrere videtur; Igitur Apogæum Iovis po&longs;ito quod prior Coniunctio
fuerit in primo gradu Arietis, erit in 4. gradu Tauri. Igitur &longs;ingulis annis
& diebus 34. Apogæum Iovis moveri videtur in con&longs;equentia 34. grad. In Saturno denique, cùm eius revolutio fiat diebus 378. ex his &longs;i detrahas
365. &longs;uper&longs;unt 13. Igitur, ne idem repetam, &longs;ingulis annis, diebus 13.
Apogæum Saturni moveri videtur in con&longs;equentia gradibus 13. circiter
Sunt autem huiu&longs;modi motus apparentes tantùm, in mea hypothe&longs;i, vt
tute&longs;cis, qui ramen ex illo reali &longs;implici&longs;&longs;imo nece&longs;&longs;ariò con&longs;equuntur,
nec alio Apogæo excentrici opus e&longs;&longs;e crediderim.
Dubito, an po&longs;&longs;is alia explicare in tua hypothe&longs;i, quæ no
&longs;træ tantum hominum plau&longs;um conciliarunt, v. g. quod Saturnus
directus Iovi & Marti conjungi non po&longs;&longs;it, ni&longs;i hi &longs;int directi; nec Marti
retrogrado, alij duo, ni&longs;i &longs;int retrogradi, licèt Saturno retrogrado alij
duo conjungi po&longs;&longs;int, licèt directi &longs;int, & Iovi retrogrado Mars dire
ctus.
pothe&longs;i facilè explicantur.
Sit enim Saturnus in I, Mars in M, Sol in C, cùm &longs;ingulis diebus, &longs;eu dìur
nis revolutionibus Mars relinquatur à Stellis Ortum versùs 3 ò. circiter,
dum &longs;cilicet directus e&longs;t, & Saturnus. 2. Sit arcus FM, grad. 22. 15. minutis
circiter; po&longs;t 45. dies Mars erit in F, Saturnus verò di&longs;tabit à puncto I,
Ortum versùs grad. 3. igitur &longs;eptimo po&longs;t die, Mars Saturno conjungetur,
directus directo; item Iupiter Marti; crat autem Saturnus in Apogæo,
vt con&longs;tat, conjunctus &longs;cilicet Soli. Supponamus autem Martem oppo
&longs;itum in R, Solem in D, Saturnum in I, cùm Saturnus à &longs;tatione haud pro
cul ab&longs;it, e&longs;t enim juxta Quadraturam, tanto intervallo Mars regredi ne
quit versùs F, vt Saturno directo jungatur; quia &longs;tatim Saturnus &longs;tatio
nem attingit, & paucis po&longs;t diebus, fit retrogradus: eadem ratio facit
pro Iove, vt &longs;cilicet nunquam Saturno directo, retrogradus jungatur. Sed vt hæc paulò accuratiùs di&longs;cutiamus; cùm Saturni & Solis conjun-
arcus intervallo, à Stellis versùs Ortum relinquitur, ac proinde revolu
tionis Conjunctionum periodus brevior e&longs;t; igitur citiùs ab Apogæo ad
Perigæum de&longs;cendit, imo inter di&longs;tantias Saturni Apogæi & Perigæi à
centro mundi, longè minor e&longs;t proportio inæqualitatis, quàm inter di
&longs;tantias Martis Apogæi & Perigæi, ab eodem mundi centro; etiam a&longs;&longs;um
ptis Axibus acce&longs;&longs;uum & rece&longs;&longs;uum æqualibus, v. g. &longs;it di&longs;tantia Saturni
Apogæi 100. Perigæi 90. Martis vero Apogæi 50. Perigæi 40. vtrinque
a&longs;&longs;umitur idem Axis, id e&longs;t, eadem differentia di&longs;tantiarum, &longs;cilicet 10.
e&longs;t autem major ratio 50. ad 40. &longs;cilicet 1/4 quam ad 90. &longs;cilicet
&longs;e habent motus, vt di&longs;tantiæ; igitur vt Saturnus in Apogæo tantulùm
versùs Ortum excurrit, ita & in Perigæo versùs Occa&longs;um; Hîc enim Stel
lam po&longs;t &longs;e relinquit; illic verò à Stella retro relinquitur; igitur modicum
arcum in &longs;ingulis revolutionibus, tum directo, tum retrogrado motu
decurrit: Mars verò longè majorem. Sit ergo Mars directus in M, Sa
turnus in I, cùm Mars longè majorem arcum directus decurrat, quàm
Saturnus, conjungitur tandem Saturno versùs Ortum, ita vt primùm pars
ortiva Martis cum occidua Saturni coëant: Sit verò Saturnus retrogra
dus in I, &longs;itque Mars in N etiam retrogradus, cùm hic etiam longè ma
jorem arcum decurrat retrogrado motu, jungetur Saturno versùs Occa
&longs;um, pars &longs;cilicet Occidua Martis, cum Ortiva Saturni: Si vero Mars &longs;it
directus in M, exi&longs;tente Sole inter CB, alter versùs alterum fertur,
jungentúrque inter FM, quo loco Mars directus e&longs;&longs;e pote&longs;t, & Saturnus
retrogradus, nempe Martis &longs;tatio e&longs;t infrà trigonum a&longs;pectum, Saturni
verò paulò infrà quadratum; hinc motus Saturni retrogradus diuturnio&longs;
e&longs;t, licèt in minore arcu fiat; quid mirum igitur, &longs;i in eodem loco con
juncti e&longs;&longs;e po&longs;&longs;int Mars & Saturnus; licèt hic &longs;it retrogradus, ille directus;
eadem ratio probat Saturno retrogrado etiam Iovem directum jungi po&longs;&longs;e;
& Iovi retrogrado Martem directum.
Nunquam profectò mihi per&longs;ua&longs;i&longs;&longs;em ex principiis Phy&longs;icis,
hæc tam facilè demon&longs;trari potui&longs;&longs;e; tota res eò reducitur, Saturnum eo
velocitatis gradu moveri, vt paulò infrà mediocrem di&longs;tantiam, æquè
citò &longs;uum circulum diurnum decurrat, ac Stellæ &longs;uum. Iupiter verò
adhuc infrà, qua&longs;i in trigono; Mars demùm infrà trigonum; idem autem
futuris &longs;æculis futurum e&longs;t; cùm eundem velocitatis gradum hi Planetæ
&longs;ervaturi &longs;int, cum gemina illa inclinatione, de qua &longs;uprà; ex hoc enim
illa, de quibus huiu&longs;que di&longs;&longs;eruimus, nece&longs;&longs;ariò con&longs;equuntur; nam
Saturnus altior motum retrogradum diuturniorem habet; licèt in mino
re arcu, quàm Iupiter & Mars, directus verò breviorem, Idem dicitur
de Iove re&longs;pectu Martis; hinc revolutio &longs;eu temporis periodus Saturni,
illa &longs;cilicet, quæ inter duas Conjunctiones intercipitur, brevior e&longs;t,
quàm Iovis, & huius etiam, quàm Martis brevior; hinc frequentiores
recurrunt &longs;tationes in Saturno, quàm in Iove, & in hoc, quà in in Mar
te; hinc Saturnus minorem arcum Eclypticæ decurrit, tum directo, tum
retrogrado motu; quia &longs;cilicet parum differt illius circulus diurnus confe-
tio vnius ad alium; hinc per plures dies &longs;tare videtur; quia licèt reip&longs;a
non &longs;tet, tam parum tamen promovetur & recedit à Stella, seu versùs
Ortum, &longs;eu versùs Occa&longs;um, vt eandem à Stella di&longs;tantiam &longs;ervare vi
deatur; Cuncta hæc ita per&longs;picua &longs;unt, vt negari profectò non po&longs;&longs;int, quale
do vltrò in hac tua hypothe&longs;i, huiu&longs;modi pa&longs;&longs;iones Planetarum æquè facilè
explicari atque in mea.
Imò longè faciliùs & cum multiplici prærogativa: Nam pri
mò &longs;implici&longs;&longs;imum motum adhibeo; realem &longs;cilicet & æquabilem, circa
mundi Centrum; tu verò duos, & fortè plures, eó&longs;que minimè æquabi
les; vtrumque in Excentrico circa centra ad libitum excogitata & ficta. Secundo, nunquam vides Planetam extrà Perigæum & Apogæum, in eo
vero loco in quo e&longs;t, ac proinde perpetuæ fallaciæ &longs;ubjaces; ego in eo
loco, in quo reverà e&longs;t, Planetam video. Tertiò, tu &longs;en&longs;um decipi
a&longs;&longs;eris, quamvis rectè applicatum; ego vt & in aliis minimè falli repo
no, nec qui&longs;quam hoc jure ad&longs;truat, ni&longs;i aliqua ratione fretus. Quartò;
denique habeo in mea cau&longs;as Phy&longs;icas, eá&longs;que tritas & vulgares in doctri
na motuum, i&longs;torum omnium effectuum, Apogæi &longs;cilicet, Perigæi, accelera
tionis, retardationis, &c. Tu verò meras fallacias, & oculorum illu&longs;iones
e&longs;&longs;e contendis. Igitur non æquè facilè in tua hypothe&longs;i, ac in mea, res i&longs;ta ex
plicatur, &longs;ed in mea longè faciliùs, planiùs, &, vt &longs;ic loquar, connaturaliùs.
Vt vt &longs;it, quoad hæc, antequam ad alia, quæ fortè magis vrgent,
accedam, ex te &longs;cire vellem, quonam modo latitudinem Planetarum in tua
hypothe&longs;i explices; quod eò libentiùs audiam, quò mirabilior mihi videtur
ille modus, quo in hypothe&longs;i no&longs;tra explicatur; in qua &longs;uppo&longs;ita orbitæ ex
centricæ Planetæ inclinatione ad planum Eclypticæ, latitudinis variatio per
diver&longs;um terræ mobilis
latitudinem metitur, in limitibus &longs;ub majore vel minore angulo apparet,
quo remotior, vel propior oculus &longs;tatuetur; quod vt in &longs;chemate explicem,
Sit centrum mundi A, planum ecli
pticæ EGKH, excentricus FGI
H, cuius centrum e&longs;t in D ; nodi G
H, arcus inclinationis excentrici F
E, IK, Tellnris orbita BLCM. Sit Terra in B, Planeta in limite Bo
reali F ; apparebit prædictus arcus
&longs;ub angulo FBE, po&longs;ita verò Terra
in C, apparebit &longs;ub angulo FCE,
qui priore minor e&longs;t; Si verò &longs;tatua
tur in limite Au&longs;trali, I & Terra &longs;it
in C, videbitur arcus IK &longs;ub an
gulo ICK, & ex B &longs;ub angulo
IBK, &longs;ed ex Optica, per&longs;pi
cuum e&longs;t, angulum ICK majorem
e&longs;&longs;e angulo FBE, quia CI minor
explicantur, &longs;cilicet Planetæ oppo&longs;iti in eodem limite majorem e&longs;&longs;e Lati
tudinem, quàm conjuncti; item Planetæ oppo&longs;iti in limite Au&longs;trino, La
titudinem majorem e&longs;&longs;e quàm in Boreali; vides, quàm clarè & per&longs;picuè
in mea hypothe&longs;i hæc explicentur.
Fateor, hæc non &longs;ine plau&longs;u ab hominibus excepta fui&longs;&longs;e; &longs;ed
re penitiùs con&longs;iderata, &longs;ummæ difficultates etiamnum re&longs;tant, quibus
&longs;uperandis tuæ hypothe&longs;eos a&longs;&longs;ertores fru&longs;trà omninò de&longs;udârunt, immò
nequidem inter &longs;e conveniunt, &longs;i rectè memini, in definienda huiu&longs;mo
di Planetarum latitudine, excentricorum inclinatione, Nodorum, &
Apogæi motu, limitum libratione; atque adeò vltro fatentur, adhuc opus
e&longs;&longs;e novis Ob&longs;ervationibus, ad rem hanc meliùs &longs;tatuendam. In mea
hypothe&longs;i res &longs;atis expeditè explicatur, per &longs;ecundam illam inclinationem
à Tropicis ad Æquatorem, & vici&longs;&longs;im, juxtà rationem motus accelerati
& retardati; cùm autem Mars modò citiùs, modò tardiùs orbem &longs;uum
decurrat, quàm Stellæ &longs;uum, &longs;emper verò citiùs quàm Sol, ni&longs;i fortè
Mars &longs;it in Apogæo, & Sol in Perigæo, & cùm motus &longs;ecundæ inclina
tionis tardiùs fiat in Marte quàm in Sole; cùm demùm Mars ab Æqua
tore declinare po&longs;&longs;it versùs Boream & Au&longs;trum, gradib. circiter 25. ex
his &longs;equitur, latitudo Martis, eaque varia, cùm aliquando relinquat
Eclipticam versùs Boream, vbi di&longs;cedit à Nodo, in Signis de&longs;cendenti
bus, in a&longs;cendentibus verò, versùs Au&longs;trum; variatur etiam Latitudo ex
varia di&longs;tantia Martis. Cæterùm vnum ob&longs;erves velim, optime Augu
&longs;tine, nullum mortalium hactenùs ad iu&longs;tos calculos minorum Planeta
rum, immò nec fortè Lunæ latitudinem reduxi&longs;&longs;e; præ&longs;ertim Martis, vt
vel ip&longs;e Keplerus vltrò fatetur, qui vult, hæc latere in pandectis
æternitatis; hinc tot excentrici, epicycli, circelli, deviationes, incli
nationes, reflexiones, librationes, centra diver&longs;a, excentricitates; ne
que adhuc Martem A&longs;tronomi tot tamque variis & multiplicatis retibus
comprehendere potuerunt; vtor igitur, ad calculos, qualibet hypothe&longs;i,
vt A&longs;trologus; vt Philo&longs;ophus eam dumtaxat admitto, quæ cum princi
piis Phy&longs;icis con&longs;entit; calculi verò difficultas ex eo provenit, quod &longs;int
ferè innumeræ combinationes Apogæorum Solis & Martis;
qui versùs Ortum in con&longs;equentia promoveri videntur; nempè ex diver
&longs;o Nodorum & Apogæorum loco ac &longs;itu, diver&longs;a Latitudinis mutatio ne
ce&longs;&longs;ariò &longs;equitur. Hæc in Saturno & Iove etiam locum habent; atque
adeò, ni fallor, ex dictis habes, in mea hypothe&longs;i, trium &longs;uperiorum
Planetarum pa&longs;&longs;iones haud difficulter explicari, idque per principia Phy
&longs;ica, quæ ex doctrina moruum &longs;upponimus: quare &longs;i me audis, ac tibi
putas à me factum e&longs;&longs;e &longs;atis, exprome alia argumenta, &longs;i quæ &longs;uppetunt
pro tua hypothe&longs;i.
Veneris & Mercurij Conjunctiones in Copernicana hypo
the&longs;i, ea claritudine explicantur, qua ne&longs;cio, an major excogitari po&longs;&longs;it,
itémque Apogæa & Perigæa, tum etiam aliorum Planetarum &longs;uperiorum,
&longs;ed jam prævideo, quid pro tua hypothe&longs;i de hoc argumento dicturus &longs;is.
Apogæa & Perigæa facillimè in mea hypothe&longs;i explicantur per
&longs;implicem motum æquabilem realiter, vt aiunt, inæqualem verò appa
renter, prima illa inclinatione, de qua &longs;uprà, in&longs;tructum; Apogæum au
tem e&longs;t &longs;emper circa Conjunctionem, & Perigæum circa Oppo&longs;itionem;
quia ii di&longs;tantiæ fines &longs;upponuntur, i&longs;que velocitatis gradus impre&longs;&longs;us vel
acqui&longs;itus, quibus &longs;uppo&longs;itis, æqualia &longs;int tempora acce&longs;&longs;us atque re
ce&longs;&longs;us, & &longs;emirevolutionis Conjunctionum & Oppo&longs;itionum; Sed hæc
abundè &longs;uprà explicata &longs;unt; quare ad Venerem & Mercurium iam venio;
quorum motus in mea hypothe&longs;i æquè facilè explicantur.
Sit enim centrum mundi B,
orbita Solis ADCE, Apo
gæum Veneris S, Perigæum I,
mediocris di&longs;tantia D: &longs;uppo
namus Venerem eo gradu ve
locitatis moveri, qui minor
&longs;it illo, quo Sol movetur, ita
vt inter di&longs;tantias BS, BN,
tardiùs quàm Sol &longs;uum orbem
decurrat, citiùs verò inter
di&longs;tantias BN, BI. Itaque
&longs;it Venus in Apogæo S, mo
vetur Occa&longs;um versùs &longs;impli
ci&longs;&longs;imo motu, &longs;imúlque ac
cedit ad mediocrem
BD, relinquitur autem à Sole
versùs Ortum, a&longs;&longs;umptòque
&longs;egmento acce&longs;&longs;us SO, Ve
nus erit in P, digre&longs;&longs;a &longs;cilicet
à Sole angulo DBP; addito
verò &longs;egmento acce&longs;&longs;us OD, erit Venus in mediocri di&longs;tantia, digre&longs;&longs;a
à Sole arcu DL; a&longs;&longs;umpto porrò &longs;egmento rece&longs;&longs;us DN, erit in M ter
mino maximæ digre&longs;&longs;ionis, quam metitur angulus DBM grad. circiter 47.
in M erit &longs;tationaria re&longs;pectu Solis, cùm nec ab eo vltrà digredi, nec ad
illum accedere videatur; Dum verò ab&longs;olvit aliud &longs;egmentum rece&longs;&longs;us
NI, redire ad Solem videtur, quia &longs;uos orbes citiùs decurrit vtpote mi
nores, donec tandem ad Perigæum I perveniat; MI accedit proximè ad
lineam rectam; idem &longs;tatuatur pro acce&longs;&longs;u ab I, ad D, & rece&longs;&longs;u à D ad
S, eritque figura integra cuius &longs;emifiguram tantùm hîc habes.
Cur amabo cum Tyconicis Epicyclum FHKG non a&longs;&longs;umis,
in quo eadem &longs;alvabis phænomena, non verò figuram irregularem & in
cognitam?
Multa ob&longs;tant, quo minùs Epicyclum adhibeam.
Primò,
Licet Venus plus temporis ponat ab Apogæo ad maximam digre&longs;&longs;ionem,
quàm ab hac ad Perigæum, non tamen iuxtà proportionem acceptam in
Epicyclo: Sit enim arcus DV 45. grad. ducatur BV, tum perpendicularis
mæ digre&longs;&longs;ionis grad. 47. &longs;emidiameter Epicycli erit paulo maior quàm
DR; &longs;ed &longs;it vt DR; haud dubiè arcus FHR e&longs;t triplus arcus RK. Igitur
tempus po&longs;itum ab Apogæo ad maximam digre&longs;&longs;ionem triplum e&longs;t illius,
quod ponitur à maxima digre&longs;&longs;ione ad Perigæum, &longs;ed reverà triplum non
e&longs;t, &longs;ed in minore proportione. Secundò BF e&longs;t ad BK ferè vt 12. ad 2.
Igitur cùm circuli &longs;int vt diametri, circulus quem Venus decurtit in Apo
gæo F, e&longs;&longs;et dodecuplus illius, quem conficit in Perigæo K ; immo & in
maiore proportione, cum angulus maximæ digre&longs;&longs;ionis &longs;it maior angulo
grad.45. nempe ad gradus 48. immò & 49. nonnunquam accedit.
pothe&longs;i, BS erit &longs;altem dupla BI, igitur circulus, quem Venus decurrit
&longs;ub radio BS, e&longs;t duplus illius, quem decurrit &longs;ub radio BI, hunc igitur
&longs;uppo&longs;ito motu &longs;emper æquabili, vt dicis, &longs;ub duplo etiam tempore Ve
nus decurrit, quod tamen Phænomenis non con&longs;entit.
Mentem meam omnino a&longs;&longs;ecutus es, & rectè contra me con
cluderes, &longs;i radium BS duplum radij BI ponere cogerer; &longs;ed vt tute &longs;cis,
in exemplis non requiritur veritas; re igitur ip&longs;a provt diver&longs;a ratio motus
po&longs;tularit, Apogæum & Perigæum ad D propiùs &longs;tatuam: ex his autem
vides, quàm facilè omnia explicentur, primò po&longs;t Conjunctionem Apo
gæam, Venus versùs ortum à Sole digreditur, quia tardiùs Sole movetur
versùs occa&longs;um. Secundò Venus vbi ad mediocrem di&longs;tantiam pervenit,
puta in L, adhuc vltra digreditur, quia tardiùs Sole movetur. Tertiò nun
quam opponitur Soli; quia antequam perveniat ad
citiùs quàm Sol orbem &longs;uum decurrit; igitur à Sole vltra non digreditur. Quartò plus temporis ponit ab Apogæo S, ad maximam digre&longs;&longs;ionem M,
quàm ab hac ad Perigæum; quia tempus acce&longs;&longs;us SL, æquale e&longs;t tempori
rece&longs;&longs;us LMI, &longs;ed MI citiùs decurritur quàm LMI; e&longs;t enim pars mi
nor toto. Secundò versùs Apogæum promoveri videtur in con&longs;equentia;
versùs Perigæum in an
Perigæum citiùs orbem &longs;uum ab&longs;olvit, ab ortu &longs;cilicet ad occa&longs;um. Sextò
Emer&longs;io Veneris po&longs;t Conjunctionem Apogæam, e&longs;t ve&longs;pertina; quia Ve
nus à Sole versùs ortum digreditur, po&longs;t Conjunctionem Perigæam, e&longs;t
matutina; quia Venus Solem po&longs;t &longs;e relinquit ver&longs;us ortum: ergo in illa
apparet ve&longs;pere, in hac verò mane; &longs;ed paulò ante Apogæum fit immer&longs;io
matutina; quia cum Venus tunc &longs;pectet Solem versùs ortum, mane appa
ret, & cùm Sol eam a&longs;&longs;equatur, mane immergitur; at paulo po&longs;t ante Pe
rigæum, fit immer&longs;io ve&longs;pertina; quia cùm Venus tunc Solem &longs;pectet
ver&longs;us occa&longs;um, ve&longs;pere apparet, & cùm Solem a&longs;&longs;equatur, ve&longs;pere im
mergitur.
Sed quid de hac linea SPL, aliquis &longs;ortè putaret e&longs;&longs;e para
bolam; hoc enim aliquando &longs;altem amicis innuere vi&longs;us es.
Multa haud dubiè con&longs;ideranda &longs;unt, vt ritè definiatur, quæ
& qualis &longs;it hæc linea: in modico arcu orbis va&longs;ti&longs;&longs;imi, qui ad in&longs;tar lineæ
rectæ a&longs;&longs;umi pote&longs;t, pro parabola, phy&longs;icè loquendo, accipi pote&longs;t, &
pe ex duplici motu recto, altero &longs;cilicet naturaliter accelerato, altero
æquabïli, hæc linea parabolica na&longs;citur, vt multi demon&longs;trarunt. Dixi
phy&longs;icè loquendo, quia neque arcus circuli e&longs;t linea recta, neque lineæ
ductæ ad idem centrum &longs;unt parallelæ, neque fortè motus apparens in
illo arcu e&longs;t æquabilis. At verò in Venere, in qua longè maior arcus a&longs;&longs;u
mitur, vt DL, cùm hic a&longs;&longs;umi non po&longs;&longs;it, vt linea recta, quæ &longs;it ba&longs;is &longs;emi
parabolæ, linea SPL non e&longs;t, etiam phy&longs;icè loquendo, parabolica. Vt
autem nonnihil, obiter &longs;altem, indicem, &longs;it BN radius illius circuli, quem
Venus æquali tempore cum Sole decurrit, &longs;it vt BS ad SN, ita circulus
&longs;ub radio BC ad arcum SX; &longs;it SO &longs;egmentum acce&longs;&longs;us ducto ex B
arcu OP, ducetur linea per punctum P: pari modo alia puncta habebun
tur; cogita punctum S moveri per SD motu accelerato, & &longs;imul cum axe
BS versùs X, circa centrum B, initio, velociùs: &longs;ub finem, tardiùs; de&longs;cri
bet curvam SPL, quæ e&longs;t &longs;pecies quædam &longs;piralis, &longs;eu fortè nova quæ
dam &longs;pecies parabolæ, in qua, arcus paralleli in locum applicatarum
&longs;ub&longs;tituuntur; ita vt v.g. quadratum OP ad quadratum DL, &longs;it vt SO,
ad SD, & vt tantulum Geometrizemus, cùm hæc figura &longs;it homogenea
&longs;emiparabolæ, &longs;unt enim arcus vt applicatæ, &longs;i ducatur arcus LD in
habebitur area dictæ figuræ: &longs;i autem idem arcus DL ducatur in
habebitur &longs;ector BLD. Igitur figura SLD e&longs;t ad dictum &longs;ectorem, vt
Sit etiam vt BD ad BS, ita BS ad tertiam BF, erit &longs;ector
BLD ad &longs;ectorem BHS, vt BD ad BF; &longs;unt enim &longs;ectores &longs;imiles in
duplicata; igitur &longs;ector BLD ad reliquum trapezium LHSD vt BD
ad DF, vel vt Igitur LSD ad dictum trapezium vt
ad
minùs
metrica, alioquin vix ab iis te ab&longs;trahere potero; probè igitur intelligo,
quomodo in hac tua hypothe&longs;i, omnia quorum huc v&longs;que memini&longs;ti Ve
neris Phænomena explicentur; nonnulla tamen &longs;uper&longs;unt, quæ fortè plus
negotij face&longs;&longs;unt v.g. cur maxima Veneris declinatio modò maior &longs;it,
modò minor, cur Venus aliquando matutina, &longs;imul & ve&longs;pertina eodem
die videatur; cur eiu&longs;dem latitudo Borealis &longs;it maior quàm Au&longs;tralis, alia
que huju&longs;modi.
Parum negotij cuncta hæc mihi face&longs;&longs;unt, &longs;ecus fortè vobis
ac proinde tot epicyclos, excentricos, circellos, librationes arcus, Ellip&longs;
&longs;es, Epicyclorum Epicyclos multiplicatis; quibus etiam admi&longs;&longs;is, vix fi
nem vobis propo&longs;itum obtinetis; itaque illa omnia cum meo &longs;implici&longs;&longs;imo
motu facillimè explico: vbi enim Venus pervenit ad M, id e&longs;t, ad illum
circulum ineundum quem æquali cum Sole tempore decurrit, dum hic
e&longs;t in mediocri di&longs;tantia D ; &longs;i Sol &longs;it in Apogæo, cum in con&longs;equentia,
id e&longs;t versùs Ortum Sol plus promoveri videatur, quia maiorem circu
lum de&longs;cribit, igitur tardiùs, haud dubiè Venus à Sole minùs digredi
videtur ad quàm Sol propiùs accedit, igitur in hoc ca&longs;u, maxima digre&longs;-
&longs;cilicet breviorem circulum, ac proinde citiùs decurrit. Igitur versùs Oc
ca&longs;um longiùs à Venere amovetur, hinc maior huius digre&longs;&longs;io, quæ dein
de pro diver&longs;o loco Solis diver&longs;a erit. Minima igitur inter maximas fiet
Sole exi&longs;tente in Apogæo ; exempli gratia; maxima verò Sole exi&longs;tente
in Perigæo, media denique, Sole mediocrem di&longs;tantiam tenente, variæ
deinde pro variis locis, in quibus Sol ab Apogæo vel Perigæo plùs, vel
minùs di&longs;tat. Quod verò &longs;pectat ad alterum po&longs;tulatum, æquè facile
plico; cùm enim latitudo Borealis veneris maior &longs;it quàm au&longs;tralis, &longs;up
ponamus Venerem non procul à Perigæo cum latitudine Boreali 9. grad. Sole v. g. exi&longs;tente iuxta Tropicum Capricorni, arcus diurnus Veneris,
longè maior e&longs;t, arcu diurno Solis, vt patet ex vulgaribus tabulis; quid
mirum; igitur, &longs;i & ante Solem oriatur, & po&longs;t illum occidat; ac pro
inde mane & &longs;ero &longs;e&longs;e videndam præbeat? neque hic re&longs;tat vlla difficultas,
ni&longs;i fortè cur latitudo Borealis Veneris &longs;it maior au&longs;trali, cum tamen Mer
curij latitudo Au&longs;tralis Boreali maior &longs;it; partim à Sole ratio petenda e&longs;t,
cuius &longs;cilicet Apogæum modò e&longs;t in &longs;ignis Borealibus, modo in Au&longs;tra
libus, partim à diver&longs;is Coniunctionum & maximarum digre&longs;&longs;ionum lo
cis, ex quibus diver&longs;æ latitudinis ratio &longs;equitur; v. g. &longs;upponamus ma
ximam digre&longs;&longs;ionem ve&longs;pertinam in. 1. gradu Acietis ab&longs;que vlla latitu
dine, erit Sol v.g. in grad. 15. Pi&longs;cium, cùm autem hinc Venus cendat
versùs Perigæum, & &longs;uos orbes citiùs Sole perficiat, haud dubiè &longs;tatim
relinquit Eclipticam ver&longs;us Ortum & Au&longs;trum; vnde &longs;equitur latitudo
Borealis & tardi&longs;&longs;imus motus in con&longs;equentia, donec tandem fiat re
trograda, & paulò po&longs;t Coniungatur Soli Perigæa, nec non tamdiu du
ret retrogradatio po&longs;t Coniunctionem, quamdiu duravit ante Coniun
ctionem, cre&longs;cente &longs;emper latitudine Boreali; donec ad maximam di
gre&longs;&longs;ionem matutinam perveniat, modò &longs;it in &longs;ignis a&longs;cedentibus, id e&longs;t
à principio Capricorni ad principium Cancri. Si autem &longs;upponamus ibi
dem Planetam, &longs;cilicet in 1. grad. Arietis ab&longs;que latitudine, in digre&longs;
&longs;ione maxima matutina, Sol erit v. g. in gr. 15. Geminorum, vt patet,
& cùm Venus hinc tendat ver&longs;us Apogæum, Orbes &longs;uos tardiùs Sole
decurrere incipit; Igitur relinquit Eclipticam versùs Occa&longs;um & Bo
ream vnde &longs;equitur latitudo Au&longs;tralis, quæ continuo cre&longs;cit versùs Can
crum: hæc forte regula generalis &longs;tatui po&longs;&longs;et, Venetis latitudo Borea
lis, quamdiu movetur tardiùs Sole, id e&longs;t à maxima digre&longs;&longs;ione matutina
v&longs;que ad maximam ve&longs;pertinam, in Signis a&longs;cendentibus, decre&longs;cit, in de&longs;
cendentibus cre&longs;cit; contra verò Au&longs;tralis in a&longs;cendentibus cre&longs;cit, &
decre&longs;cit in de&longs;centibus; quamdiu verò movetur citiùs Sole, latitudo bo
realis in a&longs;cendentibus cre&longs;cit, in de&longs;cendentibus decre&longs;cit, in his demum
Au&longs;tralis cre&longs;cit & decre&longs;cit in illis; cùm autem &longs;int ferè innumeræ con
iugationes, Signorum a&longs;cendentium & de&longs;cendentium, coniunctionum,
digre&longs;&longs;ionum, itemque Apogæi & Perigæi; Veneris & Solis; quid mi
rum, &longs;i tanta varietas in Phænomenis deprehen&longs;a A&longs;tronomos eò adegerit,
vt fateantur vltro, certum Sy&longs;tema Veneris, in quo omnia Phænomena
tiones fiant. Porrò cum Venus proximè ad terram accedat, & circa hori-
zontem vt plurimum Ob&longs;ervetur, non e&longs;t dubium, quin refractio eius La
titudinem non parum mutet, ac proinde valde difficile &longs;it, certam regu
lam ex Ob&longs;ervationibus, quæ tot fallaciis oculorum &longs;ubjiciuntur &longs;tatuere;
&longs;ed ne &longs;im prolixior, & &longs;altem extra chorum, hæc omitto, cùm manife&longs;tè
con&longs;tet, in qualibet hypothe&longs;i ; hæc valde difficilè explicari; in ea tamen,
quam indicavi longè faciliùs. De Mercurio nihil dico, quia eadem pro
illo faciunt, quæ de Venere diximus, ni&longs;i quòd &longs;uas revolutiones citiùs
ab&longs;olvit, minu&longs;que digreditur à Sole, quàm Venus; ac proinde illius Ob
&longs;ervationes longè difficiliores. De diver&longs;is pha&longs;ibus horum Planetarum
nihil etiam dico; quia non dubitas; opinor, quin facillimè citra ve&longs;tram
hypothe&longs;im explicentur: quare his peractis, vide quæ&longs;o, vtrùm alia pro
tua hypothe&longs;i &longs;uppetant argumenta.
Omi&longs;&longs;is A&longs;tronomis, quæ haud dubiè &longs;atis feliciter &longs;olvi&longs;ti,
alia duo &longs;unt, quæ magnum no&longs;træ hypothe&longs;i plau&longs;um pepererunt, pri
mùm petitur à maris æ&longs;tu, alterum à Magnete: quod ad primum &longs;pectat,
&longs;upponimus, Terram moveri motu quodam mixto ex motu orbis & cen
tri, qua&longs;i ad in&longs;tar rotæ in plano, vt iam &longs;upra in&longs;inua&longs;ti, ac proinde par
tes illius inæquali motu ferri, alias tardiùs, alias velociùs. Suppono præ
tereà aquam in va&longs;e, &longs;eu cymba vectam, vbi cymba motum remittit, ex
currere versùs illam partem, in quam cymba tendit; in oppo&longs;itam verò,
vbi cymba motum accelerat, cogita quæ&longs;o aquam Occani, qua&longs;i in va&longs;ti&longs;
&longs;ima concha, à Globo Terræ delatam & circumactam, &longs;ed dicto motu
inæquali, haud dubiè vbi motus acceleratur, aqua versù; Occa&longs;um ex
currit, vbi remittitur, versùs Ortum: En tibi germanam cau&longs;am æ&longs;tus
marini, quæ certè, vt cum no&longs;tra hypothe&longs;i optimè con&longs;entit, ita in aliis
explicari non pote&longs;t.
Negare non po&longs;&longs;um, quin hoc fuerit ingenio&longs;um inventum,
fictum tamen & commentitium. Primo enim ita æ&longs;tus diurnus &longs;uas pe
riodos metitur, vt ad motum Lunæ dumtaxat, diurnum &longs;cilicet, non
Solis aut Terræ &longs;e&longs;e componat; nam &longs;ummi æ&longs;tus, vel &longs;ummæ aquarum
elevationis terminus e&longs;t Luna meridiana, tum in hoc, tum in oppo&longs;ito
hemi&longs;phærio; principium verò e&longs;t eadem Luna, Quadrante circuli di
&longs;tans à Meridiano: Igitur Luna exi&longs;tente in Meridiano, æ&longs;tus cre&longs;cere
de&longs;init, decre&longs;cere incipit, remota vero Quadrante circuli à Meridiano,
hinc inde æ&longs;tus decre&longs;cere de&longs;init, & cre&longs;cere incipit: rem ita fieri per
&longs;e con&longs;tanti&longs;&longs;imum e&longs;t, habeturque ex indubitatis Ob&longs;ervationibus; licèt
autem per accidens fieri po&longs;&longs;it, vt crementum decremento inæquale &longs;it;
hoc tamen non ob&longs;tat, quin po&longs;tero die dementum incipiat eadem hora
Lunari, ac proinde 48. minutis tardiùs, quàm pridie. Quid autem ad
hæc, Augu&longs;tine mi, Terræ motus conferat, nemo capiat; cùm enim ea
dem motus inæqualitas, eadem &longs;emper hora, eidem Æquatoris terre&longs;tris
globi puncto in&longs;it, idem &longs;emper effectus ex eadem inæqualitate, ca
dem hora &longs;equi deberet: igitur eadem hora &longs;emper e&longs;&longs;et &longs;ummum cre-
Ob&longs;ervationibus repugnat: &longs;i enim hac ip&longs;a die, Luna in Meridie &longs;ci
licet exi&longs;tente, &longs;it &longs;ummum crementum æ&longs;tus hora meridiana, vt &longs;it in no
vilunio, cra&longs;tina die, idem &longs;ummum crementum erit minutis 48. circiter
po&longs;t Meridiem; & tertio po&longs;t die hora, 1. 36. minutis po&longs;t Meridiem, at
que ita deinceps; idem de Plenilunio dicendum e&longs;t.
Ita fortè di&longs;poni po&longs;&longs;unt prædicti duo motus, orbis &longs;cilicet
& centri, vt motus mixtus inde re&longs;ultans tales in æ&longs;tu mutationes pro
ducat.
Nullo &longs;ané modo id fieri po&longs;&longs;e, omni a&longs;&longs;everatione affirmo; quod
vt clariùs exponam.
Sit A Centrum mundi, DBLC orbita terræ, vel magnus orbis, D cen
trum terræ, quam paulò majorem de&longs;cribo, ne parvitas orbis confu&longs;io
nem patiat; dum centrum D movetur versùs B, ita volvitur circulus cir
ca D, vt Eversùs I, & F, versùs H tendat. Vnde re&longs;ultat ex vtroque mo
tu æquabili motus mixtus omnino inæqualis; nempe ab H in I, per E;
additur motus orbis, motui centri; id e&longs;t &longs;patio decur&longs;o &longs;olo motu cen
tri, &longs;patium æquale diametro IH ; ab I verò in H per F, idem &longs;patium
detrahitur &longs;patio decur&longs;o mot
menta, &longs;uprà motum centri, &longs;unt in ratione &longs;inuum ver&longs;orum arcuum
decur&longs;orum; ab E in I, in ratione &longs;inuum rectorum; decrementa pariter
ab I in F, &longs;unt in ratione &longs;inuum ver&longs;orum; ab F verò in H, in ratione
datio, in I & H merus motus centri con&longs;ideratur: itaque ab H in I per E,
aqua Oceani juxta ea, quæ dicis, versùs Occa&longs;um excurrere deberer; ab
I verò in H per F, versùs Ortum; Igitur in E &longs;emper e&longs;&longs;et maximus excur
&longs;ionis motus versùs Occa&longs;um; in F versùs Ortum; in I & H quies; quan
tum hæc Ob&longs;ervationibus repugnent, omnibus rerum i&longs;tarum peritis cogi
tandum relinquo.
Quid &longs;i aliquis diceret, Nautis in hoc fidem habendam non
e&longs;&longs;e, qui forte ad libitum prædictas ad Lunam habitudines marino æ&longs;tui
affinxerunt?
Cuique &longs;uæ artis perito credendum e&longs;&longs;e, optima ratio po&longs;tu
lat, præ&longs;ertim &longs;i periti omnes illius artis aliquid a&longs;&longs;erant, quod alioquin
nihil illorum intere&longs;t. Cùm igitur Naucleri omnes periti, & principes illi
autores, qui de hoc argumento &longs;crip&longs;erunt, omni a&longs;&longs;everatione affirment,
rem ita e&longs;&longs;e, nemo prudens fidem iis detrectet; accedit, quod illi om
nes, qui in litore Oceani Gallici, Britannici, Anglici, Belgici habitant
(neque te ad Antipodas vel Garamantas amando) omnimodam huiu&longs;ce
rei te&longs;tificationem facere po&longs;&longs;unt, cùm illam præ oculis habeant; omitto
alia innumera argumenta, quibus hoc ve&longs;trum commentum refutatur;
quia &longs;upervacaneum puto, actum iam agere, illud tamen non omitto,
quod præ cæteris vrgere videtur; &longs;uppono enim cum iis omnibus, qui
vel delibârunt hanc materiam, maximam e&longs;&longs;e vim æ&longs;tus in Plenilunio,
magnam etiam in Novilunio, in Quadraturis perexiguam; Quid porro ad
hæc terræ motus? Nihil pror&longs;us.
In Novilunio Luna propios ad Solem accedit, & minores
arcus decurrit, contraverò in Plenilunio.
Quid in de?
An fortè Luna &longs;uos motus in Terram derivat?
Mi
nimè verò, alioquin maior æ&longs;tus e&longs;&longs;etin Quadraturis, quàm in Novilunio,
quod certè cum veritate minimè con&longs;entit: deinde Terra ip&longs;a in Novilu
nio tardiùs moveretur, quod nemo vnquam &longs;omniavit.
Saltem negari non pote&longs;t, quin terræ aut Solis motus ali
quid conferat ad mutationem illam æ&longs;tuum, quam omnes huiu&longs;que cir
ca Æquinoctia Ob&longs;ervarunt; nihil enim ad hæc Luna.
Sed quid quæ&longs;o ad hæc terræ motus?
equidem in diurno ter
ræ motu, illa revolutio annua Globi, ad retinendum Axis Paralleli&longs;mum,
aliquid facit, quod tamen &longs;ub &longs;en&longs;um non cadit: nempe motui orbis
opponi videtur: &longs;ed reverà hoc nihil e&longs;t, nec quidquam ad hanc rem fa
cit, vt con&longs;ideranti patebit.
Quid autem ad hæc Luna, quis hominum aliquando dicat?
Ego fortè minimus hominum; illam enim æ&longs;tus marini cau
&longs;am affero, quæ & communibus principiis nittitur, & ad quam cuncta
phænomena, quæ per &longs;e ex marino æ&longs;tu &longs;equuntur, facilè reduci po&longs;&longs;unt:
&longs;ed cùm altioris indaginis res &longs;it, in alium congre&longs;&longs;um remittendam illam
e&longs;&longs;e putarem, ne cœpta di&longs;ceptatio intermittatur: itaque omi&longs;&longs;o maris
æ&longs;tu, quid tandem de Magnete dicis?
Facilè opinor conjicies; terram enim maiorem Magnetem
e&longs;&longs;e dicimus cum Gilberto; vnde manife&longs;tam cau&longs;am ducimus perpetui
Axis paralleli&longs;mi; &longs;ic enim polorum Magneticorum axis, Axi mundi
&longs;emper e&longs;t parallelus, id e&longs;t, ad eandem &longs;emper fixam vniver&longs;i plagam
conver&longs;i &longs;unt, immo nullum alium ab i&longs;to Axem mundi agno&longs;cimus.
Terram Magnetem e&longs;&longs;e non pauci communiter negant; neque
rationes efficaces de&longs;unt; &longs;ed demus hoc in tui gratiam, & terra, vt vis,
&longs;it va&longs;tus Magnes: igitur illius poli ad fixa cœli puncta &longs;emper &longs;pectant;
rectè, quis hoc negat? Vnde &longs;i fortè vi ab extrin&longs;eco impre&longs;&longs;a, ab hoc
a&longs;pectu & &longs;itu amoveretur, illico &longs;e&longs;e re&longs;titueret; optimè; quid inde? Ergo, inquies, terra movetur in orbe magno, quia illius Axis, circa
quem diurnos agit orbes, &longs;ibi ip&longs;i Parallelus &longs;emper e&longs;t; nego con&longs;e
quentiam; &longs;ive enim terra moveatur, &longs;ive quie&longs;cat, ille Axis ad fixa &longs;em
per cœli puncta &longs;pectat: ergo ex hoc neutra hypothe&longs;is probari pote&longs;t;
immò potiori iure mea, quàm tua inde probatur.
Fortè illam &longs;ubaudis demon&longs;trationem, qua ex tuis aliquis
no&longs;tram hypothe&longs;im labefactare molitus e&longs;t. Fru&longs;trà licet: cùm illam
Ga&longs;&longs;endus vir toto orbe literario notus illam in Docti&longs;&longs;imorum homi
num congre&longs;&longs;u, cui &longs;ummus quidam Princeps præerat, egregiè refutavit.
Certè illam demon&longs;trationis loco non habeo; nam nec terram
magnum Magnetem e&longs;&longs;e, puto, nec etiam &longs;i magnes e&longs;&longs;et, ad alia quæ
dam cœli puncta, exceptis polis, re&longs;pectum haberet, volebat enim vir
ille de re Magnetica optimè meritus, Magnetem in &longs;phæram tornatum,
in eo &longs;emper &longs;itu manere, vt omnia illius puncta ad eadem &longs;emper vni
ver&longs;i puncta &longs;pectare debeant; quod certè variis experimentis, ii&longs;que
&longs;electi&longs;&longs;imis probare conatur; non tamen meo iudicio convincit, hoc
enim provenit à communi partium Magneticarum ni&longs;u, quæ Magneti
ita in&longs;unt, vt &longs;ingulæ &longs;phæræ Magneticæ portiones æquali vi non pol
leant, &longs;ed aliæ plus, aliæ minùs; vnde fit vt ex communi omnium ni&longs;u. vnde tantùm &longs;itus haberi po&longs;&longs;it; vnde &longs;i &longs;phæra illa Magnetica æquales
vires in omnibus &longs;uis partibus haberet, æquè ille communis ni&longs;us &longs;uum
effectum &longs;ortiretur, &longs;ive hoc punctum versùs Ortum, &longs;ive Occa&longs;um ver
sùs collocetur: &longs;ed, vt verum fatear, licèt ex Magnete neutra hypothe&longs;is
demon&longs;tretur, no&longs;træ tamen potiùs, quàm tuæ Magnes favet; primò
enim licèt non demus terram Magnetem e&longs;&longs;e, hoc tamen tecum &longs;uppo
nere po&longs;&longs;umus, aut &longs;altem cum aliis, multas illi particulas Magneticas
ine&longs;&longs;e, quod certè ex multis experimentis probatur: præ&longs;ertim ex de
clinatione acus Magneticæ; &longs;ufficienti igitur virtute in&longs;tructa e&longs;t, vt ta
lem a&longs;pectum &longs;emper retineat; virtute inquam particularum Magneti
carum, quæ in&longs;unt, quarum etiam communi ni&longs;u, cùm inæqualiter
ac difformiter terre&longs;tri globo admixtæ &longs;int, obtinebitur, vt non modò
duo terræ poli ad polos Mundi, &longs;ed etiam idem punctum &longs;emper ad Or
tum, idem ad Occa&longs;um &longs;emper conver&longs;um &longs;it.
Hanc igitur Grandamici demon&longs;trationem tuo calculo do
nas, quam tamen viri Docti&longs;&longs;imi & Sapienti&longs;&longs;imi rejecerunt.
Non habeo, vt iam dixi, pro demon&longs;tratione; quia nemo
huiu&longs;que probavit, terram Magnetem e&longs;&longs;e; aut &longs;altem tot particulis
Magneticis in&longs;tructam, quæ &longs;ufficiant, ad tantam molem volvendam;
hoc tamen &longs;uppo&longs;ito, cum iam ex aliis corporibus Magneticis con&longs;ter,
virtutem illam Magneticam per totam &longs;phæram vniformiter di&longs;tributam
non e&longs;&longs;e, ex hoc nece&longs;&longs;ariò &longs;equeretur, terram ab Occa&longs;u ad Ortum, mi
nimè moveri: vnde non crat, quòd vir ille docti&longs;&longs;imus non modo de
re Magnetica, verùm etiam de Chronologica optimè meritus, à nonnul
lis adeò exploderetur; hoc enim argumentum ab illo excogitatum, ad
hominem, vt vocant, contra Gilbertum & alios, qui terram magnum
Magnetem e&longs;&longs;e dixerunt, rem i&longs;tam omnino evincit; &longs;ecus tamen contra
illos, qui terram Magnetem e&longs;&longs;e negant, aut &longs;ufficienti virtute magnetica
in&longs;tructam, qua tanta moles agi queat.
Ne&longs;cio quid aliud indicâras; hoc enim tantum primum
caput e&longs;t, ex quo Magnetem tuæ potiùs, quàm meæ hypothe&longs;i favere di
cebas, &longs;i primum e&longs;t, cur ad &longs;ecundum non venis?
Res ferè e&longs;t nullius momenti, dicam tamen, illam hypothe&longs;im
ad rem magneticam potiùs facere, in qua terræ Axis fixa &longs;emper eadem
que vniver&longs;i puncta re&longs;picit, quàm illam, in qua terræ Axis per tot mil
liarium myriades in magno orbe circumfertur; Licèt enim &longs;ibi ip&longs;i &longs;em
per parallelus &longs;it, de&longs;cribit tamen vtroque termino, circulum æqualem
magno orbi; in no&longs;tra fixus e&longs;t Axis, fixa cœli puncta, neutrum in tua
habetur, quare vt fateor vltero, neutram ex Magnete demon&longs;trari, ita &longs;anè
nemo retum i&longs;tarum rectus æ&longs;timator inficias eat, quin no&longs;tra regulis
magneticis magis con&longs;entiat; &longs;ed de hoc &longs;atis, quare vide vtrùm pro tua
hypothe&longs;i aliquid aliud &longs;uppetat.
Suppetunt quidem multa, &longs;ed ex iis, quæ à te adducta &longs;unt,
&longs;at video, quàm facilè illa &longs;olvere po&longs;&longs;is; quare de hoc argumento &longs;atis
&longs;uperque dictum e&longs;&longs;e puto.
Egregiè &longs;anè; &longs;ic æquis armis pugnamus.
Huiu&longs;que meam
hypothe&longs;im tuis argumentis impugna&longs;ti, nec dixi vnquam &longs;atis; iam
verò ex arena pedem efferre velles, ne mihi copia detur tuam impugnandi.
quaciores e&longs;&longs;e videamur.
Obiter, inquis, non pauciora certè, immo longè plura argu
menta contra tuam hypothe&longs;im habeo, quàm tu contra meam igitur, &longs;i
non plus, tantumdem &longs;altem temporis, ad hanc provinciam exequen
dam, iure meo po&longs;tulo.
Crede mihi, Antime, certamen non detrecto, nec vinci metuo,
timeo tamen ne prolixior di&longs;ceptatio nonnihil tædij
Rectè mones remittamus in
Ne tamen aliquid fortè quod &longs;upere&longs;t huic congre&longs;&longs;ui detra
hatur; tuam illam de marino æ&longs;tu &longs;ententiam exponere poteris, vt amœ
niùs hæc di&longs;ceptatio terminetur; tenes enim, ni &longs;allor, ex lis aliquam, quæ
iam ab aliis excogitatæ fuerunt.
Minimè verò; Nova e&longs;t omnino mea &longs;ententia, & à me pri
mùm excogitata, & i&longs;tarum temporis angu&longs;tiarum impatiens; quare, vt
iam indicavi &longs;upra, integrum congre&longs;&longs;um implebit.
Illa opinion Carte&longs;ij mihi &longs;tatim venerat in mentem, qui
vult à circumfluente Luna comprimi aëra, & Oceani &longs;uperficiem, ex qua
pre&longs;&longs;ione, aquarum motus &longs;equatur, quem vocat æ&longs;tum; te fortè huic ad
hærere putabam; quando quidem Lunæ mentionem feci&longs;ti.
Toto cœlo erras; illam &longs;ententiam minimè approbo, quæ &
phænomenis & veritati non con&longs;entit; ex illa enim &longs;equitur. Primò à
Luna meridiana illum maximè comprimi maris tractum, qui tali meri
diano &longs;ubjacet, aqua verò compre&longs;&longs;a &longs;ub&longs;idit, & quoquo ver&longs;um fluit;
igitur non &longs;ummum aquæ tumorem, &longs;ed maximam depre&longs;&longs;ionem meri
diana Luna conciliaret; quod repugnat ob&longs;ervationibus. Secundò Præ
dictam aëris pre&longs;&longs;ionem omnino &longs;entiremus. Tertiò In Plenilunio non
e&longs;&longs;et maior pre&longs;&longs;io, tunc enim Luna vicinior non e&longs;t, quàm in Novilu
nio & Quadraturis, igitur in Plenilunio maior æ&longs;tus non e&longs;&longs;et. Quartò
nullus æ&longs;tus e&longs;&longs;et in oppo&longs;ita parte terre&longs;tris Globi; quia nulla ibi pre&longs;
&longs;io; omitto reliqua cum hæc ad refutandum illud commentum, &longs;int &longs;atis.
tamen ex te audire cupio, quid tamen novi de hoc argumento dicturus
&longs;is. Interea antequam hunc congre&longs;&longs;um terminemus nonnulla ex te per
cunctabor, quæ licèt à te dicta &longs;int circa tuam hypothe&longs;im, vereor tamen,
vt ea rectè, vt par e&longs;t, à me fuerint intellecta. Dixi&longs;ti Solem inclinati
&longs;ur&longs;um ac deor&longs;um motu accelerato, ac retardato in reciproco acce&longs;&longs;u
& rece&longs;&longs;u; quæro ex te, vtrùm Sol novum producat impetum.
Nullo modo; alioquin &longs;i per tres continuos men&longs;es (tandum
dem enim acce&longs;&longs;us ab Apogæo ad mediocrem di&longs;tantiam) motu accele
rato moveretur, immen&longs;um penè &longs;patium percurreret; igitur non pro
ducit novum impetum, &longs;ed impetus, quem habet, vel à &longs;e acqui&longs;itum
vel aliunde impre&longs;&longs;um, huic inclinationi &longs;ervit &longs;imul & alteri; idque, vt
dixi, ad in&longs;tar motûs accelerati & retardati; &longs;ed valdè lentè, quia maior
& poti&longs;&longs;ima inclinatio, &longs;eu determinatio illius impetûs motui circulari
&longs;ervit; quòd autem idem impetus duas aut plures determinationes ha
beat, res nova non e&longs;t, &longs;ed trita; cùm hoc cuilibet motui mixto & re
flexo competat.
clinationum ad rectum acceleratum, & ad circularem æquabilem com
po&longs;itionem habeamus.
Non de&longs;unt, eáque plurima, duo in mentem veniunt, omnino
&longs;imilia; primum tale e&longs;t. Sit longior tubus vitreus altera dumtaxat ex
tremitate peruius, infundatur aqua, donec &longs;emipalmus dumtaxat circiter
vacuus re&longs;tet, & &longs;uppo&longs;ito ad extremum apertum arctè digito, tubus
invertatur, tunc cylindrus aëris lentè ac &longs;en&longs;im a&longs;&longs;urgit, à graviore aquâ
&longs;ur&longs;um extru&longs;us, dum hæc per tubilatera,
ficiem, &longs;piratim ita de&longs;cendit, quod ip&longs;is oculis per&longs;picuum e&longs;t, vt hic
initio &longs;pi&longs;&longs;iores & pre&longs;&longs;iores &longs;piræ, deinde verò di&longs;tractiores fiunt; e&longs;t
tamen tantùm vnus impetus ad motum deor&longs;um rectum per &longs;e determi
natus, qui cùm in linea recta finem &longs;uum obtinere non po&longs;&longs;it compen&longs;at
in circulari, retenta &longs;emper prima illa inclinatione ad rectum, cui quan
tum pote&longs;t, &longs;atisfacit, cùm autem etiam &longs;ecundùm id acceleratus &longs;it, in
de &longs;piras di&longs;trahi nece&longs;&longs;e e&longs;t.
Iam capio, quod ante dixeras, naturam &longs;upplere æquali
tatem motuum: nempe aqua, &longs;eu corpus grave toto illo tempore, quo
præfatus cylindrus aëris &longs;en&longs;im a&longs;&longs;urgit, motu accelerato deor&longs;um, re
moto impedimento, longum &longs;patium in perpendiculari decurreret; &longs;ed
ob&longs;tante impedimento, cùm eadem vis impetus ad&longs;it, motum rectum
&longs;pirali compen&longs;at; atque adeò &longs;i tota illa &longs;pirarum congeries in lineam
rectam explicaretur, æqualis e&longs;&longs;et lineæ rectæ in perpendiculo eodem
tempore motu accelerato confectæ, &longs;ed applica quæ&longs;o ad &longs;piras Solares.
Repete igitur figuram 2. & con&longs;idera primo loco primam in
clinationem &longs;eor&longs;im, quâ Sol ab Apogæo ad Perigæum, & vici&longs;&longs;im, per
mediocrem di&longs;tantiam, reciprocis acce&longs;&longs;ibus & rece&longs;&longs;ibus, ad imitatio
nem motus accelerati & retardati tendit reditque.
Et cogita radium AE moveri cir
ca AC, dum punctum E motu ac
celerato tendit ad V, & retardato,
ab V ad H, radius AE de&longs;cribet
&longs;uo motu &longs;uperficiem coni, cuius
ba&longs;is diameter, erit EL, punctum
verò E de&longs;cribet tot &longs;piras in dicta
&longs;uperficie coni, quot revolutiones
ab&longs;olventur, toto illo tempore,
quo ab E, pervenit in H ; hæc au
tem &longs;pira erit conica, cuius Helices
di&longs;tractiores erunt circa V, pre&longs;
&longs;iores circa E & H. Pari modo, co
gita triangulum ADE in orbem
agi, circa Axem BC dum D, motu
accelerato, tendit ad F, & retar
dato ab F, ad E; arcus DFE de
&longs;cribet partem &longs;uperficiei &longs;phæricæ,
punctum verò &longs;piram &longs;phæricam,
cuius Helices pre&longs;&longs;iores erunt cir
ca DE, di&longs;tractiores verò circa F. Si verò D iret per lineam rectam
DGE, de&longs;cribet DGE &longs;uperfi
ciem cylindricam, & D &longs;piram cylin
dricam. Iam verò
inclinatio, ita vt D partim versùs F,
ralem DQH; volvatur ADQH circa Axem BC de&longs;cribet curva DQH
&longs;uperficiem &longs;olidi cuiu&longs;dam &longs;piralis; & &longs;i interea dum punctum de&longs;cribit
eo duplici motu curua DQH moveatur circa eundem Axem BC,
de&longs;cribet in dicta &longs;uperficie &longs;piram compo&longs;itam ex totidem Helicibus;
vt autem Helices omnes &longs;int ferè inter &longs;e æquales, ob&longs;ervabis præclarum
Naturæ in&longs;titutum; &longs;upponamus Apogæum Solis in D, initio Cancri
cùm DI plus di&longs;tet ab FK quàm hæc ab HL, haud dubiè plus temporis
ponit à Cancro ad Libram, quàm à Libra ad Capricornum; en tibi ratio
nem Anomaliæ Solis; quod verò &longs;pectat ad circulos diurnos, quos &longs;in
gulæ Helices, &longs;eu &longs;p
cet vt &longs;emidiametri paralleli BD,
ctum, in quo recta DGE &longs;ecat curvam DQH ita decre&longs;cunt, vt de&longs;cri
ptus ab illo puncto &longs;it æqualis primo; ab eo verò puncto versùs H, fiunt
minores & minores circuli, ita vt vltimus, cuius radius e&longs;t CH, &longs;it ad
primum, cuius radius e&longs;t BD, vt AC ad AB, vel CH ad BD; e&longs;t
autem HE iuxta communem Anomaliæ men&longs;uram ferè
de circulus ille vltimus e&longs;&longs;et minor primo
æquali &longs;emper motu agi, longè citiès perficiet &longs;uum orbem in H quàm
in D, &longs;i movetur in circulo, nempè illo iam ab&longs;oluto, &longs;uper&longs;unt huius
12. grad. igitur tempus, quo circulus diurnus decurritur in H, e&longs;t brevius
tempore, quo decurritur in D 48. minutis horæ. Sed hoc e&longs;t ab&longs;urdum,
imò ab&longs;urdi&longs;&longs;imum; & vt natura huic incommodo occurreret, licet &longs;pa
tium CA &longs;it minus &longs;patio AB, &longs;egmentum tamen curvæ QH vix minus
e&longs;t &longs;egmento
Q ponere deberet; quia tamen ex hoc &longs;equeretur ab&longs;urda circulorum diur
norum inæqualitas, contra finem à Natura intentum, hæc enim &longs;pirarum
diurnarum æqualitatem intendit, cùm cir culi diurni omnium reliquorum
men&longs;ura &longs;int, ita di&longs;trahuntur &longs;piræ in &longs;egmento QH, vt pauciores &longs;int,
quàm in &longs;egmento
Cogita explicatam vtramque &longs;pirarum congeriem in duas lineas rectas,
maior erit ad minorem ferè vt 92.
lers igitur Natura ita attemperavit vtramque inclinationem, vt &longs;ingulæ
&longs;ingulis æquales &longs;int in quantitate, & in tempore; atque ita motum
vnum alio motu compen&longs;at, adhibita maiore, aut minore &longs;pirarum di&longs;tra
ctione.
Fru&longs;trà laboras, Antime, vt dierum æqualitatem retineas.
do naturaliter vnus motus alio compen&longs;etur, quando &longs;cilicet impeditur fi
nis Naturæ. Finis autem Naturæ e&longs;t primò, vt in connaturali di&longs;tantia
Sol circa Terram eat; data enim mole vtriu&longs;que globi, dubium non e&longs;t,
quin prædicta di&longs;tantia po&longs;&longs;it e&longs;&longs;e major, aut minor, connaturali; &longs;i major,
cuncta rigerent; &longs;i minor, conflagrarent omnia; igitur majorem inter &
minorem connaturalis, &longs;eu mediocris, aut media definienda e&longs;t; hinc
manife&longs;ta ratio primæ inclinationis, per quam Sol ab Apogæo ad mediam
in dicta di&longs;tantia, vbi obtinet illam; &longs;ed propter determinationem ac
qui&longs;itam, licèt obluctetur eadem inclinatio, pervenit v&longs;que ad Peri
gæum, &longs;imili motu recto, &longs;ed propter reluctantiam, ad in&longs;tar retarda
ti. Secundò, finis Naturæ e&longs;t, vt Sol lumen &longs;uum æqualiter, quantum
fieri pote&longs;t, di&longs;tribuat; vnde petitur ratio &longs;ecundæ inclinationis, quâ Sol
à Tropico ad Æquatorem tendit, eo modo, quo dixi; nempe definito
&longs;emel Axe mundi, circa quem &longs;phærarum cœle&longs;tium revolutiones fiant,
cuius extremitates &longs;unt Poli, vi huius inclinationis Sol à D, v.g. tendit
versùs F per arcum DF, qui cadit perpendiculariter in AD; cùm enim
à D duci po&longs;&longs;int infinitæ lineæ, versùs Æquatorem, & vna tantùm per
pendicularis, quæ e&longs;t tangens, vel arcus, cùm radius AD continuò ten
dat versùs F ; &longs;i vna e&longs;t, determinata e&longs;t; Nec dicas, rectam DG cade
re perpendiculariter in planum Æquatoris; nam non cadit perpendicula
riter in AD; cùm tamen arcus DF vtrumque præ&longs;tet; cadit enim perpen
diculariter in vtramque, &longs;cilicet in AD, AF. Accedit, quòd Sol, quan
tum e&longs;t ex &longs;e, &longs;uppo&longs;ita di&longs;tantia connaturali à centro mundi, ad eam re
tinendam inclinat; &longs;ed &longs;i in arcu DF feratur, eadem &longs;emper manebit di
&longs;tantiæ ab A. Tertiò, finis Naturæ e&longs;t, vt omnes revolutiones diurnæ So
lis &longs;int æquales, & con&longs;equenter æquè diuturnæ, cùm hæ &longs;int commu
nis men&longs;ura omnium motuum, & temporis externi munere defungantur. Porrè vt dictos fines Sol obtineat, gemina illa inclinatio ita &longs;e&longs;e attempe
rat, vt & ab Apogæo ad Perigæum Sol eat, & diurnæ revolutiones æqua
les ferè &longs;int, &longs;i tantùm habeatur ratio primæ inclinationis, &longs;piræ fient in
eodem plano, & omnes inæquales erunt, &longs;iverò &longs;ecundæ tantùm, &longs;piræ
fient in &longs;uperficie &longs;phærica, eruntque omnes inæquales, vt patet ad ocu
lum, cui figura &longs;ubjacet. Itaque &longs;ecunda inclinatio ca&longs;tigat inæqualita
tem à prima inductam, deflexo Sole versùs Æquatorem; & prima par pari
referens, corrigit inæqualitatem, quam alioqui prima induceret depre&longs;&longs;o
Sole versùs centrum A; & cùm tantùm ferè temporis à Q ad H, ponendum
e&longs;&longs;et, quantum à D ad Q &longs;unt enim &longs;egmenta DQ, QH, fere æqualia; haud
dubiè tot &longs;piræ &longs;egmento QH, ine&longs;&longs;e deberent, quot &longs;egmento DQ in&longs;unt,
vt æquè di&longs;tractæ vtrimque e&longs;&longs;ent; quia tamen tunc &longs;piræ &longs;egmenti QH
minores e&longs;&longs;ent, ac proinde inæquales &longs;piris alterius &longs;egmenti, haud dubiè
tota &longs;pirarum QH congeries brevioritempore decurreretur, quàm teta &longs;pi
rarum DQ, eodem &longs;cilicet & æquabili motu; &longs;ed &longs;upponuntur totidem
vtrimque dies; igitur dies intra &longs;egmentum QH, breviores e&longs;&longs;ent; igitur to
tum tempus, quod complectitur dies intra &longs;egmentum QH, decur&longs;os, bre
vius e&longs;&longs;et tempore, quod complectitur dies decur&longs;os intra &longs;egmentum
Sed æqualia tempora &longs;upponuntur: itaque vt huic incommodo occurra
tur, di&longs;trahuntur &longs;piræ &longs;egmenti QH, ita vt pauciores re&longs;tent, &longs;ed ferè æqua
les, atque ita in motu per QH Compen&longs;atur ille motus, qui alioqui per &longs;pi
ras obtineri non pote&longs;t, cùm breviores &longs;int, quàm par &longs;it.
An fortè Sol &longs;entit,
e&longs;&longs;e majores aut minores? Minimè verò; Quomodo igitur tam &longs;ollicitè
Quæro à te, Augu&longs;tine, An fortè aqua illa tubi vitrei &longs;entit
progre&longs;&longs;um in motu deor&longs;um &longs;ibi præcludi, & impediri, vt motum re
ctum in &longs;pirabilem convertat? Minimè verò; &longs;ed cùm habeat vim atque
impetum, eo &longs;anè motu movetur, quo & faciliùs moveri pote&longs;t, & in
quo dictus impetus totam &longs;uam vim exerit; modò vel minima determi
natio intercedat ad talem lineam motus; &longs;ic aqua in dicto tubo ad li
neam &longs;piralem determinatur à minima inæqualitate, vel inclinatione
tubi, & corpus grave, quod non pote&longs;t moveri in perpendiculari deor
&longs;um, movetur per Planum inclinatum, aut per arcum in funependulo,
aut per parabolam, vel aliam lineam in projectione; item corpus refle
xum, quod per eandem lineam motum pro&longs;equi non pote&longs;t, movetur
per aliam, ad quam determinatur partim à corpore reflectente, partim
à primo motu; &longs;ic etiam, vt alterum exemplum tibi ante à me promi&longs;
&longs;um adducam: Calamus volatilis, quem vos Italicè vocatis
pre&longs;&longs;o &longs;ibi per rectam impetu, cùm motum rectum, obluctantibus pen
nis, quæ aeri facilè cedunt, totum habere non po&longs;&longs;it, qui &longs;cilicet im
pre&longs;&longs;o impetui alioquin competeret, accito &longs;pirali motu, iacturam motus
recti compen&longs;at; cur verò in hanc potiùs, quàm in illam partem
eant &longs;piræ, à pennis in eam ab aëre deflexis, &longs;eu detortis omni
no procedit; quòd autem maior impetus dicto calamo in&longs;it, quàm qui
in eo motu recto, qui re&longs;tat, impenditur, vel ex eo liquidò con&longs;tat,
quod avul&longs;is ex theca, ca&longs;u aliquo, pennis, dum in medio aëre &longs;pira
tim movetur, theca ip&longs;a, præ&longs;ertim &longs;i o&longs;&longs;ea e&longs;t, longiùs aucto motu
recto, projici videatur; igitur ille impetus inerat. Sed vt ad rem no
&longs;tram redeam, cùm Sol à Q ad H totum &longs;uum motum, in &longs;piris ha
bere non po&longs;&longs;it &longs;uppo&longs;itis temporibus æqualibus di&longs;trahit &longs;piras, com
pen&longs;ans &longs;pirarum motum, motu per &longs;egmentum QH, quod breviore
tempore decurrit, quam DQ, non tamen proptereà &longs;piratim motus re
mittitur &longs;ed æqualis &longs;emper remanet; nempe cum Sol in Q non tendat
ad Tropicum, per curuam QH, &longs;ed per arcum interceptum inter AF,
AE, minorem arcu FE, atque adeo per arcus &longs;emper minores, donec
tandem perveniat in H, & cùm arcus minores citiùs perficiar, eadem
vi motus; quid mirum &longs;i citiùs perveniat à Q ad H, quàm à D ad Q, ac
proinde &longs;i &longs;piræ di&longs;trahantur in &longs;egmento QH, atque adeò pauciores
maneant licèt enim QH. Æqualis &longs;it DQ, non tamen per QH &longs;ecunda
inclinatio &longs;uam vim exerit, &longs;ed per arcus concentricos minores, quos
citiùs decurrit, licèt à prima inclinatione ad curvam QH detorqueatur. Hinc &longs;emoto motu circulari, & relicta gemina illa inclinatione, adhuc
&longs;ecunda inclinatio decurreret citiùs QH, q
&longs;equi vides, tum di&longs;tractionem maiorem &longs;pirarum, tum imminutum &longs;pi
rarum numerum, tum compen&longs;ationem talem motuum, ex qua perfecta
ferè &longs;pirarum diurnarum æqualitas nece&longs;&longs;ariò con&longs;equitur.
Si Apogæum &longs;it in Æquatore, quid tandem fieret?
Planum Troprci DI tantulùm accederet ad Æquatorem FK,
effet di&longs;tantia, &longs;ub æqualibus tamen &longs;emper angulis DAF, EAF. Tunc
autem po&longs;ito quod Apogæum &longs;it in principio Ar
netur ab Ariete ad Cancrum, quàm à Cancro ad Libram; & minus à Li
bra ad Capricornum, quàm ab hoc ad Arietem; tempora tamen erunt
æqualia à Cancro ad Libram, à Libra ad Capricornum, &longs;cilicet à me
diocri di&longs;tantia ad Perigæum: & ab hoc ad mediam di&longs;tantiam; erunt
item æqualia inter &longs;e tempora à Capricorno ad Arietem, & ab hoc ad
Cancrum.
Ille tuus calamus volatilis, vt vocas, mihi &longs;ummopere ar
ridet, itemque de&longs;cen&longs;i ille aquæ in tubo; aliquid &longs;imile in mentem
venit, cùm &longs;cilicet aqua, &longs;eu vinum per infundibulum in dolium mitti
tur; nam circa os infundibuli vinum in &longs;piras agitur, propter illam ra
tionem, quam attuli&longs;ti. Idem accidit in quibu&longs;dam fluminibus, &longs;eu la
cubus, ex quibus aqua in profundum hiatum &longs;eu voraginem &longs;piratim de&longs;
cendit, &longs;imulque à vortice naves ab&longs;orbentur, &longs;i quæ mala &longs;ua &longs;orte eò
appellantur.
Aliud omittis longè iucundius, vidi&longs;ti enim aliquando venti
turbinem, qui fe&longs;tucas, folia, pulverem in orbem agit ac vorticem;
immo & naves in medio mari &longs;ic à Typhone mi&longs;erum in modum abri
piuntur; vnde putas hunc venti vorticem &longs;eu turbinem ortum ducere?
Certè no&longs;tri Philo&longs;ophi communiter docent, hunc effe
ctum à varia reflexione procedere, quæ in circuma&longs;&longs;urgentibus monti
bus fiat.
Sat &longs;cio.
Sed quænam reflexio in va&longs;ta terrarum & Oceani
planitie fieri pote&longs;t? in qua nulli montes a&longs;&longs;urguat.
Alia profectò ratio
e&longs;t, ex eodem no&longs;tro principio petita; nempe vbi aliqua portio aëris &longs;u
perioris tractus den&longs;atur (den&longs;ari autem pote&longs;t multiplici ca&longs;u) gravior
redditur inferiore; cùm autem deor&longs;um cadere non po&longs;&longs;it, ni&longs;i inferio
rem exten&longs;ione æqualem &longs;ur&longs;um extrudat, nec tam citò extrudere po&longs;
&longs;it, &longs;piratim per illius latera de&longs;cendit; Hinc turbo & vortex, cujus rei
analogiam habes in adductis &longs;upra exemplis, ad hunc porrò effectum
perinde e&longs;t, &longs;ive aër Superioris tractus conden&longs;etur, &longs;ive inferioris rare&longs;
cat: Hinc cum igne Typhon, aliàs cum aqua conjunctus e&longs;t; igne qui
dem quo inferioris aëris tractus &longs;tatim rare&longs;cat, ac proinde maximo im
petu aër Superioris tractus &longs;piratim ruat; aqua verò &longs;i magna Vaporum
vis expre&longs;&longs;a cum igne, caloris vi, in &longs;uperiori aëris tractu &longs;tatim conden
&longs;etur, ac proinde aqua &longs;piratim etiam & præceps deor&longs;um ruat.
Inde fortè imber guttatim de&longs;cendit, cùm enim &longs;ur&longs;um ex
trudendus &longs;it aër, humor in de&longs;cen&longs;u in guttas dividitur ad faciliorem
de&longs;cen&longs;um.
e&longs;t, nam & gutta maior ex &longs;ublimiore tractu de&longs;cendit, vt non rarò
æ&longs;tate accidit; quia forvente æ&longs;tu, altiùs vapores a&longs;&longs;urgunt, & perexiguæ
guttæ lenti&longs;&longs;imè de&longs;cendent, vt &longs;æpè vidi&longs;ti in nebula, dum re&longs;olvitur:
dit gradu, intereà multæ aliæ guttulæ minores occurrunt in de&longs;cen&longs;u,
quas ip&longs;a colligit, vnde major evadit, & motus cre&longs;cit, donec tandem
in Terram labatur: hinc cæteris paribus, illæ gurtæ maiores &longs;unt, quæ
ex &longs;ublimiore tractu de&longs;cendunt; plures enim colligunt in de&longs;cen&longs;u mi
nores guttas, nempe ex mutuo contactu duarum guttarum &longs;equitur, vt
ex duabus vnica fiat; trita res e&longs;t, &longs;ed ratio &longs;atis ab&longs;tru&longs;a: hinc æ&longs;tate,
vt plurimum, guttæ imbris maiores &longs;unt, quàm hieme, hinc demum ali
quando accidit, vt iuxta verticem montis &longs;it nebula, imber verò in infe
riore tractu; &longs;ed quæ&longs;o ad rem no&longs;tram redeamus longiùs enim excur
rimus.
Circa tuam hypothe&longs;im multa e&longs;&longs;ent in accuratius examen
vocanda, &longs;ed per tempus non licet, aliqua tamen obiter percunctabor,
ac primum quidem illud, quid tibi velles, cùm &longs;upra diceres, gradum il
lum velocitatis acqui&longs;itum à Marte & à Sole, produci vel à Motore extrin
&longs;eco, vel ab ip&longs;i &longs;in et Planetis per motum acceleratum prævium.
Magnum certè hîc my&longs;terium non latet; cùm enim velim, pri
mum illum impetum Soli modò ine&longs;&longs;e, qui eidem initio inerat, eumque
motui æquabili, quo huiu&longs;que Sol movetur, movebiturque impo&longs;terum,
æqualem &longs;emper & eundem velocitatis gradum conciliare, cur enim & à
quo dictus impetus de&longs;trueretur, cùm nunquam fru&longs;tra &longs;it? perinde &longs;anè
mihi fuit, &longs;ive ab ip&longs;o Sole per motum acceleratum prævium acqui&longs;itus
fuerit, &longs;ive à Deo, vel Angelo eidem impre&longs;&longs;us; Dic, vt voles, vtrum
que enim fieri potuit; nec qui&longs;quam, opinor, hoc negaverit, nec dif
ficile e&longs;&longs;et, definite altitudinem illam, ex qua Sol ad hunc velocitatis
gradum acquirendum de&longs;cenderit, cognita &longs;cilicet Solis Apogæi vel
Perigæi di&longs;tantia; immo & tempus in tali de&longs;cen&longs;u po&longs;itum; cum emin ve
locitatetemporum,
&longs;cio, v.g. vno &longs;ecundo minuto corpus grave decurrere in perpendiculo
12. pedes, & velocitatem eodem &longs;ecundo minuto acqui&longs;itam &longs;ufficere,
vt motu æquabili 24. pedes decurrantur; &longs;cio quoque punctum Æqua
toris terre&longs;tris globi &longs;i hic motu orbis agatur, vno &longs;ecundo minuto con
ficere circiter 1250. pedes. Sit verò di&longs;tantia Solis à centro terræ 2000.
circiter &longs;emidiametrorum, &longs;i hic numerus ducatur in illum, productus
veniet hic tertius 2500000; Sol igitur vno &longs;ecundo minuto conficit to
tidem pedes: ducatur hic numerus in 60. productus erit, 150000000.
tot pedes conficit vno primo minuto: ducatur etiam hic in 60. produ
ctus erit 9000000000. tot pedes conficiet vna hora; hic demum duca
tur in 24. productus erit 216000000000. tot pedes conficiet vno die;
accipiatur &longs;ubduplus &longs;cilicet 108000000000. tot pedes decurri; vno die
corpus grave motu naturaliter accelerato in perpendiculo deor&longs;um; Iam
duco 24. in 60. & productum in 60. hic productus erit 864000. tot &longs;ci
licet minuta &longs;ecunda, quot in 24. horas, ducatur hic in &longs;e ip&longs;um, pro
ductus erit 7464960000. per quem &longs;i dividas 108000000000. quotiens
erit 14 1/2 circiter, tot pedes conficit corpus grave motu deor&longs;um, vno
gnat, itemque alium, qui vult corpus grave decurrere vno &longs;ecundo mi
nuto 15. pedes; quanquam hic ad verum proximè acce&longs;&longs;it, quod certè
in tanto numero 12. cifrarum, qui &longs;cilicet 200. & 16. millia milliorum
complectitur, parum e&longs;t. Hæc porrò eo animo dico, vt quorumdam
hallucinatio ca&longs;tigetur, qui cùm hoc, eo, quo par e&longs;t, modo non di&longs;
cu&longs;&longs;erint, multa ab&longs;urda &longs;uper hac re pronunciant. Immo, vt iam fortè
mecum ob&longs;ervas, &longs;i præcisè habeamus, quot pedes corpus grave in de&longs;
cen&longs;u decurrat vno &longs;ecundo minuto, habebimus haud dubiè quantum
decurrere debeat vno die integro, in linea recta deor&longs;um; quæ &longs;i du
plicetur, & inflectatur in circulum, hæc for&longs;itan erit, &longs;altem proximè,
magni orbis men&longs;ura; ita vt Sol motu recto prævio 24. horis decur
rerit &longs;patium æquale &longs;emicirculo magni orbis; &longs;ed quidquid &longs;it, &longs;ive
hic impetus accedat ab extrin&longs;eco, &longs;ive ab ip&longs;o Sole in &longs;e producatur,
perinde e&longs;t ad rem no&longs;tram; cùm Soli maximè connaturalis &longs;it, quate
nus &longs;cilicet Solaris globus ad talem finem à natura ip&longs;a, & naturæ ip&longs;ius
Autore ordinatus e&longs;t; quem vt obtineret tali tantoque impetu illi opus
erat; tantum igitur & talem vel ab extrin&longs;eco accepit, vel in &longs;e pro
duxit.
Sed quis Solern docuit in Occa&longs;um ferri, non verò in Or
tum; ire versùs di&longs;tantiam mediam, ad Æquatoris planum accedere, &
turbinis in&longs;tar circa &longs;uum axem inclinatum moveri, idque in hanc partem,
potiùs quàm illam?
tore movetur extrin&longs;eco, nimirum à Deo, Angelorum mini&longs;terio, vt
no&longs;tri Schola&longs;tici communiter docent, nec ego inficias eo, ab eodem
motore cuncta hæc recipit; at ex hypothe&longs;i, quod à &longs;e ip&longs;o moveatur,
quod certè tanti non e&longs;&longs;et, cùm id cuipiam corpori gravi competat; di
cerem, Solem conditum à Deo fui&longs;&longs;e &longs;upra di&longs;tantiam mediam, multis
terræ &longs;emidiametris, vt dixi, ex quo loco de&longs;cendit versus mundi cen
trum, obtenta verò media & connaturali di&longs;tantia, motu circulari mo
veri cœpit, versùs Occa&longs;um: cur, inquis, potiùs quàm versùs Ortum? Quia cum creatus fuerit in Tropico Cancri circa 180. grad. longitudinis
eo poti&longs;&longs;imum fine, vt in terræ &longs;uperficiem ageret, à maiori dictæ &longs;uper
ficiei tractu versùs Occa&longs;um inde excurrente ad hanc lineam determina
rus fuit, ex qua profectò prima determinatione, &longs;equuntur aliæ, &longs;cilicet,
Axis mundi, polorum, Æquatoris &c. & cùm tantulum primæ determi
nationis deor&longs;um retinuerit, debilis tamen, tota enim ferè in circularem
motum ivit, quid mirum, &longs;i ad Perigæum tendat? à quo rur&longs;um eodem
modo versùs Apogæum regreditur; adde &longs;ecundam inclinationem, de
qua iam &longs;upra, & quia globorum more, deor&longs;um in morem turbinis
de&longs;cendit, retinuit illum motum orbis circa eundem Axem &longs;ibi ip&longs;i
&longs;emper parallelum, vbi motu circulari agi cœpit, cui prædicta turbinatio
non ob&longs;tat, Vides, cuncta hæc ex communibus illis principiis deduci,
per quæ aliorum corporum motus explicantur.
Rectè, illud &longs;altem commodi ex hac tua hypothe&longs;i acci
dit, quod primi orbis incolæ diem primum integrum habuerunt, Sol
nempe in ortiuo horizontis illorum limbo conditus fuit; id e&longs;t, in &longs;emi
circulo ortiuo magni Meridiani; & verò æquum fuit, vt Sol, qui pro
pter hominem creatus e&longs;t, no&longs;tro huic primum hemi&longs;phærio, in quo &
primus homo conditus, præfulgeret: &longs;ed fortè nobilem coronam diutius
quam par e&longs;&longs;et detinemus; tuam illam, quam contra no&longs;tram hypothe
&longs;im adorna&longs;ti, di&longs;putationem, in proximum congre&longs;&longs;um remittimus.
Sit, vt voles, adero cra&longs;tina die, ni&longs;i tibi fortè grave &longs;it; multi
etiam ex nobili&longs;&longs;imis auditoribus futurum congre&longs;&longs;um &longs;ua præ&longs;entia ho
ne&longs;tabunt.
argumenta proponuntur.
DVBIVM mihi non e&longs;t, hanc di&longs;putationem ineunti, quin
pleri&longs;que fortè iam actum agere videar, CARDINALIS
EMINENTISSIMS, quotus enim qui&longs;que invenitur, vel Philo
&longs;ophorum in tractatione de Corpore Cœle&longs;ti; vel Theologo
rum in Opere &longs;ex dierum enucleando;; vel &longs;acri Textus Interpretum, in
eorum locorum expo&longs;itione, in quibus Terra &longs;tare, Sol & A&longs;tra
pa&longs;&longs;im moveri dicuntur; vel denique A&longs;tronomorum, in mundi &longs;y&longs;tema
te definiendo, qui hanc partam non adornet, &longs;uam falcem in hanc me&longs;
&longs;em non mittat, ac de mi&longs;ero Copernico novos triumphos agere nolit. Scribimus indocti, doctique poëmata: quanquam, vt ingenuè dicam,
maxima illorum argumentorum pars, quibus nonnulli præfatam Coper
nici opinionem petierunt, non parum laudis & plau&longs;us eidem concilia
vit; ita enim ab illius defen&longs;oribus rejecta fuere, vt &longs;olutionis, &longs;eu re
&longs;pon&longs;ionis facilitas qua&longs;i ad in&longs;tar
re in eidem &longs;ententia conciliârit, illud &longs;anè commune e&longs;t præliis etiam li
terariis, vt qui&longs;quis ho&longs;tem malè aggre&longs;&longs;us e&longs;t, & in ca&longs;&longs;um adortus,
pro &longs;emivicto haben
taxat adducam, quæ &longs;i non fortè ho&longs;tem omninò conficere, plurimùm
tamen labefactare videntur; tuum erit, Eminenti&longs;&longs;ime, qui per&longs;pica
ci&longs;&longs;ima ingenij acie vales, quam nihil quantumvis arduum, vel ab&longs;tru
&longs;um effugiat, &longs;i non de integra victoria, de potioribus &longs;altem partibus à
nobis in hac cau&longs;a, vt benè &longs;pero, referendis, judicare, necnon æqui&longs;&longs;i
mam ferre &longs;ententiam. Sed initium di&longs;&longs;ertationi demus.
Omittam, vt prudenter feci&longs;ti, argumentorum qui&longs;quilias,
quæ nonnulli, præ&longs;ertim ex antiquioribus rerum Mathematicarum &
Phy&longs;icarum minùs peritis contra tuam hypothe&longs;im adduxerunt, quæ pe
tita &longs;cilicet petunt à ventis, & nubibus, motu projectorum, de&longs;cen&longs;u
gravium, domorum ruina & lap&longs;u; quanquam nonnihil ad hominem ex
his eliciam; vt enim vis, ex motu orbis retardato, in Ortum &longs;equi aqua
rum excur&longs;ionem, per quam marinum æ&longs;tum ve&longs;tri explicant, quia &longs;cili
cet obimpre&longs;&longs;um ante impetum, quem facilè aqua retinet, nec enim ni&longs;i
à contrario impediri pote&longs;t, eundem pro&longs;equitur motum versùs Ortum;
cuius rei præclaram certè analogiam habetis in aqua, quæ cymba vehi
tur; cymba enim motum valdè retardante, aqua versùs portum excurrit;
hoc vnum e&longs;t ex præcipuis &longs;ententiæ ve&longs;træ argumentis.
Ita e&longs;t, & licèt ad ea, quæ repo&longs;ui&longs;ti, obmutire & ma
nus dare vi&longs;us &longs;im, quia illa omnia, quæ ad tabulas æ&longs;tus marini eiú&longs;que
phænomena pertinent, minùs calleo, vereor tamen, vt rerum i&longs;tarum peri
ris per&longs;uadere valeas; illud autem &longs;ilentium mihi poti&longs;&longs;imum impo&longs;uit,
quòd &longs;anctè jura&longs;ti, in adluc
marini peritos, &longs;ive Naucleri &longs;int, &longs;ive alij, imò & ip&longs;os litorum Oceani
vel idiotas incolas &longs;umma tor&longs;en&longs;ione convenire; itaque licèt ex &longs;ola ter
re&longs;tris globi circuitione æ&longs;tus marini adæquata cau&longs;a petenda non &longs;it, &longs;ed
ex alia quapiam, negari tamen non pote&longs;t, quin prædictus motus aliquid
conferat.
mirabilem effectum; &longs;i enim &longs;ufficit, nihil &longs;anè e&longs;t, quod ille Terræ motus
conferat; &longs;i verò non &longs;ufficit, o&longs;tende id, ad quod non &longs;ufficit, & illius
motus opem po&longs;tulat; &longs;emper enim recurret propo&longs;itum argumentum;
totum illud, quidquid tandem &longs;it, quod à præfato motu efficitur, circa
maximæ inæqualitatis cardines; id e&longs;t, circa Meridiem & mediam noctem,
vi&longs;um &longs;emper iri; quod tamen Ob&longs;ervationibus repugnat: itaque certum
e&longs;t, & per&longs;picuum ex Maris æ&longs;tu Terræ motum minimè probari; certum
tamen e&longs;&longs;e dicitis, ex illo inæquali motu, varium &longs;equi aquarum motum;
quod certè ad hominem &longs;ic vrgeo; &longs;i reverà e&longs;&longs;et hic motus, ex illius inæ
qualitate, varius aquarum motus &longs;equeretur, &longs;cilicet ex retardatione aqua
rum excur&longs;io versùs Ortum, ex acceleratione, excur&longs;io versùs Occa&longs;um;
hoc non negatis, &longs;ed conceditis vltrò; idque in cardinibus maximæ in
æqualitatis, aut &longs;altem &longs;emper in ii&longs;dem, cùm eadem cau&longs;a idem &longs;em
per præ&longs;tet; &longs;ed in nullo certo ac fixo temporis puncte huiu&longs;modi aqua
rum excur&longs;iones fiunt, quod nemo neger, &longs;i cæcus & &longs;urdus; nullus e&longs;t
igitur Terræ motus, ex quo alioqui prædicti effectus nece&longs;&longs;ariò &longs;eque
rentur.
Facilis re&longs;pon&longs;io nobis &longs;uppetit, qualem etiam ve&longs;tri adhi
bent, &longs;cilicet illam inæqualitatem motus, e&longs;&longs;e tantùm apparentem, iis
&longs;cilicet, qui ex Solari &longs;phæra oculos in Terram conjicerent; &longs;icut Cœle
&longs;tium &longs;phærarum motus nobis è Terra ob&longs;ervantibus inæquales apparent;
cùm tamen re ip&longs;a æquabiles &longs;int, igitur po&longs;ita reali motus æqualitate,
ita nec obe&longs;t: iam &longs;umus ergo pares.
Merum effugium e&longs;t; cùm &longs;it vera & realis, vt aiunt, motus
inæqualitas; & vt ad tuam figuram veniam.
Punctum E longè velociùs movetur, quàm F ; nam E in Ortum fertur,
vtroque motu, centri &longs;cilicet atque orbis, cùm tamen F toto quidem motu
centri feratur in Ortum, &longs;ed cum toto motu orbis feratur in Occa&longs;um, ex
vtriu&longs;que motus maxima oppo&longs;itione, motus ex vtroque mixtus maximè
retardatur, vt ex certi&longs;&longs;imis doctrinæ motuum principiis liquidò con&longs;tat. Prætereà non tantùm aquarum excur&longs;io ex dicta motus inæqualitate &longs;eque
retur, verùm etiam alia, quæ facilè cadere po&longs;&longs;ent, reverà caderent, &longs;ive in
Ortum in maxima retardatione, &longs;ive in maxima acceleratione versùs Occa
&longs;um; & ad hoc eadem facit analogia tranantis cymbæ; vbi enim hæc ad li
tus appellitur, homines parum cauti, qui in illa &longs;unt, non versùs puppim re
pelluntur à littore, &longs;ed versùs proram proni ruunt; cymba enim retinet
fixa ve&longs;tigia, dum interim impetus ante impre&longs;&longs;us reliquum corpus an
tror&longs;um agit; in quo etiam aliquam rationem vectis ob&longs;ervo, hinc quo
altiores &longs;unt homines, in dicto ca&longs;u, faciliùs ruunt; quia vectis longior
e&longs;t; &longs;ed Augu&longs;tine, hoc minimè fieri videmus.
Hoc tuum argumentum, Antime, equidem ad homi
nem, vt aiunt, maximi momenti e&longs;t; nec video quonam pacto illi, qui
ex dicta inæqualitate motus, eiu&longs;modi aquarum excur&longs;iones &longs;e qui volunt,
ex dicta inæqualitate, etiam &longs;uppo&longs;ita, minimè &longs;equi aquarum excur
&longs;iones, nempè eo motu &longs;ingulæ partes illius globi moventur, &longs;eu tardiùs,
&longs;eu velociùs, quo totius motus ratio illas moveri po&longs;tulàt; ac proinde il
lud globi punctum, quod ad Solem directè &longs;pectat de Meridie, tardè
movetur in Ortum, celeriter verò, vbi e&longs;t oppo&longs;itum in ip&longs;a media no
cte; quia totus globus ita moveri po&longs;tulat &longs;ingulas &longs;ui partes, imò etiam
in iis, quæ va&longs;e vehuntur, & ab extrin&longs;eco motum & impetum recipiunt,
inæqualitas motus non ex abrupto, at &longs;en&longs;im &longs;ine &longs;en&longs;u inducta nullum
alium effectum præter eandem rationem motus inducit; &longs;ic cymba qua
vehitur aqua celeri motu, &longs;i &longs;en&longs;im remittit, ac retardat motum, aut
certè tardiorem primum paulatim deinde accelerat, neque huc, neque
illuc aqua excurrit, nec &longs;tantes in navi huc aut illuc inclinari &longs;e &longs;entiunt.
Ita e&longs;t; vt dicis; hoc argumentum contra illos ad hominem,
vt aiunt, à me adductum e&longs;t, qui præfatos effectus ex illa motuum inæ
qualitate &longs;equi a&longs;&longs;erunt; at per te, mihi quæ&longs;o, liceat, idem argumen
tum etiam contra illos pro&longs;equi & vrgere, vt aiunt, qui negant dictos
effectus ex dicta inæqualitate &longs;equi, quorum ego; vt vereor &longs;en&longs;a, ita
illis, opinor, ingratum non accidet, quod rem hanc paulò accura
tiùs di&longs;cutiam, & ad certi&longs;&longs;ima doctrinæ motuum principia reducam;
Primò ergo quidem &longs;uppono ex dicta doctrina, impetum &longs;emel impre&longs;
&longs;um non de&longs;trui, quamdiu fru&longs;trà non e&longs;t, & con&longs;equi pote&longs;t &longs;uum ef
fectum, &longs;cilicet motum, qui & finis illius e&longs;t, &longs;eu per eandem lineam,
&longs;eu per aliam, ad quam e&longs;t nova determinatio; nulla enim e&longs;t alia ratio,
propter quam impetus de&longs;truatur; &longs;ic turbo v.g. di&longs;cus æneus, Axe vtrim
que extante, in levigato plano diuti&longs;&longs;imè &longs;uos orbes agit, & &longs;i nullus
e&longs;&longs;et attritus partium, & Axis ad perfectam libellam, per di&longs;ci centrum
iret, nunquam hic motus ce&longs;&longs;aret. Prætereà, &longs;i globus tornatus de&longs;cen
dat per planum declive probè lævigatum, quod po&longs;t tantulam incurvatio
nem &longs;ur&longs;um ex adver&longs;o, &longs;ub eodem inclinationis angulo deflectatur; haud
dubiè ad imum primi plani declivis globus non &longs;i&longs;tet, &longs;ed per aliud ad
æqualem ferè altitudinem a&longs;cendet, virtute impetus, in primo de&longs;cen&longs;u
acqui&longs;iti, ad hanc portò lineam ab eodem plano determinatur; analo
giam perfectam in vibrato funependulo etiam habes, & in ip&longs;a corporum
repercu&longs;&longs;ione; de&longs;truitur tamen aliquid impetus in illo a&longs;cen&longs;u, &longs;cilicet
à quodam impetu innato, non acqui&longs;ito, qui gravibus ine&longs;t, &, vt fa
cilè vobis per&longs;uaderem, ab ip&longs;a gravitate non di&longs;tinguitur; &longs;ic etiam ab
alio impetu ob&longs;tante, vel ad aliam lineam trahente, vnde &longs;equitur de
terminatio quædam mixta, &longs;en&longs;im de&longs;truitur; &longs;ed ne longiùs excurram,
illa omnia doctrinæ motuum principia hoc loco dumtaxat &longs;upponam, quæ
huius doctrinæ petiti facilè concedunt, & fusè alibi pertractata nec non
firmata fuêre. Primo igitur loco &longs;uppono, impetum nunquam de&longs;trui,
ni&longs;i quando e&longs;t fru&longs;trà, id e&longs;t, quando motus omnis impeditur, à quo
cunque tandem &longs;it ille impetus, &longs;ive impre&longs;&longs;us ab extrin&longs;eco, &longs;ive ab ip&longs;o
corpore in &longs;e productus, &longs;ive à toto, parti, &longs;ive toti à parte, &longs;ive parti ab alia
parte, nam perinde e&longs;t, quoad hoc principium.
Hoc facilè damus, imò hoc pro generali axiomate libenter
admitto, nihil vnquam de&longs;trui, ni&longs;i quando e&longs;&longs;e non pote&longs;t, ni&longs;i fru&longs;trà
&longs;it. Sic anima, quæ defectu corrupti organi non pote&longs;t ampliùs operari
in corpore, de&longs;init e&longs;&longs;e, omninò quidem, &longs;i extrà organum operari
non pote&longs;t, vt de animabus brutarum animantium Philo&longs;ophi docent, non
tamen omninò & ab&longs;olutè, &longs;ed in corpore tantùm, &longs;i extrà organum opera
ri pote&longs;t, vt anima rationalis.
Hoc idem principium ad alias qualitates etiam extendi pote&longs;t;
caloris v.g. frigoris, &c. quæ quamdiu &longs;uum finem con&longs;equi, & præ&longs;ta
re effectum po&longs;&longs;unt, in &longs;ubjecto, cui inhærent, tamdiu in eo permanent
intactæ; vt &longs;i per actionem qualitatis contrariæ novus effectus inducitur,
ac proinde, vel totus prior, vel pars illius de&longs;init, tunc prima illa qualitas
in &longs;ubjecto illo fru&longs;tra e&longs;&longs;e dicitur, ac proinde vel &longs;ecundùm &longs;e totam,
&longs;i totus effectus abactus e&longs;t, vel &longs;ecundùm &longs;ui partem, pro rata effectus
de&longs;tructi, e&longs;&longs;e de&longs;init.
Ad &longs;peciem hæc fortè cuipiam vera e&longs;&longs;e videntur; at profectò
res &longs;ecus &longs;e habet in præfatis qualitatibus, de quibus modò di&longs;putatio
in&longs;tituta non e&longs;t, &longs;atis mihi e&longs;t, &longs;i in no&longs;tro impetu res ita &longs;e habeat; ad
mitto etiam ea, quæ dixi&longs;ti, Augu&longs;tine, de anima rationali; de brutorum
animabus aliqua fortè difficultas e&longs;&longs;et, &longs;ed huius loci non e&longs;t. Sit igitur
&longs;ecundum principium ex eadem doctrina motuum huc derivatum, cor
pus eo motu movetur, quo faciliùs moveri pote&longs;t, minore &longs;cilicet &longs;um
ptu, & cum minore difficultate, compen&longs;atque vt plurimum in vno,
quod in alio difficiliùs tantùm obtinere po&longs;&longs;et; hæc iam &longs;upra indicavi in
primo congre&longs;&longs;u; &longs;ic cylindrus, vel in plano lævigato iacens, vel humido
innatans ab altera extremitate pul&longs;us, vel tractus etiam per lineam per
pendiculariter incidentem, motu recto non movetur. &longs;ed circulari, circa
centrum, quod terminat mediam proportionalem totam inter & dimi
diam, ita vt major quantitas &longs;it versùs illam extremitatem, cui potentia
motrix applicata e&longs;t.
Licèt fortè in parergum incidamus, tantulum &longs;chematis de
&longs;idero, vt rem à te &longs;olo auditam meliùs intelligam.
Non opus e&longs;t alio &longs;chemate: Supponamus enim cylindrum
BC (
ad BK, ita hæc ad BA, & ex K ducantur arcus BG, CN &longs;imiles, duca
turque GKN; cylindrus pul&longs;us, vt dixi ex B, de&longs;cribit &longs;uo motu duos
&longs;ectores BKG, CKN, quia &longs;cilicet &longs;patium vtroque contentum e&longs;t om
nium po&longs;&longs;ibilium minimum, &longs;uppo&longs;ito quolibet alio arcu, non minore
BG, & duobus radiis, qui &longs;imul coniuncti &longs;int æquales toti BC, quod
aliàs demon&longs;traui, nempe à &longs;ectoribus &longs;imilibus ad triangula propor
tionalia, & ab his ad &longs;implicem lineam gradum faciens, reduxi rem ad
hoc problema, datam quantitatem ita &longs;ecare, vt maius &longs;egmentum &longs;it
ad minus, vt hoc ad tertium, & compo&longs;ita ex duabus extremis &longs;it om
nium po&longs;&longs;ibilium minima; vel &longs;ic Datæ quantitati vnam partem detra
here, & aliam addere, vt re&longs;idua &longs;it ad detractam, vt detracta ad addi-
&longs;ed his omi&longs;&longs;is & &longs;uppo&longs;itis, eo motu hic cylindrus, atque adeò cœteris
paribus, quodlibet corpus movetur, &longs;ive ab intrin&longs;eco, &longs;ive ab extrin
&longs;eco, quo faciliùs moveri pote&longs;t; idem ob&longs;ervamus in &longs;agittis alii&longs;que
corporibus oblongis, &longs;i vel aliquando &longs;ponte &longs;ua cadunt, vel projiciun
tur; &longs;ed luculentum exemplum omittere non po&longs;&longs;um, globi &longs;cilicet per
planum declive de&longs;cendentis, cùm enim duobus modis deor&longs;um ferri
po&longs;&longs;it. Primò vno dumtaxat motu centri, quo &longs;ingulæ partes per lineas
plano inclinato parallelas eant. Secundo motu rotationis, mixto &longs;cilicet
ex motibus centri & orbis; hoc &longs;ecundo modo movetur, non verò pri
mo, quem multus partium affrictus maximoperè retardaret.
quia cùm centrum gravitatis globi &longs;it extra perpendiculum, quid mirum, &longs;i
eò inclinet, vnde motus orbis nece&longs;&longs;ariò &longs;equitur; vt facilè etiam &longs;ine
figura quivis intelligat?
Nonnihil tamen figuræ adhibeo, vt maximam difficultatem,
quam ego quidem &longs;entio, in eo, quod dicis, mihi excutias.
Sit planum inclinatum DH, & in eo
globus gravis, tangens planum in D, per
pendicularis AF, à centro globi ducta;
&longs;intque aliæ duæ lineæ BAG, CI, plano
parallelæ, de&longs;cendit globus A, vt dixi,
non quidem primo modo, ita vt punctum
C &longs;equatur lineam CI, & punctum D
lineam DH. Sed per rotationem, vt
aiunt, ita vt circa centrum A, aliæ par
tes moveantur, quia, inquis, centrum
globi A e&longs;t extra perpendiculum; de quo amabò perpendiculo intelligis
an de BD ducto à puncto contactus, an verò de AF.
Vtrumque intelligo; vt enim globus &longs;u&longs;tineatur in plano
DH, perpendiculum, quod ducitur a puncto contactus B, per centrum
A ite deberet; vnde certè planum e&longs;&longs;et horizonti parallelum; quando
verò vnum perpendiculum cum alio non concurrit, vt in hoc ca&longs;u,
tunc planum e&longs;t inclinatum; igitur cùm centrum A per lineam perpendi
cularem AE non &longs;u&longs;tineatur à plano, vlteriùs enim ad F pertingit, de&longs;cen
dat nece&longs;&longs;e e&longs;t, cùm de&longs;cendere po&longs;&longs;it; in aliis omnibus corporibus, per
fectam analogiam habes. Sit enim planum horizontale CN, & in eo
rectangulum CB, cuius centrum gravitatis F, ita
inclinetur rectangulum CB, donec perveniat ad
&longs;itum DI, exi&longs;tente centro gravitatis in H, ac
proinde cùm perpendiculam HL cadat extrà
punctum contactus D, deor&longs;um tendit, & to
tum rectangulum ruit. Idem prorsùs de globo
dicendum e&longs;t.
Crede mihi, Augu&longs;tine, multi &longs;æpè
ac &longs;æpiùs paralogi&longs;mis, & fal&longs;is præoccupatio-
dit; vt enim in tua &longs;i&longs;tamus figura; non negabis, opinor, centrum H
minimè de&longs;cen&longs;urum, &longs;i fortè propiùs ad planum CN accedere non po&longs;
&longs;et, cùm ex ip&longs;is terminis idem &longs;it de&longs;cendere, & propriùs ad planum DN
accedere; At verò centrum A (
natum DH accedere non pote&longs;t, à quo æquali &longs;emper di&longs;tantiæ men&longs;ura
di&longs;tat, &longs;cilicet radio, vnus autem radius alteri æqualis e&longs;t; hinc nunquam
di&longs;cedit à linea AG parallela Plano DH, & quodlibet perpendiculum ad
planum terminatum à centro A ductum lineæ AF æquale e&longs;t.
Proptereà globus de&longs;cendit, quia eius centrum A non
&longs;u&longs;tinetur in puncto contactus, cùm &longs;u&longs;tineri non po&longs;&longs;it ni&longs;i in perpen
diculo AF.
Rectè, Proptereà globus de&longs;cendit; &longs;ed profectò non pro
pterea globus volvitur, &longs;ive enim volvatur deor&longs;um, &longs;ive de&longs;cendat iux
ta primum modum in &longs;itu, in quo e&longs;t, centrum A per eandem lineam
AG, deor&longs;um tendit, nec vnquam ab ea di&longs;cedit, aut di&longs;cedere pote&longs;t;
cur igitur cum vtroque modo, per eandem lineam de&longs;cendere po&longs;&longs;it, hoc
&longs;ecundo potiùs, quàm illo primo de&longs;cendit? quod enim dicis, Augu&longs;ti
ne, centrum gravitatis A e&longs;&longs;e extra perpendiculum, ac proptereà de&longs;
cendere, id totum verum e&longs;t, & à me admittitur, vndè reverà de&longs;cen
dit; &longs;ed per lineam AG, infrà quam de&longs;cendere nequit ; &longs;ed cùm per eam
vtroque modo ire po&longs;&longs;it, ac proinde de&longs;cendere, cur, quæ&longs;o, vno
potiùs quàm alio? Sed hoc alio exemplo fortè luculentiore clari&longs;&longs;imè
o&longs;tendo.
Sit planum inclinatum AB, &longs;it rectan
gulum C in eo collocatum; certè &longs;i &longs;up
ponatur vtrumque lævigatum, de&longs;cen
det rectangulum, per dictum planum,
ibitque centrum gravitatis C per CP
parallelam plano; nec enim aliter per &longs;e
de&longs;cendere pote&longs;t, nec volvi circa angu
lum D, quod fieri deberet, vt
alioquin centrum C in revolutione a&longs;cen
deret, quod dici non pote&longs;t;
CD perpendiculum, & CN horizontalis, haud dubie &longs;i C volvatur
circa D, radio DC, tangens decta à puncto C, perpendicularis in
CD, ibit &longs;uprà horizontalem CN, vt patet ad oculum: Dixi per &longs;e,
nam per accidens, cùm à plani &longs;cabutie impediri po&longs;&longs;it, latus AD, &longs;u
perior p
&longs;um circum volvitur circa angulum D ; &longs;ed hoc per accidens fit. Sit autem
aliud rectangulam F in eodem plano in
rizontalis FO; certè &longs;i ducatur tangens FK perpendicularis
centium F circa M radio MF volvatur, ibit infra FO, igitur non a&longs;cen
det &longs;ed de&longs;cendet. itaque vt ad no&longs;t
nec
circa punctum D volvi po&longs;&longs;it centrum A, (
globus volvitur, vt centrum A de&longs;cendat, cùm de&longs;cendere po&longs;&longs;it, etiam&longs;i
non volvatur; igitur ideò volvitur, &longs;eu rotatur, quia cum vtroque modo
de&longs;cendere valeat centrum A, per eandem &longs;cilicet lineam AG, & cùm pri
mo modo difficiliùs de&longs;cendat, propter affrictum partium; ideò &longs;ecundo
modo de&longs;cendit, quia &longs;ic faciliùs de&longs;cendit; &longs;ic enim corpus grave non mo
do determinatum e&longs;t ad motum, &longs;ed etiam ad faciliorem, cæteris paribus,
motum.
Audivi hactenus, in rotis valere rationem vectis; e&longs;t enim
vectis quidam perpetuus; vnde manife&longs;ta petitur ratio, cur majoribus
rotis currus in&longs;truantur; nempe inde cre&longs;cit mechanicæ potentiæ mo
mentum.
Quis negat, in rotis haberi rationem vectis in vecte tamen &longs;up
ponitur aliquod punctum qua&longs;i immobile, quod in ip&longs;o Hypomoclio col
locatur; quod vt meliùs intelligatur.
Supponatur planum DH e&longs;&longs;e horizon
tale, in quo &longs;it rota, eaque trahatur fune
AG, in&longs;erto &longs;cilicet axe per
A, haud dubiè &longs;i æquè facile
mitas diametri rotæ DC adduci po&longs;&longs;et à
potentia trahente per AG vtraque extre
mitas, ac proinde reliquæ omnes partes
rotæ per parallelas AG adducerentur, &
omnes æquè citò
&longs;i rota humido innatet; at
frictum
liùs accedit; item A. &c. ac proinde citiùs
propter partium nexum, motus orbis nece&longs;&longs;ariò &longs;equitur: Iam vero &longs;uppo
ne planum inclinatum, & nullam potentiam extrin&longs;ecam applicatam e&longs;&longs;e
centro A, &longs;ed &longs;olam ine&longs;&longs;e gravitatem rotæ, quæ à centro A exeritur ab
intrin&longs;eco, eodem pror&longs;us modo, quo ante à potentia, fune applicata
in plano horrizontali, & vt potentia extrin&longs;eca movet rotam eo motu, quo
faciliùs moveri pote&longs;t, mixto &longs;cilicet ex motu centri & orbis, in hoc plano,
ita & propria rotæ gravitas in inclinato; quid clarius? maneat igitur illud
principium, quòd &longs;cilicet corpora eo motu moveantur, cæteris paribus, quo
faciliùs moveri po&longs;&longs;unt.
Do manus, & rem optimè capio, &longs;ed antequam vlteriùs per
gas, vnum ex te, Antime; re&longs;cire velim, circa ca, quæ in he&longs;terno con
gre&longs;&longs;u à te accepi. Illico probavi, vbi di&longs;ce&longs;&longs;i&longs;ti, pulcherrimum illud expe
rimentum tubi vitrei, in quo aqua per &longs;piras de&longs;cendit, dum &longs;ur&longs;um extru
dit, eo, quo dixi&longs;ti, modo inclu&longs;am illam aëtis portionem; ob&longs;ervavi
enim. illam aëris portionem in cylindrum priore contractiorem, vt labenti
aquæ &longs;ecus
&longs;upicma pars &longs;it convexa &longs;phærica infima verò ba&longs;is, omnino plana, &longs;altem
provt oculo &longs;ubjicitur.
Memini me legi&longs;&longs;e vel audii&longs;&longs;e præclari&longs;&longs;imam huius Phæno
neni rationem, nempe illa portio aëtis, aqua levior, vt in a&longs;cen&longs;u aquæ vim
& re&longs;i&longs;tentiam faciliùs frangat & &longs;uperet, huiu&longs;modi qua&longs;i cuncatam figu
ram induit.
An fortè pro demon&longs;tratione hoc venditares?
Sed vnde, quæ&longs;o,
& qua vi, &longs;eu virtute aër in hanc formam &longs;e&longs;e fa&longs;tigiat? Certè &longs;i ad per
rumpendum &longs;ur&longs;um faciliùs, mucronem illum nimis obtu&longs;um, &longs;phæricum
&longs;cilicet, in acutiorem conicum attenuare & acuere debuerat, cunei enim
eò validiores &longs;unt, quò acutiores. Deinde æquè facilè aqua &longs;uperficiem
&longs;phæricam aëris dividere pote&longs;t ac planam: præterea cur minor aëris portio
aquæ re&longs;i&longs;tentiam citiùs perrumpit, & &longs;ur&longs;um emergit? Nempe vt corpus
grave majus gravitatem &longs;uam potentiùs exerit, ita & leve majus &longs;uam le
vitatem; &longs;ed cur aqua &longs;imiliter cuneum cuneo minimè opponit? an fortè
in ratione gravis corporis aëri cedit, quatenus hic corpus leve e&longs;t? itaque
alia omnino rati
deinde &longs;uas &longs;p
&longs;en&longs;im ruere non pore&longs;t, ni&longs;i quoquo versùm cylindri aeris &longs;uperiorem
marginem qua&longs;i excutiat, & qua&longs;i &longs;e&longs;e in novam cunei formam induat, e&longs;t
enim cuneus latior in &longs;ummo, in imo acutior; neque in hoc vlla e&longs;t difficul
tas; multa &longs;anè eaque &longs;citu digna &longs;uper hoc experimento inihi dicenda e&longs;
&longs;ent, &longs;ed omitto, ne in parergis toti &longs;imus; inferior verò portio, &longs;eu ba&longs;is
plana e&longs;t; quia nullum aquæ pondu illam emarginat.
Sed quid &longs;i oleum aquæ loco adhibeas; aut certè non
aëris, &longs;ed olei portionem tubo includas, aut demum oleum &longs;imul &
aëra?
Si oleum loco aquæ, idem fiet; quanquam paulò lentiùs aëris
portio &longs;ur&longs;um evadet; &longs;i verò aëris loco, eodem modo, & &longs;ub eadem
forma, &longs;ed multò lentius; quia &longs;cilicet oleum e&longs;t longè gravius aëre: &longs;i
demum &longs;imul vtrumque, aër oleum longè po&longs;t &longs;e relinquet; &longs;i tamen dum
olei patricula mediam tubi altitudinem decurrit, po&longs;tquam aër iam emer
&longs;it tubum inverta;, aër certè oleum facilè a&longs;&longs;equitur, nec non per medium
oleum perrumpit, &longs;ervata eadem figura; quanquam tunc oleum &longs;e&longs;e non pa
rum dilatat, vt &longs;ur&longs;um aëra extrudat; aut &longs;altem vt eidem, vtpote leviori,
tran&longs;itum cedat.
Aliquando accidit in eo conflictu, vt aëris bullula &longs;upremæ
olei &longs;uperficiei adhæ&longs;erit & qua&longs;i captiva reman&longs;erit; tunc verò, vt
fidelis ob&longs;ervator refert, paulo citiùs oleum emer&longs;it, aër enim addidit
alas.
Oleum, vt probè tenetis, &longs;ua vligine particulam aëris intra
buliam continere potuit, nempe bullæ ex materia vligino&longs;a tornantur;
quod autem totum illud corpus ex aëre & oleo con&longs;tans, paulò faciliùs ab
aqua &longs;ur&longs;um extrudatur, vel à levitate viribus auctis feratur, mirum e&longs;&longs;e
non debet: de levitate hoc loco non di&longs;puto, aio tamen, ex hoc experi
mento, minime probari, immo potiùs, vt patet, ex iis, quæ dicta &longs;unt,
impugnari. Sed ad alia principia ex doctrina motuum accer&longs;enda pergen-
præ&longs;cindendo à magneticis, & electricis, in quantum illud aliquem mo
tum impedit; &longs;i enim id quod movetur nullo modo ab alio impeditur,
nullam vim pror&longs;us contra illud retorquet; & hoc nemo negaverit, qui hu
ius doctrinæ peritus &longs;it; &longs;ic directus ictus vegetior e&longs;t, obliquus verò debi
lior; in globulis, qui adhiberi &longs;olent in ludo minoris tudiculæ, res e&longs;t om
nino per&longs;picua.
Videtur e&longs;&longs;e quoddam paradoxum, quod dicis cau&longs;am &longs;cilicet
potentiùs agere, quando magis impeditur, erit fortè quædam antiperi&longs;ta&longs;is;
&longs;ic ignis
Ita e&longs;t, paradoxum e&longs;&longs;e videtur; &longs;i quis tamen rectè perpendat,
impetum eum dumtaxat finem, vel effectum habere, ac præ&longs;tare immo
bili, cui ine&longs;t, vt hoc moveatur, tali &longs;cilicet motu & modo, qui offectus
&longs;i non impeditur ab alio. fru&longs;tra certè contra illud vim &longs;uam exerit, &longs;i v.
g. corpori dum movetur, à tergo manum admoveas, aut certè à frontè, ea
ea tamen lege, vt manum admotam æquè citò moveas, nullam
vim, nullum impetum manui tuæ imprimi &longs;enties; quia hæc nullo modo
impedit illius corporis motum; &longs;i verò mobile in aliud corpus impinga
tur, quod motui obe&longs;t, in illud agit, impre&longs;&longs;oque impetu, illud amovet, vnde,
vt dixi, finis primarius impetus e&longs;t mobilis, cui ine&longs;t, motus; &longs;ecundarius
verò, & quem dumtaxat propter primum ponit, e&longs;t motus alterius cor
poris, quod dictum motum impedit; nec mirum, &longs;i impetus alium impetum
producit, in eo &longs;cilicet, quod proprij mobilis motum impedit: Hinc &longs;i Phi
lo&longs;opho in verbis ludere liceret, dici à me po&longs;&longs;et
tur,His præ
mi&longs;&longs;is, ad rem venio, Augu&longs;tine; Repetamus figuram Sextam, & primo
quidem loco vnum dicam, quod vix apud vos fidem inveniat, licèt cer
ti&longs;&longs;imum &longs;it, geometrica &longs;cilicet demon&longs;tratione confirmatum; illud
autem ad incredibilem proportionem inæqualitatis motus rotæ, in
diver&longs;is illius punctis con&longs;iderati pertinet; dico iterum incredi
bilem.
ne&longs;cit? quis oculos figens non videt, &longs;uperius rotæ punctum à plano, in
quo rota volvitur, tota rotæ diametro di&longs;tans, velociùs agi, quàm infimuru,
in quo &longs;cilicet rota planum tangit.
Serio loquor, Chry&longs;ocome, non iocor; vident omnes e&longs;&longs;e quidem
inæquales motus, &longs;ed nemo crederet tantam inæqualitatis propor
tionem.
Quanta porrò illa erit?
fac &longs;upremum illud punctum moveri
duplo citiùs infimo, aut etiam triplo, quadruplo, decuplo, vt voles; quid
tandem erit?
quam potes proportionem inæqualitatis; & videbis vtrùm illa, quam e&longs;&longs;e
con&longs;tat in rigore geometrico, &longs;it incredibilis.
Si centuplam e&longs;&longs;e dixero, vera haud dubiè longè maior erit, &
At &longs;i maiorem centupla, immo & millecupla, & centena mille
cupla e&longs;&longs;e dicerem, omnem fidem omnino detrectares? &longs;i dicerem majorem
e&longs;&longs;e quacumque de&longs;ignabili, illico iocari me diceres, Chry&longs;ocome, vt tamen
verbo dicam, res ita &longs;e habet, vt facilè demon&longs;tratur.
Sed quæ&longs;o te, noli nos vltra in geometrica retia & Labyrinthos
deducere, hæc enim totam congre&longs;&longs;ui gratiam & amœnitatem &longs;enticeta eri
piunt.
Si quando illis retibus aliquam veritatem nos fœliciter expi
&longs;cari contingat, crede mihi Chry&longs;ocome, illa retia non &longs;unt adeò inamœna,
&longs;ed vt tibi morem geram, nihil ferè dicam quod etiam ab A geometris facilè
intelligi non po&longs;&longs;it.
Sit ergo Rota D, quæ volvitur in plano FG, punctum E &longs;upre
mum, F infimum, ita autem moveatur, vt motus orbis, &longs;eu rotæ
circa centrum D, &longs;it æqualis motui eiu&longs;dem centri D ; ac proinde eodem
tempore, quo E v.g. integrum &longs;uum orbem circa D decurrit, centrum D.
lineam rectam decurrat æqualem peripheriæ eiu&longs;dem rotæ, vel circuli, mo
vetur autem E motu illo mixto per lineam curuam EQV, quam haud
improprio nomine cycloidem vocatis, cuius &longs;ubduplam dumtaxat figuram
delineavi; nam petinde e&longs;t, &longs;ive punctum Rotæ ab E &longs;upremo perveniat
ad infimum V per curvam EQV, &longs;ive ab imo V ad &longs;upremum E per
VQE.
de qua etiam opu&longs;culum geometricum edidi&longs;ti; &longs;ub nomine Antimi
Parbij.
Non agno&longs;cerem pro in ea lucubratiuncolam illam, ni
&longs;i me
quin hoc loco in&longs;ignem pro&longs;ectò Geometram
gelis digni&longs;&longs;imum magni illius Cavalerij di&longs;cipulum appellem, ei
que gratias, quam po&longs;&longs;um maximas agam, pro iis laudibus, qui
bus liberaliùs certè quàm par fui&longs;&longs;et, cùm iis longè inferior &longs;im, pro &longs;ua
humanitate, me alioquin pror&longs;us incognitum, ratione præfati opu&longs;culi cu
mulavit; &longs;ed ad rem no&longs;tram. Comparemus vtriu&longs;que puncti motus, &longs;u
premi &longs;cilicet atque infimi; quod vt clariùs &longs;uccedat, &longs;it arcus EP. trigin
ta grad. punctum E, dum prædictum arcum decurrit, deferturque à cen
tro D &longs;ini&longs;tror&longs;um, &longs;cilicet versùs V, acquirit &longs;ini&longs;tror&longs;um ratione vtriu&longs;
que motus, totum &longs;patium OQ, &longs;cilicet ratione motus orbis, rectam OP,
id e&longs;t &longs;inum rectum EP, quem &longs;uppono e&longs;&longs;e 30. grad. & ratione motus
centri, rectam PQ æqualem ip&longs;i arcui ER, tantumdem enim Spatij cen
trum decurrit, ergo ratione vtriu&longs;que totum &longs;patium
FR arcus æqualis 30. &longs;cilicet grad. punctum R eodem tempore motu or
bis acquirit dextror&longs;um
æquale arcui FR. exi&longs;tis autem duobus motibus re&longs;ultat R T. Iam compa
remus hæc duo &longs;patia, &longs;cilicet. EQ, & RT, vel OQ, & differentiam
SR, FT, &longs;it DE 100000. OP, &longs;ubdupla DE erit 50000. vt autem 7. ad
11.ita DE ad arcum EI, id e&longs;t ad 157143.cuius terti ars &longs;cilicet 52381.
erit æqualis arcui EP, vel rectæ
ro alteri, erit 102381. ducatur deinde per punctum R, &longs;ecans DR, haud
dubiè cadet vltra punctum T, versùs V, nempe tangens, quæ terminatur
ad dictam &longs;ecantem e&longs;t &longs;emilatus polygoni circum&longs;cripti; igitur major
arcu FR; igitur &longs;egmentum illud &longs;ecantis &longs;eu differentia &longs;ecantis, & &longs;inus
totius e&longs;t maior &longs;patio RT; igitur &longs;i &longs;upponamus æqualem, faciemus mo
tú R maiorem vero; accipio igitur &longs;ecantem arcus FR, & in canone inve
nio 115470. ex quo numero detraho &longs;inum totum 100000. re&longs;iduum erit
15470. hæc e&longs;t RT, qùæ ferè e&longs;t vna 7.igitur motus puncti E ad motum
puncti R toto tempore quo decurritur arcus FP, vel RS e&longs;t vt 7.
ad 1.
Sed vbinam illa tua millecupla inæqualitatis proportio?
ad populum phaleras; vos &longs;anè Mathematici, multa promittitis, pau
ca præ&longs;tatis; totum orbem movetis, & vix murum in ruinam præcipitem
&longs;u&longs;tinetis.
Parciùs i&longs;ta viris, Chry&longs;ocome, nam fortè aliquando incides in
manus cuiu&longs;piam ex iis, quos puros Geometras vocant, à quo immi&longs;ericor
diter vapulabis, iis arma profectò non de&longs;unt, &longs;agittæ &longs;cilicet, &longs;ecantes,
&longs;ecures, cunei, ro&longs;tra & vngues; expecta igitur parumper, nam pedeten
tim cum i&longs;ta rota progredimur, accipe arcum 15. grad. id e&longs;t &longs;ubduplam
cet.25038. erit compo&longs;ita ex vtraque 51228. rejecta minutia, hic erit mo
tus punct
&longs;ecantem eiu&longs;dem anguli 103290. ex qua, &longs;i &longs;ub&longs;trahas &longs;inum totum, re&longs;i
duum erit 3290. hic e&longs;t motus puncti F, eodem tempore, qui ad priorem
habet rationem
dem &longs;inum rectum 5233. compo&longs;ita ex vtraque erit 10471. differentia ve
rò &longs;ecantis & &longs;inus totius eju&longs;dem anguli 137. Cùm igitur motus E per
arcum 3. grad. &longs;it ad motum F per arcum æqualem vt 10471. ad 137. erit
vt 75.ad 1.&longs;it motus per arcum 1.grad.erit compo&longs;ita ex arcu & &longs;inu 3491.
differentia &longs;ecantis & &longs;inus totius 15.igitur ratio maioris motus ad
remAccipe arcum 30.minutorum, erit &longs;umma, arcus & &longs;inus recti 1746.
differentia 4. igitur ratio
1. igitur ratio Si vltra progredimur, &longs;ecantes ce&longs;&longs;ant in canone Pi
ti&longs;ci, et&longs;i veniamus ad quid &longs;i ad vnum &longs;e
cundum, aut tertium &c. immo quantumvis parvum arcum accipias, erit
maior proportio ex triplici capite. Primò, quia curva EQ e&longs;t maior rectâ
OQ, &longs;ed per EQ movetur punctum E, idem de aliis arcubus. Secundò,
quia differentia &longs;ecantis & &longs;inus recti e&longs;t major RT, igitur, hic accipitur
maior, illic verò minor motus, quàm reverà &longs;it. Tertiò quia E à puncto
oppo&longs;itionis versùs Q continuò retardat motum &longs;uum; igitur movetur
velociùs in primo gradu, quam in &longs;ecundo & in hoc citiùs, quàm in ter
tio, atque ita deinceps 5 cum tamen F à puncto oppo&longs;itionis ver&longs;us R mo
tum &longs;uum continuò acceleret; ac proinde moveatur citius in &longs;ecun
do gradu quàm in primo & in tertio quàm in &longs;ecundo, atque ita dein
ceps; con&longs;tat igitur: quod initio à me propo&longs;itum fuit, majorem
e&longs;&longs;e proportionem motus &longs;upremi puncti rotæ; quæ in plano volvi
tur, ad motum infimi, qualibet a&longs;&longs;ignabili; hinc paradoxum egre
gium, ita moveri duo extrema eju&longs;dem lineæ finitæ, vt vnum alio infi
nities velociùs moveatur, infinities, inquam, Syncategorematicè,
nec e&longs;t par ratio rotæ, quæ motu tantùm orbis movetur, quia centrum
illius &longs;upponitur immobile, nec vllum punctum a&longs;&longs;ignari pote&longs;t, in radio
mobili, circa alteram extremitatem, cujus motus ad motum alterius ex
tremitatis certam & finitam proportionem non habeat; denique huc etiam
plurimùm, immo totum facit angulus contingentiæ, quem prædictus circu
lus cum plano facit eo &longs;anè minorem, quo circulus major e&longs;t, cùm enim
quolibet angulo rectilineo, quamtumvis minimo, minor &longs;it, id que in infini
tum; motus puncti infimi rotæ, &longs;eu contactus, eo ip&longs;o incipit, quò tangere
planum de&longs;init, intercepto dumtaxat dicti anguli contingentiæ cu&longs;pide,
omni rectilineo minore.
Quid &longs;i aliquis diceret, punctum illud aliquantulum quie&longs;cere,
ad in&longs;tar cuiu&longs;dam polygoni infinitorum laterum? Sic enim polygonum in
plano volvitur, vt circa &longs;ingulos laterum angulos totum polygonum &longs;uc
ce&longs;&longs;ivè volvatur.
Scio, à viro docti&longs;&longs;imo hæc iam olim fui&longs;&longs;e dicta, &longs;ed Geome-
æquales &longs;unt, &longs;ecus Polygoni; deinde Polygonum in plano moveri non
pote&longs;t, ni&longs;i eius centrum modò a&longs;cendat, modò de&longs;cendat, vt patet; at
centrum circuli ab eadem linea plano, in quo volvitur parallela; nunquam
de&longs;cendit; igitur circulus polygonum dici non pote&longs;t.
infinita, vt dicis, in minutis tantummodò primis, &longs;ecundis, tertiis lo
cum habeat, non verò in arcubus paulo majoribus, vt con&longs;tat ex iis quæ
dixi&longs;ti, nihil &longs;anè obe&longs;&longs;e pote&longs;t, ac proinde parum, aut nihil nobis curan
da, qui ad illa in&longs;en&longs;ibilia, in Phy&longs;ica præ&longs;ertim, minimè attendimus.
In digitalem rotam, &longs;i fortè trahatur à te&longs;tudine, i&longs;thæc opti
mè quadrant, &longs;ecus tamen in telluris globum, cujus &longs;ingula minuta 5000.
pedes continent; & motus adeò velox e&longs;t, vt habita tantùm ratione motus
orbis, quodlibet punctum circuli æquatoris, quolibet &longs;ecundo minuto, vt
iam dixi &longs;uprà conficiat pedes 1250.circiter. Con&longs;tat igitur de illa incre
dibili motuum inæqualitate in partibus certè &longs;en&longs;ibilibus tum &longs;patij, tum
mobilis, etiam in &longs;ecundis & tertiis minutis, &longs;i terre&longs;tris globus moveatur;
con&longs;tat item maxima velocitas, quam ne quidem globi ex majoribus, vel
minoribus tormentis emi&longs;&longs;i adæquant.
Quantus apparatus, Deus bone, contra Copernicanam hypo
the&longs;im; vereor tamen vt &longs;ufficiat.
Cave, Antime, ne tibi tritum illud occinamus,
tes
verà tecum &longs;entio; aut fortè tam multis & variis initio nos fatigare, &longs;eu
potiùs obruere volui&longs;ti, vt &longs;cilicet, ea quæ oppones minus alacriter retun
damus; age igitur, nam prælu&longs;um &longs;atis; illos Oratores imitari mihi vi&longs;us es,
qui toti &longs;unt in exordiis; ita vt finito orationis exordio, ad aliud tran&longs;eant
exordium, & ab hoc &longs;ecundo ad aliud, & nunquam ad punctum, quod
probandum &longs;u&longs;ceperant, de&longs;cendunt, proloqui duntaxat & magnifica ex
ordia fabricare contenti.
Ludis, Chry&longs;ocome, &longs;ed profectò non impunè feres; nemo non
videt, ea quæ præmi&longs;i, non e&longs;&longs;e exordia, &longs;ed iacta principia, ex quibus de
inde meum ratiocinium deducam; ni&longs;i enim hoc facerem, ingenuè di
cam, ratiocinari non po&longs;&longs;em; Vt vt &longs;it, Galilæus ve&longs;ter, Augu&longs;tine, eo va
lebat ingenio, in hac præ&longs;ertim motuum doctrina, in qua, ne quid di&longs;&longs;i
mulem, parem non habuit, immo neque hoc di&longs;&longs;imulabo, quam primus
ip&longs;e invenit, vt tam audacter pronunciarit, ex dicta motuum terre&longs;tris
globi inæqualitate, Oceani huc illuc excur&longs;ionem &longs;equi; & &longs;i fortè hoc
cum principiis eju&longs;dem doctrinæ non con&longs;entit et, nunquam revera tanta
a&longs;&longs;everatione hoc dixi&longs;&longs;et. Il
aquarum motum &longs;equi ex prædicta motuum inæqualitate, nec illius inge
nium in hoc falli potuit, qui alios ferè omnes doctrinam motuum docuit;
erravit tamen in minore, in qua &longs;anè illius ingenium non de&longs;idero, &longs;ed
majorem diligentiam, nec non æ&longs;tus marini peritiam; itémque maiorem
fidem, periti&longs;&longs;imis Naucleris adhibendam; optimè docuit ex dicta inæ-
num æ&longs;tum qualis nunc e&longs;t, ex ea &longs;equi; de marino æ&longs;tu, quod &longs;it, & ta
lis &longs;it, res certa e&longs;t; oculi dumtaxat applicandi; de terræ motu, quod re
verà &longs;it, nequidem Galilæus ip&longs;e certum e&longs;&longs;e pronunciavit; dubium igitur
etiam apud vos; cùm igitur rectè componamus Telluris quietem cum eo
maris æ&longs;tu, qui modò e&longs;t, nec eum ob&longs;ervemus, qui reverà e&longs;&longs;et, &longs;uppo&longs;ito
terræ motu; quidni nece&longs;&longs;ariò, ni fallor, concludam; terram nor moveri,
cùm id nullo modo &longs;it, quod reverà e&longs;&longs;et, &longs;i terra moveretur?
Tecum &longs;entio, Antime, in hoc Galilæum, in re motuum ver
&longs;ati&longs;&longs;imum, falli non potui&longs;&longs;e, eiu&longs;que autoritatem longè pluris in hoc
faciendam e&longs;&longs;e, quàm multorum aliorum, qui tantum molo&longs;&longs;um, catelli
&longs;anè, allatrare non ce&longs;&longs;ant; ne tamen hoc tuum argumentum non tantùm
&longs;it ad hominem, &longs;ed pariter omnibus rem i&longs;tam per&longs;uadeat; &longs;epone, quæ
&longs;o, autoritatem Galilæi, & de&longs;cende ad illas conclu&longs;iones, quas ex iactis
&longs;upra principiis deducere, opinor, meditaris.
e&longs;&longs;e & ita moveri, vt &longs;upra dicebam, circuli, Æquatoris v.g. partes, inæ
qualiter, vt longè tardiùs punctum, quod &longs;pectat ad Solem, & velociùs
oppo&longs;itum moveatur, id e&longs;t F, quàm E, in hoc enim &longs;chemate &longs;i&longs;tere po&longs;
&longs;umus, nec declinatio æquatoris ab Eclyptica, nec perpetuus axis paralle
li&longs;mus, nec motus centri quinquies circiter major motu orbis, ad hanc
rem quidquam faciunt, puncta I & H ita moventur, vt motui centri ni
hil detrahant, nihil addant; ab H ad E ita additur vt crementum acce&longs;&longs;io
nis &longs;emper augeatur, donec tandem in E maximum &longs;it: hoc porrò cremen
tum acce&longs;&longs;ionis fit iuxta progre&longs;&longs;um &longs;inuum ver&longs;orum: ab E ad I; ita ad
ditur, vt crementa acce&longs;&longs;ionum &longs;emper minuantur, donec tandem in I
nullum &longs;it crementum; hoc verò crementum fit iuxta priorem progre&longs;&longs;io
nem, &longs;ed inver&longs;am ac proinde iuxta progre&longs;&longs;ionem &longs;inuum rectorum: Ab
I ad F ita detrahitur motui, centri, vt crementa detractionis &longs;emper ma
jora &longs;int, donec tandem in F &longs;it maximum, idque iuxta progre&longs;&longs;ionem &longs;i
nuum ver&longs;orum; denique ab Fin H ita etiam detrahitur, vt crementa de
tractionis &longs;emper minora &longs;int, idque iuxta progre&longs;&longs;ionem &longs;inuum recto
rum, donec tandem in H nullum &longs;it crementum: Accipe igitur punctum
circuli v.g.H, ab H movetur motu accelerato, per impetum &longs;cilicet, à
quocunque tandem producatur; igitur vbi pervenit ad E inten&longs;i&longs;&longs;imum
impetum habet, cur ergo tam cito de&longs;truitur, cùm fru&longs;trà non &longs;it, effe
ctumque &longs;uum in mobili præ&longs;tare queat?
Minimè verò, cùm enim punctum E &longs;it pars globi, eandem
cum aliis partibus di&longs;po&longs;itionem retinere debet, quod certè vt fiat, illius
motus retardari debet; &longs;i autem motus retardatur, pro rata de&longs;truitur
impetus.
Nunquid in mea & tua hypothe&longs;i, hic vel ille Oceani tractus
æquè pars e&longs;t terre&longs;tris globi, atque in Copernicana?
Fru&longs;tra interrogas; nullum enim dubium e&longs;t.
Rectè; at po&longs;tquàm modica vis venti prædicto aquarum tractui
aliquod tempus aquarum motus & agitatio non durat? quis hoc neget?
idem in latiore concha videbis; vbi enim aqua infu&longs;a plena fuerit, acce
dente minimo motu, a qua illa libratur ver&longs;us latera conchæ; ita vt huiu&longs;
modi librationes diutiùs durent, etiam po&longs;tquam omnis motus extrin&longs;e
cus ce&longs;&longs;avit; Vnde porrò hoc? rationem ex no&longs;tro primo principio facilè
deduces; durat enim aliquandiu impetus priùs impre&longs;&longs;us; quia non e&longs;t
fru&longs;tra, &longs;altem quoad aliquam portionem, cùm aliquid motus præ&longs;tare
po&longs;&longs;it; codem pror&longs;us modo, tractus Oceani circa punctum E, cum velo
ci&longs;&longs;imè moveatur, impetum impre&longs;&longs;um aliquandiu retinet, &longs;ecundùm ali
quem gradum, vi cujus excurrit ver&longs;us Ortum; nam perinde &longs;e habet, atque
&longs;i in va&longs;ti&longs;&longs;ima concha contineretur.
Movetur igitur totus ille aquarum tractus, &longs;ecundùm totam
profunditatem.
Non dico hoc, neque nece&longs;&longs;e e&longs;t, neque fieri pote&longs;t; quia vt
Conchæ &longs;upremus circulus longè major e&longs;t, quàm alij paralleli, versùs
imum conchæ, ita longè faciliùs libratur aqua, intra majorem circulum,
quàm intra minorem; quia &longs;cilicet in majore, habet liberiorem campum,
in quo excurtat, quod facilè demon&longs;trari à me po&longs;&longs;et, &longs;i hoc etiam paret
gum vobis arri&longs;erit.
Mihi opus non e&longs;t; quis enim hoc ne&longs;cit?
Sic videmus in con
chis angu&longs;tioribus, aquam difficiliùs librari, in majoribus verò faciliùs.
Ita e&longs;t, hoc videmus, quamobrem verò, non ita forte qui&longs;piam
dixerit.
Quid faciliùs dictu, Chry&longs;ocome; &longs;i vas angu&longs;tum e&longs;t, latera
minus di&longs;tant, hinc aqua nece&longs;&longs;ariò minùs excurrit, vtpote quæ à vicinis
lateribus continetur; &longs;i vas amplum &longs;it &longs;ecus accidit; quia &longs;cilicet illius la
tera à &longs;e&longs;e invicem magis di&longs;tant, nec vllo &longs;chemate opus e&longs;t ad exponen
dam vim hujus rationis.
Non agitur hoc loco, vtrum librationes aquæ intra vas angu
&longs;tum contentæ citiùs perficiantur, quam illæ quæ fiunt in majore va&longs;e;
nempe huiu&longs;modi librationes, funependulorum librationes imitantum,
quæ citò fiunt in brevi funependulo, tardiùs verò in longiore; &longs;ed alia
pror&longs;us e&longs;t difficultas, cur &longs;cilicet illa vis motus, quæ &longs;ufficit ad huiu&longs;mo
di librationes in va&longs;ta concha excitandas, non &longs;ufficiat &longs;i vas angu&longs;tum &longs;it,
nec ad majores, quæ reverà in angu&longs;to va&longs;e fieri non po&longs;&longs;unt, nec ad mi
nores, quas alioqui major vis motus excitaret; hîc tuam opem, Antime,
&longs;ed breviter, quæ&longs;o.
Brevi&longs;&longs;imè, neque hoc facerem, ni&longs;i ve&longs;tro ju&longs;&longs;u; Sit concha
DCG laxior, & alia ECF angu&longs;tior, vtraque
ferè plena; aqua longè faciliùs pote&longs;t librari in
arcu DCG, quàm in ECF; hic enim magis ar
duus e&longs;t, ille vetò longè mollior, &longs;eu mitior; mi
nùs enim recedit à plano horizontali ; hinc &longs;u
perficies aquæ DBG a&longs;cendere pote&longs;t per arcum GA, etiam cum modi
co impetu, &longs;ecus vetò per arcum FI, propter adductam rationem.
quæ à te dicta &longs;unt, hoc præ&longs;ertim opponendum mihi occurrit.
Quod &longs;cilicèt omnes partes terre&longs;tris globi, vel &longs;ingulæ &longs;e&longs;e moveant,
vel ab extrin&longs;eco moveantur; &longs;ed ita temperatè, vt omnes inter &longs;e primam,
di&longs;po&longs;itionem retineant; vnde non mirum e&longs;t, &longs;i tractus idem maris circa E
velociùs, circa I tardius moveatur.
Hoc ni fallor &longs;ummum caput e&longs;t hujus difficultatis, quod tamen
ex dictis facilè di&longs;&longs;olvi pote&longs;t; nempe &longs;ive tractus ille maris moveat &longs;e&longs;e,
&longs;ive ab alio, fieri non pote&longs;t, vt &longs;ine impetu moveatur; igitur impetum
illum acquirit proportionatum motui, quo movetur in E, vel circumcir
ca; &longs;ive illum in &longs;e producat, &longs;ive ab alio recipiat; &longs;ed impetus &longs;emel pro
ductus à
tandiu verò fru&longs;tra non e&longs;t, quamdiu
bili, non alium certè quàm motum; quantumvis
novus impetus, hoc certè non facit, vt is, qui jam productus e&longs;t de&longs;truatur;
fiat; &longs;i aqua in canali declivi motu accelerato de&longs;cendat, qui deinde per mol
liorem deflexionem &longs;ur&longs;um &longs;ub æquali, vel in æquali inclinationis angulo at
tollatur, vbi aqua ad imum canalis pervenerit, non &longs;i&longs;tet hauddubiè, &longs;ed
per aliud canalis planum inclinatum a&longs;cendet, de&longs;cendétque denuo, mul
tis qua&longs;i librationibus repetitis, hic tamen impetus productus e&longs;t ab in
trin&longs;eco, Quando animal currit per declivem collem, gradum profectò
impetum; in vibratis librati&longs;que corporibus innumera ferè &longs;uppetunt
exempla. Quid mirum igitur, &longs;i prædictus maris tractus impetum ante
impre&longs;&longs;um retineat & excurrat in Ortum; neque hoc impedit connexio
partium eju&longs;dem globi, ni&longs;i hæ &longs;clidæ &longs;int ac duræ, nec non ita inter &longs;e
connexæ, vt vna ab alia &longs;eparari non po&longs;&longs;it; tunc enim moventur iuxta
leges novi impetus de&longs;tructò priore; nec mirum, cùm fru&longs;tra &longs;it; fru&longs;tra au
tem e&longs;t, quia motum alium habere 1. on pote&longs;t, præter illum, quem novus
impetus exigit.
Si ergo in puncto E e&longs;&longs;et corpus &longs;olidum & durum, totum
priorem impetum a mitteret accedente novo.
Minimè verò, ni&longs;i arctè cum aliis corporibus duris connexum
e&longs;&longs;et, &longs;it enim v.g.globus lævigati&longs;&longs;imus in E, &longs;upra &longs;uperficiem &longs;olidam
etiam lævigati&longs;&longs;imam, vitream puta, haud dubiè curreret prædictus glo
bus versùs Ortum, præ&longs;ertim cùm ad hunc motum nullo a&longs;cen&longs;u opus &longs;it,
ac proinde nulla pror&longs;us inclinatio contraria ob&longs;tet.
Igitur ille globus ita &longs;emper moveretur in &longs;uperficie tetræ;
nihil enim de&longs;trueretillum impetum; quod
deduco, &longs;ed ex trito Mathematicorum dicto.
Hoc certè ex meis principiis non &longs;equitur, immo contrarium;
novus enim, qui præfato globo accederet, impetus ad motum oppo&longs;itum,
vel qua&longs;i oppo&longs;itum determinatus, priorem illum &longs;en&longs;im de&longs;trueret. v. g.
impetus novus accedens in P, (
e&longs;t, versùs ortum, ratione motus centri, partim per tangentem punctum
P e&longs;t determinatus; mixta autem linea &longs;eu determinatio ex vtraque illa
&longs;equitur, vt con&longs;tat ex doctrina motuum. Quod verò &longs;pectat ad tritum
illud Mathematicorum dictum, etiam in terræ immobilis hypothe&longs;i locum
habet, &longs;ed pro&longs;ectò nullum planum ita lævigari pote&longs;t, quin aliquot Sa
lebris a&longs;peretur; quod reverà &longs;ufficeret, ad illum impetum de&longs;truendum;
qualis &longs;it terræ &longs;uperficies, vides; ille porrò aquæ excurrentis tractus &longs;en&longs;im
fine &longs;en&longs;u conceptum motum remittit, propter impetum
&longs;um, vbi enim pervenit in R v.g.cum motus centri &longs;it contrarius motui
orbis, haud dubiè inde aqua aliquo modo regredi cogitur; hinc conflictus;
adde mutationem determinationis lineæ motus in &longs;ingulis punctis &longs;emi
circuli EIF; denique adde aquæ divi&longs;ionem, quæ non parum re&longs;i&longs;tit
motui, præ&longs;ertim alterius aquæ; quæ libet autem re&longs;i&longs;tentia impetum &longs;en&longs;im
de&longs;truit.
Iam mentem tuam intelligere mihi videor; vis enim quod
libet punctum terre&longs;tris globi, ratione duplicis motus, centri &longs;cilicet,
atque orbis, duas determinationes habere, quæ in tertiam mixtam de
inde abeunt, perinde atque &longs;i duplex impetus impre&longs;&longs;us e&longs;&longs;et ad motum
mixtum; finge globo, eodem tempore, duplicem impetum imprimi
alterum versùs Boream,
in eandem motus mixti lineam coale&longs;cit, vnde &longs;uppo&longs;ita vtriu&longs;que impe
tus æqualitate, globus ver&longs;us Corum ibit, id e&longs;t, Boream inter & Occa-Ita que in puncto E vna eademque e&longs;t vtriu&longs;que motus determinatio,
&longs;cilicet per tangentem versùs Ortum; in F verò, altera determinatio alteri
ex diametro opponitur; nam determinatio motus centri e&longs;t tangens ducta
in
murat; at verò determinatio motus orbis e&longs;t tangens ducta in Occa&longs;um; in
aliis punctis inter EI, & IF, in diver&longs;as partes tendunt; v.g.in puncto I de
terminatio centri e&longs;t DI producta versùs Ortum; determinatio orbis per
pendiculariter cadit versùs GF. pari modo habentur aliæ in tangentibus;
& provt vna magis aut minùs con&longs;entit cum alia, velocior aut tardior
e&longs;t motus; Sed dic mihi. &longs;odes Antime, po&longs;ito quod &longs;it globus in E, cur
per tangentem non projicitur ver&longs;us Ortum?
Cur me tentas, Augu&longs;tine, ne&longs;cire non potes, hoc jam à
Galilæo &longs;olutum fui&longs;&longs;e, in quo certè, more &longs;uo maximam ingenij vim
o&longs;tendit. Nullum corpus grave per horizontalem projicitur, quod &longs;tatim
ip&longs;o initio de&longs;cendere non incipiat; &longs;emiparabolam à &longs;ummo vertice &longs;uo
motu de&longs;cribens; &longs;ed quælibet parabola ex E vertice ducitur infra Cycloi
dem EQV, vi Geometræ demon&longs;trant; itaque dictus globus projicitur
quidem, &longs;ed ita, vt cùm a&longs;&longs;urgere non po&longs;&longs;it, in &longs;uperficie terræ volvatur, vt
alij globi volvuntur.
Quid dicam ad hæc, ne&longs;cio, certa tamen e&longs;&longs;e non puto;
alioquin actum e&longs;&longs;et de hy pothe&longs;i Copernicana; aliunde illud principium
certum e&longs;&longs;e videtur, quòd &longs;cilicét impetus aliquamdiu duret modò fru&longs;tra
non &longs;it, & aliquem motum præ&longs;tare queat, videmus enim globum proje
ctum moveri, etiam à projicientis manu ab&longs;tractum; rotam item in quo
cunque &longs;itu collocatam, vbi tantulus impetus initio impre&longs;&longs;us &longs;uerit; in
funependulis, res e&longs;t plu&longs;quam per&longs;picua, itemque in motibus, qui per
repercu&longs;&longs;ionem fiunt; commune igitur principium e&longs;&longs;e videtur, ex quo,
ni fallor, rectè deducis tractum matis, qui e&longs;t circa E, versùs Ortum deinde
excurrere; quod enim de globo dixi&longs;ti in eodem puncto E &longs;ito, ex hypothe&longs;i
dumtaxataccipio, non verò ab&longs;olutè dictum.
Immò ab&longs;olutè dictum e&longs;&longs;e velim; non ratò quippe accidit vt
globi lævigati&longs;&longs;imi in planis etiam lævigati&longs;&longs;imis collocentur, &longs;eu marmo
reis, &longs;eu vitreis; lævigata glacie nihil ferè lævius inuenio; & &longs;upra glaciem
glaciata fru&longs;tra citò & facilè currunt; itaque &longs;i aqua movetur, excurritque,
modò Ortum, modò Occa&longs;um, versùs, non video quare globus lævigati&longs;
&longs;imus in plano lævigati&longs;&longs;imo &longs;itus, vel &longs;upra lævigatam glaciem, propter
eandem motus inæqualitatem moveri non debeat; & hoc etiam ad homi
nem, contra tuam hypothe&longs;im militat; vnde ruitetiam illa re&longs;pon&longs;io iam
&longs;upra indicata; quod &longs;cilicet terræ motus æ&longs;tus quidem matini cau&longs;a &longs;it,
&longs;ed non adæquata, vt aiunt; nempe quidquid tandem motus in aquas
traducat, in globulum eo modo &longs;itum, quo dictum e&longs;t, etiam traducere
deberet, cùm æquè facile traduci queat; accipio enim globulos tam fa
cilè mobiles, vt nihil mobilius excogitari po&longs;&longs;it, tornatos &longs;cilicet ex Mer
curio.
De puncto E fortè &longs;atis dictum, & plu&longs;quàm &longs;atis; de aliis
Non dubito enim, quin de iis aliquid dicturus &longs;is; ad quid
enim duo alia principia præmi&longs;i&longs;&longs;es?
Etiam &longs;i nihil aliud dicerem, an fortè illa, quæ de puncto E
dixi non &longs;ufficiunt ad tuam &longs;ententiam impugnandam? Sed agedum,
quandoquidem me &longs;timulas, etiam de aliis punctis nonnulla dicenda &longs;unt,
eaque ex duobus aliis principiis, quæ &longs;upra data opera præmi&longs;i eruenda. Si terræ globum quoquo versùm obtegeret aqua, ita vt v.g.ex 8. partibus
&longs;emidiametri, octava, &longs;uprema &longs;cilicet, aquea e&longs;&longs;et, extremaque &longs;uperfi
cies terræ convexa, cui &longs;uperficies aquæ incubat, lævis e&longs;&longs;et, nullis mon
tibus, nullis &longs;alebris a&longs;pera; Iam verò quàm celerrimè interior ille & in
aquis latens terræ globus circa &longs;uum centrum immobile volvatur; an for
tè putas, tunc motum in portionem aqueam traductum iri?
Traducendum e&longs;&longs;e omnino crederem; terra enim illam etiam
aquam &longs;u&longs;tineret; igitur &longs;ecum vna deferret.
At ego &longs;ecus &longs;entio; hic enim ca&longs;us no&longs;tro &longs;imilis e&longs;t; &longs;i
enim vas probè tornatum aqua plenum in &longs;itu horizontali circa axem
verticalem accurati&longs;&longs;imè & citra vllam inclinationem erectum, etiam ce
lerrimè vertatur, immotam pror&longs;us aquam videbimus; Quid vis tibi di
cam, Chry&longs;ocome, oculos meos te&longs;tes appello, & &longs;i fidem detrectes,
vel in &longs;cutella &longs;tannea, quamvis imperfectè tornata, hoc ip&longs;um videbis.
Aqua igitur non &longs;u&longs;tinetur à va&longs;e, alioquin &longs;i vas illam &longs;u
&longs;tineret, &longs;ecum illam circumferret, &longs;ic librum hunc, quem manu teneo,
manus ip&longs;a, quocumque fertur, traducit.
Standum e&longs;t experimentis; tu fortè quid, Antime?
qui litem
movi&longs;ti, & cautè &longs;ubrides.
Dicam quod &longs;entio, & quod verum e&longs;t; Aqua certè quie&longs;cit,
dum vas pernici&longs;&longs;imè volvitur; & &longs;i vas probè tornatum e&longs;&longs;et, & circa
axem minimè inclinatum volveretur, eaque demum e&longs;&longs;et cava &longs;uperficie,
quam nulla pror&longs;us ruga, nulla &longs;alebra, quantumvis in&longs;en&longs;ibilis a&longs;peraret,
dico nunquam fore, vt cum va&longs;e aqua moveretur; & hîc applico princi
pium &longs;upra iactum, &longs;cilicet nunquam motum, vel impetum ab aliquo mo
bili imprimi alteri, ni&longs;i hoc motum illius impediat, aut retardet: in hoc
autem ca&longs;u, aqua va&longs;e contenta motum va&longs;is nullo modo impedit, non
per &longs;uam molem, &longs;eu molis pondus; quia moles &longs;eu pondus re&longs;i&longs;tit tan
tummodo motui, &longs;ur&longs;um; &longs;ed nulla pars va&longs;is, in hoc motu a&longs;cendit; nulla
igitur aquæ pars attollenda e&longs;t; præterea nulla pars ob&longs;i&longs;tit motui va&longs;is,
quia id tantùm per contactum fieret; &longs;ed nulla pars tangens ob&longs;i&longs;tit, cùm
nulla pars cavæ va&longs;is &longs;uperficiei extare, & dam movetur, in aquam impin
gi &longs;upponamus; vt tamen dicam, quod res e&longs;t, cùm & axis ab&longs;que aliqua
inclinatione erigi, & &longs;ic &longs;tare vix po&longs;&longs;it, & quod caput e&longs;t, nullum &longs;it
corpus durum, quantumvis lævigatum, &longs;ine poris, rugis, & &longs;alebris, hinc
fit, aquam dicto va&longs;e contentam tantulùm ob&longs;i&longs;tere motui va&longs;is, ac proin
de non mirum videri, &longs;i initio quidem immota maneat, quia tamen &longs;en&longs;im
&longs;ine &longs;en&longs;u vires acquirit, circumferri tandem cum &longs;uo va&longs;e cernitur, & hoc
adjicere debueras, Augu&longs;tine, vt &longs;emper &longs;uus &longs;it veritati locus.
Quid verò fieret, &longs;i vas in circulo verticali verteretur?
Eadam &longs;uppone; vas &longs;cilicet cylindricum, aut &longs;phæricum ca
vum, lævigata intus &longs;uperficie, circa axem plano horizontis planè paral
lelum; idemque &longs;ucce&longs;&longs;um iri puta; cùm eadem ratio vtrimque & æquè
militet.
Immo ex alio tuo principio, quo dicis, eo motu moveri
mobile, quò faciliùs moveri pote&longs;t, colligo, ni fallor, longè potiori iure
pro i&longs;to vltimo ca&longs;u rationem militare; cùm enim faciliùs aqua illa à &longs;uo
va&longs;e, dum in plano horizontali volvitur, moveri po&longs;&longs;it, quàm ab eodem
in hoc &longs;ecundo ca&longs;u; quia vt imprimo illo moveatur aqua, ne latum quidem
vnguem attollenda e&longs;t, nullam igitur difficultatem, &longs;eu re&longs;i&longs;tentiam ex hoc
capite vas &longs;entit; cùm tamen in &longs;ecundo ca&longs;u, illa portio aquæ, quæ con
tinetur in inferiore parte dolij, &longs;eu cylindri, ad &longs;uperiorem partem cylin
dri locum attollenda &longs;it; vnde difficultas & re&longs;i&longs;tentia; igitur cùm mobi
le eo motu moveatur, quo facilius moveri pote&longs;t, longè facilius e&longs;t, vas
moveri &longs;ine aqua in &longs;ecundo ca&longs;u, quàm in primo
Plurimùm &longs;anè me tibi ob&longs;trinxi&longs;ti, mi Chry&longs;ocome, cogita
bam &longs;tatim principium illud iam &longs;upra iactum, ac fusè non &longs;ine querela
expo&longs;itum, huc accer&longs;ere; &longs;ed ab hoc pen&longs;o me libera&longs;ti, ita e&longs;t; cùm vas
vtrumque faciliùs moveri po&longs;&longs;it, quie&longs;cente aqua, vt patet, etiam ab&longs;que
vlla penitus &longs;ui motus iactura; ita &longs;anè ex illo quoque principio probatur,
va&longs;a &longs;ine aqua contenta moveri; quod autem addis, longe facilius in
&longs;ecundo ca&longs;u quam in primo, pace tua dixerim; quia &longs;cilicet æquè facilè
vtrimque aqua cum &longs;uo va&longs;e movetur, nec ob&longs;tat inferiorem aquæ partem
in &longs;ecundo ca&longs;u ab imo ad &longs;upremum va&longs;is locum attolli, ac proinde illius
pondus ob&longs;tare ac re&longs;i&longs;tere; nam ita attollitur, vt eodem tempore, æqualis
portio deprimatur, e&longs;t enim perfectum æquilibrium, vt vides; &longs;ic vbi libra
in æquilibrio ver&longs;atur, &longs;i vel minimam vim alteri lancium &longs;ur&longs;um impre&longs;&longs;e
ris, illa &longs;tatim &longs;ur&longs;um attollitur; an fortè illa vis minima impre&longs;&longs;a ad hoc
&longs;ufficit? Minimè vero; &longs;ed minima illa acce&longs;&longs;ione tollitur æquilibrium:
quid mirum ergo, fi portio præponderans, deor&longs;um eat, & oppo&longs;itam at
tollat? Sic æquè facilè rota volvitur in &longs;itu horizontali ac verticali.
ratus &longs;um, vt compertæ veritati numquam non me &longs;ubjiciam; movetur
autem aqua cum &longs;uo va&longs;e, vt dicis, per accidens
propter a&longs;peritatem & inæqualitatem interioris &longs;uperficiei; at numquid
non po&longs;&longs;et ab hoc vitio liberari, obducto &longs;cilicet oleo, vel alio quopiam
vliginis genere?
An fortè putas, oleum &longs;uis rugis & &longs;triis, nec non filaminibus
carere? Vidi&longs;ti, ni fallor, aliquando, majores illas guttas &longs;ive butyro, &longs;eu
va&longs;ibus vnctis oleo adhære&longs;cere, an fortè in plani&longs;&longs;ima &longs;uperficie adhæ
rete po&longs;&longs;ent?
Sed vnde quæ&longs;o, i&longs;tæ guttulæ; rem illam &longs;æpè ob&longs;ervavi, cu
jus tamen rationem vix ac ne vix quidem mente a&longs;&longs;equor.
Sunt quædam &longs;uperficies ita di&longs;po&longs;itæ inter &longs;e, vt in earum rimas
pennis avium aquatilium v.g. An&longs;erum, Anatum, aliarumque &longs;imilium,
hoc ip&longs;um ob&longs;ervamus, immo in multis foliis, vt bra&longs;&longs;icæ, in quibus hu
ju&longs;modi aquæ guttulæ, qua&longs;i totidem liquatas gemmas, po&longs;t pluviæ vel
roris lap&longs;um &longs;æpè vidi&longs;ti; quia &longs;cilicet laxioribus rugis &longs;eu &longs;triis in longum
& rectam lineam ductis con&longs;tant, per quas aqua &longs;tatim de&longs;cendit, atque
effluit, ni&longs;i aliqua fo&longs;&longs;ula in&longs;it, in qua major gutta ex reliquis longè mi
noribus eò per rugam declivem confluentibus, componitur; in &longs;uperficie
butyri rectas huiu&longs;modi &longs;trias tantùm non videmus; nec fortè mirum;
vligino&longs;a ex multis filaminibus con&longs;tant; fila autem in longum ducuntur;
iunge &longs;imul multas acus, & aliquid fortè &longs;imile a&longs;picies; cur verò guttæ
illæ majores in iis fo&longs;&longs;ulis tornatæ deinde non cadant, etiam &longs;i vas vnctum,
cui adhærent, ever&longs;o &longs;itu &longs;tatuatur, eadem ratio e&longs;t, propter quam na&longs;o, pa
leæ, ligno, alií&longs;que corporum extremitatibus gutta adhæret, ac de illis pen
det quam certè hoc loco explicare non po&longs;&longs;um, cùm inde va&longs;ti&longs;&longs;imus allis
experimentis ad &longs;uas veras cau&longs;as phy&longs;icas reducendis campus ape
riatur.
Auguror rem grati&longs;&longs;imam fore, & fortè altero congre&longs;&longs;u
quandoquidem tam latè patere dictitas; &longs;ed ad propo&longs;itum, qùæ&longs;o, redea
mus: Con&longs;tat igitur, illum terræ globum ver&longs;um iri, licèt aqua circum
po&longs;ita nullo modo moveretur; huc enim faciunt duo illa tua principia,
quæ libenter admitto, vtpote quæ cum experimentis mirabiliter con&longs;en
tiant; &longs;i verò terræ globum con&longs;ideremus, provt modò e&longs;t, & aquarum
congeries &longs;tagnat in va&longs;ti&longs;&longs;imis illis terrarum conchis; &longs;i terræ glo
bus volvatur, nunquid non &longs;uo motu aqueam illam molem &longs;ecum abri
piet?
Abripiet &longs;anè majorem partem, eam &longs;cilicet, quàm arctiùs
&longs;uis brachiis &longs;tringit, & quæ à &longs;uperficie conchæ intror&longs;um &longs;atis &longs;uperque
di&longs;tat; huc facerent exempla concharum, quibus vulgò vtimur; &longs;ed ne
dicta repetam, libens omitto, Vt vt &longs;it, &longs;i
remus haud dubiè facilior e&longs;t &longs;i aliqua portio aquæ retroagatur, ea &longs;cilicet,
quæ à &longs;uperficie parum di&longs;tat, cum tantula elevatione, ratione cujus in &longs;u
perficiem oppo&longs;itam excurrit, & in litora occidua deinde impingi, &longs;eu po
tiùs elevari, excurrere & in litus impingi videtur, eo quippe litus ip&longs;um fer
tur, & in aquam vel immobilem vel tardiorem impingitur, nempe quoad
effectum &
put incurrat: hoc autem potiori iure in terræ globo duplici illo motu, de
quo jam &longs;upra, locum habet, nempe à puncto H ad E cre&longs;cit motus per HE,
non tantùm ratione motus orbis, verùm etiam motus centri; idque per cre
menta majora & majora, vt iam o&longs;tendi; Igitur, aqua, iuxta &longs;uperficiem &longs;al
tem tantulùm ex currit in
fiat, motu æquali &longs;uppo&longs;ito, potiori iure &longs;uppo&longs;ito inæquali, ac &longs;emper cre&longs;
cente: itaque ex iis. quæ diximus huc
facilè defini: i po&longs;&longs;et æ&longs;tus marini ratio, in dicta hypothe&longs;i ; nempe aqua
à puncto E ad punctum I, id e&longs;t à media nocte ad Solis Ortum (&longs;up-
ab I ad F, id e&longs;t ab ortu ad meridiem, nullo modo excurreret, &longs;altem
&longs;en&longs;ibiliter; &longs;i enim tantulùm, hoc motui centri prævalenti cedet; igitur
versùs Occa&longs;um, id e&longs;t, ab F, versùs R. quanquam determinatio mixta hoc
etiam compen&longs;at; pari modo ab F ad H nullo modo excurrit, &longs;altem &longs;en
&longs;ibiliter; &longs;i enim tantulùm, cedit motui centri, quanquam etiam determi
natio mixta hoc ip&longs;um compen&longs;at; igitur à Solis ortu v&longs;que ad occa&longs;um,
nulla fit &longs;en&longs;ibilis excur&longs;io; ab occa&longs;u ad mediam noctem, fit in occa
&longs;um, à media nocte ad ortum Solis, fit in ortum: mixtam illam determi
nationem facilè qui&longs;piam intelliget, &longs;i dividat æqualiter angulum, qui fit
à tangente datum aliquod punctum, & à linea motus centri, quæ &longs;emper
e&longs;t parallela HI, linea enim dictum angulum æqualiter dividens e&longs;t deter
minatio motus mixti. Iam verò, &longs;i mihi non creditis, oculis ve&longs;tris credite,
& probate experimenta à me expo&longs;ita, in navi &longs;cilicet velorum dumtaxat
impul&longs;u acta, in aliquo tranquillo lacu, &longs;eu flumine; &longs;i enim &longs;tatuatur in
media navi, concha aquâ plena, pauio laxios in &longs;uperiore labro, &longs;ed mo
dicæ profunditatis, ad in&longs;tar illius, in qua cera liquari &longs;olet, ad cereos tor
nandos, videbitis haud dubiè, &longs;i navis motum acceleret, conchæ aquam
versùs puppim ire;
fides detrahi non debet, nec fortè mihi, nec aliis, qui hujus experimenti
oculati te&longs;tes fuerunt: & hæc de prima ratione contra tuam hypothe&longs;im,
Augu&longs;tine, jam ad alias de&longs;cendam.
Sentio difficultatem, inficiari non po&longs;&longs;um; illud &longs;altem con
&longs;equi videor quod Galileus no&longs;ter à vero minime aberrarit, quando a&longs;&longs;e
ruit, prædictos motus ex hypothe&longs;i terræ mobilis, nece&longs;&longs;ariò &longs;equi.
Ita e&longs;t; in eo tamen deceptus, quòd eo&longs;dem motus pro Marino
æ&longs;tu venditarit, licèt omnino di&longs;&longs;imiles &longs;int. Iam verò vt ad alia tran&longs;eam ar
gumenta, è terra nobis migrandum e&longs;t, in qua profectò nihil aliud invenio
ex quo &longs;olidum argumentum ducere valeam &longs;altem, quod mihi faciat &longs;atis.
Ludis, opinor, Antime; nunquid enim ex diver&longs;is motibus,
tum naturalibus, tum violentis docti&longs;&longs;imi viri ducunt in&longs;olubilia pror&longs;us
argumenta, contra præfatam hypothe&longs;im, in qua nequidem corpus grave
per lineam rectam de&longs;cenderet, nec accelerationis, nec retardationis, nec
percu&longs;&longs;ionis ratio explicari po&longs;&longs;et.
Ridere &longs;oleo quorumdam hominum &longs;implicitatem, vt
&longs;ic loquar, qui cum Galileo no&longs;tro de motu contendunt, qui cerrè
doctrinæ motuum primus Autor & inventor fuit; nemo quippe
alius hanc laudem &longs;ibi arroget; Crede mihi, Chry&longs;ocome, &longs;uarum
rerum & inventionum vir ille amantior erat, quàm vt aliquem inter
eas conflictum pateretur, vidit, haud dubiè, vidit, motus accelera
ti progre&longs;&longs;ionem Geometricam, ita cum hypothe&longs;i Copernicana con
&longs;entive, vt in ea æquè facilè atque in tua explicari & ad &longs;ua princi
pia reduci po&longs;&longs;it; equidem in primis &longs;uis Dialogis de vtroque &longs;y&longs;tema
te, dubius aliquantulum hæ&longs;i&longs;&longs;e vi&longs;us. e&longs;t, qua&longs;i motus gravium non
e&longs;&longs;et per &longs;e acceleratus, &longs;ed tantùm per accident; at in illo mirabili
to &longs;crip&longs;it, vt nullum po&longs;t &longs;e dubium reliquerit.
Hic lapis te petit, Antime, vtpote qui, &longs;i rectè memini,
contra Galileum &longs;crip&longs;i&longs;ti, aliamque induxi&longs;ti motus naturaliter accele
rati progre&longs;&longs;ionem.
Contra Galileum nihil me vnquam &longs;crip&longs;i&longs;&longs;e memini; è qui
dem Mon&longs;nerius meus tractatum de motu locali, ex meis prælectionibus
excerptum edidit, nihil tamen in eo contra Galileum.
Immò ex profe&longs;&longs;o Galileum, &longs;ub Mon&longs;nerij nomine, im
pugnas, nec tibi, opinor, è memoria excidit? nempe Galileus docet, &,
ni fallor, demon&longs;trat, motum gravium accelerari iuxta progre&longs;&longs;ionem geo
metricam, &longs;ecundùm quam decur&longs;a &longs;patia &longs;unt vt temporum quadrata, ac
proinde &longs;i primo tempore decurrat &longs;patium 1. &longs;ecundo æquali decurrit 3.
tertio 5. quarto 7. atque ita con&longs;equenter &longs;ecundum &longs;eriem numerorum
imparium, tu verò, Antime, vis, hanc &longs;eriem fieri &longs;ecundùm progre&longs;&longs;io
nem Arithmeticam &longs;impliorem numerorum 1.2.3.4.&c.
Si rectè memini, Antime, omnibus experimentis hypothe&longs;is
tua repugnat; nam etiam &longs;umma quandoque altitudo &longs;umpta fuerit, Flo
rentiæ, Romæ, Bononiæ, & vt audio, in Gallia pa&longs;&longs;im, quantum tamen
periti&longs;&longs;imorum hominum oculis credendum e&longs;t, prima progre&longs;&longs;io illa Ga
lileana in decur&longs;is æquali tempore &longs;patiis &longs;emper apparuit.
Summoperè lætor & gaudeo, quod &longs;ive ca&longs;u, &longs;ive &longs;tudio, hu
ju&longs;ce rei mentio à vobis facta fuerit; dico igitur, iterumque atte&longs;tor, ac
tertiò, nec meam hypothe&longs;im experimentis repugnate, nec à Galileana
di&longs;crepare in communi &longs;ententia quantitatis, tum continuæ, tum di&longs;cretæ;
nempe, vt probè &longs;citis, res quantitatis eas difficultates continet, quas huc
v&longs;que nemo ita &longs;olvit vt &longs;olutio vel omnibus arri&longs;erit, vel etiam illius a&longs;
&longs;ertoribus difficilis vi&longs;a non fuerit, in tempore præ&longs;ertim explicando; &longs;unt
enim qui capere nequeunt, vt quidquid temporis e&longs;t, ab eo, quod non
e&longs;t, &longs;ed fuit, vel erit, omnino di&longs;tinctum, in&longs;tans indivi&longs;ibile non &longs;it; &longs;ic
enim divi&longs;ibile e&longs;t in plura, ergo plura temporis &longs;imul exi&longs;tunt, quod di
ci nequit ; &longs;i autem ea in quæ e&longs;t divi&longs;ibile, non &longs;unt quidem, &longs;ed vel fue
runt, vel erunt; ergo id quod e&longs;t, quidquid &longs;it, ab iis omnino di&longs;tingui
tur; cùm repugnet, idem &longs;imul e&longs;&longs;e & non e&longs;&longs;e, igitur illud quod e&longs;t, ab
omni alio, quod non e&longs;t, di&longs;tinctum, in&longs;tans e&longs;t, indivi&longs;ibile e&longs;t: nec ju
vat à nonnullis dici, tempus e&longs;&longs;e fluenter; nempe fluenter e&longs;&longs;e; nihil e&longs;t
aliud, quàm vnum e&longs;&longs;e, &longs;eu fluere po&longs;t aliud, nec-plura &longs;imul e&longs;&longs;e po&longs;&longs;e; &longs;i
quid dicatur aliud, multorum captum & mentem &longs;uperat.
Ad quid hæc: Galileus enim docet, componi tempus ex in
&longs;tantibus ii&longs;que Mathematicis.
Sat &longs;cio; &longs;ed cùm alij huiu&longs;modi in&longs;tantia minimè admittant,
partibus dumtaxat in infinitum divi&longs;ibilibus, vel &longs;initis contenti in&longs;tan
tibus, &longs;cilicet phy&longs;icis, dico hypothe&longs;im Galilei circa progre&longs;&longs;ionem mo
tus accelerati, habere quidem locum in hypothe&longs;i in&longs;tantium infinitorum,
vel partium infinitarum, non ramen in hypothe&longs;i finitorum in&longs;tantium
vnum dumtaxat dico, illam progre&longs;&longs;ionem alteri præferendam e&longs;&longs;e, quæ &
vtrique quantitatis hypothe&longs;i &longs;atisfacit, & ip&longs;is experimentis non repu
gnat: quòd autem progre&longs;&longs;io Galileana in hypothe&longs;i finitorum in&longs;tan
tium non &longs;ub&longs;i&longs;tat, per&longs;picuè demon&longs;tro; Sit enim motus qui&longs;piam natu
ralis, qui duret per 4. in&longs;tantia, in quorum primo, mobile acquirat &longs;pa
tium 1. in &longs;ecundo 3. in tertio 5. in quarto 7. cùm velocitas cre&longs;cat, vt
tempus, in &longs;ecundo in&longs;tanti velocitas erit dupla, quomodo igitur acquiri
tur triplum &longs;patium?
Nihil facilius triangulo Galileano, in quo res i&longs;ta clari&longs;&longs;i
mè demon&longs;tratur: Sit enim triangulum AEI, &longs;it
tempus divi&longs;um in 4.partes æquales, & primo tempo
re AB, &longs;patium acqui&longs;itum &longs;it triangulum ABF, &
velocitas acqui&longs;ita BF, &longs;ecundo tempore erit veloci
tas acqui&longs;ita CG, cre&longs;cit enim, vt tempus, & vt AB
ad BF, ita AC ad CG ; idem dico de quolibet alio
temporis puncto accepto inter BC ; igitur &longs;patium ac
qui&longs;itum erit trapezium BCGF, triplum trianguli
ABF, nempe cum velocitate BF æquabili motu, tem
pore BC, acquireret rectangulum BM, &longs;ed virtute ve
locitatis acqui&longs;itæ tempore BC æqualis velocitati BF, acquiritur triangu
lum FMG æquale ABF; igitur &longs;ecundo tempore triplum &longs;patium
prioris.
nempe velocitas BF acquiritur &longs;ucce&longs;tivè tempore AB, quod &longs;i &longs;uppona
tur e&longs;&longs;e in&longs;tans phy&longs;icum, accipienda e&longs;t velocitas. BF tota &longs;imul, re
&longs;pondeo
vè acqui&longs;ita, igitur &longs;patium debet accipi in rectangulo, non verò in trian
gulo; v.g. Sit tempus AE 4. in&longs;tantiam, &longs;it pri
mus gradus velocitatis AG, & &longs;patium acqui
&longs;itum rectangulum AV; &longs;ecundo in&longs;tanti ve
locitas acqui&longs;ita erit BH, dupla &longs;cilicet AG;
nempe tota prior remanet, & tantumdem ab ea
dem cau&longs;a, æquali tempore ponitur; igitur &longs;pa
tium e&longs;t duplum prioris, ac proinde erit rectan
gulum CH duplum prioris.
Duo ab&longs;urda ex his mihi deducere videor; primò enim, pri
mo tempore AB, duplum &longs;patium trianguli Galileani a&longs;&longs;umis; nempe re
ctangulum AV duplum e&longs;t trianguli ABV, cùm tamen æquale primum
tempus a&longs;&longs;umi debeat, ad perfectam comparationem; &longs;ecundò longè majus
&longs;patium decurritur &longs;ecundùm tuam progre&longs;&longs;ionem, quàm &longs;ecundùm Ga
lileanam, in qua &longs;patium decur&longs;um tempore AE continet 16. triangula
æqualia triangulo ABV, in tua verò continet 10. rectangula æqualia
AV; igitur 20. triangula æqualia ABV, igitur &longs;patium Galileanum erit
ad tuum vt 16. ad 20. &longs;eu vt 4. ad 5. igitur majus vna quarta parte, quod
con&longs;entiunt.
Nemo vnquam hujus rei periculum fecit in 4. in&longs;tantibus,
&longs;ed tantùm in 4. temporibus &longs;en&longs;ibilibus, nempe in&longs;tantia &longs;ub &longs;en&longs;um non
cadunt; at &longs;upponuntur hoc loco 4.in&longs;tantia. iuxta &longs;ingularem illam tem
poris hypothe&longs;im ; equidem &longs;i tempus AE ex quatuor partibus temporis
&longs;en&longs;ibilibus componas &longs;ecundùm communem, aut etiam Galileanam tem
poris hypothe&longs;im, & dividas AE in 8. tempora æqualia; in progre&longs;&longs;ione
Galilei, tempore AE, idem &longs;patium decurritur; at verò in mea decurritur
&longs;patium, quod complectitur 18.triangula æqualia ABV; igitur &longs;patium in
mea decur&longs;um majus erit Galileano, vna octava; & &longs;i adhuc tempora bi
fariam dividas, majus erit vna decima &longs;exta; atque ita deinceps decre
&longs;cent exce&longs;&longs;us iuxta hanc &longs;eriem 1/4. igitur.
&longs;i vel in
&longs;tantia infinita &longs;unt, vel partes infinitæ, differentia &longs;patiorum in mea
progre&longs;&longs;ione & Galileana decre&longs;cit in infinitum; ac proinde Illa &longs;patia
æqualia cen&longs;enda &longs;unt, quorum vnum aliud &longs;uperat, exce&longs;&longs;u, minore quo
libet a&longs;&longs;ignabili: Hæc &longs;i non nemo paulò attentiùs con&longs;idera&longs;&longs;et, meam
progre&longs;&longs;ionem tam citò vt fal&longs;am & experimentis omnino repugnantem
minimè rejeci&longs;&longs;et, nec adeò dubita&longs;&longs;et de vera hujus accelerationis cau&longs;a,
quæ in eo po&longs;ita e&longs;t, quod prioribus gradibus impetus novi gradus conti
nuè accedant, idque &longs;i quodlibet tempus ex infinitis con&longs;ter, vel etiam ex
finitis, &longs;ed innumerabilibus, in triangulo; &longs;i verò ex paucis finitis, in
rectangulis, iuxta figuram AEF di&longs;po&longs;itis; nec alia &longs;uper hoc, meo judi
cio, difficultas re&longs;tat; vnde concludo, meam progre&longs;&longs;ionem alteri præfe
rendam e&longs;&longs;e, quia &longs;cilicet vtrique hypothe&longs;i facit &longs;atis; quanquam ad v&longs;um. Galileana omnino adhibenda e&longs;t, cùm in eam mea re&longs;olvatur, vt verò ad
cau&longs;am phy&longs;icam accelerationis res reducatur pro vtraque hypothe&longs;i, mea
certè non modò præferenda e&longs;t, verùm etiam nece&longs;&longs;ariò tenenda; &longs;ed tam
multa de hac re &longs;crip&longs;imus, vt de his plura &longs;cribere operæ pretium non &longs;it.
Ne&longs;cio, quomodo dicas, nullam &longs;upere&longs;&longs;e difficultatem,
cùm in&longs;uperabilis adhuc re&longs;tet; nempe &longs;i primo in&longs;tanti mobile acquirit
AV, & &longs;ecundo, &longs;patium CH, duplum, igitur, cùm mobile e&longs;&longs;et ih &longs;pa
tio AV tanquam in loco adæquato erit in CH duplo &longs;cilicet, tanquam
in loco adæquato majore.
hypothe&longs;i, &longs;i rèm ip&longs;am, non verba con&longs;ideremus,
ferè in&longs;uperabilis; immò & in Galilei opinione, qui
vult, tempus ex infinitis in&longs;tantibus Mathematicis
componi, in&longs;olubilis nodus e&longs;t; &longs;i enim in tempore
AE accipiantur duo in&longs;tantia, &longs;cilicet B & C, nem
pe vt linea AE repræ&longs;entat tempus, ita quodlibet illius
punctum repræ&longs;entat vnum in&longs;tans, porrò mobile,
quod movetur tempore AE, in&longs;tanti B e&longs;t in &longs;pa
tio BF, in&longs;tanti C in &longs;patio CG duplo prioris;
quia vt arca trianguli AEI repræ&longs;entat, totum
&longs;patium, in que fuit in&longs;tanti B; & CG, &longs;patium, in quo fuit in&longs;tanti
C &c. In hypothe&longs;i in&longs;tantium phy&longs;icorum hæc difficultas omnino ce&longs;
&longs;at; &longs;ed ne huc accer&longs;am integram, & benè longam tractationem, in
qua natura temporis & motus explicanda e&longs;&longs;et, con&longs;ule, &longs;i vis, Chry
&longs;ocome, tractatum no&longs;trum, de motu locali; itemque Metaphy&longs;icam
non vno loco, ibi enim hoc munere perfuncti &longs;umus, quo certè in præ
&longs;enti congre&longs;&longs;u perfungi non vacat. Addo tantùm, hypothe&longs;i Coperni
canæ nihil ob&longs;tare motum acceleratum, vt dicebas, &longs;icuti eidem mo
tui non ob&longs;tat navis motus, vt plu&longs;quam mille experimentis comproba
tum e&longs;t.
Rectè omninò, nempe corpus grave de&longs;cenderet, motu
quodam mixto, ex æquabili, & accelerato; in navi exemplum luculen
tum e&longs;t, immò & in di&longs;co projecto per inclinatam &longs;ur&longs;um, qui non mo
dò per curvam &longs;ur&longs;um a&longs;cendit, verùm etiam per curvam deor&longs;um ruit
& licèt æqualia &longs;patia in dicta curva æqualibus temporibus omnino de
currat, &longs;altem ad &longs;en&longs;am, hoc tamen non ob&longs;tat, quin ratione perpen
dicularis, in quam vi motus naturalis inclinat, & in qua majora &longs;pa
tia decurrit. eodem pror&longs;us modo quo fieret, &longs;i motus naturalis cum alio
horizontali conjunctus non e&longs;&longs;et; hoc inquam non ob&longs;tat, quin ratio
ne perpendicularis, dictum corpus grave motu accelerato moveatur; &longs;ed
&longs;i motus acceleratus e&longs;t, cre&longs;cit. impetus; hinc major ictus &c.
Non
cre&longs;cunt &longs;patia, inquies; Re&longs;pondeo: non cre&longs;cunt in horizontali, con
cedo: vnde ratione horizontalis, e&longs;t motus æquabilis; non cre&longs;cunt in per
pendiculari, nego; &longs;ed profecto &longs;i non cre&longs;ceret impetus, in perpendicula
ri &longs;patia non cre&longs;cerent.
Omitte quæ&longs;o hæc argumenta, à motu gravium, vel levium
petita, quæ &longs;anè multiplicem paralogi&longs;mis materiam nonnullis præ
buerunt, quos aliis, amabo di&longs;cutiendos
mediocriter doctis, & i&longs;tarum rerum peritis cuncta hæc per&longs;pecta &longs;int;
vnum tantùm: in quo non nemo maximam vim facit, obiter indico;
&longs;i moveatur terra, inquit, explodaturque catapulta, vel quodlibet
aliud projectionis organum, versùs polum directè, globus projectus
incidet in planum oppo&longs;itum obliquè; igitur vis ictus longe minor erit,
quàm &longs;i explodatur versùs ortum, vel occa&longs;um; quod tamen expe
rimentis repugnat: Sed facilè re&longs;pondeo, dicti globi explo&longs;i motum
mixtum e&longs;&longs;e ex duobus, altero communi aliis partibus terræ, versùs
ortum, altero impre&longs;&longs;o à machina versùs polum; vterque totum effe
ctum habet, qui &longs;ibi competit; e&longs;t enim reverà duplex impetus, quo
rum vnus independenter ab alio id totum præ&longs;tat, quod præ&longs;tare po
te&longs;t; clari&longs;&longs;imum exemplum habemus in navi; vnde argumentum illud
facilè &longs;olvitur, nempe ictus per lineam obliquam minor e&longs;t, quando
vnus tantùm impetus ine&longs;t, ad talem lineam determinatus; at verò quan
do duplex impetus ine&longs;t, & alter per directam lineam determinatus e&longs;t, &longs;ive
alius in&longs;it, five non, æqualis ictus infligitur.
Sed, quæ&longs;o te, Antime, quandoquidem alia non &longs;up
petunt argumenta in terre&longs;trl globo, ad confutandum illius motum pro
fer amabo, locos illos ex quibus alia erui po&longs;&longs;int.
Nullus globus terre&longs;tri vicinior e&longs;t, quàm Luna; in Lunari
globo nonnihil habeo, quod fortè non minùs negotij tibi face&longs;&longs;et, Augu
&longs;tine, quàm Marinus æ&longs;tus.
Immò in Iove mobili, circa quem moventur quatuor
Ioviales Lunæ, clari&longs;&longs;imam analogiam habemus terræ mobilis, circa
quam Luna volvitur; nonnihil &longs;imile in Saturno habemus, circa quem
etiam &longs;ua Stella, &longs;eu Luna Saturnia circumfertur; Luna igitur no&longs;træ
hypothe&longs;i non obe&longs;t, immò no&longs;tra hypothe&longs;is Lunari &longs;y&longs;temati favet,
quod &longs;cilicet, & à deformibus &longs;piris, & à motu raptus versùs Occa&longs;um
liberat.
Negari non pote&longs;t, quin ex ip&longs;i&longs;&longs;imis, non illorum modò,
qui communem A&longs;tronomorum &longs;ententiam tenent, verùm etiam prin
cipium Copernicanæ &longs;ententiæ defen&longs;orum principiit, Planetarum mo
tus reales, vt vocant, æquales &longs;int, quamvis inæquales nobis appa
reant; hanc realium motuum inæqualitatem Antiqui omnes, ad vnum,
vt A&longs;tronomiæ pe&longs;tem ac mortem relegarunt; ex recentioribus verò
Copernicus ve&longs;ter, illam humano intellectui horrori e&longs;&longs;e dixit, Cla
vius &longs;ummæ dementiæ; Reinholdus imperitæ imaginationis; alij deni
que, vt Tycho, æqualem motum, in cœle&longs;tibus Sphæris, pro certo
& indubitato axiomate po&longs;uerunt: Scio, Keplerum, quem deinde pauci
alij &longs;ecuti &longs;unt, inæqualitatem motuum realium ad&longs;truxi&longs;&longs;e, in id dum
taxat ab ip&longs;a de&longs;peratione inductum extremi&longs;que angu&longs;tiis, in quas illum
multa phænomena redegerant, quæ &longs;cilicet &longs;uppo&longs;itis motibus realibus in
&longs;ua hypothe&longs;i explicare non poterat; hæc vnica huius con&longs;ilij cau&longs;a fuit,
quod certè penitus ruit, &longs;i po&longs;itis motibus æqualibus, cuncta phænomena
explicari po&longs;&longs;unt.
In hac parte tecum facilè &longs;entio, & verò à Ptolemæo
alii&longs;que antiquis A&longs;tronomis, itemque à Tychone, Longomontano,
Copernico, Galileo, Lansbergio, Clavio, Magino, alii&longs;que rei A&longs;tro
nomicæ Principibus, in hoc di&longs;cedere, vix au&longs;im ; nec ratio dee&longs;t, quæ
meo &longs;altem iudicio, rem conficit; nempe omnis motus per &longs;e inæquabi
lis vel acceleratus, vel retardatus e&longs;t, neutrum de cœle&longs;tibus motibus
dici pote&longs;t; cùm enim eadem &longs;emper e&longs;&longs;et accelerationis vel retardatio
nis cau&longs;a, certè in infinitum acceleraretur, vel retardaretur; quod vel
ab&longs;urdum dictu e&longs;t; omitto certi&longs;&longs;imam totius A&longs;tronomiæ ruinam
ac de&longs;tructionem, cùm inæqualitas certis ac perpetuis regulis minimè
&longs;ubjaceat; incerta &longs;cilicet, varia, ignota; cùm enim vna dumtaxat
fit æqualitas, infinitæ &longs;unt ac variæ inæqualitates; cur hæc potiùs quam
illa?
Multas tamen apud Autorem Neotericum de re A&longs;tro
nomica optimè meritum, rationes legi, quibus probare conatur, inæ
qualitatem realium motuum, quantum porrò conjicio, in &longs;ingula-
motuum &longs;alvari non po&longs;&longs;e, ni&longs;i in hypothe&longs;i Copernicana, in qua
&longs;cilicet &longs;pectantis hominis oculus extra orbitarum cœle&longs;tium centrum
collocatur.
Scio, quem intelligas, Chry&longs;ocome, rationes illæ de
bili&longs;&longs;imæ &longs;unt, & eadem facilitate de&longs;truuntur, qua ad&longs;truuntur; præ
&longs;ertim in hypothe&longs;i hujus no&longs;tri Antimi, in qua, motus realis vnicus
&longs;implex & æquabilis e&longs;t ab ortu in occa&longs;um; reliqui tantùm apparentes,
hos quidem inæquales e&longs;&longs;e do vltrò, &longs;ecus tamen realem & phy&longs;icum,
qui &longs;anè ita æqualis e&longs;t, vt æqualibus temporibus, æqualia &longs;patia in &longs;uis
&longs;piris &longs;eu revolutionibus Planeta decurrat.
Non e&longs;t etiam, quod aliquis timeat, ne præ&longs;ata æqualitas hy
pothe&longs;i Copernicanæ &longs;uffragetur; ex illa enim poti&longs;&longs;imum contra i&longs;tam
argumentum duci pote&longs;t, vt paulò po&longs;t evincam.
Vnum omi&longs;eram, quod &longs;cilicet in Luna maximè rea
lium motuum inæqualitas ponenda e&longs;&longs;et, quia &longs;cilicet Men&longs;es tum Sy
nodici, tum Periodici inter &longs;e inæquales &longs;unt; at etiam in mea hypothe
&longs;i, Luna &longs;pectatur ex eo centro, circa quod &longs;uos orbes agit; igitur ideò
æqualitas abigenda non e&longs;t, quod in hypothe&longs;i terræ mobilis, &longs;al
vari tantùm po&longs;&longs;it; cùm & in alia hypothe&longs;i fortè &longs;alvetur, & in illa,
Lunæ motus quamvis ex &longs;uo centro &longs;pectati, valde inæquales appa
reant.
Ne dicas,
litatem illam optimè & facilè &longs;alvo; vt probè, ni fallor, intelligis ex iis,
quæ in proximo congre&longs;&longs;u de meo Solis &longs;y&longs;temate obiter expo&longs;ui.
De Sole non abnuerim, &longs;ed de Luna quid?
In qua non
nulli ex tuis, etiam in tua hypothe&longs;i, motuum realium inæqualitatem
admittunt, propter vnam dumtaxat inæqualitatem men&longs;ium; nempe li
cèt motus inæqualitas in hoc, vel illo arcu orbitæ in meram apparen
tiam, &longs;alva &longs;emper æqualitate reali, refundi po&longs;&longs;it, &longs;i tamen brevior &longs;it
vna integra revolutio, quàm alia, realis profectò erit, non verò apparens
inæqualitas, &longs;ed hoc non vrgeo contra te, quia eadem vterque difficultate
laboramus.
Nullo negotio præfatam men&longs;ium inæqualitatem in mea hy
pothe&longs;i explico; Cùm Lunæ æquè ac Soli motum &longs;implici&longs;&longs;imum attri
buam ab ortu ad occa&longs;um, cum gemina illa inclinatione, de qua &longs;upra,
& hac vna &longs;ingulari differentia, quòd terminus &longs;ecundæ inclinationis in
Sole &longs;it Æquator, in Luna verò &longs;it Ecliptica; longioris operæ res e&longs;&longs;et, i&longs;ta
fu&longs;iùs pro&longs;equi, præ&longs;ertim cùm appellata men&longs;ium inæqualitas alioquin
facilè in hac mea hypothe&longs;i intelligatur: fac enim, v. g. Solem e&longs;&longs;e cir
ca Apogæum, Lunæ conjunctum; Sol tardiùs &longs;uos orbes diurnos ab
&longs;olvit: igitur breviore intervallo Lunam po&longs;t &longs;e relinquit versùs or
tum; vnde nece&longs;&longs;ariò &longs;equitur, copulam deinde tardiùs fieri; vnde
men&longs;em illum periodicum longiorem e&longs;&longs;e, nece&longs;&longs;e e&longs;t; contra verò
breviorem illum, qui Sole in perigæo exi&longs;tente currit; quod verò
Luna ab Occa&longs;u ad Ortum totum Zodiacum decurrere videtur; modò
longior, modò brevior e&longs;t, pro diver&longs;o Nodorum &longs;itu; &longs;i enim Nodi
exi&longs;tant, in punctis Eclipticæ Æquinoctialibus, haud dubiè Luna
&longs;uas &longs;piras agens longiùs versùs Polos excurrit, minùs verò longè
Nodis in punctis Sol&longs;titialibus exi&longs;tentibus; &longs;ed quò longiùs excur
rit, plus temporis ponit; Major igitur e&longs;t periodus; quid clarius
&longs;upet hoc dici, vel excogitari po&longs;&longs;it, vereor &longs;anè vt qui&longs;piam vi
deat.
Mirum mihi accidit, Antime, cur adeò in motuum rea
lium inæqualitatem inveharis, cùm tamen motum vtriu&longs;que inclinatio
nis inæqualem in tuo &longs;y&longs;temate &longs;tatuas; acceleratum &longs;cilicet & retar
datum.
Hanc in&longs;tantiam facilè &longs;olvere, vel; vt veriùs dicam, eludere
po&longs;&longs;em, &longs;i dicerem, e&longs;&longs;e motus rectos, qui ex natura &longs;ua accelerati &longs;unt,
vel retardati; nempe vel ad &longs;uum naturalem terminum tendunt, vel ab eo
recedunt; &longs;i primum, acceleratos; &longs;i alterum, retardatos e&longs;&longs;e, oportet;
&longs;ed hi re verà motus non &longs;unt, qui tantùm con&longs;iderantur in decur&longs;i &longs;patij
linea, in qua æqualibus temporibus æqualia &longs;emper &longs;patia à Planeta de
curruntur, licèt inæqualia nobis appareant: & verò æquabilem mo
rum e&longs;&longs;e, nece&longs;&longs;e e&longs;t, cuius æqualis eademque cau&longs;a &longs;emper manet, idem
&longs;cilicet impetus, vel initio impre&longs;&longs;us, vel eo, quo dixi modo, acqui
&longs;itus.
Nunquid tantulùm &longs;altem retardat medij re&longs;i&longs;tentia, vt in
projectis, immò & deor&longs;um cadentibus fieri videmus?
Certè non retardat, &longs;i medium &longs;imul & Planeta eodem
motu moveantur; Sed hoc ad&longs;truere non cogimur, cùm nulla ratio
ne nitatur; medium enim commune e&longs;t; Re&longs;pondeo igitur, cladem
illam à re&longs;i&longs;tentia medij acceptam à Planeta continuo re&longs;arciri, vel,
vt meliùs dicam, impediri; vt enim iuxta optimum Naturæ in&longs;titutum,
impetum non auget, ne &longs;cilicet obtinendo fini adver&longs;etur, ita nec eun
dem impetum minui &longs;init, quod non minùs eidem repugnaret in
&longs;tituto.
Sed ne totus &longs;is in præludiis, ad tuum illud argumentum con
tra meam hypothe&longs;im à Luna petitum veniendum e&longs;&longs;et.
His præmi&longs;&longs;is, ad illud venio, ac dico, in tua hypothe&longs;i, realem
Lunæ motum, eum &longs;cilicet, qui nobis æqualis ferè apparet, adeò inæqualem
fore, vt aliquando infinities tardior aut velocior e&longs;&longs;et.
Somnia narras, Antime, quis vnquam hoc dixit, vel cogita
vit? Luna circa terram iret, quamvis mobilem, inæquali certè motu, quoad
apparentiam, re ip&longs;a tamen ferè æquali; cùm arcus vno die decur&longs;us paucis
minutis arcum alio die decur&longs;um &longs;uperet; hæc e&longs;t trita illa anomalia, eaque
multiplex in Luna, quam no&longs;tri per excentricos, vel epicyclos, vel circellos
explicant; &longs;ed hæc inæqualitas præterquàm quòd apparens, non verò rea
lis e&longs;t tanta, non &longs;tatuitur, ne dum infinita.
Non &longs;omnio, Augu&longs;tine; nihil dixi, quod demon&longs;trare non
po&longs;&longs;im.
Sit enim
Solem &longs;tatuitis; &longs;it arcus magni orbis
DB, 29. circiter grad. quem &longs;cilicet
terra decurrit, toto illo tempore; quo
Luna ab vna copula, ad aliam ve
nit; Sit AD. 2000.Semidiam. terræ
DH 60. DB 508.circiter; vnde HD
in DB octies fere continetur. Sit au
tem primùm Lunain copula H, vt
deinde tran&longs;eat per oppo&longs;itionem G
ad &longs;equentem copulam I eo tempore,
quo terra decurrit arcum DCB: divi
datur arcus DC in 4.partes æquales
DELMC: ita progreditur terra cum
Luna, vt terra &longs;itin D, Luna in H ;
terra in E, Luna in O; terra in L,
Luna in E; terra in M, Luna in P ;
terra in C, Luna in G ; codem pro
gre&longs;&longs;ionis ordine terra à C tendit in B, & Luna à G tendit in I. En tibi
veram ac germanam lineam Lunaris motus in tua hypothe&longs;i ; eodem por
rò tempore Luna &longs;egmenta HE & EG conficit; vnde vides, quàm &longs;it inæ
qualis motus; & multò majorem inæqualitatis proportionem invenies, &longs;i
compares &longs;egmentum HO cum &longs;egmento EP, vel PG; & vt &longs;egmentum
HO decurrit Luna, eo tempore, quo primum octantem &longs;uæ periodi, ap
parenti motu decurrere videtur, id e&longs;t 45. grad. &longs;i accipiamus minorem
arcum v. g. 12. grad. paulò plùs, qui e&longs;t arcus illius ferè diurnus, et&longs;i com
paremus &longs;patium, quod acquirit intereà, reali motu, tum circa Novilu
nium H, tum circa Plenilunium G, longè maior erit inæqualitatis propor
tio inter illa duo &longs;patia, æqualibus temporibus decur&longs;a, licèt quoad appa
rentiam æqualia &longs;patia videantur. Vnde nece&longs;&longs;ariò &longs;equitur, Lunam inæ
quali motu moveri, reali &longs;cilicet & phy&longs;ico, atque in tanta inæqualitatis pro
portione, vt qualibet a&longs;&longs;ignabili major &longs;it.
Si nihil aliud habes, hæc minimè nos vrgent; nam &longs;uppo
nimus Lunam moveri in epicyclo, cujus terra centrum e&longs;t, ac proinde
Luna movetur motu mixto ex motu orbis & motu centri, vtroque certè
æquabili; &longs;ed ex duobus motibus æquabilibus, motum mixtum minimè
æquabilem re&longs;ultare mirum dictu non e&longs;t; immo ne&longs;cire non potes, cuili
bet hypothe&longs;i, quæ epicyclos ad&longs;truit, hoc e&longs;&longs;e commune.
Non dubitabam, quin hæc dicturus e&longs;&longs;es, &longs;ed antequàm vlteriùs
progrediar, non admittis, opinor, in Luna realem epicyclum; &longs;i enim realis
Epicyclus e&longs;&longs;et, haud dubiè cum &longs;uperficie terræ intra 24.horas &longs;uum orbem
ab&longs;olveret, quod certè ab&longs;urdum dictu e&longs;t; cùm decurrat tantùm eo tempo
re 12.gradus paulò plus.
Accipe quæ&longs;o, totum Sy&longs;tema telluris globi, quod non modò
&longs;ublunarem omnem tractum, verùm etiam Lunarem complectitur; finge
totum illud ad modum vnius Epicycli, ita tamen, vt globus terræ, & por
tio vicinior circumfu&longs;i ætheris volvatur ab occa&longs;u ad
rum, &longs;uperior verò multò tardiùs, & Lunaris
acquirat, in tanta enim di&longs;tantia, vis rapic
cit, &longs;altem plurimùm remittitur.
Ingeniosè pror&longs;us; vis enim vim illam motricem à terre&longs;tri glo
bo, ad Lunarem traduci, eamque valde remi&longs;&longs;am, propter di&longs;tantiam, cujus
rei analogiam petes in mea quoque hypothe&longs;i, a Iove, qui quatuor Lunas
&longs;ecum ita volvit, immò & à Sole qui Venerem & Mercurium &longs;ecum in or
bem agit; &longs;ed vt duo &longs;unt motus in terre&longs;tri globo, centri &longs;cilicet, atque or
bis, cur debilitatur vis motrix in Lunam traducta à motu orbis, intacta re
manente traducta à motu centri, vtramque enim, vel neutram di&longs;tantia
æquè debilitat.
Si fingas totum illud Sy&longs;tema vtroque motu moveri, fieri non
pote&longs;t, quin motus centri toti &longs;y&longs;temati communis &longs;it, atque adeò omnes
&longs;y&longs;tematis partes per &longs;e illo motu æquè moveantur, licèt aliquæ plus, aliæ
minùs propter motum orbis.
Fingo facilè totum illud &longs;y&longs;tema ad in&longs;tar &longs;phæræ, cujus majo
rem tantùm circulum accipio, qui &longs;it ad in&longs;tar epicycli ; &longs;ed cùm retardetur
motus orbis propter di&longs;tantiam, non video, cur propter eandem non re
tardetur etiam motus centri; & verò, &longs;i &longs;olida quæpiam e&longs;&longs;et partium hu
jus &longs;y&longs;tematis inter &longs;e connexio, optimè intelligerem, quomodo vterque
motus omnibus communicetur; &longs;ed hoc po&longs;ito, æquè citò omnes motum
orbis ab&longs;olverent; &longs;ed cùm hæc &longs;olida connexio non &longs;it, quid mirum. &longs;i vter
que motus tum orbis, tum centri communicetur.
Vnum tibi facilè &longs;uggererem, quod ad rem præ&longs;entem pluri
mùm facit; nempe &longs;i motus orbis à globo terre&longs;tri in Lunarem traducitur;
igitur hic motus Lunæ versùs ortum iret per arcus parallelos circulis diur
nis, &longs;imilis enim terræ motus &longs;imilem produceret; cùm tamen orbita Lu
næ non modò Æquatori parallela non &longs;it, &longs;ed nequidem Eclipticæ; ac
cedit quod totum illud &longs;y&longs;tema modò ad Au&longs;trum, modò ad Boream cum
terre&longs;tri globo librari deberet, hoc enim &longs;it in terre&longs;tri globo ad retinen
dum axis paralleli&longs;mum; quare cùm non videatur quomodo Lunæ motus
à telluris motu profici&longs;ci, vel traduci queat dicerem potiùs, (
riori Schemate
revera nullum videmus epicyclum, idque per lineam curvam HE
PGFI.
Ab Angelo igitur inæquali motu reali movetur; & hoc ip&longs;um
e&longs;t, quod ip&longs;e Antimus intendit, & opponit contra meam hypothe&longs;im ; hoc
autem argumentum eju&longs;dem pror&longs;us e&longs;t energiæ, &longs;ive dicatur Luna moveri
ab Angelo per lineam HPG, &longs;ive à &longs;e ip&longs;a.
realis &longs;cilicet, omnino inæqualis e&longs;t, vt iam dixi.
Ille motus, qui fit per lineam HPG mixtus e&longs;t ac proinde
inæqualis, &longs;ed ex duobus æquabilibus, vt iam dixi.
Vnde porrò &longs;unt illi duo motus æquabiles' à quo principio?
&
quo tandem organo traducuntur?
Affulget novæ lux re&longs;pon&longs;ionis; &longs;uperficies terræ inæquali
ter movetur, etiam in eodem circulo majore ; nempe ille arcus, qui ad
Solem convertitur, tardi&longs;&longs;imus e&longs;t, oppo&longs;itus verò veloci&longs;&longs;imus, quid mi
rum igitur, &longs;i hic Lunam longiùs promovet, &longs;cilicet circa Plenilunium,
ille verò longè minùs, &longs;cilicet circa Novilunium.
Non negarim, acutam, & non nemini fortè inexpectatam re
&longs;pon&longs;ionem; &longs;ed præterquam quod &longs;ub&longs;i&longs;tunt alia &longs;upra oppo&longs;ita; quia nec
in arcubus, diurnis circulis parallelis Luna movetur, non videtur, cur mo
tus centri in Lunam traductus debilior non exi&longs;tat.
Miror, hæc à te dici, cùm vterque debilior exi&longs;tat, vt mani
fe&longs;tum e&longs;t; &longs;ic enim ab H ad O parum progreditur, tum motu centri, tum
motu orbis; igitur à puncto terræ oppo&longs;ito &longs;uam vim accipit, majorem
&longs;cilicet, cùm velociùs illud movetur, quamvis alioquin motu mixto; mi
norem verò cùm tardiùs, quid ad aliud de arcubus parallelis re&longs;pondeam,
non habeo, ni&longs;i fortè dicam, Lunam à &longs;e ip&longs;a, vel ab Angelo per illam or
bitam moveri: Sed cur per illam movetur inæqualiter? deinde hæc orbita
re&longs;pectum habet ad terram, quæ in &longs;ua libratione diver&longs;am periodum ha
bet, malim ergo ingenuè fateri, me ne&longs;cire, quid ad hoc re&longs;pondeam.
Re&longs;umo quod &longs;upra dicere cœperam; præter illa argumenta,
inquam, quibus allata re&longs;pon&longs;io non congruit, dico aliam eamque in&longs;o
lubilem re&longs;tare difficultatem; admi&longs;&longs;a enim prædicta re&longs;pon&longs;ione, fateris
in puncto G majorem vim impetus à puncto terræ oppo&longs;ito Lunam ac
cipere, minorem verò à puncto H, cur ergo Luna impre&longs;&longs;um impetum
deinde non retinet? cum nihil &longs;it à quo de&longs;truatur; nec enim ob&longs;tat, à
novo puncto terræ oppo&longs;ito ad aliam tangentem determinari, quia cùm
hoc fiat per novi impetus acce&longs;&longs;ionem, hic aditus priori majorem vim
facit; igitur nulla e&longs;&longs;et ratio, cur deinde motus retardaretur versùs Qua
draturas.
Vereor, vt inde qui&longs;piam cau&longs;am deducat, rei mi&longs;&longs;ionis marini
æ&longs;tus in Quadratoris; nempe, vt in Oppo&longs;itione vegetior e&longs;t, ita in Quadra
turis minor e&longs;t & flaccidior; quia, inquiet, cùm à Luna procedat, Lunæ
motus in plenilunio maior e&longs;t, minor in Quadraturis; minorem igitur in
his, majorem in illo motus effectum producit.
Sed in Novilunio Lunaris motus adhuc minor e&longs;t, quam in
Quadraturis, & tamen nemo ne&longs;cit, æ&longs;tum in Novilunio majorem e&longs;&longs;e; alia
igitur ratio prædictæ differentiæ inve&longs;tiganda e&longs;t.
Aliud in mentem venit, quod expromendum e&longs;&longs;e puto;
nempe &longs;i &longs;upponam Lunam 24. horarum &longs;patio orbem &longs;uum circa terram
ab&longs;olvere, illius velocitas ad velocitatem puncti æquatoris in &longs;uperficie
terræ erit vt 60.ad 1.&longs;unt enim motus vt circuli, hi vtrò, vt &longs;emidiametri;
igitur non mirum e&longs;t, cùm motus tardus velocem producere nequeat, &longs;i
Neque hoc &longs;ufficit; quia cùm vnus motus alium æqualem ad
&longs;ummum producere po&longs;&longs;it, e&longs;to terræ motus æqualem Lunæ imprimat,
hic erit
&longs;ectis 360. grad. igitur erit tantùm 6. graduum; &longs;ed e&longs;t 12.grad. diurnus
&longs;cilicet; aliunde igitur cau&longs;a hujus motus petenda e&longs;t: &longs;ed nulla e&longs;&longs;e po
te&longs;t, ni&longs;i hic motus inæqualis &longs;upponatur; igitur ex hoc etiam capite i&longs;ta
hypothe&longs;is terræ mobilis non &longs;ub&longs;i&longs;tit, quia &longs;cilicet in ea motus realis in
æqualis per&longs;o e&longs;&longs;et.
Eadem difficultate tua laborat hypothe&longs;is, in qua Lunaris
motus &longs;ine vno &longs;altem epicyclo explicari nequit.
Nullum Epicyclum pono
parenti verò vtcumque, &longs;implicem dumtaxat motum admitto, ab ortu ad
occa&longs;um, longè tamen tardiorem motu Solis, ita vt &longs;ingulis men&longs;ibus Sy
nodicis Sol Lunam a&longs;&longs;equatur, atque adeò
pra illam acquirat; adde vtramque inclinationem, quâ &longs;cilicet tum ab
Apogæo ad Perigæum & vici&longs;&longs;im, tum à Borea ad Au&longs;trum, & vici&longs;&longs;im
Planeta librari videtur; vtriu&longs;que tamen periodus in Luna diver&longs;a e&longs;t à
Solari; vnde Lunæ Apogæum recurrit frequentiùs; præterea Lunæ &longs;ecun
da inclinatio habet pro termino Eclipticam, vt jam dixi; anomaliæ primæ,
&longs;eu periodicæ ratio eadem e&longs;t, quæ anomaliæ Solaris; neque hîc repeto,
quæ jam dixi in alio congre&longs;&longs;u; quod verò pertinet ad aliam inæqualita
tem, vel anomaliam &longs;ynodicam, vt vocant. in mea hypothe&longs;i, facilè ratio
redditur multiplicis inæqualitatis, quam huc v&longs;que, vt verum fatear, non
dum accuratè indagarunt A&longs;tronomi, nedum &longs;tatuerunt; hinc vnus negat,
quod alius ad&longs;truit; &longs;cilicet eò qui&longs;que dumtaxat &longs;pectat, vt ob&longs;ervatio
nes ad Sy&longs;tematis excogitati formam accommodet; &longs;ed hæc fu&longs;iùs di&longs;cu
tere huius loci non e&longs;t; hoc tantùm indica&longs;&longs;e contentus, ex diver&longs;o Lu
næ &longs;itu, multiplicem inæqualitatem, apparentem &longs;cilicet, eamque variam
&longs;equi po&longs;&longs;e: vtrùm verò Lunæ apogeæ di&longs;tantia maior &longs;it in quadraturis,
quàm in copulis, & perigeæ minor, non de&longs;unt, etiam inter principes
A&longs;tromos, qui negent: & verò punctum ac momentum veræ ac germa
næ quadraturæ vix di&longs;cerni pore&longs;t, maximè intra &longs;patium duorum vel qua
tuor graduum; de Latitudine Lunæ nihil dico; cùm eam nullo negotio
explicemus; itemque Nodorum motum in antecedentia; quia citiùs &longs;ecun
dæ inclinationis motus perficitur, quàm motus in Zodiaco; vnde nece&longs;
&longs;ariò &longs;equitur motus Nodorum apparens contra &longs;eriem Signorum; motus
apogæi etiam apparens eodem modo explicatur, quo jam in Sole illum
explicuimus; itemque eorundem motuum inæqualitas, &longs;uppo&longs;ito motu
reali æquabili&longs;&longs;imo; & vbi certæ omnino & in omnibus con&longs;entientes
ob&longs;ervationes aliquando definientur, nullus dubito, quin ex jactis princi
piis facilè in hac no&longs;tra hypothe&longs;i explicentur, quod tamen modò fieri ne
quit, cùm multa etiamnum incerta maneant, & vix de Apogæo con&longs;tet,
vbi &longs;it, & qualis &longs;it excentricitas, an hæc &longs;emper eadem &longs;it; di&longs;tantia verò
Lunæ maxima, etiam incerta e&longs;t.
Probè intelligo tuum &longs;y&longs;tema Lunare; vis enim Lunam &longs;im
plici motu moveri ab Ortu ad Occa&longs;um, &longs;ed longè tardiùs, quàm &longs;tellas;
ita vt intra tempus vnius men&longs;is periodici Luna à Stellis retro relicta ver
sùs Ortum, videatur totum Zodiacum percurrere, & ad idem punctum
redire; & quia Sol toto eo tempore versùs Ortum relictus e&longs;t, qua&longs;i 27.
grad. antequam ad copulam Luna redeat, duobus diebus & aliquot horis
opus e&longs;t: hunc men&longs;is Synodicus longior periodico; addis vtriu&longs;que incli
nationis motum, ita vt &longs;ecundæ terminus &longs;it Eclyptica; & quia motus &longs;e
cundæ ab&longs;olvitur paulò ante finem periodici, hinc motus Nodorum ver
sùs Occa&longs;um, itemque Apogæi versùs Ortum; quia periodus intra quam
Luna redit ad Apogæum, paulò longior e&longs;t men&longs;e periodico: inæqualitas
&longs;implex eodem modo à te explicatur in Luna, & in Sole; aliæ ex diver&longs;a
combinatione vtriu&longs;que inclinationis na&longs;cuntur: Latitudinem per motum
&longs;ecundæ inclinationis facilè omninò explicas, Vtrùm verò major &longs;it Lati
tudo in Quadraturis, quàm in Copulis, incertum putas, itemque multa alia
incerta, quæ &longs;upra obiter recen&longs;ui&longs;ti; optimè demum explicas, quomodo
men&longs;es Periodici modò majores &longs;int, modò minores, itèmque Synodici,
men&longs;es enim Periodici majores &longs;unt, quando Nodi &longs;unt circa Æquato
rem, minores verò, quando &longs;unt circa Tropicos; Synodici autem majores
&longs;unt, dum Sol e&longs;t circa Apogæum, dum verò circa Perigæum minores;
neque in his vlla re&longs;tat difficultas; vnum tantùm ex te re&longs;cire velim, Anti
me, quid cen&longs;eas de libratione illa Lunari, qua &longs;it, vt quædam interdum
maculæ ad margines di&longs;ci Lunaris propiùs accedant, aliàs, ab iis longiùs
recedant.
ob&longs;ervatori, in his detrectari fidem, non au&longs;im ; hic autem vult, Lunam
ita librari, vt cùm maximè ab Æquatore declinat, versùs Boream, macu
læ Boreales in ejus di&longs;co recedant à margine, Au&longs;trales contra ad margi
nes accedant; & vici&longs;&longs;im cùm maximè declinat versùs Au&longs;trum, au&longs;tra
les recedant, accedant verò Boreales. Nonnulli ex ve&longs;tris, Augu&longs;tine, &longs;ta
tuunt ad hunc finem, Lunarem axem &longs;ibi ip&longs;i parallelum, & Axi mundi; &longs;ed
meo judicio perperam &longs;atis, dum enim versùs Tropicum Cancri acce
dit Luna, extremitas Borealis axis attolleretur, vt patet, igitur & Semicir
culus di&longs;ci Borealis, & Au&longs;tralis de primeretur; ex quo contraria Phænome
na &longs;equerentur; Malim dicere Lunarem Globum magnetica for&longs;an virtute
pellere, ac proinde habere duos polos magneticos; igitur codem pror&longs;us
modo &longs;e&longs;e componit ad terre&longs;trem Globum, quo terrella quæpiam, vel
acus magnetica; igitur quando Luna versùs Boream tendit ab Æquatore,
extremitas borealis axis deprimitur, Au&longs;tralis verò attollitur, & vici&longs;&longs;im;
cùm Luna ab Æquatore versùs Au&longs;trum excurrit; Au&longs;tralis deprimitur,
Borealis attollitur, ex quo prædicti effectus nece&longs;&longs;ariò con&longs;equuntur.
Parum admodùm abe&longs;t, quin hoc apprimè capiam; nonni
hil &longs;chematis de&longs;iderarem, vt hoc meliùs inculcetur
Id mihi præ&longs;tandum &longs;u&longs;cipio: &longs;it meridianus Lunaris SBTK,
Axis magneticus BK, &longs;emicirculus ad terram conver&longs;us BSK, qui in
quas exhibeo parallelas, propter anguli tenuitatem; &longs;it A in Æquatore,
Axis BK &longs;ecat Æquatorem ad an
gulos rectos; &longs;i verò A &longs;it in Tro
pico Cancri, punctum B deprimitur
in G, & K attollitur in H ; Hinc ante
depre&longs;&longs;ionem macula E videbatur
in C, igitur vicina margini, N verò
in L. remota igitur à margine; at
verò po&longs;t depre&longs;&longs;ionem dicti Axis
Macula E erit in F, ac proinde vide
bitur in D: igitur recedit à margi
ne; at verò N erit in M ; igitur vi
debitur in I; accedit igitur ad mar
ginem; hæc adeò per&longs;picua &longs;unt, vt
nihil clariùs dici, vel excogitari po&longs;&longs;e
videatur. Vnum tamen dubium re
&longs;tat de fide &longs;cilicet Hevelij, cùm non
defuerit, qui dictam fidem pror&longs;us elevarit, adductis ob&longs;ervationibus
omnino contrariis.
Scio, non defui&longs;&longs;e; Hevelio tamen adhærendum, eique fi
dem habendam e&longs;&longs;e, putarem, præ&longs;ertim cum nonnulla ex iis, quæ con
tra illum adducuntur, minimè &longs;ub&longs;i&longs;tant; Sed hæc di&longs;cutere non vacat;
Vt vt &longs;it, &longs;uppo&longs;ita veritate dictorum Hevelij. con&longs;tat rationem huius
librationis à me allatam per&longs;picuam e&longs;&longs;e; &longs;i res &longs;ecus &longs;e habeat, vt mihi,
Augu&longs;tine, non nocet, ita tibi nullo modo prode&longs;t. Sed iam ad alias ratio
nes veniamus.
Re&longs;tat, Antime, vt ad alios cœle&longs;tes globos gradum facias, in
quo lepidi&longs;&longs;imum itineris extatici autorem imitari cuipiam fortè videberis;
quod ne&longs;cio an Copornicanis metuendum &longs;it.
Ne timeas, Chry&longs;ocome, &longs;i&longs;temus gradum in terra, nec de Ve
nere quidquam a&longs;truam, ni&longs;i quod omnes facilè probare po&longs;&longs;int; Dico
igitur iuxta Copernicanam hypothe&longs;im, Venerem tam propè ad nos acce
dere, circa conjunctionem &longs;cilicet ve&longs;pertinam, & tam procul abe&longs;&longs;e,
circa matutinam, vt eius diameter vna vice &longs;eptuplo ferè major, quàm
alia videnda &longs;it; quod vt in facili Schemate o&longs;tendam.
Sit (
BCDE, &longs;int diametri BD, CE, &longs;itque angulus ABC grad 47. & &longs;uppo
natur maxima digre&longs;&longs;io Veneris à Sole; ducatur AF perpendicularis in
BC, & &longs;ub radio AF de&longs;cribatur circulus FGHIK, hic erit orbis Veneris;
igitur Perigæum Veneris erit in K, po&longs;ito quod terra &longs;it in B; Apogæum
verò in H cuncta hæc pro conce&longs;&longs;is habeo; licèt Perigæum aliquando
propiùs accedat ad B, tum quia interdum major e&longs;t Veneris digre&longs;&longs;io; tum
etiam quia moveri cen&longs;etur in excentrico,; igitur cum &longs;imul e&longs;t in aphelio
& Perigæo, propiùs ad B haud dubiè accedit. Sit ergo in K, citra acura-
parvitatem anguli, cùm linea recta pro arcu accipi po&longs;&longs;it, Veneris diame
ter in K videtur Sexcupla illius, quæ videtur in H &longs;unt enim anguli vt
di&longs;tantiæ permutando, acuti&longs;&longs;imi &longs;cilicet, qualem hoc loco con&longs;idera
mus: &longs;ed profectò nemo vnquam vidit Venerem perigæam quadragecu
plam apogææ.
Miror, hæc à te dici, qui per&longs;picillorum majorum &longs;atis, opi
nor, peritus es; illius &longs;altem amicus & familiaris, qui præ cæteris optima
& longi&longs;&longs;ima fabricat; Galileus &longs;uo tubo&longs;picillo in&longs;tructus, argumentum
à te propo&longs;itum jam olim diluit, vt pote qui omnino comperit, Venerem
perigæam quadragecuplam apogææ, etiam mediocris tele&longs;copij operâ vi
deri, vt non &longs;emel ip&longs;e typis mandavit.
Sciò, hoc a&longs;&longs;ertum ab eo fui&longs;&longs;e; &longs;ed miror, à nemine, &longs;altem
quod &longs;ciam, in dubium vocatum.
Quis amabò hac de re dubitaret, & fidem huic homini detre
ctaret, qui tam multa in cæle&longs;ti regione à &longs;e primùm explorata &longs;ub a&longs;pe
ctum mortalium adduxit, quique &longs;uo tempore, optima omnium vitra tor
nari & componi curavit.
De his non di&longs;puto, nec quidquam de cuiu&longs;piam laude velim
detractum, dico tamen, me optimis alioquin tele&longs;copiis v&longs;um, nunquam
Venerem perigæam quadragecuplam apogææ vidi&longs;&longs;e; Non nego per&longs;pi
cilla Galilei eximia fui&longs;&longs;e, &longs;ed longè iis breviora, quibus v&longs;us &longs;um; negari
ctam fabricandorum tele&longs;copiorum artem eò adduxerit, quò illam nemo
hactenus adduxit; itaque optimo vtor tele&longs;copio, quò Venerem perigæam
majorem quidem apogæa video, non tamen quadragecuplam; ad omnium
oculos provoco.
In qua proportione majorem diametrum perigææ vides?
Plu&longs;quam &longs;excuplam videre deberem; at non dicam &longs;excuplam,
aut quintuplam triplá non video; & hinc nece&longs;&longs;aria
Copernicanam hypothe&longs;im corruere, in qua nece&longs;&longs;e e&longs;t, diametrum Vene
ris perigeæ plu&longs;quam &longs;excuplam videri diametri eiu&longs;dem apogeæ.
Tantulum &longs;chematis de&longs;iderarem; licèt enim multam fidem tibi
habeam, mens tamen maximè recreatur, &longs;i eadem quæ aure accepimus
oculorum etiam te&longs;timonio confirmentur.
Antimum ab hoc onere levabo; Sit AF radius partium
100000. & angulus ABF 47. graduum, tanta enim e&longs;t plerumque
maxima Veneris digre&longs;&longs;io; erit &longs;ecans AB 136733. igitur tota BH
236733. & KB 36733. igitur KB e&longs;t ad BH vt vnum ad 6.
plus.
Sit autem quælibet linea P. ad MQ, vt vnum ad
bet diameter PN quæ videatur et M &longs;ub angulo NMP, tum eadem &longs;ta-
QL, vel PN, vt MP ad MQ, id e&longs;t vt 1.ad 6.
OMP e&longs;t ad angulum NMP, vt PO, ad PN, nempe in acuti&longs;&longs;imis angu
lis, qualis &longs;upponitur is, &longs;ub quo videtur Veneris diameter, arcus &longs;unt
ad &longs;en&longs;um vt tangentes; igitur angulus OMP e&longs;t ad angulum NMP vt
1. ad 6.
6
NP ad PO, id e&longs;t vt 6
appatens e&longs;t ad di&longs;cum apogeæ vt 40.
canæ &longs;ententiæ defen&longs;ores pronunciant.
Cur appellas Copernicanæ &longs;ententiæ defen&longs;ores?
alios etiam
appellare debueras, cùm etiam ex Tychonico &longs;y&longs;temate eadem pror&longs;us
diametrorum apparentium ratio, &longs;eu proportio con&longs;equatur.
Fac enim terram e&longs;&longs;e immobilem in B, Solemque per orbem ANML
ire, ac &longs;ecum deferte centrum epicycli Veneris; hauddubie Venus erit
perigæa in K, apogæa in H.
Hoc ip&longs;um in primo no&longs;tro congre&longs;&longs;u à quo aberas, Chry&longs;oco
me, indicatum à me &longs;uperat, vt videte e&longs;t, in V.figura, & ideò non circularem
epicyclum de&longs;crip&longs;i nec etiam ellipticum, &longs;ed &longs;pital: quadam, &longs;eu qua&longs;i pa
rabolica linea terminatum ab apogæo ad maximam digre&longs;&longs;ionem, & hinc
ad perigæum alia curva ad rectam proxime accedente: porrò no&longs;tro
pote&longs;t.
Habe bis omnes A&longs;tronomos tibi refragantes, non &longs;olùm
illos, qui Copernico adhærat, verùm etiam omnes propemodùm alios,
immo ex tuis non de&longs;unt viri docti&longs;&longs;imi, & cœle&longs;tium ob&longs;ervationum
periti&longs;&longs;imi, qui non modò Veneris perigææ dictum quadragecuplo,
&longs;ed etiam quinquagecuplo & vltra majorem e&longs;&longs;e, quàm apogææ liberè pro
nunciant.
Quid faceres?
meis oculis fidem detractam non po&longs;&longs;um,
optimum tele&longs;copium adhibui; longè tamen minorem proportionem
inæqualitatis e&longs;&longs;e comperi, quanquam &longs;ententiarum diver&longs;itas etiam inter
Principes A&longs;tronomiæ multam mihi hac de re &longs;u&longs;picionem injicit, quorum
aliqui Veneria perigææ diametrum 7.minut.e&longs;&longs;e volunt, alij 4. alij 3.2.alij
demum 1. eadem diver&longs;itas diametrorum apparentium Mercurij, Martis
& Iovis apud eo&longs;dem Autores ob&longs;ervatur. Sed, inquiet aliquis, ob&longs;er
vationes meæ accuratiores &longs;unt, idem alius de &longs;uis &longs;entiet; Vt vt &longs;it ad om
nium oculos provoco, nam &longs;æpè ac &longs;æpiùs Venerem a&longs;pexi, non procul
à perigæo, &longs;cilicet paulo ante, vel paulò po&longs;t conjunctionem ve&longs;pertinam,
diver&longs;is etiam modis adhibitis, nunquam tamen illius di&longs;cum quadrage
cuplum comperi, illius quem in eadem non procul ab apogæo &longs;ita ob&longs;er
varam, &longs;ed longè minorem; idem de Mercurio perigæo, quem nunquam
octuplum apogæi, idem de Marte, quem nunquam &longs;exagecuplum, multò
minùs octoge cuplum aut
morum hominum ob&longs;eruationibus & fidei
&longs;i oculis meis plus tribuam; vereor autem vt aliqui, vt &longs;y&longs;temati á &longs;e fabri
cato, aut reformato meliùs
&longs;ertim, quoad minuta &longs;altem &longs;ecunda, fallaciæ haud parum obnoxiis, ea
nonnunquam ad&longs;truant, quæ dubito, an reliquis deinde ob&longs;ervationibus
&longs;ubjaceant. Vnum deinde in Venere notatu dignum e&longs;&longs;e puto, eam &longs;cilicet,
cùm circa perigæum vel apogæum ob&longs;ervatur, non procul abe&longs;&longs;e ab ho
rizonte, ac proinde non modicam radios vi&longs;uales refractionem pati. quæ
hauddubie apparentem illius diametrum variabit; de&longs;iderandum, vt Ve
nus &longs;ub Solis di&longs;cum aliquando veniret, tunc enim exceptis trajecti&longs;que
radiis &longs;olaribus tele&longs;copio, nec non projectis in planum directè
oppo&longs;itum, vel ip&longs;is oculis ratio diametrum Veneris ad diametrum Solis &longs;ub
jiceretur.
Libenter ex re re&longs;cirem vtrùm &longs;it aliquod Veneris phœnome
non; quod in tua hypothe&longs;i explicari non po&longs;&longs;e putes.
Vix crediderim vllum e&longs;&longs;e; de certis enim loquor & indubi
tatis; nempe: modò &longs;upponam. Venerem &longs;implici motu moveri ab ortu
ad occa&longs;um, eoque æquabili&longs;&longs;imo, cum illa duplici inclinatione, itus ac re
ditus reciproci, ad in&longs;tar motus accelerati & retardati; prima quidem ab
Apogæo ad di&longs;tantiam mediam, eandem curn di&longs;tantia media Solis, & hinc
ad Perigæum, ita vi Venus infra mediam di&longs;tantiam orbem &longs;uum i&longs;ochro
non cum Sole perficiæ ; Secunda verò ab eo latitudinis puncto, in quo
&longs;upra dictum e&longs;t.
Qua quæ&longs;o linea, curva an recta?
deinde an perpen
diculariter cadente in planum Eclipticæ? an verò in planum Æqua
toris?
Ad vtrumque re&longs;pondeo; ad primum quidem, per curvam fieri;
vt dixi de Sole v.g. per arcum D.
F, vt eandem retineat à centro
mundi di&longs;tantiam, vi &longs;cilicet hujus
motus, &longs;eu inclinationis; quænam
verò &longs;it accelerationis ratio à D ver
sùs F, iam &longs;upra indicavi. Suppone
horizontale planum AF & &longs;uperfi
ciem &longs;phæræ inclinatam DF, in
qua de&longs;cendat corpus grave motu
accelerato, hæc e&longs;t accelerationis
progre&longs;&longs;io; quæ in &longs;ecundam incli
nationem apprimè quadrat;
porrò & qualis &longs;it hæc progre&longs;&longs;io
motus accelerati, altioris e&longs;t indagi
nis; Licèt enim
quam &longs;ervant funependula in de
&longs;cen&longs;u, ab ea tamen petenda e&longs;t;
Vt vt &longs;it, hæc di&longs;cu&longs;&longs;io hujus no&longs;tri
in&longs;tituti non e&longs;t, ad &longs;ecundum re
&longs;pondeo, Lineam illam cadere per
pendiculariter in planum Æquato
ris,
culi parallelo Plano Æquatoris, eius
tamen terminus e&longs;t Ecliptica, vt di
xi; nempe Plánetæ hinc terram a&longs;pi
ciunt, cui &longs;erviunt, lumenque refun
dunt; inde verò Solem, &longs;ub primo re&longs;pectu, &longs;uos orbes agunt circa
terram, tanquam circa &longs;uum centrum; &longs;ub alio verò, Solis &longs;equun
tur ve&longs;tigia, qui cùm ab Ecliptica nunquam di&longs;cedat, hic &longs;olus circulus
&longs;ecundam inclinationem Planetarum tanquam terminus determinat. Ex
his autem per&longs;picuas rationes reddo, in mea hypothe&longs;i, acceleratio
nis, retardationis, retrogre&longs;&longs;ionis, &longs;tationis, Nodorum motus, itemque
Apogæi & Perigæi, variæ digre&longs;&longs;ionis & latitudinis, vt jam &longs;upra indicavi
mus.
Antequam alia argumenta expromas, per te mihi liceat,
Antime, vnum quidpiam, quod jam in mentem venit, breviter expo
nere; &longs;cilicet in Copernicana hypothe&longs;i, cuncta fetè gratis, vt aiunt,
& ad nutum con&longs;truentis ad&longs;trui, id e&longs;t &longs;ine vlla cau&longs;a, vel ratione, quæ
hoc, vel illud fieri po&longs;tulet; v.g. terram moveri volunt in excentrico; cur Cur non circa Solem,
qui e&longs;t in Mundi centro? aut &longs;i vis, moveri in Eclip&longs;i, cur hanc adhibes po
tiùs quàm cur Sol in hoc.
vmbilico,
centro? deinde cur & vnde movetur Apogæum?
cur in con&longs;equentia potiùs
quàm in antecedentia? cur terra ab occa&longs;u ad ortum, tum motu centri, tum
etiam orbis &longs;ecundùm hemi&longs;phærium à Sole aver&longs;um? cur per Eclipticam
cum tanta declinatione ab Æquatore? vnde etiam motus orbis annuus
diurno contrarius? denique vnde ip&longs;a vertigo Solis?
cur tanta, non major
aut minor? Cuncta hæc,
gente Copernicana hypothe&longs;is habet, eo tantùm nomine, quod ad &longs;alvan
da phænomena, nece&longs;&longs;aria e&longs;&longs;e credantur, quæ tamen alio modo &longs;alvari
po&longs;&longs;unt.
Par pari haud dubiè referre po&longs;&longs;um: nunquid enim hæc ead&etail;m
in ve&longs;tra hypothe&longs;i ad &longs;alvanda phænomena gratis & ab&longs;que alia cau&longs;a non
a&longs;truuntur? nunquid non poniti sex centricos, epicyclos, Apogæi Nodorum
que motum?
Scio, à multis in no&longs;tra hypothe&longs;i, hæc gratis ad&longs;trui; Anti
mus tamen no&longs;ter, vt jam non &longs;emel audii&longs;ti, vno &longs;implici motu æqua
bili, & gemina inclinatione illa omnia explicat, & ad &longs;uas cau&longs;as re
ducit.
Tuo illo argumento, Chry&longs;ocome, contra Copernicum non &longs;e
mel v&longs;us &longs;um, re tamen paulò accuratiùs
&longs;y&longs;temati favent, pro explicatione illorum capitum, quæ &longs;upra recen&longs;ui&longs;ti,
ad Copernicanum facilè traduci po&longs;&longs;unt, & pro illo æquè militant.
Magno certè beneficio me tibi ob&longs;tringes, &longs;i rem hanc me do
cueris, quæ certè quanti momenti futura &longs;it, vix dici à me pote&longs;t; &longs;i enim
Keplerus pro metis nugis & fabulis, in quibus cau&longs;as phy&longs;icas cæle&longs;tium
phænomenon collocabat, tantom gloriam apud omnes obtinuit; quid de
illo faturum putas, qui veras eorundem cau&longs;as in hac hypothe&longs;i Copernici
ad duxerit? inde &longs;altem maxima tua ingenuitas con&longs;picua & palam fiet
vel no&longs;ti arma porrigas, quibus &longs;e defendat.
Libenter faciam; nec enim in hi&longs;ce di&longs;&longs;ertationibus literariis, ali
quorum dolus mihi probatur, qui ea celant adver&longs;arium, quæ illius cau&longs;æ
&longs;uffragantur; mihi &longs;anè &longs;ecus agendum e&longs;&longs;e puto. Itaque &longs;upponamus So
lem in centro mundi A &longs;tabulari, terram in apogæo C.circulum CHFP in
plano Eclipticæ, per quem terræ
in con&longs;equentia Signorum, &longs;i e&longs;&longs;et in mediocri, vel | connaturali di&longs;tantia; &longs;ed
quia ab Apogæo ad mediocrem di&longs;tantiam tendit, &longs;en&longs;im motu accelerato
accedit versùs A, &longs;imulque, tendit motu circulari ver&longs;us H, vnde
per arcum CH, &longs;ed per alium CG ; &longs;upponamus autem AG e&longs;&longs;e mediocre
di&longs;tantiam; in ea non &longs;i&longs;tit; &longs;ed motu retardato progreditur vltrà versus Peri
gæum; & quia rece&longs;&longs;us à mediocri' di&longs;tantia æqualis e&longs;t acce&longs;&longs;ui, æquali tem
pore decurret arcum GE, atque ita erit Perigæum in E, ex quo pari modo
pervenit in I, nam AI e&longs;t mediocris di&longs;tantia, reditque per i&longs;ochronum
rece&longs;&longs;um, ad Apogæum C; &longs;ive autem arcus CGE &longs;it &longs;emicirculus, vel
lerato per radium AC eo tempore quo radius AC circa centrum A in
eodem plano ductus pervenit in AG, ferens &longs;ecum punctum illud mobi
le, quod tunc erit in G ; deinde idem punctum moveatur motu retardato
ab R in D, dum prædictus codem motu pervenit in AE, tunc certè præ
dictum punctum erit in E &longs;cilicet in Perigæo ; quare hæc linea erit vna ex
&longs;piralibus Archimedis, quæ ad &longs;emicirculum proxime accedit; quia vero
differentia &longs;en&longs;ibilis nen e&longs;t, &longs;emicirculus &longs;upponi pote&longs;t, in quo cen
trum terræ motu æquabili movetur; pari modo punctum illud redit à D
in R, & ab R ad A, dum idem radius ab AE redit in AC.
piis deducantur; vna tamen difficultas &longs;e&longs;e oculis meis objicit ; nam
æquali tempore, vt dicis, radius AC circumducitur in AG, vel AN, &
ab AN ad AF, igitur inæqualiter movetur, cùm arcus CN minor &longs;it
arcu NF.
Equidem extremitas radij AC movetur inæqualiter in cir
culo CHFP; punctum tamen C, &longs;eu centrum terræ ita movetur per
CGE motu mixto ex circulari, & recto, vt hic pror&longs;us æquabilis re&longs;ul
tet: Hinc circulus CGEI e&longs;t quidem excentricus, non tamen verus, in
quo &longs;cilicet terra motu &longs;implici moveatur, &longs;ed apparens; & con&longs;equen
ter centrum B, tantùm apparens; item excentricitas AB; quæ omnia ex
prædicto motu mixto con&longs;equi, nece&longs;&longs;e e&longs;t; itemque anomaliam, id e&longs;t,
in G ; & à G in r
rent ; nempe dum terra decurrit arcum CG, quadratum &longs;cilicet &longs;ui
Orbis, videtur nobis detumi&longs;&longs;o arcum CN minorom quadrante; & dum
decurrit GE æqualem CH, videtur nobis decurrere arcum NF majo
rem, perinde quippe e&longs;t, &longs;ive terram in G a&longs;picias ex A, &longs;ive ex G Solem
in A &longs;pectes; vt &longs;cilicet illum videas in puncto Eclypticæ, oppo&longs;ito,
puncto G.
Sed vndo Apogæi motus, i&longs;que in con&longs;equentia.
Fac terram ex C, peracto &longs;emicirculo nondum ad Perigæum
perveni&longs;&longs;e, nec peracto orbe integro ad Apogæum ; inde nece&longs;&longs;ariò &longs;e
quitur, Apogæum promoveri in con&longs;equentia, &longs;cilicet à G versùs H ; in
antecedentia autem moveretur, &longs;i terra ad Apogæum reditet nondum
peracto orbe integro.
Omitte, quæ&longs;o hæc enim faciliora &longs;unt, quàm vt longio
rem explicationem po&longs;tulent; &longs;ed vnde quæ&longs;o orbis annuus centri; vnde
diurnus orbis, itemque annuus illi oppo&longs;itus?
Neque in hoc multùm laboro; &longs;i enim &longs;upponas terræ globum
ita demi&longs;&longs;um fui&longs;&longs;e ex &longs;ublimi, ad acquiren dum illum velocitatis gradum,
qui nece&longs;&longs;arius &longs;it, vt vna pars globi fortè præponderans, ante aliàs de
&longs;cenderit, vnde motus quidam mixtus &longs;equatur, ex motu orbis & cen
tri; &longs;i hoc &longs;upponas, inquam, vbi dictus globus ad di&longs;tantiam mediam
pervenit, illico motu circulari moveri cœpit in eam partem, in quam
motus Orbis prævius illum determinat; analogiam habes in globo vel
di&longs;co, qui deor&longs;um præfato modo dimi&longs;&longs;us de&longs;cendit; vbi enim planum
horizontale attingit, in eo movetur, &longs;eu rotatur, priore determinatione
durante. v. g. &longs;it globus BCDE, (
per lineam perpendicularem AH, vt centrum quidem A rectam de&longs;cri
bat; aliæ verò partes etiam moveantur circa A, v.g. B in C, D, E, vbi
globus attinget planum horizontale KL, in H, vi prioris determina
tionis, &longs;eu motus Orbis, F tendet in GH, I, vnde rotabitur globus in
dicto plano versùs K. Idem dicendum de globo terræ tali modo de
mi&longs;&longs;o, cujus centrum movetur motu æquabili in Plano Eclipticæ cum
eo velocitatis gradu, quem in primo illo de&longs;cen&longs;u acqui&longs;ivit, qui
deinde &longs;emper intactus manet; pari modo motus Orbis etiam durat,
cùm eadem &longs;it pro vtroque motu ratio, vt videre e&longs;t in prædicto
globo.
Sed cur circa talem axem potiùs quàm circa alium?
deinde
cur libratur prædictus axis? denique cur omnes circuli diurni Æquatori
&longs;unt paralleli?
Ni&longs;i orationem meam interrupi&longs;&longs;es, hæc continuò æquè facilè
explicabam; Suppono terræ globum vel magnum Magnetem e&longs;&longs;e, vel &longs;al
tem magnetica virtute in&longs;tructum, vnde nece&longs;&longs;e &longs;it, duos polos magneticos
ine&longs;&longs;e, & axem ad vtremque polum terminatum, quem etiam &longs;ibi ip&longs;i &longs;em-
bus volvitur; alioquin &longs;i circa
Ex hoc codem axis paralleli&longs;mo, &longs;equitur
tio, qua fit, vt idem globi punctum modò &longs;upra Eclipticæ planum attolla
tur, modò infra deprimatur; vnde Æquinoctia, Sol&longs;titia & quatuor anni
tempe&longs;tates nece&longs;&longs;ario con&longs;equuntur; nempe, vt jam monui, &longs;upra, ille mo
tus annuus orbis e&longs;t tantùm apparens, & ex præfato axis, circa quem fit mo
tus diurnus, paralleli&longs;mo re&longs;ultat.
Omnia probè intelligo; re&longs;tat, vt cau&longs;am afferas Solaris re
volutionis.
Pro hac nihil occurrit in hac hypothe&longs;i, quod &longs;olidum &longs;it, ni&longs;i
fortè dicamus. Solarem globum vi motrice pollere; non &longs;anè quòd vivat,
hoc enim ab&longs;urdum puto; &longs;ed quòd ea vi pollere po&longs;&longs;it, qua etiam vilia no
&longs;tra elementa pollent; ac proinde cùm jus finis &longs;it &longs;uo calore & luce alia
corpora perfundere, mirum non e&longs;le, fi qua&longs;i ab aliis globis inuitatus &longs;eu
determinatus, circa &longs;uum centrum immobile volvatur, vt &longs;altem illam po
tentiam quæ ine&longs;t, exerceat; alioquin per totum æternitatem hæc fru&longs;tra
e&longs;&longs;et, quod dixerit.
Bea&longs;ti me, Antime; jam facile ad alios Planetas adductas à
te rationes traducam. hoc vnum præ cæteris mihi mole&longs;tum erat, quòd
in no&longs;tra hypothe&longs;i, omnia ferè aratis dici atque adduci crederem;
huic &longs;anè incommodo abundè occurri&longs;ti, cùm omnia, ni fallor attigeris,
præce&longs;&longs;ionem Æquinoctiorum lenti&longs;&longs;imus ille &longs;tellarum motus &longs;atis ex
plicat.
Ingenuitati meæ, opinor, tribues, quòd tibi ea &longs;ugge&longs;&longs;erim,
quibus mole&longs;tum illud, vt ais, argumentum refellere valeas. Vnum tibi
per&longs;uadeas velim, cuncta hæc non obe&longs;&longs;e quidem ve&longs;træ hypothe&longs;i, &longs;ed non
prode&longs;&longs;e; &longs;icuti no&longs;træ nec ob&longs;unt, nec pro&longs;unt; de obliquitatis Eclipticæ
mutatione, idem tecum &longs;entio; præce&longs;&longs;ionem
no explicas per lenti&longs;&longs;imum illum fixarum motum; nec in tua hypothe&longs;i
alius modus e&longs;&longs;e videtur; Licet enim Copernicus, Keplerus, aliíque ex ve&longs;tris
velint fixarum motum non e&longs;&longs;e realem, &longs;ed apparentem, eo quòd, inquiunt,
Æquinoctialia puncta tantulùm adducantut versùs occa&longs;um, &longs;cilicet in an
tecedentia, quia libratio terre&longs;tri globi citiùs ab&longs;olvitur, quàm motus in
Zodiaco, hoc tamen, in eo &longs;altem iudicio, non &longs;ub&longs;i&longs;tit, nempe prædicta li
bratio, vt &longs;ic loquar, oritur ex motu orbis integro, circa axem axi Eclipticæ
parallelum, &longs;eu ex paralleli&longs;mo axis terræ, circa quem orbes diurni erunt;
hoc autem in ii&longs;dem punctis Eclipticæ Æquinoctialia puncta e&longs;&longs;e &longs;uppo
nit, &longs;ed hæc ad rem no&longs;tram nihil faciunt.
Expecta tantulùm, Antime, hic enim &longs;tellarum motus
in tua hypothe&longs;i difficilè, &longs;altem, vt audio, explicatur; vnde for
tè meam vel hoc nomine, tuæ qui&longs;piam præferendam e&longs;&longs;e putaret.
Longè faciliùs, Augu&longs;tine, &longs;tellarum motus, quàm Planeta
rum, in qualibet hypothe&longs;i explicatur pro quo &longs;uppono 1. fixum æter
numque e&longs;&longs;e Naturæ in&longs;titutum, vt &longs;tellæ omnes eundem inter &longs;e ordinem
& &longs;itum &longs;ervent. 2. Nunquam mutari illarum latitudinem: His po&longs;itis,
cogita &longs;tellam quampiam in ip&longs;a Ecliptica, cogita etiam circulum quem
libet immobilem, puta meridiànum, in quo &longs;tella, primùm &longs;ita &longs;it, co
gita denique ip&longs;am Eclipticam, circa Axem mundi, &longs;uum
ita vt idem punctum, quod erat in dicto meridiano ad illum redeat, orbe
peracto ab ortu, in occa&longs;um 24.horis. Iam cogita &longs;tellam illam &longs;imul cum
Ecliptica ab ortu in occa&longs;um ferri, & circumduci, & paulo tardiùs, vt eo
momento, quo dictum punctú Eclipticæ, in quo erat, attingit meridianum,
ip&longs;a tantulùm versùs ortum remaneat, non quidem extra Eclipticam,
&longs;ed in ip&longs;amet Ecliptica: nec enim perfectum orbem de&longs;cribit, &longs;ed
talem &longs;piram, vt &longs;emper Ecliptice re&longs;pondeat; aliæ verò, quæ &longs;unt extra Ecli
pticam, eandem &longs;emper ab illa di&longs;tantiam retineant, vnde præter circularé
motum, altera &longs;altem inclinatioue opus e&longs;t, cujus terminus &longs;it æquator,
Ecliptica; ita tamen moventur, vt &longs;emper eandem ab Ecliptica di&longs;tantiam
retineant: inde præce&longs;&longs;io Æquinoctiorum facilè explicatur, quæ tamen
ex eo explicari non pote&longs;t, quod Sol in diver&longs;is punctis Æquatorem &longs;ecet;
quia cum Sol &longs;emper Eclipticæ in&longs;i&longs;tat, licèt versùs occa&longs;um &longs;ectio Ecli
pticæ cum Æquatore, ip&longs;o Æquinoctij momento &longs;ingulis, annis promo
veatur, non tamen ex hoc &longs;equitur Æquinoctiorum præce&longs;&longs;io, ne
que propterea &longs;tulla quæpiam ab Æquinoctij puncto versùs Ortum remove-
ce&longs;&longs;io, quod Stellæ &longs;ingulis diebus & annis, tantulùm versùs Ortum qua
&longs;i retroagantur, id e&longs;t, non omnino diurnum orbem conficiant plenis 24.
horis. Illum autem inclinationis motum lenti&longs;&longs;imum e&longs;&longs;e oportet; quod
fortè propter maximam di&longs;tantiam accidit; &longs;eu veriùs propter veloci&longs;&longs;i
mum circularen motum, qui nihil ferè. prædictæ inclinationi relictum
&longs;init.
Sed quæ&longs;o te, Antime, ad alias rationes, &longs;i quæ tibi re&longs;tant,
orationem converte, ne huc totam A&longs;tronomiam accer&longs;ere videaris.
In Venere, Mercurio, & Marte, illud præ&longs;ertim Copernicanæ
hypothe&longs;i repugnare &longs;upra dictum e&longs;t, quòd Venus in Perigæo quinqua
gecuplo, Mercurius nonecuplo, Mars octogecuplo, majores videri debe
rent; quod tamen: vt dixi, meis ob&longs;ervationibus repugnat in Iove, qui &longs;e
quitur, aliquid etiam invenio; vnde tua hypothe&longs;is, Augu&longs;tine, impugne
tur: Iovem igitur, vt fortè putabas, ita propitium non habes.
Immò nobis præ cæteris favet, cum &longs;uis a&longs;tris medicæis quæ
totidem Lunæ circa Iovem erunt, vt Luna circa terram, Venus & Mercu
rius circa Solem, & circa Saturnum Satellites.
Non ita profectò res &longs;e habet, vt jam intelligere debui&longs;&longs;es ex
opu&longs;culo Diviniano, adver&longs;us Chri&longs;tiani Hugenij viri &longs;ane docti&longs;&longs;imi a&longs;
&longs;ertionem; primò enim accipiamus vnam ex præfatis Iovialibus Lunis;
codem pror&longs;us modo circa Iovem &longs;uum circulum agit, quo Luna circa
terram mobilem, in tua &longs;cilicet hypothe&longs;i ; ac proinde &longs;i accipia arcum
HI, &longs;imilem illi, quem Iupiter de
currit, eo tempore, quo quæpiam
ex Lunis Iovialibus &longs;uum circulum
ab&longs;olvit, hæc haud dubiè de&longs;cribet
reali motu, ab vno Perigæo ad aliud,
lineam &longs;imilem HGI, eodemque
motus genere; igitur longè; tardiùs
in H, quàm in G, reali &longs;cilicet mo
tu, idque in ea inæqualitatis pro
portione, quæ a&longs;i
minor erit, quod videtur ab&longs;urdi&longs;&longs;i
mum, & jam &longs;upra demon&longs;tratum
e&longs;t; neque hic repeto, cùm &longs;it ea
dem vtrimque ratio; & ne hoc ip&longs;um
paulò po&longs;t repetere cogar, hæc ca
dem ratio Lunæ Saturniæ à Chri
&longs;tiano Hugenio primùm detectæ, eo
demque modo contra tuam hypo
the&longs;im applicatur. Igitur contra
illam ab a&longs;tris Medicæis & Iove, immò & Luna Saturnia eadem ratio pe
titur, quam &longs;upra ex Lunæ motu deduximus.
Secundò, vt in præfato opu&longs;culo
ob&longs;curas irent; &longs;unt enim lucidi&longs;&longs;imæ, illarumque candidi&longs;&longs;imus color à
&longs;ubob&longs;curo zonatum colore adhibito præ&longs;ertim optimo tele&longs;copio, quo re
verà vti po&longs;&longs;umus, facilè di&longs;tingueretur; nempe &longs;i Stellulæ à love teguntur
versùs Apogæum, intercepto &longs;cilicet Iovis di&longs;co, inter oculum & Stellam,
certè in Perigæo Iovem ex aliqua parte tegent; nec qui&longs;piam celeriorem
Stellæ tran&longs;itum cau&longs;ati debet, cùm &longs;ub lovis di&longs;eo, per horam ferè integram
manere debeat, vt in dicto opu&longs;culo demon&longs;tratum fuit; cùm autem &longs;ub
lovis di&longs;co nunquam dictas Stellas videre potuerimus, nanquam haud du
biè &longs;ub illum de&longs;cendunt, quod certè tuæ hypothe&longs;i repugnat, vt nemo
negat; nec &longs;alli potuimus in ob&longs;ervando, qua&longs;i Conjunctionem Stellæ in
Apogæo, à
di&longs;tinctu facilè fuit; illa enim Conjunctio fit in Perigæo, quæ maximam di
gre&longs;&longs;ionem Ortivam &longs;equitur, vt in Venere & Mercurio.
Tertiò cùm Iupiter lumen &longs;uum à Sole habeat, vt Mars, Venus, aliique
Planetæ, Stella Medicæa &longs;altem vicinior vmbram in Iovis di&longs;cum projice
ret, quod negati non pote&longs;t ab vllo, qui rem hanc intelligat; nunquam au
tem vmbram illam videre potuimus, quamvis Stella circa Perigæum e&longs;&longs;et;
Igitur Stellæ illæ &longs;ub Iovem minimè de&longs;cendunt; quod certè tuæ hypo
the&longs;i non favet.
Quartò adhibito etiam longi&longs;&longs;imo tele&longs;copio Stellas Medicæas &longs;plen
dentes &longs;emper micante&longs;que fixatum ad in&longs;tar, non verò tornatas in di&longs;cum,
vt reliquos Planetas a&longs;picimus; vnde, ni fallor, deduco, ip&longs;o Iove longè al
tiores e&longs;&longs;e, quod periti Optices, opinor, minimè negabunt: Adde his, ob&longs;er
vationes non re&longs;pondere calculis factis in orbe, vel Epicyclo. Ex his, ni fal
lor, non leve contra tuam hypothe&longs;im ducitur argumentum; ac proinde,
vt ante dicebas, Iupiter non adeò vobis propitius e&longs;t.
In tua verò hypothe&longs;i quonam pacto Stellarum Medicæarum
motum explices, non intelligo, vt de&longs;cen&longs;um illarum &longs;ub Iovem &longs;alves; quid
enim aliud de iis dicere potes, ni&longs;i illud ip&longs;um quod de Venere & Mercurio
&longs;upra dixi&longs;t? Atqui Venus & Mercurius &longs;ub Solis di&longs;cum de&longs;cendunt.
Si ex ob&longs;ervationibus haberemus, Stellas illas &longs;ub Iovis di&longs;cum
de&longs;cendere, æquè facilè illarum motum
curij motum explicui; &longs;ed quandoquidem infra Iovem non de&longs;cendunt, non
minùs facilè illarum motum explicamus, a&longs;&longs;umpta illarum mediocri di
&longs;tantia &longs;upra Iovem, ita vt in mediocri di&longs;tantia æquè citò ac Iupiter orbem
&longs;uum diurnum, infra verò illam citiùs, &longs;upra demum tardiùs ab&longs;olvant, &
periodus acce&longs;&longs;uum & rece&longs;&longs;uum, quibus Stella redit ad Apogæum, intra
idem tempus perficiatur, quo &longs;uum orbem quælibet Stella decurrere com
muniter dicitur; &longs;ed quia in dicto opu&longs;culo hæc &longs;atis in&longs;inuata fuerunt, ne
huc eadem traducam, eò vos remitto.
Nihil, opinor, amplius re&longs;tat, quod contra meam hypothe&longs;im
afferre po&longs;&longs;is; jam enim Saturnus &longs;uam Lunam tibi &longs;uppeditavit, cujus
&longs;altem intentares.
Aliud quidpiam e&longs;t, quod tibi fortè novum videbitur: Annulus
probè in&longs;tructo, ingeniosè profectò excogitatus, & quem ve&longs;tris mirum in
modum placui&longs;&longs;e intelligo; &longs;i fortè verus e&longs;&longs;et, quod &longs;anè maximè percu
pio, ve&longs;træ hypothe&longs;i vltimam fetè ruinam afferret; cùm enim præfatus an
nulus plano Æquatoris &longs;emper parallelus &longs;it, haud dubiè non movetur per
Eclipticam, alioquin &longs;itum acciperet, in quo Eclipticæ plano parallelus e&longs;
&longs;et; eo quippe motu movetur, quo faciliùs moveri pote&longs;t, iuxta regulam ex
doctrina motuum a&longs;&longs;umptam, de qua jam &longs;upra. Et verò nemo non videt,
annulum planum longè faciliùs moveri, & cum minore medij re&longs;i&longs;tentia, &longs;i
in plano annuli, &longs;it ip&longs;a linea motus; igitur cùm illud planum annuli Æqua
toris plano parallelum &longs;emper &longs;it, haud dubiè in eo circulo movetur, cujus
planum Æquatoris plano parallelum e&longs;t; igitur in parallelo diurno, iuxta
no&longs;tram hypothe&longs;im, licèt enim &longs;piræ planum tantulùm ab Æquatoris pla
no declinet, hoc tamen &longs;ub &longs;en&longs;um non cadit: Hæc ratio &longs;ingularis e&longs;t; quia
præfatus annulus e&longs;t etiam valdè &longs;ingularis, & ante Hugenium incompertus
orbi, faxit Deus, vt ex futuris ob&longs;ervationibus Saturno præ&longs;ertim circa
Æquatorem exi&longs;tente, ita luce nova confirmetur, vt de illo nullus vltra du
bitare po&longs;&longs;it; quod maximoperè, vt dixi, percupio, cùm in no&longs;tram hypo
the&longs;im mirificè Quadret; & hæc &longs;unt, quæ contra tuam hypothe&longs;im, Augu
&longs;tine dicenda mihi occurrunt.
Addere poteras per&longs;picua Scripturæ loca, ex quibus con&longs;tat
terram &longs;tare & Solem moveri iuxta literalem illorum &longs;en&longs;um, qui profecto
retinendus e&longs;t, &longs;i ab&longs;que ab&longs;urdo retineri queat; adde Sanctorum Patrum
auctoritatem, quæ certe maximi momenti e&longs;t, pro definiendo legitimo San
ctæ Scripturæ &longs;en&longs;u; ex his enim &longs;equitur per&longs;picua mens Eccle&longs;iæ, quæ
S.Scripturæ &longs;en&longs;um ex Sanctis Patribus &longs;emper eruit; denique cùm divina
potentia in &longs;acro textu laudati velit, & magni fieri, ex celerrimo illo motu,
quo a&longs;tra cientur, quis hanc illi laudem jure detrahat? nemo certe, illorum
præ&longs;ertim, qui &longs;acram Scripturam admittunt.
Licèt manus omnino dare nequeam, negati tamen à me non
pote&longs;t, quin aliquid &longs;altem plau&longs;us no&longs;træ hypothe&longs;i &longs;ubduxeris, & in tuam
traduxeris; &longs;ed de hac re &longs;atis.
Optimè mones; quate hic &longs;u&longs;tinendum e&longs;&longs;e iudico, ne nimia
fortè huius congre&longs;&longs;us prolixitas nobili&longs;&longs;imæ coronæ tædium affetat.
Prudenti&longs;&longs;imè judica&longs;ti; quare hoc vnum re&longs;tat, vt primo
congre&longs;&longs;ui diem indicamus.
Po&longs;t triduum, ni&longs;i vobis &longs;it incommodum; Sed quodnam erit
di&longs;putationis argumentum?
Meam &longs;ententiam, &longs;eu veriùs hypothe&longs;im de Marino æ&longs;tu, vobis
exponam; interim con&longs;ulite tabulas Nauticas, vt inde vobis &longs;uppetat, quod
mihi opponatis.
& demonstratur.
REM magnam aggredior, Princeps Eminenti&longs;&longs;ime, adeó
que difficilem, vt Philo&longs;ophorum maximi, Stagiritæ &longs;ui
principis mi&longs;erando ca&longs;u & naufragio territi, in&longs;uperabilé
illam & Mortalium ingenio inacce&longs;&longs;am publicis monu
mentis in lucem editis declararint. Vnde factum e&longs;&longs;e,
reor, vt quique illorum prudenti&longs;&longs;imi hunc &longs;copulum
cautè prætergre&longs;&longs;i, vix extremo indice illum indicarint; cùm tamen alij
certè incauti ad illum propiùs acce&longs;&longs;erint, ibique tanquam in ridicula &longs;ce
na, the&longs;es &longs;uas communi &longs;apientum ludibrio expo&longs;uerint. Et verò vix ea
in &longs;omniantis animum caderent, quæ ip&longs;i excogitarunt, ad cau&longs;am Ma
rini æ&longs;tus explicandam; &longs;unt qui Soli, alij Terræ, neutri quidam præfa
tam cau&longs;am attribuunt: in Luna multiplicem virtutem, &longs;eu vim alij agno
&longs;cunt; magneticam, qua &longs;cilicet a quas adducit atque attollit; humefacti
vam, cùm &longs;it humoris vehiculum, quo humida corpora variè afficiuntur,
pro diver&longs;o Lunæ a&longs;pectu; compre&longs;&longs;ivam, rarefactivam &c. Sed in Ple
nilunio, de Meridie, Luna in puncto oppo&longs;ito exi&longs;tens, qua vi, amabo,
ciet æ&longs;tum? Qui ad Solem confugiunt, dicere nequeunt, quid Sol præ&longs;tet,
cum bis &longs;ingulis men&longs;ibus in Novilunio &longs;cilicet & Plenilunio æ&longs;tum
in media nocte, ab&longs;ente Sole habeamus. Vapores tepidos accer&longs;unt aliqui;
&longs;ed vnde, à quo excitati? Quid iis cum Luna, cuius motum Marinus æ&longs;tus
æmulatur? Vapores demum aquam in bullas attollunt, non verò in tu
morem; & quid nitrum ad hoc conferat, divinare, ni&longs;i fingam, profectò
non po&longs;&longs;um; Terræ motum inæqualem, cui aliqui tribuunt æ&longs;tum, iam
&longs;upra rejecimus; item aëris compre&longs;&longs;ionem à præterlabente Luna æquè
facilè explodimus; quia Luna in Meridiano exi&longs;tente, ibi compre&longs;&longs;ionis
maxima vis e&longs;&longs;et; nullus igitur æ&longs;tus. Omitto alia figmenta potiùs quàm
argumenta, & ex communibus principiis rem i&longs;tam ita definio, vt ex iis,
etiam ab ignaro æ&longs;tus Marini, immò qui nequidem Oceanum e&longs;&longs;e &longs;ciat,
illi omnes effectus, qui &longs;en&longs;ibus no&longs;tris & ob&longs;ervationibus &longs;ubjiciuntus,
deduci po&longs;&longs;int: id &longs;altem erit operæ pretium, quod hanc hypothe&longs;im
meam cen&longs;uræ tuæ &longs;ubjectam, vel inde nobili&longs;&longs;imo & docti&longs;&longs;imo calculo
probatam, vel ju&longs;to, à quo ab&longs;que temeritatis nota, nemo appellarit,
judicio reprobatam e&longs;&longs;e, non &longs;ine voluptate intelligam: &longs;ed ad rem ve
niamus.
Multa &longs;anè, ac ferè omnia in memoriam revocavi, vt facilè
mihi per&longs;uadeo, quæ pro ad&longs;truenda Marini æ&longs;tus cau&longs;a, dicturus e&longs;tes;
&longs;ed nihil occurrit profectò, quod iam ab aliis dictum, &longs;eu fictum non fuerit:
nempe, vt vel inde initium di&longs;&longs;ertationis ducamus, negari non pote&longs;t, quin
Lunaris globus in hac &longs;cena &longs;uas, ea&longs;que præcipuas partes agat; quid por
rò Luna præ&longs;tare queat, quod jam excogitatum, &longs;eu fictum non &longs;it, immò
& rejectum? intume&longs;cit aqua in æ&longs;tu, quod nemo peritus negare au&longs;it;
cùm tantus &longs;it in quibu&longs;dam oris aquarum tumor, vt ad quinquaginta pe
dum altitudinem facilè a&longs;cendat; quibus porrò organis, &longs;eu trochleis,
& qua vi Luna hunc aquis motum imprimat, præ&longs;ertim, cùm ab&longs;ente
Luna aqua etiam per æ&longs;tum intume&longs;cat, conjicere non po&longs;&longs;um. Video,
Lunam Marini æ&longs;tus cau&longs;am e&longs;&longs;e, cùm ex diver&longs;a Lunæ applicatione, im
mò & a&longs;pectu, diver&longs;is æ&longs;tus con&longs;equatur; quonam verò pacto, id Luna
præ&longs;tet, nec video, nec alij profectò vident.
occultas & ignotas Mortalibus e&longs;&longs;e voluit; ita vt ingeniosè iuxta atque
&longs;apienter ille recentior dixerit, Marinum æ&longs;tum humanæ curio&longs;itatis nau
fragium e&longs;&longs;e; &longs;ed quid tandem tu, Antime? Modicam Augu&longs;tinus de te
&longs;pem habere videtur, qua&longs;i &longs;uper hac re nihil novi afferre valeas; ego ve
ro te adeò imprudentem e&longs;&longs;e, non puto, vt fidem tuam fru&longs;tra & in ca&longs;&longs;um
oppigneratis, vt antiquum, de quo jam &longs;upra, adagium in &longs;cenam revoces;
Parum quidem admodùm mihi arrogo; &longs;pero tamen, aliquid
me adducturum, idque ex communibus principiis, quod &longs;i fortè non mul
tis, nonnullis tamen arrideat: Concedo igitur. Augu&longs;tine, id quod paulò
ante dicebas, Lunam &longs;cilicet in hoc negotio &longs;uas agere partes, nempe &longs;unt
qua&longs;i tres Marini æ&longs;tus periodi, diurna &longs;cilicet, men&longs;trua, annua; &longs;ingulis
ferè diebus bis accedit, & affluit æ&longs;tus, bis recurrit; dico ferè, quia hic ge
minus cur&longs;us & recur&longs;us non 24. &longs;ed 25. horis, paulò minùs perficitur, &longs;ci
licet ad Lunæ motum; nempe Luna, vt redeat ad idem Meridiani pun
ctum, qua&longs;i 25. horas ponit; igitur &longs;ingulis diebus vna ferè hora tardior
æ&longs;tus tumet, v.g. &longs;i hodie hora Meridiana fuit &longs;ummum æ&longs;tus, cra&longs;tina die
erit ferè prima po&longs;t Meridiem hora: die verò &longs;equenti, hora po&longs;t Meri
diem &longs;ecunda; atque ita con&longs;equenter. Hic porrò Lunæ motus e&longs;t; altera
periodus e&longs;t men&longs;trua; nempe pro diver&longs;o Lunæ a&longs;pectu, æ&longs;tus major, vel
minor e&longs;t; v. g. in Plenilunio major e&longs;t, quàm in Novilunio, & in hoc
major quàm in Quadraturis, cùm igitur ex Lunæ motu & a&longs;pectu tota il
la æ&longs;tuum varietas procedat, negari non pote&longs;t, quin à Luna pendeat. Tertia demum periodus e&longs;t annua, nam ob&longs;ervatum fuit in Æquinoctiis
& Sol&longs;titiis, non modicam fieri mutationem æ&longs;tuum præ&longs;ertim in Æqui
noctiis, ita vt in Æquinoctio, v.g. Autumnali cum Plenilunio conjuncto,
&longs;emper &longs;it maximus æ&longs;tus, in quo etiam Luna &longs;uo munere defungitur; &longs;i
enim fiat Æquinoctium in Quadratura, modicus æ&longs;tus e&longs;t.
Lunam, cau&longs;am e&longs;&longs;e fateor vltrò; &longs;i autem cau&longs;a e&longs;t, aliquid
agit & confert; quid porrò illud e&longs;t? fac age, me doceas, & eris mihi magnus
Apollo.
Dare non po&longs;&longs;um, Lunam Marini æ&longs;tus cau&longs;am e&longs;&longs;e; &longs;i enim
cau&longs;a e&longs;t, cau&longs;at, & aliquid præ&longs;tat: &longs;ed nihil penitus præ&longs;tat.
Ludis nos, Antime, Lunæ totum hunc effectum paulò ante
tribuebas; cur igitur modò cau&longs;am e&longs;&longs;e negas? Si cau&longs;a non e&longs;t, ad æ&longs;tum
nullo modo pertinet; Solve i&longs;tum nodum.
Communi di&longs;tinctione vtor, ad &longs;olvendum hunc nodum;
Luna ita pertinet ad Marinum æ&longs;tum, vt &longs;ine illa hic non &longs;it, licèt revera
Luna cau&longs;a non &longs;it, id e&longs;t, tumorem illum aquæ minimè attollat, vel aquas
cieat; nullum enim motum aquis imprimit, nullum humorem affundit,
qui &longs;cilicet ad cel&longs;um illum tumorem &longs;ufficiat; quomodo igitur ab illa
æ&longs;tus pendet? Verbo dico; Luna Marini æ&longs;tus cau&longs;a non e&longs;t, &longs;ed mera Oc
ca&longs;io, qua reverà &longs;ublata, æ&longs;tus non e&longs;&longs;et.
Ne quæ&longs;o ludas in verbis; &longs;olus enim verborum ludus ad
res phy&longs;icas explicandas non &longs;ufficit; quid igitur illud e&longs;t, quod dicis, nam
profectò non intelligo.
Faciam intelligas, Chry&longs;ocome, &longs;ed priùs illa principia jacien
da &longs;unt, ex quibus res i&longs;ta deducitur. Suppono igitur primò, illum e&longs;&longs;e fi
nem gravitatis, quæ gravibus ine&longs;t, vt &longs;ingulæ partes globi totalis versùs
illiùs centrum, ni&longs;u quodam communis con&longs;pirationis tendant; quod re
verà nece&longs;&longs;arium fuit, tum ad conflandum totalem globum, tum ad eun
dem &longs;ervandum; fac enim omnes partes alicujus globi totalis à &longs;e ip&longs;is di&longs;
&longs;itas e&longs;&longs;e, illico communi dictæ con&longs;pirationis vel inclinationis, versùs
idem centrum, vi, &longs;eu ni&longs;u, &longs;eu impetu &longs;e&longs;e iterum in orbem component;
deinde fac partes globi totalis non contra niti vlla re&longs;i&longs;tentia; &longs;tatim mi
nima ferè ventorum, vel alterius impul&longs;us vi di&longs;&longs;ipabuntur; igitur non
potuit facilior modus excogitari, tum ad conflandum, tum ad &longs;ervandum
globum totalem; id e&longs;t, tum ad colligendas omnes partes, in vnum glo
bum; tum ad impediendum, ne à globo facilè avellantur, non potuit, in
quam facilior modus excogitari, quàm &longs;i partes &longs;ingulæ nativa quadam vi
& inclinatione, versùs idem & commune centrum eant, &longs;eu tendant, atque
nitantur.
Illud commune e&longs;t principium, vt gravia deor&longs;um, levia
&longs;ur&longs;um &longs;ua &longs;ponte ferantur, nec enim opinor eorum &longs;ententiam defenditis,
quos tacito nomine Stagirita no&longs;ter refutavit, qui &longs;uperum, atque inferum
negabant: mundi ac terræ centrum deor&longs;um e&longs;t; cælum verò &longs;ur&longs;um; hoc
igitur &longs;uperum, illud inferum.
De iis ferè omnibus, quæ paucis complexus es, dubitarem,
de eo præ&longs;ertim, quod dicis, gravia deor&longs;um, levia &longs;ur&longs;um &longs;ua &longs;ponte ferri;
de gravibus vltrò concederem; nec enim illorum commentum approba
re po&longs;&longs;um, qui volunt, corpus grave à terra deor&longs;um trahi, &longs;pi&longs;&longs;i cuju&longs;dam
capillitij opera; aut certè trudi à ficta ne&longs;cio qua &longs;ubtili materia, quæ &longs;en
&longs;um omnem fugit; nempe, &longs;i trudit illa materia, motum in &longs;e habet, & à
&longs;e; &longs;i enim ab alio, de hoc idem dicam; Satius igitur e&longs;t dicere, corpus
grave à &longs;e moveri, ac deor&longs;um ire, quod &longs;cilicet videmus atque palpamus,
quàm trudi ab illa &longs;ubtili materia, mota à &longs;e ip&longs;a, quàm nullo tactu, nullo
corpus grave deor&longs;um trudi ab Angelo, quod tamen nulla ratione, nullo
que experimento probari pote&longs;t, quàm ij, qui dicunt, ab ea &longs;ubtili materia
trudi, cùm nulla ratione, & nullo experimento id probare po&longs;&longs;int.
Rectè omnino; neque id ab vllo cordato viro negari pote&longs;t,
gravia &longs;cilicet &longs;ponte &longs;ua deor&longs;um ire.
Sed non item levia, quæ ideò &longs;ur&longs;um eunt, quia &longs;ur&longs;um à
graviore medio extruduntur; Supponamus enim corpus aliquod levius
graviori &longs;ube&longs;&longs;e; vel gravius
extrudet; vel tantùm hoc &longs;ua &longs;ponte &longs;ur&longs;um a&longs;cendet, ac deor&longs;um ex
trudet gravius; vel &longs;imul vtrumque &longs;ua &longs;ponte ibit; quod levius tantùm
nemo dixerit, & manife&longs;tæ convinci po&longs;&longs;et fal&longs;itatis.
Scio neminem e&longs;&longs;e, qui hoc dicat; &longs;ed quæ&longs;o te, fac, aliquem
e&longs;&longs;e; quomodò illum convinceres; dic mihi &longs;odes.
In hunc modum; eo modo, quo &longs;ur&longs;um extruditur corpus
leve à gravi, aër v.g. ab aqua, cui &longs;ube&longs;t, corpus grave deor&longs;um detrude
retur à levi, aqua, v. g. ab aëre, qui aquæ &longs;ube&longs;&longs;et: &longs;it ergo globus plum
beus in aëre, ideò de&longs;cendit, quia aër, qui &longs;ube&longs;t, &longs;ua &longs;ponte a&longs;cendens,
illum deor&longs;um extrudit; ille autem Cylindrus aëris in globum levitat; ita
mihi loqui fas &longs;it, qui à globo ad terram v&longs;que extenditur, vt patet; nec
enim is, qui e&longs;t &longs;upra globum in illum levitat, &longs;ed potiùs gravitaret; corpus
enim gravitat deor&longs;um, &longs;ur&longs;um verò levitat; igitur &longs;i prædictus Cylin
drus aëris primò &longs;it pedalis, ac deinde bipedalis, cùm tota vis gravitatio
nis, &longs;eu detru&longs;ionis deor&longs;um &longs;it ab aëre, qui e&longs;t infra globum, & in eum le
vitat; erit dupla vis detru&longs;ionis, &longs;eu gravitationis, quando aëris Cylin
drus plumbeo globo &longs;ubjectus erit duplus; dupla enim cau&longs;a duplum effe
ctum producit.
Id quod dicis ex hoc experimento probari pote&longs;t.
Sit v. g.
Scyphus vacuus &longs;ecundum perpendiculum in aquam immer&longs;us, ore præ
vio, ita vt nihil pror&longs;us aëris ante in Scypho contenti avolare po&longs;&longs;it;
haud dubiè, quo profundiùs immergitur, major vis &longs;ur&longs;um illum extru
dens ip&longs;o tactu &longs;entitur; nempe totus aquæ &longs;uperpo&longs;itæ, Cylindrus cujus
ba&longs;is ori va&longs;is, &longs;eu Scyphi circiter æqualis e&longs;t, in aëra Scypho conten
tam gravitat, magis autem, Cylindrus altior.
Igitur &longs;i prædictus Scyphus ita immergatur, vt primum
vno palmo à &longs;uprema &longs;uperficie aqua di&longs;tet, ac deinde profundiùs im
mergatur, ita vt di&longs;tet ab eadem &longs;uperficie duobus palmis, dupla tunc erit
vis gravitationis ; quia duplæ cau&longs;æ duplus effectus e&longs;t: igitur cùm &longs;it eadem
ratio, duplus Cylindrus aëris &longs;ubjecti globo duplam vim motus in illum
execet, &longs;cilicet levitationis, quod tamen fal&longs;um e&longs;&longs;e con&longs;tat.
Non dico duplam vim motus, &longs;ed tantùm dico majorem vim,
quod certè ad tuum propo&longs;itum &longs;atis e&longs;&longs;e puto; cùm prædicti globi pon
dus idem &longs;it, eademque vis illa, qua deor&longs;um fertur, &longs;ive vnum, &longs;ive duos
palmos altus à terra pendatur.
Non dicis duplam vim motus?
dupla cau&longs;a duplum effe-
Non nego, duplum e&longs;&longs;e effectum, &longs;ed nego, duplam e&longs;&longs;e vim
morus, id e&longs;t motum duplum, &longs;eu duplo velociorem, & ne diutiùs te &longs;u
&longs;pen&longs;um habeam, &longs;imili ferè experimento rem i&longs;tam explico: Sit vas quod
libet AB; &longs;itque in&longs;erta fi&longs;tula in B, per quam,
&longs;i aperiatur, effluat aqua priùs infu&longs;a; & primò
quidem aqua occupet totam altitudinem AB,
Tum deinde &longs;ubduplum BE, non e&longs;t dubium,
quin Cylindrus BA extrudat aquam per fi&longs;tulam
BC, majore vi, quàm Cylindrus EB; non ta
men duplo majore, licèt Cylindrus BA fit du
plus Cylindri BE; &longs;i enim dupla e&longs;&longs;et vis motus,
id e&longs;t motus ille, quo per fi&longs;tulam aqua erumpit,
duplo velocior, duplæ cau&longs;æ, quadruplus e&longs;&longs;et ef
fectus; nam &longs;i motus e&longs;t duplo velocior, eo tem
pore, quo data quantitas aquæ v.g. vncia effluit,
extru&longs;a à Cylindro BE, effluent duæ vnciæ ex
tru&longs;æ à Cylindro BA; &longs;ed extrudere duas vncias,
duplo motu, e&longs;t quadruplus effectus: nempe extrudere vnam duplo motu
e&longs;t effectus duplus, ergo extrudere duas, duplo motu, e&longs;t quadruplus.
Rem capio, igitur ad effectum quadruplum, opus e&longs;t cau&longs;a qua
drupla; igitur Cylindrus BA producet duplam vim motus, comparatus
cum Cylindro AF &longs;ub quadruplo. Et verò licèt in majore &longs;axo aliqua cau
&longs;a motrix eundem morum producat, quem in minore, non propterea æqua
lis effectus dicendus e&longs;t; vt patet: Vnde minùs cautè duplum illum dixe
ram motum.
Effectus igitur &longs;unt vt cau&longs;æ, cau&longs;æ vt altitudines, motus in &longs;ub
duplicata altitudinum, effectus demum in compo&longs;ita motuum & quanti
tatum; & quia motus &longs;unt vt quantitates, effectus &longs;unt in duplicata mo
tuum, vel quantitatum.
Mihi tamen gravis &longs;uboritur difficultas; nam in &longs;cypho illo im
mer&longs;o, vna tantùm e&longs;t quantitas aëris; igitur non cre&longs;cit effectus ex quan
titate, quæ non cre&longs;cit; igitur tantùm ex motu; igitur &longs;i cau&longs;a dupla e&longs;t,
motus erit duplus.
Acutè pror&longs;us: facilis tamen e&longs;t re&longs;pon&longs;io, cùm perinde gravitet
Cylindrus aquæ in &longs;ubjectum aëra, atque &longs;i hic &longs;tatim extruderetur, & alius
&longs;uccederet; &longs;icut Cylindrus AB primum gravitat in primam vnciam, quam
extrudit, &longs;ive deinde
ditur fi&longs;tula; inde igitur vis motus extru&longs;ionis petenda e&longs;t, quod produca
tur vis motus dupla, ac proinde prima vncia duplo velociore motu extru
datur; igitur &longs;ubduplo tempore; igitur reliquo &longs;ubduplo &longs;ecunda vncia,
vel extrudatur eodem motu, vel extrudi po&longs;&longs;it, licèt non extrudatur; idem
dicendum de aëre immer&longs;o &longs;cypho contento, in quem Cylindrus ea vi gra
vitat, qua illum extruderet, &longs;i extrudi po&longs;&longs;et; eadem igitur e&longs;t vtrinque
ratio.
Quem porrò effectum prædicta illa gravitatio producat, non
video; cùm nec moveri, nec extrudi po&longs;&longs;it.
Manu ip&longs;a, &longs;cyphum illum ne &longs;ur&longs;um extrudatur immer&longs;um reti
nente, vim illam, impul&longs;um illum, vel impetum, vel impre&longs;&longs;ionem &longs;entimus;
præterquam quod vis illa gravitantis aquæ comprimit aëra &longs;chypho con
tentum.
Rectè; inde petitur ratio quorumdam fontium artefacto
rum in quibus aër ab aqua compre&longs;&longs;us aliam aquam, cujus &longs;uperficiem
premit, &longs;ur&longs;um extrudit; &longs;i quis verò non aquam, &longs;ed Mercurium ad
comprimendum aëra adhibeat, longè major vis pre&longs;&longs;ionis &longs;equetur, &
longè altiùs aqua extrudetur; &longs;ed jam hæc trita &longs;unt; vnum tantùm ob&longs;er
vo; hallucinari &longs;cilicet illum, qui in magno va&longs;e in aquas, iuxta prædi
ctum modum immer&longs;o, vivere &longs;e po&longs;&longs;e credidit, & profundum maris &longs;cru
tari; nempe aër in illo va&longs;e altè immer&longs;o vi &longs;upra gravitantis aquæ ita com
primetur, vt ducendo halitui minimè aptus e&longs;&longs;et: immo ip&longs;e aër thorace
contentus & abdomine, ita comprimeretur, vt mu&longs;culi ducendo aëri &longs;er
vientes, vix ad &longs;uam functionem habiles re&longs;tarent; &longs;ed quæ&longs;o re&longs;ume alia
capita, hoc enim tibi damus vltrò; &longs;cilicet corpus grave à levi deor&longs;um non
detrudi, &longs;ed &longs;ua &longs;ponte de&longs;cendere.
Hoc ip&longs;um e&longs;t, quod volo, nimirum, corpus grave tantùm &longs;ua
&longs;ponte deor&longs;um ire, & ab eo leve &longs;ubjectum extrudi.
Licèt fatear corpus grave à levi deor&longs;um non detrudi, &longs;ed
&longs;ponte &longs;ua de&longs;cendere, non tamen propterea dare cogor, à gravibus de&longs;
cendentibus, levia &longs;ur&longs;um extrudi, nam & gravia deor&longs;um, ac levia &longs;ur&longs;um
ire &longs;ua &longs;ponte cum Ari&longs;totele cen&longs;eo.
Fingamus &longs;altem, Chry&longs;ocome, corpus grave tantùm &longs;ua
&longs;ponte de&longs;cendere, præci&longs;a qualibet alia virtute, &longs;eu potentia, quæ
corpori levi in&longs;it; quæro ex te, vtrùm aliquid diver&longs;um ab eo, quod
modò apparet, in de&longs;cen&longs;u gravium, hoc po&longs;ito, futurum &longs;it, nihil pror
&longs;us, lapis enim v.g.per medium aëra de&longs;cenderet, & &longs;ur&longs;um aëra extrude
ret, cùm aliter de&longs;cendere non po&longs;&longs;it, idemque pror&longs;us fieret, quod modò
fieri videmus.
Eadem ratio probat, corpus leue ea vi pollere, qua &longs;ur&longs;um fe
ratur, quæ id probat, de corpore gravi; vt enim corpus grave ea pollet, vt
feratur in locum &longs;uum, versùs centrum Mundi, ita & leue, vt tendat in &longs;uum
ab eodem centro remotum, in hanc rem multos Ari&longs;totelis textus adducere
po&longs;&longs;em; &longs;ed fru&longs;tra, cùm Philo&longs;ophi mentem tibi per&longs;pectam e&longs;&longs;e non du
bitem.
Quid quæ&longs;o corpori gravi cum Mundi centro?
quid ab eo
loco commodi refert? cur igitur illud adeò appetit?
corpus verò leve,
quid rixæ aut di&longs;&longs;idij habet cum illo centro? quid ab eo &longs;ibi timet?
cur illud
fugit, vt infe&longs;tum ho&longs;tem? Præterea &longs;i rectè memini, Stagirita ve&longs;ter lib.
4. de Cœlo textu 39. expre&longs;sè dicit aëra deor&longs;um ferri, &longs;i aqua vel terra
&longs;ubtrahatur, non verò &longs;ur&longs;um, &longs;ubtracto illo corpore, cui &longs;ube&longs;t; & tamen
non minùs levis e&longs;t, quàm gravis, nec minor, vt dicis, illi virtus intrin-
Denique, vt hoc vel obiter dicam, ad quem amabò finem huju&longs;modi cor
porum lationes Natura de&longs;tinavit, ni&longs;i ad rectam Vniver&longs;i di&longs;po&longs;itionem? quod nec ip&longs;e Ari&longs;toteles vnquam negavit; atqui finis ille certò obtinetur,
modò graviora, quibus levia &longs;ub&longs;unt, deor&longs;um eant, & partes omnes
versùs idem centrum, cùm fieri non po&longs;&longs;it, vt graviora de&longs;cendant, ni&longs;i le
viora &longs;ur&longs;um trudantur; Quod &longs;pectat ad
profectò habet, quæ cum veritate minùs con&longs;entiunt in iis præ&longs;ertim, quæ
&longs;crip&longs;it de motu locali; quòd enim Cœli &longs;int &longs;olidi; quòd &longs;tellæ nullum ha
beant motum, præter motum primi Mobilis, quòd Mundus &longs;it ab æterno,
quòd Cœlum ortum non habuerit, nec corrumpi po&longs;&longs;it; quòd cuncta, quæ
ortum habuerunt, &longs;int interitura, quòd duplo gravius duplo velociore
motu de&longs;cendat, quod Deus &longs;it Agens nece&longs;&longs;arium, aliaque huju&longs;modi, non
modò in iis Ari&longs;totelem non debemus &longs;equi, &longs;ed eidem apertè à nobis re
pugnari, par e&longs;t.
Addo vnum, quod in re præ&longs;enti ponderandum e&longs;t, &longs;cilicet, non
agi hoc loco, vtrùm terra &longs;it ab&longs;olutè ac &longs;impliciter gravis, ignis verò ab&longs;o
lutè & &longs;impliciter levis; de aqua & aëre tantùm &longs;ermo e&longs;t; vtrumque au
tem ab&longs;olutè leve e&longs;&longs;e Philo&longs;ophus negat lib. 4. de Cœlo text. 27. ni fallor,
additque text. 39. in &longs;uo loco pondus habere non levitatem; id pa&longs;&longs;im re
petit aliis locis, & expre&longs;sè fatetur, præ&longs;ertim text. 30.aëra gravem e&longs;&longs;e;
adde &longs;is, quod habet lib. 3. text. 10. grave nihil aliud e&longs;&longs;e, quàm den&longs;um,
& leve nihil aliud quàm rarum; Idem habet lib. 4. Phy&longs;ic. cap. 9. item
lib. 8. c. 7. & alibi pa&longs;&longs;im. Non de&longs;unt etiam Autores cla&longs;&longs;ici præter Ar
chimedem, & quotquot de Statica & innatantibus humido &longs;crip&longs;erunt,
quorum hac in re autoritas maximi &longs;anè momenti e&longs;t, vt Iavellus tract. 1.
in 4. de Cœlo, cap. 3. concl. 3. Cabeus Tom. 4. Meteor. Tract. 14. Ru
vius lib.4.de Cœlo cap.6.quæ&longs;t. 1.Bovius lib.3.Philo&longs;oph. p.
221. & multi
alij, quos facilè adducerem; &longs;ed vt jam dixi, ad rem præ&longs;entem hæc contro
ver&longs;ia non &longs;pectat, &longs;atis enim mihi e&longs;t, &longs;i aër & aqua gravia &longs;int, &longs;altem &longs;e
cundum quid; quid quid tandem &longs;it de levitate po&longs;itiva, qua levia &longs;ua &longs;ponte
&longs;ur&longs;um ferantur, quam vobis quæ&longs;tionem animi gratia di&longs;putandam relin
quo; quantum enim ex iis, quæ huiu&longs;que à vobis dicta &longs;unt, alter eam ad
ftruit, alter verò de&longs;truit.
Ita e&longs;t, illam ad&longs;truo, non &longs;anè quòd ratio à priori
me moveat; nullam enim e&longs;&longs;e, quæ hoc mihi certò per&longs;uadeat, vl
tro fateor; &longs;ed quia nonnulla &longs;unt experimenta, quæ id pror&longs;us
evincunt.
Huc volo te; refer quæ&longs;o illa experimenta, iis enim, &longs;i ta
lia &longs;unt, & hoc &longs;anctè iuro, illico cedam & dabo manus.
mitas probè ob&longs;tructa &longs;it, altera verò aperta, infundatur aqua, non
tamen v&longs;que ad &longs;ummum, tum admoto pre&longs;sè digito, ne aqua effluat,
inver&longs;oque tubo, illa portio aëris, quæ in tubo reman&longs;it, &longs;ur-
lyndrica &longs;it, &longs;uperior tamen habet &longs;uperficiem qua&longs;i &longs;phæricam,
&longs;eu &longs;phæroidalem, hanc porrò induit aër, vt qua&longs;i cuneatim aqua
perrumpat; propria igitur &longs;pontè; vi &longs;cilicet levitatis, qua
pollet.
Si primo no&longs;tro congre&longs;&longs;ui interfui&longs;&longs;es, Chry&longs;ocome, hoc
experimentum, dubio procul omni, minimè adduxi&longs;&longs;es, ob&longs;erva&longs;&longs;es
enim aquam &longs;ecundùm latera tubi &longs;piratim de&longs;cendere, & ab ea &longs;ur&longs;um
aëra extrudi, longè tardiore motu; quia &longs;ur&longs;um aër motu recto fertur,
aqua verò deor&longs;um, non recto, &longs;ed &longs;pirali, quo rectum acceleratum im
peditum compen&longs;at; illud porro aëris fa&longs;tigium qua&longs;i cuneatum, non ab
aëre vi propria induitur, &longs;ed inducitur ab aquæ pondere versùs tubi late
ra deflectente ad de&longs;cen&longs;um; alioquin &longs;i aër propria vi hanc figuram in
duit, cur non conicam, quæ ad a&longs;cen&longs;um & aquam perrumpendam lon
gè aptior e&longs;&longs;et; nec enim difficiliùs vnam quàm aliam indueret; immo
fortè conicam, quæ ad cylindricam propriùs accedit. Vtinam æquè
facile mihi e&longs;&longs;et, definire, quænam figura illa &longs;it, illiu&longs;que cau&longs;am
afferre, quam nemo, &longs;altem quod &longs;ciam, huiu&longs;que adinvenit; hîc
tuam operam, Antime; nec enim eum me reputo
&longs;olvam.
Non e&longs;t mihi dubium, quin hæc &longs;uperficies curva ab aqua ver
sùs latera va&longs;is inclinante formetur; cùm enim aqua de&longs;cendere non po&longs;&longs;it,
ni&longs;i aër loco cedat, extru&longs;us &longs;cilicet ab aqua, & hic &longs;ur&longs;um extrudi non
po&longs;&longs;it, ni&longs;i humor illi &longs;e&longs;e &longs;upponat, vt hoc faciat, eundem aëra qua&longs;i
complexa per tubi latera &longs;piratim de&longs;cendit. An verò dicta &longs;uperficies pa
rabolica &longs;it, dubium e&longs;t; cum enim aqua versùs latera va&longs;is tendat, &longs;imul
& deor&longs;um motu accelerato, inde re&longs;ultas motus mixtus, qui lineam pa
rabolicam po&longs;t &longs;e relinquit, vt jam alij demon&longs;trarunt; &longs;ed vnde erit mo
tus ille horizontalis cum perpendiculari conjunctus? an fortè dicendum
e&longs;t, aquam &longs;piratim de&longs;cendere, cœpta qua&longs;i à centro &longs;pira; donec ad
latera va&longs;is perveniat; ab illa autem &longs;pira deor&longs;um producta &longs;upremum
illud aëris fa&longs;tigium tornari, cùm aliter &longs;piræ deor&longs;um produci non po&longs;
&longs;int: &longs;ed his omi&longs;&longs;is, cùm cylindrus aëris ab aqua &longs;tringatur, per latera
delabente, tantulùm a&longs;&longs;urgat, nece&longs;&longs;e e&longs;t; vnde aqua, cui &longs;uprema illius
ba&longs;is &longs;ube&longs;t, cedit locum; & cùm hæc attolli non po&longs;&longs;it, versùs latera
eat oportet, vbi dumtaxat ei locus patet; &longs;cilicet inter aëra & late
ra va&longs;is, vnde linea parabolica re&longs;ultat; hinc &longs;i tubus &longs;it angu&longs;tior, vix
aqua cylindrum inter aëris & latera tubi intercipi pote&longs;t; vnde prædicta
&longs;upremi fa&longs;tigij forma non &longs;equitur, quæ certè minùs convexa e&longs;t, &longs;eu
acuta, quò rima inter aëra & latera va&longs;is, qua perrumpit aqua, e&longs;t angu
&longs;tior: immo &longs;i tubus inclinetur, convexitas prædicti fa&longs;tigij deor&longs;um ver
sùs inferiùs tubi inclinati latus producitur; quia eò major ponderis aquæ
vis fertur, ex quo etiam manife&longs;tè colligitur, hanc convexi fa
&longs;tigij figuram ab aqua versùs latera va&longs;is labente tornari. Porrò ne&longs;cio an
turbinari inferiorem aëris ba&longs;im, qua&longs;i ad in&longs;tar lentis, i
min
ra ab aqua ambiente inducitur, cùm inter omnes &longs;implici&longs;&longs;ima &longs;it, &
inter æquales minimam &longs;uperficiem habeat; &longs;ed hæc tantulum figuræ de
&longs;iderant.
Sit tubus AD vitreus, plenus aqua, excepta por
tone aëris, quæ &longs;i innataret occuparet cylindrum
FG ; primùm ita re&longs;tringitur, vt ba&longs;is diameter &longs;it
TV, occupante aqua Spatia HTGV, ex cujus
lap&longs;u, cùm duo corpora &longs;e&longs;e penetrare non po&longs;&longs;int,
cylindrum aëris re&longs;tringi ac turbinari versùs K, vbi
labens aqua versùs & &longs;ecus latera, locum illi cedit
pror&longs;us nece&longs;&longs;e e&longs;t: cùm
de&longs;cendens &longs;piratim, præ impetu, in aquam conten
tam cylindri portione CE altè &longs;ubeat, &longs;uperficies
aquæ FE nece&longs;&longs;ariò attollitur; vnde portionem aë
ris I &longs;ur&longs;um extrudi, nece&longs;&longs;e e&longs;t; idque &longs;en&longs;im, in
proportione a&longs;&longs;ignabili; detracto enim cylindro &longs;ub
ba&longs;i TV, ex cylindro FG, vt re&longs;iduum ad cylin
drum FG, ita motus ba&longs;is TV ad motum aquæ la
bentis per &longs;patia HTGV, præ&longs;cindendo à &longs;pira. Iam verò &longs;it cylindrus aëris OM minor priore; at
tollitur quidem in X, & cum aqua lap&longs;a versùs N reflectatur à lateribus
tubi, &longs;tatimque cum aqua inferiore mi&longs;ceatur, ita vt per &longs;piram integram
minimè de&longs;cendat, qua&longs;i tondet marginem inferioris ba&longs;is cylindruli aë
ris, eamque in &longs;uperficiem
non integra labentis aquæ, lens aëris extru&longs;a &longs;ur&longs;um, huc illuc libratur
eundo, quia cùm modò hinc, modò illinc labens aqua &longs;e&longs;e &longs;ubjiciat aëri,
quid mirum, &longs;i prædicta libratio, &longs;eu tremor quidam con&longs;equatur:
quod etiam accidit in cylindrulis aëris minoribus, propter eandem
rationem; in majoribus enim de&longs;cendens aqua cum majore impetu
aliam aquam &longs;ubit, vnde hæc &longs;ecundùm Planum horizontale &longs;en&longs;im at
tollitur.
Sit demum tubus AC in &longs;itu inclinato, cylindrus
aëris EH ita conformatur, vt convexitas MFN multo
longiùs producatur, quàm connexitas ME; nempe
aqua gravior in latus inferius CB inclinat & versùs
punctum H lateris inferioris CB de&longs;inunt &longs;piræ, quod ad
oculum patet.
Ex iis omnibus manife&longs;tum fit, aëra
&longs;ur&longs;um ab aqua extrudi, non verò &longs;ua &longs;ponte ire;
alioquin cur illæ &longs;piræ? aut illa parabola?
cur ini
tio a&longs;cen&longs;us, cylindri aërei fa&longs;tigium à Plano pa-cur &longs;i aëris portio modica &longs;it, etiam ima ba&longs;is convexa e&longs;t?
cur major aëris portio tardiùs, minor citiùs a&longs;cendit?
imò &longs;i
qualis &longs;it, per &longs;egmentum angu&longs;tius tardiùs aër incedit, citiùs per laxius;
quia in angu&longs;tiore aër in longiorem cylindrum producitur; cur ille tre
mulus motus Lentium aëris? Cur figura Lentis, non Sphæræ?
cur in tubo in
clinato longior e&longs;t convexitas aëris versùs latus interius, versùs &longs;uperius,
brevior. Cuncta hæc explicari non po&longs;&longs;unt, &longs;i aër &longs;ur&longs;um &longs;ua &longs;ponte a&longs;cen
dit; &longs;cire tamen velim, cur eadem aëris portio in tubo angu&longs;tiore tardiùs,
in laxiore citiùs a&longs;cendat.
Miror à te rationem non videri; in angu&longs;tiore tubo aëris por
tio in cylindrum longiorem formatur; igitur aqua per latera de&longs;cen
dens longius &longs;patium decurrere debet, antequam cum aqua inferiore
conjungatur, & aëra &longs;ur&longs;um extrudat; igitur in eo plus temporis
ponit.
Satis e&longs;t, rem intelligo, vnde etiam per&longs;picua ratio ducitur,
cur modica portio aëris in eodem tubo citiùs a&longs;cendat, quàm major, quia
hæc in longiorem cylindrum extenditur; quid mirum ergo, &longs;i tardiùs a&longs;
cendat?
Infunde, quæ&longs;o te, in tubum aliquid olei; multa enim vi
debis, quæ tibi fortè oppo&longs;itum per&longs;uadeant: primo enim oleum tar
diùs a&longs;&longs;urgit, quia longè gravius e&longs;t aëre. Secundo eandem figuram induit
quam Aër, tertio Aëris cylindrus per medium oleum citi&longs;&longs;imè &longs;ur&longs;um per
rumpit: quartò Aër nonnunquam oleum &longs;ecum longè citiùs rapit, quàm
Oleum per &longs;e ip&longs;um a&longs;&longs;urgeret; nihil horum explicari pote&longs;t, ni&longs;i dicamus,
aëra &longs;ur&longs;um &longs;ua &longs;ponte ferri.
Immo nihil horum explicari pote&longs;t, &longs;i hoc dicamus; primò
igitur Aër citiùs fertur, tardiùs Oleum, cæteris paribus quia aliquando
accidit, vt modica olei portio &longs;ur&longs;um citiùs avolet; tardiùs aurem æqua
lis portio; quia minus e&longs;t aquæ momentum adversùs gravitatem, &longs;eu pon
dus olei, & majus adversùs pondus aëris. Secundo de figura nihil adden
dum e&longs;&longs;e puto; ni&longs;i quòd inferior ba&longs;is ni&longs;i longior &longs;it olei cylindras, con
vexa e&longs;t. Tertio vbi aëris cylindrus ad cylindrum aëris pervenit, &longs;tatim
de&longs;cendit Oleum, in libero &longs;cilicet aëre, & ab aquæ lap&longs;u circumagitur
in mille orbes & &longs;piras; & verò Oleum in aëre po&longs;itum &longs;ua &longs;ponte citò
de&longs;cendere, mirum non e&longs;t. Quarto Aëris bulla aliquando &longs;upremo cylin
dro olei adhæret, & tunc citiùs a&longs;&longs;urgit; quia &longs;cilicet totum illud per
modum vnius attollitur; neque in hoc e&longs;t difficultas; Supponamus enim,
e&longs;&longs;e vnciam aëris, & vnciam olei; certè major e&longs;t proportio momenti
duarum vnciarum aquæ adversùs pondus aggregati, ex vna vncia
olei, & vna aëris, quàm vnius vnciæ aquæ, adver&longs;us vnam
Olei; nec ob&longs;tar aggregatum illud e&longs;&longs;e gravius alterutro; quia in
comparatione duorum gravium, æqualis &longs;emper vtriu&longs;que exten&longs;io,
&longs;eu moles accipitur. Sed hæc &longs;unt facilia, nec in his explicandis tua
opera indigeo, Antime; in his tamen non dubito, quin alia multa à
&longs;tulo.
Negare non po&longs;&longs;um, quin multa mihi &longs;uppetant in hac ma
teria, quæ tamen quia à propo&longs;ito argumento aliena &longs;unt, in alium lo
cum tractanda & exponenda remitto.
Vnde igitur motus levium &longs;ur&longs;um acceleratus?
quòd certè
in diver&longs;is globulis aqua levioribus probatum e&longs;t; immo in aëris cylindro
per tubum a&longs;&longs;urgente, per&longs;picuè videtur; itemque in cylindro ligneo, per
vim ad fundum latioris va&longs;is vel putei detento, qui &longs;ur&longs;um ita erumpit,
vt longè altiùs a&longs;cendat; etiam &longs;i in imo va&longs;is fundo foramen &longs;it.
Ita e&longs;t; ii globuli motu accelerato a&longs;cendunt, diver&longs;o tamen
à gravium motu; Supponimus enim liberum &longs;patium in ampli&longs;&longs;imo va&longs;e
aqua pleno, ex quo leviora corpora, per mediam aquam a&longs;cendunt; v.g.
cylindrus ligneus motu accelerato non quidem &longs;ponte, &longs;ed impre&longs;&longs;o ab
aqua extrudente; nempe impetus initio productus durat deinde; quid
mirum ergo, &longs;i motus inde acceleratus evadat?
Igitur ad in&longs;tar gravium e&longs;&longs;et acceleratus, quod tamen
omnibus experimentis repugnat;
accedunt, vt fit in motu gravium, &longs;ed minora &longs;emper & minora, priùs ta
men acqui&longs;itis &longs;emper remanentibus; an fortè vt in de&longs;cen&longs;u fune
penduli?
Minimè verò; cùm enim velocitates &longs;int vt motus, & hi in
&longs;ubduplicata altitudinum vt &longs;upra demon&longs;tratum e&longs;t.
Sit &longs;emiparabola ABC, &longs;patium
acqui&longs;itum motu naturaliter acce
lerato erit AB, velocitas verò ac
qui&longs;ita &etail;rit BC ; &longs;it etiam AB altitu
do aquæ, intra quam corpus leve
per vim intruditur & ex qua, præ
valente eju&longs;dem aquæ pondere &longs;ur
&longs;um deinde extruditur; &longs;it ergo BH
æqualis BA item IN æqualis IH
&longs;itque alia &longs;emiparabola NKC ita
vt CI &longs;it Axi parallela; erit motus
corporis levis initio extru&longs;ionis vt
BC emen&longs;a verò tota aquæ altitu
dine erit vt HN: nempe vt ab A
ad B acquiritur velocitas BC, & in
patio DB &longs;upra DE jam acqui&longs;i
tam in &longs;patio AD, acquiritur EG ; ita in BH acquiritur IN &longs;upra jam
acqui&longs;itam BC, & vt in DB acquiritur EG ita in BL acquiritur MK
æqualis EG ; denique vt in AD acquiritur DE ita in LH acquiritur ON. Sed quid de foramine in fundo va&longs;is aperto, cujus &longs;upra Chry&longs;ocomus
meminit?
De re mihi non con&longs;tat, nunquam enim hoc à me ob&longs;erva
tum e&longs;t.
Omninò di&longs;tinguendum e&longs;t; &longs;i enim tale e&longs;t, vt tantumdem
aquæ per illud effluat, quantum infra cylindrum de&longs;cendit; cylindrus
erit immobilis; &longs;i minùs de&longs;cendat, quàm effluat, cylindrus ip&longs;e, &longs;i de
&longs;cendere pote&longs;t, de&longs;cendet; &longs;i verò plus aquæ de&longs;cendat, quàm ex fora
mine effluat, tantulùm cylindrus a&longs;&longs;urgit.
Hoc ip&longs;um per&longs;picuè probat, corpus leve non attolli &longs;ua
&longs;ponte; quod enim gravius deor&longs;um de&longs;cendat, non impedit, quò minùs
leve &longs;ua &longs;ponte a&longs;cendat: &longs;ed accipe luculentum experimentum, iis ta
men &longs;imile, quæ jam expo&longs;ita fuere. Sit pixis quælibet, in cujus fundo he
mi&longs;phærium, vel minor Sphæræ portio accuratè & affabrè ita excavetur,
vt Sphæram ligneam omninò capiat, nulla relicta intercapedine; tum
pixis impleatur aqua; Sphærula lignea, quamvis levior, nullo modo a&longs;
cendit; quia &longs;cilicet cum aqua in cavitatem illam &longs;ubire non po&longs;&longs;it, ab ea
Sphæra &longs;ursùm extrudi non pote&longs;t.
Dicerem non a&longs;&longs;urgere Sphæram, ne detur vacuum; idem
enim fieri videmus, &longs;i duo plana probè congruant.
Hoc dictum iri &longs;ciebam; &longs;ed fiat foramen in medio cavita
tis, quò &longs;cilicet aër ambiens facile &longs;ubeat, non propterea Sphærula a&longs;cen
dit, licèt nullum re&longs;tet vacui periculum: per vos etiam mihi liceat, hic
obiter, ea &longs;altem indicare, quæ tuam illam &longs;ententiam, Chry&longs;ocome, om
ninò expugnare videntur. 1. Quandoquidem per vnum principium
motus cuncta explicari po&longs;&longs;unt, quo &longs;cilicet corpus grave &longs;ua &longs;ponte
deor&longs;um fertur, quod inficiatur nemo, & leve &longs;ur&longs;um extrudi pote&longs;t,
fru&longs;tra ponitur aliud principium: Hæc ratio, licèt communis &longs;it, maximi
&longs;anè momenti e&longs;t. Secundò, cùm ab eodem centro multæ lineæ ducantur,
fi corpus levi&longs;&longs;imum e&longs;&longs;et, in centro, non po&longs;&longs;et vllo modo a&longs;&longs;urgere; cur
enim potiùs per vnam lineam quam per aliam?
Facilè retorqueo argumentum, nec enim pariter &longs;ur&longs;um ex
trudi po&longs;&longs;et; cur enim potiùs per vnam lineam quàm per aliam?
Hoc quidem verum e&longs;t, modò ambiens gravius æqualis e&longs;&longs;et
momenti; per omnes lineas; &longs;ed hoc per accidens; illud autem per &longs;e
præterea, linea motus recti à termino, ad quem determinatur; cùm au
tem vnum centrum &longs;it, a&longs;&longs;umpto quolibet quncto extra centrum, ab illo
ad centrum vnica tantùm linea ducitur, cùm tamen ab eodem, plures ad
periphætiam duci po&longs;&longs;int; vna quidem producta ad centrum; &longs;ed quomo
do à centro determinatur hæc linea, quod neque &longs;it terminus ad quem,
nec terminus à quo illius motus? Tertiò non pote&longs;t idem corpus in par
tes oppo&longs;itas &longs;imul moveri; igitur nec &longs;imul conniti, &longs;cilicet ab intrin&longs;e
co; quod vt meliùs intelligatur, &longs;it vas aqua plenum, &longs;itque pondus aquæ
40. libr. Sit fru&longs;tum ligni in fundo va&longs;is retentum pendens 5.libr.
appen
datur &longs;imul vtrumque, &longs;u&longs;tinebitur à 45. libris po&longs;itis in altera lance li
bræ, eritque æquilibrium, &longs;tatimque impedimento &longs;ublato, lignum emer
git, &longs;ur&longs;umque attollitur eodem pror&longs;us æquilibrio manente; igitur hic
rectè, ergo &longs;e ip&longs;um lignum non &longs;u&longs;tinet; igitur multò minùs &longs;e movet. Omitto innumera ferè experimenta, quæ rem hanc penitùs evincunt; &longs;ed
ne in Parergum prolixius abeamus, cœptam di&longs;putationem à te re&longs;umi
velim, Antime, præ&longs;ertim cùm hæc ad rem præ&longs;entem parùm faciant,
modò enim aër gravis &longs;it, hoc tibi &longs;atis e&longs;t.
Vt igitur partes omnes terre&longs;tris globi versùs commune cen
trum nituntur, ita etiam partes aëris ambientis: Sed cùm aër &longs;ive purior,
&longs;ive impurior, nam perinde e&longs;t, ambiat etiam alios totales globos, putà
Lunam, globum enim totalem appello illum, qui alterius pars non e&longs;t, &
&longs;eor&longs;im po&longs;itus manet, medium quoddam commune dici pote&longs;t.
Et cùm &longs;inguli globi totales &longs;uo centro gaudeant, versùs
quod omnes illorum partes connituntur; hæc enim veri&longs;&longs;ima e&longs;t ratio,
qua totales globi tornari, & figuram obtentam &longs;ervare po&longs;&longs;unt, aëris
etiam, &longs;eu communis medij ambientis portio, versùs illos globos gravitat,
&longs;eu nititur.
Rectè omninò; cùm enim medium commune tot v&longs;ibus nece&longs;
&longs;arium &longs;it, non minùs pertinet ad vnum globum, quàm ad alium; vnde
rationiac rerum naturæ con&longs;entaneum e&longs;&longs;e videtur, vt versùs vtrumque
gravitet; quota verò pars versùs vnum, & quota versùs alium, non diffi
cilè definiri pote&longs;t.
Sit enim centrum A terre&longs;tris globi CBED, &longs;it centrum Lunæ I, du
catur recta AI, connectens
pote&longs;t hujus cylindri portio, quæ versùs A, & ea; quæ versùs I gravitat;
Primo divi&longs;a AI bifariam in F ; & &longs;ic FK gravitat versùs I & FB versùs A. Secundo divi&longs;a bifariam BK in M, & &longs;ic BM versùs A, & MK
versùs I. gravitat. Tertiò ita divi&longs;a AI vt &longs;egmentum gravitans ver
sùs A, &longs;it ad aliud gravitans versùs I, vt globus A ad globum I. Quartus modus addi pote&longs;t, vt &longs;cilicet BK &longs;ecetur juxta dictam propor
tio nem globorum. Quidquid autem ex his dicatur, ad rem no&longs;tram perinde
e&longs;t; quare majoris facilitatis gratia, primum modum accipio, & per punctum
F duco GFH perpendiculariter, quæ vocetur dirimens connectentem
centra, &longs;eu linea confinium. Quod dixi de AF, IF, de AN, IN dictum e&longs;to,
item de reliquis lineis, &longs;eu cylindris.
Multis &longs;anè, præ&longs;ertim Peripateticis, hæc tua doctrina mi
nimè probabitur, qui juxta mentem Philo&longs;ophi docent, centrum terræ
idem e&longs;&longs;e cum centro Vniver&longs;i, versùs quod omnia gravia tendunt; nega
bunt igitur portionem aëris &longs;upra dirimentem GH, versùs Lunæ cen
trum gravitare.
Videtur quidem Stagirita hoc ip&longs;um, quod dicis ad &longs;truere; præ
&longs;ertim lib.2. de cœlo text. 100.
e&longs;&longs;e, ac Vniver&longs;i,
verò ad centrum Vniver&longs;i; de hoc tamen lib. 3. text.33. dubitare videtur;
vbi enim dixi&longs;&longs;et, quidquid pondus habet, ferri ad medium, &longs;eu versùs
centrum, &longs;tatim &longs;ubdit hæc:
feratur, cùm idem medium &longs;it ip&longs;orum, alia ratio e&longs;t.
cœlos &longs;olidos po&longs;uerit, & Sphæram ignis aëre &longs;uperiorem, & quintam
e&longs;&longs;entiam, quam animatam e&longs;&longs;e indicare videtur, quid mirum, cùm ele
menta no&longs;tra, juxta illum, vltra concavum Lunæ non extendantur, & &longs;uis
orbibus &longs;olidis &longs;olidi Planetæ affixi &longs;int, nihil vltra prorsùs gravitare aut
levitare, ac proinde gravium & levium commune centrum in Mundi &
Terræ centro collocavit. Si tamen cœlum e&longs;&longs;e fluidum puta&longs;&longs;et, & cœ
le&longs;tes Sphæras in illo communi medio moveri, & &longs;uos agere orbes; &longs;i
Cometas de novo gigni & mori in ætherea regione, nec non faculas &
maculas in Solis di&longs;co. Martem propiùs ad terras nonnunquam accedere
quàm Solem; novas Stellas in Cœlo na&longs;ci; &longs;i demùm alia multa, quæ
jam ex ob&longs;ervationibus comperta &longs;unt, &longs;civi&longs;&longs;et, non e&longs;t dubium, quin alia
de Cœlo & Vniver&longs;i con&longs;tructione &longs;crip&longs;i&longs;&longs;et; quanquam cum Ari&longs;totele
Dico centrum terræ Vniver&longs;i centrum e&longs;&longs;e, circa quod cœle&longs;tes Sphæræ
&longs;uos orbes agunt, versùs quod illa omnia gravia tendunt, &longs;ublunaria &longs;ci
licet, quæ Ari&longs;toteles agnovit; &longs;ed cùm hoc commune medium vltra
extendatur, & eadem ratione pro formatione & con&longs;ervatione militet
in aliis globis; tot pono centra, in quæ partes circumpo&longs;itæ nituntur,
quot &longs;unt globi totales; gravitas enim non totius, &longs;ed partium proprietas
e&longs;t, cujus vi quælibet pars versùs &longs;uum centrum nititur, & contranititur,
ne ab eo &longs;eparet ut, & &longs;i vnquam ab eo &longs;eparetur, in illud denuò &longs;e reci
pit. Quid vero ad conmmne medium &longs;pectat, illius po
(quanquam non video cur ab&longs;olutè non po&longs;&longs;it ad&longs;trui) permittat &longs;altem
hoc à me &longs;upponi, & ex illa hypothe&longs;i, ratiocinando, di&longs;cutere, quid ex
illa &longs;equatur, & hæc qua&longs;i dicta ex hypothe&longs;i accipiat.
Quintam illam e&longs;&longs;entiam in cœlis nunquam probavi; cùm
cœle&longs;tia corpora ex no&longs;tris elementis conflata e&longs;&longs;e communis &longs;it apud
Sanctos Patres &longs;ententia, quos vide&longs;is apud Scheinerum, Ricciolum, Ce
ladam &c. immo Beda expre&longs;&longs;is verbis a&longs;&longs;erit,
&longs;patium in quo &longs;idera ferri perhibentur. In his autem, &longs;acræ Scripturæ &longs;an
cti&longs;que Interpretibus &longs;tandum potiùs e&longs;&longs;e duxerim; quam Peripateticis. Porrò ex &longs;uppo&longs;itione, quod cœle&longs;tia corpora ex no&longs;tris elementis con
&longs;tent, de quo po&longs;t novas ob&longs;ervationes dubitari nequit ; non video, quo
modo &longs;alvari omnia po&longs;&longs;int, ni&longs;i
ita vt &longs;inguli globi totales &longs;uum &longs;ingulare centrum habeant, versùs quod
partes omnes eju&longs;dem globi connituntur, cum illa communis medij,
aëris &longs;cilicet portione, quæ ad illud propiùs accedit, quàm ad
aliud; centrum verò terræ, præter illam centri rationem, quæ illi
cum aliis globis communis e&longs;t, habet aliam rationem, quæ illi
dumtaxat competit, centri &longs;cilicet Vniver&longs;i, quod certè terre
&longs;tri globo &longs;ingulare e&longs;t cui reliqui globi &longs;erviunt; nam propter ho
mines terre&longs;tris globi incolas totum corporeum mundum Deus condidit,
nec aliis globis res viventes in&longs;unt, etiam, vt vocant, vegetantium vita,
nihil enim hæc ad terræ incolas conferre po&longs;&longs;ent, vt patet; & quidquid
&longs;uper his ad&longs;truitur, fictitium e&longs;t, & merum commentum; hinc circa ter
ram immobilem eunt cœle&longs;tes &longs;phæræ, eidem famulantes; vel diffu&longs;a luce,
vt Sol, vel eadem repercu&longs;&longs;a, vt reliqui Planetæ, & &longs;tellæ veri&longs;imiliùs; adde
quod diver&longs;is variorum motuum periodis tempora &longs;ignant, vt &longs;tellæ
fixæ loca, propter invariabilem, quem inter &longs;e habent ordinem; &longs;ed quæ
&longs;o, perge, hæc à te &longs;uppo&longs;ita libenter admitto, etiam citra maris
æ&longs;tum.
Secundo loco &longs;uppono, corpus liquidum, humidum, voca
vt voles, &longs;i ab omni parte æquali ni&longs;u prematur, figuram &longs;phæricam in
duere; cùm enim corpori humido v. g aquæ figura va&longs;is facilè inducatur,
nempe humidum terminis alienis facilè continetur, certè &longs;i æqualiter ab
omni parte prematur, nulla e&longs;t ratio, cur potiùs hinc cedat, quàm illinc; inde
igitur nece&longs;&longs;ariò figura &longs;phærica &longs;equitur: &longs;i verò minùs ab vna parte, quàm
ab aliis, reliquæ haud dubiè prævalent, ac proinde hæc tantulum cedat &
attollatur, nece&longs;&longs;e e&longs;t; In his, quæ per&longs;picua &longs;unt, diutiùs non hæreo.
Tertiò &longs;uppono corpus liquidum, cui corpus grave admixtum e&longs;t, inde
graviùs effici; &longs;ic aqua, cui &longs;al admixtum e&longs;t, gravior evadit, item aër
gravior, &longs;i multæ humoris particulæ, vt fit in nebula, admi&longs;ceantur; in
hoc etiam nulla e&longs;t difficultas. His &longs;uppo&longs;itis, ad marinum æ&longs;tum explican
dum venio; & varias a&longs;&longs;ertiones ad&longs;truo ex iactis principiis deductas. Sit
terra in A, vt dixi, & Luna in I, cum reliquo apparatu, vt &longs;upra, totus
sùs centrum A; totus aër &longs;upra GH, gravitat versùs I; hic enim propriùs
accedit ad I, quàm ad A; ille verò propiùs ad A, quàm ad I. Prætereà
linea FB e&longs;t minor NV: itemque illæ minores, quæ propiùs accedunt
ad FB; &longs;upponantur infinitæ, hinc inde, quarum maxima erit ES paral
lela dirimenti GH cum oppo&longs;ita æquali ZC: cùm autem prædictæ lineæ
&longs;int totidem cylindri aëris gravitantis, haud dubiè gravitatio inæqualis e&longs;t,
& con&longs;equenter pre&longs;&longs;io; igitur &longs;i &longs;upponatur globus totus aqueus, &longs;altem
quo ad &longs;uperficiem, &longs;eu corticem exteriorem ex dicta pre&longs;&longs;ione inæquali,
&longs;equitur figuræ &longs;phæricæ mutatio; & cùm ES, CZ &longs;int omnium maximæ
in punctis E & C, maximum e&longs;t pre&longs;&longs;ionis momentum; igitur deprimun
tur C & E in Q & I v. g. igitur attollitur B in P, punctum enim B, in quo
e&longs;t minimum pre&longs;&longs;ionis momentum, prævalentibus aliis, tantulùm attolli
nece&longs;&longs;e e&longs;t.
Quàm magnum mihi campum aperis; pudet me, hæc priùs
non cogita&longs;&longs;e; tam facilia, tam obvia, tam trita & communia: fac quæ&longs;o
circulum DCBE volvi circa axem BD, punctum X de&longs;cribit circulum,
cujus radius e&longs;t XB, in cujus tota peripheria fit æqualis pre&longs;&longs;io, &longs;cilicet
vt XO, quæ e&longs;t major BF; item C de&longs;cribet peripheriam circuli radio
CA, in qua tota e&longs;t æqualis pre&longs;&longs;io, &longs;ed longè major, quàm in priore;
tum quia circulus major premitur, tum quia in &longs;ingulis punctis major e&longs;t
pre&longs;&longs;io; in &longs;ingulis verò punctis inter CD, circuli pre&longs;&longs;ionum minores
&longs;unt; quilibet &longs;cilicet &longs;ub &longs;inu recto; cùm autem pre&longs;&longs;iones &longs;int, vt præ
dicti circuli, ac proinde major &longs;it pre&longs;&longs;io in CE, &longs;equitur nece&longs;&longs;ariò de
pre&longs;&longs;io punctorum C & E & elevatio B & D, in oppo&longs;itis &longs;cilicet punctis,
per quæ ducitur linea connectens centra, &longs;cilicet ID; vna tamen mihi
re&longs;tat difficultas, cui &longs;olvendæ imparem profectò me &longs;entio, nempe in
&longs;ingulis punctis quadrantis CD, æqualis e&longs;t vis pre&longs;&longs;ionis; cur igitur
a&longs;&longs;urgit in R? cur vnum prævalet &longs;upra aliud;
Hic nodus indi&longs;&longs;olubilis e&longs;&longs;et, &longs;i tantùm pre&longs;&longs;io fieret in pun
ctis C & D, alií&longs;que eiu&longs;dem arcus CD ; &longs;ed quia æqualis radiorum, &longs;eu
linearum pre&longs;&longs;io fit in circulo, v. g. in circulo radio CA, in circulo ra
dio ba, alií&longs;que parallelis, certè pre&longs;&longs;iones &longs;unt vt peripheriæ prædi
ctorum circulorum, & hæ vt radij CA, ba &c. vnde &longs;equitur, majorem
e&longs;&longs;e vim pre&longs;&longs;ionis circuli, cujus radius e&longs;t CA, quàm circuli, cujus ra
dius e&longs;t Ba, deprimitur ergo aqúa in prædicto circulo CE, quem dein
ceps circulum maximæ pre
versùs P & R, qui &longs;unt poli prædicti circuli, &longs;eu puncta maximæ eleva
tionis: hinc ex &longs;phæra fit &longs;phærois, licèt autem pre&longs;&longs;io in b &longs;it major quam
in X ; hoc tamen pro nihilo habendum e&longs;t; cùm primaria cau&longs;a elevatio
nis aquæ &longs;it à circulis pre&longs;&longs;ionis, non procul à circulo maximæ pre&longs;&longs;ionis
di&longs;tantibus; accedit quod cùm non ob&longs;tante circulo pre&longs;&longs;ionia, radio ba, in
tume&longs;cat aqua in R, ac proinde in
lit potiùs punctum b per ba
majoris pre&longs;&longs;ionis altiùs attollatur ver&longs;us AP; itemque minùs premit per
XB; b verò magis re&longs;i&longs;tit directa pre&longs;&longs;ione per bA, vnde ab aliis circulis
majoris pre&longs;&longs;ionis minùs a tollitur; plus tamen per ba, quam vocare
po&longs;&longs;umus obliquam pre&longs;&longs;ionem; vnde vides vnam compen&longs;ari per aliam;
nempe X habet minorem pre&longs;&longs;ionem tum directam, tum obliquam; hinc
ratione directæ plus attollitur, ratione obliquæ minùs, b verò habet majo
rem vtramque, ac proinde ratione directæ minùs attollitur, & plus ra
tione obliquæ; en vobis per&longs;picuam compen&longs;ationem. Denique licèt
aliqua e&longs;&longs;et differentia elevationis, parum admodùm referret; de quo
infra.
Huiu&longs;que qua&longs;i meditabundus conticui; negari tamen non
pote&longs;t, quin peregrinum inventum &longs;it; modò omnia probè con&longs;entiant,
ac phænomenis non repugnent; vnum tamen occurrit, quod mihi diffici
le videtur; cur &longs;cilicet pre&longs;&longs;io per vnum dumtaxat majorem circulum fiat,
cujus radius e&longs;t CA; cur enim per alios non fit, quotum radij &longs;int XA, VA,
BA. &c.
Rectè mones, hoc enim mihi explicandum incumbit, equi
dem fit pre&longs;&longs;io per omnes circulos majores, vt fit in circulo ma
jore, BCDE, &longs;ed quia propter pre&longs;&longs;ionem inæqualem, huju&longs;modi
circuli in Ellip&longs;es, vel qua&longs;i Ellip&longs;es mutantur, con&longs;idero tantùm
pre&longs;&longs;ionem in iis circulis, in quibus æqualis, vel vniformis e&longs;t pre&longs;&longs;io,
inter quos vnus dumtaxat major e&longs;t, quem maximæ pre&longs;&longs;ionis &longs;upra voca
vi, in quem axis ab&longs;idum, &longs;eu maximæ elevationis, perpendiculariter
cadit; aliíque minores eidem paralleli. Nempe &longs;i pre&longs;&longs;io vniformis e&longs;t,
ni&longs;u quodam communi execitur, nec vnum eju&longs;dem circuli punctum ab
alio attollitur; &longs;i verò difformis & inæqualis, ni&longs;us communis non e&longs;t, vt
patet. Po&longs;ita igitur Luna in I, eaque immobili, terra in A, ita vt tota il
lius &longs;uperficies aquea &longs;it, terra non jam &longs;phæra, &longs;ed &longs;phærois erit ad in&longs;tar
pruni, cujus major diameter e&longs;t axis ab&longs;idum, vel in linea connectente
centra, minor verò e&longs;t diameter circuli maximæ pre&longs;&longs;ionis. Et &longs;i Luna &longs;it
in Æquatore, prædictum Planum BCDE erit in plano Æquatoris, CE
erit Meridianus, polus in C erecta CA perpendiculari ad planum Æqua
toris.
Quæ &longs;equuntur facilia reputo; demus enim moveri Lunam
per IHS, eodem motu moveri videbitur punctum P ; & vbi Luna per
venerit in S, punctum maximæ elevationis erit in E, erítque EC linea ab
&longs;idum, & BD diameter maximæ pre&longs;&longs;ionis; atque ita prædictus aquæ tu
mor motum Lunæ omninò æmulatur, & orbe peracto, Luna redeunte
ad punctum I, tumor rediret ad punctum P. Pro quo etiam fingendum
e&longs;t, &longs;imul cum Luna, eodemque motu, circa centrum A, moveri lineam
connectentem centra A, I, cum ip&longs;a linea dirimente GFH, &longs;ed profe
ctò hic æ&longs;tus ab eo diver&longs;us e&longs;t, quem modò habemus, vel ob&longs;ervamus in
mari.
Ita e&longs;t, fateor vltro; quia totam terre&longs;tris globi &longs;uperficiem aqua
V, haud dubiè eo tempore, quo tumor aquæ re&longs;ponderet radio AV, &longs;ecun
dùm eundem radium a&longs;&longs;urgit aqua per clivum montis, donec
vi non &longs;u&longs;tinetur amplius; hinc fiet æ&longs;tus reciprocus,
&longs;ive, vt Si verò ad
mare inclinet; hinc inde maximus erit aquæ tumor ad
occiduum &longs;cilicet, atque ortivum; & Luna tendente versùs S, &longs;en&longs;im &longs;ub&longs;i
det aqua, excurrétque, hinc versùs ortum, inde occa&longs;um versùs; vt autem
refluit aqua in partes oppo&longs;itas, abeunte Luna, ita Luna accedente à parti
bus oppo&longs;itis,
versùs terræ tractum V, & vtrimque ad vtrumque clivum &longs;en&longs;im attolli
tur. Hinc &longs;i per medium terræ trectum, angu&longs;tum fretum perrumperet, aqua
hinc inde &longs;imul a&longs;&longs;urgente, in medio freto gemini æ&longs;tus concurrerent.
na extra Æquatorem &longs;ita.
Faciam intelligas: finge tibi terram ad in&longs;tar &longs;phæroidis, id e&longs;t,
Solidi Elliptici; cogita prunum PQRT, quod obtinebis, &longs;i ellip&longs;im hanc
circa axem RP volvi iubeas. Finge autem prædictum prunum cujus &longs;ectio
PQRT e&longs;t in plano Æquatoris, librari circa
modò versùs Au&longs;trum, per
neam
diculariter erectum, eodem pror&longs;us
tum etiam prædictæ librationis, en tibi germanum marini æ&longs;tus &longs;y&longs;tema.
Maxima difficultas &longs;e&longs;e mihi objicit ; nempe po&longs;ita linea ab&longs;i
dum extra Planum Æquatoris, Luna v.g.in Tropico Capricorni exi&longs;tente, &longs;i
accipiamus quodlibet punctum extra Æquatorem, elevatio aquæ in eo
puncto inæqualis e&longs;&longs;et, licèt Luna in Meridiano &longs;ita &longs;upponatur; & vt cla
riùs hanc difficultatem exponam.
Sit circulus verticalis & meri
dianus in globo terre&longs;tri ADCF,
cus Cancri HI, Capricorni GL,
Axis mundi PM; &longs;upponatur Lu
nain G, &longs;cilicet in Tropico Capri
corni, & in meridiano &longs;upra hori
zontem; circulus maximæ depre&longs;
&longs;ionis e&longs;t
quod a&longs;&longs;umptum e&longs;t extra Æqua
torem;
nis, quod e&longs;t in G, e&longs;t enim line
quo tamen circulus maximæ de
pre&longs;&longs;ionis di&longs;tat tantùm arcu BM, po&longs;ita verò Luna in
L, circulus maximæ depre&longs;&longs;ionis erit NO, Linea ab&longs;idum LH, arcus di&longs;tan-
æ&longs;tus nocturnus longè major e&longs;t in loco D, quàm diurnus; immo &longs;i accipia
tur punctum B, in eo erit maxima depre&longs;&longs;io aquæ, Luna po&longs;ita in G ; &longs;cilicet
de meridie, po&longs;ita verò in L, de media nocte, di&longs;tabit B à puncto maximæ
depre&longs;&longs;ionis arcu BN; cuncta hæc repugnare videntur ob&longs;ervationibus, cùm
æ&longs;tus diurnus & nocturnus æquales &longs;int.
Fateor vnum e&longs;&longs;e ex præcipuis Nodis, qui mihi &longs;olvendi &longs;unt,
qui tamen facilè a me &longs;olvitur, in hypothe&longs;i facta. Nempe dato quod tota
&longs;uperficies terre&longs;tris globi &longs;it aquea, cuncta hæc, vt dicis, &longs;uccederent; duo
tamen ob&longs;erves, velim; primum e&longs;t, di&longs;tinguendam e&longs;&longs;e aquarum elevatio
nem, &longs;eu tumorem, ab earundem rapido cur&longs;u; vnum enim ab alio di&longs;tin
guitur, licèt vnum ex alio con&longs;equatur; vnde fieri pote&longs;t, vt cum minore ele
vatione &longs;eu tumore, rapidior cur&longs;us conjunctus &longs;it; & vici&longs;&longs;im minùs rapi
dus cur&longs;us, cum majore elevatione propter loci &longs;itum: Secundum e&longs;t, versùs
Polos æ&longs;tus ferè &longs;ine legibus ire, quia cum punctum elevationis, quod non
procul à Pol
Mundi, quid mirum, &longs;i maxima inde aquarum perturbatio na&longs;catur; & verò
præ&longs;cindendo à vario terrarum &longs;itu, qui multa variat, versùs Polos, qua&longs;i
vortex quidam tumentis aquæ, &longs;patio 24. horarum min 48. circa polum iret,
ex quo reverà non modica aquarum perturbatio &longs;ine certa lege &longs;equere
tur. Sed de hoc infra.
Porrò fateor vltro,
& po&longs;ito quod tota &longs;uperficies terre&longs;tris globi aquea e&longs;&longs;et, in puncto D, tu
morem aquæ altiorem fore de meridie quàm de media nocte, Luna exi&longs;ten
te in Tropico Cancri, contra verò in Tropico Capricorni; immo Luna exi
&longs;tente in Cancro de meridie, vel in Capricorno, de media nocte, altiorem
fore tumorem in D, quàm &longs;i Luna exi&longs;teret in Æquatore. Cur verò hoc
modo
tis aquæ cur&longs;u, variaque illius deflexione, reflexione, inclinatione, contra
ctione &c. de quibus infrà, omninò &longs;equitur.
Itaque jam mihi &longs;ufficit, hanc
veram cau&longs;am e&longs;&longs;e prædicti aquarum tumoris & motus, eju&longs;demque revo
lutionis, ad Lunæ motum diurnum ita compo&longs;it&etail; vt Luna in Meridiano exi
&longs;tente, &longs;ive &longs;upra, &longs;ive infra horizontem, præfatus tumor maximus &longs;it in lo
cis, &longs;ub eodem Meridiano &longs;itis: maxima verò ibidem depre&longs;&longs;io, Luna 90.
gradibus à dicto Meridiano di&longs;tante; &longs;ic enim &longs;ingulis diebus tumor vna
ferè hora tardiùs accedit; quia talis e&longs;t Lunæ motus, & jam vides, ni fallor,
Chry&longs;ocome, quid ad mirabilem i&longs;tum effectum Luna conferat, & quàm
providè antè dixerim, Lunam marini æ&longs;tus cau&longs;am non e&longs;&longs;e, nec enim re
verà cau&longs;a e&longs;t, &longs;ed mera occa&longs;io; cau&longs;a verò, inæqualis aëris gravitatio, eo
modo, quo dixi. Ex qua po&longs;ita Luna, eju&longs;que motu ab ortu in occa&longs;um, ne
ce&longs;&longs;ariò &longs;equitur æ&longs;tus, id e&longs;t, aquarum elevatio & tumor, in dato quolibet
Oceani puncto; &longs;uppo&longs;ita &longs;cilicet tota &longs;uperficie globi aquea, idque bis &longs;in
gulis diebus, &longs;cilicet de meridie, & media nocte Lunari; meridiem autem,
&longs;eu mediam noctem Lunarem voco, illud temporis punctum, quo Luna e&longs;t
in Meridiano, cui prædictus locus &longs;ube&longs;t; vtrùm verò tumor de meridie Lu
nari, &longs;it æqualis tumori de media nocte, jam dictum e&longs;t &longs;upra; nimirum
dum Luna versùs Tropicos excurrit; quid autem accidat, in hoc rerum
&longs;tatu, nimirum ex diver&longs;o marium ac terrarum &longs;itu, paulò po&longs;t dicam,
nec me opinor, ab onere illo eximetis.
Germanam ac facilem cau&longs;am habemus marini æ&longs;tus, qui
&longs;ingulis diebus bis a&longs;&longs;urgeret in illa hypothe&longs;i totius &longs;uperficiei aqueæ, de
qua vltra di&longs;putandum e&longs;&longs;e, non puto; quare ad aliam marini æ&longs;tus pro
prietatem venio; prima enim diurna e&longs;t, de qua huc v&longs;que; juxta illam
hypothe&longs;im ; &longs;ecunda men&longs;trua, tertia denique annua. Quod &longs;pectat ad
men&longs;truam, nemo ferè ne&longs;cit, æ&longs;tum maximum e&longs;&longs;e in Plenilunio, medio
crem in Novilunio, minimum in Quadraturis; Quæro igitur ex te, vtrùm
in hac eadem hypothe&longs;i, ratio & cau&longs;a reddi po&longs;&longs;it huju&longs;modi varietatum.
Non e&longs;t dubium, quin po&longs;ita majore vi pre&longs;&longs;ionis, major ex
illa tumoris, vel elevationis effectus con&longs;equatur, nimirum cre&longs;cente cau
&longs;a, cre&longs;cit effectus; atqui in Plenilunio major pre&longs;&longs;ionis vis e&longs;t, quàm in
Novilunio; & in vtroque, quàm in Quadraturis; quia &longs;cilicet major vis
e&longs;t gravitationis ; hæc verò major, quia tunc aër longè gravior.
a&longs;&longs;eris, &longs;ub&longs;i&longs;tat; at, vt ingenuè dicam, non video, cur aër &longs;it gravior in
Plenilunio.
Aliquid fortè novi afferam; quod tamen cum reliquis experi
mentis, immo & principiis con&longs;entit; nempe certum e&longs;t circa Plenilu
nium omnibus corporibus &longs;pongio&longs;is & humidis, plus humoris & &longs;ucci
ine&longs;&longs;e; vt videre e&longs;t in ovis, cancris, medulla, cerebro, alii&longs;que corpori
bus, quibus humor facilè affunditur; Hæc profectò negari non po&longs;&longs;unt
ab iis, qui vel oculis in&longs;tructi &longs;unt; accedit, quod in corporibus appel
latis, non modò cre&longs;cit moles, &longs;ed etiam pondus, vt quivis probare pote
rit; quidni ergo longè plus humoris aëri circa Plenilunium in&longs;it, cùm aër
facilè humorem excipiat, divi&longs;um &longs;cilicet in perexiguas, quæque omnem
fugiant &longs;en&longs;um particulas. Humor autem aëri admixtus majus pondus
conciliat, vt &longs;uppono ex jactis &longs;upra principiis.
Immo etiam fortè major e&longs;t aquæ vis circa Plenilunium; hu
mor enim humori facilè admi&longs;cetur; quod licèt nunquam expertus &longs;im,
judico tamen probabile; licèt in parvis aquarum receptaculis &longs;en&longs;um
omné facilè fugiat; &longs;ecus in majoribus, vt in Mari; &longs;ed cùm
cerim, vix affirmare au&longs;im, licèt inaudierim in
reis &longs;ubterraneis,
Ita e&longs;t, apud Arelaten&longs;es aliquid &longs;imile e&longs;&longs;e dicunt, &longs;ub templo
Patrum S Franci&longs;ci de Paula; nempe illorum cœnobium &longs;itum e&longs;t extra
vrbem, in eo loco, quem Campum Eli&longs;ium vocant, in quo innumeri vi
dentur tumuli lapidei, &longs;eu potiùs cap&longs;æ, in crypta verò &longs;ub templo, &longs;unt
aliquot huju&longs;modi &longs;epulchra, in quorum vno paulo elatiore, aqua cre&longs;ce
re, ac decre&longs;cere dicitur, pro diver&longs;o Lunæ ad&longs;pectu; hoc non a&longs;&longs;ero, quia
periculum non feci; mihi tamen vrna illa o&longs;ten&longs;a e&longs;t, & hoc mihi ab illis
Patribus Vt vt &longs;it, cùm circa Plenilunium plus
cet exugunt, aëri quoque plus humoris ine&longs;&longs;e, nece&longs;&longs;e e&longs;t, cùm facillimè
tenuis humor ab illo exugatur.
Sed vnde amabò ille humor; an fortè Luna ex corporibus
illum educit, circa Plenilunium, tunc enim major illius vis e&longs;t.
Si Luna humorem illum educeret, inde certè corpora humi
da &longs;icciora manerent, vt patet ex terminis, & vt mole ita & pondere im
minuta; cùm tamen &longs;ecùs accidat.
Vnde procedat hic humor, cujus major vis ine&longs;t aëri, &longs;icuti aliis
corporibus, circa Plenilunium, ad præ&longs;entem effectum nihil facit, pro
quo &longs;atis e&longs;t, rem ita e&longs;&longs;e, à quacumque tandem cau&longs;a &longs;it; certum e&longs;t, ta
men, Lunam cau&longs;am e&longs;&longs;e, vel occa&longs;ionem, pro cujus &longs;cilicet diver&longs;o ad
&longs;pectu, humoris affu&longs;i diver&longs;a ratio e&longs;t.
Rem mihi grati&longs;&longs;imam feceris, &longs;i vel obiter &longs;altem indicâ
ris, quid &longs;entias de cau&longs;a illa; ni&longs;i enim fallor, fieri non pote&longs;t, quin aliquid
apud te &longs;tatueris.
Dicam, &longs;ed ex hypothe&longs;i ; &longs;upponamus, Lunam ex no&longs;tris ele
mentis con&longs;tare, ac præ&longs;ertim ex multo humore, longè no&longs;tro &longs;ubtiliore,
& puriore; nempe lympha no&longs;tra non e&longs;t pura, &longs;ed mixta ex aliis elemen
tis; quis &longs;cit, an aquæ illæ ibi &longs;int, quæ &longs;uper cœlos in &longs;acro textu e&longs;&longs;e
dicuntur; nullos tamen in iis pi&longs;ces e&longs;&longs;e putes, nulla animantium, aut
vegetantium &longs;emina; ibi enim fru&longs;tra e&longs;&longs;ent, cùm hæc propter hominem
&longs;int terre&longs;tris orbis incolam; Sol autem, vt agit in terram, ita & in Lu
nam, & caloris vi, multum humoris rarefacti educit; cùm enim &longs;ubtilior
&longs;it, longè faciliùs calore &longs;olvitur, educitúrque; hic porrò humor aëri ad
mixtus, caloris vi etiam vltra rare&longs;cit; donec tandem à Luna recedens,
in conum vmbræ terræ immergatur, vbi præ frigore, den&longs;atur, & pri&longs;ti
næ gravitati re&longs;tituitur; quia verò Luna versùs occa&longs;um interim non pa
rum deflectit, ille tractus aëris, cui prædictus humor admixtus e&longs;t, pro
pior terræ fit, quàm Lunæ, atque adeò, infra lineam dirimentem, versùs
ip&longs;am terram gravitat. Sed vt hoc clariùs explicetur, nonnihil &longs;chematis
adhibeo: Sit
po&longs;itus, &longs;ecundùm lineam LAK, erit Plenilunium; ac proinde
Lunaris globi BED &longs;olaribus radiis illu&longs;tratur, quorum vi, humor ex illo
educitur, &longs;ecundùm lineas eductas ex centro L, vt fit in globo terræ;
cùm pariter Luna globus totalis &longs;it: Cùm autem vmbram &longs;uam terra proji
ciat &longs;ecundum lineam AL, haud dubiè &longs;i Luna &longs;it in Nodis, &longs;eu in plano
Eclipticæ, in dictam vmbram immer&longs;a e&longs;t, &longs;ecus verò, &longs;i à dicto plano
ab&longs;it, & quia interea Luna ab L tran&longs;it in M, K, R, aëris tractus, cui prædictus
humor admixtus e&longs;t, paulò inde gravior redditus,
quam Lunæ, versùs terram tendit; vnde fit, vt redeunte Luna in L,
immer&longs;us,
tem
A ; ac
lineam KP, alia&longs;que à centro K ductas; vnde prædictus vapor longiùs
recedit à terra, ac proinde vbi Luna, orbe peracto, redit in K, licèt non
modica illius portio infra dirimentem de&longs;cenderit, minor tamen quàm an
te; quia versùs terram longè majus &longs;patium decurrendum fuit: hæc au
tem in terram circumquaque gravitat quidem, &longs;ed minùs; vnde minor
pre&longs;&longs;io; igitur minor æ&longs;tus. At verò po&longs;ita Luna in Quadraturis M & R,
&longs;uppono enim Solem in eodem loco; illu&longs;trantur Hemi&longs;phæria GIF,
STV; vnde po&longs;tquam Luna, peracto orbe, redit in M, aëris
tractus, cui admixtus e&longs;t eductus humor, per MI, alia&longs;que ductas à centro
M, propior e&longs;t Lunæ, quàm terræ; vnde in Lunam gravitat, & cùm Lu
na tendat ab M in K, ad illum aëris tractum ip&longs;a accedit; ac proinde ma
ximam educti humoris partem colligit; immò Luna exi&longs;tente in K, Sol fe
rè lineæ AS re&longs;pondet, vnde ille aëris tractus inter MK, cui eductus hu
mor admixtus e&longs;t, majori ex parte intra vmbram à Luna projectam jacet,
vnde &longs;tatim adden&longs;atur humor, & in ip&longs;am Lunam de&longs;cendit: Idem dico
de Luna po&longs;ita in altera Quadratura R ; humor enim educitur per RT,
alia&longs;que rectas ex centro R directas; cùm autem Lunæ motus &longs;it ab R in
L, humor per RT eductus recedit ab vmbra projecta ab vtroque globo;
vnde parum omninò den&longs;atur ; igitur etiam &longs;i terræ propior &longs;it, quàm Lu
næ, non tamen inde gravitatio cre&longs;cit; igitur neque pre&longs;&longs;io; igitur nec
æ&longs;tus: igitur inde conveniens; ni fallor, ratio redditur, cur plus humoris
in Quadraturis; in Novilunio demum minùs quidem quam in Plenilunio,
plus verò quam in Quadraturis.
nonnihil difficilè. Fingamus enim Lunam in L, vaporemque eductum
attolli &longs;ecundùm altitudinem LE, quem vocemus radium Atmo&longs;phæræ
Lunaris; erit prædictæ Atmo&longs;phæræ Hemi&longs;phærium BED; & in toto
illo orbe LMKR, æquale Hemi&longs;phærium, vt HGI, QNO, TVX fin
gendum e&longs;t. In Novilunio verò, Hemi&longs;phærium Atmo&longs;phæræ Lunaris
erit QPO, & in orbe illo diurno, TSX, BCD, HFI, in Quadratura
verò M, erit GIF, PQN, SXV, CDE, denique in Quadratura R, erit
STV, CBE, GHF, PON. Vnde &longs;equitur meo judicio, æqualem
&longs;empet e&longs;&longs;e humoris educti copiam circumfu&longs;am, ac proinde æqualem
gravitationem & pre&longs;&longs;ionem; igitur æqualem æ&longs;tum.
Fateor vltro æqualem ferè &longs;emper e&longs;&longs;e portionem humoris Lu
naris educti, admixtique aëris tractui intra Atmo&longs;phæram orbitæ Lunaris
contenti, &longs;ed hic parum den&longs;atur, ac proinde vix gravior evadit, ni&longs;i intra
vmbras ab alterutro globo projectas immergatur; neque hoc &longs;ufficit, ni&longs;i
gravior factus propior terræ &longs;it, quàm Lunæ; hoc autem circa Plenilunium
fieri con&longs;tat, in quo &longs;cilicet vmbra terræ projicitur qua&longs;i directè versùs Lu
nam; vnde magna humoris educti copia in dictam vmbram immergitur,
ac proinde den&longs;atur, & gravior evadit; Lunâ autem recedente ab L, ver
sùs M, & K, humor ille tandem propior terræ fit: quid mirum igitur, &longs;i
aër, cui admixtus e&longs;t magis in terram gravitet? Idem dico de Novilunio.
Vbi enim Luna ex K Novilunij puncto pervenit per R in L, Sol ferè li
neæ EC re&longs;pondet, vnde vtraque vmbra tum Lunæ, tum terræ projicitur
in illum aëris tractum, qui e&longs;t circa P, & cui eductus humor admixtus e&longs;t;
hinc valdè den&longs;atur & gravior fit, & cùm &longs;it propior terræ, ver&longs;us illam
tendit, de&longs;cenditque infra dirimentem: Si autem Luna ponatur in Quadra
tura M, vmbræ Lunæ ille aëris tractus, qui e&longs;t inter IO, & cui humor
eductus admixtus e&longs;t, &longs;tatim diuque immergitur, vt patet; &longs;ive vmbra pro
jecta &longs;it à Luna, Sole po&longs;ito inter QT, & Luna inter OI, &longs;ive ab ip&longs;a
terra, Sole &longs;ito paulò vltra R & Luna in K ; hinc den&longs;atur & gravior fit, &
cùm Luna tunc fit propior, in eam gravitat & tendit. Denique &longs;i Luna
ponatur in Quadratura R, ille aëris tractus, cui humor eductus admixtus
e&longs;t, vmbræ terræ immergitur, quando Sol pervenit ferè in M ; Sed tunc Lu
na e&longs;t circa K, igitur vicinior, igitur in Lunam gravitat; pari modo, So
le po&longs;ito inter IO, Luna verò inter QT, immergitur in vmbram Lu
næ; &longs;ed tunc etiam gravitat in Lunam, cui propior e&longs;t.
Rem hanc probè intelligo, & nihil clarius e&longs;&longs;e videtur; duo
tantùm ex te &longs;cire velim, immò tria; primum e&longs;t, vtrùm Sol æquali
ter agat in illud Hemi&longs;phærium Lunæ, quod illu&longs;trat, v.g.in BED, quan
do e&longs;t Plenilunium; Secundum e&longs;t, quid tandem fiat de humore illo ex
Luna educto, terri&longs;que illap&longs;o. Tertium vtrùm ip&longs;o Plenilunij die &longs;it ma
ximus æ&longs;tus, an paulò ante, &longs;eu po&longs;t
Ab hoc vltimo incipiam, in quo licèt varij &longs;int ij Autores, qui
de hoc argumento &longs;crip&longs;erunt, quorum aliqui maximam vim æ&longs;tus die 17.
Lunæ fieri volunt, quos arguit manife&longs;ta experientia; dico tamen etiam
iuxta præmi&longs;&longs;am hypothe&longs;im, in qua totam &longs;uperficiem globi aqueam e&longs;&longs;e
&longs;upponimus, maximam vim æ&longs;tus, &longs;eu quod idem e&longs;t, aquarum elevatio
nem, non fieri vbique in ip&longs;o Oppo&longs;itionis, &longs;eu Plenilunij puncto; &longs;ed tan
tùm in illo Meridiano, &longs;ub quo fit oppo&longs;itio, vel Plenilunium, idque per &longs;e,
& in præfata hypothe&longs;i ; nam ratione &longs;itus, accidere pote&longs;t, vt iis omnibus,
qui &longs;ub eodem Meridiano &longs;unt, eodem momento maximus æ&longs;tus non fiat,
de quo infra; dixi etiam per &longs;e; nam per accidens &longs;ecus erit, vt &longs;i ex ortiva
di&longs;ci Lunaris parte, plus humoris educatur, quàm ex occidua: & verò &longs;i
maculæ Lunares aquæ &longs;unt, quanquam diver&longs;æ à no&longs;tris, & &longs;ine pi&longs;cibus,
& virtute aliqua &longs;eminali, in parte ortiva longè plures & majores &longs;unt;
Vnde &longs;equitur plus humoris educi paulò po&longs;t Plenilunium, quàm ante;
quia Sol magis directè in eam partem Lunaris di&longs;ci agit, cui plus humoris
educendi ine&longs;t.
Ni fallor, apud aliquos Autores legi maximam vim
æ&longs;tus vno vel altero die, po&longs;t Plenilunium e&longs;&longs;e; quod rectè in hanc rem
Quadraret.
Legi&longs;ti haud dubiè; nam ad Diepam & alibi, vt Furnerius ob&longs;er
vat, &longs;ummum incrementum e&longs;t Die 17. Lunæ, biduo &longs;cilicet po&longs;t Plenilu
nij punctum; idem te&longs;tatur Cre&longs;centius lib. 3. Nautic. cap.2. idem Plin.
lib.2. cap.97. vbi habet, maximè fervere æ&longs;tum, non in plena, aut novi&longs;&longs;i
ma, &longs;ed po&longs;tea: alibi tamen, vt in ora Gallica, te&longs;te Scaligero, exercit.52.
cui &longs;ub&longs;crip&longs;it Furnerius lib.9.cap.21.in ip&longs;o Plenilunio maximè attollitur. Itaque ex diver&longs;o &longs;itu, hæc diver&longs;itas procedit; in præmi&longs;&longs;a tamen hypo
the&longs;i, eductoque vniformiter & æqualiter humore ex globo Lunari, ma
ximus æ&longs;tus fieret &longs;ub illo Meridiano, in quo fit Oppo&longs;itio; in aliis verò
punctis citiùs vel tardiùs; ortiva &longs;cilicet intra Quadrantem citiùs, occidua
verò tardiùs: ex illa verò hypothe&longs;i macularum Lunæ, quam tamen non
ad&longs;truo, haud dubiè maximus æ&longs;tus fieret po&longs;t Plenilunium, ob rationem
allatam. Sed jam ad &longs;ecundum tuum po&longs;tulatum re&longs;pondeo, mi Augu&longs;ti
ne, &longs;cilicet humorem illum, & facilè admi&longs;ceri no&longs;tris elementis, & facilè
ex iis educi; nec enim cum iis mixtum quodpiam componit: ac proinde non
mirum, &longs;i vt facilè educitur, atque avolat, ita facilè in Lunam redeat,
cùm &longs;cilicet immergitur in vmbram, &longs;ive à terre&longs;tri, &longs;ive à Lunari globo
projectam, & e&longs;t propior Lunæ, quàm terræ; in quo, meo judicio, nulla
e&longs;t difficultas, nec e&longs;t quod aliquis timeat, ne hic vapor in nubes concre
&longs;cat quia nubes contexi non po&longs;&longs;unt ni&longs;i ex halitu heterogeneo; hic autem
Lunatis vapor totus e&longs;t Homogeneus. Quod verò pertinet ad primum quæ
&longs;itum, dico Solem in eam globi Lunaris &longs;ectionem, &longs;eu portionem in quam
radij magis directi incidunt, fortiùs agere; v. g. plus agit in arcum EY,
quàm in YD, ita vt actio Solis in EY, &longs;it ad actionem in YD, vt Sinus re
ctus EY id e&longs;t LB, ad BD Sinum ver&longs;um arcus YD; & hoc in ip&longs;a &longs;e
ctione Lunæ; &longs;i enim accipiatur &longs;uperficies, actio in EY e&longs;t ad actionem
Quadrati BD & ex permutata Quadrati &longs;ub chorda arcus EY ad differen
tiam Quadrati &longs;ub chorda arcus ED, vel ex ratione Quadrati LB, ad Qua
dratum bD, plus bis rectangulum &longs;ub LbD, &longs;eu ad rectangulum &longs;ub bD,
& aD, & Lc. ad cE &c.
Non intelligo hæc Geometrica, tam enim jejunè illa pro
ponis; cùm tamèn ab&longs;tru&longs;as demon&longs;trationes contineant; vix ea curtim &
raptim indicata potiùs quàm expo&longs;ita qui&longs;quam mente capiat.
Suppono ea, quæ jam aliàs demon&longs;travi, &longs;cilicet circulum &longs;ub
radio, æquali chordæ, æqualem e&longs;&longs;e portioni &longs;uperficiei Sphæræ, quam
metitur, vel gignit arcus, cujus e&longs;t chorda, v. g. &longs;i accipiatur circulus &longs;ub
radio æquali chordæ &longs;ubten&longs;æ arcui EY, erit æqualis portioni &longs;uperficiei
Sphæræ,
hinc chorda &longs;ubten&longs;a arcui ED e&longs;t æqualis radio circuli æqualis &longs;uperficiei
Hemi&longs;phærij; demon&longs;tratum e&longs;t item, portionem &longs;uperficiei genitæ ab arcu
YE e&longs;&longs;e ad genitam ab arcu YD, vt Ec, ad cL; præterea lumina inci
dentia, per parallelas, &longs;unt vt ba&longs;es, &longs;i con&longs;iderentur in &longs;e; &longs;i verò con&longs;i
derentur in &longs;ubjecto, id e&longs;t in diver&longs;a &longs;uperficie, cui incidunt, &longs;i &longs;int
æqualia lumina, erunt in &longs;ubjecto, vt &longs;uperficies illu&longs;tratæ permutando; v.
g. &longs;i eadem vis, &longs;eu quantitas luminis, (&longs;ic enim vocare liceat) incidat in
&longs;uperficiem duplam alterius, erit lumen, vel luminis inten&longs;io &longs;uperficiei
duplæ ad aliam, vt 1.ad 2. Si verò &longs;uperficies &longs;unt æquales, &longs;ed lumina inæ
qualia, erunt inten&longs;iones, vt ip&longs;a lumina; &longs;i demum & &longs;uperficies inæqua
les &longs;unt, erunt inten&longs;iones in ratione compo&longs;ita luminum & &longs;uperficierum
permutando; jam applica.
Satis e&longs;t, probe intelligo; inde autem con&longs;tat, quod jam
&longs;ubindicare vi&longs;us es, vim Solis poti&longs;&longs;imum effectum habere circa Polum
Hemi&longs;phærij Lunaris ab eo illu&longs;trati, v. g. circa E, intra arcum Zy, vltra
verò versùs B & D parum valet; hinc etiam &longs;imilis ratio ducitur, cur Sol
Oriens vel Occidens, terræ &longs;uperficiem parum afficiat, plus verò de meri
die, plus demum, quò Sol propiùs ad punctum verticale accedit; hinc vis
debilior radij obliqui, non tantùm à radij reflexi carentia petenda e&longs;t; vt
aliqui faciunt.
Ex iis, quæ dicis, Antime, &longs;equeretur Lunaris di&longs;ci, vel
Hemi&longs;phærij extremitates, minùs &longs;plendidas & illu&longs;tratas videri; nul
lum tamen ego di&longs;crimen ob&longs;ervo; oculis autem meis magis credo, quàm
ve&longs;tris demon&longs;trationibus.
Demon&longs;tratio, Chry&longs;ocome, nunquam fallit, nec fallere pote&longs;t
&longs;tatue igitur oculum in A; Lunam, licèt Sphærica &longs;it, vt planum di&longs;cum
a&longs;picis, cujus diameter e&longs;t BD, paulò minor; & Ba, &longs;egmentum &longs;cilicet
apparentis Semidiametri, vides &longs;ub angulo BAa; aL verò &longs;ub angulo
aAL; &longs;ed ob parvitatem anguli BAL, qui vix e&longs;t 16.minutorum, anguli
&longs;ub quibus videntur &longs;egmenta aB, aL, &longs;unt vt ip&longs;a &longs;egmenta; igitur tanta
lux videtur in aB quanta in aL; quia in eadem ratione videtur contra
ctior, in qua primùm incidit di&longs;tractior; vt enim rem in plano tantùm,
pter di&longs;tantiam &longs;ecare arcum EB in Z, cùm lux incidens in &longs;e
gmentum aB, & incidens in &longs;egmentum aL, &longs;it æquè inten&longs;a; inci
dentis verò in BZ inten&longs;io; &longs;it ad inten&longs;ionem incidentis in ZE, vt
aB, ad al, & cùm tota incidens in ZB, videatur contracta in aB;
haud dubiè æquè inten&longs;a videbitur; & perinde atque &longs;i reverà incideret in
rectam Bl: &longs;ecus autem accideret, &longs;i in arcum BZ directè radij vi&longs;uales
inciderent.
BZ profectos, à recta Ba profici&longs;ci; vnde opticè transfertur totum, id
quod ine&longs;t BZ, in rectam Ba; &longs;ed in BZ tota illa luminis quantitas vi
detur, quæ, &longs;i radij liberum tran&longs;itum nacti e&longs;&longs;ent, ip&longs;i Ba incidi&longs;&longs;et; &longs;cio,
ex his multa optica, eaque præclara deduci, v.g. cur flamma procul &longs;pe
ctata minùs candida appareat; cur Mars, dum minor apparet, candidior
&longs;it; aliaque huju&longs;modi, quæ ad Opticam ac præ&longs;ertim rem colorum perti
nent; &longs;ed his omi&longs;&longs;is, vt ad rem no&longs;tram veniam, quæro à te, vtrùm reverà
in Novilunio major æ&longs;tus &longs;it, quàm in Plenilunio.
Quibu&longs;dam in locis major e&longs;&longs;e dicitur in Novilunio; &longs;ecus ve
rò in aliis, idque vt plurimùm in Plenilunio; quod vel ex majore humoris
affu&longs;i copia rectè deducitur: & verò iuxta præmi&longs;&longs;am hypothe&longs;im, nihil &longs;u
per hoc definiri pote&longs;t, ni&longs;i fortè ex &longs;uperiore aver&longs;oque Lunæ Hemi&longs;phæ
rio, plùs vel minùs humoris educatur; minùs autem educi videtur, tum
quia minùs terris affunditur, tum quia ex libratione Lunæ apparet, gran
diores maculas in aver&longs;o Hemi&longs;phærio non e&longs;&longs;e; cùm demum ex fideli&longs;&longs;imâ
omnium peritorum artis nauticæ relatione, maxima vis æ&longs;tus in Plenilu
nio e&longs;&longs;e dicatur, his, meo &longs;altem judicio &longs;tandum e&longs;t, quod reverà &longs;i &longs;uppo
natur, ad præmi&longs;&longs;a principia facilè reducitur: &longs;ed expectabam, Augu&longs;tine,
vt quædam fortè &longs;ingularia ex iis, quæ diximus, pro ea qua vales ingenij
&longs;agacitate deduceres.
Multa quidem animo volvi atque revolvi, &longs;ed vix temerè me
committere au&longs;us &longs;um, ne the&longs;es meas ludibrio exponerem; non dubito ta
men, cùm hæc dicas, quin aliquid occurrat tibi &longs;citu dignum, quapropter
te etiam atque etiam rogo, vt nobis illud participare digneris.
Illud &longs;anè te minimè effugi&longs;&longs;et; &longs;ed ad meas nugas non
adeò &longs;edulò mentem applicas, quin circa alia longè fortè graviora
ver&longs;eris.
Non ita res profectò &longs;e habet, &longs;ed cùm res i&longs;tæ tuæ novæ mi
hi accidant, vix eas primò intuitu mente complector; quomodò igitur,
quid ex iis nece&longs;&longs;aria con&longs;ecutione &longs;equatur, videre po&longs;&longs;em? Mon&longs;tra quæ&longs;o
viam;
Illud inprimis &longs;equi videtur, aëra &longs;cilicet infimæ hujus regionis
e&longs;&longs;e compre&longs;&longs;um vi ponderis innitentis.
Quodnam pondus intelligis?
An fortè Carte&longs;ij &longs;ententiam
ad&longs;truis, qúi volebat à præter labente Luna aëra terram inter & Lunam in
terjectum comprimi?
Ab&longs;it, vt hoc dicam; licet enim fortè tantula compre&longs;&longs;io in Lunari
Atmo&longs;phæra fiat, non tamen ad nos v&longs;que
&longs;ione majoris bombardæ, ex qua circumfu&longs;i aëris compre&longs;&longs;io &longs;equitur, quæ
tamen ad modicam di&longs;tantiam producitur; intelligo igitur de ip&longs;ius aëris
pondere; vt enim aquæ pondus aëra in fontibus illis artefactis, quos &longs;æpè
videritis, contentum, comprimit, quidni pondus &longs;uperioris aëris alium
comprimat? cogita Cylindrum plumbeum tantæ altitudinis, quanta opus
e&longs;t, vt tanti ponderis vi, versùs ba&longs;im &longs;ub&longs;idat, ac dilatetur; multò magis
&longs;i columnam ceream, vel ex butyro, aut charta erectam, maximæ &longs;cilicet
altitudinis tibi ante oculos ponas; &longs;ub&longs;idet enim pars inferior, quanquam
inæqualiter, erunt enim pre&longs;&longs;iones, vt altitudines, nimirum vt pondera;
quidni ergo aër, qui certè dilatari nequit, vt butyrum, nec enim locus e&longs;t,
&longs;ed tantùm comprimi, innitentis ponderis vi comprimatur? cùm perinde
&longs;it, ex quacumque tandem materia pondus con&longs;tet, & mille aëris libræ eun
dem effectum gravitando habeant, quem totidem aquæ, vel alterius mate
riæ libræ haberent.
Sentiremus haud dubiè ingens illud pondus, nec ferendo pa
res e&longs;&longs;emus.
An fortè &longs;entiunt vrinatores immer&longs;i ingens aquæ pondus
illorum capiti &longs;uperfu&longs;um? Minimè verò; immò &longs;entire non debent, cùm
præcipuus corporis gravitantis, liquidi &longs;cilicet, effectus &longs;it corpus
&longs;ubjectum levius non deor&longs;um, at &longs;ur&longs;um extrudere; &longs;ic aqua in li
gnum immer&longs;um gravitat; equidem aqua in fundum va&longs;is lignei gravitat,
deor&longs;umque pellit, &longs;i aër &longs;ubtus e&longs;t, vt patet, & &longs;imile pondus aquæ, ma
nus foramini in fundo dicti va&longs;is appo&longs;ita &longs;entiret, modò manus foramen
adæquaret: at &longs;i lignum vel corpus levius aquæ immergatur, in id aqua
ita gravitat, vt illud &longs;ur&longs;um extrudat, non verò deprimat deor&longs;um; &longs;i ve
rò &longs;it gravius aqua, ex parte &longs;altem illud &longs;u&longs;tentat, vnde appen&longs;um in
aqua, minùs illius pondus &longs;entitur: ab illo igitur periculo immunes &longs;umus,
nec timendum nobis e&longs;t, ne ab aëre obruamur: at ni fallor, ex præmi&longs;&longs;a
gravitatione longè latéque aëris &longs;uperfu&longs;i, &longs;equitur egregium illud experi
mentum Mercurij in tubo vitreo contenti, & immer&longs;a alterius illius ex
tremitate, in &longs;ubjectum Mercurium, &longs;cutella contentum; &longs;u&longs;tinetur enim ad
duos pedes altitudinis paulò plus reliquo tubo vacuo pror&longs;us manente, ab
aëris gravitantis Cylindro.
De hoc argumento in hoc congre&longs;&longs;u agere non po&longs;&longs;umus, cùm
&longs;ufficiens alterius materia e&longs;&longs;e queat; in quo præclari&longs;&longs;ima & &longs;anè mirifica
phænomena explicabimus & demon&longs;trabimus, quæ tum ab aliis, tum
à nobis explorata fuerunt; illud vnum vel obiter indica&longs;&longs;e &longs;ufficiat, &longs;cilicet
experimentum illud nullo modo cum à te præmi&longs;&longs;a hypothe&longs;i con&longs;entire;
quod ni fallor per&longs;picuè demon&longs;tro. Sit enim di&longs;tantia Lunæ à terra 50.
Semidiametrorum terræ & Semidiameter terræ iuxta vulgarem calculum
&longs;it pa&longs;&longs;uum Geometricorum 3436363. quem numerum &longs;i ducas in 25.
quæ e&longs;t &longs;emidi&longs;tantia à terra &longs;cilicet ad lineam dirimentem, de qua &longs;upra
venient 86909075. pa&longs;&longs;us, hæc e&longs;t altitudo aëris gravitantis ; &longs;i autem
gravitatem e&longs;&longs;e ad gravitatem aëris non vt 400.ad 1.vt non nemo voluit,
&longs;ed vt 1000. ad 1. dividatur vltimus numerus per 1000. quotiens veniet
rejecta minutia, 434544. igitur Cylindrus aëris prædictæ altitudinis adæ
quabit pondere Cylindrum aquæ altum pedes 434544. Sit autem aqua ad
Mercurium, ad &longs;ummum, vt 1.ad 15. prædictus Cylindrus aëris adæquabit
pondere Cylindrum Mercurij altum pedes 28969. quomodo igitur, duos
tantum pedes altum adæquat & &longs;u&longs;tinet?
Rectè omnino; hoc enim confirmat illorum &longs;ententiam,
qui volunt Mercurium &longs;u&longs;tineri ab aëre compre&longs;&longs;o, cuius vis tanta e&longs;t, vt
Mercurij Cylindrum 2.pedes altum adæquet.
Hoc etiam dici non pote&longs;t, cùm enim aëris compre&longs;&longs;i vis per
Cylindres æqualibus ba&longs;ibus non exeratur, &longs;icuti exeritur vis aëris gravi
tantis, certè quo major e&longs;&longs;et ba&longs;is tubi vitrei, eo minor e&longs;&longs;e deberet altitudo
Mercurij ab aëre compre&longs;&longs;o &longs;u&longs;tentati; alia igitur ratio e&longs;t & cau&longs;a, quæ di
ctum Mercurium &longs;u&longs;tinet.
Maxima igitur aëris no&longs;tri compre&longs;&longs;io e&longs;&longs;et ab illa imma
nis ponderis vi proveniens, ac proinde vix nobis toleranda; & vereor, vt
per illam re&longs;pirare, vt aiunt, aut ducere anhelitum liceret.
Modica pror&longs;us illa vis e&longs;t; & jam olim Galileus, pro &longs;ummo,
quo pollebat, ingenio, ob&longs;ervavit vim percu&longs;&longs;ionis infinitam propemo
dùm rationem habere ad vim gravitationis ; quod facilè probabis, vel vni
co ictu mallei, in glandem plumbeam impacti; illa enim ictus vi depre&longs;&longs;a
ita dilatatur, vt &longs;imilis effectus vix ab immani ponderis gravitantis mole
obtineri po&longs;&longs;it; omitto rationes phy&longs;icas, alioquin pulcherimas, ne à pro
po&longs;ito fine longiùs declinem; admitto igitur inferiorem aëris tractum pau
lò compre&longs;&longs;iorem e&longs;&longs;e, ac proinde parùm admodùm aut certè nihil ducen
do anhelitui obe&longs;&longs;e: licèt enim Thorax inde paulò difficiliùs explicetur,
nonnihil tamen compen&longs;ationis ex eo fieri videtur, quod intra pulmones
explicatos faciliùs adducatur, cùm jam &longs;ponte &longs;ua eò tendat, tum ratione
gravitationis, tum ratione compre&longs;&longs;ionis, pari modo licèt aëris expul&longs;io
ni præfata compre&longs;&longs;io tantulum ob&longs;it, re&longs;i&longs;tit enim aër compre&longs;&longs;us; aliun
de tamen aër compre&longs;&longs;us ambiens thoracem, eju&longs;dem contractionem ju
vat; hinc etiam aliqua fit compen&longs;atio: prætereà e&longs;to, aër compre&longs;&longs;us tan
tulum impediat præfatam naturæ functionem; alia pariter alias impediunt;
hinc motu ip&longs;o defatigamur.
ex Ari&longs;totele, nullum &longs;cilicet animal, ni&longs;i æ&longs;tu recedente expirare; quod
inter fabulas referebam; nunc verò hujus dicti aliqua ratio affulget; nem
pe cùm accedente æ&longs;tu &longs;it minor aëris gravitatio, ac proinde minor illius
pre&longs;&longs;io; contrà verò recedente; inde fit, re&longs;pirationem faciliorem e&longs;&longs;e, ac
ce&longs;&longs;us, quàm rece&longs;&longs;us tempore; cùm autem moribundi tantùm non vi
vant, & re&longs;pirandi pote&longs;tas in iis tantùm non extincta &longs;it; accedente mi
nimo illo impedimento, quod à compre&longs;&longs;ione aëris provenit, eo tempore,
&longs;altem vt plurimùm, vitæ &longs;imul & anhelitus filum rumpitur.
Nihil potuit meliùs applicari, & facilè crediderim ex hac do
ctrina, non pauca Medicos in rem &longs;uam derivare po&longs;&longs;e in prædicendo ægro
rum animam agentium tran&longs;itu.
Vnum e&longs;t, ne quid di&longs;&longs;imulem, à me lectum, apud celeberri
mum illum Hydrographiæ &longs;criptorem Furnerium lib.9.cap.1.plus humo
ris &longs;cilicet ine&longs;&longs;e corporibus eo tempore, quo mare per æ&longs;tum intume&longs;cit;
minùs verò tempore refluxus, vt vocant; illud autem, ita mihi difficilè vi
detur, vt huic nodo &longs;olvendo impar &longs;im.
Ex præmi&longs;&longs;is principiis non adeò difficilè mihi videtur;
cùm enim maximus æ&longs;tus &longs;it in Plenilunio, & tunc multus humor Lunari
effluvio terris affundatur; quid mirum, &longs;i quo tempore maximus æ&longs;tus e&longs;t,
corpora multo humore abundent.
Propo&longs;itæ à me difficultatis vim non capis; nec enim agi
tur de ip&longs;o æ&longs;tu Plenilunij, &longs;ed de quolibet alio. Et verò in Plenilunio fit
refluxus, quo tempore minùs humoris corporibus ine&longs;t, & in Quadratu
ris etiam fit æ&longs;tus; & tunc corporibus multus humor ine&longs;t: &longs;i nobis non
&longs;uccurras, Antime, animum de&longs;pondeo; ni&longs;i fortè rem ip&longs;am in dubium
voces.
In dubium revocanda non e&longs;t; is enim non e&longs;t Furnerius, qui
aliis imponat; & verò miror à vobis non videri, ex præmi&longs;&longs;is principiis
hoc ip&longs;um &longs;equi: nempe in eo loco, in quo fit æ&longs;tus, aër minùs compre&longs;
&longs;us e&longs;t, quia minùs gravitat, vt jam diximus, nec repetendum e&longs;&longs;e du
xerim, &longs;i autem e&longs;t minùs compre&longs;&longs;us, minùs gravis e&longs;t, vt patet ex
terminis; corpus enim den&longs;um &longs;eu compre&longs;&longs;um gravius evadit; igi
tur Lunatis ille humor admixtus difficiliùs, aut tardius a&longs;cendit;
quo enim medium gravius e&longs;t, corpus leve eò faciliùs &longs;ur&longs;um ex
truditur; at verò tempore refluxus aër magis gravitat, in eum &longs;ci
licet tractum, in quo refluxus e&longs;t, igitur aër compre&longs;&longs;ior gravior
evadit; quid mirum igitur, &longs;i Lunaris humor &longs;ur&longs;um faciliùs extrudatur? igitur tempore æ&longs;tus &longs;eu fluxus plus humoris ine&longs;t, minùs verò, tempore
refluxus.
Libenter mihi &longs;uccen&longs;erem, qui rem ob oculos po&longs;itam non
viderim; illud &longs;altem video ex dictis con&longs;tare, quæ & quanta &longs;it Lunæ
vis in corpora &longs;ublunaria; multi enim effectus, in ægris præ&longs;ertim corpo
ribus ob&longs;ervantut, qui à celeberrimis Medicis Galenum &longs;ecutis Lunæ tri
buuntur; quid porrò Luna conferat, non vt cau&longs;a, &longs;ed vt &longs;ubjectum & oc
ca&longs;io, patet ex dictis huiu&longs;que; &longs;c licet majorem vel minorem humoris
vim, majorem item vel minorem aëris compre&longs;&longs;ionem, gravitatem, levita
tem, gravitationem; quid etiam in malè affectis corporibus cuncta hæc
præ&longs;tare po&longs;&longs;int nemo non videt; quid ad hæc diver&longs;i Lunæ a&longs;pectus, im
mò & fortè diver&longs;us Lunarium macularum &longs;itus, &longs;i fortè vt nonnullis vi
&longs;um e&longs;t, aqua &longs;it, à no&longs;tra tamen diver&longs;a; quid denique deliquium Solis
vel Lunæ conferat ad diver&longs;as in &longs;ublunaribus corporibus mutationes; im
mò quid conus vmbræ ab vtroque globo projectæ, pro vario &longs;itu; nempe
vapor Lunatis immer&longs;us vmbræ, den&longs;atur & gravior evadit, ferturque
mer&longs;a vapor non educitur, vnde nova in &longs;iccitatis aut humoris vi muta
tio &longs;equitur, immò & minor æ&longs;tus diebus, qui deinde &longs;equuntur; quia &longs;ci
licet totus ille humor de&longs;ideratur, qui toto Lunaris deliquij tempore So
lis vi eductus fui&longs;&longs;et.
Vnum omittis, quod certè dignum &longs;citu e&longs;t; &longs;it enim lagenula
quæpiam A, ex cuius ventre a&longs;&longs;urgat &longs;ur&longs;um
canaliculus GF ad in&longs;tar ro&longs;tri; impleatur aqua
&longs;it què &longs;uprema &longs;uperficies aquæ BC, per cana
liculum a&longs;turgit &longs;upra libellam CD ; an fortè eo
tempore, quo tumet æ&longs;tus, id e&longs;t, quo Luna e&longs;t
in Meridiano; minùs a&longs;&longs;urgit
verò, puta in F, eo tempore quo à Meridiano 90.
gradibus di&longs;tat.
Rem magnam narras, Antime; &longs;ed fortè fabulam narras,
cuipiam haud ab&longs;imilis, qui aquam Marinam in canaliculo contentam flu
xum & refluxum pati a&longs;&longs;erebat.
Seriò loquor, in his enim religioni ducerem, tibi alii&longs;que tui
&longs;imilibus imponere: &longs;ed miror à te non videri; totum hoc ex præmi&longs;&longs;a do
ctrina &longs;equi; nempe aër in hoc infimo tractu compre&longs;&longs;us, vt dixi, premit
&longs;uperficiem aquæ BC ; &longs;ed cùm &longs;uperficiem D minùs premat, quid mirum,
&longs;i pre&longs;&longs;io in BC prævaleat? Minùs autem premitur &longs;uperficies D, quàm
CF; quia compre&longs;&longs;um corpus exerit &longs;uam vim quoquo versùm per om
nes lineas, v.g. centrum ba&longs;is BC, aër &longs;uperfu&longs;us per omnes lineas premit,
contentas intra conum maximè obtu&longs;um, & ba&longs;im D, per lineas contentas
intra conum valdè acutum; quid mirum igitur, &longs;i pre&longs;&longs;io in BC &longs;uperet
pre&longs;&longs;ionem in D, ac proinde aqua a&longs;&longs;urgat.
Nunquid hoc tribui non po&longs;&longs;et Cylindro aëris gravitanti
in ba&longs;im BC, qui longè gravior e&longs;t Cylindro gravitante in ba&longs;im D ; &longs;unt
enim Cylindri ; vt ba&longs;es.
Nullo modo, nempe &longs;i habeatur ratio gravitatior.
is, non
a&longs;cendit aqua &longs;upra D ; quia gravitatio in perpendicularibus parallelis
accipienda e&longs;t; neque in hoc vlla e&longs;t difficultas; cum &longs;it primum qua&longs;i
principium Hydraulicæ, aquarum
attenta &longs;cilicet dumtaxat aquæ gravitate, &longs;ecus tamen res &longs;
bientis pre&longs;&longs;io accedat; in hoc quippe gravitatio à pre&longs;&longs;ione di&longs;fert, quod
hæc in Sphæram agat; ac proinde in idem punctum pre&longs;&longs;æ &longs;uperficiei per
lineas infinitas ad illud idem punctum terminatas, illa verò per lineas
parallelas deor&longs;um; ac proinde in idem punctum &longs;uperficiei vna tantùm
linea gravitationis cadat; vnde ratio petitur propter quam Cylindrus
major aquæ BG attollere minorem GD &longs;upra D non po&longs;&longs;it. Porrò ex te
&longs;cire velim, Antimo, vtrùm in refluxu aqua altiùs a&longs;&longs;urgat quam in fluxu
per canaliculum GF.
Omnia ferè complecti vi&longs;us es, & &longs;ingularem aëris compre&longs;&longs;i
effectum per&longs;picuè di&longs;tinxi&longs;ti ab ip&longs;o ni&longs;u gravitationis ; &longs;i vel vnum ver-
co; aër in æ&longs;tu &longs;eu fluxu e&longs;t minùs compre&longs;&longs;us; in refluxu verò compre&longs;
&longs;ior; quid mirum ergo fi compre&longs;&longs;ior majorem vim & ni&longs;um exerat, &
fortè attollat aquam in F ; minùs verò compre&longs;&longs;us in E; dixi fortè; quia
nondum periculum feci; faciam tamen brevi; quanquam &longs;i res non &longs;uc
cedat, non propterea phy&longs;ica ratio deerit.
Igitur pariter in Plenilunio altiùs a&longs;&longs;urget aqua; quia tunc
aër gravior e&longs;t; igitur compre&longs;&longs;ior.
Gravior e&longs;t, vltrò concedo, quia multus humor admixtus; igi
tur compre&longs;&longs;ior, nego con&longs;equentiam; quia illud non comprimitur, ra
tione cujus gravior e&longs;t; cùm tamen &longs;ecus accidat, quàndo gravior e&longs;t, ra
tione altioris Cylindri: Vt vt &longs;it, in Plenilunio differentiá altitudinis aquæ
ob&longs;ervare non potui, &longs;altem quæ &longs;ub &longs;en&longs;um cadat; &longs;i forte ab aliquo dein
ceps ob&longs;ervetur, ex jactis principiis ratio in promptu e&longs;t. Hîc autem aliud
experimentum omittere non po&longs;&longs;um, quod dictam hypothe&longs;im æquè con
firmat; Sit vas ABG, cui tantulùm Mercurij in&longs;it, cujus &longs;uperficies EF ;
fit tubus vitreus Mercurio plenus, admotoque ori digito, inver&longs;us im
mergatur in Mercurium va&longs;e contentum; &longs;ubducto digito, ruit cum impe
tu magna pars Mercurij tubo contenti, cujus tamen portio CI &longs;u&longs;pen&longs;a
manet; fui&longs;&longs;e autem ob&longs;ervatum aiunt, Luna exi&longs;tente in Meridiano,
Mercurij &longs;uperficiem infra C deprimi: di&longs;tante verò à Meridiano 90. grad.
&longs;upra C attolli; modica fortè vtrimque differentia; hoc experimentum, &longs;i
verum e&longs;&longs;et, omnino evinceret æ&longs;tus cau&longs;am ab aliqua aëris pre&longs;&longs;ione, cui
Luna occa&longs;ionem præbeat, petendam e&longs;&longs;e.
Immò evinceret Cylindrum Mercurij ab aëre extrin&longs;eco
in &longs;uperficiem Mercurij EI gravitante &longs;u&longs;tineri, quod tamen ante negare
vi&longs;us es.
Crede mihi, Augu&longs;tine, primò a&longs;pectu ita e&longs;&longs;e videtur; rem
tamen penitiùs & accuratiùs in&longs;picienti &longs;ecus e&longs;&longs;e videbitur; hîc tantùm
obiter indico; plus humoris ine&longs;&longs;e &longs;ublunaribus corporibus tempore flu-
tio petitur, &longs;i tamen verus e&longs;t, de quo aliàs.
Huc potiùs accer&longs;erem diver&longs;am pre&longs;&longs;ionem; hæc enim mi
nor e&longs;t in fluxu, in refluxu major ; quid mirum igitur &longs;i in fluxu Mercurij
&longs;uperficies minùs, in refluxu altiùs &longs;upra C attollatur, premit enim aër
compre&longs;&longs;us &longs;uperficiem Mercurij EF.
Vel ex hoc conjicere poteris, quàm fallax &longs;it vnum experimen
tum, & quàm facilè in errorem inducat, ni&longs;i ab aliis experimentis corri
gatur; con&longs;ulenda e&longs;t igitur tota experimentorum collectio, vt error vi
tetur, quod maximè in hoc ca&longs;u locum habet; Si enim vas A impleas
Mercurio, non jam vt ante aqua, a&longs;&longs;urgit in E
vel F, per canaliculum, &longs;ed infra D &longs;ub&longs;idit: plu
ra de hoc argumento non dicam, quod reverà
adeò &longs;ingulare e&longs;t & amplum, vt &longs;ingularem con
gre&longs;&longs;um po&longs;tulet; eò igitur vos remitto, præ&longs;er
tim cùm vix tempus &longs;uppetat ad reliqua pro&longs;e
quenda, quæ ad &longs;u&longs;ceptum de Marino æ&longs;tu argu
mentum pertinent.
Optimè mones, in proximum congre&longs;&longs;um remittamus,
vt ea quæ re&longs;tant de maris æ&longs;tu pro&longs;equamur; de quo, ni fallor, illa
omnia diligenter expo&longs;ui&longs;ti; quæ in præmi&longs;&longs;a hypothe&longs;i fierent, &longs;uppo&longs;ita
&longs;cilicet tota &longs;uperficie aquea, quæ ad diurnam & men&longs;truam mutationem
pertinent: duo re&longs;tant, opinor, primum ad mutationem annuam &longs;pectat,
quæ fit in punctis anni cardinalibus, vt vocant, nimirum in Æquinoctiis
& Sol&longs;titiis; alterum verò vt ex jactis principiis explices, varias æ&longs;tuum
mutationes, quæ in diver&longs;is globi terraquei locis ob&longs;ervantur; &longs;uppo&longs;ita
&longs;cilicet, ea globi &longs;uperficie, quæ modò e&longs;t.
Pri
mò, Luna exi&longs;tente in Æquatore, maxima e&longs;&longs;et elevatio aquarum iis, qui
&longs;unt &longs;ub Æquatore, minima &longs;ub Polis; major autem vel minor pro majore
vel minore loci a&longs;&longs;umpti di&longs;tantia ab Æquatore; e&longs;&longs;et autem diurnus æ&longs;tus
æqualis nocturno. Secundò, Luna exi&longs;tente in Tropico Cancri, minor
e&longs;&longs;et æ&longs;tus, quàm ante, iis, qui &longs;unt &longs;ub Æquatore;
lis nocturno; iis verò, qui &longs;unt in Latitudine Boreali vltra Tropicum Can
cri, diurnum majorem haberent, quàm ante, minorem verò nocturnum;
& vici&longs;&longs;im ij, qui &longs;unt in Latitudine Au&longs;trali, majorem nocturnum,
diurnum; & permutatis vicibus, exi&longs;tente Luna in Tropico Capricorni, i&longs;ti
majorem diurnum, minorem nocturnum, illi verò nocturnum majorem,
diurnum minorem: Porrò ad vitandam appellationum confu&longs;ionem, il
lum æ&longs;tum diurnum appello, qui fit die Lunari, id e&longs;t Luna in Meridiano
&longs;upra horizontem exi&longs;tente. Tertiò, Quod pertinet ad alia loca inter Æqua
torem & Tropicos &longs;ita, &longs;ervata proportione, æ&longs;tus major aut minor definiri
pote&longs;t, vt major &longs;it iis diurnus æ&longs;tus, ad quorum verticem Luna propiùs
accedit. Quartò, Linea ab&longs;idum per centrum terræ &longs;emper ducitur, & cùm
bit planum circuli; at verò extra Æquatorem de&longs;cribit &longs;uperficiem coni
acutioris, vel obtu&longs;ioris, pro majore vel minore Lunæ di&longs;tantia ab Æqua
tore. Quintò, Maxima depre&longs;&longs;io in eo circulo &longs;emper e&longs;t, in cujus planum,
& centrum, linea ab&longs;idum perpendiculariter cadit. Sextò, Diver&longs;am quoque
mutationem inducere pote&longs;t diver&longs;us gradus caloris in aëre; nempe aër ca
lidior, rarior e&longs;t & levior, frigidior verò; den&longs;ior & gravior, unde varij ef
fectus gravitationis, pre&longs;&longs;ionis, Lunatis humoris, motus, &c. Hinc fortè il
lud, quod à nonnullis ad&longs;truitur, cum veritate con&longs;entit; &longs;cilicet majores
cieri æ&longs;tus Luna in Aquarij Signo &longs;ita; quia Luna in Plenilunio, in quo ma
jor æ&longs;tus con&longs;ideratur, &longs;i e&longs;t in Aquario, Sol, cui opponitur, e&longs;t in Leone,
tunc igitur maximè ardet æ&longs;tus ; aër igitur valdè calidus e&longs;t; igitur rarus &
levis, vnde majore cum impre&longs;&longs;ione, aër Superior, humorque Lunaris gra
vitant in inferiorem tractum; &longs;ed hoc parum profectò, aut nihil ju
vat; nec cum obfervationibus con&longs;entit; & quam vis dici po&longs;&longs;it, va
rietatem, quæ ex diver&longs;is ob&longs;ervationibus habetur, ad diver&longs;um ter
ra tum tractum reduci po&longs;&longs;e; quia tamen non tantùm aër calidus, qui
ad terras proximè accedit con&longs;ideratur, nec is, qui prædicto climati re
&longs;pondet, &longs;ed is totus quantus quantus e&longs;t, qui versùs terræ centrum gravi
tat, nulla fortè inde mutatio induci videtur. Hæc &longs;unt, ni fallor, quæ
&longs;tando in præmi&longs;&longs;a hypothe&longs;i, de mutationibus, quæ per annum fiunt in
Marino æ&longs;tu, dici po&longs;&longs;unt. Alterum re&longs;tat, quod fortè paulò difficilioris
e&longs;t operæ.
Duo &longs;uggero, quæ mihi veniunt in mentem; primum
e&longs;t, inter effectus diver&longs;æ & inæqualis gravitationis aëris, recen&longs;eri
po&longs;&longs;e ventum illum, qui cum æ&longs;tu conjunctus e&longs;t, levis quidem, &longs;en&longs;ibi
lis tamen, vbi &longs;cilicet montium obices non ob&longs;tant, nec aliæ cau
&longs;æ ob&longs;unt, ab ortu versùs occa&longs;um, de quo dubium e&longs;&longs;e nequit,
cùm longè faciliùs navigetur versùs occa&longs;um, quàm ver&longs;us ortum; cùm
enim aër, Luna in Meridiano po&longs;ita, &longs;it minùs pre&longs;&longs;us, haud dubiè le
vior e&longs;t; igitur ab alio, qui versùs ortum e&longs;t, vtpote graviore extruditur;
accedit, quòd altior e&longs;t aër in O, quàm in F ; (
de&longs;cendere pote&longs;t.
Sed cur potiùs aër, qui e&longs;t in O, de&longs;cendet in F, ab ortu &longs;cili
cet ad occa&longs;um, quà is, qui e&longs;t in N, versùs ortum; cùm eadem vtriu&longs;que
&longs;it pre&longs;&longs;io, gravitas, altitudo.
Rem haud dubiè hoc argumento conficeres, &longs;i Luna
immota in I &longs;emper e&longs;&longs;et, &longs;ed admi&longs;&longs;o illius motu versùs S aër N le
vius redditur, & aër O gravius; quid mirum ergo, &longs;i O prævaleat? Alterum fortè altioris indaginis e&longs;&longs;et; obiter tamen indicabo: nem
pe varij Autores referunt, vatias inundationes accidi&longs;&longs;e eo tempore,
quo varij Planetæ Conjuncti erant; cujus ratio ex præmi&longs;&longs;is facilè,
meo judicio, deducitur; Sit enim Luna I in principio Arietis, So
li conjuncta; Sint etiam Mercurius, Venus, Mars ibi conjuncti; ad-
de &longs;is Iovem; haud dubiè linea AS ad maximam di&longs;tantiam producendæ
erit, antequam incidat in aliam lineam dirimentem re&longs;pectu alterius cu
ju&longs;libet globi totalis; vnde major erit circulus maximæ pre&longs;&longs;ionis, vt &longs;u
pra vocabas, Antime; igitur major illius vis atque pre&longs;&longs;io, igitur major
aquæ tumor; major igitur inundatio; vt tamen de &longs;ingulis &longs;eor&longs;im aliquid
definiatur; varius terrarum &longs;itus con&longs;iderandus e&longs;t; & hoc e&longs;t alterum ca
put, Antime, quod tibi explicandum re&longs;tat.
Egregia pror&longs;us ob&longs;ervatio; inde enim per&longs;picua & qua&longs;i pal
pabilis cau&longs;a & ratio multorum effectuum &longs;tatuitur, qui vulgò virtutibus
occultis tribuuntur; &longs;ed vt pen&longs;um impo&longs;itum per&longs;olvam, terre&longs;tris globi
Plani&longs;phærium ve&longs;tris oculis &longs;ubjicio, & antequam oculos in globum
conjiciaris, nonnulla &longs;uppono ex præmi&longs;&longs;is. Primò, Vim pre&longs;&longs;ionis, quæ
tum à circulo maximæ pre&longs;&longs;ionis, vt &longs;upra appellavi, tum ab aliis paral
lelis procedit, ita variari, ac perturbari po&longs;&longs;e, vt diver&longs;um æ&longs;tus effectum
producat, etiam &longs;ub eodem Parallelo; variatur autem &longs;eu perturbatur ex
eo quod terre&longs;tris globi &longs;uperficies tota aquea non &longs;it, &longs;ed partim aquea
partim continens; nempe arcus ille circuli pre&longs;&longs;ionis, cui continens &longs;ub
e&longs;t, nullum pre&longs;&longs;ionis effectum con&longs;equitur, reliquo tamen eju&longs;dem circuli
arcu, cui aqua &longs;ube&longs;t, effectum præ&longs;tante; brevitatis ergo, hunc arcum
vtilem vocemus; illum verò inutilem. Secundò, Non tantùm vim pre&longs;
&longs;ionis con&longs;iderandam e&longs;&longs;e, quatenus e&longs;t ab vno arcu, &longs;ed quatenus e&longs;t etiam
ab aliis; ita vt ab illo commuai qua&longs;i ni&longs;u aqua elevari cen&longs;eatur, quæ re-
pienda e&longs;t, vt aqua à circulo maximæ pre&longs;&longs;ionis ad punctum maximæ ele
vationis excurrat, totumque illud &longs;patium conficiat, &longs;ed vt pars aquæ aliam
partem pellat, & hæc aliam; cogita ve&longs;icam aqua plenam, quam vel ma
nu, vel fune in &longs;piras acto &longs;tringis, ac proinde temporis ferè momento tu
mor attollitur, quod certè per motum obtineri non po&longs;&longs;et. Tertiò, per
motum aquam elevatam versùs litus excurrere, & aver&longs;is ire fluminibus,
ad in&longs;tar majoris cuju&longs;dam dolij; vbi enim litore altior e&longs;t, in litus exun
dat; idem dico de &longs;uprema fluminum &longs;uperficie: & hæc e&longs;t ratio cur
aqua, per æ&longs;tum exundet, quia cum prædictæ pre&longs;&longs;ionis vi, etiam ver
sùs oram & litus extollatur, in litus ip&longs;um, quod inferius e&longs;t, & in &longs;ub
jacentis fluminis alveum excurrit, &longs;ublata verò pre&longs;&longs;ione, aqua illa,
quæ priùs exundarat in litus, cum &longs;it altius ip&longs;a maris, po&longs;tquam detu
muit, &longs;uperficie, versùs ip&longs;um mare refluit. Quartò, Majorem arcum
vtilem plùs, minorem verò minùs præ&longs;tare; præ&longs;ertim cùm &longs;uo modo
accedat ratio vectis, &longs;icuti brevior baculus difficiliùs curvatur, quàm
longior; hinc major arcus minorem &longs;uperat, & major &longs;uperficies aquæ
ex præ&longs;atis arcubus con&longs;tans vincit minorem ex arcubus etiam con&longs;tan
tem; &longs;unt autem huju&longs;modi arcus paralleli circulo maximæ pre&longs;&longs;ionis;
& cum in &longs;ingulis punctis circuli vtilis, æqualis pre&longs;&longs;io cen&longs;eatur, inæ
qualitas pre&longs;&longs;ionis directæ accipienda e&longs;t in arcubus ad angulos rectos
&longs;ecantibus prædictos pre&longs;&longs;ionum arcus. Quintò, Suppono ad aquam extru
dendam, per angu&longs;tiorem alveum, &longs;eu canalem, minorem pre&longs;&longs;ionis vim de
&longs;iderari, vt con&longs;tat ex doctrina motuum; nempe major mobilis, &longs;eu moven
di corporis moles motui magis re&longs;i&longs;tit.
Cuncta hæc &longs;atis intelligo; &longs;tatuo enim globum i&longs;tum in
&longs;itu Sphæræ rectæ; ita vt axis & poli &longs;int in plano horizontis; a&longs;&longs;um
ptoque &longs;upremo globi puncto, &longs;eu vertice, illius horizon, qui per Po
los de&longs;cribitur, e&longs;tque vnus ex Meridianis & di&longs;tat à puncto a&longs;&longs;umpto
90. grad. circulus maximæ pre&longs;&longs;ionis erit, cui &longs;i omnes parallelos acci
piam, omnes circulos pre&longs;&longs;ionum habeo, & probè di&longs;tinguo arcus
vtiles ab inutilibus, & portionem &longs;uperficiei ab vtilibus rectam, &longs;eu
occupatam, ab alia; quæ profectò quantum varia &longs;it, cùm hinc expli
cetur, illinc contrahatur, inde versùs Ortum, hinc versùs Boream ex
currat &longs;atis patet. Vt autem majoris, vel minoris vim definiam, ratio
ne &longs;cilicet puncti a&longs;&longs;umpti, initio ducto ab horizonte, &longs;eu circulo ma
ximæ pre&longs;&longs;ionis, con&longs;idero ac metior &longs;uperficiem vtilem
co, quam arcus vtiles occupant) pro cujus diver&longs;o &longs;itu, & diver
&longs;a exten&longs;ione, diver&longs;a &longs;equitur pre&longs;&longs;io & elevatio in puncto a&longs;&longs;um
pto Æquatoris; Hoc &longs;at benè intelligo; vellem tantùm, vt illud quod
vltimo loco ad&longs;truxi&longs;ti, de aqua in angu&longs;tias redacta paulò fu&longs;iùs ex
plicares.
Per me licet; &longs;upponamus ita extrudi per canalem ADH.
vt altitudo alvei pleni &longs;it AC, latitudo verò initio &longs;it AB, &longs;ed qui
retenta eadem altitudine, contrahatur &longs;ecundùm latitudinem, ac proin-
alij demon&longs;trarunt velocitatem aquæ in AB ad velocitatem aquæ in HK
&longs;uppo&longs;ita eadem vi motrice, e&longs;&longs;e vt HE ad AD, id e&longs;t vt HK ad AB, id
e&longs;t in ratione latitudinum permutando, &longs;i verò decre&longs;cat etiam altitu
do, ita vt altitudo in HK, &longs;it HI, velocitas in AB e&longs;t ad velocita
tem in HK, vt HF, ad AD vel in compo&longs;ita latitudinum & altitu
dinum permutando; hoc inquam jam alij demon&longs;trarunt; cùm enim
tota aqua fluat per planum AD, & per planum HE, quæ ad in&longs;tar duo
rum foraminum con&longs;iderare po&longs;&longs;umus, &longs;uppo&longs;ita &longs;emper eadem vi motri
ce, haud dubiè velociùs fluere debet per HE, quàm per AD, idque in ea
proportione, in qua AD major e&longs;t quàm HE; in hoc nulla e&longs;t difficultas,
& omnibus congruit experimentis; hinc aqua quæ &longs;ur&longs;um extruditur, di
latatur, quæ verò &longs;ua &longs;ponte de&longs;cendit, contrahitur; quia hæc motu acce
lerato, illa retardato fertur.
Hoc &longs;æpè miratus &longs;um in filo labentis olei, quod certè ad hunc
effectum aptius e&longs;t, quàm aqua, propter vliginem; contrahitur enim & ex
tenuatur filum illud; &longs;ed rem grati&longs;&longs;imam faceres, &longs;i demon&longs;trares in qua
proportione contrahatur.
Hoc jam alij demon&longs;trarunt; quia tamen nihil e&longs;t, quod tibi
negare au&longs;im ; &longs;upponamus e&longs;&longs;e vas CB, in cujus
fundo &longs;it foramen CD, accipiatur quæcunque
altitudo puta CF, &longs;it quælibet Semiparabola
AFH, &longs;ub axe FA, ducanturque applicatæ CE,
FH; in Parabola &longs;i accipiatur motus accelera
tus, axis erit &longs;patium, applicatæ verò tem
pus & velocitas; igitur &longs;patium acqui&longs;itum
tempore CE erit ad acqui&longs;itum tempore FH,
vt AC ad AF, &longs;unt enim &longs;patia, vt tempo
rum Quadrata; igitur velocitas aquæ in CD
erit ad velocitatem in FG vt CE ad FH,
&longs;ed tran&longs;itus aquæ &longs;unt vt velocitates, per
mutando, vt jam dixi &longs;upra; igitur vt FH
ad CE, ita circulus CD ad circulum FH; igitur &longs;i vt Diameter CD
ad FG, ita hæc, ad K, erit vt FH, ad CE, ita CD ad K. &longs;it vt
media proportionalis N, erit vt FH ad CE, vel CD ad M, ita AF ad
AC; igitur AF e&longs;t ad AC in ratione quadruplicata CD ad FG, id e&longs;t,
vt CD ad M, facilè autem invenitur FG, quia vt FH ad CE, ita CD,
quam habeo ad K ; inter K & D invenio mediam proportionalem FG ;
item inter K & M &longs;cilicet N. Sed hæc &longs;ufficiant, jam ad &longs;u&longs;ceptum pro
po&longs;itum redeo, & quia omnia &longs;ingularia explicari non po&longs;&longs;unt; fru&longs;tra
enim id fieret, mihi &longs;atis e&longs;&longs;e videtur, &longs;i vnum vel alterum &longs;ingulare ex
ponam. Accipio igitur punctum in Æquatore 345. longitudinis, vt vi
des in globo; cum circa illum tractum, celeberrimus ille fluvius, quem
Amazonum vocant, ex Orientali Americæ ora in mare influat, & maxi
mum &longs;tatis horis patiatur æ&longs;tum, qui ad 300. milliaria per alveum flu
minis a&longs;cendit; huic tractui Luna oritur in Meridiano longitudinis 75. &
tunc maxima e&longs;t pre&longs;&longs;io circa tractum longitudinis 545. quæ &longs;en&longs;im ver
sùs Ortum decre&longs;cit; quid mirum ergo, &longs;i versùs oram Guineæ ad Afri
cam, mare intume&longs;cat? Vbi præ&longs;ertim Luna per 30. gradus versùs occa&longs;um
progre&longs;&longs;a e&longs;t, vbi verò tandem pervenit ad grad. 345. tunc ibi maxima
e&longs;t aquarum elevatio; & quia longè ante aqua a&longs;&longs;urgere cœpit, ab eo
&longs;cilicet momento, quo à grad.75. Luna occa&longs;um versùs progre&longs;&longs;a e&longs;t, quid
mirum &longs;i a&longs;&longs;urgens aqua in apertum & &longs;atis directum fluminis alveum ex
currat? In quem tamdiu excurrit; quamdiu a&longs;&longs;urgit aqua ad illam oram;
hæc autem tamdiu a&longs;&longs;urgit, quamdiu pre&longs;&longs;io decre&longs;cit; hæc demum tam
diu decre&longs;cit, quamdiu Luna ad Meridianum longit.745. accedit; vbi
enim Meridianum illum attingit, maxima e&longs;t aquarum elevatio, nec vltra
pre&longs;&longs;io decre&longs;cit; &longs;ed deinde cre&longs;cit pre&longs;&longs;io, progrediente ad occa&longs;um Lu
na, idque continuè donec perveniat ad nonage&longs;imum inde gradum, id
e&longs;t, ad longitud. grad. 255. hinc refluit aqua, non modò proprio acta
pondere, &longs;ed accedente majore vi pre&longs;&longs;ionis &longs;ollicitata, idque, quam
diu pre&longs;&longs;io cre&longs;cit, vnde per &longs;e tamdiu fluxus durat, quamdiu refluxus,
& hoc vt plurimum fieri &longs;olet, licet per accidens alter altero diuturnior &longs;it,
de quo infra præterea progrediente Luna à gradu 255. ad 165. in hoc
puncto erit maxima elevatio; igitur circulus maximæ pre&longs;&longs;ionis &longs;ecabit
Æquatorem in punctis 255. & 75. vt patet, at in ii&longs;dem punctis circulus
maximæ pre&longs;&longs;ionis Æquatorem &longs;ecabat, quando Luna erat in gradu 345.
igitur in eodem tractu maxima e&longs;t aquarum elevatio; &longs;en&longs;im enim ibi a&longs;
&longs;urgit aqua, vbi &longs;en&longs;im pre&longs;&longs;io decre&longs;cit; igitur dum Luna à puncto 255.ad
punctum 165. progreditur, cre&longs;cit æ&longs;tus ad prædictam oram, & in fluminis
alveum intrat. Denique peracto circulo Luna redit ad grad.75. & tunc e&longs;t
maxima pre&longs;&longs;io in dicto tractu 345. Vides quàm facilè cuncta hæc ex præ
mi&longs;&longs;is deducta præfato tractui applicentur.
Duo mihi occurrunt difficilia; primùm e&longs;t, &longs;ita Luna in gradu
longit. 345. circulum maximæ pre&longs;&longs;ionis Meridianum illum e&longs;&longs;e, qui
Æquatorem &longs;ecat in grad. 255. ac proinde per medium qua&longs;i mare paci
ficum ducitur; licèt autem hujus maris pre&longs;&longs;io aliquem effectum habere
po&longs;&longs;it, non tamen vllam vim derivare pote&longs;t in oram maritimam,
tractus ob&longs;tet; &longs;ecat etiam Æquatorem in grad. Longit.75. Sed hic locus
non mari &longs;ed terris incubat, ducitur enim per mediam ferè Æthiopiam
& Africam ab Au&longs;tro in Boream; igitur cùm mare non premat, nullus in
de pre&longs;&longs;ionis effectus &longs;equitur.
Antequam ad &longs;ecundam difficultatem orationem convertas,
hæc quam expo&longs;ui&longs;ti, mihi priùs &longs;olvenda e&longs;t; & fateor, vel nullam, vel
minimam pre&longs;&longs;ionis vim à &longs;emicirculo maximæ pre&longs;&longs;ionis per mare pa
cificum ducto, ad grad Longit.255.ad o&longs;tia præfati fluminis traduci, pro
pter interjectum continentis Americæ impedimentum; dixi vel mini
mam, quia negari non pote&longs;t, traduci aliquam tum versùs Au&longs;trum per
freta Magellanicum, Marium &c. tum versùs Septentrionem per freta
Davi&longs;ium, Hud&longs;onium &c. Fateor etiam minimam vim traduci ad præfa
ta o&longs;tia à &longs;emicirculo ortivo maximæ pre&longs;&longs;ionis Æquatorem &longs;ecante ad
grad Longit.75. cùm major illius pars &longs;it inutilis, arcus verò vtiles hinc
versùs Septentrionem, indèversùs Au&longs;trum, à promontorio, quod bo
næ Spei vocant, excurrant, cùm tamen vis pre&longs;&longs;ionis non tantùm &longs;it
à prædicto circulo maximo, &longs;ed etiam ab aliis minoribus parallelis,
prædictæ elevationis ad illa o&longs;tia plu&longs;quam &longs;ufficientem cau&longs;am ha
bemus.
Cur verò ad 300. milliaria per alveum fluminis æ&longs;tus a&longs;
cendit? cùm tamen ad oram Guineæ oppo&longs;itam longè minus a&longs;cendat:
& hæc e&longs;t altera difficultas.
Ex illo communi pre&longs;&longs;ionis ni&longs;u, motus quidam mixtus vel
eju&longs;dem motus linea re&longs;ultat, &longs;ecundùm quam æ&longs;tus in oram excurrit; cùm
igitur circuli pre&longs;&longs;ionum, qui mari Atlantico incumbunt, aquam attol
lant extrudantque qua&longs;i versùs Au&longs;trum, ac proinde versùs Borealem
Americæ oram; circuli verò qui Æthiopicum premunt, extrudant aquam
per fauces illas inter Bra&longs;iliam & Africam interceptas, versùs Caurum;
ex vtroque ni&longs;u, mixtus quidam re&longs;ultat ver&longs;us Libycum, ac proinde in
o&longs;tia præfati fluminis, qua&longs;i directè incidit æ&longs;tus; Quid mirum igitur, &longs;i
longiùs excurrat? accedit quod fluminis alveus per 10. integros gradus
id e&longs;t 600.milliaria, qua&longs;i &longs;ecundùm rectam lineam versùs Libycum fer
tur; quod reverà plurimùm confert ad hoc, vt æ&longs;tus per dictum alveum
longius excurrat: At verò ad oram Guineæ licèt rapidi&longs;&longs;imus æ&longs;tus a&longs;
&longs;urgat torrentis ad in&longs;tar, quia in prædictam oram ad Au&longs;trum conver
&longs;am, versùs Boream extru&longs;us qua&longs;i directè fertur; non tamen per alveum
fluminum longè excurrit, cùm nec &longs;int capaces alvei, nec &longs;ecundùm di
rectam lineam eant, neque, vt vides in hoc globo, Guinea magnos flu
vios habeat; equidem ad 7. grad. Latit. Au&longs;tralis magnus fluvius Zaire in
Oceanum influit, &longs;ed à 6. gradu ad promontorium bonæ Spei perexiguus
æ&longs;tus e&longs;t; præterquam quòd linea æ&longs;tus in eo tractu; (&longs;ic deinceps appel
labo) tendit ad Vulturnum, vel Euronotum; vnde valdè obliquè in oram
illabitur; non mirum igitur &longs;i potiùs præterfluat, quàm irrumpat. Vnum
omi&longs;eram, &longs;cilicet, Oceanum Æthiopicum in iis faucibus, quas in
coërceri, vnde intume&longs;cat a&longs;&longs;urgatque cum impetu, nece&longs;&longs;e e&longs;t, adver
sùs oppo&longs;itam &longs;ibi, qua&longs;i aggerem, Guineæ oram.
Non e&longs;t dubium, quin æ&longs;tus linea ad tem hanc multùm, ne
dicam totum conferat; nondum tamen &longs;atis capio, vnde & quomodò
hæc linea &longs;tatuatur potiùs quàm alia; hac enim &longs;emel &longs;uppo&longs;ita, inde
facilè deducam, vtrùm magnus, an parvus æ&longs;tus &longs;it, in data quali
bet ora.
Rem acu tetigi&longs;ti; hæc enim linea æ&longs;tus, &longs;eu cur&longs;us
quem &longs;i paulò vehementior &longs;it & contractior, Eurippum vocant, ab ea
dem cau&longs;a procedit, à qua æ&longs;tus ip&longs;e, vel aquarum elevatio; &longs;cilicet ab in
æquali aëris pre&longs;&longs;ione, & inæquali ni&longs;u; itaque ex pluribus capitibus hæc
linea æ&longs;tus determinari pote&longs;t. Primò, in præmi&longs;&longs;a hypothe&longs;i &longs;olus e&longs;&longs;et
aquarum motus ab ortu in occa&longs;um, vt jam &longs;upra dictum e&longs;t; nempe ille
idem pre&longs;&longs;ionis ni&longs;us &longs;emper duraret, & tantus e&longs;&longs;et aquarum tumor,
&longs;ub vno Meridiano, quantus &longs;ub alio, &longs;ub eodem &longs;cilicet Parallelo; at
po&longs;ita tali &longs;uperficie terræ qualis modò e&longs;t, in &longs;ingulis ferè punctis eju&longs;
dem Paralleli, mutatur ni&longs;us; quia mutatur illius cau&longs;a; diver&longs;a e&longs;t enim
arcuum vtilium ratio; hinc diver&longs;a linea &longs;equitur; &longs;i enim æqualis &longs;it
ni&longs;us ab Au&longs;tro; Aquilone & Ortu, & minor, aut nullus ab occa&longs;u, in
occa&longs;um linea motus ibit; &longs;i æqualis ab Au&longs;tro, Occa&longs;u & Ortu, & mi
nor in Aquilone, ad Aquilonem ibit; atque ita de aliis; & cùm infinitæ
&longs;int combinationes ni&longs;uum, vt &longs;unt infinitæ diver&longs;arum pre&longs;&longs;ionum,
etiam &longs;ub eodem Parallelo, quia infinitæ-mutationes &longs;uperficierum
ex arcubus vtilibus con&longs;tantium, tum in magnitudine, tum in &longs;itu,
inde &longs;equitur infinitas e&longs;&longs;e po&longs;&longs;e, ac reverà e&longs;&longs;e lineas æ&longs;tus, quæ ex
diver&longs;o ni&longs;u na&longs;cuntur: Primum igitur caput, ex quo talis linea &longs;tatui
tur, e&longs;t talis ratio ni&longs;us, &longs;eu pre&longs;&longs;ionis. Secundò à quibu&longs;dam locorum
angu&longs;tiis petitur, &longs;eu maris &longs;eu freti, quod &longs;ecundùm talem vel talem
lineam excurrit; cùm enim aqua pre&longs;&longs;ionis vi extrudatur, & continen
tis vtrimque aggeres aquam contineant, quid mirum, &longs;i per freta
currat, atque adeò ab alveo freti linea æ&longs;tus determinetur. Tertiò, Si
vtrimque vis pre&longs;&longs;ionis in vtrumque freti o&longs;tium aquam intrudat, in
tra fretum æ&longs;tus concurrent. Quartò, quando æ&longs;tus valdè obliquè in
cidit in aliquam oram, non reflectitur, &longs;ed ip&longs;am oram præterlabitur;
immò &longs;i ip&longs;a hora ad modum &longs;inus cavi e&longs;t, æ&longs;tus &longs;emiorbe peracto, ver
sùs eam partem, vnde venerat, declinat; hinc mutatio lineæ: ad hoc ca
put revoca reflexionem. Quintò, Æ&longs;tus alterius maris ex angu&longs;tis fauci
bus erumpens, & in alium incidens, lineam mutat; nempe ex vtroque qui
dam motus mixtus re&longs;ultat, ac proinde nova linea.
Cuncta hæc in rem hanc optimè quadrant: quare nihil aliud
re&longs;tat, ni&longs;i vt fidelis & accurata Marini æ&longs;tus hi&longs;toria de&longs;cribatur, vt &longs;cia
mus quænam &longs;it linea æ&longs;tus in qualibet ora; Tu verò me tibi &longs;ummopere
ob&longs;tringeres, &longs;i aliquot exempla breviter afferres, quibus ea, quæ dixi&longs;ti,
meliùs con&longs;tarent.
Prædicta hi&longs;toria ad rem hanc maximè opportuna, immò &
nece&longs;&longs;aria e&longs;&longs;et, in qua tamen à rei Nauticæ Scriptoribus nonnulli de&longs;i
dera&longs;&longs;ent, vt &longs;altem in præcipuis Oceani oris fideliter retuli&longs;&longs;ent de ma
ris æ&longs;tu; Primo quàm altus. Secundo quantum excurrat; Tertio quamdiu
a&longs;&longs;urgat; Quarto quamdiu refluat; Quinto quâ horâ &longs;ummus æ&longs;tus &longs;it. Sexto quo die &longs;ynodalis periodi, maxima in æ&longs;tu aquarum elevatio, & quo
die minima; Septimo, quo anni Plenilunio aut Novilunio &longs;it maximus
æ&longs;tus. Octavo, quænam &longs;it æ&longs;tus linea, quæ fortè &longs;ingulis diebus tantulum
mutatur; mutatur enim pre&longs;&longs;ionis ratio, quia mutantur &longs;uperficies ex ar
cubus vtilibus con&longs;tantes; hi porrò mutantur; quia mutatur ab&longs;idum linea,
cuncta hæc in qualibet ora ob&longs;ervanda e&longs;&longs;ent.
Tuæ &longs;ententiæ omnino &longs;ub&longs;cribo, & hæc eadem in præfatis
Hi&longs;toricis de&longs;iderarem; &longs;ed quæ&longs;o te, &longs;i me amas, profer aliquot exempla,
quæ tibi haud dubiè memoria &longs;uggeret.
Hujus globi a&longs;pectus nonnulla fortè in memoriam mihi revo
cabit. Primo loco circa polum vnum occurrit; ad &longs;ummum enim pro
montorium Finnomarchiæ currit Eurippus à Cauro &longs;cilicet versùs Eu
ronotum &longs;eu Vulturnum ; &longs;unt enim angu&longs;tiæ maris inter Nieulandiam &
Groelandiam, per quas mare facilè extruditur vi pre&longs;&longs;ionis, tum Oceani
Tartarici, tum illius qui Americam Septentrionalem alluit, nec non ver
sùs dictam oram per dictam lineam pellitur. Secundo, A pulchra In&longs;ula,
quæ novæ Franciæ Borealis e&longs;t, ad fretum Davi&longs;ium, à medio Iulio ad fi
nem Augu&longs;ti; linea æ&longs;tus tendit ad Au&longs;trum, reliquo tempore ad Occa&longs;um,
quo æ&longs;tus in &longs;inum S. Laurentij irrumpit; ratio e&longs;t, quia men&longs;e Augu&longs;to
glacies maris congelati liquatæ &longs;unt, ac proinde liberè fluunt, aquæ ex
freti Davi&longs;ij & Hud&longs;onij angu&longs;tiis versùs Vulturnum ; itémque ex iis quæ
&longs;unt Fri&longs;landiam inter & continentem Groelandiæ in Libycum; item ex
iis quæ &longs;unt inter Fri&longs;landiam & I&longs;landriam in Vulturnum ; ex iis demum,
quæ &longs;unt inter I&longs;landiam & Britannicas in&longs;ulas in occa&longs;um, &longs;eu Zephyro
Libycum; igitur motu quodam mixto in Au&longs;trum æ&longs;tus currit, cùm tamen
reliquis men&longs;ibus, concreto mari glaciali ex prioribus angu&longs;tiis æ&longs;tus vix
currat, &longs;ed liberè tantùm in occa&longs;um feratur; ob&longs;tant enim in&longs;ulæ Britan
nicæ, ne in Au&longs;trum eat, ac proinde in &longs;inum S. Laurentij inde apertum &longs;u
beat; cùm tamen ex prædictorum fretorum aqua erumpens æ&longs;tum à
prædicto &longs;inu S. Laurentij facilè amoveret. Tertiò, Inter promontorium
floridæ & Havanam Cubæ Eurippus versùs ortum veloci&longs;&longs;imè currit,
non tantùm propter multa flumina, quæ in &longs;inum Mexicanum intrant; &longs;ed
quia aqua pre&longs;&longs;a circa Antillas, qua&longs;i circuitu facto, vi pre&longs;&longs;ionis, per
fretum versùs ortum extruditur. Et verò versùs Antillas & Mexicanum
&longs;inum æ&longs;tus obliquè incidit, per lineam quæ ad Libycum
parum attollitur, & frangitur illius vis ab innumeris ferè in&longs;ulis; quæ
circa o&longs;tia prædicti &longs;inus qua&longs;i totidem aggeres &longs;itæ &longs;unt; addo etiam
præfatum &longs;inum innumeris in&longs;ulis &longs;eminatum e&longs;&longs;e, quæ tum pre&longs;&longs;io
nem, tum æ&longs;tum impediunt. Velociter autem prædictus Eurippus
fluit, quia per angu&longs;tum alveum magnum aquæ pondus aquam velo
debi&longs;que quam cito per canalem applicatum aqua erumpat.
Hoc&longs;æpè probavi, & hæc veri&longs;lima cau&longs;a e&longs;t pernici&longs;&longs;imi
Euripporum motus, &longs;eu cur&longs;us; immo lu&longs;i aliquando hoc experimento,
plenum aqua tubum cylindricum, di&longs;co æreo apprimè tubi o&longs;tio appo&longs;ito,
ex cujus centro angu&longs;tus canaliculus a&longs;&longs;urgebat, tantulùm premebam,
& aqua per dictum canaliculum pernici&longs;&longs;imè a&longs;&longs;urgebat erumpebatque;
vellem autem &longs;cire proportionem velocitatis, de&longs;cen&longs;um inter operculi,
& erumpentis aquæ a&longs;cen&longs;um.
Velocitates &longs;unt vt ba&longs;es permutando; cùm enim illa tota por
tio extru&longs;æ aquæ per canaliculum tran&longs;eat, &longs;ub&longs;idente interim operculo,
motus operculi in tubo e&longs;t ad motum aquæ in canaliculo, vt ba&longs;is canali
culi ad ba&longs;im cubi, neque in hoc e&longs;t difficultas.
Satis e&longs;t; optimè capio: alia difficultas occurrit; &longs;upra di
xeras, ni fallor, geminos æ&longs;tus concurrere in fretis &longs;upra appellatis; quo
modò igitur fieri pote&longs;t, vt ex angu&longs;tiis, quæ ex dictis fretis &longs;ubjiciuntur
æ&longs;tus in Vulturnum eat.
Bellè; Linea fluxus versùs Caurum in dictis angu&longs;tiis, & fre
to Hud&longs;on, in freto Davi&longs;io versùs Septentrionem tendit; at verò linea
refluxus, in freto Davi&longs;io versùs Au&longs;trum, in Hud&longs;onio & dictis faucibus
in. Vulturnum ; &longs;ed ad propo&longs;itum redeo.
Quartò, igitur à maris tractu in
ter Fortunatas & He&longs;peridum in&longs;ulas interjecto, æ&longs;tus currit versùs Oc
ca&longs;um, nempe in eam partem mare curvatur ad in&longs;tar &longs;inus immen&longs;i; &longs;ed
versùs &longs;inuum extremitates vt plurimùm mare currit: ratio ex præmi&longs;&longs;is
principiis nece&longs;&longs;ariò &longs;equitur; cùm enim &longs;inus versùs extremitates con
trahantur, aut &longs;altem contractiores &longs;int eo maris tractu, ex quo &longs;uo modo
na&longs;cuntur &longs;inus, arcus pre&longs;&longs;ionum &longs;inui minores, reliquo tractui majores
incumbunt; quid mirum ergo, &longs;i prævaleant i&longs;ti, & aqua illuc versùs ex
tremum &longs;inum extrudatur? Finge &longs;inum e&longs;&longs;e fretum, &longs;ed ob&longs;tructum;
inde quoque &longs;equitur, motu velociore extrudi, quando &longs;inus e&longs;t longè
contractior; hinc magnus æ&longs;tus in &longs;inu Gangetico, Per&longs;ico, Arabico, in
quo longè major e&longs;&longs;et, cùm maxima vi mare ab ortu eò feratur, ni&longs;i ab
In&longs;ulis circa illius o&longs;tia &longs;itis, itemque ab angu&longs;ti&longs;&longs;imo aditu, vis æ&longs;tus fran
geretur; ad de &longs;is &longs;inum Adriaticum, in quo versùs extremitatem æ&longs;tus non
minimus e&longs;t, extra Quadraturas, propter rationem expo&longs;itam, quæ maxi
mè hîc locum habet.
Sed quæ&longs;o te, cur etiam in mari Mediterraneo, quod maxi
mi &longs;inus ad in&longs;tar e&longs;t, æ&longs;tus non attollitur.
Equidem Oceani æ&longs;tus per Gaditanum fretum influit, remi&longs;
&longs;ior tamen; quia cùm versùs Cæciam linea æ&longs;tus huic oræ illap&longs;i eat,
valdè obliquè in o&longs;tra freti incidit; vnde valdè remittitur, atque adeò in
oram Syriæ oppo&longs;itam vix traducitur; traducitur tamen, & &longs;en&longs;u perci
pitur in Novilunio & Plenilunio; licèt verò mare mediterraneum longi&longs;
&longs;imum &longs;it, quia tamen multis in&longs;ulis interrumpitur, & ab occa&longs;u in ortum
recta excurrit, & æqualis ferè e&longs;t illius latitudo, arcus pre&longs;&longs;ionum in eo
prævalet &longs;upra aliam, igitur nullus æ&longs;tus; is enim; qui e&longs;t ad oram Syriæ
minimus quidem, &longs;ed jam olim à Phænicibus ob&longs;ervatus; item ad oram
Provinciæ, vt Scaliger ip&longs;e ob&longs;ervavit, ab Oceano per fretum Gaditanum
traducitur, non certè motu &longs;ed pre&longs;&longs;ionis vi, at verò cùm in &longs;inu Adriati
co arcus pre&longs;&longs;ionum longè minores &longs;int, quàm in reliquo mari, quid mi
rum &longs;i æ&longs;tus in eo fiat, effectus &longs;cilicet nece&longs;&longs;arius inæqualis pre&longs;&longs;ionis? mi
nor tamen propter angu&longs;tias o&longs;tij, & Corcyram ad prædictum o&longs;tium &longs;i
tam, in qua vis æ&longs;tus frangitur; item in Africæ ora prædicto maris Adtia
tici o&longs;tio, &longs;ecundum eundem Meridianum, è regione oppo&longs;ita; ibi enim
mediocris &longs;altem æ&longs;tus attollitur; nempe ibi mare &longs;e&longs;e explicat, & versùs
Africam qua&longs;i in &longs;inum lunatur; item in reliqua ora Africæ versùs Tune
tum, in quam vis æ&longs;tus per fretum traducta à Balearibus & Sardinia ad Bo
ream &longs;itis coërcita, impingitur; æ&longs;tus porrò ad dictam oram Africæ a&longs;&longs;ur
gentis jam olim meminit S. Augu&longs;tinus.
Sed vnde quæ&longs;o Eurippus ille mirabilis in freto Siculo, de quo
multi multa?
Certum e&longs;t, rapidum illum motum e&longs;&longs;e ab æ&longs;tu; quia cum
motu Lunæ omnino con&longs;entit; & verò vis æ&longs;tus per Gaditanum traducta,
à Balearibus & Sardinia coërcita, & ab angu&longs;tiis illius tractus maris qui
inter Africam & occiduum promontorium Siciliæ interjacet impedita,
immo ab ip&longs;a Sicilia repre&longs;&longs;a, declinat tantulùm versùs fauces freti Siculi,
in cujus angu&longs;tiis aqua velociùs currit, proptèr rationem &longs;upra explicatam;
&longs;imiliter in &longs;inum Tarentinum æ&longs;tus a&longs;cendit propter eandem rationem;
ad Ravennam item & Aquileiam; quia &longs;itæ &longs;unt versùs extremum &longs;inum; ad
oram Dalmatiæ, ab&longs;que tumore, aqua &longs;ur&longs;um versùs extremum &longs;inum ire vi
detur; ad oppo&longs;itam verò Italiæ oram ver&longs;us o&longs;tium & fauces de&longs;cendere;
&longs;ed hic motus, &longs;i tamen veritati con&longs;entit, vel ab æ&longs;tu diver&longs;us e&longs;t, vel ex eo
procedit, quod æ&longs;tus in fauc&etail;s &longs;inûs irrumpat per
dit; & cùm &longs;inus ab extremo faucium collo, declinet &longs;ini&longs;tror&longs;um versùs
Caurum, motus etiam aquæ versùs eandem partem declinat, &longs;ecundum
oram Dalmaticam; in refluxu verò, qua&longs;i circuitu facto, per oram Italiæ
oppo&longs;itam priori de&longs;cendit; æ&longs;tus etiam minimus ob&longs;ervatur ad Melitam,
Sardiniam, Cor&longs;icam, Iluam, Cretam, &longs;ed vix ad &longs;emipedem attollitur;
Ma&longs;&longs;iliæ & Tolone ad pedem integrum; quia &longs;cilicet cùm prædictæ in&longs;u
læ, tum pre&longs;&longs;ionis inæqualitatem inducant, tum etiam vim pre&longs;&longs;ionis tra
ductam &longs;i&longs;tant, quid mirum, &longs;i aliquam vim æ&longs;tus &longs;entiant; & verò ad
oram occiduam Sardiniæ & Cor&longs;icæ vis pre&longs;&longs;ionis ab Oceano traducta
impingitur; & magna e&longs;t maris latitudo; &longs;ub Meridiano Ma&longs;&longs;iliæ, quod
&longs;anè ad pre&longs;&longs;ionis inæqualitatem multùm confert; accedit, quòd &longs;i ad
oram Africæ, in qua e&longs;t Hippona &longs;entitur æ&longs;tus, quidni ad oram Provin
ciæ oppo&longs;itam? Æ&longs;tus porrò ad oram ortivam Sardiniæ & Cor&longs;icæ, item
que ad Iluam procedit à pre&longs;&longs;ionis vi traducta ab extremo mediterraneo
ortivo; ad Melitam, Cretam, Siciliam, à vi pre&longs;&longs;ionis ab vtraque parte pro
veniente. In reliquo mediterraneo nullus æ&longs;tus &longs;entitur; in quibu&longs;dam oris.
&longs;en&longs;ibilis, propter &longs;itum: & verò qui&longs;quis rem in hanc longo illo Medi
terranei tractu attentè con&longs;iderabit, &longs;tatim comperiet, ex præmi&longs;&longs;is princi
piis optimè explicari.
pe in freto illo Siculo, diver&longs;us e&longs;t vtrimque æ&longs;tus, cùm &longs;imul & &longs;emel ab
vna parte deor&longs;um, ab alia &longs;ur&longs;um ire videatur, quod nonnulli in cavitates
&longs;ubterraneas rejiciunt, quas etiam volunt cum iis quæ Monti Æthnæ &longs;ub
jiciuntur, & incendio materiam &longs;uppeditant, per cuniculos e&longs;&longs;e conjun
ctas: Vnde Abbas Maurolycus, aiunt, vnum ex alio conjiciebat; &longs;cili
cet ex diver&longs;a incendij ratione, diver&longs;am rationem æ&longs;tus, & vi
ci&longs;&longs;im.
Hoc etiam &longs;pero ex ii&longs;dem principiis deductum iri; con&longs;ide
ra enim fretum Siculum qua&longs;i in meditullio Mediterranei &longs;itum, & recta
directum ab Au&longs;tro ad Septentrionem, atque inde ad extremam Medi
terranei oram, ortivam &longs;cilicet, ferè numerati triginta gradus longitudi
nis; vnde certè &longs;ufficiens pre&longs;&longs;ionis vis e&longs;&longs;e videtur; accedente præ&longs;ertim
maxima latitudine eju&longs;dem maris, à faucibus Adriatici ad oram Africæ
oppo&longs;itam exporrecta, vt aqua per fretum ab Au&longs;tro ad Septentrionem
extrudatur &longs;imiliter vis pre&longs;&longs;ionis traducta ab Oceano per Gaditanum, re
pre&longs;&longs;aque, vt jam dictum e&longs;t, à faucibus Africam inter & Sardiniam in
terjectis, ac proinde tantulùm declinans &longs;ini&longs;tror&longs;um, plu&longs;quam &longs;uffici
ens e&longs;t ad extrudendam aquam per idem fretum, à Septentrione ad Meri
diem; quamvis enim paulò obliquiùs incidat, cùm tamen priore major
&longs;it, licèt frangatur ab obliquo appul&longs;u, vel potiùs &longs;uo modo reflectatur,
&longs;ufficiens e&longs;t, vt dixi, ad
Au&longs;trum; quid mirum igitur &longs;i agatur æ&longs;tus in contrarias partes, & gemini
&longs;ibi invicem occurrant, vt jam de aliis fretis diximus? cùm autem vtrim
que aqua obliquè incidat, quid mirum &longs;i ex illius reflexione à cavo & di
ver&longs;imodè &longs;ito litore, ad Scyllam &longs;cilicet & Charybdim; diver&longs;i aquarum
vortices & gyri con&longs;equantur? neque in hoc, &longs;altem meo judicio, re&longs;tat
vlla difficultas; cùm enim con&longs;tet, prædictum motum ab æ&longs;tu e&longs;&longs;e,
nempe accedunt & concurrunt aquæ &longs;enis quibu&longs;que horis, & cùm in
aliis fretis, æ&longs;tus etiam concurrant, negari non pote&longs;t, quin primaria
huju&longs;modi motuum cau&longs;a &longs;it æ&longs;tus; nempe ex tali illap&longs;u, concur&longs;u, collu
ctatione, reflexione, mirabilis motuum varietas na&longs;citur, vnde non tantum
24. vt non nemo dicebat, &longs;ed longè plures ob&longs;ervari po&longs;&longs;unt; &longs;ed jam ad
Oceanum redeamus.
Benè e&longs;t; vnum tamen præ cæteris ex re &longs;cire velim, vtrùm
prædictus æ&longs;tuum concur&longs;us in medio freto fiat.
poris momento vtrimque ad o&longs;tia freti perveniat; quod in Siculo facilè con
ce&longs;&longs;erim, quod &longs;cilicet, &longs;ub ea linea porrigatur, quæ eidem Meridiano &longs;ub
jacet, at verò de illo æ&longs;tu, qui fit in freto Magellanico, &longs;ecus dicendum e&longs;t,
cum ortivum, quàm occiduum decurrat, inde fit, &longs;ummam elevationem
ad o&longs;tium ortivum primùm fieri, ac deinde ad occiduum; vnde &longs;equitur
concur&longs;um æ&longs;tuum, longiùs di&longs;tare ab o&longs;tio Orientali, quàm Occidentali,
quod certè cum ob&longs;ervationibus omnino con&longs;entit; Nam Arnaldus Nau
clerus non ignobilis ob&longs;ervavit, concur&longs;um æ&longs;tuum fieri &longs;eptuage&longs;ima ab
Orientali o&longs;tio leuca, & trige&longs;ima
freti 100 circiter
longi&longs;&longs;imum Oceanus de&longs;init; ac proinde aquam vel æ&longs;tum, qua&longs;i admo
to infundibulo in fretum pellit de freto Hud&longs;onio eadem ratio militat,
cùm ab ortu in occa&longs;um eat; &longs;ecus de Davi&longs;io, qui ab Au&longs;tro ad Septen
trionem. Sed ad Eurippos redeo & lineas æ&longs;tuum; jam dixi &longs;upra, cur æ&longs;tus
in oram Guineæ incidentis linea ad Cæciam tendat; in Africum verò, inci
dentis in o&longs;tium fluminis Amazonum: frequentes &longs;unt Eurippi inter Cycla
das, Maldivas, Moluccas, Iaponicas in&longs;ulas &c hoc enim &longs;olemne e&longs;t, &longs;i vis
pre&longs;&longs;ionis ad&longs;it omnibus Marium angu&longs;tiis, augu&longs;tias autem in&longs;ulæ pa&longs;&longs;im
&longs;eminatæ Hinc
per
&longs;tus Igitur inter
&longs;iliam
Iulij, æ&longs;tus currit versùs
po&longs;itam
tem
Sol à 20. Martij ad 22. Iunij ab Æquatore versùs
&longs;cit Mare glaciale, quo certè glaciato, vis pre&longs;&longs;ionis minor e&longs;t; quia arcus gla
ciei incubantes inutiles
leat, & aquas per fauces trudat versùs
circa 26. Iulij glaciato mari
lantici, prævalet igitur, & aquas per ea&longs;dem angu&longs;tias versùs
retrudit; reliquo verò tempore, cùm iterum Mare versùs Boream concre&longs;
cat, ac proinde vis pre&longs;&longs;ionis Atlantici minuatur, aër verò temperatæ Au
&longs;tralis rare&longs;cat, Sole præ&longs;ertim perigæo, inde vis pre&longs;&longs;ionis Æthiopici mi
nuitur, vnde per&longs;picua e&longs;t compen&longs;atio, & mare in neutram partem currit;
adde &longs;is mare Au&longs;trale incognitum etiam gelu concre&longs;cere; vnde quoque
mutatur pre&longs;&longs;ionis ratio.
Vix crediderim in alia hypothe&longs;i cuncta hæc phænomena
&longs;alvari po&longs;&longs;e; &longs;ed perge quæ&longs;o.
Sexto.
Inter In&longs;ulam Madaga&longs;car & Africam à 10. grad. Latit.
Au&longs;tralis ad promontiorum Bonæ &longs;pei versùs Au&longs;trum it mare; habes
enim angu&longs;tias, intra quas Eurippi currunt; cùm autem ab ortu in di
ctam oram æ&longs;tus veniat, obliquè omnino incidit; vnde ad Au&longs;trum li
neam motus determinari, nece&longs;&longs;e e&longs;t; &longs;ic enim ex tali aquarum illap&longs;u li
nea motus pa&longs;&longs;im determinatur, & æ&longs;tus in Eurippum, &longs;i angu&longs;tiæ ad
&longs;int, degenerat. Septimo, Ad Parallelum grad. 30. Latit. Boreal. inter Phi-
Californiam navigetur; quia cùm &longs;ub Zona torrida in toto mari Pacifico
æ&longs;tus & aqua in occa&longs;um liberè feratur, modico circuitu facto refluit per
Septemtrionalem oram Americæ, quam relegit: cujus &longs;anè mirabilis effe
ctus alia ratio e&longs;&longs;e non pote&longs;t.
Haud dubiè rem citiùs expedies, &longs;icut Oceanus, ita & oratio
tua terrarum oras breviter & raptim ip&longs;um æ&longs;tum æmulata, præterlegat,
initio ducto v.g. à Gaditano freto.
Libenter faciam & ne prolixior evadam, rem &longs;anè in pauca con
traham, præ&longs;ertim cum & Mediterraneum & maximam Oceani partem jam
lu&longs;traverimus; & primo loco à prædicto freto Gaditano versùs Boream a&longs;
cendam, majorí&longs;que di&longs;tinctionis gratia numeros adhibebo.
Primò, Occurrit Ora Bæticæ in quam &longs;atis magnus æ&longs;tus incidit Cæciam
versùs cùm vis maxima pre&longs;&longs;ionis ab Africo veniat; hinc quia directè in
Bætim &longs;ubit, ad 30. milliaria fluvius regreditur; &longs;ecus verò Anas non pro
cul hinc di&longs;tans; quia in ejus o&longs;tia æ&longs;tus obliquè incidit; hujus enim flumi
nis cur&longs;us in Au&longs;trum recta linea tendit.
Secundo.
Succedit ora Hi&longs;paniæ occidua, quæ recta ferè ad Septentrio
nem ducitur, in qua æ&longs;tus modicus e&longs;t, quia incidit per eandem lineam ver
&longs;us Cæciam; igitur obliquè; paulò tamen major e&longs;t, ad o&longs;tia Tagi, quia
ille tractus qua&longs;i quoddam æ&longs;tui illabenti receptaculum & &longs;inum
aperit.
Tertiò.
In ora boreali Hi&longs;paniæ nullus, vel modicus e&longs;t, nempe hic quo
que fertur in Cæciam, propter rationem adductam; nempe à Septemtrio
ne In&longs;ulæ Britannicæ, & minor Britannia magnum obicem ponunt; cùm
igitur æ&longs;tus in Cæciam eat, vix in prædictum litus incidit; id que ferè v&longs;que
ad o&longs;tia Garumnæ, ibi enim, & ad rotam oram Aquitanicam, immo ad
extremum v&longs;que minoris Britanniæ promontorium magnus æ&longs;tus e&longs;t; nem
pe ibi mare ad in&longs;tar &longs;inus in terras excurrit, & propter adductam ratio
nem in Cæciam æ&longs;tus currit: vnde &longs;atis directè illabitur, præ&longs;ertim in oram
Meridionalem minoris Britanniæ.
Quartò Ad extremam oram, occiduam &longs;cilicet, minoris Britanni&etail; à fonte
navia ad promontorium Clarium, currit æ&longs;tus ab Hypotra&longs;cia, ac proinde
obliquè incidit, & minùs a&longs;&longs;urgit licèt rapidi&longs;&longs;imus &longs;it in freto fontenaviæ,
propter angu&longs;tias; &longs;ic autem incidit, quia ab ea parte liberiùs excurrit; con
trahitur enim Oceanus in hoc tractu versùs occa&longs;um; hinc eò currit æ&longs;tus,
vt fit in reliquis &longs;inubus, ac proinde obliquè incidit, & minor e&longs;t; haud
procul verò, quia lunatur mare vulturnum versùs in minorem & acu
tiorem &longs;inum, eò directè fertur æ&longs;tus, & hic maximè a&longs;&longs;urgit ad fanum &longs;cili
cet S. Maclovij, & ad Sanctum Michaelem, non procul hinc &longs;itum; inde
porrò Cadomum v&longs;que currit versùs Libycum, ac proinde obliquiùs; per
aliam autem lineam vix in hanc oram Neu&longs;triæ incidere pote&longs;t, vt patet ex
ip&longs;a in&longs;pectione; cùm vis pre&longs;&longs;ionis à mari Germanico per fretum Gallicum
eò traducatur; ad o&longs;tia Sequanæ altiùs a&longs;&longs;urgit æ&longs;tus, quia illic mare luna
tur in &longs;inum.
Quintò, Inde Gravelingam v&longs;que, per eandem ferè lineam incidit
propter eandem rationem; &longs;en&longs;im tamen declinat ad Au&longs;trum, cùm à
longto Maris Germanici tractu, versùs Boream ad Polum v&longs;que porre
cto, vis pre&longs;&longs;ionis Au&longs;trum versùs incumbat; ac proindo obliquè incidit
in oram illam Belgicam, hinc flante Cauro, quo fit, vt æ&longs;tus directè incidat,
longè major æ&longs;tus cietur, vt & in fretis, æ&longs;tuariis, &longs;inubus &c. Pro quibus
nihil e&longs;t, quod addam, cùm jam &longs;upra rationem attulerim, porrò concur
runt æ&longs;tus haud procul à Freto Gallico; vis enim pre&longs;&longs;ionis ab vtro
que mari, Britannico &longs;cilicet & Germanico procedit; concurrunt autem
æ&longs;tus, vt dixi extra fretum, versùs occa&longs;um; rationem jam &longs;upra adduxi,
cum de Freto Magellanico.
Sextò, Ad ortivam oram Angliæ innumeris ferè &longs;inubus, fretis, æ&longs;tua
riis a&longs;peratam, tendit æ&longs;tus versùs Au&longs;trum; vnde parvus e&longs;&longs;et æ&longs;tus,
propter illap&longs;um valdè obliquum, &longs;ed propter illam oræ a&longs;peritatem
& inæqualitatem, nec non locorum angu&longs;tias, illap&longs;us directus e&longs;t,
& altior æ&longs;tus, & multi Eurippi: ad oram verò Meridionalem, æ&longs;tus
qua&longs;i ad Cæciam tendit, versùs Ortum tantulùm deflectens; cùm enim
Mate Britannicum &longs;it ad in&longs;tar magni &longs;inus, na&longs;centis ex Oceano Oc
cidentali, in quo, vt &longs;upra dictum e&longs;t, fluit æ&longs;tus in Cæciam; nihil mi
rum, &longs;i in Britannico versùs eandem partem eat; ab extremo verò An
gliæ termino Occidentali, quem Lezardum vocant, deflectit æ&longs;tus ma
gis ad Ortum; hinc maximus e&longs;t ad Bri&longs;toliam, vbi Mare a&longs;&longs;urgit ad
pedes 66. quia in extremis &longs;inubus, modò æ&longs;tus in eandem cum &longs;inu
plagam excurrat, mare plurimùm a&longs;&longs;urgit; deflectit autem tantulum
ad Ortum, propter obicem Hiberniæ versùs Septemtrionem &longs;itæ. Denique inter Angliam & Hiberniam non parum &longs;ævit æ&longs;tus
propter fretorum locorumque angu&longs;tias; vnde multi na&longs;cuntur Eu
rippi.
Septimò, Suprà Scotiam liberiùs æ&longs;tus excurrit, ac ferè &longs;ine lege; item
ad oram Norvegiæ inter Bergam & Stadem, propter Eurippos valde in
&longs;ignes, ob in&longs;ulas è regione &longs;itas: ad oram Finnomarchiæ & Lappiæ
æ&longs;tus à Cauro fluunt, vnde vis major pre&longs;&longs;ionis e&longs;t; hinc ad extremum
Lappiæ &longs;inum, Ortum versùs, in quem æ&longs;tus directè incidit, in&longs;ignis
æ&longs;tus e&longs;t: Ad Fretum Na&longs;&longs;ovium concurrunt æ&longs;tus, traducta ab
vtroque mari vi pre&longs;&longs;ionis, Tartarico &longs;cilicet & Septemtrionali: De
Nieulandia jam &longs;upra dictum e&longs;t; quanquam facilè crediderim, illo Ma
ri per Brumam glaciato, diver&longs;am in vicinis oris æ&longs;tuum rationem & li
neam &longs;equi.
Iam ferè dixi&longs;ti de reliquis oris, quas Oceanus alluit, præter
lectis &longs;upra litoribus Americæ & Africæ; re&longs;tat vt ad alia tran&longs;eamus, non
dum enim hoc argumentum probè exhau&longs;tum e&longs;t, Ante omnia &longs;cire velim,
cur æ&longs;tus alicubi major, alicubi minor a&longs;&longs;urgat.
Hoc facilè deducere poteras ex iis, quæ dicta &longs;unt; multis au
tem nominibus cre&longs;cit; Primò, ex majori vi pre&longs;&longs;ionis quæ ex duplici ca
pite cre&longs;cit: primum petitur à majore &longs;uperficie, quam occupant vtiles
lus e&longs;t; ex hoc capite maximus æ&longs;tus fit ad Indi O&longs;tia, ad Guineam, ad
O&longs;tia fluminis Amazonum, ad oram Peruviæ. Secundum caput e&longs;t major
aëris gravitas, quæ oritur ab humore admixto, vel aëre den&longs;o, & compre&longs;&longs;o.
Tertium caput omittis, nempe quando Luna altior e&longs;t, altior
quoque e&longs;t aëris gravitantis tractus, & linea dirimens à centro terræ lon
giùs di&longs;tat.
Hoc mihi reverà exciderat, quod exqui&longs;ita ob&longs;ervatione con
firmare po&longs;&longs;um; quando enim Luna in Apogæo exi&longs;tit, tunc æ&longs;tus minor
e&longs;t: itaque vis pre&longs;&longs;ionis alia major e&longs;t exten&longs;ivè, alia inten&longs;ivè; exten&longs;ivè
à majore &longs;uperficie, cui arcus pre&longs;&longs;ionis incumbunt, idque cæteris pari
bus; modò &longs;cilicet inæqualem pre&longs;&longs;ionem inducant; inten&longs;ivè autem à
majore aëris gravitatione, quæ vel e&longs;t à majore altitudine aëris, vel à ma
jore humoris copia admixta; hinc major æ&longs;tus in Plenilunio, minorverò
Luna Apogæa. Secundò, Cre&longs;cit æ&longs;tus ex illap&longs;u magis directo; &longs;ic enim
excurrit in illam oram, præ&longs;ertim per fluminum alveos: nempe a&longs;&longs;urgit
æ&longs;tus per majores vndas, doliorum in&longs;tar, quarum vna aliam &longs;equitur; vn
de fit, vt &longs;i obliquè incidat, non in oram, &longs;ed in ip&longs;um mare excurrat; &longs;i au
tem in litus impingeret, altera &longs;uperveniente, a&longs;&longs;urgeret aqua, & plus ad
huc tertiæ vndæ appul&longs;u. Tertiò, Cre&longs;cit æ&longs;tus ratione &longs;inuum, nempe, vt
jam dixi, &longs;i æ&longs;tus directè in &longs;inum paulò acutiorem & breviorem incidat,
mirum quantum attollatur aqua, non tantùm propter angu&longs;tias va&longs;is, &longs;ed
propter directum appul&longs;um; &longs;ic ad Bri&longs;toliam, vt dixi, & ad fanum Sancti
Michaëlis alti&longs;&longs;imus æ&longs;tus e&longs;t, hic 70. illic 66. pedes; ad O&longs;tia fluminis Ama
zonum, ni&longs;i per alveum fluvij excur&longs;us pateret, altior for&longs;itan e&longs;&longs;et: dixi &longs;u
pra breviorem & acutiorem &longs;inum; vt enim expre&longs;&longs;ione &longs;uperficiei aquæ
quolibet va&longs;e contentæ per canaliculum altiùs a&longs;cendit, quàm per majorem
canalem; ita pror&longs;us æ&longs;tus in breviore & Pyramidem de&longs;inente &longs;inu;
cùm enim minùs capax &longs;it, intru&longs;a per vim pre&longs;&longs;ionis aqua altiùs a&longs;cendat,
nece&longs;&longs;e e&longs;t. Inter in&longs;ulas, vt plurimùm minùs a&longs;&longs;urgit aqua, tum quia vis
pre&longs;&longs;ionis interrumpitur, tum quia cùm aqua per freta & angu&longs;tias di&longs;cur
rat, ac proinde effluat, tam altè a&longs;cendere non pote&longs;t.
Sed cur alicubi velociùs & rapidiùs, alibi &longs;en&longs;im æ&longs;tus
currit?
Velocior motus, qui ab æ&longs;tu e&longs;t, à multis cau&longs;is procedit.
Primò
à majore vi pre&longs;&longs;ionis
lociùs per foramen iuxta ba&longs;im apertum extrudit; major autem vis pre&longs;
&longs;ionis e&longs;t à majore &longs;uperficie ex arcubus vtilibus con&longs;tante. Secundò, ab an
gu&longs;tiis per quas aqua extrudenda e&longs;t, vi pre&longs;&longs;ionis; &longs;icut dixi &longs;upra, in Fre
tis, rapidus æ&longs;tus e&longs;t, v.g. in angu&longs;tiis ad Havanam, & alibi pa&longs;&longs;im; &longs;ic
in fluminis alveo contracta aqua velociùs currit. Tertiò à breviore angu
&longs;tiarum alveo; &longs;ic per breviorem fi&longs;tulam foramini admotam, aqua velo
ciùs extruditur
Ne quid di&longs;&longs;imulem, hoc non capio, quanquam auguror ali
quid &longs;citu digni&longs;&longs;imum, ex hoc ip&longs;o argumento affulgere.
Faciam capias.
Sit tubus AB &longs;emper aquâ plenus, &longs;it fi&longs;tula
primum GH, per quam aqua extruditur, vi
ponderis AB. haud dubiè &longs;i &longs;it fi&longs;tula GI duplo
longior, extrudetur aqua per GH, velociore
motu, & tardiore per GI. experientia hujus rei
per&longs;pecta e&longs;t; quia &longs;æpè probata; ratio verò
non ita fortè cuipiam in promptu e&longs;t.
Iam mihi venit in mentem; nem
pe vis eadem motrix minus mobile velociùs,
majus verò tardiùs movet; quid mirum igitur,
&longs;i minorem aquæ molem fi&longs;tula GH contentam,
vis ponderis GH faciliùs & velociùs extrudat,
quàm duplò majorem contentam fi&longs;tula GI. im
mò facilè crediderim, motus e&longs;&longs;e, vt longitudines
permutando.
Ab hoc vltimo incipio, quod manife&longs;tè fal&longs;um e&longs;&longs;e, demon
&longs;tro, nempe inde &longs;equeretur infinitè velociùs extrudi aquam per nudum &
nulla fi&longs;tula in&longs;tructum foramen B, quàm per fi&longs;tulam quamlibet etiam bre
vi&longs;&longs;imam; prætereà cùm per fi&longs;tulam GH, aut GI aqua extru&longs;a motu
æquabili moveri cen&longs;eatur, acqui&longs;ito &longs;cilicet in ip&longs;a extru&longs;ione, id e&longs;t, in
ip&longs;o foramine: &longs;i in præci&longs;a vi motrice &longs;i&longs;tamus, cùm hæc æqualem mo
tum omnibus partibus extru&longs;is imprimat, quem deinde retinent per totam
fi&longs;tulæ longitudinem, non videtur, cur velociùs per breviorem, tardiùs per
longiorem moveatur; aliunde igitur illa motuum inæqualitas petenda
e&longs;t; nimirum ab impedimento & re&longs;i&longs;tentia fi&longs;tulæ; nempe cava illa &longs;uper
ficies, non ita e&longs;t lævigata, quin aliquid &longs;cabrum, aliquæ &longs;alebræ, &longs;triæ, aut
rugæ in&longs;int; cum enim aqua nullum &longs;patium liberum habeat intra fi&longs;tu
lam, vix credi pote&longs;t, quantum inde illius cur&longs;us retardetur; & verò aquæ
currentis &longs;uperficies adeò plana e&longs;&longs;e non &longs;olet, præ&longs;ertim &longs;i velociore motu
fluat; vt igitur &longs;uperficies aquæ convexa probè congruat &longs;uperficiei cavæ
fi&longs;tulæ, id certè non &longs;ponte, &longs;ed vi quadam fieri dumtaxat pote&longs;t; vnde illius
cur&longs;um retardari nece&longs;&longs;e &longs;it: cùm igitur in longiore fi&longs;tula longior &longs;it &longs;u
perficies, longius &longs;eu majus erit impedimentum; igitur per longiorem fi
&longs;tulam plus remoræ nacta, tardius aqua extruditur.
In qua porro proportione vnus motus alium &longs;uperat?
extru&longs;a per nudum foramen B, factum in lamina qua&longs;i indivi&longs;ibili, cùm ea
quæ per fi&longs;tulam GH extruditur, æquali tempore, motus erunt vt quanti
tates permutando; fiatque vt differentia quantitatum &longs;it ad aliam vt GH,
ad GI, id e&longs;t, in ratione dupla, erit aqua extru&longs;a per GH ad extru&longs;am per
GI, vt aqua extru&longs;a per nudum foramen, minus prima differentia ad ean
dem, minùs &longs;ecunda differentia; erunt autem motus vt quantitates aquæ
extru&longs;æ: hic non con&longs;idero modicam illam & in&longs;en&longs;ibilem re&longs;i&longs;tentiam,
quæ procedit à peripheria foraminis laminæ; quia hæc &longs;upponitur indivi
&longs;ibilis &longs;uperficies, ac proinde quælibet &longs;uperficies cava ad illam peripheriam
Hoc certè callent ij, qui aquæ ex publicis fontibus di&longs;tri
buendæ præ&longs;unt, nempe æquales longitudine fi&longs;tulas omnibus aquædu
ctibus apponunt, &longs;ive tubi majores &longs;int, &longs;ive minores; vt &longs;cilicet æqualis &longs;it
ratio impedimenti quod ex longitudine fi&longs;tulæ ducitur, ac proinde extru&longs;æ
aquæ quantitates &longs;int vt tubi, &longs;eu tuborum ba&longs;es.
In hoc etiam errant, Augu&longs;tine, quod vt liquidò demon&longs;trem,
&longs;upponantur duæ fi&longs;tulæ æqualis longitudinis GH, &longs;ed ba&longs;is inæqualis,
&longs;itque exempli gratia Diameter ba&longs;is minoris vnius digiti, & Diameter
majoris, duorum digitorum, cùm æquali longitudine fi&longs;tularum & al
titudine fontis BA, haud dubiè vires erunt, vt ba&longs;es, ac proinde &longs;i
præcisè vis ponderis gravitantis, & aquam extrudentis con&longs;ideretur,
eadem e&longs;t vtrimque ratio; nempe mobilia &longs;unt vt ba&longs;es, ba&longs;es vt vires;
igitur æquales vtrimque motus; quia vires vt 4. æquè facilè movebunt
pondus vt 4. ac vires vt vnum pondus vt vnum. Igitur &longs;tando præci
sè in ip&longs;a vi ponderis extrudentis, quo tempore, per majorem fi&longs;tu
lam ex appellatis, fluunt 4. libræ aquæ, vna tantùm libra per minorem
effluet; &longs;ed hoc per&longs;picuis experimentis repugnat; nec demon&longs;tratio dee&longs;t;
nempe vt eadem proportio maneret, impedimenta ex cava &longs;uperficie fi&longs;tu
læ petita deberent e&longs;&longs;e proportionalia; igitur cùm hæc impedimenta &longs;int,
vt &longs;uperficies cavæ, &longs;uperficies cava majoris fi&longs;tulæ deberet e&longs;&longs;e quadrupla
&longs;uperficiei cavæ minoris, cùm tamen &longs;it tantùm dupla; &longs;unt enim illæ vt Peri
pheriæ circulorum, & hæ vt Diametri: igitur cùm major &longs;it ratio impe
dimenti in minore fi&longs;tula, quàm in majore, quid mirum, &longs;i aquæ quantitas
extru&longs;æ per majorem, &longs;it plu&longs;quam quadrupla extru&longs;æ per minorem? e&longs;&longs;et
autem pror&longs;us & accuratè quadrupla, &longs;i major fi&longs;tula longitudine dupla
minoris &longs;it.
Bellè omninò, vt hæc mihi nova, ita gravi&longs;&longs;ima pror&longs;us acci
dunt. Sed quid &longs;i aliquis æqualem in fi&longs;tulis longitudinem &longs;ervare velit,
cupiat tamen apponere fi&longs;tulam majorem, per quam extrudatur, a&longs;&longs;umpta
eadem fontis altitudine, quadrupla quantitas aquæ, quanta ba&longs;is fi&longs;tulæ a&longs;&longs;i
gnanda erit?
Hoc etiam facilè haberi pote&longs;t: &longs;i enim major fi&longs;tula longi
tudine dupla & ba&longs;i quadrupla extrudit præcisè quantitatem aquæ qua
druplam, &longs;it ba&longs;is majoris 16. minoris 4. ac proinde Diameter minoris 2.
majoris 4. erit ba&longs;is 16. ad &longs;uperficiem cavam majoris fi&longs;tulæ, vt ba
&longs;is 4. ad cavam minoris; igitur vires majoris ad impedimentum fi&longs;tulæ
majoris, vt vires minoris ad impedimentum eju&longs;dem; &longs;it minoris impe
dimentum vt vnum, erit majoris impedimentum vt 4. & &longs;i impedimen
tum vt 1. &longs;ubducit vnam partem aquæ, vel motus ex 4. impedimen
tum vt 4. &longs;ubducit partes 4. ex 16. vnde re&longs;idua erunt in eadem pro
portione, &longs;cilicet vt 3. ad 12. jam verò &longs;i longitudo dupla ma
joris fi&longs;tulæ &longs;ubducit 4. partes, longitudo &longs;ubdupla &longs;ubducet tantùm
2. igitur &longs;i major fi&longs;tula æqualis longitudine a&longs;&longs;umatur extrudet 14.
partes &longs;eu libras aquæ. Vt autem inveniatur ba&longs;is fi&longs;tulæ, eju&longs;dem cum
fluat, ad i&longs;tud problema præparatorium res reducitur; dato Quadrato, cui
&longs;ubtractum &longs;it &longs;ubquadruplum, id e&longs;t Quadrato &longs;emilateris, invenire Qua
dratum cui &longs;ubtracto rectangulo, &longs;ub eius latere, & quarta parte laceris
prioris, re&longs;iduum &longs;it quadruplum, primi re&longs;idui, &longs;en triplum primi Qua
drati. Supponamus CB e&longs;&longs;e latus, &longs;eu Diame
trum ba&longs;is minoris fi&longs;tulæ, & LA e&longs;&longs;e Quadra
tum quæ&longs;itum, ita vt &longs;ubtracto HE &longs;ub latere LH,
& LE æquali MB, quæ e&longs;t &longs;ub quadrupla BA,
re&longs;iduum EA &longs;it triplum Quadrati CA: &longs;it au
tem latus Quadrati 12 KN, quod mihi notum
e&longs;t, hoc enim e&longs;t triplum Quadrati CA; &longs;it etiam
KR, æqualis MB, mihi notæ, e&longs;t enim &longs;ubqua
drupla BA; his præmi&longs;&longs;is, &longs;ic formo problema
decretorium: Data media proportionali, &longs;cilicet
KN, & differentia extremarum, &longs;cilicet KR, invenire
extremas; dividatur RK bifariam in S & &longs;ub radio SN
de&longs;cribatur &longs;emicirculus ONB, erunt KO, KP, extre
mæ quæ&longs;itæ, vt patet; igitur KO e&longs;t latus quæ&longs;itum,
æquale &longs;cilicet LH. Pari modo procedam &longs;i velim ha
bere fi&longs;tulam eju&longs;dem longitudinis, ex qua eodem tem
pore tripla, vel dupla quantitas effluat.
Non paucæ mihi &longs;uboriuntur difficultates circa hæc, quæ à
te dicta &longs;unt; primò enim, &longs;i longitudo fi&longs;tulæ GH
tale impedimentum affert, vt vnam quartam
partem motus auferat; igitur dupla longitudo
GI, duplum auferet; igitur quadrupla totum
motum; nihil aquæ igitur ex illa efflueret, quod
ab&longs;urdum e&longs;t.
Si&longs;te quæ&longs;o, neque enim huc Hydrau
lica traducenda e&longs;t, cùm &longs;it res longioris operæ;
dicam igitur breviter, motum retardari po&longs;&longs;e in
infinitum, vt nemo. ne&longs;cit; vnde &longs;i longitudo fi
&longs;tulæ GH. Subtrahitvelocitatis, longitudo
GI &longs;ubtrahet 1/4. & dupla GI
totam; &longs;ed huc v&longs;que &longs;upponitur fi&longs;tula &longs;emper
plena, eaque in &longs;itu horizontali ; vbi autem
aqua ea tarditate, movetur, vt pars aquæ &longs;uprema proprio pondere qua&longs;i
per planum inclinatum ire po&longs;&longs;it, de&longs;cendit haud dubiè, & tunc &longs;uperior
fi&longs;tulæ cavitas, vacua re&longs;tat: &longs;ed quæ&longs;o te ad rem no&longs;tram redeamus, cùm
hæc hujus in&longs;tituti non &longs;int.
Inde tantùm colligo, quantum detrimentum ij patiantur in
di&longs;tributione aquarum, qui parvas fi&longs;tulas habent, & quantum vici&longs;&longs;im
commodi ij, qui magnas habent; nempe illi, cui aquæ vncia competit, da
tur fi&longs;tula, cujus ba&longs;is Diameter v. g. vncia e&longs;t; alteri verò cui competunt
prioris, &longs;ed eo tempore, quo per illam minorem fi&longs;tulam tanta aquæ quantitas ex
ctis; igitur vt legitimæ aquarum men&longs;uræ e&longs;&longs;ent, vel modus &longs;upra expo&longs;i
tus adhibendus e&longs;&longs;et, vel fi&longs;tularum longitudines, vt Diametri e&longs;&longs;e deberent,
&longs;ed his mi&longs;&longs;is ad ae&longs;tum redi.
Iraque ex dictarum fi&longs;tularum analogia, explicabam &longs;upra,
cur per breviorem freti, vel angu&longs;tiarum tractum, aqua vi pre&longs;&longs;ionis ve
lociùs extrudatur, ad proinde rapidiore motu; illud tamen di&longs;criminis
intercedit, quòd in fi&longs;tulis, cre&longs;cente ba&longs;i fi&longs;tulæ, ponderis gravitantis
viros cre&longs;cant
eadem vis pre&longs;&longs;ionis e&longs;&longs;e &longs;upponitur, in eodem tractu, quando &longs;cilicet
maxima pre&longs;&longs;io e&longs;t, re&longs;pectu illius, &longs;ive contractiores &longs;int angu&longs;tiæ freti, &longs;ive
laxiores; &longs;ive longior illius tractus, &longs;ive brevior &longs;it: Vnde duplici nomine,
quando brevior, e&longs;t, rapidiùs extruditur; nimirum quia arctus e&longs;t, & quia
brevis; ex vtro quo enim capite aquæ extrudendæ moles minuitur.
Sed quæ&longs;o te, cur alicubi longè breviore tempore æ&longs;tus a&longs;
&longs;urgis, excurritque; alicubi verò plus temporis ponit?
Ita e&longs;t; nempe ad Guineam, non procul ab o&longs;tio Nigri flumi
nis 4. horis æ&longs;tus a&longs;&longs;urgit; item ad oram Cambaiæ, iuxta Indi fauces, dua
bus horis æ&longs;tus ad 30. leucas excurrit, ad o&longs;tia Garumnæ, &longs;eptem horis
a&longs;&longs;urgit, quinque refluit, vt ait Scaliger exerc. 52. Sed accuratior Ob&longs;er
vator, idemque nobili&longs;&longs;imus Geometra D. Candala, expre&longs;&longs;is verbis te&longs;ta
tur, Garumnam attolli &longs;ex integris horis, deprimi verò &longs;ex horis & 24.
minutis cui plus fidei habendum e&longs;&longs;e nemini dubium erit; vtpote qui ad
accuratiùs ob&longs;ervanda acce&longs;&longs;us rece&longs;&longs;u&longs;que tempora, circa Garumnæ
o&longs;tium, magnum horologium con&longs;trui curaverit, quod etiam minuta &longs;i
gnabat, vt ip&longs;emet te&longs;tatur in libello à &longs;e in lucem edito Ann. 1575. Quem
etiam citat Furnerius. Quod ad me attinet, exi&longs;timo, æqualia vtrimque e&longs;&longs;e
tempora; cùm enim æ&longs;tus initio & &longs;ub finem parum cre&longs;cat, vt dicam pau
lò po&longs;t, id e&longs;t, iuxta minimam ferè proportionem, facilè fieri potuit, vt
minimum coementum primis 16. minutis & 16. vltimis &longs;ub &longs;en&longs;um & ob
&longs;ervationem v enim non potuerit; ac proinde æquè diu acce&longs;&longs;us atque re
ce&longs;&longs;us duraverit.
Metiri ergo æ&longs;tum debemus horis Lunaribus, divi&longs;a &longs;cilicet
integra revolutione Lunæ, &longs;eu die Lunari in 24. partes, &longs;eu horas æqua
les, ita vt quælibet hora Lunatis &longs;it major hora Æquinoctiali 2. minutis;
ac proinde &longs;enis &longs;emper horis Lunaribus æ&longs;tus reciproci fiunt per &longs;e, aut
certè &longs;enis horis Æquinoctialibus & 12. minutis; non verò &longs;ex horis tem
poralibus, inæqualibus &longs;cilicet, iuxta formam horologij antiqui, vt vocant;
& ita intelligendum e&longs;&longs;e Plinij locum
miror illorum errorem, qui volunt incipere æ&longs;tum vbi Luna &longs;upra Ho
rizontem vno Signo elevata fuerit, & continuo cre&longs;cere donec Luna Me
ridianum illius loci attigerit; decre&longs;cere verò ab hoc puncto, donec Luna
æqualem po&longs;t Meridiem arcum decurrit terminatum &longs;cilicet ad 30. gra-
mâ declinatione Au&longs;trali, arcus illius diuinus ab Ortivo puncto Horizon
tis ad Meridianum, vix e&longs;t 60. graduum; igitur &longs;i detrahantur 50. &longs;uper
&longs;unt 30. quos dum Luna decurrit, duabus &longs;cilicet horis Æquinoctialibus
& 4. minutis, durat æ&longs;tus; quod apertè fal&longs;um e&longs;&longs;e con&longs;tat; tamdiu re
fluxus duraret. Prætereà, æ&longs;tus, qui fieret po&longs;t Occa&longs;um Lunæ, longè
major e&longs;&longs;et priore; nempè arcus illius paralleli &longs;ub Horizonte, longè ma
jor e&longs;t alio; quem Luna &longs;ũmpta Horizontem excurrit,
mentis repugnant. Dix i&longs;uprà, per &longs;e, cùm per accidens fieri po&longs;&longs;it, vt tem
pora fluxus & refluxus inæqualia &longs;int.
Ex præmi&longs;&longs;is principiis hoc manife&longs;tè deducitur
gulis pænè momentis, mutatur in globo punctum, &longs;eu Polus maximæ ele
vationis, ac proinde centrum circulorum & arcuum pre&longs;&longs;ionis, quorum
cum diver&longs;a &longs;it ratio & proportio, propter varios continentis & Maris
tractus, in &longs;uperficie globi, &longs;ine certâ lege di&longs;tinctos, inde nece&longs;&longs;ariò &longs;e
quitur diver&longs;a vis pre&longs;&longs;ionis, diver&longs;a impre&longs;&longs;io, diver&longs;a appul&longs;us, vel illa
p&longs;us linea: quod vt meliùs intelligas fige pedem circini ad Occiduum
Guineæ Promontorium, non procul ab O&longs;tio Nigri, ductí&longs;que innumeris
circulis ex illo centro, concentricis & parallelis, di&longs;tingue arcus vtiles ab
inutilibus, &longs;en&longs;imque promoto versùs Ortum illo centro, v&longs;que ad 60.
gradus, &longs;i vlteriùs illud promoveas, v&longs;que ad 90. circuli pre&longs;&longs;ionis
maxima ex parte, vel continenti Africæ, Europæ, A&longs;iæ vel Indico Ocea
no incumbent, ac proinde inutiles erunt re&longs;pectu prædicti loci: quid mi
rum igitur, &longs;i 4. dumtaxat horis in eo æ&longs;tus a&longs;&longs;urgat, deprimatur verò plu
ribus? Nam promoto versùs Oceanum centro, diver&longs;a e&longs;t circulorum pre&longs;
&longs;ionis ratio. Aliquid &longs;imile ob&longs;ervabis, fixo circini pede ad litus Cam
baiæ; tanquam in centro: accedit, quòd ex multis capitibus prædicta
æ&longs;tuum inæqualitas inducitur; Primò, per planum magis inclinatum, lon
giùs excurrit & velociùs, licèt plus temporis ponat in decurrendo magis
inclinato, cuncta hæc ex doctrina motuum per&longs;picua &longs;unt; tantumdem
temporis aqua ponit in de&longs;cen&longs;u per planum inclinatum., quantum in
a&longs;cen&longs;u. Secundò, Si po&longs;t quàm aqua regredi cœpit, nova quædam fiat
æ&longs;tus reflexio, versùs fluminis fauces, vel &longs;i aqua libero quidem aditu &longs;u
beat, &longs;ed exitu difficiliore, tunc acce&longs;&longs;us breviore tempore fiet quàm re
ce&longs;&longs;us. Tertiò, Si nova reflexio accedat, antequam aqua regredi incipiat,
vel agger quidam appo&longs;itus ad fauces &longs;inus, aut fluminis primam vim ac
ce&longs;&longs;us retundat, vt videre e&longs;t ad fauces Sequanæ & Garumnæ, rece&longs;&longs;us bre
viore tempore fiet quàm acce&longs;&longs;us. Quartò, Pro diver&longs;o æ&longs;tus ad oram ap
pul&longs;u, vel illap&longs;u, longiùs per alveum fluviorum vel minùs longè aqua ex
currit; item pro diver&longs;a alvei inclinatione; hinc facilè crediderim, alveum
illorum fluminum, in quibus ad aliquot centena milliaria æ&longs;tus excurrit,
e&longs;&longs;e valde inclinatum Quintò, Dicam ampliùs, ratione eju&longs;dem loci, non
modò æ&longs;tum altiùs aut minùs altè attolli, verùm e&longs;&longs;e aliquando acce&longs;&longs;um
majorem, aliàs minorem e&longs;&longs;e po&longs;&longs;e; quia mutatur &longs;ingulis diebus centrum
circulorum pre&longs;&longs;ionis, etiam re&longs;pectu eju&longs;dem loci; item aliquando ac-
cuncta hæc ex diver&longs;a pre&longs;&longs;ionis ratione pendent: e&longs;t autem diver&longs;a ratio
pro diver&longs;o tractu &
Sed quaero ex te vtrùm eadem &longs;emper hora Meridiana
Lunari, id e&longs;t, eo momento, quo Luna Meridianum loci attigit, &longs;ummus
æ&longs;tus &longs;it?
Per &longs;e quidem &longs;ummns æ&longs;tus &longs;emper e&longs;t, exi&longs;tente Luna in Me
ridiano loci, &longs;ive &longs;upra, &longs;ive infra Horizontem; per accidens tamen &longs;ecus
accidit; & Primò quidem ex diver&longs;a pre&longs;&longs;ionis ratione; Nempe fieri po
te&longs;t, vt hora decima Lunari re&longs;pectu alicujus loci, &longs;it maximus pre&longs;&longs;ionis
effectus, ac proinde &longs;ummus æ&longs;tus. Secundò, Ob concur&longs;um æ&longs;tuum Ge
mini Matis tractus, vt fit in Germanico & Britannico, nempe longè ante
Meridiem Lunarem, re&longs;pectu Dieppæ & O&longs;tij Sequanæ Oceanus Septem
trionalis intume&longs;cit, à quo in Germanicum vis pre&longs;&longs;ionis traducitur, & hinc
per Fretum Gallicum, Dieppam, & ad O&longs;tium Sequanæ ; quò etiam cùm ex
Britannico, qua&longs;i ex aver&longs;o vis pre&longs;&longs;ionis incumbat, licèt paulò tardiùs
quàm ex Germanico, quod ad Ortum &longs;itum e&longs;t, vtriu&longs;que concur&longs;u &longs;um
mus æ&longs;tus Dieppæ a&longs;&longs;urgit, itémque ad O&longs;tium Sequanæ ; hîc quidem priùs
vna ferè hora propter reflexionem magis directam. Hinc fieri pote&longs;t; vt a&longs;
&longs;urgat &longs;ummus æ&longs;tus in duobus locis &longs;ub diver&longs;o Meridiano &longs;itis, eodem
tempore, v.g. &longs;i accipiatur alter locus di&longs;tans Dieppa 7. grad.1/2. ver&longs;us Or
tum, in quo &longs;ummus æ&longs;tus &longs;it hora vndecima Lunari; illic enim & Dieppæ
eodem tempore &longs;ummus erit æ&longs;tus. Pari modo facilè dici pote&longs;t, cur mul
tis in locis &longs;ummus æ&longs;tus &longs;it po&longs;t Meridiem v, g. Burdigalæ, ad Garumnam,
Antuerpiæ ad Scaldim, Hamburgi ad Albim, &longs;ummus æ&longs;tus e&longs;t hora &longs;exta
Lunari po&longs;t eju&longs;dem Meridiem, quia per motum æ&longs;tus a&longs;cendit in alveo
fluminum; igitur tardiùs pervenit ad loca longè di&longs;&longs;ita à fluminis faucibus:
Am&longs;terodami 3. hora Lunari po&longs;t Meridiem; in ip&longs;o verò Meridie Lu
nari, Encu&longs;æ, haud procul po&longs;itæ; quia per diver&longs;os mæandros in
eo maris &longs;inu, Am&longs;terodamum æ&longs;tus appellit, liberiùs Encu&longs;am; in
oram Fri&longs;iæ adhuc liberiùs; hinc tertia hora Lunati ante Meridiem Luna
rem, ibi fit &longs;ummus æ&longs;tus; nempe ab Oceano Septemtrionali tantulùm
versùs Ortum declinante vis pre&longs;&longs;ionis traducitur in Germanicum, & qua
&longs;i directè in oram Fri&longs;iæ; Oceanus autem Septemtrionalis propter mo
dicam Meridianorum di&longs;tantiam in eo Boreali tractu, in Germanicum
incumbit, antequam Luna ad illum Meridianum perveniat; cui Ma
re Germanicum &longs;ube&longs;t, vnde prior ratio indicata plurimùm confirmatur. Itaque ex dictis con&longs;tat, &longs;ummum æ&longs;tum e&longs;&longs;e po&longs;&longs;e &longs;ub diver&longs;is Meridia
nis, eodem tempore, & &longs;ub eodem, in diver&longs;is locis, diver&longs;o, & &longs;in
gulares quo&longs;libet ca&longs;us ad præmi&longs;&longs;a & communia principia reduci, mo
do &longs;ingulares circum&longs;tantiæ habeantur, ratione quarum, vel &longs;ummus æ&longs;tus
cum Lunæ motu convenit, vel tardiùs aut citiùs accidit; mihi &longs;atis &longs;it ali
quas obiter indicate.
Primò, Si nihil appul&longs;um æ&longs;tus impediat, nihil promoveat, &longs;ed mare
ab incubante aëre pre&longs;&longs;um inæqualiter, liberè intume&longs;car, &longs;ummus æ&longs;tus
quo Luna Meridianum illius loci attingit, &longs;ive &longs;upra, &longs;ive infra Hori
zontem,
Secundo.
Si res ita compo&longs;itæ, &longs;eu di&longs;po&longs;itæ &longs;int, vt concurrant æ&longs;tus, vel
in freto, vel vltra freti fauces, in quibu&longs;dam tractibus &longs;ummus æ&longs;tus erit
ante meridiem, vt Dieppæ; quia &longs;cilicet aqua citiùs per freti angu&longs;tias extru
ditur; adde reflexionem quamdam, quæ &longs;equitur ex vtroque ni&longs;u maris ver
sùs fretum connitentis.
Tertio.
Si mare versùs Au&longs;trum eat, &longs;en&longs;imque declinet ora versùs
Boream, ad oram illam, &longs;ummus æ&longs;tus erit ante meridiem Lunarem vt in
Fri&longs;iæ ora.
Quarto.
Si per varios &longs;inus & mæandros mare in terras &longs;e&longs;e in&longs;inuat, &longs;um
mus æ&longs;tus erit po&longs;t meridiem Lunarem, vt Am&longs;terodami, & in iis locis, quæ
&longs;ita &longs;unt ver&longs;us extremum &longs;inum.
Quinto.
Si æ&longs;tus per alueos fluviorum a&longs;cendat, quò longiùs di&longs;tat ab
o&longs;tio fluvij locus aliquis, eò tardiùs &longs;ummum æ&longs;tum habet, &longs;ci′icet
po&longs;t meridiem Lunarem, vt Burdigala, Hamburgum, Rotomagus, An
tuerpia.
Sexto.
Si aliquis terræ tractus longiùs in mare porrigatur, citiùs habet
&longs;ummum æ&longs;tum, & tardiùs, vt dixi, extremitas &longs;inuum.
Septimo.
Diver&longs;us litorum &longs;itus ad talem vel talem reflexionem di&longs;po
&longs;itus non parum confert; reflexionem, inquam, ni&longs;us, &longs;eu pre&longs;&longs;io
nis aquæ cuju&longs;vis ab oppo&longs;ito latere &longs;eu littore versù; aliud qua&longs;i refle
ctitur.
Octavo.
Adde lineam cur&longs;us aquæ, prout &longs;cilicet vel obliquiùs, vel minus
obliquè incidit.
Nono.
Adde etiam diver&longs;am pre&longs;&longs;ionis rationem, qua fieri pote&longs;t, vt
&longs;umma vis pre&longs;&longs;ionis non &longs;it re&longs;pectu alicujus loci con&longs;tituto centro ar
cuum pre&longs;&longs;ionis in dicto loco, &longs;ed in alio, &longs;eu versùs ortum, quo po&longs;ito,
&longs;ummus æ&longs;tus erit ante meridiem Lunarem; &longs;eu versùs occa&longs;um, quo &longs;up
po&longs;ito, po&longs;t meridiem Lunarem in dicto loco erit. Ex his reliqua, ni fallor,
facilè intelligetis, aut &longs;altem &longs;i quid difficile, re&longs;tet &longs;ignificare dignabi
mini.
Pauca haud dubiè re&longs;tant, quæ vel abundè non fuerint ex
po&longs;ita, vel ex iis, quæ à te dicta &longs;unt, facilè non intelligantur, & mihi
videor rationem afferre po&longs;&longs;e illorum omnium, quæ in hac materia maxi
mam admirationem conciliare &longs;olent v.g. cur multa litora, vel nullum vel
modicum æ&longs;tum patiantur, alia verò maximum; quid Luna ad æ&longs;tum con
erat, ita vt in Plenilunio & Novilunio maximus æ&longs;tus &longs;it, eiu&longs;que &longs;ummum,
Luna in Meridiano exi&longs;tente, ni&longs;i per accidens &longs;ecus fiat; cur in duobus
locis, &longs;ub eodem Meridiano &longs;itis diver&longs;o tempore, eodem verò, &longs;ub di
ver&longs;o Meridiano; cur in fretis gemini æ&longs;tus concurrant; cur is, qui fer
tur ab ortu intra fretum longiùs accedat, minus verò, qui venit
ab occa&longs;u; cur alibi rapidi&longs;&longs;imus &longs;it, mitior alibi, cur alicubi ante
meridiem Lunarem, alibi po&longs;t; pa&longs;&longs;im tamen in ip&longs;o meridie;
rò plus rece&longs;&longs;us; quàm acce&longs;&longs;us, licèt vnus per &longs;e alteri &longs;it aquè diutur
nus; cur per &longs;e mare &longs;ex horis 12. minutis a&longs;cendat, & totidem depri
matur, cur &longs;ingulis diebus vna ferè hora, hoc e&longs;t 48.minutis æ&longs;tus tardiùs
a&longs;&longs;urgere incipiat, quàm pridie, idque &longs;emper & per &longs;e, Luna in Meridia
no horæ &longs;extæ exi&longs;tente; cur in quibu&longs;dam oris ad 70. & 80. pedum alti
tudinem mare per æ&longs;tum in Plenilunio attollatur, in aliis vix ad vnum pe
dem, in multis verò nihil pror&longs;us; cuncta hæc & alia multa ex principiis
à te jactis nullo negotio deducuntur; alia quædam occurrunt, quæ mihi
vel dubia &longs;unt, vel eorum ratio incomperta; à dubiis initium duco. Pri
mum e&longs;t quod aliqui dicunt, in Plenilunio &longs;cilicet majorem e&longs;&longs;e vim æ&longs;tus,
quàm in Novilunio ad Calecutium; cùm tamen ad indi o&longs;tia in Novilunio
majores &longs;int æ&longs;tus; alterum verò quod alij referunt, quibu&longs;dam in
per totos quindecim dies, à Novilunio &longs;cilicet, ad Plenilunium continuò
æ&longs;tum cre&longs;cere; ita vt &longs;ummum crementum &longs;it in Novilunio & Plenilunio,
ac totidem diebus aquam &longs;ub&longs;idere, vt ob&longs;erva tum e&longs;t, inquiunt, circa
Cubam & Hi&longs;paniolam; item in fluvio Vanna vel Van&longs;one ad Pachinum
Sinarum
Ab hoc vltimo incipio, quia involvit repugnantia; nempe cùm
in prædictis, vt & in multis aliis Mediterranei locis, æ&longs;tus &longs;it tantùm &longs;en&longs;i
bilis in Plenilunio & Novilunio, quia cùm tunc Majores &longs;int, vt &longs;upra di
ximus, con&longs;tatque experientia; quid mirum, &longs;i tunc &longs;en&longs;ibiles &longs;int? vnde
non nemo occa&longs;ionem arripuit, dicendi, cre&longs;cere continuo in iis locis
per totos 15. dies, à Novilunio &longs;cilicet ad Plenilunium; quod fal&longs;i&longs;&longs;imum
e&longs;t; quia &longs;ingulis diebus - bis cre&longs;cit, & bis refluit. Sed in&longs;en&longs;ibiliter, ni&longs;i
paucis diebus ante & po&longs;t Novilunium ac Plenilunium; hæc autem &longs;unt
inter &longs;e repugnantia, decre&longs;cere continuo à Plenilunio ad Novilunium ac
proinde in Novilunio mare e&longs;&longs;e maximè depre&longs;&longs;um, cùm in eo &longs;it terminus
decrementi, & toto reliquo men&longs;e nullum &longs;en&longs;ibilem æ&longs;tum apparere;
fieri tamen aquarum tumorem &longs;en&longs;ibilem in Novilunio & Plenilunio. Ve
nio ad primum, & dico, de eo mihi maximum dubium e&longs;&longs;e, quanquam
pro diver&longs;o Lunæ &longs;itu, non negarim fieri po&longs;&longs;e, vt major æ&longs;tus &longs;it in Novi
lunio, quàm in Plenilunio; cum enim fauces Indi &longs;int ferè &longs;ub Tropico
Caneri, &longs;i &longs;upponamus Novilunium fieri in Tropico Cancri, de Meridie
maximus erit ibi aquæ tumor, cùm linea ab&longs;idum eo terminetur, minor
tamen erit de media nocte; quia extremitas lineæ ab&longs;idum inde di&longs;tat 47.
gradibus; &longs;i verò Plenilunium fiat in Tropico Capricorni, de Meridie ma
ximus æ&longs;tus ibidem erit, quia vt linea ab&longs;idum à Tropico ad Tropicum
per centrum globi tunc eat, de Meridie extremitas prædictæ lineæ, quæ
ad Tropicum Cancri terminatur, re&longs;pondet lineæ Meridianæ; itaque &longs;i
compatetur diurnus Plenilunij cum nocturno Novilunij, in Novilunio mi
nor æ&longs;tus erit, quàm in Plenilunio, &longs;ive diurnus
nilunij, major erit in Novilunio, &longs;ed profectò de&longs;unt ob&longs;ervationes, & Au
tores &longs;uper hoc in &longs;en&longs;us contrarios eunt, vtpote qui non tam ex ob&longs;erva
tionibus, quàm ex propriis conjecturis multa deducant & &longs;cribant, quæ
tio rem hanc plurimùm variat; immo Autores &longs;uper hoc &longs;ibi non con&longs;tant,
& vnus illorum, &longs;i rectè memini, cùm docui&longs;&longs;et, incrementa matis majora
fieri in Pleniluniis ad Calecutium, in Noviluniis verò ad Indi o&longs;tia, &longs;equen
ti &longs;tatim pagina dicit, alicubi majora e&longs;&longs;e in Noviluniis, vt ad Calecu
tium, alibi verò majora in Pleniluniis, vt ad Indi O&longs;tia; idem re
petit po&longs;t quintam paginam; vnde vides, cuncta hæc parum certa
e&longs;&longs;e.
In hac re nihil aliud de&longs;idero, ni&longs;i novas & accuratas ob&longs;er
vationes, circa diurnum & nocturnum æ&longs;tum, dum Luna &longs;ita e&longs;t
extra Æquatorem, ac præ&longs;ertim circa Tropicos; alia quædam de
quibus certò con&longs;tat, quorum cau&longs;æ mihi compertæ non &longs;unt, ex
te quærenda re&longs;tant: primum e&longs;t, cur dum æ&longs;tus a&longs;&longs;urgit &longs;ub initium
& finem minoribus, crementis a&longs;&longs;urgat, majoribus verò &longs;ub me
dium.
In Sinu Tarentino dum æ&longs;tus &longs;ex horis a&longs;&longs;urgit, & fortè duo
decim minutis, quæ &longs;ub &longs;en&longs;um non cadunt, vt dixi &longs;upra, & toti
dem refluit, hæc accuratè ob&longs;ervata &longs;unt, in Novilunio v. g. prima
hora lentè accedit, &longs;ecunda tantulùm intenditur motus, tertia &
quarta, longè velocior evadit, quinta remittit, vt in &longs;ecunda: in &longs;ex
ta denique vt in prima: idem fit in Plenilunio: vegetior autem æ&longs;tus e&longs;t
quatriduo ante & quatriduo po&longs;t Novilunium & Plenilunium, reliquo
tempore longè remi&longs;&longs;ior. Hæc literis ad me datis à
viro &longs;apienti&longs;&longs;imo qui præ&longs;ens illa in&longs;piciebat, acce
pi ac fideliter retuli: Vt autem rationem, quam
petis exponam, &longs;uppono ex Geometria, &longs;inus com
plementi, quo magis accedunt ad &longs;inum totum,
habere minorem proportionem inæqualitatis. Sit
enim quadrans MLN in quo accipiantur arcus
æquales L, P, E, R, Z, & ducantur &longs;inus com
plementi XP, TE, SR, VZ, dico ML ad XP, habere minorem
proportionem inæqualitatis, quàm XP ad TE, & XP, ad TE,
quàm TE ad SR, atque ita deinceps quod vel ex ip&longs;is &longs;inuum Ta
bulis con&longs;tat; hoc &longs;uppo&longs;ito, cùm aqua intume&longs;cat magis vel minùs
iuxta proportionem inæqualis pre&longs;&longs;ionis, & pre&longs;&longs;io inæqualis &longs;it iuxta
rationem circulorum pre&longs;&longs;ionis inæqualium, hi porrò inæquales &longs;int
iuxta rationem prædictorum &longs;inuum com
plementi, mare per æ&longs;tum intume&longs;cit ad
in&longs;tar pruni, vel &longs;phæroidos, vt jam &longs;upra
dictum e&longs;t. Sit autem quadrans ellip&longs;eos
ABD, & quadrans circuli ABY di
vi&longs;us in quotcunque arcus æquales; item
quadrans circuli AGD; &longs;int anguli
GAF, DAE æquales, quadrans
ABY e&longs;t ad quadrantem ellipticum
neæ, vt vocare &longs;oleo; item quadrans ABD e&longs;t ad quadrantem AGD, vt
AY ad AD; igitur figura YDB e&longs;t ad figuram BGD, vt AY ad AD, &longs;unt
que duæ i&longs;tæ figuræ homogeneæ; igitur vt YD ad GB, ita EO ad CI,
ita HO ad CF, ita K a ad ab; &longs;ed YD, BG &longs;unt æquales, igitur OE
& IC æquales, item OH & CF, item a K & ab, igitur tantum cre&longs;
cit aqua vi pre&longs;&longs;ionis à B in I, quantum ab H ad Y, vel ab E in D ; igitur
&longs;ub initium & finem cre&longs;cit aqua modicis incrementis, ii&longs;que reciprocè
æqualibus hinc inde, a&longs;&longs;umptis &longs;cilicet angulis æqualibus; majori
bus verò &longs;ub medium; en tibi germanam & facilem tui quæ&longs;iti ra
tionem, quæ dubito, an æquè facilè in qualibet alia hypothe&longs;i afferri
po&longs;&longs;it.
Quid dici queat, quod in rem hanc meliùs quadret, certè non
video; &longs;ed cur in Æquinoctiis æ&longs;tus major e&longs;t?
Iam &longs;upra ea &longs;uper hoc expo&longs;ui, quæ tibi facerent &longs;atis, &longs;i for
tè in memoriam revocares; nempe, vt jam indicavi, &longs;i Autores illos
con&longs;ulamus, qui de hoc argumento &longs;crip&longs;erunt, nihil ferè ni&longs;i repugnan
tia inter &longs;e inveniemus; nimirum aliqui &longs;crip&longs;erunt, æ&longs;tum maximum e&longs;&longs;e
in Sol&longs;titiis, minimum verò in Æquinoctiis, alij contra maximum in
Æquinoctiis, minimum in Sol&longs;titiis; alij majorem in Æquinoctio ver
no; alij majorem in autumnali; alij majorem in Sol&longs;titio Brumali, mi
norem in Æ&longs;tivo; alij majorem in æ&longs;tivo, minorem in Brumali nihil af
fingo; Augu&longs;tine, hæc adeò repugnantia apud Autores invenies. De Sol
&longs;titiis nihil certi, cùm etiam in hoc Autores varient, non dubito tamen,
quin, id quod e&longs;t, in no&longs;tram notitiam venire po&longs;&longs;it, fidelis ob&longs;ervatio
nis opera, in eodem &longs;cilicet loco; nempe pro diver&longs;is locis, diver&longs;a ra
tio e&longs;t, cùm diver&longs;a &longs;it pre&longs;&longs;io; &longs;ed pro eodem loco facilè ob&longs;ervari po
te&longs;t in vtroque Sol&longs;titio æ&longs;tus a&longs;&longs;urgentis men&longs;ura, tum diurni, tum no
cturni; cùm multum inter vtrumque di&longs;crimen e&longs;&longs;e po&longs;&longs;it; nulla autem re
gula certa &longs;tatui pote&longs;t, propter diver&longs;am pre&longs;&longs;ionis rationem, ob &longs;uperfi
ciem globi variis, &longs;ine lege & ordine, maris & continentis tractibus di
&longs;tinctam. Quod pertinet ad Æquinoctia; hoc vnum certò con&longs;tat, maxi
mum in iis cieri æ&longs;tum, Luna &longs;cilicet plena aut nova, &longs;altem in no&longs;tro
Oceano, intra Europam; rationem hic globus tibi &longs;uggeret, in quo
vides, Luna exi&longs;tente in Æquatore arcus pre&longs;&longs;ionum e&longs;&longs;e majores; vbi
verò Luna declinat versùs Boream, in quo tractu, Europa no&longs;tra &longs;ita e&longs;t,
vides, ni fallor, quantam prædictorum arcuum aream circulus maximæ
pre&longs;&longs;ionis re&longs;cindat, traducátque ad oppo&longs;itum hemi&longs;phærium, exi&longs;ten
te Luna infra horizontem ad Meridianum; qua &longs;ita &longs;upra horizontem, de
meridie &longs;cilicet Luna nova, de media nocte, in Plenilunio vides quan
tam maxima pars Americæ inutilem reddat: vbi porro Lu
Au&longs;trum, eadem pror&longs;us ratio militat; po&longs;ita enim Luna in Tropico
Capricorni, in Novilunio de meridie idem e&longs;t circulus maximæ pre&longs;&longs;io
nis, qui erat de media nocte dum Luna nova e&longs;&longs;et in Tropico Can
cri; in Plenilunio verò, de meridie, idem e&longs;t circulus maximæ
Cancri; vnde vt vides, eadem pro vtroque Sol&longs;titio ratio militat.
e&longs;&longs;e; at gravi&longs;&longs;imi Autores dicunt majorem e&longs;&longs;e in Æquinoctio autumnali
v.g.ad o&longs;tia Garumnæ.
Ita e&longs;t æquè pro vtroque probat hæc ratio, & ita e&longs;&longs;e nemo
inficiatur. Scilicet per &longs;e; nam per accidens &longs;ecus accidere pote&longs;t; v.g.eo
quod major vis humoris aëri admixta &longs;it &longs;ub Æquinoctium Autumnale,
quàm &longs;ub Vernum; & verò cum &longs;it terminus æ&longs;tatis, dubium non e&longs;t,
quin longè major humoris &longs;eu vaporis, in quem humor abit copia aëri ad
mixta &longs;it; vnde major evadit gravitatio, major pre&longs;&longs;io, & major æ&longs;tus: in
Zona torrida & Au&longs;trali &longs;ecus dicendum e&longs;t; accedit, quod in Æquino
ctio, rarò fit Novilunium aut Plenilunium; &longs;ed tantùm aliquot ante, vel
po&longs;t diebus; adde diver&longs;am venti vim, quæ ad majorem æ&longs;tum non parum
confert; &longs;i hæc tibi non faciant &longs;atis, nihil habeo vltra quod tibi ex
ponam.
Faciunt haud dubiè; nec dubito, quin paucis aliis po&longs;tu
latis, quæ mihi re&longs;tant etiam facturus &longs;is &longs;atis; quæro igitur ex,
te, vtrum vrinatores, qui profundiùs immerguntur, vim & motum æ&longs;tus &longs;en
tiant.
Ga&longs;&longs;endus hoc ip&longs;um probari curavit, invenítque non &longs;entiri
æ&longs;tum pluribus pa&longs;&longs;ibus infra &longs;uperficiem maris, quod certè ex præmi&longs;&longs;is
omnino &longs;equitur; nempè infra arcum BY ne minima quidem impre&longs;&longs;io
aquæ accidit; in quo meo judicio, nulla e&longs;t difficultas; vnde fabulam reputo,
ab ebulliente mari per æ&longs;tum, marinas belluas &longs;ur&longs;um ad &longs;uperficiem pelli,
illud fortè verius, &longs;eu veri&longs;&longs;imilius, ad litus Per&longs;icum allidi pi&longs;ces
ad &longs;copulos, quod aliquando vi &longs;ævi&longs;&longs;imæ tempe&longs;tatis actum e&longs;&longs;e
ferunt; hinc pi&longs;ces &longs;æviente procella in maris profundum &longs;e reci
piunt.
Illud etiam fabulo&longs;um crediderim; quod à quibu&longs;dam Auto
ribus refertur, &longs;cilicet ad Norvegiam, e&longs;&longs;e quemdam maris tractum, in quo
&longs;enis horis Naves & grandia cete &longs;orbentur à mari, & aliis Senis extrudun
tur; itémque inter Angliam & Nortmanniam e&longs;&longs;e voraginem, versùs quam
naves veloci&longs;&longs;imo cur&longs;u actæ etiam vicinæ gurgiti repelluntur. Hæc meta
&longs;unt Nautarum garrientium figmenta.
Idem quoque &longs;entio; quanquam prædictus gurges Angliam
inter & Nortmanniam, ip&longs;e fortè e&longs;t gemini æ&longs;tus concur&longs;us, qui non
di&longs;&longs;imilem effectum præ&longs;taret, vt con&longs;ideranti patebit; Ille verò tractus
ad Norvegiam, qui naves votat, ac deinde evomit, dubito an &longs;it circel
lus maximæ depre&longs;&longs;ionis, quem circa Polum mundi de&longs;cribit punctum di
&longs;tans à Parallelo Lunari 90. gradibus nempe ad in&longs;tar cuju&longs;dam voraginis
e&longs;t, &longs;ub&longs;idente aqua &longs;enis horis, ae totidem a&longs;&longs;urgente; &longs;ed dum res certò
non con&longs;tet, quod &longs;it, fru&longs;tra quæritur, propter quid &longs;it: Non negarim
versùs Norvegiam, in quo re verà tractu mare profundi&longs;&longs;imum e&longs;t, qua&longs;dam
fectus.
Proba&longs;ine quod aliqui &longs;cribunt, in cingulis ex Lupi marini co
tio factis, per æ&longs;tum pilos erigi & &longs;tare, in refluxu verò deprimi, hoc etiam
fabulam olet, ni fallor.
Vt vt &longs;it, quædam humore rige&longs;cunt, ac proinde eriguntur,
vt funes ex canabe, præterea per æ&longs;tum, aër minus compre&longs;&longs;us e&longs;t, magis
in refluxu; quid mirum ergo, &longs;i refluxus tempore pilos illos de
primat.
Sed quid cen&longs;es de iis fontibus & puteis, quorum aliqui at
tolluntur cum Oceano per æ&longs;tum, alij contra &longs;ub&longs;idunt.
Multa etiam fabulo&longs;a de his Scriptoribus promulgata fue
runt; difficile tamen non e&longs;t; rationem horum adducere; nempè altior
aqua per æ&longs;tum, plus aquæ extrudit per exiguos areno&longs;æ terræ meatus;
minus verò aqua &longs;ub&longs;idens; quòd &longs;i per longiores mæandros aqua tradu
cenda e&longs;t, ad putei, &longs;eu fontis recepta culum non tam citò pervenit, &longs;ed fortè
&longs;ex horis tardiùs. Sic
tertio po&longs;t die, pro diver&longs;a for nicis cra&longs;&longs;itudine; nec obe&longs;t, aquam dul
cem e&longs;&longs;e; quia marina per arenam percolata dulce&longs;&longs;it: nihil dico de aliis
multis fontibus, qui aliquoties per diem intume&longs;cunt, ac deinde &longs;ub&longs;i
dunt, nulla tamen temporum &longs;ervata lege, quia ad hoc argumentum non
pertinent: quanquam in diver&longs;is fontibus artefactis facilè videmus, quid
etiam indu&longs;trio&longs;a natura in hac materia præ&longs;tare valeat.
Alia Exciderant; quid enim de Mari Ca&longs;pio, de Ponto Euxino,
de Mari Baltico, de Eurippo ad Eubeam, de quibu&longs;dam lacubus in Ameri
ca, in quibus æ&longs;tus fieri dicitur?
In Ca&longs;pio, Euxinio, Baltico, vel nullus, vel modicus æ&longs;tus e&longs;t
cùm ab Oceano traduci non po&longs;&longs;it, & tractus aquarum breviores &longs;int, &
ita &longs;iti, vt &longs;en&longs;ibilem pre&longs;&longs;ionis inæqualitatem non inducant. De lacubus
Americæ memoratis, dicendum e&longs;t, vel e&longs;&longs;e tantæ longitudinis vt 700.
etiam milliaria adæquent, quod &longs;ufficit, vt aliqua pre&longs;&longs;ionis inæqualitas
inducatur, vel per majorem fluminis alveum ab Oceano vim æ&longs;tus eò tra
duci, quod &longs;altem meo judicio, difficultate caret. Iam de celeberrimo
illo Græciæ Eurippo nunc dicam, de quo fabulo&longs;a multa narrantur; nem
pe aliàs &longs;epties &longs;ingulis diebus æ&longs;tua&longs;&longs;e dicitur, nunc verò quater in die:
quod ad me &longs;pectat, fateor vltro, me nunquam vidi&longs;&longs;e; quantum tamen
ex incolarum relationibus audire potui, bis &longs;ingulis diebus in præfato Eu
rippo recurrit æ&longs;tus; &longs;ed quia it reditque duodecim horis, alii&longs;que duo
decim pariter fluit, ac re&longs;init æquè rapido cur&longs;u, quater in die æ&longs;tuare vi
detur; hujus autem Eurippi eadem ratio e&longs;t, quæ aliorum, de qua jam
&longs;upra; fieri ta
rant in i&longs;to gemini æ&longs;tus, ab vtraque &longs;cilicet extremitate, nempe ad orti
vam vis æ&longs;tus traducitur per fauces illas, quæ &longs;unt inter Cretam & Orien
tale Peloponen&longs;i cornu, non procul ab In&longs;ula Cythere, vulgò
verò per medium qua&longs;i Ægeum vis æ&longs;tus appellitur; ex præfato verò con
cur&longs;u varij vortices na&longs;ci videntur, qui vulgo ventorum vi, vel aliis cau&longs;is
tribui &longs;olent; vnum dumtaxat libenter addo, anilem fabulam jam olim de
Ari&longs;totele &longs;par&longs;am fui&longs;&longs;e, cum &longs;cilicet, præ de&longs;peratione, Eurippi cau&longs;am
non capientem &longs;e&longs;e in medium Euripum præcipitem dedi&longs;&longs;e; quis hoc
amabò credat? ni&longs;i qui nimiæ laboret vitio credulitatis?
Sed quid tamdiu
taciturnus fui&longs;ti, &longs;uavi&longs;&longs;ime Chry&longs;ocome? cur huc v&longs;que de argumento
adeò difficili di&longs;&longs;erentem non interpella&longs;ti? An fortè res i&longs;ta tibi non pla
cuit?
Placuit haud dubiè, neque hoc in&longs;iciari po&longs;&longs;um; &longs;ilui tamen,
nec interpellavi vnquam, quia multa &longs;anè volvebam animo, quæ contra ea,
quæ dicebas, mihi opponenda e&longs;&longs;e videbantur, quæ mihi haud parum diffi
cultatis præferre videbantur.
Su&longs;tine tanti&longs;per Antime, & per te mihi liceat nodos
i&longs;tos à Chry&longs;ocomo contextos di&longs;&longs;olvere mentem tuam callere ap
prime mihi videor; &longs;i quid in &longs;olutione mea de&longs;ideretur facilè &longs;upplere po
teris.
Legem accepto; profer igitur, Chry&longs;ocome, illa omnia,
quæ volvi&longs;ti animo adversùm nos: vtrumque di&longs;&longs;erentem libenter au
diam.
Primo quidem loco incredibile e&longs;&longs;e videtur, tantam
vim ine&longs;&longs;e aëri, qua immen&longs;um propemodum aquarum pondus attolle
po&longs;&longs;it.
An fortè putas, totam aquarum molem ab aëre gravitante
attolli, aut &longs;u&longs;tineri? falleris; cùm illa tantùm aquæ portio &longs;u&longs;tineatur,
quæ &longs;upra libellam maximæ depre&longs;&longs;ionis attollitur, & quæ mihi videtur
per exigua, & ferè nulla, &longs;i cum tota aëris móle comparetur; & verò &longs;i
tota vis prementis aëris libera e&longs;&longs;et; id e&longs;t, &longs;i omnes circuli & arcus pre&longs;
&longs;ionis vtiles e&longs;&longs;ent; id e&longs;t, &longs;i totam globi &longs;uperficiem aqua tegeret, æ&longs;tus
profectò longè altiùs a&longs;&longs;urgeret: &longs;ed dic mihi, &longs;odes, quanta &longs;it altitudo
aëris gravitantis in circulum maximæ pre&longs;&longs;ionis, &longs;eu depre&longs;&longs;ionis; ne ti
bi nimius videar, la&longs;&longs;umo tantùm 1000. &longs;emidiametros terræ; igitur
859000.leucas, quarum quælibet continet 4. millaria, vt quodlibet mil
liare 1000. pa&longs;&longs;us geometricos, quilibet pa&longs;&longs;us 5. pedes; &longs;upponamus au
tem aquam e&longs;&longs;e graviorem aëre millie
tudinis iuxta communem innatantium legem, aquæ innataret, vna &longs;ui
mille&longs;ima parte immergeretur, atque adeò &longs;egmentum immer&longs;um
859. Leucarum e&longs;&longs;et; tantumdem igitur aquæ attolleret; miror
igitur, illum, de quo dubitare videris, aëris gravitantis ni
&longs;um majorem non e&longs;&longs;e: immo inde facilè colligo, longè majo
rem e&longs;&longs;e gravitatis aquæ proportionem ad gravitatem aëris, & in
feriorem aëra fortè graviorem &longs;uperiore, tum propter humorem ad
mixtum, tum fortè, quia compre&longs;&longs;ior e&longs;t: ca&longs;tiga igitur præoccupatum
erit.
hoc nomine &longs;u&longs;pécta multis e&longs;&longs;e videbitur.
Fateor vltro, hanc &longs;ententiam novam e&longs;&longs;e, &longs;ed ex antiquis
& certis principiis deducta; quòd &longs;i minimè liceat, nullus vnquam re&longs;
literariæ progre&longs;&longs;us &longs;perandus e&longs;t: & verò quid damni ex hac novitate ti
meri po&longs;&longs;it, non video; &longs;upponit enim hæc &longs;ententia marinum
omnibus phænomenis, quæ à rerum i&longs;tarum periti&longs;&longs;imis ob&longs;ervata fuere;
docet, prædictum æ&longs;tum e&longs;&longs;e à Luna, eiu&longs;que incrementum in Novilunio
& Plenilunio; decrementum in Quadraturis; maximam vim circa Æqui
noctia; agno&longs;cit aëta gravem e&longs;&longs;e; quis hoc neget? atque adeò &longs;uo ni&longs;u,
&longs;ua vi pro&longs;&longs;iva pollere, quæ toties in actum exeritur, quoties major e&longs;t,
quàm re&longs;i&longs;tentia; docet præterea Lunam ex no&longs;tris elementis compactam
e&longs;&longs;e; & hæc communis e&longs;t Sanctorum Patrum &longs;ententia; ac proinde So
lis & caloris vi humorem educi ex Luna; denique docet commune me
dium versùs illum globum gravitare, cui propiùs e&longs;t, vnde gravitationis,
ac proinde pre&longs;&longs;ionis inæqualitatem &longs;equi, nece&longs;&longs;e &longs;it, & ex hac, aqua
rum tumorem & æ&longs;tum. Cuncta hæc, etiam præ&longs;cindendo ab æ&longs;tu, ita à
natura con&longs;tituta e&longs;&longs;e putarem; &longs;i vltra dubitas, ponamus ex hypothe&longs;i,
nec enim, opinor, negabis ita e&longs;&longs;e po&longs;&longs;e; fingamus igitur, ita
e&longs;&longs;e; & vide, vtrùm cuncta æ&longs;tus marini phænomena rectè expli
centur.
Si aër gravitat, cur eius pondus non &longs;entimus?
deinde quomo
dò fieri pote&longs;t, vt idem aëris tractus modò versùs vnum, modò ver&longs;us aliud
centrum gravitet? An fortè novit, cui proprior e&longs;t?
denique, humor ille
Lunaris, vbi &longs;emel terræ illap&longs;us e&longs;t, cùm hæc immobilis con&longs;i&longs;tat, non
videtur, quomodò in maternum patriumque &longs;inum & globum denuò redi
re valeat.
aëris pondus &longs;icuti nec vrinatores pondus aquæ; nempe ideò me
dium gravitat, vt corpus &longs;ubjectum levius &longs;ur&longs;um extrudat; nihil
ergo ab eius pondere nobis timendum e&longs;t, qui aëre graviores &longs;u
mus; immo id vnum dumtaxat aëris, vel alterius medij gravita
tio in nobis præ&longs;tat, vt minùs graves &longs;imus, detracta nobis ea
gravitatis, &longs;eu gravitationis parte, quæ pondus tantæ molis aëris, quan
tæ nos &longs;umus, adæquat. Secundum verò &longs;ic diluo; terminus extrin&longs;ecus
determinat lineam motus gravium, ex naturæ in&longs;ti
fine; nec opus e&longs;t, vt mobile cognitione, aut &longs;en&longs;u polleat; &longs;ed cum &longs;uum
finem obtinere debeat, &longs;uam vim exerit ad illum obtinendum; cùm igitur
corpus grave debeat con&longs;tituere vnum totum, &longs;eu
aliis corporibus, &longs;eu partibus
versùs commune centrum, in quo natura con&longs;tituit terminum illius latio
nis; vnde &longs;i fortè centrum illud locum mutaret, etiam corpus grave lineam
motus mutaret. Res e&longs;t per&longs;picua in terræ mobilis hypothe&longs;i, quæ licèt vera
Quemadmodùm
verò corpus grave determinatur à termino extrin&longs;eco, id e&longs;t, à centro, ad
talem lineam gravitationis, licèt centrum illud non videat, nec cogno&longs;cat,
ita determinatur ab eodem termino vel centro, cui propius e&longs;t, licèt ne&longs;ciat,
cuinam propius &longs;it. Tertium denique jam &longs;upra &longs;olutum e&longs;t; nempe caloris
vi, Lunaris humor longè no&longs;tro liberior ac proinde &longs;ubtilior, facilè rare&longs;cit,
atque avolat, is præ&longs;ertim, qui extra vmbram terræ po&longs;itus &longs;olares radios
diu excipit; in quo, meo judicio, nulla e&longs;t difficultas.
In quadraturis eadem ratio pre&longs;&longs;ionis e&longs;&longs;et; quia eadem
gravitationis inæqualitas, quæ e&longs;t in copulis & oppo&longs;itione; æqualis igitur
æ&longs;tus, quod tamen ob&longs;ervationibus repugnat, deinde in lacubus Lunari
globo &longs;ubjectis, æ&longs;tus attolli deberet; denique in Oceano Septentrionali mo
dicus æ&longs;tus e&longs;&longs;et, quia &longs;cilicet à punctis maximæ elevationis multum di&longs;tat.
draturis eadem &longs;it ratio pre&longs;&longs;ionis, ratione altitudinis Cylindrorum aëris
gravitantis, diver&longs;a tamen e&longs;t ratione medij; nempe in Quadraturis aëri
versùs terram gravitanti, minus humoris ine&longs;t igitur; inde &longs;equitur, e&longs;&longs;e
minùs gravem, ac proinde minorem exeri gravitationis effectum, æ&longs;tum
videlicet. Secundùm jam &longs;upra dilutum e&longs;t; cùm enim lacuum &longs;uperficies
paucos admodùm gradus complectatur, inæqualitas pre&longs;&longs;ionis in ea &longs;en&longs;i
bilis non e&longs;t; quid mirum ergo, &longs;i effectus illius, nimirum æ&longs;tus, &longs;en&longs;ibilis
non &longs;it; hinc vbi &longs;unt majores lacus vt Americani illi, de quibus &longs;uprà, vel
vbi lacus per aliquod Fretum Oceano conjuncti &longs;unt, &longs;en&longs;ibilis in iis æ&longs;tus
ob&longs;ervatur. Tertium denique &longs;ic rejicio; in prima illa hypothe&longs;i, qua &longs;up
ponitur tota globi &longs;uperficies aquea; ita res &longs;e haberet; at &longs;ecundùm præ
&longs;entem rerum &longs;tatum, eáque globi terraquei &longs;uperficie &longs;uppo&longs;ita, quæ modò
e&longs;t propter diver&longs;as reflexiones, pre&longs;&longs;iones, angu&longs;tias, eò currit æ&longs;tus, quo
major vis, vel alia quæpiam lineæ determinatio inclinat; hinc ad eandem
&longs;æpè oram etiam in locis parum di&longs;&longs;itis, adeò diver&longs;us æ&longs;tus e&longs;t.
Per aver&longs;a igitur flumina non a&longs;cenderet æ&longs;tus, in quorum &longs;u
perficie inæqualitatis pre&longs;&longs;ionis &longs;en&longs;ibilis non e&longs;t.
Non ideò a&longs;cendit per alveum fluminis, quòd fluminis &longs;uper
ficies prematur, &longs;ed quòd &longs;uperficies maris, cùm per æ&longs;tum intume&longs;cat, &
&longs;it &longs;upra &longs;uperficiem fluminis, more gravium, versùs eam partem excurrat;
neque in hoc vlla difficultas re&longs;tat.
Circuli pre&longs;&longs;ionum ad libitum à vobis accipiuntur; cur enim po
tiùs hi, quàm illi? vnde, ni fallor, ruit præcipua hujus ve&longs;træ &longs;ententiæ &longs;ub
&longs;tructio.
Nego, fingi ad libitum; nempe non fingitur linea Ab&longs;idum,
vel connectens centra; neque linea confinium, &longs;eu dirimens, neque circuli
paralleli, per quotum centra, Ab&longs;idum linea ducitur, cadit que perpendicu
lariter in eorum plana; nec æqualis gravitatio, &longs;eu pre&longs;&longs;io in quolibet pun
cto circuli paralleli; nec communis ni&longs;us ab omnibus punctis eju&longs;dem cir
culi; quia &longs;cilicet æqualis; &longs;i enim e&longs;&longs;et inæqualis, vna aliam &longs;uperaret; igi
tur adversùs illam ageret; igitur actio communis non e&longs;&longs;et. Hinc mani-
punctis ni&longs;us inæqualis e&longs;t; cuncta hæc igitur non ad libitum &longs;tatuuntur,
&longs;ed ex linea connectente centra, quæ ex globorum &longs;itu &longs;emper re&longs;ultat, ne
ce&longs;&longs;ariò con&longs;equuntur: non ruitigitur hujus &longs;ententiæ fundamentum, &longs;ed
maximoperè inde confirmatur.
Verbulum addo, & con&longs;idero lineam connectentem centra; ad
in&longs;tar axis coni, cuius vertex ad centrum terræ de&longs;init; Diameter verò ba
&longs;is, in quam prædictus axis perpendiculariter cadit, e&longs;t ip&longs;a linea confinium;
con&longs;idero item infinitos conos, &longs;eu &longs;uperficies conicas, quarum ba&longs;es &longs;int
circuli concentrici in plano prædictæ ba&longs;is, & quarum maxima e&longs;t planum
circuli majoris, parallelum prædictæ ba&longs;i; minima verò præfata Ab&longs;idum
linea; quælibet &longs;uperficies conica, &longs;ecat &longs;uperficiem globi terraquei in cir
culo, & omnes huju&longs;modi &longs;ectiones &longs;unt circuli paralleli, per quorum cen
tra linea Ab&longs;idum rectâ ducitur; hi &longs;unt circuli pre&longs;&longs;ionum, inæquales qui
dem inter &longs;e, ita tamen, vt in quolibet eju&longs;dem circuli puncto, æqualis pre&longs;
&longs;io fiat; vereor, vt alius modus e&longs;&longs;e po&longs;&longs;it pre&longs;&longs;ionis inæqualis, re&longs;pectu eju&longs;
dem centri. Reliqua omitto; perge Chry&longs;ocome.
Si æ&longs;tus à Lunæ motu e&longs;&longs;et, ad Lunæ motum &longs;e&longs;e compone
ret; ac proinde nunquam æ&longs;tus ab occa&longs;u ad ortum excurreret, quod certè
omnibus experimentis refragatur.
Si aqua totam globi terraquei &longs;uperficiem tegeret, tumor il
le, &longs;eu maximæ elevationis punctum, quod nunquam Lunæ non re&longs;pondet
&longs;emper ab ortu in occa&longs;um ire videretur; at in hoc rerum &longs;tatu versùs litus
humilius a&longs;&longs;urgens per æ&longs;tum aqua excurrit, quoquo ver&longs;um tandem &longs;pectet,
idque maximè &longs;i linea cur&longs;us in oram illam directè incidat.
Ventus impediret vim æ&longs;tus, cùm tamen illam augeat, aëre
&longs;cilicet acto, per lineam Horizontalem, ac proinde impedito illius gravi
tationis ni&longs;u.
ligno humido innatante, quod licèt ad in&longs;tar naviculæ per Horizontalem
impellatur; totum tamen illius pondus &longs;uam vim exerit gravitando; v. g.
fit vas aqua plenum 20.libr.&longs;it lignum aquæ innatans.5.libr. quod per Ho
rizontalem moveatur, haud dubiè, &longs;i vas ip&longs;um tunc appendas, 25.librarum
pondus &longs;enties: &longs;ic aqua, quæ &longs;upra fundum alvei currit; in hoc &longs;uæ gravi
tatis vim totam exerit; idem dico de globo in plano Horizontali rotato:
aër igitur quantumvis agitatus totius gravitationis effectum præ&longs;tat.
Vix crediderim, lapidem per Horizontalem projectum, to
tius gravitationis &longs;uæ vim exerere; alio quin recta deor&longs;um iret; igitur nec
aër per lineam Horizontalem à Vento actus.
Ex eo quod lapis totam vim &longs;uæ gravitationis exerat, non
&longs;equitur, quod recta deor&longs;um ire debeat, cùm motu quodam mixto movea
tur, idque per Parabolam, vt jam multi demon&longs;tra&longs;&longs;e dicuntur: Deinde non
e&longs;t par ratio lapidis & aëris; lapis enim non gravitat cum aëre gravitatio
per Horizontalem movetur, cum aliis &longs;ibi &longs;ubjectis, & impo&longs;itis, gravitatio
ne communi gravitat.
Per vos mihi liceat, breve Parergon interferete, vt hæc meliùs
intelligantur. Corpus, quod e&longs;t in medio, vel eju&longs;dem e&longs;t cum medio gra
vitatis, vel majoris, vel minoris; &longs;i minoris, innatat medio; &longs;i majoris, im
mergitur; &longs;i æqualis, in quocunque loco illud colloces, ibi manet: porrò
corpus humido innatans, gravitatione communi cum ip&longs;o medio gravitat;
cujus rei luculentum exémplum, vel experimentum attuli&longs;ti, Augu&longs;tine; nem
pe totum illud vas appen&longs;um 25.libr.pendit, &longs;ive lignum quie&longs;cat, &longs;ive flu
ctuet; &longs;ive in fundo va&longs;is atte retineatur; &longs;ive &longs;ur&longs;um emergat; &longs;ive per
Horizontalem feratur: Et verò vbi nihil propriæ & &longs;ingularis gravitatio
nis retinet, in communem gravitationem totam &longs;uam vim refundit; hinc
manus ligno innatanti &longs;uppo&longs;ita nullum pondus &longs;entit, ni&longs;i fortè illud tan
tulum attollas, vel filo ex parte immer&longs;um &longs;u&longs;tineas; tunc enim vas ip&longs;um
minùs pendit; v.g. &longs;i dum lignum ex parte immer&longs;um &longs;u&longs;tines, &longs;entis trium
libr.pondus, vas 22.libr. tunc erit; hinc &longs;i vas dextrâ, lignum verò filo ap
pen&longs;um &longs;ini&longs;trâ &longs;u&longs;tineas, vtraque &longs;imul totum pondus, &longs;ed qua propor
tione plus ligni &longs;ini&longs;tra &longs;u&longs;tinet, eadem in va&longs;e dextera minus pondus &longs;u
&longs;tinet: porrò &longs;i corpus aqua gravius &longs;it, v.g.plumbum, haud dubiè immer
gitur, &longs;it v.g, idem vas 20.libr.&longs;it pila plumbea 10. libr. vbi hæc fundum
va&longs;is attigit, totum va&longs;is pondus erit 30.libr.at &longs;i vas pendatur eo dumtaxat
tempore, quo pila plumbea per aquam de&longs;cendit, &longs;upra 20.libr. illam tan
tum ponderis acce&longs;&longs;ionem &longs;enties, quam aqua, vt &longs;ic loquar, plumbo detra
hit, æqualem &longs;cilicet ponderi portionis aquæ, eju&longs;dem molis; &longs;upponamus
autem gravitatem plumbi e&longs;&longs;e decuplam gravitatis aquæ, vas erit 21. libr. idem &longs;iet, &longs;i pila omnino immer&longs;a filo &longs;u&longs;tineatur.
Hinc duo Paradoxa facilè
deducetis; primum &longs;it, corpus leve, quod &longs;ur&longs;um per mediam aquam va&longs;e
contentam emergit, magis gravitat in eum, qui vas ip&longs;um &longs;u&longs;tinet, quàm
corpus grave, quod per mediam aquam deor&longs;um fertur: ac proinde corpus
levius majorem vim gravitationis exerit, quàm gravius; hinc quò plus &longs;in
gularis gravitationis corpus retinet intra medium va&longs;e contentum, mino
rem vim facit adversùs illum, qui vas &longs;u&longs;tinet; & quoad vim ponderis, perin
de e&longs;t, &longs;ive prædicta pila plumbea liberè per aquam deor&longs;um eat, &longs;ive aquæ
immer&longs;a & filo appen&longs;a &longs;u&longs;tineatur; contra verò quò minus &longs;ingularis gra
vitationis corpus retinet, eò magis gravitat in eum, qui præfatum vas &longs;u
&longs;tinet. Alterum Paradoxum e&longs;t: Qui&longs;quis prædictum vas portat, præter 20.
libr.aquæ 1.libram plumbi &longs;u&longs;tentat, quamvis alioquin plumbum immer
&longs;um & filo appen&longs;um ab infinita potentia &longs;u&longs;tineatur; quia &longs;cilicet me
dium
aëris tractus, qui à vento igitur, nihil propriæ gravitationis retineat, &longs;ed to
tam in communem conferat, quamvis per diver&longs;as lineas &longs;ur&longs;um deor&longs;um
ve, dextror&longs;um aut &longs;ini&longs;tror&longs;um à vento agatur, nullam tamen proprij pon
deris jacturam facit, &longs;ed totam illius vim ac ni&longs;um exerit gravitatione com
muniquare hoc nodo &longs;oluto, vide, an quidpiam aliud ocourrat, quod nobis
opponas.
Nihil prorsùs: vnicum tantùm dubium re&longs;tat; vtrùm &longs;ci
licet diver&longs;a vmbræ projectæ ratio in Novilunio ac Plenilunio aliquod
di&longs;crimen in æ&longs;tu faciat.
Fat
nempe in Novilunio vmbra à globo Lunari projicitur in Hemi&longs;phærium
&longs;upra Horizontem, & à terre&longs;tri in Hemi&longs;phærium infra Horizontem; in
Plenilunio verò ab vtroque globo projicitur in Hemi&longs;phærium, noctu &longs;u
pra, diu infra Horizontem; &longs;ed hoc magnum di&longs;crimen in æ&longs;tu non facit;
præ&longs;ertim cùm humor ille dumtaxat Lunatis ad æ&longs;tum aliquid conferat,
qui terre&longs;tri globo propior e&longs;t, &longs;ive den&longs;ior &longs;it, &longs;ive rarior, ju&longs;ta enim fit com
pen&longs;atio; quippe &longs;i rarior e&longs;t, plus loci occupat, igitur illius gravitatio in
plura di&longs;trahitur, ac proinde &longs;inguli Cylindri minorem vim habent; &longs;i au
tem den&longs;ior e&longs;t, deor&longs;um tendit, hinc minùs confert in gravitationem com
munem: vnde vides vnum ab alio compen&longs;ari: &longs;ed jam &longs;atis de hoc argu
mento, quod certè majorem di&longs;cu&longs;&longs;ionem po&longs;tularet, quam vobis ve&longs;tro
commodo faciendam relinquo.
Su&longs;tine parumper, Antime, maximum dubium mihi injeci&longs;ti;
&longs;i enim humor Lunaris den&longs;ior minùs confert in gravitationem commu
nem, nulla igitur ratio e&longs;t, cur in Novilunio & Plenilunio major æ&longs;tus
fiat.
Multa, crede mihi, adhuc ratio re&longs;tat; nam præter eam, quæ à
projectis vmbris, vt &longs;upra dictum e&longs;t, peti po&longs;&longs;et, non ignoras corpu&longs;cula
etiam gravi&longs;&longs;ima tum aquæ, tum aëri innatare, ac proinde vtrumque ele
mentum inde gravius reddi; &longs;ic fœtæ nubes, & multus vapor affu&longs;us ab au
&longs;tro, aëra graviorem reddunt, vt Sal vel Sabulum aquæ admixtum; idem de
præfato humore Lunari dictum puta: cur verò corpu&longs;cula illa gravi&longs;&longs;ima
leviori medio innatent, non e&longs;t hujus loci di&longs;cutere, &longs;ed quæ&longs;o vos, huic
congre&longs;&longs;ui finem imponamus, ne docti&longs;&longs;imorum hominum auribus & pa
tientia, immodica garrulitate abutamur.
Rectè mones; &longs;ed quando nobis commodum erit ad pro
ximum congre&longs;&longs;um redire?
Quando voles, diem indicendum tibi relinquo.
Po&longs;t tridum igitur vos expecto, vt pulcherrimum illud argu
mentum de a&longs;&longs;urgente per fi&longs;tulam humido & Mercurio in eadem ab ex
teriori aëris Cylindro, vt multi volunt, ad certam altitudinem &longs;u&longs;tentato,
di&longs;cutiamus.
Hoc ip&longs;um e&longs;t, quod nobis di&longs;cutiendum re&longs;tat; quare con&longs;ulite
illos Autores, qui de hac materia &longs;crip&longs;erunt, vt ex variis probati&longs;que expe
rimentis, veritas tandem eluce&longs;cat; nonnihil addemus, delibando &longs;altem,
de vi electrica, quam aliqui ad rem hanc nonnihil conferre putarunt.
& Mercurio di&longs;putatur.
AMOENISSIMVM argumentum, quod tibi fortè
arrideat, Princeps Eminenti&longs;&longs;ime hodierna die di&longs;cutien
dum &longs;u&longs;cepi, vtinam feliciter, quod tuis au&longs;piciis futurum
&longs;pero, demon&longs;trandum. Antiquis omnino intactum fuit,
& paucis ex recentioribus compertum experimentum;
primùm ca&longs;u innotuit; at deinde &longs;tudio & arte, vltra
promotu
explorandam, quod vtrùm cuipiam pro votis &longs;ucce&longs;&longs;e
&longs;im; &longs;ed vt meliùs di&longs;&longs;ertatione pareat, huic demus initi
bus præludiis, quæ & ad rem de qua agitur, parum aut nihil conferunt, &
tibi Cardinalis Eminenti&longs;&longs;ime alioquin occupati&longs;&longs;imo, nihil aliud ni&longs;i me
rum tædium afferrent.
Para&longs;ti, vt video, dulci&longs;&longs;ime Augu&longs;tine, totam illam &longs;upelle
ctilem, quæ ad ea, de quibus di&longs;putare in&longs;tituimus, experimenta pertinent;
video limpidi&longs;&longs;imam in va&longs;e aquam admoto&longs;que canaliculos vitreos vtrim
que pervios; video Mercurium in va&longs;e & longiorem fi&longs;tulam vitream al
tera parte clau&longs;am; accipio vnum ex i&longs;tis canaliculis, in &longs;uperficiem aquæ
immergo, humor &longs;tatim per canaliculum a&longs;&longs;urgit, ad digitalem ferè altitu
dinem, vt vides.
Video quidem, &longs;ed miror magis; canaliculum inclino, altiùs
humor a&longs;cendit; & quod fortè mirabilius e&longs;t, breviorem canaliculum aquæ
admoveo, ad tantam altitudinem minimè a&longs;cendit; longiorem adhibeo
eju&longs;dem omnino ba&longs;is, altiùs humor a&longs;cendit; alterum orificium admo
to pre&longs;sè digito, claudo, non a&longs;&longs;urgit humor; digitum amoveo, illicò
a&longs;&longs;urgit.
Dicerem, ab illo impetu aquam attolli, quo canaliculus
aquæ admovetur; &longs;ed admoto canaliculo, cujus &longs;upremum orifi
cium digito clauditur, & jam eo quie&longs;cente, cùm nullus impetus
re&longs;tet, amoto digito, humor illico a&longs;&longs;urgit; vnde nece&longs;&longs;ario &longs;equi
tur, minimè a&longs;&longs;urgere, propter impetum appul&longs;us canaliculi: aliquis
fortè diceret, nonnihil rarefactionis accedere; &longs;ed hoc totum inutile e&longs;t;
cur enim aqua intra canaliculum potiùs rare&longs;ceret, quàm intra vas ip&longs;um? deinde æquè frigida ac calida a&longs;&longs;urgit; item æquè vinum ac oleum, &longs;altem.
vt audio.
Ita e&longs;t; in his omnibus &longs;æpè probavi; item in &longs;piritu vini, &
variis aquis di&longs;tillaris ; immò &longs;i canaliculum oleo immergas, paulò altiùs
a&longs;&longs;urgit, qúod non ad evidentiam expertus &longs;um; &longs;ed cuncta hæc ex
perimenta luculentiora &longs;unt in &longs;cypho, vel ampulla, cujus imaginem ha
bes pag. &longs;equenti, in qua &longs;cilicet humor per canaliculum GF a&longs;&longs;urgit &longs;upra
&longs;uperficiem BC, eo profectò altiùs, quo canaliculus angu&longs;tior erit.
An fortè dici po&longs;&longs;et, pondus aquæ contentæ in majore am
pulla, longè majus e&longs;&longs;e pondere aquæ contentæ intra minorem canalicu
lum GF, ac proinde prævalere, & inde aquam altiùs extrudi, &longs;eu
attolli.
Scio, non neminem e&longs;&longs;e, cui hæc cogitatio in mentem venit,
quæ tamen, meo &longs;altem judicio, legitima non e&longs;t, cùm aqua ratione pon
deris, &longs;eu gravitatis ad perfectam libellam &longs;e&longs;e componat; nempe gravi
tat per Cylindros parallelos, &longs;eu lineas parallelas, in quocunque &longs;itu cana
les &longs;tatuantur; &longs;int enim canales ABC, IDE;
infundatur aqua per Orificium AB, &longs;it libella
Horizontalis ABFG; &longs;i canales æqualis &longs;int
cra&longs;&longs;itudinis &longs;uperficies aquæ vtrimque &longs;i&longs;tet in
ABFG, vt patet; tunc enim perfectum erit
æquilibrium; &longs;i verò canalis IDE &longs;it angu&longs;tior,
a&longs;&longs;urget aqua v. g. in DE, &longs;upra libellam AG,
ratione tamen gravitationis, Cylindrus aquæ
cujus ba&longs;is æqualis &longs;it FG, facit perfectum æqui
librium cum Cylindro aquæ æquali IG, vt patet;
&longs;i enim tota moles aquæ contentæ in ABC, &longs;u
&longs;tineret contentam intra IDE, cùm illa hujus po&longs;&longs;it e&longs;&longs;e decupla, centu
pla, & in quavis data proportione majoris inæqualitatis, aqua per cana
liculum IDE ad quamcunque po&longs;tulatam altitudinem a&longs;cenderet, quod
manife&longs;tè fal&longs;um e&longs;t; igitur totus Cylindrus aquæ ABC non facit æqui
librium cum Cylindro aqueo IDE, &longs;ed tantùm Cylindrus eju&longs;dem ba&longs;is
DE; &longs;ed hic facit æquilibrium cum Cylindro IFG, vt patet; igitur inde
per&longs;picuum fit, aquam per canaliculum IDE non a&longs;&longs;urgere in DE &longs;upra
libellam, propter majorem vim ponderis ABC. Accedit quod &longs;i ba&longs;is
AB Diameter &longs;it bipedalis, & ba&longs;is DE &longs;it pedalis, non a&longs;&longs;urget aqua in
DE, immò ad &longs;en&longs;um &longs;i&longs;tet in FG, cùm tamen pondus aquæ ABC &longs;it
quadruplum aquæ IFG; igitur in majoribus canalibus aqua non a&longs;&longs;urgit,
vt in minoribus; vnde manife&longs;tè con&longs;tat, hunc effectum e&longs;&longs;e ab alia cau&longs;a.
po&longs;ui&longs;&longs;em, illico re&longs;pondit vim quandam adhæ&longs;ivam in corporibus præ&longs;er
tim liquidis, &longs;ibi compertam e&longs;&longs;e, ratione cujus, vnum alteri accedit, &longs;e&longs;e
arctiùs conjungit; &longs;ic inquiebat ille, &longs;i aquæ gutta tangat aliam guttam,
in vnam majorem guttam &longs;tatim mutuo qua&longs;i amplexu coale&longs;cunt; &longs;ic duo
flammæ con
lum minimè a&longs;&longs;urgeret, ni&longs;i priùs cava illius &longs;uperficies maduerit, quod vbi
à me probatum e&longs;t, dicto re&longs;pondit eventus: ne&longs;cio vtrùm hæc ratio vobis
arrideat.
Minimè verò, & alia ratio e&longs;t congre&longs;&longs;us guttarum & cono
rum flammæ, de qua infra. Primò, enim gratis affingitur prædicta vis
adhæ&longs;iva liquidis corporibus, ex iis &longs;cilicet effectibus, qui aliis cau&longs;is tri
buendi &longs;unt. Secundò, etiam&longs;i canaliculus ante non maduerit, aqua
tamen a&longs;&longs;urgit, &longs;i paulò laxior e&longs;t; centies probavi infu&longs;o in ampullam
A oleo; & ne qui&longs;piam diceret, oleum a&longs;&longs;urgere
per GF, propter impetum infu&longs;ionis, infudi
oleum, inclinata versùs B ampulla; ita vt &longs;uper
ficies olei per canaliculum vix a&longs;&longs;urgeretin H ;
tum deinde erecta ampulla, oleum a&longs;cendit in F,
licèt inferior canaliculi &longs;uperficies &longs;icca omnino
e&longs;&longs;et; idem fiet admoto canaliculo &longs;uperficiei
olei, &longs;i paulo major &longs;it. Tertiò, Non video cur
major aquæ portio minorem potiùs ad &longs;e non adducat, quàm minor ma
jorem; &longs;i enim prædicta vi vtraque pollet, major certè majore, &longs;cilicet
exten&longs;ivè, vt major flamma magis calefacit, quàm minor; accedit, quod
in hoc ca&longs;u, minor longè faciliùs ad majorem accederet, &longs;cilicet de&longs;cen
dendo, quàm major ad minorem a&longs;cendendo. Quartò, in majore tubo
madefacto eadem ratio militaret; nec dicas ob&longs;tare majorem vim pon
deris; quia cùm vis illa adhæ&longs;iva omnibus partibus aquæ in&longs;it, eadem e&longs;t
illius proportio ad re&longs;i&longs;tentiam ponderis in majore, quæ in minore; &
vt duæ partes in minore &longs;uperant duas partes ponderis; ita mille partes in
majore &longs;uperabunt mille partes ponderis. Quintò, Cur oleum altiùs a&longs;
&longs;urgit, quàm aqua? Cur Mercurius ferè nihil?
dico ferè, quia infra evin
cam tantulùm a&longs;&longs;urgere; Cur aliquando ip&longs;a aqua altiùs, aliàs minùs
altè a&longs;cendit? Nihil horum cum illa vi adhæ&longs;iva &longs;tare pote&longs;t.
Sextò,
Cur aqua per canaliculum inclinatum longiùs excurrit? Cur per bre
viorem, quamvis madefactum interiùs, minùs altè, & &longs;i adhuc breviorem
accipias, ferè nihil a&longs;&longs;urgit? Cur per tubulos alioquin &longs;icci&longs;&longs;imæ materiæ,
vt panis bis cocti, panni, telæ &c. Ex his vides, ni fallor, Chry&longs;ocome, aliam
omnino hujus effectus cau&longs;am quærendam e&longs;&longs;e.
Sed cur per canaliculum &longs;iccum non a&longs;&longs;urgit, atque adeò ca
va illius &longs;uperficies humectanda e&longs;t?
Si canaliculus paulò laxior &longs;it, & majoris ba&longs;is etiam per &longs;ic
cum a&longs;cendit; non a&longs;cendit, tamen &longs;i angu&longs;ti&longs;&longs;imus &longs;it, ni&longs;i &longs;en &longs;im ac
lentè; quia licèt &longs;uperficies vitri lævigata e&longs;&longs;e videatur, mille tamen
&longs;alebris & rugis, &longs;eu &longs;triis a&longs;peratur, quæ ni&longs;i affu&longs;o humore com
planentur, a&longs;perum iter faciunt, & modicam aquæ portionem faci
lè &longs;i&longs;tunt; cùm tamen in majore canaliculo non ob&longs;tent; quin major
aquæ copia a&longs;&longs;urgat; accedit, quod &longs;i juxta Figuras præcedentes va&longs;a
conformentur, aqua etiam per canaliculum &longs;iccum a&longs;cendit; cur au
tem aquæ gutta intra aliam &longs;ubeat, vel flamma intra flammam, dicemus
po&longs;tea.
Ex his ergo con&longs;tat, totam rem i&longs;tam ab aëris com
pre&longs;&longs;ione petendam e&longs;&longs;e, vt jam indica&longs;ti in &longs;uperiore congre&longs;&longs;u,
cumbit.
Rectè mones, rem hanc paulò fu&longs;iùs explicandam e&longs;&longs;e; quod
ut meliùs fiat; nonnulla &longs;uppono experimenta, partim commu
nia & trita, partim &longs;ingularia. Primùm &longs;it hoc.
Ampulla vitrea
DACB, cui per os D canaliculus vitreus vtrim
que pervius in&longs;eratur, & probè ob&longs;tructo ori
ficio D, exugatur ducto anhelitu per E, aër
intra ampullam contentus; tum &longs;tatim, vbi
removetur ab ore, immergatur in aquàm ex
tremitas E; &longs;ugitur enim aqua, dum aër intra
dilatatus &longs;e&longs;e contrahit; &longs;ic demum AB &longs;uper
ficies aquæ per &longs;uctum adductæ; tum extremo
E ore admoto, pul&longs;us anhelitus magna vi in
trudatur; inde &longs;it, vt aër ABD appul&longs;u novi
aëris comprimatur, & compre&longs;&longs;us &longs;uperficiem
aquæ AB premat, ac proinde &longs;upra &longs;uperficiem AB aqua per canalicu
lum CE a&longs;&longs;urgat; immò &longs;i &longs;it magna vis pre&longs;&longs;ionis, ad in&longs;tar jaculi erum
pat. Idem fiet opera di&longs;ci, &longs;uperficiem aquæ prementis, vt jam dixi in &longs;u
periore congre&longs;&longs;u.
Certum & per&longs;picuum e&longs;t, illum aquæ jactum e&longs;&longs;e ab vna
pre&longs;&longs;ione aëris va&longs;e contenti & compre&longs;&longs;i; quia &longs;cilicet aquæ &longs;uperficiem,
cui incumbit, premit; & cùm nihil ob&longs;i&longs;tat pre&longs;&longs;ioni intra canaliculum,
prædicta vi aqua facilè extruditur; hæc vt dixi, adeò certa &longs;unt, vt nul
lum po&longs;t &longs;e dubium relinquant. Sed quid hoc ad aquam, per canaliculum
in aëre libero a&longs;&longs;urgentem? Licèt enim concedam, aëra e&longs;&longs;e compre&longs;&longs;um,
cùm non minùs premat &longs;uperficiem aquæ intra canaliculum contentæ;
quàm intra majus vas, v.g. &longs;uperficiem DE, quàm
AB, neque hinc, neque illine vis illa pre&longs;&longs;ionis
prævalere pote&longs;t.
Fateor, maximum di&longs;crimen e&longs;&longs;e in
ter experimentum Figuræ 31. & 32. quia in hac,
aër ADB novam compre&longs;&longs;ionem patitur, qua
tamen aër exterior caret; vnde non modò tan
tulùm a&longs;&longs;urgit aqua per canaliculum CE, vt
fit, etiam &longs;i nova compre&longs;&longs;io minimè accedat,
& os ampullæ D pateat; &longs;ed magna vi, ad in&longs;tar
jaculi extruditur; quem reverà effectum il
la modica vis pre&longs;&longs;ionis, quæ ine&longs;t aëri, præ&longs;tare non po&longs;&longs;et; por
rò licèt aër exterior incumbat vtrique &longs;uperficiei aquæ &longs;cilicet AB
& GF, major tamen vis premit AB, quam FG, quia corpus
pre&longs;&longs;um quoquo ver&longs;um pellit in orbem; igitur eò major vis e&longs;t,
quo &longs;ub majori angulo incidit; v. g. a&longs;&longs;umatur centrum &longs;uperficiei
AB, premitur per infinitos radios, vnde quaque illap&longs;os; cogita co
num, cujus vertex prædicto centro incumbat; igitur quò prædictus
quò ille acutior; Sit autem centrum &longs;uperficiei FG canaliculo contentæ,
in quod aëris prementis conus incumbat, vides, ni fallor, quàm acu
tus angulus futurus &longs;it; ac proinde vis pre&longs;&longs;ionis minor; quid mi
rum ergo, &longs;i pre&longs;&longs;io in AB prævaleat, ac proinde aqua &longs;upra FG a&longs;
&longs;urgat?
Quid verò fiet, &longs;i canaliculi &longs;egmentum &longs;ũmpta FG, &longs;it minus
FE? an fortè aqua vi prædictæ pre&longs;&longs;ionis effluet per canaliculum? &longs;i hoc
fieret, perpetuum motum haberemus.
Prævideram, te in hunc &longs;copulum impacturum; nempe, in
quis, &longs;i aqua per canaliculum majore vi pre&longs;&longs;ionis vigente in AB, a&longs;&longs;ur
git in DE, haud dubiè &longs;i re&longs;cindatur &longs;egmen
tum canaliculi ME, effluet per os ML, cum
eadem vis pre&longs;&longs;ionis aplicata &longs;it in in AB; &longs;ed
reverà non effluit ex ML ; & hoc e&longs;t alterum
experimentum; cùm tamen alioquin iuxta com
munes Hydraulicæ regulas faciliùs &longs;it effluere
ex ML, quàm in DE attolli; ratio e&longs;t, quia vt
in centrum ba&longs;is AB aëris pre&longs;&longs;io incumbit,
&longs;ecundùm angulum, &longs;eu conum maximè obtu
&longs;um, ita in ba&longs;im DE, vel in ba&longs;im ML, re&longs;ecto
&longs;egmento canaliculi ME, &longs;ecundùm æqualem
angulum incumbit; quid mirum ergo, &longs;i neutra pre&longs;&longs;io prævaleat? At
verò &longs;i non re&longs;cindatur &longs;egmentum ME, incumbit in centrum ba&longs;is
ML, &longs;ecundùm angulum acutum, cujus ba&longs;is e&longs;t DE, & latus recta ducta
à D, ad centrum ML. Vnde pre&longs;&longs;io in AB omnino prævalet.
Sed infra, pre&longs;&longs;io in AB &longs;emper major e&longs;t pre&longs;&longs;ione in ML ;
etiam re&longs;ecto &longs;egmento ME; nempe vt aëris pre&longs;&longs;io incumbit centro
ba&longs;is AB, idque in reliquis punctis &longs;ecundùm æqualem pre&longs;&longs;ionis angu
lum, &longs;eu conum, item in &longs;ingula puncta ba&longs;is ML, &longs;ecundùm æqualem
priori angulum, refecto &longs;cilicet &longs;egmento ME; igitur pre&longs;&longs;iones &longs;unt,
vt ba&longs;es; initur ba&longs;is AB, quæ longè major e&longs;t prævalet; igitur &longs;i tua
pre&longs;&longs;ionis ratio &longs;ub&longs;i&longs;teret, aqua ex ML omnino efflueret; non effluit ta
men, vt fateris vltrò.
Acutè omnino paralogizas; vt enim gravitatio aquæ con
tentæ in canali AC, exerit tantùm &longs;uam vim, attollendo cylindrum IG,
ad libellam v&longs;que, &longs;ecundùm cylindrum æqualem IG, vt &longs;upra o&longs;ten
&longs;um e&longs;t; ita vis pre&longs;&longs;ionis ba&longs;is AB exeritur, attollendo aquam per ca
naliculum &longs;ecundùm ba&longs;im æqualem ML, vbi autem aqua elevata e&longs;t in
ML, æqualis incumbit pre&longs;&longs;io vtrimque, &longs;cilicet in ba&longs;i ML, & ip&longs;i æqua
li a&longs;&longs;umptæ in AB; &longs;i verò aquæ fuper&longs;icies &longs;upponatur in FG, haud
dubiè minor e&longs;t pre&longs;&longs;io in FG, quàm in ML ; igitur quàm in æquali
ML a&longs;&longs;umptæ in AB; igitur hæc prævalet; vnde a&longs;&longs;urgit aqua ex FG
in ML: cogita quæ&longs;o duci totidem cylindros parallelos deor&longs;um præ
&longs;ci&longs;a gravitatione, ex &longs;ingulis punctis ba&longs;is AB, quibus totidem pre&longs;-
contranituntur, &longs;inguli &longs;cilicet cylindri cum &longs;ingulis; igitur neutra pars
prævalet, &longs;i verò non re&longs;cindatur &longs;egmentum ME, equidem &longs;inguli
cylindri ducti ex &longs;ingulis punctis ba&longs;is ML pugnant cum &longs;ingulis ductis
ex ba&longs;i AB, hi tamen victores &longs;unt; quia fortiores; cùm &longs;ingulis vis
pre&longs;&longs;ionis &longs;ecundùm majorem conum, vel angulum incumbat; igitur
quamvis alioquin angu&longs;ti&longs;&longs;imus &longs;it canaliculus, &longs;i tamen &longs;upra libellam
AG non producatur, par vtrimque e&longs;t vis pre&longs;&longs;ionis; ac proinde
neutra pars prævalet; vnde, ni fallor, tuus ille paralogi&longs;mus &longs;olutus
manet.
Ex dictis rectè deduco, aquam attolli altiùs in longiore, ca
naliculo; nempe in longiore, angulus pre&longs;&longs;ionis acutior & minor e&longs;t,
quàm in breviore v. g. angulus DFE, minor e&longs;t angulo DME, vt
patet.
Hoc erat tertium experimentum; aqua enim in canaliculis
longioribus tantulùm immer&longs;is altiùs a&longs;&longs;urgit: & ni&longs;i nimiæ ob&longs;tarent
angu&longs;tiæ, per quas &longs;ine aliqua vi aqua traduci nequit, ad quamcumque
certè altitudinem aqua a&longs;&longs;urgeret.
Prudenter occurri&longs;ti in&longs;tantiæ, quam tibi facere meditabar;
alia tamen longè difficilior &longs;e&longs;e mihi objicit ; cùm enim &longs;inguli pre&longs;&longs;ionis
cylindri &longs;ingulis contranituntur; perinde e&longs;t, five laxior &longs;it canaliculus,
&longs;ive angu&longs;tior, quod tamen experimentis repugnat, cùm per canalicu
lum angu&longs;tiorem longè altiùs humor a&longs;&longs;urgat.
Haud inficior, difficultatem à te propo&longs;itam eam e&longs;&longs;e, quæ in
genio tuo digna e&longs;&longs;e videatur; quam tamen, ni fallor, &longs;atis facilè &longs;olvo:
nempe aër pre&longs;&longs;us majorem vim non imprimit &longs;uperficiei majori AB
quàm minori DE; Cogita di&longs;oum ligneum, quo premitur &longs;uperficies A
B, motu vt vnum, itemque alium minorem, quo premitur &longs;uperficies DE,
motu vt vnum; certè vterque æqualem vim imprimit &longs;uperficie, DE &
AB; licèt enim alter major &longs;it, & majorem &longs;uperficiem premat; quia
tamen idem aër compre&longs;&longs;us circumfu&longs;us vtramque æquè premit, æqua
lis &longs;emper pre&longs;&longs;ionis effectus &longs;equitur, id e&longs;t, eju&longs;dem quantitatis aquæ
elevatio; cæteris tamen paribus: vbi enim hæc elevata e&longs;t, & ab eadem
vi premente &longs;u&longs;tinetur, nullus alius effectus illi competit, cùm tota in
eo exeratur; dixi cæteris paribus, id e&longs;t, &longs;uppo&longs;ita eadem proportione
pre&longs;&longs;ionis aëris incumbentis &longs;uperficiei canaliculi, &longs;i enim propter bre
vitatem canaliculi prædicta proportio cre&longs;cat, vel &longs;it major canaliculus,
ac proinde angulus pre&longs;&longs;ionis major, itemque major pre&longs;&longs;io, haud dubiè
aqua minùs altè per canaliculum a&longs;cendit: Suppo&longs;ita autem eadem pro
portione pre&longs;&longs;ionum, altitudines aquæ elevatæ in diver&longs;is canaliculis,
&longs;unt vt ba&longs;es permutando, vt pater, v.g. &longs;i ba&longs;is vnius &longs;it dupla ba&longs;is alte
riùs, altitudo ejus erit dupla altitudinis illius, vt &longs;cilicet cylindri æqua
les &longs;int.
Iam optimè intelligo id, quod paulò ante capere non po
teram; quod &longs;cilicet, vt aiebas, ad quamcumque altitudinem aqua po&longs;-
enim proportione decre&longs;cit ba&longs;is, cre&longs;cit, altitudo; &longs;ed quæ&longs;o te, quid fiet,
&longs;i aquæ &longs;uperficies non &longs;it in AB, &longs;ed in HK.
Certum e&longs;t, minorem inde fore aquæ elevationem; quia pre&longs;
&longs;io in ba&longs;im HK minor e&longs;t quam in ba&longs;im AB; quia fit &longs;ub minore an
gulo, v.g. &longs;tante ba&longs;i in AB, a&longs;&longs;urgeta qua in DE &longs;upra libellam FG, de
pre&longs;&longs;a verò ba&longs;i in HK &longs;upra libellam HP, a&longs;&longs;urget aqua in R, eritque
PR minor quàm GE. Hîc autem ob&longs;ervo aliud experimentum, reverà
pulcherrimum, nempe &longs;uperficies aquæ in HK, non e&longs;t plana, nedum
convexa, &longs;ed omnino concava; cùm tamen AB modo humor extet, &longs;it
convexa.
Hoc etiam &longs;æpiùs ob&longs;ervavi, & cau&longs;am huju&longs;ce peregrini
effectus curiosè per&longs;crutatus &longs;um; nec crediderim ab vllo v&longs;piam prodi
tam fui&longs;&longs;e.
Ex præmi&longs;&longs;is facilè deducitur, modò tantulum Geometriæ ac
cedat. Suppono enim AB qua&longs;i ba&longs;im trianguli, cujus vertex terminetur
ad HK, cujus trianguli angulus verticis major e&longs;t, qui cadit in centrum
D prædictæ ba&longs;is, quàm is, qui cadit in extremitates ba&longs;is H vel K ; vt pa
tet ex Geometria; igitur major vis pre&longs;&longs;ionis incumbit in centrum O,
quàm in H vel K, & con&longs;equenter in ea puncta major, quæ accedunt
propiùs ad centrum O; quid mirum igitur, &longs;i punctum O &longs;ub&longs;idat, &
tota &longs;uperficies HOK cava &longs;it, propter inæqualem illam pre&longs;&longs;ionis vim.
Sed quæ&longs;o te, Antime, cur aquæ &longs;uperficies AB convexa e&longs;t?
video enim, cur cava non &longs;it, cùm inæqualis illa pre&longs;&longs;io de&longs;ideretur; cur
tamen convexa &longs;it, non plana, haud &longs;atis video.
Res &longs;atis trita e&longs;t; nempe illa humoris &longs;uperficies à centro
mundi æqualiter di&longs;tat &longs;ecundùm omnes partes; &longs;i enim aliqua longiùs
à præfato centro di&longs;taret, quàm aliæ, de&longs;cenderet illico; hæc certè vt ve
ritati con&longs;ona, negari ab vllo non po&longs;&longs;unt; &longs;ed profectò hæc convexitas
in&longs;en&longs;ibilis e&longs;t, nempe arcus vnius minuti continet 1000. pa&longs;&longs;us geome
tricos, vnius &longs;ecundi arcus 16. pa&longs;&longs;us &
vnius tertij vnum pedem tubos vix habemus majoris diametri; quis
porrò arcum vnius tertij minuti à linea recta &longs;en&longs;u di&longs;tinguat? Cùm igi
tur convexam &longs;uperficiem aquæ probè di&longs;cernamus, aliam omnino e&longs;&longs;e
nece&longs;&longs;e e&longs;t (& hoc &longs;it aliud experimentum) nempe vbi humor extremita
tes A & B ba&longs;is attigit, non effluit aqua, &longs;ed intume&longs;cit in centro &longs;uper
ficiei; centro enim minor vis pre&longs;&longs;ionis incumbit, quàm partibus extre
mis, v.g. in centrum V vis pre&longs;&longs;ionis incumbens infra horizontalem AB
non cadit, cum tamen incumbens in A & in B infra prædictam horizon
talem de&longs;cendat, vt patet, quò fit, ne aqua ex A vel B effluat & hæc vera
e&longs;t & legitima triti hujus experimenti ratio.
Non bene capio quid tibi velis; nonnihil, quæ&longs;o te,
&longs;chematis adhibe, tunc enim oculis potiùs quàm auribus fidem ha
bebo.
Sit vas quodpiam aqua plenum AEDB, &longs;it aquæ &longs;uprema
per HG perpendicularem, verùm etiam per infirmas contentas inter
HG. AG, item inter GH, GB; nulla autem
e&longs;t infra AB horizontàlem per quam punctum
G prematur, vt per&longs;picuum e&longs;t, at verò punctum
A, versùs quod aqua effluere nititur, proptia
gravitatione, non tantum premitur à perpendi
culari IA & ab aliis contentis inter IA, MA,
item inter IA, AB, &longs;ed etiam ab aliis infra MA
ductis, vt à PA. idem dico de puncto B, item
que de aliis in totius marginis orbe di&longs;po&longs;itis,
in quibus haud dubiè pre&longs;&longs;io prævalet, vnde aquam in &longs;uperficiem con
vexam intume&longs;cere nece&longs;&longs;e &longs;it. Hinc quò major e&longs;t va&longs;is &longs;uperficies mi
nùs intume&longs;cit; quia ad tumorem æquè altum; plus aquæ, vi pre&longs;&longs;ionis
attollendum e&longs;&longs;et; &longs;ic vt jam dixi, per canaliculum angu&longs;tiorem altiùs a&longs;
&longs;urgit aqua, per majorem &longs;eu laxiorem, minùs altè, e&longs;t enim ead
sùs ratio.
Vnum mihi venit in mentem; ne&longs;cio vtrùm tuo calculo
probaturus &longs;is, Antime; redeo ad primum &longs;chema & &longs;uperficiem AB,
(
no; &longs;uperficiem verò ML, excurrente canaliculo v&longs;que ad DE, conca
vam; quo po&longs;ito, numquid dici po&longs;&longs;et, partes extremas A & B, quibus ma
jor vis pre&longs;&longs;ionis imprimitur, quam centro V efficere vt partes extremæ
alterius ba&longs;is ML, altiùs affurgant; Vnde vt ex hac in
æquali pre&longs;&longs;ionis vi ba&longs;is AB convexa evadit, ita & ba&longs;is ML concava.
Quàm acute paralogi
in HK majoris canalis, & in R minoris, vtraque cava per&longs;picitur; vnde,
ni fallor, ruit tua ratio; quare vis illa pre&longs;&longs;ionis inæqualis, quæ incum
bit in &longs;uperficiem &longs;upremam AB, alium effectum præ&longs;tat, nimirum illum
quem dixi; attollit enim &longs;uperficiem AB &longs;upra libellam, eamque tornat
in convexam; ideò verò cava e&longs;t &longs;uperficies HK; quia vis pre&longs;&longs;ionis in
O major e&longs;t, quàm in H vel in K, quia &longs;ub majore angulo incumbit.
Hoc jam &longs;uprà dixeras, &longs;ed ne quid di&longs;&longs;imulem, non mihi
&longs;tatim occurrit demon&longs;tratio illa geometrica, quam appella&longs;ti quidem,
non tamen expo&longs;ui&longs;ti.
Ad prima elementa me reducis, Chry&longs;ocome, &longs;int latera va
&longs;is AE, BF; os verò AB; &longs;uperficies aquæ EF, cen
trum C, &longs;int anguli ACB, AEB, dico ACB e&longs;&longs;e
majorem, ducatur enim circulus per 3. puncta ABC,
fecat BE in D ; ducatur AD, anguli ADB, ACB &longs;unt
æquales quia &longs;u&longs;tinent eundem arcum AB, &longs;ed ADB
e&longs;t major prædicto AEB, cùm &longs;it exterior; igitur an
gulus AEB e&longs;t minor ACB; idem de quolibet alio
demon&longs;tratur: &longs;ed jam ad alia experimenta venia
mus, Sit ampulla A, de quà &longs;upra; aquæ &longs;uperfi-
cies KI in canaliculo verò &longs;it D ; volam manus admove
ori BC cum modica pre&longs;&longs;ione; &longs;tatim aqua per canalicu
lum altiùs a&longs;&longs;urgit versùs F ; vbi verò repentino motu ma
nus ab ore AB, amovent, de&longs;cendit aqua præceps in G.
&longs;ed &longs;tatim denuo a&longs;&longs;urgit versùs F.
Ex præmi&longs;&longs;is huius experimenti facilè ratio
nem afferam, nempe aër vola pre&longs;&longs;us aquæ &longs;uperficiem KI premit, ex cujus
pre&longs;&longs;ione, per canaliculum nece&longs;&longs;ariò altiùs ar&longs;&longs;urgit : amota autem repente
vola, aquæ &longs;uperficiem AB &longs;ecum tantulum adducit, attollítque; vnde
aquam per canaliculum &longs;ub&longs;idere nece&longs;&longs;e e&longs;t.
Inde omnium huiu&longs;modi experimentorum communem ratio
nem reddo: &longs;i enim aër magis compre&longs;&longs;us aquam per canaliculum attol
lit; certè minùs altè attollit; nullo modo pre&longs;&longs;us non attollit; adductus
verò, &longs;ecum versùs G aquam m canaliculo contentam adducit. Et verò,
vt tandem ad rem propiùs accedam, cùm hic motus, quo aqua a&longs;&longs;urgit,
non &longs;it ab intrin&longs;eco, vt con&longs;tat ex dictis, nec enim aqua &longs;pontè &longs;ua a&longs;
cendit, ab alia cau&longs;a extrin&longs;eca illum e&longs;&longs;e, nece&longs;&longs;e e&longs;t; eaque profectò
applicata quænam porrò illa e&longs;t, ni&longs;i aër? quidquid tandem aër &longs;it, &longs;ive
purus, &longs;ive impurus, id e&longs;t aliis corporibus admixtus; aër porrò applica
tus motum illum imprimere nequit, ni&longs;i vel gravitando, vel illo ni&longs;u, qui
ex compre&longs;&longs;ione corporum &longs;equitur; primum dici non pote&longs;t, cùm enim
gravitet per cylindros parallelos, æquè gravitat in minorem aquæ &longs;uper
ficiem, ac in majorem ; ac proinde vtraque, &longs;i gravitationis dumtaxat ra
tio habeatur, in eadem libella &longs;ita e&longs;t, nec vna a&longs;&longs;urgit &longs;upra aliam, re
&longs;tat igitur, vt dicamus, aëra tantulum compre&longs;&longs;um cum ni&longs;um exerere in
&longs;uperficiem BC, non quidem per cylindros parallelos; &longs;ed per conos,
quorum &longs;inguli vertices &longs;ingulis &longs;uperficiei punctis incumbunt; ac proin
de minorem ni&longs;um exeri adversùs &longs;uperficiem aquæ CD canaliculo con
tentæ, quia &longs;ub minoribus angulis exeritur, vt &longs;upra luculenter o&longs;ten&longs;um
e&longs;t; prævalet igitur pre&longs;&longs;io incidens in &longs;uperficiem BC ; ac proinde aliam
CD attollit versùs F.
Iam ob&longs;ervo inde germanam duci rationem, illius addu
ctionis atramenti; vbi enim atramenti guttam calami ro&longs;trum extre
mum attingit, (quod pueri facere &longs;olebamus) attramentum illico
a&longs;&longs;urgit, & cavum calami ro&longs;trum implet; in alio liquore idem &longs;uc
ce&longs;&longs;um iri, certi&longs;&longs;imum e&longs;t; calamum tamen priùs humectatum fui&longs;&longs;e
oportet.
Luculentam rationem jam attulit Antimus; &longs;ic enim com
planatur &longs;uperficies calami, alioquin multis rugis & &longs;alebris &longs;triata & a&longs;
perata, huic autem experimento communis illa ratio Antimi facilè ap
plicatur, ab inæqualis pre&longs;&longs;ionis ni&longs;u petita; nam reverà in totam guttæ
&longs;uperficiem, excepto &longs;cilicet puncto illo contactus, in quo extre
mum ro&longs;trum guttæ immergitur, major e&longs;t pre&longs;&longs;ionis ni&longs;us, quàm in ca
vam ro&longs;tri &longs;uperficiem; quid mirum ergo &longs;i prævaleat illa, & humor per
cavum ro&longs;trum a&longs;cendat? aliquid &longs;imile in omnibus guttis ob&longs;ervo, ad-
currit.
Guttarum res nonnihil fortè &longs;citu dignum nobis exhibet; &longs;ed
ne hoc excidar, antequam illam aggrediar; &longs;i ro&longs;trum calami longiùs &longs;it,
& valde tenue, & in mucronem extenuatus, quamvis extremum ro&longs;trum
guttæ immergas, nihil aut parum attramenti a&longs;&longs;urgit: ratio e&longs;t, quia par
vum, aut nullum ferè obicem ponit ad pre&longs;&longs;ionis inæqualitatem inducen
dam; nempe tenuis illa ro&longs;tri linea pauci&longs;&longs;imos pre&longs;&longs;ionis radios intercipit;
nulla igitur vel modica inæqualitatis pre&longs;&longs;ionis proportio; ex hoc etiam
experimento efficax, meo judicio, argumentum ducitur, quò per&longs;picuè
concluditur, huju&longs;modi aquarum elevationem ab inæquali ambientis aëris
pre&longs;&longs;ione procedere.
Quid &longs;i cylindrus &longs;olidus immergatur, an fortè ali
quid aquæ attollitur; cùm hic obex inæqualem pre&longs;&longs;ionem in
ducat?
Aliquid omnino, quod tamen longè melius ad oculum
patet, &longs;i prædictus tantulum &longs;triatus &longs;it, pro quo eadem, vt vides, ratio
militat.
Quid verò fieret, &longs;i canaliculus in alium paulo am
pliorem immergatur? vel duo &longs;imul quorum minor majori inclu
&longs;us &longs;it?
Pro diver&longs;a canalium & immer&longs;ionum ration
dunt à me ob&longs;ervata experimenta & ad idem principium &longs;atis feliciter re
ducta.
Primò enim &longs;it canalis major HB aqua plenus; ad.
moveatur, vt priùs dictum e&longs;t, minor canaliculus MN,
humori illico a&longs;&longs;urgit in K, perinde atque &longs;i in quam
libet aliam aquæ, etiam majore va&longs;e contentæ &longs;uperfi
ciem immergatur; propter eandem rationem, de qua
huc v&longs;que.
Secundò.
Si aquæ &longs;uperficies &longs;it tantùm in C & de
mittatur canaliculus MN in C, a&longs;&longs;urget aqua v.g. in G
ita
inæqualitatis proportio in pre&longs;&longs;ionibus,
tet; minor igitur illius effectus, minus igitur attollitur
aqua: &longs;uppono enim
terceptam
nalis &longs;uperficiem, quàm per minorem canaliculum.
Tertiò.
Si &longs;ecus accidat, id e&longs;t, &longs;i cavitas canaliculi
major e&longs;t prædicta vacuitate intercepta, humor per
vacuitatem illam a&longs;cendet v.g. in FE, &longs;ed nullo modo
per canaliculum NC a&longs;&longs;urget; quia major e&longs;t aëris pre&longs;&longs;io per canalicu
lum, quàm per vacuitatem interceptam.
Quartò.
Si æqualis &longs;it vtriu&longs;que &longs;patij, id e&longs;t, cavitatis & vacuitatis ca
pacitas, & canaliculus demittatur in C, neque hinc, neque illinc
valet.
Quintò.
Iam verò ad aliud quæ&longs;itum venio, & &longs;uppono vtrum
que canaliculum pervium, ita vt minor intra majorem, qua&longs;i intra vagi
nam conditus &longs;it, & tunc etiam pro diver&longs;a di&longs;po&longs;itione varia &longs;uccedunt;
Primò, &longs;it &longs;uperficies Aquæ AB, &longs;it carnalis major FE,
& minor inclu&longs;us HD, vterque eju&longs;dem altitudinis,
& &longs;imili modo immer&longs;us; &longs;i vacuitas majoris (&longs;ic de
inceps appellabo interceptum illud &longs;patium) æqualis
&longs;it minori canaliculo, &longs;cilicet eiu&longs;dem cavitati, per
vtramque æquè altè humor a&longs;&longs;urgit; v.g. in LK, quia
vis æqualis pre&longs;&longs;ionis exeritur ; quod vt fiat ba&longs;is ma
joris FG debet e&longs;&longs;e dupla minoris IH ; dico ba&longs;im,
non diametrum ba&longs;is, ne fortè &longs;chema vos deci
piat.
Secundo.
Si ba&longs;is majoris &longs;it major dupla, altiùs a&longs;
&longs;urgit aqua per minorem, quàm per majorem, v.g.
per minorem in LK, per majorem in MN; quia ma
jor e&longs;t proportio inæqualitatis pre&longs;&longs;ionum ad mino
rem; quàm ad vacuitatem interceptam; igitur & ef
fectum.
Tertio.
Si verò ba&longs;is majoris &longs;it minor dupla, &longs;ecus
accidet; & a&longs;&longs;urget humor altiùs per vacuitatem, quàm per canaliculum, ra
tio patet ex dictis.
Quartò.
Si major altiùs immergatur, quàm minor, cæteris paribus, humor
altiùs a&longs;cendet per minorem, &longs;uppo&longs;ita tamen ba&longs;i majoris &longs;altem dupla
ba&longs;is minoris.
Quinto.
Si verò canaliculus minor profundiùs demittatur, certè ex
hoc capite altiùs deberet a&longs;cendere per majorem, quàm per minorem;
quia tamen major e&longs;t portio renitentis aëris, ne aqua per majorem a&longs;
cendat, quæ priùs non erat, compen&longs;atio fieri videtur, & pro diver&longs;a
ba&longs;ium ratione, modò altiùs, modò æquè altè, modò minùs altè a&longs;
&longs;urgit.
Sexto.
Si &longs;olus major immergatur, ac proinde tantulum a&longs;cendat aqua, &longs;i
deinde minor canaliculus in cum, vt priùs, immittatur, altiùs per vtrumque
aqua a&longs;&longs;urget, tum quia minus &longs;patij occupandum e&longs;t, tum quia vis reni
tentis aëris minor e&longs;t.
Septimo.
Si minor &longs;olus profundiùs immergatur, v.g. v&longs;que in O, minùs
altè a&longs;cendet, quàm ante; per minorem quidem, quia brevius, &longs;upra &longs;uperfi
ciem aquæ &longs;egmentum extat; per majorem verò, quia cum angulus pre&longs;&longs;io
nis renitentis cre&longs;cat, minùs altè humor a&longs;&longs;urgit.
Octavo.
Si verò major &longs;olus profundiùs deprimatur, retento minore in
codem &longs;itu, paulò altiùs a&longs;cendit per minorem; quia vis pre&longs;&longs;ionis circa illius
infimam ba&longs;im cre&longs;cit; hæc autem ratio facit, ne per majorem æquè altè a&longs;
&longs;urgat.
Nonò.
Pro diver&longs;
cavitat
las &longs;upra traditas; nunquam tamen quantum
per illum a&longs;&longs;urgens ex illo effluet.
Decimò, Vbi minoris convexa &longs;uperficies cum majoris cava conjungi
tur, aqua intercepta illico a&longs;&longs;urgit, & qua&longs;i quodam glutine vna cum alia
conjungitur: idem ferè fiet, &longs;i duæ &longs;uperficies convexæ conjungantur. Ex his, quæ huc v&longs;que dixi, de duobus canaliculis, quorum vnus alteri
immittitur, reliqua facilè conjicies.
Nunquam per&longs;uadere mihi potui&longs;&longs;em, in re hac minima
tantam ob&longs;ervationum &longs;ylvam recondi; ex qua ego, &longs;olo ratiocinio mul
tas alias deducere po&longs;&longs;em. Sed quæro ex te, quot &longs;int capita, ex quibus
humor altiùs per canaliculum immer&longs;um a&longs;cendat.
Sex aut &longs;eptem, ni fallor, recen&longs;eo.
Primò, quo longior e&longs;t ca
naliculus, altiùs humor a&longs;cendit, non tamen vbi valdè producitur in pro
portione &longs;en&longs;ibili; Secundò, quo minor e&longs;t canaliculi ba&longs;is; vt patet. Ter
tiò, quo minùs altè immergitur canaliculus, altiùs a&longs;&longs;urgit aqua. Quartò,
major aëris ambientis libertas, & major angulus pre&longs;&longs;ionis, vi cujus hu
mor a&longs;&longs;urgit. Quintò major vel minor aëris ambientis compre&longs;&longs;io.
Sextò
Minor gravitas liquoris attollendi. Septimò, major eju&longs;dem flu
humiditas, &longs;ic &longs;piritus vini altiùs a&longs;cendit quàm aqua, & metallum li
quatum nihil aut parum admodùm.
Quid porrò de Mercurio?
nonnulla enim de illo mihi veniunt
in mentem, quæ vix a&longs;&longs;erere au&longs;im ; quia nunquam illa experimento
probavi.
Exprome tamen, vt &longs;altem videamus vtrum rectè ratioci
neris; cùm fieri non po&longs;&longs;it, quin Antimus illa ob&longs;ervarit.
Primò Mercurius, aut nihil aut parum a&longs;&longs;urgere debet per
canaliculum propter cra&longs;&longs;itudinem & &longs;ummam vim ponderis. Secundò,
Suprema &longs;uperficies intra canalem depre&longs;&longs;a, non e&longs;t cava, &longs;altem &longs;en&longs;ibi
liter, propter eandem rationem. Tertiò, Mercurij gutta per calami ro&longs;trum
non a&longs;&longs;urgit, vt reliqui humores. Quartò non a&longs;&longs;urgit, etiam &longs;i cylindrus
&longs;olidus immergatur, licèt tantulùm a&longs;cendat aqua, &longs;i in ejus &longs;uperficiem
immergatur.
Parum abes à &longs;copo, Augu&longs;tine, eaque tantùm non prævidi&longs;ti,
quæ nonnulli in Mercurio cum &longs;ummo &longs;tupore mirantur. Primò enim &longs;i
canaliculus Mercurio &longs;ecundum alteram extremitatem immergatur, non
modò non a&longs;&longs;urgit per canaliculum, &longs;upra libellam exterioris &longs;uperficiei,
&longs;ed tantulùm &longs;ub&longs;idit, quod hi&longs;ce oculis centies ob&longs;ervavi. Secundò, Non
modo &longs;uprema illius &longs;uperficies cava non e&longs;t, &longs;ed omnino convexa; &
vbi ad os tubi, in quo continetur pertingit, longè convexior, quàm &longs;uper
ficies aquæ. Tertiò, Non modò non a&longs;&longs;urgit gutta Mercurij per ro&longs;trum
calami, &longs;ed ne quidem ro&longs;trum in eam &longs;ubit, &longs;ed vel cedit, non &longs;ine fo&longs;&longs;ula
in puncto contactus, vel repentino motu &longs;e&longs;e &longs;ubducit. Quartò, non
&longs;uperficiem acta &longs;ub&longs;idit, & circa fo&longs;&longs;ulam Mercurij &longs;uperficies attollitur,
idque ad &longs;en&longs;um & evidentiam.
Non video, ne quid di&longs;&longs;imulem, quomodo hæc ex præmi&longs;&longs;is
con&longs;equi po&longs;&longs;int; ac proinde non mirum &longs;i ex iis à me non deducta.
Con&longs;equuntur tamen; nempe cùm Mercurius vitro non adhæ
reat, vt per&longs;picuum e&longs;t, in tantum enim corpus humidum aliorum corpo
rum &longs;uperficiei adhæret, in quantum in cavitates, &longs;trias & pororum o&longs;tiola
&longs;ubit; certè Mercurius præ cra&longs;&longs;itudine in eas angu&longs;tias &longs;e&longs;e minimè inge
rit; vnde aëri locus vitrum inter & Mercurium relinquitur; nec enim va
cuum datur. Sit &longs;uperficies Mercurij AB, in quam
immergatur Cylindrus vitreus EC, &longs;ub&longs;idet M rcurius
in fo&longs;&longs;ulam GH, quæ optimè concipitur, &longs;i tota hæc
Figura circa Cylindri EC axem volvi &longs;upponatur;
cùm enim non adhæreat Mercurius lateri ED, aër
compre&longs;&longs;us qua&longs;i cuneatim penetrat v&longs;que ad G, & fa
cilè à latere ED Mercurium removet; hinc tantulum
attolli Mercurium nece&longs;&longs;e e&longs;t; hinc circa &longs;uperficiem Cylindri EC fo&longs;&longs;ula,
& circa fo&longs;&longs;ulam modicus tumor; vt enim cuneus dum &longs;ubit vnum ab alio
removet, ita premens aër ad in&longs;tar cunei interceptus inter &longs;uperficiem Cy
lindri & Mercurium, hunc ab illa tantulum removet; atque ita, vt vides,
quartum experimentum ad commune no&longs;trum principium reducitur.
Iam verò &longs;ecundum, eodem modo, te duce explicabo, nempe
aër etiam &longs;e&longs;e in&longs;inuat ad in&longs;tar cunei inter &longs;uperficiem cavam canalis &
Mercurium contentum, vn de
ac proinde circa
&longs;ed quid de primo? vix enim video, quonam pacto ad idem principium re
duci queat; idem de tertio dictum &longs;it; &longs;uggere quæ&longs;o mihi, quid &longs;entias.
Per admotum canaliculum Mercurius non a&longs;&longs;urgit; tum quia
cùm longè cra&longs;&longs;ior &longs;it reliquo humore in angu&longs;tias difficiliùs intruditur;
vnde per telam, &longs;eu pannum non colatur, vt aqua; quia per exigua coli fo
ramina difficilè trajicitur; tum quia prædicta fo&longs;&longs;ula exterior circa canali
culi immer&longs;i &longs;uperficiem convexam excavata vim pre&longs;&longs;ionis di&longs;trahit à &longs;u
perficie Mercurij, quæ ba&longs;i canaliculi adhæret, eam que in contrariam par
tem traducit; vnde non mirum, &longs;i vi pre&longs;&longs;ionis Mercurius per canaliculum
non a&longs;&longs;urgat. Sed potiùs ex vtroque capite Mercurius intra canaliculum
&longs;ub&longs;idat infra &longs;uperficiem exteriorem, cùm & vitrum &longs;uo appul&longs;u, & vis
pre&longs;&longs;ionis, quæ per canaliculum exeritur, &longs;upra aliam prævalens, ob ratio
nem expo&longs;itam, Mercurium deprimant. Inde quoque ratio ducitur tertij
experimenti; nempe ro&longs;trum calami propter cra&longs;&longs;itudinem Mercurij in
eum non &longs;ubit, &longs;ed potiùs Mercurius ro&longs;tro cedens in fo&longs;&longs;am &longs;ub&longs;idit; cùm
difficiliùs quàm aqua dividatur; vnde mutatur pre&longs;&longs;ionis ratio, ac proinde
per ro&longs;trum admotum non a&longs;&longs;urgit, vt aqua.
Quid &longs;i in va&longs;e compo&longs;ito iuxta formam præ&longs;criptam &
delineatam in Figura &longs;equente.
Hoc ip&longs;um &longs;ubnectere meditabar; &longs;ed præveni&longs;ti; infundo igi
tur Mercurium in AB, donec totum vas plenum
&longs;it, &longs;tatue libellam AG; ob&longs;erva quantumlibet,
vides Mercurium a&longs;&longs;urgere in FG ; equidem cir
ca centrum V altiùs attollitur, quàm &longs;i e&longs;&longs;et aqua,
propter rationem à me &longs;upra expo&longs;itam; tantu
lum enim &longs;ubït cuneus aëris inter latera va&longs;is &
Mercurium, quod inaqua non fit; vnde altiùs
centrum V. attollitur; minus verò centrum &longs;u
perficiei FG, quia minor e&longs;t &longs;uperficies: vides ta
men, vix oculo di&longs;cerni po&longs;&longs;e, vtra &longs;uperficies al
tiùs a&longs;&longs;urgat; equidem &longs;i canaliculus IE angu
&longs;tior e&longs;&longs;et, difficilius per illum cra&longs;&longs;ior Mercurius a&longs;&longs;urgeret; hinc minùs
altè, in plumbo, & melle idem probabis; &longs;i verò, vt hic, paulò laxior ad ean
dem &longs;en&longs;ibiliter a&longs;cendit altitudinem, & licèt tantulum a&longs;&longs;urgat, per cana
liculum id compen&longs;atur ab altiore tumore &longs;uperficiei AB. Illud porrò tan
tulum, quo a&longs;&longs;urgit ab eadem ratione inæqualis pre&longs;&longs;ionis procedit; cùm
enim aquæ gravitas &longs;it ad
aquæ &longs;upra libellam AG a&longs;&longs;urgens, FL; dividatur linea FM in 15.partes
æquales, vna ex illis erit altitudo &longs;egmenti Mercurij a&longs;&longs;urgentis in canali
culo ID; &longs;i tamen paulò laxior &longs;it, vt dixi; &longs;i enim angu&longs;tior, præ cra&longs;&longs;itudi
ne minùs a&longs;&longs;urgit: vides quàm facilè cuncta hæc ad commune illud princi
pium reducantur, immò ad aliud reduci nequeant; ac proinde ex præmi&longs;&longs;is
omnibus experimentis idem principium etiám &longs;tatuitur & confirmatur. Sci
licet humorem attolli in canaliculo propter inæqualem aëris pre&longs;&longs;ionem.
culus intra alium in&longs;eratur, quando &longs;cilicet in Mercurium immergitur, ex
te re&longs;cire de&longs;idero, cùm mihi dubium non &longs;it, quin cuncta hæc probaveris.
Rectè conjicis, à me probata e&longs;&longs;e: Sit ergo
Cylindrus vitreus AD, cavus, &longs;ed clau&longs;us in CD,
apertus in AB; in quem tantulum Mercurij infu&longs;us
occupet &longs;egmentum CO, & in&longs;eratur canaliculus
vtrimque pervius IE; non a&longs;&longs;urgit Mercurius &longs;upra
libellam NO, &longs;ed tantulum deprimitur in canaliculo;
a&longs;&longs;urgit verò in vacuitate intercepta, propter rationem
jam expo&longs;itam. Si verò infundatur aqua in prædictam
vacuitatem interceptam, tantulum Mercurius in præ
dicta vacuitate contentus deprimitur infra libellam
NO, a&longs;&longs;urgit verò &longs;upra in canaliculo, puta in G ; quod
certè fieri debet, vt &longs;it perfectum æquilibrium; cùm
&longs;cilicet non modò pondus Mercurij NE attollat Mer
curium, verùm etiam pondus &longs;imul aquæ infu&longs;æ; igitur
&longs;i pondus &longs;olius Mercurij &longs;u&longs;tinet &longs;egmentum Mercu
rij EE, majus pondus, vtpote compo&longs;itum ex Mercu
rio & aqua infu&longs;a, majus Mercurij &longs;egmentum &longs;u&longs;tinet, puta EG ; &longs;i autem
tra vacuitatem.
Prætereà &longs;i his &longs;tantibus, attollatur canaliculus IE, v&longs;que ad imam aquæ
&longs;uperficiem, puta v&longs;que ad NO, tunc de&longs;cendente Mercurio ex &longs;egmento
FG, &longs;ubit aqua canaliculum impletque, tum canaliculum, tum vacuitatem,
&longs;i&longs;titque vtraque aquæ &longs;uperficies, tum intra, tum extra canaliculum, in ea
dem libella, puta HM nec a&longs;&longs;urgit aqua per canaliculum altiùs contra mo
rem &longs;olitum; ratio ex eo petitur, quòd aëris pre&longs;&longs;io aquam per canaliculum
attollere nequeat, ni&longs;i &longs;imul attollat Mercurium; &longs;upponitur enim canali
culus tantulum immer&longs;us in Mercurium; hunc autem, vt dixi, attollere non
pote&longs;t; hinc &longs;i canaliculus ita attollatur, vt ima illius extremitas &longs;it &longs;upra
&longs;uperficiem Mercurij, tunc aqua altiùs a&longs;&longs;urgit &longs;upra libellam HM, puta
in I, quia tunc inæqualis aëris pre&longs;&longs;io &longs;uum effectum habet; neque ad
hunc finem Mercurius, vt ante, attollendus e&longs;t, &longs;ed aqua &longs;ola; &longs;i demum
ex illo &longs;itu, quo ima ba&longs;is canaliculi &longs;upremæ Mercurij adhæret, & vtra
que &longs;uperficies aquæ, tum in vacuitate, tum in canaliculo æquè a&longs;&longs;urgit in
HM, deprimas canaliculum v&longs;que ad E, aquæ &longs;uperficies in vacuitate
a&longs;cendit &longs;upra HM, infra quam de&longs;cendit in canaliculo; quia &longs;egmentum
canaliculi immer&longs;um Mercurio ex eo loco imi va&longs;is, quem occupat, extru
dit Mercurium in vacuitatem interceptam faciliùs quàm in canaliculum,
propter angu&longs;tias; quid mirum ergo, &longs;i &longs;uperficies aquæ in vacuita
te a&longs;&longs;urgat &longs;upra HM, hanc enim attollit extru&longs;us à &longs;egmento im
mer&longs;o Mercurius, in canaliculo verò &longs;ub&longs;idente Mercurio, incu
bans aqua etiam &longs;ub&longs;idit, ex his, ni fallor, reliqua facilè intelli
getis.
Cuncta hæc illam aëris pre&longs;&longs;ionem omnino evincunt, ad
quam etiam multa alia, quæ vi cuidam tractrici vulgò tribuuntur, æquè
facilè reducere po&longs;&longs;um. Sic &longs;pongio&longs;a corpora humorem dicuntur exuge
re, vt panis, præ&longs;ertim bis coctus, aut recens, &longs;pongia, pannus, terra
&longs;icca, pumex, aliaque huju&longs;modi; nam pori &longs;eu meatus, quantumvis
obliqui totidem canaliculos faciunt, per quos aqua facilè a&longs;&longs;urgit: Vn
de vis illa tractrix, vt omnino fictitia, rejicitur; item illa Fromondi fa
bula, qui ni&longs;i me fallit memoria lib. 5. Meteor. cap.2. art.2. Vbi Conimbri
cen&longs;ium aliorumque &longs;ententias rejeci&longs;&longs;et, recurrit ad qua&longs;dam partes aquæ
tenuiores, quæ &longs;ur&longs;um a&longs;cendunt; &longs;ed illa aqua, vbi deinde &longs;pongia expri
mitur, æquè cra&longs;&longs;a e&longs;t atque alia, & aëre longè gravior; cur ergo a&longs;cen
dit? Idem Fromondus aquam frigidi&longs;&longs;imam exugi negat; &longs;ed merum men
dacium e&longs;t.
Sine quæ&longs;o i&longs;tum hominem; &longs;ufficiat à te optimè deduci, il
los effectus, qui vulgò &longs;uctioni, &longs;eu vi tractrici tribuuntur, ad idem prin
cipium no&longs;trum reduci; vt autem ad illud redeam, novum experimentum
adduco, per quod, meo judicio, mirificè confirmatur: Sit vas quodlibet
aqua plenum, admoveatur canaliculus, in &longs;itu perpendiculari, illico aqua
a&longs;&longs;urgit; appendatur in hoc eodem &longs;itu canaliculus, fideli bilance, aqua, quæ
&longs;ubit, nullum momentum addit ponderi canaliculi vitrei; quod vt accura-
lancis; ita vt deor&longs;um ire non po&longs;&longs;it, &longs;ed tantùm parum immergatur in
&longs;uperficiem aquæ &longs;ubjecto va&longs;e contentæ; occludaturque &longs;upremum os ca
naliculi cera, aut &longs;uilla ve&longs;ica, antequam immergatur, ac deinde immer&longs;um
illius pondus accuratè appendatur, admoto &longs;cilicet iu&longs;to pondere oppo&longs;itæ
lanci; po&longs;teà verò aperiatur acu &longs;upremum os prius ob&longs;tructum; a&longs;&longs;urgit
illico aqua per canaliculum, licèt nihil ponderis pror&longs;us accedat: Illa igi
tur aquæ portio, quæ per canaliculum a&longs;cendit, dicto filo pendulo non
&longs;u&longs;tinetur, &longs;ed ab alio principio, eoque applicato; &longs;cilicet ab aëre com
pre&longs;&longs;o; hoc experimentum, &longs;i accuratè fiat, rem i&longs;tam evincit.
Sed vnde huju&longs;modi aëris compre&longs;&longs;ionem e&longs;&longs;e putares?
Huic tuo quæ&longs;ito faciam &longs;atis; &longs;i dixero ex duplici capite pro
venire, Primò, ex admixtione vaporis & halitus; cùm enim no&longs;ter aër purus
non &longs;it, multa huju&longs;modi habet admixta, vnde illius compre&longs;&longs;io &longs;equitur. Secundò, ex pondere &longs;upremi aëris incubantis: fieri enim non pote&longs;t, quin
aër &longs;ubjectus inde compre&longs;&longs;us evadat.
Primò, totus aër gravitat gra
vitatione communi; ne igitur pars inferior in &longs;e ip&longs;um gravitare dica
tur, dicendum videtur. Superiorem aëris tractum in inferiorem non
gravitare.
Dare non po&longs;&longs;um totum aëra gravitatione communi gravi
tare in quodlibet corporis &longs;ubjecti punctum; nec enim vllum centrum
gravitatis commune habet, quod iis dumtaxat gravibus competit (de
phy&longs;ico loquor) quorum tota vis gravitationis per vnicam lineam à præ
dicto centro ductam exeritur ; corpus liquidum, vt aqua, & &longs;pirabile, vt
aër, ni&longs;i contineantur in va&longs;e, per Cylindros deor&longs;um, parallelos, gra
vitant; &longs;cilicet ad &longs;en&longs;um; cùm alioquin omnes Cylindri gravitationis
versùs idem centrum eant; vnde paralleli e&longs;&longs;e non po&longs;&longs;unt; equidem &longs;e
cundùm eundem Cylindrum gravitatio omnium partium, quæ illum
componunt, ita communis e&longs;t, vt omnes &longs;imul in corpus &longs;ubjectum gra
vitent, & &longs;ingulæ &longs;upra &longs;ingulas &longs;ubjectas immò &longs;upra eandem &longs;ubjectam
omnes &longs;uperiores, in eodem tamen Cylindro; cogita lapidem lapidi &longs;uppo
&longs;itum, &longs;ubjectus enim omnes &longs;uperiores ferre cen&longs;etur.
Tota igitur illa gravitatio reducitur in lineas; &longs;inguli enim
Cylindri &longs;unt totidem lineæ; linea autem, aut nihil, aut parum ponde
ris habet; nulla igitur inde compre&longs;&longs;io, aut certè modica; quid enim
tam parvi ponderis vis efficeret: ponamus enim Cylindrum aqueum da
tæ ba&longs;is & altitudinis pendere vnam libram; &longs;upponamus item aquæ gra
vitatem e&longs;&longs;e ad gravitatem aëris vt 1000. ad 1. haud dubiè Cylindrus aë
ris æqualis pendit tantùm vnam mille&longs;imam partem vnius libræ; igitur
&longs;i 1000. huju&longs;modi Cylindros ita di&longs;ponas, vt vnus alteri imponatur, om
nes &longs;imul vnam libram pendent; cùm autem in infinitum contrahi ba&longs;is
po&longs;&longs;it, & in eadem proportione cre&longs;cere altitudo, certè habebis Cylindrum
petitæ cuju&longs;libet altitudinis, qui vnam libram pendat, licèt ad lineam non
dum redactus, &longs;eu contractus &longs;it.
Nulla e&longs;t in hoc difficultas, & valde miror, te in hoc ar
gumento diutiùs hærere; in qua enim proportione decre&longs;cit pondus, de
cre&longs;cit re&longs;i&longs;tentia; id e&longs;t, in qua proportione contrahitur ba&longs;is Cylindri
comprimentis, contrahitur & Cylindri compre&longs;&longs;i: nempe, vt &longs;e habet
comprimens Cylindrus, cujus ba&longs;is e&longs;t vt quatuor, ad Cylindrum com
pre&longs;&longs;um ba&longs;is vt quatuor, ita &longs;e habet Cylindrus ba&longs;is 2.ad Cylindrum ba
&longs;is vt 2.eju&longs;dem &longs;cilicet altitudinis.
Quis, quæ&longs;o capiat, tantam pre&longs;&longs;ionis vim, quam haud du
biè immane pondus incubantis aëris omninò efficeret, etiam &longs;i demus,
aëris gravitatem e&longs;&longs;e ad gravitatem aquæ vt 1. ad 1000. aut etiam &longs;i vis,
duplo, vel triplo minorem; porrò aëra parum admodum compre&longs;&longs;um e&longs;&longs;e,
vel ex eo probatur argumento, vt aiunt, ad hominem, quod tantulum aquæ
dumtaxat elevet.
In hoc &longs;altem hallucinaris, quòd eandem aëris gravitantem
vbique e&longs;&longs;e &longs;upponas, quod tamen à veritate pror&longs;us alienum e&longs;t, nempe
aër inferior gravior e
cùm enim aëris altitudinem certam ne&longs;ciamus, &longs;uper hoc, ni&longs;i tantùm in
genere, aliquid definire nequimus; quòd autem modicam vim pre&longs;&longs;ionis,
&longs;eu potiùs compre&longs;&longs;ionis aëris ex eo probes, quòd modicus &longs;it illius effe
ctus, aqua &longs;cilicet per canaliculum a&longs;&longs;urgens, rectè, meo judicio, non de
ducis; cùm etiam aër exterior compre&longs;&longs;us, per &longs;upremum os canaliculi per
vij eam vim retundat; minùs tamen; vnde alia pre&longs;&longs;io prævaleat nece&longs;
&longs;e e&longs;t.
Immò tu potiùs hallucinaris, Augu&longs;tine, licèt enim retun
dat, repellatque humorem per caniculum a&longs;&longs;urgentem aër compre&longs;&longs;us, per
eundem &longs;cilicet canaliculum &longs;uam vim exerens; quia tamen vires pre&longs;&longs;io
nis &longs;unt vt anguli, &longs;eu coni pre&longs;&longs;ionum, de quibus ante, haud dubiè pre&longs;&longs;io
intra canaliculum vix e&longs;&longs;et millecupla alterius, ac proinde mille&longs;imam
tantùm effectus, &longs;cilicet elevationis partem impediret, quæ reverà &longs;ub &longs;en
&longs;um non cadit.
Sentio vim hujus argumenti, cui &longs;olvendo vix parem me &longs;en
tio; immò alia duo mihi veniunt in mentem, quæ non parum negotij mihi
face&longs;&longs;unt; fer opem, Antime, nempe de tua cau&longs;a & &longs;ententia hîc agitur.
Citiùs quàm par e&longs;&longs;et, animum de&longs;pondes; quid quæ&longs;o hîc diffi
cile? Repete Figuram &longs;uperiorem.
Sitque &longs;uperfi
cies aquæ AB, in quam vis pre&longs;&longs;ionis exeritur ;
itemque FG, in quam etiam vis pre&longs;&longs;ionis
cadit, minor certè, &longs;ed in minima proportione
inæqualitatis incumbit; nempe totus aër æqua
liter premit AB & FG, v&longs;que ad terminum
DE, cùm æquè liber &longs;it, vt patet; illa &longs;olùm
aëris portio contenta in &longs;egmento canaliculi
FE inæqualitatem inducit; nimirum totus aër
liberè premit FG, &longs;ed excepta portione FE;
cujus angulus pre&longs;&longs;ionis contrahitur, de hoc
&longs;o, vides, quàm modica &longs;it pre&longs;&longs;ionis differentia, ac proinde minimus ferè
illius effectus.
Ea, quæ modò dixi&longs;ti, multam mihi lucem attulerunt; &
jam mihi &longs;olvere po&longs;&longs;e videor illa, quæ mihi paulò ante in mentem ve
nerunt; primum erat, quod in imo aëris tractu, aqua per canalicu
lum altiùs attolli deberet, quod tamen fieri non exi&longs;timo; &longs;ed hoc facilè
&longs;olvitur; quia modica illa differentia in vtroque &longs;itu &longs;ub &longs;en&longs;um non ca
dit. Alterum erat paulò difficiliùs, quod &longs;cilicet in Plenilunio & Novi
lunio longè altius attolli deberet, quia tunc aër gravior e&longs;t; &longs;ed profe
ctò cùm illa gravitas aëris ab humore admixto procedat, qui reverà non
comprimitur, non &longs;equitur, aëra compre&longs;&longs;iorem e&longs;&longs;e, licèt gravior &longs;it,
non quidem per &longs;e, &longs;ed per accidens, vt aiunt. Te
jam &longs;upra indicaveras, cuipiam fortè difficillimum videbitur; nempe
tempore &longs;ummi æ&longs;tus, cùm minor incubet aëris gravitatio, aër minus
compre&longs;&longs;us e&longs;t; &longs;ub finem verò refluxus cùm major incubet gravitatio, ac
proinde aër compre&longs;&longs;ior fit; hac hora humor per canaliculum altiùs, il
la verò minùs altè a&longs;&longs;urgeret, quod tamen, opinor, minimè &longs;uccedit;
facilè tamen re&longs;ponderi pote&longs;t, immò re&longs;pondeo, hoc non facere, vt hu
mor al
proportio; &longs;ive aër compre&longs;&longs;ior, &longs;ive minùs compre&longs;&longs;us &longs;it; &longs;ed hoc jam
&longs;upra indica&longs;ti, Antime; Non nego tamen compre&longs;&longs;ioris aëris alios ef
fectus e&longs;&longs;e po&longs;&longs;e; &longs;ed in hoc ca&longs;u novus effectus non e&longs;t; hæc porrò re
&longs;pon&longs;io in primum illud, quod &longs;upra expo&longs;ui, optimè quadrat, vt patet:
antequam autem ad tuas guttulas & bullas orationem convertas, &longs;cire ve
lim, cur humor aliquando a&longs;&longs;urgat per canaliculum veloci&longs;&longs;imo motu, ali
quando verò tardiùs; præ&longs;ertim &longs;i canaliculus inclinetur, quod aliquando
memini, à me probatum fui&longs;&longs;e.
Citò a&longs;&longs;urgit, quando humefacta &longs;uperficie cava canali
culi, nullas &longs;alebras, nulla impedimenta humor invenit; vbi tamen in
dictas a&longs;peritates a&longs;&longs;urgens humor incurrit, tardiùs haud dubiè progredi
tur; cujus rei clari&longs;&longs;imam analogiam habes in aqua per &longs;iccum alveum
currente, cujus cur&longs;us ab inæquali alvei &longs;uperficie &longs;i&longs;titur & impedi
tur, ac proinde lentiùs fluit; ideò porrò per inclinatum alveum prædi
cta motus tarditas ob&longs;ervatur, quia &longs;cilicet ex parte, in dictam vitri
&longs;uperficiem incumbit, ac proinde in prædictas &longs;alebras magis incur
rit; &longs;ed jam ad guttas & bullas venio, & ante omnia, quæro ex te,
Augu&longs;tine, vnde illam Figuram Sphæricam habeat gutta, præ&longs;ertim &longs;i pau
lò minor e&longs;t.
Varij varia de hoc argumento, quæ quia merè commenti
tia e&longs;&longs;e puto, & fictitia, ad &longs;alvandum hoc experimentum vltro præter
mitto, præ&longs;ertim cùm ex iis, quæ huc v&longs;que à te dicta &longs;unt, veram hu
jus rei cau&longs;am, germanamque rationem conjiciam; nempe cùm ab aë
re compre&longs;&longs;o æquali ni&longs;u tota guttæ &longs;uperficies prematur, quid mi
rum &longs;i inde Sphæriea Figura inducatur. Vix obnitente, &longs;eu reluctan-
tur, & partes inter &longs;e aliquam tenacitatem habeant, & premens aër
vndequaque premat, ac proinde ab ima parte qua&longs;i &longs;u&longs;tineat latera
les humoris partes, hæ minimè &longs;ub&longs;idunt; hinc vbi major e&longs;t humoris
quantitas, &longs;ub&longs;idit humor, & gutta deprimitur, prævalente &longs;cilicet humo
ris pondere.
Rectè omninò mentem meam & &longs;en&longs;um a&longs;&longs;equeris; hinc
multa experimenta omnibus obvia ad idem principium reduco. Primò,
vbi vna gutta in aliam incidit, duæ in vnam eandemque abeunt; nem
pe in eo contactus puncto, in quo vna tangit aliam, ab externo aëre non
premitur, &longs;ed in aliis omnibus; hinc cedit humor in eo puncto, atque
adeò vna intra aliam intruditur. Secundò, Gutta pendula hæret aliquan
do vel in &longs;uperficie ligni, quæ deor&longs;um vergit, vel extremo na&longs;o; vnde
hoc? quia premit aër ab omni parte, ea dumtaxat excepta, quæ ligno
vel na&longs;o adhæret; ea autem vis e&longs;t pre&longs;&longs;ionis, quæ guttam hærentem &longs;u
&longs;tineat; &longs;i autem &longs;cire velis, quanta &longs;it hæc gutta, illico reponam, æqua
lem e&longs;&longs;e humoris portioni, quæ per canaliculum attollitur, vt &longs;æpè pro
bavi. Tertiò, Si partem inferiorem guttæ pendulæ, vel minima fe&longs;tu
ca tangas, &longs;tatim effluit per admotam fe&longs;tucam; quia in eo puncto, in
quo fe&longs;tuca guttæ admovetur, aër non premit, quia non tangit; aliæ
igitur partes prementes prævalent; igitur accedente præ&longs;ertim gravita
te, &longs;eu pondere guttæ pendulæ, gutta decidit. Quartò, Si verò tangas in
&longs;uperiore portione laterali, & lentè fe&longs;tucam adducas, gutta &longs;equitur,
non quòd vlla vis tractrix in&longs;it, quæ in hoc præ&longs;ertim ca&longs;u fictitia e&longs;t,
&longs;ed quia partem illam aër non premit, &longs;ed oppo&longs;itam, illa cedit huic præ
valenti; vnde &longs;i fe&longs;tuca reducitur, vi pre&longs;&longs;ionis, in prædicta parte oppo&longs;i
ta, guttam &longs;equi nece&longs;&longs;e e&longs;t. Quintò, Guttæ humoris, plano in &longs;itu ver
ticali &longs;ito etiam adhærent, propter eandem rationem, quam non re
peto. Sextò, In guttis Mercurij id di&longs;criminis e&longs;t, quod paulò majores
non adhæreant, propter majus pondus, &longs;ecus minores, pro quo e&longs;t eadem
ratio, i&longs;tæ autem perfectiùs tornantur; quia Mercurius tenacior e&longs;t & cra&longs;
&longs;ior; accedit, quòd in planorum Strias & Salebras non &longs;ubit, vt aqua; igi
tur faciliùs &longs;e&longs;e &longs;u&longs;tinet.
De bullis vel ampullis, idem facilè dixero; quæ &longs;ic tornan
tur ab aëre pre&longs;&longs;o tum interiore, tum exteriore: fe&longs;tucam etiam admotam
ac deinde reductam &longs;equitur bulla, propter eandem rationem: in hoc certè
nullam video difficultatem; &longs;ed perge quæ&longs;o, Antime, ac recen&longs;e alia expe
rimenta, quæ haud dubiè ob&longs;erva&longs;ti.
Hoc facere meditantem interpella&longs;ti.
Septimò, Igitur vbi pup
pus vel extremam linguam papillæ mammæ affigit, lac &longs;tatim effluit;
quia &longs;cilicet aër vndequaque mammæ &longs;uperficiem premit, excepta illa par
te extrema, cui lingua puppuli adhæret ; quid mirum igitur &longs;i lac exprima
tur? Octavò, Ni&longs;i extra chorum &longs;altare timerem, huc etiam adducerem co
nicam flammæ Figuram, ad quam inducendam aëris pre&longs;&longs;io non parum
confert; cùm enim ab halitu igneo &longs;ur&longs;um extru&longs;o aër valde rare&longs;cat,
conicam &longs;equi nece&longs;&longs;e e&longs;t; &longs;ed hoc argumentum alterius loci e&longs;t; in libro
&longs;ingulari de igne rem hanc fusè pro&longs;ecutus &longs;um. Nonò, Arborum trun
ci & rami, immò & pili, o&longs;&longs;a, nervi, & multa alia Figuram Cylindricam
habent, cùm enim initio molliora e&longs;&longs;ent, ab aëre premente tornata
fuerunt. Decimò, Si linguam vulneri admoveas, dum recens e&longs;t,
illico &longs;anguis effluit, ob aëris &longs;cilicet pre&longs;&longs;ionem in circumpo&longs;itam car
nem. Omitto alia ferè innumera, quæ ex dictis facilè & nullo negotio intel
ligetis.
Vna difficultas re&longs;tat, eaque maxima: nempe intelligo, hu
morem etiam per canaliculum a&longs;&longs;urgere intra vas, in quo aër maximè di
latatus e&longs;t; vnde manife&longs;tè colligi videtur, non attolli propter aëris com
pre&longs;&longs;ionem.
Non nego, difficilè argumentum e&longs;&longs;e; &longs;ed quia connexum e&longs;t
cum illo celebri experimento &longs;u&longs;pen&longs;i in fi&longs;tula vitrea Mercurij, vel alio
recipientis vitrei, in quo aër vi emboli adducti dilatatur, quæ paulò po&longs;t
di&longs;cutiemus, rem illam eò remitto; antequam porrò de præfato experi
mento agam, vnum profectò non omittam, quod viro ingenio&longs;i&longs;&longs;imo
meique amici&longs;&longs;imo aliquando in mentem venit, &longs;cilicet ab ea vi humo
rem per canaliculum attolli, quàm vulgò electricam vocant, quod tamen,
meo judicio, dici non pote&longs;t; cùm diver&longs;i&longs;&longs;ima &longs;int vtriu&longs;que motio
nis principia; nempe vis electrica in eo po&longs;ita e&longs;t, quod Vi&longs;cidorum fi
laminum ten&longs;orum priùs ac deinde reductorum vi, facilè mobilia &longs;imul
adducantur, affiganturque &longs;uccino, ex quo prædicta filamina effluvio quo
dam perenni erumpunt; quid porrò hæc ad elevationem humoris per ca
naliculum?
Inaudij aliquid de hoc argumento à te fui&longs;&longs;e excogitatum,
&longs;ed majori &longs;altem ex parte mihi excidit; quare rem mihi grati&longs;&longs;imam facies,
&longs;i obiter &longs;altem explanes, neque hoc Parergum Chry&longs;ocomo di&longs;plicebit; im
mò inde meliùs con&longs;tabit eorum veritas, quæ huc v&longs;que de humoris per ca
naliculum elevatione nobis expo&longs;ui&longs;ti.
Per me licèt, Augu&longs;tine, &longs;ed obiter; &longs;uccinum igitur po&longs;t
modicum affrictum in modica di&longs;tantia, trahit, & ad &longs;e adducit corpo
ra facilè mobilia, eaque omnis generis, excepta dumtaxat flamma, alii&longs;
que accen&longs;is, vt prunis, ferro candente, idque in omni &longs;itu, &longs;ur&longs;um, deor
&longs;um, dextror&longs;um, &longs;ini&longs;tror&longs;um, modò nihil pror&longs;us interponatur; &longs;i
enim vel tenui&longs;&longs;imum chartæ folium interponatur, nihil trahit, præ
ter ip&longs;um folium; trahit autem corpora facilè mobilia omnis generis,
vt dixi, & in omni corporis &longs;tatu; duro &longs;cilicet, liquido, &longs;pirabili; &longs;ic
fumum trahit agitque in diver&longs;os vortices &longs;eu turbines, pulverem,
aquam, oleum, &c. Videres enim guttam aquæ vel olei, cui &longs;uc
cinum admovetur extendere &longs;e&longs;e atque attolli; Videres innumera pul
veris grana tripudio quodam &longs;alientia, Atomos intra Solis ra
dium, conclavi probè clau&longs;o fluitantes, admoto &longs;uccino turmatim
accurrere, fumum in mille, ductum filamina hinc & illinc &longs;uccino
lancem in perfecto æquilibrio &longs;tatutam, vel attolli, &longs;i &longs;ur&longs;um &longs;uccinum
applicetur, vel deprimi, &longs;i deor&longs;um, dixi, po&longs;t affrictum &longs;uccini; quia ta
men ad diver&longs;i corporis &longs;uperficiem prædictus affrictus fieri pote&longs;t, ob
&longs;ervavi etiam, diver&longs;os inde effectus &longs;equi; nempe &longs;i affrictus fiat ad
pannum omnis generis, &longs;ed præ&longs;ertim ad coactilem, tunc &longs;uccinum ma
ximè trahit; ad telam etiam, &longs;ed minus, item ad cutem, chirothecam,
corium, modo pinguius non &longs;it, chartam, olo&longs;ericum, barbam, capillos,
ad o&longs;&longs;a, metalla, cornu, ceram, ligna, te&longs;tam, vitrum, vel nihil, vel pa
rum admodum: item &longs;i affrictus fiat ad cutem, humore, melle, bal&longs;a
mo, atramento, adipe ferè omnis generis, therebinthina, &longs;ucco mali au
rei, &longs;apone, aquis di&longs;tillatis ferè omnis generis, dilutam &longs;eu perfu&longs;am,
itemque &longs;i pulvere a&longs;per&longs;o affrictus fiat; &longs;ecus tamen &longs;i butyro, &longs;uillo
adipe, oleo fere omnis generis; tunc enim &longs;altem parum trahit, ni&longs;i &longs;al
oleo admixtum &longs;it, quod mihi ante aliquot annos indicavit vir acuti&longs;&longs;imi
ingenij meique amanti&longs;&longs;imus Laurentius Magalottus. Accedit, quod
non &longs;uccinum modò, vt vulgò dicitur, vi electrica pollet, &longs;ed alia multa
corpora, vt Lacca, quàm vulgò ceram Hi&longs;panicam vocant, gagates,
concretum &longs;cilicet bituminis genus, adamas, multique lapilli; non ta
men vnio; cry&longs;tallus & multa alia, nullum tamen ligni genus, te&longs;tæ, me
talli, carnis &c. Illud vnum ob&longs;ervo, corpus omne electrica virtute pol
lens e&longs;&longs;e vitrificum, vt &longs;ic loquar, id e&longs;t, quod ad in&longs;tar vitri malleo frangi
&longs;eu teri, non verò duci, aut findi, aut friari po&longs;&longs;it.
Tam multa, tam varia in vnum conge&longs;&longs;i&longs;ti experimenta, re
ticitis tamen rationibus, vt mentem potiùs obrueris, quàm refeceris, aut
recrearis; &longs;ingula quæ&longs;o te repetamus & reducamus ad certa principia,
vt inde veritas phy&longs;ica eluce&longs;cat, itaque ante omnia, edi&longs;cere nobis tuam
hypothe&longs;im.
In vno tantùm corpore electrico hypothe&longs;im meam &longs;tatuo,
cùm &longs;cilicet pro aliis omnibus eadem ratio militet; accipio igitur Laccam
&longs;eu ceram hi&longs;panicam, tum quia magis obvia e&longs;t, tum quia vi electrica
maximè pollet; illamque adhibui ad omnia ferè experimenta, con&longs;tat
multo igne; quippe accenditur; & multa vligine, quia ducitur &longs;eu ne
tur in filamina vi&longs;cofa; ignis autem qui ine&longs;t, perenni actione in partes
vicinas agit, quas haud dubiè rarefacit, ac proinde intra pororum an
gu&longs;tias contractæ inde nituntur erumpere, qua data porta; pori enim ob
&longs;tructi &longs;unt; &longs;ublata autem huju&longs;modi ob&longs;tructione per affrictum, ma
teria intus compre&longs;&longs;a erumpit ad in&longs;tar &longs;ulphurei jaculi; & quia vi&longs;co&longs;a
e&longs;t, netur in filamen tenui&longs;&longs;imum, quod præ impetu, quo erumpit, cum
intus altera ejus extremitas, propter vi&longs;co&longs;itatem aliis partibus eju&longs;dem
materiæ adhæreat; maximè tenditur; at &longs;tatim ce&longs;&longs;ante impetu, redu
citur vt chorda ten&longs;a, & &longs;ecum a&longs;portat corpu&longs;cula facilè mobilia, quæ
occurrunt.
Hoc fortè gratis dicitur; quis enim filamina illa vnquam vi
dit, aut &longs;en&longs;it? quis alia multa his &longs;imilia non fingat?
Perennia corporum effluvia agno&longs;cimus omnes, quod ex odo
re, &longs;itu, &longs;iccitate ac re&longs;olutione corporum facilè probamus; accedit,
quod partes ignis, eá&longs;que multas ine&longs;&longs;e con&longs;tat, quæ vi activa eaque ne
ce&longs;&longs;aria pollent; multùm item materiæ rectè di&longs;po&longs;itæ, in quam ignis
agat, vligino&longs;æ &longs;cilicet & pinguis; quidni ergo effectus nece&longs;&longs;arius ex
cau&longs;a nece&longs;&longs;aria? Calor &longs;cilicet & rarefactio eju&longs;dem materiæ; &longs;ed cum
intra pororum angu&longs;tias comprimatur, pori enim, majore &longs;cilicet ex par
te ob&longs;tructi &longs;unt; vbi deinde affrictu, pori os ab&longs;tergitur, inde erumpit
cum impetu, & cùm materia vi&longs;co&longs;a &longs;it, ducitur in filum, cujus altera ex
tremitas intra porum hæret.
Sed quid tandem poros ob&longs;truit?
deinde vnicus affrictus &longs;uf
ficeret, cùm tamen aliquo po&longs;t affrictum tempore fortè non trahat.
Ille halitus vligino&longs;us, &longs;ic enim vocare liceat, ductus in fila
men, eo ferè modo, quo fumus; netur in fila; &longs;i enim candelam recèns
extinctam a&longs;picias, &longs;itam inter oculum & Solem, vel luculentam flam
mam, incredibilem prorsùs tenui&longs;&longs;imorum filaminum vim miraberis;
quia verò &longs;tatim concre&longs;cit externo frigore, ad o&longs;tium pori omnino riget,
inde manife&longs;ta ob&longs;tructionis cau&longs;a, concretum &longs;cilicet ad pori os
filamen.
Inaudij &longs;emper, affrictum illum fieri, vt inde calor produ
catur, quem nece&longs;&longs;arium e&longs;&longs;e, dicunt, ad virtutem illam electricam exci
tandam.
Scio pro&longs;ectò, hæc vulgò dici ac doceri; non tamen res ita &longs;e
habet; Lacca enim, &longs;i nimium incale&longs;cat, nihil trahit, deinde &longs;i po&longs;t af
frictum; Laccam vel &longs;uccinum in aliqua di&longs;tantia flammæ admoveas, ac
deinde ad ea corpu&longs;cula, quæ alioquin facilè trahuntur, applices, nihil
prorsùs trahit, vt millies &longs;altem probavi; calor igitur vim electricam non
excitat, &longs;ed potiùs impedit; equidem &longs;i denuò Laccam panno affrices,
corpu&longs;cula, vt ante, illico trahit, ea porrò di&longs;tantia flammæ, vel primis
lacca admovetur, qua, vt modicum &longs;altem trahat, corpu&longs;culis admo
vetur.
Non video, quid flamma ad id conferat, vt tractionem im
pediat.
Id tamen video; licèt tu ip&longs;e longè oculatior &longs;is; nempe fi
lamina illa vligino&longs;a &longs;unt, ac proinde ignem &longs;tatim concipiunt, abeuntque
in auras; &longs;ublata igitur cau&longs;a tractionis, filaminum &longs;cilicet ten&longs;ione &
adductione ce&longs;&longs;at tractio ; immo licèt jam corpu&longs;culum &longs;uccino adhæ
reat, v. g. fru&longs;tum chartæ, &longs;i ju&longs;ta di&longs;tantia flammæ admovetur, eo ip&longs;o à
&longs;uccino avellitur, ac deor&longs;um proprio pondere cadit; quia &longs;cilicet funicu
los illos con&longs;umit ignis, quibus affixum tenebatur.
Nihil addi pote&longs;t, adeòque i&longs;ta difficultas penitus exhau&longs;ta e&longs;t;
con&longs;tat igitur non ideò affrictu opus e&longs;&longs;e, ad excitandum calorem, &longs;ed ad
&longs;uperficiem ab&longs;tergendam, & purganda pororum o&longs;tiola, vt &longs;cilicet nova
filamina ex iis erumpant; non negarim tamen, affrictu illo aliquid etiam
caloris produci, & colligi ignis partes; calor enim congregat homoge-
rioris effluvij cau&longs;a e&longs;t; perfectam, ni fallor, hujus rei analogiam habe
mus in corporibus odoratis, præ&longs;ertim durioribus; certum enim e&longs;t,
odorem diffundi in halitu odorifero; affrictu autem eorundem corpo
rum major vis prædicti halitus educitur: primarius tamen affrictus finis
in electricis alio &longs;pectat, &longs;cilicet ad pororum o&longs;tia expurganda: hinc pan
no potiùs, quàm tela, aut &longs;erico, prædictus finis obtinetur; quia pannus
laneus a&longs;perior e&longs;t: ad id porrò quod dicebas, à nemine vnquam præ
dicta filamina vi&longs;a fui&longs;&longs;e, vt cum tua bona venia dicam, futile e&longs;t; quis enim
pariter halitum odoratum vidit? aut contagio&longs;um?
eumque, in quem &longs;in
gulis diebus aliqua no&longs;tri corporis pars avolat? proba &longs;is, in&longs;igni aliquo
micro&longs;copio; quod ad me &longs;pectat, nonnihil videre, auribu&longs;que percipere
mihi videor. Videre quidem, adhibitis divinianis micro&longs;copiis, quæ iure
omnibus huc v&longs;que fabricatis anteponenda e&longs;&longs;e duxerim; audire verò
admota auribus tenui&longs;&longs;ima lamina, quæ &longs;onora vi maximè polleat, cui
&longs;tatim po&longs;t affrictum &longs;uccinum applicatur; minimum enim & acuti&longs;&longs;imum
tinnitum audite mihi videor, qui edi non pote&longs;t, ni&longs;i à prædictorum fila
minum appul&longs;u; neutrum tamen pro certo vendito: neque id nece&longs;&longs;e e&longs;t,
cùm aliundè con&longs;tet; nec enim prædicta corpu&longs;cula propria vi, &longs;eu vir
tute a&longs;cendunt; v.g. pulvis gravi&longs;&longs;imus; aliunde igitur moventur; non ab
aëre; quid enim ad hoc affrictus iuvaret? quid noceret flamma?
cur alia
corpora ad eundem finem æquè idonea non e&longs;&longs;ent, ac electrica? à &longs;uc
cino igitur adducuntur; qua vi amabo? tractrice, inquies; cur ergo af
frictu opus? cur obe&longs;t flamma?
cur major Laccæ aut &longs;uccini fru&longs;tum
majus pondus non attollit? deinde &longs;uccinum vertibile accedit ad quod
libet corpus, ni&longs;i ignitum &longs;it; &longs;i ad vnum tantùm, vt magnes ad ferrum,
& vici&longs;&longs;im, e&longs;&longs;et aliqua analogia, &longs;ed quod ad omnia; nativa vi ab intrin
&longs;eco, non dictu modò, &longs;ed cogitatu ridiculum e&longs;t: Itaque, cùm jam
aliunde, & ex communibus principiis habeam, præ&longs;atum filaminum efflu
vium; & cum iis adductis, illi omnes motus explicari facilè po&longs;&longs;int, ad
duci verò nece&longs;&longs;e &longs;it, &longs;i priùs tendantur, tendi autem oporteat, &longs;i cum im
petu ex poro erumpant; itemque cum impetu erumpere, &longs;i priùs materia
vligino&longs;a & vi&longs;co&longs;a vi partium ignis rarefacta; ob&longs;tructis poris avolare
prohibita, compre&longs;&longs;a intus retineatur, ac demum erumpant prædicta fila
mina, &longs;i affrictu, obex tollatur: fru&longs;tra oculorum, quorum aciem fu
giunt, te&longs;timonium quæritur; nec ea propter meritò dici pote&longs;t, hæc à
me gratis ad&longs;trui; accedit, quòd multæ ob&longs;ervationes hæc filamina pror
&longs;us evincunt. Primò, &longs;i po&longs;t affrictum, &longs;uccinum pulveri admoveatur, quo
quover&longs;um di&longs;pergitur pulvis, adducitur que. Secundò, fru&longs;tula chartæ,
quibus admovetur, eodem modo di&longs;perguntur. Tertiò, vbi ad ducuntur
illa in diver&longs;os gyros & &longs;piras eunt, &longs;itumque mutant, & modo hinc, mo
dò illinc trahuntur. Quartò, Nonnunquam a&longs;&longs;urgunt ex plano, in quo ja
cebant, & &longs;ic erecta manent, licèt &longs;uccinum non tangant. Quintò, Vnum
alteri catenatim adhæret, quod non fit alio corpore admoto. Sextò, vidi
aliquando, idque non &longs;emel, fru&longs;tum chartæ citra contactum, è &longs;uccino
chartæ filamentum. Septimò.
Vbi fru&longs;tra illa levi digito moveo, Sen&longs;io re
&longs;i&longs;tentiam omnino illi &longs;imilem, quam &longs;entirem, &longs;i tenui&longs;&longs;imo reticulo impli
cata e&longs;&longs;e
&longs;e&longs;e, &longs;ed huc illuc, ab aliis filaminibus abripiuntur. Octavo.
Quando po&longs;t af
frictum, fru&longs;tum adducitur, qua&longs;i tripudio quodam huc illuc agitur; vix hæc
aliaque multa &longs;imilia &longs;ine prædictis filaminibus explicari po&longs;&longs;unt, immo nec
intelligi.
Perge quæ&longs;o, & alia nobis expone, quæ ad rem hanc per
tinent.
Per me licet; Nono, igitur &longs;i po&longs;t affrictum, &longs;uccinum &longs;uccu
tias, eoque tundas aliud corpus, non trahit, vel longè minùs; quia prædicta
filamina &longs;uccu&longs;&longs;u illo di&longs;&longs;ipantur. Decimò.
Item &longs;i valido anhelitu &longs;uccinum
perfles, etiam po&longs;t affrictum; quia &longs;ic eadem filamina difflantur. Vndecimò.
Idem accidit, &longs;i Aquiloni.
Vel Au&longs;tro vehementi, po&longs;t affrictum, exponas.
Duodecimò.
Item &longs;i po&longs;t affrictum &longs;uccinum, vel humido immergas, vel
humore perfundas; nempe illa filamina humor diluit; hinc ad ten&longs;ionem
inepta: Analogiam habes in membrana tympani. Decimo-tertiò.
Po&longs;tquam
traxit, &longs;ibique affixit pulverem &longs;uccinum, licèt illud admoveas fru&longs;tulis
chartæ, illa vix trahit; ab&longs;ter&longs;o tamen pulvere, citra novum affrictum, char
tulas trahit; quia filamina circa pulverem occupata, aliud quidqiam non
trahunt; ab&longs;ter&longs;o tamen pulvere, fractis &longs;cilicet vinculis, nova erumpunt,
quæ prædictum præ&longs;tant effectum, ad quem præ&longs;ertim præfata ab&longs;ter&longs;io
plurimum confert. Pari modo, po&longs;tquàm traxit aliquot fru&longs;ta chartæ, vix
pulverem trahit, propter eandem rationem. Decimo - quartò.
Si po&longs;t a&longs;tri
ctum, &longs;uccinum immergas Oleo, non ob&longs;tat, quo minùs trahat, quia Oleum
prædicta filamina vligino&longs;a non diluit. Decimo - quintò.
Sicuti humorem
affundas, & in ea &longs;uccinum frices, po&longs;t affrictum nihil trahit, quia affu&longs;us
humor filamina diluit, & ten&longs;ionem impedit; idem dico de aquis di&longs;tillatis,
vino, oxymo, aceto, &longs;ucco mali aurei, propter eandem rationem; idem de
&longs;apone adipe, melle, bal&longs;amo, therebinthjna propter nimiam tenacitatem,
quæ filamina impedit. Decimo - &longs;extò.
Si perfundatur cutis oleo, po&longs;t af
frictum in ea &longs;uccini, &longs;equitur tractio ; quia vt jam dixi &longs;upra, Oleum non
ob&longs;tat, ni&longs;i &longs;al Oleo admi&longs;ceatur, quia &longs;cilicet poros &longs;uccini ob&longs;truit; idem
de butyro, & &longs;uillo adipe recente, propter eandem rationem. Decimò - &longs;e
ptimò. Si pulverem cuti a&longs;pergas, ac deinde frices, nihil trahit; quia pulve
ris admoti mordacitas, vel a&longs;peritas filamina &longs;ecat. Decimo - octavò.
Si affri
ctus fiat in capillis, & tenera barba, tractioni non obe&longs;t; quia e&longs;t ad in&longs;tar la
næ. Ex his, ni fallor, reliqua facilè intelligetis; quare illa omitto, ne prolixior
&longs;im.
Experimentorum, quæ Primò loco ad duxi&longs;ti, rationem &
cau&longs;am afferre omi&longs;i&longs;ti, &longs;upple illam quæ&longs;o.
Non omi&longs;it, &longs;ed eam &longs;uppo&longs;uit, cùm facile ex dictis elici po&longs;
&longs;it, nam primo di&longs;perguntur grana pulveris huc illuc; quia diver&longs;a filami
na huc illuc erumpunt, & vbi reducuntur multa grana male implicata pro-Secundò fru&longs;ta chartæ à diver&longs;is filaminibus appul&longs;is,
nece&longs;&longs;ariò agitantur, di&longs;perguntùrque, & in multos gyros & &longs;piras agun
tur, à diver&longs;is &longs;cilicet filaminibus adducta; eunt autem filamina &longs;ecundùm
lineam pororum. Tertiò, quod nonnunquam a&longs;&longs;urgant citra tactum, ideò fit,
quia in ea di&longs;tantia, pauciora filamina eò appul&longs;a non &longs;ufficiunt, ad tantum
pondus attollendum. Quartò Corpus interceptum etiam tenui&longs;&longs;imum fila
mina &longs;i&longs;tit, ideò tractionem impedit. Vnum tamen fru&longs;tum chartæ alteri
applicatum adhæret, propter filamina lateralia. Quintò.
Tripudium illud
fru&longs;tri chartæ adducti diver&longs;is filaminibus, per diver&longs;as lineas trahentibus,
tribuendum e&longs;t: Vides, quàm facilè rationes de&longs;ideratæ deducantur; reli
quis experimentis &longs;ubjectæ fuerunt. Vnum fortè dee&longs;t, cur &longs;cilicet affrictus
in quibu&longs;dam corporibus factus tractionem, vel omnino, vel ex majore
parte impediat; quod tamen dictu facile e&longs;t; quia &longs;cilicet, quorumdam affri
ctu, nec excitatur calor, nec pori ob&longs;tructi ab&longs;terguntur; &longs;ic ad ter&longs;ionem
charta inepta e&longs;t; tela aptior; pannus verò apti&longs;&longs;imus, præ&longs;ertim, &longs;i quid ca
loris excitandum e&longs;t: omitto vortices illos adducti fumi; con&longs;tat enim ex fi
laminibus, quæ cum aliis filaminibus agglomerantur; hic enim e&longs;t diver&longs;æ
tractionis effectus; &longs;ed vnde e&longs;t? mi Antime, cinericius ille color fumi &longs;ucci
no advoluti.
Puta fuliginem qua&longs;i &longs;ublimatam, vt &longs;ic loquar, &longs;eu flo
rem quemdam fuliginis, aut fumi, in &longs;uperficie &longs;uccini concre&longs;
centem; corporum autem &longs;ublimatorum & calcinatorum color, vt
plurimum ad album accedit, &longs;ed de coloribus hîc di&longs;putandi locus
non e&longs;t.
An fortè hic effectus in vacui metum referri po
te&longs;t?
Non de&longs;unt profectò, qui præ&longs;atam tractionem in Vacui me
tum reducant, &longs;ed meo judicio, perperam; quis enim amabò, & vnde
hic vacui metus? dato enim prædicto effluvio, minùs loci e&longs;t, quàm opor
teat, non plus; prætereà cur aër potiùs non accurrit, vel adducitur ad fu
gam Vacui, quàm charta, vel alia corpora, quæ longè difficiliùs moven
tur quàm aër? denique e&longs;to, vacui metu vnum corpus alteri adhæreat, ac
proinde hoc &longs;ine illo moveri
tum movetur, vt luculentis experimentis o&longs;tendi à me po&longs;&longs;et, hinc
rum &longs;ententiam rejicio, qui volunt effluvium illud in capillitium quoddam
concre&longs;cere, cui fe&longs;tucæ,
recentior hanc &longs;ententiam typis mandavit, &longs;ed multis ante annis, &longs;cilicet
ann. 1646, in Philo&longs;ophia per propo&longs;itiones dige&longs;ta, hanc ip&longs;am, quam vo
bis expo&longs;ui, jam edideram; vnde me ab illo non accepi&longs;&longs;e per&longs;picuum fit,
quanquam citra eruptionem illam, ten&longs;ionem & reductionem filaminum,
&longs;i vnum vel alterum experimentum demas nullum ex reliquis explicari
pote&longs;t, adhibito etiam præ&longs;ato capillitio, vt con&longs;ideranti patebit; quare vltra
refutare illam &longs;ententiam operæ pretium non e&longs;t.
Scite averem, vtrùm &longs;upponas tua illa filamina rumpi præ
nimia ten&longs;ione & impetu.
Non negaverim, frangi aliqua; quod tamen non ob&longs;tat; cùm
alterum &longs;egmentum, cujus altera extremitas poro &longs;uccini adhæret, redu
catur po&longs;t fractionem; opus tamen non e&longs;t, vt rumpantur; cùm ad præfa
tos effectus explicandos &longs;atis &longs;it filamen, ten&longs;um priùs, deinde cum im
petu &longs;uccinum versùs reduci, vt fieri videmus in chordis ten&longs;is: habetis
igitur &longs;implicem iuxta atque facilem modum à me aliàs excogitatum,
explicandæ virtutis electricæ; nec effluvium illud gratis, vt dicebas, à me
fingitur, quod &longs;cilicet tam multa & varia experimenta evincunt; quod
que (ita &longs;altem mihi videtur) vi&longs;u & auditu percipi pote&longs;t; dicerem etiam
tactu, ni&longs;i vobis ri&longs;um movere timerem; nam præter illam re&longs;i&longs;tentiam,
quam digitus &longs;entit, dum fe&longs;tucam affixam removere lentè conatur, &longs;i
po&longs;t affrictum &longs;uccinum validum & probè lævigatum proximè admoveam
extremæ linguæ, vel oculis, vel parti cuipiam læ&longs;æ, quæ vel levi&longs;&longs;imum
tactum ferre nequeat, aliquem appul&longs;um &longs;entire mihi videor; probate
&longs;ulcis, &longs;ed de his fortè prolixiùs, quam par e&longs;&longs;et; jam ad Mercurij elevatio
nem veniendum e&longs;t.
Per vos mihi liceat vnum proferre; quod diu in mente volvo;
&longs;cilicet, aëra mihi videri æquè compre&longs;&longs;um in quolibet tractu, &longs;ive ille
&longs;uperior, &longs;ive inferior &longs;it: demus enim infimum pre&longs;&longs;iorem e&longs;&longs;e, vtpote
cui totum pondus &longs;uperioris incumbat, quod &longs;upra innui&longs;&longs;e vi&longs;us es,
Antime; igitur aër compre&longs;&longs;us intra vas, inde non erumpit, licèt vas ape
riatur: aut certè adversùs alium aëra erumpit, eique &longs;e&longs;e admi&longs;cet, &
pre&longs;&longs;ionem æquè dividit; dico igitur, infimum aëris tractum equidem ma
gis comprimi, majoris ponderis vi gravitantis ; &longs;ed ita contraniti, vt tra
ctum &longs;uperiorem continuum comprimat; atque adeò communis & æqua
lis &longs;it vtriu&longs;que compre&longs;&longs;io; nempe aër in aëre compre&longs;&longs;us &longs;e&longs;e dilatat, do
nec æqualis vtrimque &longs;it compre&longs;&longs;io; & hoc, ni fallor, longè faciliùs &longs;ol
vit argumentum illud &longs;upra adductum, petitumque ab intolerabili com
pre&longs;&longs;ione, quæ ex tanta ponderis, aëris &longs;cilicet, gravitantis vi &longs;equeretur;
itemque illud ex eo ductum, quod in vertice alti&longs;&longs;imi montis aqua per
canaliculum minùs altè a&longs;&longs;urgeret, itemque tempore fluxus; nam vt dicam
quod res e&longs;t, illæ tuæ re&longs;pon&longs;iones, licèt di&longs;&longs;imularim, mihi plenè non fe
cerunt &longs;atis.
Fateor tuam illam longè faciliorem e&longs;&longs;e, cui etiam vltro &longs;ub
&longs;cribo: neque illud, quod aliqui afferunt, de lanæ cumulo cujus pars in
ferior compre&longs;&longs;ior e&longs;t, quidquam negotij face&longs;&longs;it; nec enim lana propriè
loquendo comprimitur; &longs;ed tantùm extruditur aër inter lanæ filamina
contentus; neque hæc vera e&longs;t compre&longs;&longs;io, ea &longs;cilicet, ex qua tantam vim
motus &longs;equi videmus: &longs;ed tandem ad Mercurij fi&longs;tulam venio.
Pulcherrimum fortè ac celeberrimum experimentum e&longs;t illorum
omnium, quæ hoc currente &longs;æculo, &longs;ub mortalium venerunt ad&longs;pe
ctum: primus illius inventor fuit docti&longs;&longs;imus Torricellus, vir certè,
quem inter principes hujus temporis Geometras iure annumero; qui
cùm à Galilæo aliquando audii&longs;&longs;et, vel potiùs ab eo typis mandatum
legi&longs;&longs;et, aquam attolli non po&longs;&longs;e in Siphone, &longs;upra altitudinem 18.cubi-
illico prædixit, fore vt Mercurius attolli non po&longs;&longs;et &longs;upra altitudinem
pedum 2 3/4 vel 1/3 circiter; quod cùm in fi&longs;tula vitrea proba&longs;&longs;et; provt præ
dixerat, &longs;ucce&longs;&longs;it eventus; in hunc porrò modum probavit; Sit vas ABG,
in quo &longs;it Mercurius EBF, &longs;it fi&longs;tula vitrea BCD probè clau&longs;a in D,
apertain B, repleatur Mercurio, tum admoto pre&longs;&longs;è digito in B, immerga
tur extremitas B intra Mercurium, &longs;tatutaque fi&longs;tula in perpendiculari &longs;itu
&longs;ubducatur digitus ex B, de&longs;cendit Mercurius, nullo aëre &longs;ubeunte, ita
tamen, vt &longs;egmentam extantis Mercurij CI; &longs;ive longior &longs;it fi&longs;tula, &longs;ive
brevior, &longs;it &longs;emper pedum 2. 1/4 circiter, &longs;ive tubus angu&longs;tior &longs;it, &longs;ive
laxior.
Huius experimenti primum inventorem & auctorem P.
Va
lerianum Magnum fui&longs;&longs;e, accepi, immo hic, ni fallor, libellum de hoc ar
gumento in lucem edidit, in quo hoc idem atte&longs;tatur, quantum &longs;cilicet
memini&longs;&longs;e po&longs;&longs;um.
Nihil profectò magis à veritate alienum; Torricellus haud
dubiè, & citra omnem controver&longs;iam, primus inventor fuit; immo alij
multi hoc idem argumentum ante Valerianum tractarunt; cujus ratio, &
cau&longs;a phy&longs;ica vtinam æquè facilè & certo &longs;tatui à nobis po&longs;&longs;et, atque in
ventor; nempe res mihi difficillima e&longs;&longs;e videtur, &longs;tatuere, quid occupet &longs;e
gmentum illud fi&longs;tulæ CD, quod vacuum e&longs;&longs;e videtur; & qua vi alterum
IC &longs;upra &longs;uperficiem EF, &longs;u&longs;tineatur; in his duobus enucleandis, tua
de&longs;udabit, opinor, indu&longs;tria, Antime; vtinam, de quo valde dubito,
fœliciter.
Tentabo &longs;altem, idque vnum operæ pretium erit, quod nec in
mea, nec in alia cuju&longs;piam hypothe&longs;i, difficultatem, &longs;i quæ fortè in&longs;it, di&longs;
&longs;imulaturus &longs;im. Ab illa autem initium duco, quæ & Torricelli & mul
torum hodie num e&longs;t, in qua &longs;cilicet, præfatum experimentum in hunc
curium IC, eju&longs;dem &longs;cilicet cum illo ponderis; e&longs;tque perfectum inter
vtrumque æquilibrium; &longs;egmentum verò fi&longs;tulæ CD omni corpore va
cuum remanet, hæc porrò hypothe&longs;is ex duplici præ&longs;ertim capite effi
caciter, vt aiunt ab a&longs;&longs;ertore probatur. Primò, ex eo quod quæcumque tan
dem &longs;it fi&longs;tulæ altitudo & latitudo, &longs;egmentum extans (&longs;ic appello IC)
æqualis &longs;emper &longs;it altitudinis IC. 2. &longs;cilicet pedum, & 1/3 vel 1/4. Secundò,
ex eo quod aquæ &longs;egmentum extans 32. &longs;cilicet pedum circiter
cum &longs;egmento Mercurij extante ponderis; e&longs;t enim fere gravitas Mercurij
ad gravitatem aquæ vt 14. ad 1. vis ergo æqualis &longs;u&longs;tinet &longs;egmentum ex
tans Mercurij 2. pedum 1/3, & &longs;egmentum extans aquæ 32. pedum; &longs;ed illa
vis alia e&longs;&longs;e nequit à cylindro aëris gravitante.
Accedit non leve adminiculum, ex eo quod à vitis accura
ti&longs;&longs;imis probatum fuit, in vertice alti&longs;&longs;imum montium &longs;egmentum ex
tans Mercurij e&longs;&longs;e minus IC ; quia &longs;cilicet cylindrus aëris gravitantis ac
&longs;u&longs;tinentis prædictum &longs;egmentum extans, brevior e&longs;t; igitur minor illius
vis & ni&longs;us. Qaod autem &longs;egmentum CD omnino vacuum &longs;it, vel ex eo
con&longs;tat, quod inclinata fi&longs;tula in BK, a&longs;&longs;urgit Mercurius & totum &longs;e
gmentum CD occupat, non tamen videtur, quò abeat, aut &longs;e recipiat cor
pus illud, quod vacuitatem CD occupabat, &longs;i fortè aliquod e&longs;&longs;et; ex quo,
ni fallor; nova confirmatio prioris partis ducitur; cum illa vis, quæ &longs;u&longs;ti
net &longs;egmentum Mercurij IC in perpendiculo; &longs;ufficiat ad &longs;u&longs;tinendum
&longs;egmentum BK in plano inclinato, quod ex doctrina motuum facilè de
mon&longs;trarem, &longs;i res ita po&longs;tularet.
Non de&longs;unt etiam alia adminicula, de quibus infra; accedunt
tamen gravi&longs;&longs;imæ difficultates; omitto leviores, ne in nugis vos deti
neam, & vt ab ea parte, quæ ad vacuum &longs;pectat, initium ducam, multa
reverà, opponuntur, quæ dubito, an &longs;olvi po&longs;&longs;int. Primò, Qui&longs;quis ad&longs;truit
huiu&longs;modi vacuum in &longs;egmento fi&longs;tulæ CD, de omni corpore quamvis
alioquin tenui&longs;&longs;imo, negat, quod &longs;patium illud occupet; at &longs;i dixero, ibi
e&longs;&longs;e vel tenuem materiam Carthe&longs;ij, vel æthera, vel &longs;ubtili&longs;&longs;imum humo
rem dilatatum, non dico certò, &longs;ed probabiliter tantùm, quo quæ&longs;o ar
gumento prædictum vacuum probare poterit? Secundò, Si vacuum e&longs;t,
quomodo lumine perfunditur? Si enim lumen con&longs;i&longs;tit in effluvio quo
dam igneo; vel in motione cuju&longs;dam materiæ &longs;ubtili&longs;&longs;imæ, vt docent De
mocritici; cum vacuitatem illam &longs;ubeat, occupet, impleat, ibi certè va
cuum non e&longs;t; aut certè lumen e&longs;t meta qualitas per medium diffu&longs;a, vt
docent ij, qui meliùs cen&longs;ent; atque ita cùm qualitas &longs;ine &longs;ubjecto e&longs;&longs;e
non po&longs;&longs;it, Tertiò, Si
vacuum e&longs;&longs;et, totus quantus aër & æther, qui terre&longs;tri globo vicinior e&longs;t,
in dictum &longs;egmentum gravitaret ad &longs;tatuen dum æquilibrium.
Su&longs;tine, quæ&longs;o; dici enim pote&longs;t, æthera non e&longs;&longs;e gravem;
aut certè &longs;i gravis &longs;it; incredibilem e&longs;&longs;e proportionem gravitatis aëris ad
gravitatem ætheris, vtrum que de&longs;truit vim huius argumenti.
Immo &longs;unt, qui dicunt, atmo&longs;phæram tantùm gravitare,
ex ratione texturæ ramorum & filaminum in communis ætheris, &longs;eu, vt vo
cant &longs;ubtilis materiæ medio natantium.
Fateor, multam vim halitus aëri admixtam e&longs;&longs;e; &longs;ed aqueus
frigore conce&longs;&longs;it, terre&longs;tris verò partim de&longs;cendit, partim cum Atomis flui
tat in aëre, aëra autem voco illud, quod non e&longs;t vapor; hic enim totus li
que&longs;cit; vbi frigore den&longs;atur ; nec filaminum agglomeratorum cumulus, &longs;ed
illud medium, in quo dicta filamina, &longs;eu filaminum ramenta, vel exuviæ
fluitant & natant: fateor etiam, aëra multo humore foetum graviorem e&longs;
&longs;e, quod certè inficietur nemo: quòd autem cra&longs;&longs;iores nubes altiùs non at
tollantur, non probat, &longs;uperfu&longs;um aëra non gravitare, &longs;ed tantùm minùs gra
vitate; quod fateor vltro; æther ille ab aëre fortè non di&longs;tinguitur; aut &longs;i
di&longs;tinguitur, incredibilis non e&longs;t illius gravitatis proportio ad gravitatem
hujus; Vt vt &longs;it, juxta illa mea principia, quæ jam in &longs;uperioribus congre&longs;
&longs;ibus præmi&longs;i, hoc argumentum omnino inefficax non e&longs;t; &longs;ecernatur ta
men, vt vultis; ne cuiquam moveam litem; alia pro&longs;equor. Quartò, So
nus editur intra illud &longs;egmentum CD, appenditur enim filo tintinnabu
lum intra ampullam vitream, quæ ad extremitatem D facilè componitur;
nec e&longs;t, quòd aliquis dicat, &longs;onum, &longs;eu tremulum motum traduci per filum
in fi&longs;tulam; quia hoc fal&longs;um e&longs;&longs;e con&longs;tat, ex luculento experimento; &longs;i enim
tintinnabulum appendas filo ad ferreum axem, ob&longs;tructis auribus; licèt den
tibus prædictum axem tangas, nullum &longs;onum percipies, quamvis tintinna
bulum re ip&longs;a &longs;onet; igitur filum aptum medium non e&longs;t, ad prædictum
motum traducendum: deinde ita di&longs;poni pote&longs;t tintinnabulum, in&longs;erto fi
&longs;tulæ filo ferreo, ex quo pendeat, vt fi&longs;tulam nullo modo tangat, nec me
diatè, nec immediatè, vt aliquando probavi; &longs;en&longs;i tamen vt antè, &longs;onum; &longs;o
nus autem propagari non pote&longs;t, ni&longs;i per medium. Quintò, Ignis intia
idem &longs;egmentum accenditur; hic porrò accendi non pote&longs;t, ni&longs;i vel parti
culæ ignis eò penetrent, vt Democriti ci dicunt; vel calor, qui, vt Peripate
tici docent, qualitas e&longs;t, eò v&longs;que ad pabulum diffundatur, per medium &longs;ci
licet; immò ignis accenditur tantùm per collectionem partium calidi, quæ
certè colligi non po&longs;&longs;unt, ni&longs;i humoris interceptæ partes extrahantur, vt
fit per re&longs;olutionem; rare&longs;cens enim humor avolat; vnde ignis &longs;eu calidi
particulas congregari, &longs;eu colligi, nece&longs;&longs;e e&longs;t; nunquam autem partes hu
moris avolarent, &longs;i vacuum e&longs;&longs;et, vt pater.
Certis experimentis con&longs;tat fumum in dicto &longs;egmento non
a&longs;&longs;urgere &longs;ur&longs;um, &longs;ed deor&longs;um cadere; flammam item &longs;tatim extingui; vn
de fortè vacuum e&longs;&longs;e, qui&longs;piam putaret.
Scio de quibus experimentis &longs;ermonem facias; libellum legi,
& mihi nobili&longs;&longs;imi Autoris Roberti Boyle diligentia, nec non accurata
indu&longs;tria &longs;ummopere placuit: Ille igitur ignem accendit in &longs;uo recipiente
vitreo (&longs;ic enim vas illud vocat, ex quo anthliæ opera, maxima contenti
aëtis pars exugitur & educitur) nempe in eo, & ignem ex &longs;ilice excu&longs;&longs;it, &
pulverem tormentarium accendit, non tamen opera lentis v&longs;toriæ, licèt hoc
aliis pro vobis &longs;ucce&longs;&longs;erit; ille autem ob&longs;ervat fumum intra recipiens ex
vacuum facilè explicatur; nihil enim vetat aëre dilatato intra recipiens,
fumum graviorem e&longs;&longs;e; cùm etiam rarefacto gravior &longs;it; &longs;ic vbi Sol æ&longs;tivus
de Meridie in os camini &longs;uis radiis paulò altiùs penetrat, vix fumus a&longs;&longs;ur
git; quia tunc aër Meridiano æ&longs;tu rare&longs;cit, & levior redditur, ac proinde
minimè de&longs;cendere pote&longs;t, vt &longs;ur&longs;um extrudat fumum; immò licèt intra
recipiens aër non dilatetur, fumus tamen po&longs;t aliquod tempus in infe
riorem va&longs;is tractum de&longs;cendit, vt idem Autor ob&longs;ervat; quia remitten
te caloris vi den&longs;atur, immò & ab aëre comprimitur, vnde gravior evadit;
de&longs;cendat, igitur nece&longs;&longs;e e&longs;t; nihil ergo ex prædicto fumi de&longs;cen&longs;u deducitur
per quod vacuum in dicto &longs;egmento CD ad&longs;truatur. Porrò quòd ignis in
vacuo accendi non po&longs;&longs;it, patet; vtpote, qui tantummodò accenditur, ex
collectione partium ignis, vt dixi, quæ ex eo colliguntur, quod partes hu
moris interceptæ avolent, vel per excu&longs;&longs;ionem, vt in affrictu &longs;ilicis, vel per
ratetactionem, per quam &longs;cilicet redduntur leviores; &longs;ed &longs;i nullum e&longs;t
medium, avolare non po&longs;&longs;unt, quamvis alioquin levi&longs;&longs;imæ evadant, quia
&longs;cilicet rari&longs;&longs;imæ.
Sunt, qui dicunt, non totum quidem &longs;egmentum CD va
cuum remanere, &longs;ed tantùm illius partem aliquam.
Hoc ip&longs;um in&longs;inuare videtur &longs;upra laudatus Autor; &longs;ed pro&longs;e
ctò, &longs;i quid video, hoc &longs;tare non pote&longs;t; quia &longs;i aliqua pars dicti &longs;egmen
ti vacua &longs;it, quidquid ine&longs;t &longs;ubtilis materiæ innatare illi non pote&longs;t; igitur
&longs;upremus &longs;egmenti tractus vacuus e&longs;t; infimum verò &longs;ubtilis illa materia,
vel aër dilatatus occupat; in &longs;upremo igitur tractu &longs;egmenti nullum obje
ctum videri, nullus &longs;onus auditi, nullus ignis accendi po&longs;&longs;et: nec e&longs;t quod
dicant aliqui, di&longs;tincta e&longs;&longs;e ad in&longs;tar pororum vacuola; quia cùm ferè to
tus aër ex recipiente educatur, longè majora e&longs;&longs;ent prædicta vacuola reli
quo &longs;patio, ab aëre, vel &longs;ubtili materia occupato; ac proinde lumen conti
nuum, vel objectum continuo lumine illu&longs;tratum minimè videretur, &longs;ed
di&longs;tinctum majoribus maculis nigerrimo colore tinctis; nihil enim atrius
vacuo excogitari pote&longs;t.
Sed quæ&longs;o te, ad alias rationes orationem converte; hæc
enim, meo &longs;altem judicio, exhau&longs;ta e&longs;t; quod tamen antequam facias, le
vem &longs;crupulum mihi excutias, velim, circa ea quæ de &longs;ono dixi&longs;ti; legi enim
in dicto Autore, immi&longs;&longs;o Horologio rotato in recipiens, &longs;trepitum rotæ
denticulatæ auditum fui&longs;&longs;e, antequam ex eo aër per anthliam educeretur;
quo tamen educto, vix, ac ne vix quidem ille &longs;trepitus admotas pervenit ad
aures.
Subnectere debueras, quæ apud eundem Autorem legi&longs;ti, pul
&longs;atæ campanulæ &longs;onum in dictum recipiens immi&longs;&longs;æ, etiam educto aëre
auditum fui&longs;&longs;e. Fateor quidem, minimum &longs;onum vix audiri; nec enim
dubium e&longs;t, quin vt nimia compre&longs;&longs;io aëris, ita nimia ten&longs;io propagationi
&longs;oni tantulum ob&longs;tet; quippe qui per motum particularem eju&longs;dem medij
propagetur, quas certè vt pre&longs;&longs;um medium repellit, ita ten&longs;um retinet, &
qua&longs;i ad &longs;e adducit: &longs;ed jam ad alias rationes venio. Sextò, Igitur ferro
fra C, idem præ&longs;tat aër ambiens calidior; hic tamen &longs;en&longs;im, illud verò
temporis ferè momento; idem dico de flamma, de lacca caloris vi molli
ta; rare&longs;cit igitur illa materia &longs;egmento CD contenta; nec enim calor
in vacuum agit; premitque &longs;uperficiem Mercurij C, illamque deprimit,
vt &longs;e&longs;e dilatet, quod certè cuilibet corpori rarefacto competit.
Diceret fortè aliquis, vitrum ip&longs;um calore tantulum dilatari,
non verò materiam &longs;egmento CD contentam, cùm nulla in&longs;it.
Hoc jam mihi venerat in mentem, &longs;ed, vt tute &longs;cis, vana e&longs;t ra
tionis vmbra, &longs;eu larva, & mera hallucinatio; quia &longs;ive fi&longs;tula ID &longs;it laxior,
&longs;ive angu&longs;tior, eadem &longs;emper e&longs;t extantis Mercurij altitudo IC.
An fortè dici po&longs;&longs;et, calorem derivari ex vitro in Mercu
rium?
Hoc reverà dici non pote&longs;t: nam e&longs;to id fiat, ac proinde tan
tulum incale&longs;cat & rare&longs;cat Mercurius; inde &longs;equitur altiùs a&longs;&longs;urgere;
quia paulò levior e&longs;t: deinde &longs;i &longs;egmento CI, in quo extans Mercurius
continetur, ferrum candens admoveatur, non &longs;ubfidit &longs;uperficies Mercurij
C; &longs;ed aliquot bullæ ex Mercurio &longs;ur&longs;um evolant &longs;i&longs;tunt que in &longs;uperficie
C, idque &longs;en&longs;im, de quibus infra. Manet igitur illa &longs;exta ratio, adver&longs;us
vacuum. Septimò, Si intra CD &longs;it acus pendula magnetica, & magnes ex
trin&longs;ecus admoveatur, illam movet adducitque ad &longs;e, vel à &longs;e repellit; igi
tur aut virtus magnetica e&longs;t pura qualitas diffu&longs;a, atque adeò per medium,
ac proinde medium illud &longs;upponitur in &longs;egmento DC; igitur non e&longs;t va
cuum; aut prædicta virtus in corpu&longs;culorum effluvio po&longs;ita e&longs;t; ac proinde
hæc per poros vitri &longs;ubeunt; igitur alia pariter æquè tenuis materia per
eo&longs;dem poros &longs;ubire poterit; non e&longs;t igitur &longs;egmentum DC vacuum. Octa
vò, Totum vas ABG, cum fi&longs;tula ID, in hoc eodem &longs;itu, & &longs;egmento
Mercurij extantis IC, immi&longs;&longs;um e&longs;t à laudato &longs;upra Autore in dictum re
cipiens, eductoque aëre de&longs;cendit Mercurius ver&longs;us I; &longs;ub&longs;i&longs;tit tamen &longs;n
pra I, licèt aër per multum temporis, Anthliæ opera, educeretur; &longs;i autem
CD e&longs;&longs;et vacuum & potiori iure ip&longs;um recipiens, nulla e&longs;&longs;et ratio, propter
quam &longs;upra I extaret intra fi&longs;tulam Mercurius; quod enim prædictus Au
tor dicit, aëra compre&longs;&longs;um adhuc manere intra recipiens, ac proinde, &longs;u
perficiem Mercurij EF ab eo tantulum premi, atque adeò Mercurium in
fi&longs;tula &longs;upra I attolli; hoc, inquam nemo &longs;ibi per&longs;uadeat, cùm prædictus
aër po&longs;t Anthliam tamdiu exercitam valde dilatatus re&longs;ter, vt multis expe
rimentis probate po&longs;&longs;um.
Cur igitur educto ex recipiente aëre Mercurius in fi&longs;tula
de&longs;cendit, nunquam tamen v&longs;que ad I?
Aliam rationem, eamque germanam, ni fallor, affero; nempe
&longs;egmentum CD aliqua materia valde ten&longs;a occupat, quæ cum pro rata re
&longs;i&longs;tat cum aëre intra recipiens contento, & cum Mercurius, &longs;emoto agen
te extrin&longs;eco, in eadem altitudine EIF e&longs;&longs;e debeat, po&longs;ito quod materia
illa intra fi&longs;tulam ten&longs;a re&longs;i&longs;tat, & &longs;uperficiem Mercurij retineat, aër verò
intra recipiens tën&longs;us &longs;uperficiem EF ad &longs;e adducat, corpus enim ten&longs;um
proinde Mercurium intra fi&longs;tulam contentum deprimit, non tamen omni
no; quia materia &longs;ubtilis intra fi&longs;tulam ten&longs;a pro rata re&longs;i&longs;tit; igitur &longs;uper
ficies Mercurij &longs;upra I, &longs;emper extat; præ&longs;ertim cùm materia illa ten&longs;a in
tra LD magis re&longs;i&longs;tat, quàm intra CD dilatata.
Quid &longs;i extra recipiens extet extremitas D, ita tamen vt ad es
recipientis probè agglutinata &longs;it, & educto maxima vi aëre ex recipiente
perforetur fi&longs;tula in D.
Non probavit Autor, probarunt tamen alij, de&longs;cendit que Mer
curius in B. Subiitque aër tum proprio pondere, tum etiam adductus ab aë
re ten&longs;o intra recipiens; hic enim adducit &longs;uperficiem Mercurij EF, eam
que attollit; hæc autem &longs;ecum trahit, educit que Mercurium ex fi&longs;tula,
quem &longs;equitur aër, qui deinde à Mercurio &longs;ur&longs;um in recipiens extruditur;
cuncta hæc ex no&longs;tris principiis facilè explicantur.
Nonnulli capore nequeunt, &longs;eu nolunt, vim illam tractivam,
qua &longs;cilicet fit, vt corpus ten &longs;um, dum &longs;e&longs;e reducit, corpus contiguum tra
hat; quo enim vinculo, quo fune illud trahit?
licet æquè facilè concipi vnum corpus ten&longs;um, &longs;eu dilatarum &longs;e&longs;e intror
sum reducere, atque concipitur, corpus compre&longs;&longs;um &longs;e&longs;e extror&longs;um exten
dere; item corpus ten&longs;um, dum &longs;e&longs;e reducit, aliud corpus, cui contiguum
e&longs;t, &longs;e cum adducere, & corpus compre&longs;&longs;um, aliud corpus à &longs;e amovere; nec
alio fune opus e&longs;t ad hunc finem; cùm enim juxta Naturæ in&longs;titutum om
nia corpora &longs;int partes vniver&longs;i, & partes, quæ totum aliquod componunt,
conjunctæ e&longs;&longs;e debeant, alio quin patres non e&longs;&longs;ent, &longs;i &longs;eor&longs;im e&longs;&longs;e po&longs;&longs;ent;
ideo vnum corpus adhæret alteri, quando &longs;cilicet hoc moveri nequit, ni&longs;i
vel aliud adducatur, vel talis &longs;eparatio fiat, vt vacuum intercedat; nempe
&longs;upponamus corpus dilatarum &longs;e&longs;e in pri&longs;tinum &longs;tatum reducere, ac &longs;e&longs;e
contrahere, etiam &longs;i corpora contigua &longs;imul non adducantur, vnde qua que
vacuum erit; ac proinde corpus illud &longs;eor&longs;im ab omnibus aliis &longs;ejunctum;
igitur non e&longs;&longs;et amplius vniver&longs;i pars. Itaque cum tale &longs;it Naturæ in&longs;titu
tum, vt omnia corpora &longs;int partes vniver&longs;i, &longs;eor&longs;im e&longs;&longs;e non po&longs;&longs;unt; &longs;em
per igitur vnum aliis adhæret ; & ne &longs;eor&longs;im fiat, perinde &longs;e habent omnis,
atque &longs;i vnita effent; hinc vacui fuga; hinc Naturæ vinculum & funis. Vt
vt &longs;it (de his enim alibi di&longs;putavimus) quando corpus ten&longs;um &longs;e&longs;e re&longs;ti
tuit, &longs;eu contrahit, cùm perinde &longs;e habeat, atque &longs;i alteri contiguo conjun
ctum e&longs;&longs;et in ordine ad hunc finem Naturæ in&longs;tituto definitum, vt &longs;cilicet
omnia corpora &longs;int parces vniver&longs;i, qui revera finis po&longs;tulat, vt vacuum ar
ceatur, quid mirum, &longs;i &longs;ecum illud adducat, vnde fateor vltro, multum cor
pus moveri metu vacui; vnum tamen alteri adhærere, non quidem imme
diatè, ad vitandum vacuum, &longs;ed ad &longs;ervandum inde omnem prædictum Natu
ræ finem.
Non deerunt inter Democriticos, qui fines illos & Naturæ
in&longs;tituta rideant, vt à rebus phy&longs;icis planè aliena.
Sat &longs;cio: eò tamen illos, quamvis invitos, venire nece&longs;&longs;e e&longs;t:
ten&longs;os, aut certè per motum longiorum Atomorum, qui majus &longs;patium
po&longs;tulet; &longs;ed ex iis quæro, cur &longs;pira illa ten&longs;a &longs;it, vel compre&longs;&longs;a; & cur in
eo &longs;itu, in quam redacta e&longs;t, non permaneat; ac demum, vnde vim illam
habeat, qua &longs;e reducit, &longs;eu reducere nititur.
Re&longs;pondebunt illico, rationem ab ip&longs;a &longs;piræ, vel aëris figu
ra petendam e&longs;&longs;e, vt videre e&longs;t in artefactis, quorum analogia &longs;atis
favet.
Sed in&longs;to, & quæro, vnde habeant prædictæ
vt &longs;piræ &longs;int, vel arcus, vt hanc potiùs, quàm aliam figurám po&longs;tulent, ac
proinde ami&longs;&longs;a illa ac mutata, tantum ni&longs;um exerant, vt &longs;e&longs;e in eam re&longs;ti
tuant; prætereà vnde tanta vis motrix, tum in &longs;piris, vel arcubus aëris, tum
etiam &longs;ecundùm aliam hypothe&longs;im, in oblongis illis particulis? ad quid
enim motus ille circularis? quid quæ&longs;o hic ad illam particulam facit, aut
confert? Pro his alii&longs;que &longs;imilibus, ad primum naturæ in&longs;titutum omnino
confugient; cur ergo idem mihi non liceat? Quod verò &longs;pectat ad analo
giam artefactorum, non habet locum in hac controver&longs;ia; alioquin peti
tur, vt aiunt, principium: quæro enim, cur arcus ten&longs;us, vel &longs;pira ten&longs;a tan
ta vi redeat, ac &longs;e&longs;e re&longs;tituat; & dico rationem inde petendam e&longs;&longs;e, quod
&longs;cilicet pori ita &longs;int di&longs;po&longs;iti, vt ex Lunatione arcus v.g. multa compre&longs;&longs;io
contentæ in iis materiæ con&longs;equatur; ditis autem illam materiam ideò
comprimi, &longs;eu tendi quia ex minimis &longs;piris, vel arcubus con&longs;tat; idem igi
tur probas per idem. Itaque, quidquid e&longs;t, quidquid agit, &longs;eu movetur,
propter illum finem e&longs;t, ad quem à Natura de&longs;tinatur, movetur que, vt il
lud obtineat; video lapidem, & alia corpora tam recta linea, &longs;ublato im
pedimento ad idem centrum tendere, vt nunquam ab illa di&longs;cedant: quam
obrem verò? quia &longs;cilicet finis lapidis aliorumque corporum gravium e&longs;t
globum totalem con&longs;tituere, &longs;eu componere &longs;imul cum aliis; vt ergo fi
nem illum vel obtineant, vel obtentum indemnem &longs;ervent, illa vi pollent,
qua deor&longs;um ferantur, aut &longs;altem connitantur; finem autem retum ex ip&longs;o
v&longs;u, v&longs;um &longs;en&longs;u ip&longs;o percipimus; ex his vides, non e&longs;&longs;e fortè, cur hæc
Democritus rideat; &longs;ed hæc obiter, quæ hujus in&longs;tituti non &longs;unt, nec hujus
loci.
quæ&longs;o te, ad alias rationes orationem ac &longs;ermonem reevoca.
Nonò, &longs;i ve&longs;icam cyprinam, vel alterius generis, aperto fora
mine priùs exhau&longs;tam aëre, eoque expre&longs;&longs;o, arcto ligamine ad foramen &longs;tri
ctam, appen&longs;amque circa extremitatem interioris fi&longs;tulæ D, tum infu&longs;o
Mercurio, admotoque, ac deinde &longs;ubducto, vt ante, digito, vbi de&longs;cendit
Mercurius in CI, præfata ve&longs;ica ita intume&longs;cit, vt vix immi&longs;&longs;o anhelitu,
adeò tensè intume&longs;cene videatur: hoc experimen
multi probarunt.
Iam aliquid de illo in audieram; &longs;ed quid inde contra va
enum?
Quid inde, inquis; miror à te non videri; &longs;i enim &longs;patium CD
quæ cau&longs;a hanc ve&longs;icam ita di&longs;ten
dit? non intrin&longs;eca, cùm tota aëre evacuata fuerit; extrin&longs;eca nulla e&longs;t, &longs;i
&longs;patium CD vacuum e&longs;t.
Quid ad hæc ille recentior, quem jam &longs;upra lauda&longs;ti?
Idem pror&longs;us, quod nonnulli Pari&longs;ien&longs;es cum Pecquero; &longs;cili
cet partes aëris inter rugas &longs;eu plicas ve&longs;icæ remanere, quæ cùm liberio
res &longs;int, à prima compre&longs;&longs;ione in pri&longs;tinam exten&longs;ionem &longs;eu dimentionem
re&longs;tituunt &longs;e&longs;e; quod certè priùs non faciebant, nimirum ab extrin&longs;eco aëre
æquè compre&longs;&longs;o impeditæ.
conjicio, non multùm tibi arridet.
Genium meum no&longs;ti; di&longs;&longs;imulare non po&longs;&longs;um, id quod &longs;entio;
& quando quidem liberè in hoc congre&longs;&longs;u, quod intus &longs;entimus, exponi
mus, fateor, rationem illam mihi non probari. Primò, enim quis &longs;ibi per
&longs;uadeat, ambientem nos aëra adeò compre&longs;&longs;um e&longs;&longs;e, vt ad mille &longs;imam &longs;uæ
exten&longs;ionis partem redactus &longs;it? nempe paucæ illæ rugæ interioris ve&longs;icæ
po&longs;t accuratam expre&longs;&longs;ionem, vix mille&longs;imam partem &longs;patij occupant, il
lius, quod ten&longs;a & tumida ve&longs;ica continet; tanta vis aëris pre&longs;&longs;i no&longs;tris cor
poribus valdè noceret, & vix liceret ducere anhelitum. Secundò, Si tan
tulum inclinetur fi&longs;tula BD, a&longs;&longs;urgit Mercurius &longs;upra C, &longs;en&longs;imque ve&longs;ica
detume&longs;cit; antequam a&longs;&longs;urgens Mercurius eam attingat; quid ergo de
nuo aëra in ea contentum comprimit? Tertiò, Si aqua &longs;patium CD oc
cupet, provt facilè po&longs;t a&longs;cen&longs;um Mercurij illud occupare pote&longs;t, de quo
infra, ve&longs;ica detume&longs;cit; &longs;ed vnde hoc? aquam enim compre&longs;&longs;am non e&longs;
&longs;e apud omnes con&longs;tat; ab illa igitur aër ve&longs;ica inclu&longs;us non comprimi
tur; dicet haud dubiè laudatus Autor aëra intra plicas exteriores ve&longs;icæ
priùs contentum, vbi Mercurius de&longs;cendit in CI, &longs;e&longs;e in pri&longs;tinam exten
&longs;ionem re&longs;tituere, comprimi verò denuò ab a&longs;&longs;urgente Mercurio, vel ab
aqua inducta; igitur &longs;egmentum CD non e&longs;t vacuum, quod hîc dumtaxat
probare intendo; deinde, quis credat prædictum aëra e&longs;&longs;e in &longs;patio centies
millecuplo illius, quod ante obtinebat intra in&longs;en&longs;ibiles plicas?
Fieri non pote&longs;t, quin præfatus Autor de ve&longs;icis recipiente
inclu&longs;is aliqua habeat.
Habet haud dubiè; inclu&longs;a, inquit, intra recipiens ve&longs;ica, edu
ctoque deinde aëre, ve&longs;ica priùs ligata intume&longs;cit; cujus tumoris cau
&longs;am vult e&longs;&longs;e re&longs;iduum aëris intra ve&longs;icam contenti, qui cùm liberè dila
tari po&longs;&longs;it, educto &longs;cilicet externo aëre contranitente, maximè dilatatur ac
&longs;e&longs;e explicat; hinc, vt vides, præviam dicti aëris compre&longs;&longs;ionem accer
&longs;it; eam &longs;cilicet, ac tantam, quæ omnem fidem &longs;uperet; ego certè di
cere malim, illud tantulum aëris intra ve&longs;icæ rugas relicti, ab extrin&longs;eco
ambiente, Anthliæ vi educto dilatari, vnde &longs;i ve&longs;ica perforata &longs;it, vel minùs
arctè ligata; cùm aër internus externo contiguus &longs;it, citra tumorem ve&longs;icæ
adducitur, nec non tenditur; hinc &longs;i aër in recipiens inver&longs;o Epi&longs;tomij
verticillo immittatur, cùm ce&longs;&longs;et dilatatio, ve&longs;ica detume&longs;cit; aliud ad
dit, &longs;cilicet ve&longs;icam ita exten&longs;am & compre&longs;&longs;am, vt nulla plica inter-
&longs;it, educto licet aëre ex recipiente, non tamen propterea tume&longs;cere, quia
&longs;cilicet dee&longs;t materia intus dilatanda, in quo nulla e&longs;t difficultas, nulla &longs;al
tem mihi e&longs;&longs;e videtur.
Quid &longs;i mediocris &longs;altem aëris quantitas intra ve&longs;icam ob
&longs;tricto valide collo, relinquatur, vt facilè fieri pote&longs;t?
Hoc &longs;anè præfatus Autor minimè omi&longs;it, &longs;ed inde validum
pro &longs;ua hypothe&longs;i confirmanda, duxit argumentum; nempe; po&longs;t exhau
&longs;tum ex recipiente aëra, ve&longs;ica di&longs;cinditur, vnde &longs;tatim concludit, majo
ris quantitatis aëtis interni, &longs;ubducto externo contranitente, majorem ac
liberum ni&longs;um exeri; vnde non mirum, &longs;i ve&longs;ica rumpatur; vt etiam ma
gno cum fragore di&longs;rumpitur, &longs;i jam inflata arctè &longs;tricto collo, luculento
igni proximè admoveatur.
Hoc experimentum rem ip&longs;am conficere videtur; atque ita
ex eo præfati Autoris &longs;ententia omnino demon&longs;trari.
Expecta quæ&longs;o, Augu&longs;tine, &longs;trenui pugilis non e&longs;t, tam
citò deditionem facere; immò &longs;i rem attentè perpendas, no&longs;træ hypo
the&longs;i æquè favet; nempe major aëris quantitas magis dilatari pote&longs;t, quàm
minor, vt patet; quid mirum ergo, &longs;i cum externa vi, aër intra ve&longs;icam
contentus in majus &longs;patium explicari queat, debiliora ve&longs;icæ latera, quæ
tantam dilatationem non ferunt, cedere cogantur; in parte &longs;cilicet debi
liore? illa autem analogia ve&longs;icæ igni admotæ ad rem no&longs;tram facit; nam
vt aër inclu&longs;us præ calore plus æquo rare&longs;cens, ve&longs;icam di&longs;rumpit; ita &
aër plus æquo externa vi acris adducti dilatatus eundem effectum præ
&longs;tat.
Iam mihi res clari&longs;&longs;ima videtur; in ferenda &longs;ententia nimis
præceps fui; &longs;u&longs;tinendum fuerat, vt rectè monui&longs;ti; &longs;ed jam ad alias ratio
nes progredi poteris, cum hæc difficultas exhau&longs;ta &longs;it.
Decimò, Si po&longs;tquam de&longs;cendit Mercurius in fi&longs;tula extante
&longs;egmento BC, digitum ori B pre&longs;sè admoveas, ne quid aëris &longs;ubeat, &
fi&longs;tulam invertas, &longs;enties digiti pulpam fortiter attrahi atque intume&longs;cere,
codem pror&longs;us modo, quo intume&longs;cit caro, admota cucurbitula; immò
cum aliqua difficultate avellitur: deinde digitus, perinde atque &longs;i cucurbi
tula avelleretur; &longs;i autem ante quam digitus admoveatur, punctim acu, vel
cultello pulpa illa configatur, vbi deinde admovetur ori B, & invertitur fi
&longs;tula, copio&longs;us &longs;anguis exugitur, eodem pror&longs;us modo, quo fieri &longs;olet in
cucurbitulis.
Sed quid inde contra vacuum?
nec enim video quò &longs;pe
ctes.
Iamjam videbis; &longs;i enim vacuum e&longs;&longs;et in &longs;egmento CD, vel
inver&longs;a fi&longs;tula in &longs;egmento CD, quid quæ&longs;o digiti pulpam in tumorem at
tolleret? quid &longs;anguinem exugeret?
aëris externi pondus, inquies; &longs;ed
nullum pror&longs;us pondus &longs;entitur, nulla pre&longs;&longs;io in externa digiti parte; im
mò aër &longs;ubire nequit, vt pater; deinde cùm Mercurius in de&longs;cen&longs;u, pro
pter motum acceleratum primùm de&longs;cendat infra C, licèt deinde po&longs;t va-
gmento e&longs;t, infra C, admoveatur digitus in B, ac deinde fi&longs;tula invertatur,
longè majore vi & pulpa digiti in tumorem attollitur, & &longs;anguis exugi
tur; idem tamen aëris pondus gravitat: vnde igitur diver&longs;us effectus? certè à materia ten&longs;iore in &longs;egmento CD contenta; &longs;i enim ten&longs;ior e&longs;t,
majore vi trahit; & digiti pulpam ad &longs;e adducit; &longs;ic arcus ten&longs;ior &longs;agittam
longiùs ejiculatur: & verò amoto illo vacuo, & in ejus locum materia
illa ten&longs;a &longs;ub&longs;tituta, cuncta hæc facilè explicantur.
Sic etiam facilè explicarem aliud experimentum prædicti
Autoris, qui exhau&longs;to aëre ex recipiente, dicit, operculum illius alioquin
levi&longs;&longs;imum, gravi&longs;&longs;imum &longs;entiri, propter pondus aëris externi &longs;uperimpo
&longs;itum; hic tamen effectus aëri externo tribui non debet &longs;ed aëri interno
valde ten&longs;o ac dilatato, nempe cùm operculum illud attolli non po&longs;&longs;it, ni&longs;i
aër internus vltra dilatetur, huic majori ten&longs;ioni valde re&longs;i&longs;tit; co
gita quæ&longs;o arcum ten&longs;um, qui non ni&longs;i longè majore vi vltra tendi
pote&longs;t.
Diceret haud dubiè &longs;upra laudatus Autor, intra pulpam
digiti multas e&longs;&longs;e partes, quæ &longs;emota pre&longs;&longs;ione ambientis erumperent,
& liberiorem &longs;ortitæ motum, maximam inducerent mutationem; at
profectò nihil tale &longs;en&longs;i; &longs;ed tumorem dumtaxat illum; nec pul&longs;us ratio
mutatur; vno verbo nihil accidit, quod exuctioni validæ tribui non po&longs;
&longs;it: equidem &longs;i digitus arctè funiculo &longs;tringatur, &longs;upra illam extremita
tem, quæ ori B, affigitur, propter majorem &longs;anguinis vim in eo tractu
retenti, impeditur enim circulatio, major etiam &longs;anguinis copia exugi
tur: &longs;i quis autem totam manum in &longs;egmentum CD immitteret, ita vt
tamen nullus aër &longs;ubire po&longs;&longs;et, &longs;imilem quidem, majorem tamen dictæ
exuctionis effectum &longs;entiret, non &longs;ine aliquo periculo manus intume&longs;
centis, vt alicui accidi&longs;&longs;e intelligo: Alligavi deinde extremo digito ve
ficam cyprinam, quæ &longs;tatim inver&longs;a fi&longs;tula intumuit; item medullam
&longs;ambuci, & fru&longs;tulum &longs;pongiæ, &longs;ed in his nulla mutatio contigit,
aperti enim &longs;unt laxiores pori, per quos aër educitur & dilatatur;
ex præmi&longs;&longs;is igitur certum re&longs;tat, &longs;egmentum CD vacuum non re
&longs;tare; quo verò corpore plenum &longs;it, paulò po&longs;t dicam. Ad aliam
partem tran&longs;eo, in qua dicebatur &longs;egmentum Mercurij IC, &longs;u&longs;tinerià
Cylindro aëris eju&longs;dem ba&longs;is, ita vt perfectum &longs;it vtrimque æquibrium;
contra hanc &longs;ententiam nonnulla militant, quæ &longs;incerè vobis exponam. Primò, Si appendatur fi&longs;tula BD, po&longs;tquam &longs;ubducto digito, de&longs;cendit
Mercurius in IC, &longs;tatera fideli adhibita, & &longs;ignetur ponderis ratio, ac dein
de citra Mercurij de&longs;cen&longs;um, eadem fi&longs;tula cum æquali quantitate Mercu
rij appendatur, eadem ratio ponderis invenietur, paulò major ; æqualem
quantitatem Mercurij intelligo &longs;egmento IC ; & dico paulò majorem ;
nempe immer&longs;um &longs;egmentum fi&longs;tulæ IB ad primum pondus nihil confert;
immò potiùs aliquid detrahit; quia Mercurio levius e&longs;t; &longs;ed mihi &longs;ufficit,
modo vtrinque proximè æqualis &longs;it ratio ponderum, qualis reverà e&longs;t, vt
&longs;æpè probavi: Ex hoc autem experimento &longs;ic mihi rectè ratiocinari videor;
ctum &etail;quilibria &longs;unt, igitur
brarum, æquilibrium facit cum cylindro aëris etiam trium
aliud pondus
æquilibrium facere nequit, alioquin &longs;ex libris Mercurius Æquiponderaret
quod legibus Staticæ repugnat. Et verò Mercurius CI ab aëris cylindro
&longs;tentatus
gotio educi & immitti po&longs;&longs;et per
&longs;u&longs;tentatus fi&longs;tulæ pondus non augeret; & hæc e&longs;t &longs;ecunda ratio; aperto
enim foramine in D, inductoque embolo in cavitatem BC, &longs;i eum digito
tantulum attollis, clau&longs;o foramine in D, & fi&longs;tula appendatur,
præfatus cylindrus nullum pondus addit fi&longs;tulæ; igitur, nec Mer
curius CI, à cylindro aëris &longs;u&longs;tentatus; cùm vtrimque par &longs;it
ratio.
Diceret forta&longs;sè aliquis, Mercurium contentum Segmento IC
gravitate in latera fi&longs;tulæ; &longs;i enim fi&longs;tula perforetur in L v.g. per foramen
Mercurius effluit.
Scio, ita aliquos re&longs;pondere; &longs;ed hæc re&longs;pon&longs;io, meo &longs;altem
judicio, nodum non &longs;olvit; quando enim latera va&longs;is ita non adhærent
contento, quin ea liberè, &longs;ine illo moveri po&longs;&longs;int, de primi &longs;cilicet, at
que attolli, in ea certè corpus contentum non gravitat; quia non ob
&longs;tant, quo minùs illud deor&longs;um eat; hoc autem luculento experimento de
mon&longs;tro.
Sit Vas BAC oblongum, clau&longs;um in C, apertum
in AB, plenum aqua, illudque ex ligno levi&longs;&longs;imo, &
valde cra&longs;&longs;um; immergatur in aquam, donec &longs;it in
æquilibrio, immer&longs;o &longs;egmento DC, extante verò
Segmento DA, aqua contenta &longs;egmento DA, extans
&longs;upra &longs;uperficiem aquæ GDF, eodem modo gravitat
in latera va&longs;is CADB, quo Mercurius in latera præ
dictæ fi&longs;tulæ; &longs;i tamen appendatur vas CA, in hoc
&longs;itu nullum pondus habet, quia &longs;cilicet ab aqua &longs;u&longs;ti
netur; nihilo tamen minus, &longs;i perforetur latus DB,
per foramen effluet aqua, &longs;icuti Mercurius per fora
men apertum in fi&longs;tula effluit. Sed alio experimento lu
culentiore rem hanc explico: Sit vas HB continens Mercurium FB &longs;ic tu
bus ligneus oblongus, ex materia levi&longs;&longs;ima, MC, vtrimque pervius, &longs;i
imponatur altera eius extremitas C Mercurio, tantulum &longs;egmentum im
mergetur; infundatur mox aqua in prædictum tubum, per os &longs;uperius M,
donec proximè ad C Mercurij tubo contenti &longs;uperficies deprimatur, aqua
verò tubo infu&longs;a a&longs;&longs;urgat in K ; denique appendatur tubus CM, nullam
profecto ponderis vim exerit, quia &longs;cilicet &longs;u&longs;tinetur à Mercurio; immo
&longs;i deprimatur infra C, &longs;ur&longs;um extruditur à Mercurio, æquali, vel potiùs
eodem aquæ &longs;egmento &longs;emper extante; & &longs;i tantulum attollatur &longs;upra C,
extantis aquæ &longs;uperficies manebit in K ; atque ita &longs;i
po&longs;t prædictam
ex eret quidem
qua aqua extans nullam partem habet, &longs;ed tantùm
tubus ligneus, qui minore &longs;egmento, quam par e&longs;&longs;et,
ad æquilibrium immer&longs;us e&longs;t: licèt, facto in tubo
MC foramine inter KN, aqua tubo contenta per il
lud effluat? &longs;i autem aquam infundas in vacuitatem
interceptam HCI attolletur, a&longs;&longs;urgétque Mercurius
per tubum CM, nulla tamen tubo fit ponderis ac
ce&longs;&longs;io. Ex quibus, ni fallor, evidenter concluditur,
corpus ab alio &longs;u&longs;tentatum, novam vim ponde
ris non exerere, quando appenditur; ac proin
de &longs;i appen&longs;um totam vim ponderis exerit, ab
alio corpore non &longs;u&longs;tentari, igitur &longs;egmen
tum extantis Mercurij ab exterioris aëris cylindro non
&longs;u&longs;tinetur, quia &longs;cilicet appen&longs;um totam vim ponde
ris exerit.
Sunt, qui dicant, &longs;i rectè memini, ab aëris cylindro, qui
ba&longs;i D incumbit, æquè deor&longs;um deprimi, ac &longs;ur&longs;um attollitur, ab alio
gravitante in ba&longs;im B; mediante &longs;cilicet Mercurio.
Hoc facilè reijcitur;
D, &longs;ive mercurio, &longs;ive aqua, &longs;ive aëre fi&longs;tula plena &longs;it, vt patet; Vnde, &longs;i
quem haberet effectum, eundem &longs;emper haberet; &longs;ed hæc in&longs;tantia futi
lis e&longs;t;
nem
gmentum IC &longs;emper &longs;u&longs;tinet; &longs;ed hoc experimento repugnat;
nam &longs;i tantulum aëris antequam demittatur Mercurius in fi&longs;tula re
linquatur, Mercurius de&longs;cendet infra C; in C autem &longs;u&longs;tineri de
beret; &longs;i à cylindro aëris exterioris, &longs;u&longs;tineretur, vt patet; im
mo de&longs;cendit infra C non juxta men&longs;uram cylindruli aëris in fi&longs;tula
relicti, &longs;ed juxta majorem ; vnde illum aëra multùm dilatari, nece&longs;&longs;e
e&longs;t; vnde fortè aliam materiam intra fi&longs;tulam dilatatam e&longs;&longs;e di
cemus.
Huc recurrit hypothe&longs;is Autoris &longs;upra laudati; dicent enim
illius &longs;ententiæ a&longs;&longs;ertores, illud tantulum aëris intra fi&longs;tulam relicti, po&longs;t de&longs;
cen&longs;um Mercurij liberiorem nanci&longs;ci campum, ac proinde cùm ante com
pre&longs;&longs;us e&longs;&longs;et, explicare &longs;e&longs;e ac dilatare, & premere &longs;uperficiem Mercurij,
vnde hic infra C de&longs;cendit.
Tantam compre&longs;&longs;ionem aëris jam &longs;upra &longs;atis efficaciter refu
tavi; hic tantùm addo, &longs;i vacuum remanet &longs;egmentum CD, illam aëris par
ticulam &longs;atis &longs;patij habere, vt explicet &longs;e&longs;e, ac proinde non premere &longs;uper
ficiem Mercurij, ideo enim illam premere dicitur quia nititur explicare &longs;e
&longs;e, cùm plus æquo compre&longs;&longs;us &longs;it. Si verò &longs;egmentum CD non e&longs;t
&longs;ed plenum, jam videndum e&longs;t, quare
la haud dubiè dilatatur, compre&longs;&longs;a igitur non manet; &longs;i æthere, vt volunt ali
qui, per poros adducto, certè illa, tantùm ætheris, vel &longs;ubtilis materiæ por
tio exugitur, &longs;eu per poros adducitur, quæ ad
ne vacuum re&longs;tet, nece&longs;&longs;aria e&longs;t: &longs;ed primus locus cedit intra
tum præfatæ aëris portioni; &longs;i demum e&longs;t alia &longs;ubtilis materia ten&longs;a, potio
ri jure prædictus aër tenditur ac dilatatur; igitur compre&longs;&longs;us non ma
net, igitur &longs;uperficiem Mercurij &longs;egmento CI contenti deor&longs;um non
premit.
Cur ergo Mercurias de&longs;cendit infra C? ne&longs;cio, vtrùm aliam
cau&longs;am excogitare quis po&longs;&longs;it.
Non dee&longs;t alia cau&longs;a, nempe Mercurij IC pondere prædicta
aëris particula dilatatur; vt enim aër Mercurij pondere comprimitur in
fontibus quibu&longs;dam arte factis, ita & eodem dilatatur; quid mirum ergo,
&longs;i Mercurius infra C de&longs;cendat? hoc autem novo experimento per&longs;picuè
demon&longs;tro; &longs;i enim fi&longs;tulam BD & vas ABG, non Mercurio, &longs;ed aqua
impleas, admotóque digito, extremum B in aquam EF immergas, di
gitúmque &longs;ubducas; fi&longs;tula plena manet; &longs;i autem non pror&longs;us aquâ fi&longs;tu
lam impleveris, admotóque digito extremum B immer&longs;eris, &longs;ubduxerí&longs;
que digitum, aqua tantulum de&longs;cendit v. g. &longs;i dum admotus e&longs;t digitus
extremo B immer&longs;o &longs;uprema &longs;uperficies aquæ &longs;it in M, &longs;ubducto digito
de&longs;cendit, qua&longs;i in N; hac tamen ratione, vt dum &longs;uperficies aquæ e&longs;t circa
mediam altitudinem ID, puta in C &longs;egmentum de&longs;cen&longs;us prædictæ &longs;uper
ficiei majus &longs;it; minus verò, quo dicta &longs;uperficies accedit propriùs ad D
vel ad I.
aquæ &longs;ubducto digito de&longs;cendit, quia pondus aquæ fi&longs;tulæ contentæ re
lictam in fi&longs;tula portionem aëris dilatat; &longs;i autem dicta &longs;uperficies acce
dit propius ad D, e&longs;t quidem magnum aquæ pondus, ad majorem dilata
tionem præ&longs;tandam, &longs;ed dee&longs;t &longs;ubjectum, &longs;eu materia majoris dilatatio
nis capax; &longs;i verò propiùs ad I, e&longs;t quidem &longs;ubjectum capax majoris dila
tationis, &longs;cilicet major aëris portio; e&longs;t tamen minima vis ponderis ad il
lam præ&longs;tandam; &longs;i demum &longs;uperficies &longs;it in C, & &longs;atis magna e&longs;t vis
ponderis, &longs;egmentum, &longs;cilicet aquæ IC, & &longs;ubjectum &longs;atis capax,
&longs;cilicet portio aëris CD ; major igitur &longs;equitur dilatatio, majus igitur
&longs;egmentum de&longs;cen&longs;us. At &longs;cire ex te velim, Antime, vtrùm idem in Mer
curio fiat.
Idem prorsùs &longs;æpiùs probavi in fi&longs;tula duos pedes alta; vt &longs;ci
licet majus &longs;egmentum e&longs;&longs;et, quo &longs;uprema &longs;uperficies Mercurij ad me
dium altitudinis fi&longs;tulæ extantis, propiùs accederet. Si autem altiorem
fi&longs;tulam adhibeamus, in qua &longs;cilicet &longs;ubducto digito ex A, Mercurius de
&longs;cendat, donec extet in &longs;egmento IC duorum circiter pedum & 1/4 vel
curij &longs;egmentum infra C; pro quo illa quam luculenter expo&longs;ui&longs;ti, Au
gu&longs;tine, ratio militat; equidem quando fi&longs;tula altior e&longs;t, vt rectè ob&longs;er
vat &longs;upra laudatus Autor, æqualis aëris portio intra fi&longs;tulam relicta,
tam longum de&longs;cen&longs;us infra C &longs;egmentum non præ&longs;tat; quia prædictus
aër in majore Mercurij de&longs;cen&longs;u v&longs;que ad C, magis dilatatur, quàm in
minore; vnde non mirum, &longs;i deinde eundem minùs dilatet Mercurius in
fra C de&longs;cendens: hinc etiam quo major erit portio aëris in &longs;egmento
CD, eò majus erit &longs;egmentum de&longs;cen&longs;us Mercurij infra C. Hinc diver
&longs;æ conjugationes &longs;eu combinationes majoris &longs;cilicet aëris &longs;egmenti, vel
minoris, ante dilatationem; majoris altitudinis fi&longs;tulæ vel minoris; ma
joris &longs;egmenti Mercurij vel minoris; prædicta &longs;ex variè combinari po&longs;
&longs;unt; & &longs;ic cuncta ad præmi&longs;&longs;a principia facilè reducuntur; nempe ma
jus Mercurij &longs;egmentum &longs;eu pondus idem &longs;egmentum aëris magis di
latat; majus &longs;egmentum aëris ab eodem Mercurij &longs;egmento magis dila
tatur; denique majus de&longs;cen&longs;us &longs;egmentum à D in C eandem portionem
aëris magis dilatat, quàm minus.
alias.
Sit igitur quarta ratio: &longs;i per compre&longs;&longs;ionem corporis liqui
di, admoto &longs;cilicet di&longs;co &longs;upremæ &longs;uperficiei, attollatur liquor in fi&longs;tula,
nullum illius pondus, appen&longs;a fi&longs;tula &longs;enties; ratio in promptu e&longs;t,
quia à di&longs;co admoto attollitur & &longs;u&longs;tinetur; illius ergo pondus nullam
aliam vim exerit; igitur pari modo Mercurius extans in &longs;egmento IC
nullam vim ponderis exerit, &longs;i vel ab exteriore aëre compre&longs;&longs;o, vel ab aë
ris cylindro &longs;u&longs;tineatur; par enim e&longs;t vtrimque ratio; & in&longs;tantia &longs;upra
facta hîc etiam eodem modo refellitur; cùm non minùs liquor à pre-
to in extante fi&longs;tulæ &longs;egmento foramine, tam vnus effluat, quàm alius;
& vt dicam &longs;uper hoc, quod &longs;upra exciderat, quonam pacto Mercurius
extans in &longs;egmento fi&longs;tulæ IC gravitet in latera eju&longs;dem, facto foramini
in L, totum pondus Mercurij CL exerit vim &longs;uam, qua extrudit Mercu
rium &longs;ubjectum per foramen L: itaque omnes partes Mercurij gravi
tant in B vltimam &longs;uperficiem fi&longs;tulæ; hæc autem &longs;u&longs;tinetur, vt volunt
à cylindro exterioris aëris; ex hac porrò gravitatione qua&longs;i repercu&longs;&longs;a
&longs;eu reflexa &longs;equitur, vt illius ni&longs;u, &longs;i pars &longs;ubjecta versùs latera cedere
po&longs;&longs;it, versùs illa extrudatur; hinc aperto foramine, tanta vi erumpit;
igitur ni&longs;us ille non pellit fi&longs;tulam, vel illius latera deor&longs;um, &longs;ed
quoquo versùm per horizontalem di&longs;trahit, in quo, meo judicio, nul
la e&longs;t difficultas; &longs;altem apud eum; qui rem i&longs;tam paulò attentiùs per
pendat.
Antime, ex eo quod fi&longs;tula cum extante Mercurio appen&longs;a totam vim &longs;ui
ponderis exerat, evinci, &longs;egmentum extantis Mercurij à cylindro exte
rioris medij, &longs;cilicet aëris, minimè &longs;u&longs;tineri.
Reducitur, non inficior; cùm tamen novum &longs;it experimentum,
illudque &longs;atis luculentum, novæ rationis mihi loco e&longs;t.
Quid &longs;i non aëris, &longs;ed aquæ &longs;egmentum in fi&longs;tulam immitta
tur, antequam Mercurius de&longs;cendat in CI?
Hoc alij jam probarunt, inveneruntque, Mercurium &longs;ub&longs;idere
infra C (1/14) altitudinis &longs;egmenti aquæ immi&longs;&longs;æ, quia pondus cylindri aquej
14. pedum v. g. e&longs;t æquale ponderi cylindri Mercurij vnum pedem alti;
at verò &longs;i aëra, non aquam immi&longs;eris, Mercurius &longs;ub&longs;idit infra C, &longs;patio
majore ip&longs;o &longs;egmento aëris immi&longs;&longs;i, ita illi, &longs;ed pace illorum dixerim;
&longs;it enim fi&longs;tula BD 4 pedum; immittatur &longs;egmentum aëris altum vnum
pedem, tum Mercurius, fiatque more &longs;olito, non &longs;ub&longs;idit Mercurius in
fra C &longs;egmento vnius pedis, ne dum majore ; itaque &longs;i &longs;egmentum aëris
immi&longs;&longs;i &longs;it paulo minus, non nego fieri po&longs;&longs;e, vt &longs;egmentum de&longs;cen&longs;us
Mercurij infra C &longs;it majus &longs;egmento aëris immi&longs;&longs;i, quod tamen genera
tim dici nequit ; &longs;ed hæc &longs;upra jam di&longs;cu&longs;&longs;imus. Venio ad quintam ratio
nem. Segmentum fi&longs;tulæ CD non e&longs;t vacuum, &longs;ed plenum alia materia,
eaque valde ten&longs;a, ten&longs;o aëri haud ab&longs;imilis, qui exhau&longs;to per anthliam
multo aëre, in recipiente, de quo &longs;upra re&longs;tat.
Equidem jam &longs;upra proba&longs;ti, ad evidentiam, meo &longs;altem ju
dicio, &longs;egmentum CD vacuum non e&longs;&longs;e; &longs;ed aliqua tenui materia plenum;
hoc facilè conce&longs;&longs;erim, ten&longs;am tamen e&longs;&longs;e nondum à te, quod &longs;altem
à me perceptum &longs;it; huc v&longs;que probatum.
Deducere facilè poteras, ex adducto experimento ve&longs;icæ cy
prinæ, quæ po&longs;t de&longs;cen&longs;um Mercurij adeò intume&longs;cit; rejecimus enim re
&longs;pon&longs;ionem vel hypothe&longs;im &longs;upra laudati Autoris, quod &longs;cilicet aër in pli
cis inclu&longs;us, compre&longs;&longs;us priùs, &longs;uæ deinde libertati relictus, &longs;e&longs;e explicet,
infletque ve&longs;icam; nam & tanta compre&longs;&longs;io aëris repugnat &longs;en&longs;ui, cùm
perveniat; vnde manife&longs;tè &longs;equitur, ideò aëra intra ve&longs;icam dilatari, &
tendi, quia ab ambiente ten&longs;o quoquo ver&longs;um adducitur.
Ex alio experimento ten&longs;am materiam e&longs;&longs;e in &longs;egmento CD,
&longs;atis efficaciter probari po&longs;&longs;e, arbitror; nimirum ex eo quòd, vt &longs;upra
dixi&longs;ti, Antime, pulpa digiti valide adducatur ab illa materia; exugatur
copio&longs;us &longs;anguis; caro intume&longs;cat vberis ad in&longs;tar; nec enim aëri extrin
&longs;eco hic effectus tribui pote&longs;t, vt jam &longs;upra &longs;atis inculca&longs;ti; immo &longs;i incli
netur fi&longs;tula, cujus extremum B Mercurio immergitur, po&longs;tquàm denuò
pre&longs;sè admotus e&longs;t extremo aperto B, exugitur, vt antea, digitus, vber
que intume&longs;cit, denique vt res magis per&longs;picua fiat, admoto digito ex
tremo ori fi&longs;tulæ ligneæ, vtrimque perviæ, altéque immer&longs;o extremo illo,
cui pre&longs;sè digitus admotus e&longs;t, ita vt nihil aquæ &longs;ubingredi queat; licet
cylindrus aquæ gravitet in cylindrum aëris fi&longs;tula contenti immer&longs;um, non
tamen propterea exugitur digitus, intume&longs;cit digiti pulpa, a&longs;&longs;urgit vber;
ille igitur digiti admoti effectus ab aëris exterioris cylindro non procedit:
cuncta hæc, ni fallor, evincunt, intra CD materiam ten&longs;am ine&longs;&longs;e; nec quid
quam in contrarium opponitur, quod expeditè &longs;olvi non po&longs;&longs;it; non dee
runt tibi, Antime, aliæ rationes.
Non de&longs;unt haud dubiè: en tibi vnam ex poti&longs;&longs;imis; &longs;i infun
datur aqua &longs;upra Mercurium EF, attollatúrque fi&longs;tula, donec extremum
B &longs;uperet &longs;uperficiem EF, illico Mercurius IC a&longs;&longs;urgit tanto impetu ver
sùs D, vt quandoque præ nimia ictus vi, fi&longs;tula di&longs;&longs;iliat; idem accidit, &longs;i
extremum ex Mercurio adductum in aëre &longs;tatuatur; idem etiam accidit &longs;i
valde inclinetur fi&longs;tula; ingreditur enim Mercurius maximo cum impetu,
& versùs fundum D impactus maxima vi nonnunquam fi&longs;tulam
frangit.
Hunc effectum, dubio procul omni, exterioris aë
ris cylindro prævalenti attribuent, &longs;icut in libra, vbi alteri lan
ci majus pondus imponitur, hæc alteram lancem &longs;ur&longs;um attol
lit.
Acutè omnino, ad &longs;peciem tamen, cùm reip&longs;a hæc ratio legi
tima non &longs;it; nec enim tanto impetu pondus de&longs;cendens aliud paulo mi
nus in altum tollit; &longs;ed longè tardiore motu, quàm &longs;i pondus motu acce
lerato deor&longs;um &longs;ine impedimento ferretur; atqui cylindrus aëris, vt ip&longs;i
fatentur, eju&longs;dem e&longs;t ponderis cum &longs;egmento extante Mercurij IC, ef
fluente igitur modica Mercurij particula, ip&longs;ique &longs;uccedente particula
aquæ molis æqualis, minima e&longs;t ponderum differentia; igitur quamvis
cylindrus aëris prævaleat, illud tamen modicum di&longs;crimen virium tantum
motum ciere non pote&longs;t, quia &longs;cilicet motus acceleratus deor&longs;um circa
initium tardi&longs;&longs;imus e&longs;t, &longs;ecus tamen motus ten&longs;orum, vel compre&longs;&longs;orum;
nimirum corpus compre&longs;&longs;um &longs;tatim initio maxima (
183.) vi erumpit; præterea &longs;uppponamus tubum geminum BCA, infun
datur aqua per os B; &longs;en&longs;im hæc a&longs;&longs;urgit per canalem CA; &longs;it clavicula
&longs;eu verticillus in H, ita vt &longs;egmentum HA vacuum aqua relinquat, &
B, tum volvatur verticillus H, illico aqua a&longs;cendit in A, non tamen
tanto cum impetu; idem fit, &longs;i Mercurius infundatur; ex quo deduco
tantam vim motus, (
curij per CD, non e&longs;&longs;e à pondere cylindri aëris, cùm par &longs;it vtrimque ra
tio; idem probari poterit in canali tantulùm inflexo vel incurvato; nempe
licèt in altero brachio prævaleat aquæ pondus, non tamen ea propter tan
ta
rius adducitur, qua digiti pre&longs;sè affixi pulpa &longs;eu caro; hæc autem à mate
ria ten&longs;a
hic effectus æquè attribui po&longs;&longs;et cylindro aëris, ac ten&longs;æ in &longs;egmento C
D materiæ, cùm tamen aliqua &longs;int in hoc ca&longs;u, quæ cylindrus aëris &longs;al
vare non pote&longs;t, licèt &longs;uppo&longs;ita illa materia ten&longs;a optimè &longs;alventur; non e&longs;t
dubium, quin totus effectus huic potiùs, quàm illi cau&longs;æ attribuen
dus &longs;it.
Demus igitur in &longs;egmento CD materiam ten&longs;am con
tineri; quid inde? an fortè illa Mercurij &longs;egmentum CI &longs;u
&longs;tinet?
Haud dubiè, cùm dilatari ac tendi vltra non po&longs;&longs;it: vnde vide
tur e&longs;&longs;e quoddam qua&longs;i &etail;quilibrium, ita vt nec materia ten&longs;a attollere po&longs;&longs;it
majus pondus Mercurij, quam CI, neque hoc pondus Mercurij dilatare vl
tra materiam ten&longs;am in CD.
Non ita profectò res &longs;e habet, Augu&longs;tine; nam &longs;i hoc e&longs;&longs;et,
quo altius e&longs;&longs;et &longs;egmentum materiæ ten&longs;æ CD, majore vi polleret addu
ctiva, vt ita loquar: igitur Mercurium &longs;upra C attolleret; infra C verò,
quò brevius e&longs;&longs;et illius &longs;egmentum; quod omnibus experimentis repu
gnat; &longs;ive enim longior, &longs;ive brevior &longs;it fi&longs;tula, modò &longs;it paulo altior
IC ; æquale &longs;emper &longs;egmentum Mercurij extat; dicerem igitur, data
præfa ta hypothe&longs;i materiæ ten&longs;æ, Mercurium ip&longs;i adhærere; hanc verò
fi&longs;tulæ, iuxta Naturæ in&longs;titutum, de quo &longs;upra, vnde &longs;u&longs;tinetur Mercurij
&longs;egmentum IC ab illa vi, quæ fi&longs;tulam &longs;u&longs;tinet, ita pror&longs;us &longs;cyphus ex
aqua non plènè eductus, &longs;ecum aquam adducit, cujus pondus is profectò
&longs;entit, qui &longs;cyphum &longs;u&longs;tinet; &longs;ic Mercurius breviorem fi&longs;tulam &longs;egmento
IC totam occupat, licèt immergatur in Mercurium EF ; adhæret enim
Mercurius vitro, & ab eo &longs;u&longs;tinetur, qui fi&longs;tulam &longs;u&longs;tentat; vbi verò al
tior e&longs;t fi&longs;tula, & tantùm e&longs;t Mercurij pondus quantum requiritur ad ex
primendam, exugendam, educendam, eliciendam illam materiam ten
&longs;am, vndecunque tandem exugatur, de quo infra, de&longs;cendit Mercurius
in CI, adhærétque materiæ ten&longs;æ, & hæc fi&longs;tulæ; ita vt fi&longs;tula &longs;u&longs;tineri
non po&longs;&longs;it, ni&longs;i &longs;imul tum materia, tum Mercurius extans &longs;u&longs;tineatur. Sup
po&longs;ita igitur illa materia ten&longs;a, &longs;egmentum Mercurij CI non &longs;u&longs;tinetur à
cylindro aëris, &longs;altem &longs;olo, nam illo etiam &longs;ublato, cùm pondus Mercurij CI
æquale &longs;it re&longs;i&longs;tentiæ, qua materia ten&longs;a in &longs;egmento CD majori ten&longs;ioni
&longs;ito Naturæ in&longs;tituto repugnat, vt patet.
Scire velim, cur particulam illam
deris, qua&longs;i fortè putes cylindrum illum aëris nonnihil con
ferre.
Dicam paulò po&longs;t; &longs;i enim materia illa ten&longs;a rarior e&longs;t aëre, exter
nus aër haud dubiè nonnihil confert, de quo infra; ne rationes contra illam
hypothe&longs;im, quam impugno, interrumpam. Sit ergo &longs;enta ratio; Quan
do admovetur corpus
Lacca liquata, &longs;eu ferrum candens, Mercurius &longs;ub&longs;idit infra C, igitur
non &longs;u&longs;tinetur à cylindro aëris externi, quod, ni fallor, per&longs;picuè pro
bare po&longs;&longs;um; nam cùm idem maneat cylindrus aëris exterioris, eadem
vis illius manet; igitur idem Mercurij &longs;egmentum IC &longs;u&longs;tinet; cur ergo
de&longs;cendit Mercurius infra C? hoc autem &longs;equitur, &longs;ive &longs;egmentum CD
vacuum &longs;it, &longs;ive tenui materia plenum; primum quidem, vt patet; alte
rum verò, quia cùm materia illa frigore den&longs;atur, & contrahitur, vel
&longs;ecum adducit in illa contractione Mercurij &longs;uperficiem C, atque ita aër
exterior &longs;egmentum Mercurij extantis non &longs;u&longs;tinet, &longs;ed hoc materiæ te
nui adhæret, & hæc fi&longs;tulæ; vel
Mercurius &longs;upra C a&longs;&longs;urgit, cùm &longs;upra illud attolli non po&longs;&longs;it à Cylindro
exterioris aëris, cujus pondus idem manet, ac proinde ii&longs;dem viribus
pollet.
cylindrus enim aëris exterioris, à quo, vt nonnulli volunt, Mercurij ex
tantis &longs;egmentum &longs;u&longs;tinetur, neque plus, neque minus pote&longs;t &longs;u&longs;tinere; igi
tur &longs;i ferrum candens admoveatur &longs;egmento CD, & hoc vacuum &longs;it; nul
la e&longs;t ratio, cur &longs;uperficies C &longs;ub&longs;idat; &longs;ub&longs;idit tamen; &longs;i verò nix, vel trita
glacies admoveatur CD, & hoc plenum &longs;it tenui materia, hæc quidem
contrahitur, ni&longs;i tamen &longs;ecum &longs;uperficiem C adducat, attollátque, hæc
haud dubiè non a&longs;&longs;urgit; cùm à cylindro aëris vltra C attolli non po&longs;&longs;it; &longs;i
autem, eam materia illa &longs;e&longs;e contrahens &longs;ecum adducat, attollátque; ad
&longs;u&longs;tinendum &longs;egmentum Mercurij IC adhærentis prædictæ materiæ, vt
hæc fi&longs;tulæ, cylindri exterioris æquipondio non e&longs;t opus.
Quid &longs;i dicerem, vitrum ip&longs;um fi&longs;tulæ contrahi præ frigore, &
præ calore explicari; ac proinde materiam illam ratione va&longs;is, modò con
trahi, modò explicari, ex quo etiam Mercurij &longs;uperficies &longs;ub&longs;idat, vel a&longs;
&longs;urgat?
&longs;uppo&longs;ito &longs;egmento CD vacuo, &longs;i verò &longs;upponatur plenum &longs;ubtili materia,
contrarium omnino accideret; vbi enim laxatur vitrum, cùm plus &longs;patij re
&longs;tet, dicta materia
tet, cùm tamen præ calore &longs;ub&longs;idat; vbi verò vitrum contrahitur, minus &longs;pa
tij &longs;upere&longs;t intra &longs;egmentum CD, quod cùm non &longs;ufficiat, tenui materiæ
&longs;uperficiem Mercurij premit, ac proinde hæc &longs;ub&longs;idit, cùm tamen præ figu-
&longs;o alias, &longs;i quæ fortè re&longs;tant.
Non parum, vt video, roboris prædictæ rationi per te acce&longs;&longs;it;
&longs;ed ad &longs;eptimam venio; &longs;i po&longs;tquam &longs;ub&longs;idit | Mercurius in CI, vas BAG
ita claudatur, vt nulla rima &longs;uper&longs;it, per quam aër &longs;ubeat, non tamen pro
pterea Mercurius CI &longs;ub&longs;idit, &longs;ed tunc non &longs;u&longs;tinetur à cylindro aëris; quia
&longs;cilicet non e&longs;t applicatus, hæc ratio non minus per&longs;picua e&longs;&longs;e videtur an
tecedente.
Nollem, hoc dixi&longs;&longs;es, Antime, in meridiana luce cæcutire vi
deris, quod certè lynceos oculos non decet; quare tibi autor e&longs;&longs;em, vt per
peram dicta revoces, aut &longs;altem procures, vt omnes intelligant, hæc à te di
cta e&longs;&longs;e per jocum animi gratia.
Me, tibi &longs;ummopere ob&longs;trinxeris, Augu&longs;tine, &longs;i cæcucienti ba
culum &longs;altem ducem porrigas, qui me juxta atque no&longs;tratem Carte&longs;ium,
rectiùs philo&longs;ophari doceat; quod de lynceis oculis &longs;ubdidi&longs;ti; &longs;cio, quò
&longs;pectet, indignum pror&longs;us me reputo &longs;ummo illo honore, quo me &longs;ereni&longs;
&longs;imus, pro illa &longs;ingulari qua pollet humanitate, cumulare dignatus e&longs;t: &longs;ed
quæ&longs;o te, dedoce me; rectè enim meo &longs;altem judicio, mihi videor ratioci
nari, dum ex eo, quod cylindrus aëris exterioris, probè clau&longs;o va&longs;e &longs;uperfi
ciei Mercurij EF applicatus non &longs;it, ab eo nullo modo &longs;u&longs;tineri &longs;egmentum
Mercurij extantis IC, deduco.
po&longs;itum contentus re&longs;i&longs;tit; cùm vltra comprimi non po&longs;&longs;it, à Mercurio C
I, &longs;icuti neque antequam operculum apponeretur, à cylindro aëris, exte
rioris eju&longs;dem ponderis cum Mercurio IC vltra comprimi poterat, reti
net enim totam compre&longs;&longs;ionem à prædicto aëris cylindro ante impre&longs;&longs;am;
cùm igitur Mercurius IC de&longs;cendere non po&longs;&longs;it, ni&longs;i prædictum aëra vl
tra comprimat, hunc porrò comprimere vltra nequeat; quid mirum
amabo te, &longs;i de&longs;cendere non valeat, ac proinde &longs;u&longs;pen&longs;us maneat in
IC?
Igitur cylindrus aëris non &longs;u&longs;tinet Mercurium IC ; &longs;ed prædi
ctus aër, operculum inter & &longs;uperficiem Mercurij EF interceptus, impedit,
ne cadat; quid quæ&longs;o aliud dico? quid intendo probare, ni&longs;i
curij extantis Iam verò facilè
do
lum & &longs;uperficiem EF, vlteriori
operculo, & extante Mercurio in IC, aperiatur foramen in D, Mercurius il
lico infra C de&longs;cendit, idque notabili &longs;egmento; et&longs;i vacuitas EFGA cana
liculo FR conjungatur cum ampli&longs;&longs;imo va&longs;e P vacuo, majore adhuc &longs;e
gmento Mercurius IC de&longs;cendit, vt non &longs;emel probavi.
In&longs;igni paralogi&longs;mo nos ludis, Antime; retices enim novam
vim accedentem, per quam Mercurius IC deprimitur, & dictus aër inter
ceptus vltra comprimitur; cylindri &longs;cilicet aëris, per foramen in D apertum
&longs;uperficiei Mercurij C applicati; cùm igitur dupla vis ponderis aëri inter
cepto incumbat, nimirum &longs;egmenti Mercurij IC & ponderis ip&longs;i
aëra interceptum vltra comprimat, atque adeò Mercurius infra C de
&longs;cendat?
Ad vltimam metam, opinor, hanc difficultatem promovi&longs;ti; ego
quoque vltimam manum admoveo, ac dico, non magis comprimi aëra
interceptum inter EF & dictum operculum à Mercurio IC, & cylindro
aëris gravitantis per foramen D, quàm remoto operculo & clau&longs;o foramine
D, ab eodem Mercurio IC, & eodem cylindro aëris exterioris; nam perin
de e&longs;t, &longs;ive tota vis pre&longs;&longs;ionis per lineam vnicam incidat, vel applicetur,
five &longs;ubduplum per vnam, & &longs;ubduplum per oppo&longs;itam; &longs;uppone, &longs;i vis, tu
bum; altera parte clau&longs;um, in quem immi&longs;&longs;o embolo
matur, applicata potentia vt 8.fac &longs;egmentum &longs;eu compre&longs;&longs;ionis men&longs;uram
e&longs;&longs;e 4. digitorum; &longs;i idem tubus &longs;it vtrimque pervius, & duo emboli hinc
inde immittantur, applicata vtrimque potentia vt 4.idem haud dubiè com
pre&longs;&longs;ionis effectus con&longs;equetur: igitur quantumvis tum Mercurius CI, tum
aër gravitans per foramen D, communi quodam ni&longs;u in aëra interceptum,
de quo &longs;upra, agant, vt magis illum comprimant, certè vltra comprimere
non po&longs;&longs;unt; quia jam compre&longs;&longs;us e&longs;t à viribus æqualibus, id e&longs;t ab ii&longs;dem
ponderibus, &longs;ed diver&longs;o modo applicatis; aperto igitur foramine in D,
Mercurius CI &longs;ub&longs;idere non po&longs;&longs;et, &longs;ub&longs;idit tamen, cùm priùs
foramine, minimè &longs;ub&longs;ideret. Vnde, ni fallor, per&longs;picuè deduco, non ideò,
admoto &longs;cilicet operculo in AG, extare Mercurium IC, & minimè &longs;ub&longs;i
dere; quia &longs;cilicet dictus aër interceptus inter &longs;uperficiem Mercurij FE &
admotum operculum, comprimi vltra
D, cui Mercurius adhæret, tendi vltra nequit, ni&longs;i major vis ponderis ap
plicetur; aperto verò foramine in D, cum vlteriori ten&longs;ione opus non &longs;it,
ad de&longs;cen&longs;um Mercurij CI, non parum de&longs;cendit, aérque interceptus tan
tulum comprimitur; accedente quoque va&longs;e vacuo P, vt dictum e&longs;t &longs;upra,
profundiùs Mercurius CI de&longs;cendit, quia tantulum compre&longs;&longs;ionis multo
aëri faciliùs di&longs;tribuitur, quam modico; cùm &longs;ingulis partibus minùs com
pre&longs;&longs;ionis competat.
Iam multa lux ex iis, quæ hactenus à te dicta &longs;unt, a&longs;&longs;equendi
veritatem, mihi afful&longs;it: jam enim clari&longs;&longs;imè con&longs;tat, &longs;egmentum CD va
cuum non e&longs;&longs;e, in quo, ni fallor, omnes ferè conveniunt.
Omi&longs;eram pulcherrimum argumentum cuilibet obvium, in quo
vel ip&longs;is oculis, &longs;patium illud non e&longs;&longs;e vacuum comprobatur, po&longs;tquam
enim &longs;ub&longs;idit Mercurius in CI, &longs;i fene&longs;tras conclavis in quo degis claudi
jubeas, excepto modico foramine per quod radius &longs;olaris traiciatur, &
&longs;egmentum CD intra radium trajectum immergas, videbis illico intra ca
vitatem CD radio & luce perfu&longs;am atomos fluitantes: vnde nece&longs;&longs;e dictu
&longs;it, fluitare in materia no&longs;tro aëri non ab&longs;imili, vt jam &longs;upra indica
veram.
Iucundum &longs;anè, juxta atque facilè experimentum, quod
vacuum omnino profligat: con&longs;tat etiam non &longs;u&longs;tineri extantem Mercu
rium CI ab exterioris aëris cylindro, &longs;altem &longs;olo, vt jam obiter monui&longs;ti:
compre&longs;&longs;i plus Mercurij attolleret: plus autem e&longs;&longs;et aëris compre&longs;&longs;i adjun
cto va&longs;e P: tunc igitur plus Mercurij attolleretur: cùm tamen minùs attol
latur, & profundiùs &longs;ub&longs;idat extans Mercurius CI. Iam re&longs;tat, vt quid &longs;en
tias, exponas.
Antequam illud exequar, alia quædam hypothe&longs;is rejicienda
e&longs;t: Nempe aliqui volunt, e&longs;&longs;e quoddam corpus tenui&longs;&longs;imum, aere no
&longs;tro longè &longs;ubtilius (&longs;unt qui æthera vocent) quod per poros omnium
corporum facilè penetret, &longs;eu permeet: hoc autem adduci volunt à Mer
curio de&longs;cendente per poros vitri, donec re&longs;i&longs;tentia partium aëris, quæ
vltra con&longs;tipari non po&longs;&longs;unt, vt &longs;ic loquar, ni&longs;i à majore pondere, quàm &longs;it
pondus extantis Mercurij CI pondus adæquet &longs;egmenti Mercurij ex
tantis.
remi&longs;tam ad circulationem Platonicam reducat: qua fiat &longs;cilicet, vt dum
vnum corpus pello, hoc etiam aliud pellat, & hoc aliud, & &longs;ic deinceps, do
nec vltimò pul&longs;um, facto qua&longs;i circuitu, in locum primi pul&longs;i &longs;uccedat: &longs;ic
adduci volunt, aquam, per &longs;yringam, educto embolo: nempe &longs;egmentum
emboli eductum pellit aëra, & illius
& hic alium: donec tandem vltimò pul&longs;us, &longs;uperficiem aquæ pellat, & hæc
aquam in &longs;yringam intrudat, in locum &longs;egmenti emboli educti: atque ita
nullus e&longs;t vacui metus, nulla corporum adhæ&longs;io, & omnia per communia
principia explicantur.
rabiles difficultates militare videntur: & primò quidem contra id, quod vl
timo loco dicebas, Chry&longs;ocome luculentum facit experimentum: &longs;i enim
&longs;egmentum emboli, quod ex &longs;yringa educitur, in alium tubum, cujus cavi
tati probè congruat, & alterum extremum clau&longs;um &longs;it, compre&longs;&longs;o &longs;cilicet
aëre immittas, aqua pariter per &longs;yringam citra prædictam aëris circulatio
nem attollitur.
Dicerem attolli ab aëris cylindro incubantis in &longs;uperficiem
aquæ: nec enim, opinor, negabis, dato quod &longs;egmentum &longs;yringæ, educto
embolo, vacuum maneret, futurum, vt aër in aquam gravitans, eam per &longs;y
ringam ad occupandum vacuum impelleret.
Nihil probas, contra me, hoc enim non facit, quin citra prædi
ctam circulationem aëris, educto embolo, aqua attollatur, cùm nulla peni
tus circulatio in hoc ca&longs;u intercedat: deinde admoto va&longs;i, in quo aqua
tinetur
&longs;uperficiem aquæ & admotum operculum intercepta remaneat, adducto
embolo, attollitur aqua: igitur nec cylindro aëris incubantis, nec per circu
lationem attollitur: nec e&longs;t, quod ad prodigio&longs;am illam aëris compre&longs;&longs;io
nem confugias, quam &longs;upra jam rejecimus, neque hic repetere vacat.
Dicent æthera per appo&longs;iti operculi poros intro &longs;u
bire, ac premere &longs;uperficiem aquæ, vnde non mirum, &longs;i hæc attol
litur.
Sed æquè facilè, immo faciliùs intra ip&longs;am &longs;yringam æther ille
&longs;ubiret per poros: dico faciliùs: quia id fieret citra elevationem aquæ, cui
pondus eju&longs;dem &longs;e&longs;e opponit, deinde æther ille per poros aquæ
facilè &longs;ubiret in locum ab embolo relictum, intra &longs;yringam. Deni
que, quo plus e&longs;t aëris intercepti, operculum inter & &longs;uperfi
ciem aquæ, eò faciliùs adducto embolo, aqua per &longs;yringam attolli
tur: ídque multò magis, &longs;i &longs;patium illud ab aëre intercepto occupa
tum, canaliculo cum majore va&longs;e vacuo conjungatur, eo modo, quo &longs;upra
dictum e&longs;t.
Sed dic mihi, &longs;odes, Antime, numquid putas, aquam educto
embolo, ideò attolli, quia ab aëris cylindro in &longs;uperficiem aquæ gravitante
attollitur?
Dum adduco embolum, totum aquæ pondus &longs;entio, illius
&longs;cilicet, quæ attollitur: quomodo igitur à dicto aëris cylindro attollitur,
aut &longs;u&longs;tinetur? prætereà &longs;egmentum emboli, quod educitur attollit æqua
lem cylindrum aëris: aqua igitur quæ extremæ emboli ba&longs;i adhæret, cum
embolo adducitur eo modo, quo &longs;upra dictum: equidem &longs;i quis per fi
&longs;tulam, &longs;eu cannam catapultæ longioris, cujus cavitas accuratè ac dili
genter tornata &longs;it, & immi&longs;&longs;æ glandi pror&longs;us æqualis, admoto ore addu
cat, vt fieri &longs;olet, anhelitum, glans ip&longs;a tanto cum impetu adducitur, vt
hæc in dentem maximo cum impetu, non tamen &longs;ine periculo impingatur,
quia &longs;cilicet adducto aëre pilam inter & buccam intercepto, totus cylin
drus aëris adver&longs;us glandem à tergo gravitationis &longs;uæ vim exerit: quid
mirum ergo, &longs;i prædictam glandem magna vi impellat? hujus rei pericu
lum fecit vir jam &longs;upra, &longs;ed nunquam &longs;atis laudatus Eu&longs;tachius, cum fracti
dentis jactura, vt mihi deinde narravit.
Sed quæ&longs;o te, quid in hac hypothe&longs;i adducti æthe
ris in &longs;egmentum CD tibi di&longs;plicet? Mercurius enim in vas de&longs;
cendens extrudit è &longs;ummo va&longs;e illam aëris portionem, vt ejus locum oc
cupet: hæc vt locum inveniat alias pellit, & cùm nihil vacui &longs;it præ
ter &longs;egmentum CD, & cum eo aër intrudi non po&longs;&longs;it, &longs;ubtilior æther intru
ditur.
Multa ob&longs;unt huic hypothe&longs;i: Primo ve&longs;icæ cyprinæ adeò
intume&longs;centis, po&longs;tquam Mercurius de&longs;cendit in CI, phænomenon in
dicta hypothe&longs;i explicari nequit, cùm tumere non po&longs;&longs;it ni&longs;i ab aëre intus
compre&longs;&longs;o, vel ambiente dilatato: æther neutrum præ&longs;tat. Secundo pul
pa digiti intus adducta, vis impacti Mercurij, & alia quamplurima, quæ
vim illam exuctivam, vt &longs;ic loquar, manife&longs;tè demon&longs;trant atque adeò
materiam dilatatam in &longs;egmento CD, præfatæ hypothe&longs;i repugnant:
nempe illa materia prædictos effectus impediret potiùs, quàm produce
ret. Tertio, cùm maxima &longs;it ætheris copia, Mercurius de&longs;cendens ex C in
I, æquè facilè portionem hujus ætheris in fi&longs;tulam intruderet ad occu
pandum &longs;patium CI, ac cylindrus aëris, vel alia quælibet cau&longs;a in fi&longs;tu
lam inclinatam regerit Mercurium, & extrudit æthera ex &longs;egmento CD,
& verò cum totus ni&longs;us in eo po&longs;itus &longs;it, vt &longs;cilicet intrudatur æther in
the&longs;im; quia illius ponderis vis non &longs;ufficit, vt intrudat plus ætheris per
poros fi&longs;tulæ; quid ergo amabo in fi&longs;tulam inclinatam retrudit Mercu
rium, & ex CD æthera extrudit? non certè cylindrus aëris, in quem hæc
hypothe&longs;is hoc phænomenon non refert; deinde æqualia &longs;unt momen
ta Mercurij extantis CI, & præfati cylindri; cùm igitur vis ponderis CI
minor &longs;it, quàm par &longs;it, ad intrudendum æthera in &longs;egmentum CI, vis
etiam cylindri aëris minor erit, quàm par &longs;it ad extrudendum æthere ex
CD, eadem enim vi extruditur, qua intruditur.
Dicent, aëra compre&longs;&longs;um manere po&longs;t de&longs;cen&longs;um Mercurij,
immo inde fortè compre&longs;&longs;um e&longs;&longs;e, quòd partes ætheris ante interceptæ,
expre&longs;&longs;æ fuerint, & in fi&longs;tulam per poros intru&longs;æ; vltra autem comprimi
non pote&longs;t, ni&longs;i vis major &longs;it pondere extantis Mercurij CI; vbi verò in
clinatur fi&longs;tula, vis aëris compre&longs;&longs;i, cùm decre&longs;cat momentum ponderis
Mercurij CI, illud facilè &longs;uperat, novumque Mercurium in fi&longs;tulam re
trudit.
Nihil horum cum recta ratione con&longs;entit; Primò, quia aër ex
ternus po&longs;t de&longs;cen&longs;um Mercurij nullo &longs;en&longs;u compre&longs;&longs;ior percipi pote&longs;t. Secundò; Illius partes non &longs;unt magis con&longs;tipatæ quàm ante, cùm æthe
ris copia affatim &longs;uppetat. Tertiò, flante vento novus aër identidem fi&longs;tu
lam ambit. Quartò, illa vis aëris compre&longs;&longs;i, quam ponis, &longs;i potis e&longs;t, non
modò per fi&longs;tulam inclinatam Mercurium attollere, novumque intrude
re, verùm etiam æthera per poros fi&longs;tulæ ex &longs;egmento CD extrudere,
potiori iure intruderet in &longs;egmentum CI fi&longs;tulæ perpendiculariter ere
ctæ, externum æthera, præ&longs;ertim cùm nihil extantis Mercurij deor
&longs;um ad prædictam intru&longs;ionem concurrat: adde &longs;is omnes alias ratio
nes
æquè ferè militent contra i&longs;tam, tu vide &longs;is, nam repetere non
vacat.
Sed quid tandem tu
candum cylindrus aëris non &longs;ufficit, nec vacuum, nec aëris compre&longs;&longs;io,
nec æther, quid tibi quæ&longs;o re&longs;tabit.
Sen&longs;u duce, in hanc hypothe&longs;im veni, vt dicerem in &longs;egmento
CD tenuem quandam materiam ten&longs;am contineri, quæ cùm à pon
dere Mercurij extantis CI tendi vltra non po&longs;&longs;it, & alioquin adhæreat
fi&longs;tulæ, ip&longs;ique Mercurius; non mirum e&longs;t, &longs;i Mercurius maneat &longs;u&longs;
pen&longs;us: dixi &longs;en&longs;u duce; dum enim video præfatam ve&longs;icam intume&longs;
cere, in de&longs;cen&longs;u Mercurij, in a&longs;cen&longs;u verò, inclinata fi&longs;tula, detume&longs;ce
re, antequam Mercurius ve&longs;icam tangat, illud dumtaxat occurrit, vt
dicam, ab ambiente materia ve&longs;icam illam dilatari ac tendi, quod quo
modo fiat fingi non pote&longs;t, ni&longs;i materia illa ten&longs;a &longs;it. Secundò, dum &longs;en
tio carnem digiti attolli, & in vber tume&longs;cere, eo modo, quo &longs;upra ex
po&longs;itum fuit, immo & &longs;anguinem exugi, licèt oppo&longs;ita digiti pars nihil
prorsus &longs;entiat, nihil aliud in mentem venit, ni&longs;i trahi ab intrin&longs;eco, ac
proinde ab aliqua ten&longs;a materia. Tertiò, Dum video Mercurium incli-
ficiem EF extremo aperto B; item &longs;i admoto pre&longs;&longs;è digito extremo B
fi&longs;tula educatur, inclineturque; cuncta hæc attentè con&longs;ideranti, & in
tuenti nulla tanti impetus cau&longs;a extrin&longs;eca e&longs;&longs;e videtur, vt patet ex iis
quæ fusè à me &longs;upra di&longs;putata &longs;unt; immo admoto pre&longs;&longs;è digito, nulla
cau&longs;a exterior applicata e&longs;t; igitur interna e&longs;t, vel intrin&longs;eca; igitur vel
à corpore compre&longs;&longs;o vel ten&longs;o: Non primum, nam non loci, &longs;ed locati
&longs;unt angu&longs;tiæ; igitur alterum. Quartò, dum admoto pre&longs;&longs;è digito,
eductam fi&longs;tulam &longs;ic libro, vt modo in D, modò in B Mercurius magna
vi impingatur, hoc ferè in in&longs;tanti fieri videtur, ad in&longs;tar qua&longs;i fulguris
coru&longs;cantis; &longs;ed tanta vis motus tribui non pote&longs;t motui gravium in
plano inclinato, cùm vix fi&longs;tula à plano horizontali tantulum deflectat,
ac proinde planum hoc adeò celerem motum non patitur; alia igitur
cau&longs;a e&longs;t tam velocis motus; non compre&longs;&longs;io, vt dixi; igitur ten&longs;io. Quintò, Illa materia quæ priùs occupabat &longs;egmentum CD, inclinata fi&longs;tu
la & labente Mercurio in CD, temporis ferè momento tran&longs;it in CI,
nec vlla via apparet, qua tran&longs;eat; ten&longs;am igitur e&longs;&longs;e nece&longs;&longs;e e&longs;t; ten&longs;a
enim illico adducuntur.
Hanc hypothe&longs;im apprimè intelligo, videoque, multa &longs;anè
in ea explicari po&longs;&longs;e. Primò, cur extet Mercurius CI, quia &longs;cilicet re&longs;i
&longs;tentia ad vlteriorem materiæ ten&longs;ionem, adæquat vim ponderis Mer
curij CI. Secundò, Cur &longs;emper eadem &longs;it extantis Mercurij CI nimi
rum pedum 2. & ferè
proportione cre&longs;cit re&longs;i&longs;tentia materiæ ad vlteriorem ten&longs;ionem, in qua
cre&longs;cit pondus Mercurij extantis. Tertiò, Cur inclinata fi&longs;tula adduca
tur Mercurius in CD ; quia tunc minus e&longs;t ponderis Mercurij momen
tum in plano inclinato; quid mirum ergo; &longs;i à ten&longs;ionis momento &longs;u
peretur, quod &longs;upponitur æquale momento ponderis in perpendiculo. Quartò, cur ve&longs;ica cyprina infletur, pulpa digiti ad in&longs;tar vberis attolla
tur, &longs;anguis exugatur; ten&longs;a enim materia alia corpora, quibus e&longs;t con
tigua, ad &longs;e adducit & trahit. Quintò, Cur Mercurius educta fi&longs;tula ex
Mercurio, tanta vi in oppo&longs;itam fi&longs;tulæ ba&longs;im impingatur; tribus illis
modis, de quibus &longs;upra; vis enim ten&longs;ionis, quæ tunc prævalet; initio
maxima e&longs;t; in hoc di&longs;&longs;imilis potentiæ motrici gravium, quæ initio mi
nima e&longs;t. Sextò, Cur applicato ferro candente &longs;egmento fi&longs;tulæ CD &longs;ub
&longs;idat Mercurius infra C; quia tunc rare&longs;cit illa materia, vnde magis ex
tenditur; hinc deor&longs;um Mercurium CI nece&longs;&longs;ariò deprimit; &longs;ecus verò
applicato gelu den&longs;atur, atque adeò contrahitur, & Mercurium &longs;ur&longs;um
attollit. Septimò, Cur appen&longs;a fi&longs;tula DB totum extantis Mercurij CI
pondus &longs;entiatur; quia Mercurius adhæret materiæ ten&longs;æ, & hæc fi&longs;tu
læ. Octavò, Cur &longs;tatim po&longs;t de&longs;cen&longs;um, libretur aliquamdiu Mercurius,
ita vt modò &longs;upra C a&longs;cendat, modò infra deprimatur; quia cùm de
&longs;cendat motu accelerato vires acquirit eundo, ac proinde re&longs;i&longs;tentiæ
momentum &longs;uperat; at decre&longs;cente pondere, prævalet tandem ten&longs;io
nis re&longs;i&longs;tentia; vnde &longs;ur&longs;um denuò Mercurius adducitur; atque ita ali-
ex chorda ten&longs;a vel arcu. Nonò, Cur &longs;i tantulum aëris in fi&longs;tula relinqua
tur, Mercurius po&longs;t de&longs;cen&longs;um &longs;ub&longs;idat infra C: quia illud tantulum
aëris tum à Mercurio, tum à materia ten&longs;a dilatatur, vnde majus &longs;pa
tium occupet nece&longs;&longs;e e&longs;t; ac proinde, vt &longs;patium CD explicatur, ita
CI contrahitur; &longs;ecus accidit intru&longs;a aqua, loco aëris; quia aqua, vt
ad compre&longs;&longs;ionem, ita ad ten&longs;ionem inepta e&longs;t. Decimò, Cur admoto
pre&longs;&longs;è digito ori B, & librata huc illuc fi&longs;tula, illa materia tam cito tran
&longs;eat ab extremo ad extremum: nam propter ten&longs;ionem, non modò ci
ti&longs;&longs;imè adducitur, verùm etiam facilè contrahitur, inter fi&longs;tulam &
Mercurium. Cuncta hæc & alia quamplurima, quæ facilè &longs;uggeres, in
hac tua hypothe&longs;i explicare po&longs;&longs;em; &longs;ed vnde quæ&longs;o i&longs;ta materia? &
quo tandem illa, cùm inclinata fi&longs;tula a&longs;&longs;urgit Mercurius, & totam
implet?
Vel inde tibi maximoperè ob&longs;trictus &longs;um, quod ab onere illa
explicandi me liberum e&longs;&longs;e volueris; quæ obiter quidem, clari&longs;&longs;imè ta
men &longs;ub vnum eundemque ad&longs;pectum adduxi&longs;ti; reliqua &longs;i quæ &longs;uper
&longs;unt, per&longs;tringam; &longs;ed ante omnia, declarandum mihi e&longs;t, vnde or
tum ducat, & quò tandem abeat illa materia ten&longs;a. Et verò quemad
modum alij, vt naturales effectus explicent, eorumque indagent cau
&longs;as, multa fingunt, quæ &longs;en&longs;ibus minimè &longs;ubjiciuntur, vt &longs;piras aëris,
arcus, ramos, æthera, &longs;ubtilem materiam, cochleas magneticas, bul
las, &longs;phærulas, ramenta, & motus diver&longs;i generis; licèt nihil horum
videant, aut &longs;entiant, &longs;ed gratis fortè &longs;tatuant, ad effectus &longs;en&longs;ibiles
explicandos, quos ex communibus principiis explicari non po&longs;&longs;e &longs;ibi
per&longs;ua&longs;erunt; quidni & mihi aliquid &longs;imile fingere liceat, vel vt ve
riùs dicam &longs;tatuere & ex communibus principiis deducere? Lico igi
tur, vt rem paulò altiùs repetam, elementa no&longs;tra pura non e&longs;&longs;e, &longs;ed
omnino mixta, vt omnes mihi facilè concedent; etiam ip&longs;am aquam,
quam bibimus, ip&longs;um aëra quem haurimus; & cùm omne mixtum ex
mi&longs;cibilibus con&longs;tet, haud dubiè quælibet mixti pars longè major e&longs;t
parte mi&longs;cibilis, totum &longs;cilicet &longs;ua parte majus; hinc aër per poros
corporum etiam laxiores non &longs;ubit, multò minùs aqua; immo aliqua
corpu&longs;cula aquis &longs;tygiis in&longs;unt, quæ &longs;ubtilis humoris vehicula in du
ri&longs;&longs;imorum etiam corporum poros &longs;ubeunt, eorumque &longs;olvunt plexum;
hæc porrò mixta e&longs;&longs;e, nemo inficias eat; igitur longè minores &longs;unt par
tes mi&longs;cibilium, ex quibus illa con&longs;tant. Cùm autem ad multum natu
ræ v&longs;um, tenuis quædam materia, quæ ad purum aëris elementum lon
gè propiùs accedit, quàm aër, qui nos ambit, nece&longs;&longs;aria e&longs;&longs;et, illam
haud dubiè omi&longs;&longs;am fui&longs;&longs;e, ac de&longs;iderari nemo dixerit; & vt &longs;unt præ
cipui tres corporum &longs;tatus, duri &longs;cilicet, &longs;eu concreti, liquidi & &longs;pira
bilis, nec non innumeræ &longs;ub quolibet genere &longs;pecies; nihil ob&longs;tat, quin
aliquæ &longs;int corporis &longs;pirabilis &longs;pecies, quæ longè majorem tenuitatem
præ &longs;e ferant.
Non video, quem v&longs;um nece&longs;&longs;arium huic &longs;ubtili ma-
Nihil fingo, nihil ad&longs;truo, quod ex communibus principiis
non deducatur; & primò quidem, certum e&longs;t, corpori etiam gravi&longs;&longs;i
mo & den&longs;i&longs;&longs;imo poros ine&longs;&longs;e; nullum enim e&longs;t corpus durum &longs;ine
poris; pori autem illi vacui non &longs;unt, iuxta naturæ in&longs;titutum; de quo
&longs;upra; aliqua igitur materia pleni, quæ certè aëre longè &longs;ubtilior &longs;it,
immo &longs;it ip&longs;e aër purior, id e&longs;t, mixtum aëreum, &longs;eu &longs;pirabile, ad pu
rum elementum aëris propiùs accedens, quàm no&longs;ter aër, addere po&longs;&longs;em
&longs;onorum rem, quæ vix &longs;ine illa materia &longs;ubtili explicari pote&longs;t.
Multi &longs;anè non admittunt quintam illam e&longs;&longs;entiam, quæ
vix ab æthere di&longs;tinguitur; & verò vt atomos illas democriticas nun
quam probavi, ita nec &longs;ententia quorumdam Peripateticorum; &longs;eu po
tiùs Platonicorum, qui ne&longs;cio quam e&longs;&longs;entiam ætheream ab iis quin
tam appellatam, eamque, vt nonnullis vi&longs;um e&longs;t, animatam po&longs;uerunt,
mihi vnquam arri&longs;it.
Mentem meam reverà non capis, Chry&longs;ocome, nullam enim
quintam e&longs;&longs;entiam approbo, nullum corpus &longs;tatuo, quod vel &longs;implex
elementum non &longs;it, vel ex elementis compo&longs;itum; nempe hæc &longs;ubtilis
materia, cujus multiplici v&longs;u natura indiget, ex aëre humore, igne,
ac terra compo&longs;ita e&longs;t, quanquam ad aëra purum propiùs accedit; alius
autem illius v&longs;us e&longs;t, præter illos quos &longs;upra indicavi, vt ad ten&longs;ionem
& compre&longs;&longs;ionem corporum multum conferat, vnde fortè aër compre&longs;
&longs;ionis ac ten&longs;ionis præ cæteris corporibus patiens e&longs;t, quia multa ine&longs;t
aëri, immo aëris cra&longs;&longs;iores & majores partes in dicta materia qua&longs;i in
medio natant, eiu&longs;dem ferè cum eo gravitatis: Itaque &longs;uppo&longs;ita illa
materia, cujus maxima pars aëri commixta e&longs;t, vnde hic tam facilè com
primi & dilatari, &longs;eu tendi po&longs;&longs;it, ratione &longs;cilicet hujus materiæ, alia
verò intra poros omnium corporum latet, ex quibus citra ten&longs;ionem
educi non pote&longs;t; tendi porrò non pote&longs;t ab&longs;que vi, &longs;eu ponderis, &longs;eu
alterius potentiæ motricis applicatæ; vtrumque experimento proba
tur, primum quidem in fi&longs;tula BD, nempe Mercurius &longs;ubducto digito
de&longs;cendens educit ex vitro; immo & ex &longs;e ip&longs;o qua&longs;i ex propriis vi&longs;ceri
bus, materiam illam, quæ cum poros vitri non de&longs;tituat, alioquin vacui
manerent, eam tendi ac dilatari nece&longs;&longs;e e&longs;t, vt totam vacuitatem CD im
pleat, alterum verò in embolo, qui magna vi ex va&longs;e clau&longs;o, cui congruit,
educitur.
Quot & quantæ difficultates qua&longs;i turmatim &longs;e&longs;e mihi ob
jiciant, vix ac ne vix quidem dicere valeo.
Libenter eas excipiam; &longs;i enim &longs;olvendo non &longs;im, facilè &longs;en
tentiam mutabo; expone igitur illas, Augu&longs;tine, rem enim grati&longs;&longs;imam
mihi feceris.
Primo loco illam expono, quæ longè difficillima mihi vi
detur; &longs;i enim Mercurius ideò de&longs;cendit ex CD in CI, quia &longs;uperat re
&longs;i&longs;tentiam prædictæ materiæ, ne dilatetur, &longs;eu tendatur; cur igitur vt
magnum pondus prædictam materiam valdè tendit; ita minus quod tamen repugnat experimentis; &longs;i enim fi&longs;tula
&longs;it tantum vel vnum vel duos pedes alta, etiam &longs;ubducto digito non de&longs;cen
dit Mercurius, vt patet, de&longs;cendere tamen deberet, licèt minus.
Fateor gravem e&longs;&longs;e difficultatem; ad quam tamen re&longs;pondeo,
duo e&longs;&longs;e capita, ex quibus dicta re&longs;i&longs;tentia petitur; primum e&longs;t, vt educatur
ex poris, alterum vt tendatur; &longs;i tantùm &longs;ecundum caput con&longs;ideretur, ma
gna vis ponderis, multum; parva verò, parum illam materiam tendit; quo
ad verò primum, ea e&longs;t re&longs;i&longs;tentia, quæ determinatam vim exigit, vt &longs;u
peretur; Cogita quæ&longs;o fixum in ligno clavum, qui tanta vi dumtaxat re
figitur, non verò minore; ita pror&longs;us ex poris corporum illa materia edu
ci nequit, ni&longs;i tanta vis applicetur; vbi verò &longs;emel educta e&longs;t, pro majo
re vel minore pondere magis vel minùs tenditur; hinc &longs;i aëris tantulum
immittatur in fi&longs;tulam BD, non tantùm infra C de&longs;cendit Mercurius,
verùm etiam materia illa, quæ jam educta e&longs;t, & aëri admixta, maximè
dilatatur.
Non video, quæ vis de&longs;ideretur, vt educatur ex Mer
curio, corpore &longs;cilicet liquido, quod parum re&longs;i&longs;tit: idem de aqua di
cendum e&longs;t,
Immò videtur, quod minore vi opus &longs;it ad educendam illam
materiam ex Mercurio, quàm ex vitro, cùm multæ partes movendæ,
& qua&longs;i amovendæ &longs;int; cùm tamen in corpore &longs;icco paulò liberiores &longs;int
pori; non e&longs;t igitur dubium, quin aliqua re&longs;i&longs;tentia &longs;it; cogita rete quod
dam perexiguis annulis di&longs;tinctum, quod &longs;ine aliqua re&longs;i&longs;tentia ex aqua
non educitur, non e&longs;t igitur mirum, &longs;i cum illa materia ex tot meandris &
pororum labyrinthis eruenda &longs;it, tanta &longs;it in hoc difficultas, vt majore vi ad
eam &longs;uperanda, opus &longs;it, quàm reverà &longs;it pondus Mercurij extantis CI.
analogia clavi refigendi, præ&longs;ertim &longs;i per diver&longs;os anfractus eat, rem i&longs;tam
ob oculos ponit.
Illa igitur materia per poros vitri abundè ab extrin&longs;eco aëre
intra fi&longs;tulam adduci pote&longs;t; nulla ergo ten&longs;io intercedit; immò hæc &longs;en
tentia eadem e&longs;&longs;e videtur cum illa, quam vltimo loco impugnabas.
Licèt ex poris vitri educatur, non tamen ex hoc &longs;equitur, illam
ab aëre extrin&longs;eco elici; nec enim pori illi ita &longs;unt pervij, vt liber tran&longs;i
tus pateat; alioquin, nullum corpus vnquam comprimi po&longs;&longs;et, nullum
tendi, aut dilatari; equidem in corpore liquido &longs;ecus accidit; cùm enim
non &longs;ine aliquo partium motu hæc fiat, ex iis eductio, inde fit, vt materia
illa dilatabilis meliùs colligatur, ad aliquam &longs;cilicet altitudinem. Acce
dit quòd in illo de&longs;cen&longs;u agitantur corporis liquidi partes, & hæc agita
tio collectionem materiæ dilatabilis non parum juvat; hinc fortè procedit,
vt laudatus &longs;upra Autor etiam ob&longs;ervat, longè majore vi opus e&longs;&longs;e ad edu
cendum ex Cylindro cavo embolum, cujus extrema ba&longs;is ita adhæret fun
do Cylindri, vt nihil aëris interceptum maneat.
Putabam fieri non po&longs;&longs;e, vt embolus abeo fundo vlla vi hu
mana avelleretur; immò putabam te e&longs;&longs;e in eadem &longs;ententia.
In ea fui aliquando, ne quid di&longs;&longs;imulem, novis tamen experi-
liùs educitur ex corpore &longs;icco illa materiæ copia, quæ ad occupandum to
tum illud vacuum nece&longs;&longs;aria e&longs;t; &longs;ed hæc nihil ad præ&longs;entem quæ&longs;tionem;
accedit, quod embolus &longs;ino corio, Cylindro cavo rectè non congruit; co
rium autem poro&longs;um e&longs;t & &longs;pongio&longs;um, at que adeò multum aëra, multum
que prædictæ materiæ continet.
Sed quæ&longs;o te, quando alti&longs;&longs;ima e&longs;t fi&longs;tula, vnde tanta copia il
lius materiæ, qua &longs;cilicet &longs;egmentum CD repleatur, quando longi&longs;&longs;i
mum e&longs;t?
Demus hoc, nec enim vnquam probatum e&longs;t, in longi&longs;&longs;imis
illis fi&longs;tulis; Demus, inquam; cavæ &longs;uperficies vitri &longs;unt vt altitudines; item
labentis Mercurij quantitates, &longs;eu Cylindri ; quid mirum ergo, &longs;i in eadem
proportione materia dilatabilis &longs;uppeditetur?
Nunquid fortè meliùs diceres, &longs;i partibus dumtaxat aëris inter
Mercurium & cavam &longs;uperficiem fi&longs;tulæ interceptis hoc tribueres?
Non &longs;unt haud dubiè aëris partes inter partes Mercurij, nec
etiam inter Mercurium & dictam &longs;uperficiem cavam, &longs;ed tantùm partes
illius materiæ dilatabilis, quæ cadente Mercurio inde facilè educitur: &
verò cùm aër, &longs;i quis intru&longs;us &longs;it, ita &longs;uum locum occupet, vt inclinata fi
&longs;tula Mercurius totam cavitatem CD non occupet, &longs;ed &longs;patium nece&longs;&longs;a
rium aëri relinquat; vbi Mercurius a&longs;&longs;urgens nullum &longs;patium vacuum re
linquit, vt aliquando accidit, nullus profectò aër ine&longs;t.
Legi apud Autorem &longs;upra laudatum, &longs;i fi&longs;tula multiplici &longs;uc
cu&longs;&longs;u fatigetur, dum in eam Mercurius infunditur, &longs;egmentum Mercurij
extantis inde altius fore; immò &longs;i ferrum candens admoveatur lateri fi
&longs;tulæ CI, a&longs;cendunt quædam aëris bullulæ; aër igitur Mercurio inerat:
idem in aqua fieret.
Illæ bullæ non &longs;unt aëre plenæ, &longs;ed vel humore rarefacto, qui
multus ine&longs;t Mercurio, vel illa materia tenui, quæ facilè rare&longs;cit; quan
quam dicerem potiùs, humorem rarefactum; vt enim materiam illam te
nuem ad elementum aëris propiùs accedentem, vtpote nece&longs;&longs;ariam ad
multos naturæ v&longs;us agno&longs;co, ita & admitto humorem quendam &longs;ubtilem,
ad elementum aquæ proximè accedentem, &longs;ine quo fortè frigoris, effe
ctus explicari non po&longs;&longs;unt: &longs;ed veni quæ&longs;o ad alias, quæ tibi &longs;ubortæ &longs;unt
difficultates.
Illa materia, quæ po&longs;t de&longs;cen&longs;um Mercurij &longs;egmentum
CD obtinet, e&longs;t rarior & levior aëre; igitur aër extrin&longs;ecus per medium
Mercurium in illam gravitat; &longs;i ergo hæc vis gravitationis Cylindri aëris
extrin&longs;eci major e&longs;t vi gravitationis Mercurij extantis CI, illam haud
dubiè &longs;uperabit, attollet que Mercurium; idem faciet, &longs;i æqualis &longs;it; acce
dente &longs;cilicet vi ten&longs;æ materiæ; &longs;i denique minor e&longs;t, cur non vincitur de&longs;
cenditque Mercurius infra C?
Licèt hæc omnia darem, nihil tamen inde contra meam hy
pothe&longs;im; &longs;upponamus enim exempli gratia, vim Cylindri aëris extrin
&longs;eci plu&longs;quam centuplo majorem vi gravitationis Mercurij CI; non po-
quia &longs;upponamus &longs;u&longs;tineri; cùm hic Mercurius gravitet, & hæc vis gra
vitationis &longs;uperet re&longs;i&longs;tentiam prædictæ materiæ educendæ & dilatandæ,
non e&longs;t dubium, quin prævalere debeat, atque adeò Mercurius de&longs;cendere;
illa materia educi & tendi, donec ad punctum C perveniat, in quo æqua
lis e&longs;t vis gravitationis Mercurij CI prædictæ re&longs;i&longs;tentiæ; licèt autem &longs;u
perficies Mercurij EF tantulum attollatur, non tamen propterea totus Cy
lindrus, cujus ba&longs;is incumbit in &longs;uperficiem EF attollendus e&longs;t, &longs;ed tantu
lum comprimitur aër per appul&longs;um & exceptionem illius, qui Mercurio
in vas ABG illap&longs;o in locum cedit; &longs;ic pror&longs;us per appul&longs;um fumi, va
poris cuju&longs;libet halitus, immò alicujus aëris rare&longs;centis tractus, reliquus aër
comprimitur; nempe dictu, immò & cogitatu ridiculum e&longs;t, totum aëris
Cylindrum inde attolli; ex hac &longs;olutione manife&longs;tum argumentum ducitur,
contra primam illam hypothe&longs;im, quam &longs;upra refutavi.
a&longs;&longs;erunt, præfatum vtriu&longs;que Cylindri, aëris &longs;cilicet, & Mercurij æquili
brium, ducta à duobus aliis Cylindris, aquæ &longs;cilicet & Mercurij analogia;
licèt enim in his præfatum æquilibrium locum habeat, &longs;ecus tamen in il
lis, & manife&longs;tum di&longs;crimen e&longs;t, quia Mercurius de&longs;cendere nequit, ni&longs;i
vel aquæ Cylindrus attollatur, vel aqua, aut ip&longs;e Mercurius, vi ponderis
&longs;eu pre&longs;&longs;ionis comprimatur; &longs;ed aqua comprimi nequit, nedum Mercu
rius; vt jam &longs;uprà dictum e&longs;t; &longs;ervatur igitur æquilibrium; at verò aër
facilè comprimi pote&longs;t, vt patet; vnde Mercurij Cylindrus ID facilè de&longs;
cendit; nempe aër tantulùm comprimitur; nec ideò infra C non de&longs;cen
dit, quod &longs;it æquilibrium inter Cylindrum aeris, & Cylindrum Mercu
rij IC, &longs;ed quia de&longs;cendere nequit, ni&longs;i &longs;uperet re&longs;i&longs;tentiam materiæ di
latabilis, eamque geminam, vt &longs;upra rectè di&longs;tinguere mihi vi&longs;us es; &longs;ed
ad alias objectiones venio; dicunt enim oppo&longs;itæ &longs;ententiæ a&longs;&longs;ertores, &longs;e
gmentum Mercurij extantis IC in ima Valle e&longs;&longs;e longius, in vertice mon
tis brevius; ita probatum fui&longs;&longs;e ferunt, in montibus Alverniæ, & Majo
ris Britanniæ; hoc autem, quia in ima Valle Cylindrus aëris altior e&longs;t;
igitur majus illius pondus; igitur longius Mercurij &longs;egmentum &longs;u&longs;tinet;
&longs;ecus in vertice montium.
Si laudatus &longs;upra Autor, qui hæc refert, te&longs;tis oculatus fui&longs;&longs;et,
non detrectarem fidem Autori ac curati&longs;&longs;imo; &longs;ed quia hæc à &longs;e tan
tum auribus accepi&longs;&longs;e vltro fatetur, plenam fidem adhibendam e&longs;&longs;e non
crediderim, præ&longs;ertim cum aliquando contigerit, vt hoc experimentum
in alti&longs;&longs;imis regionibus probatum, &longs;ecus quàm illi ferunt, &longs;ucce&longs;&longs;erit; præ
terquam quod cuipiam homini, qui primus hoc proba&longs;&longs;e dicitur in mon
tibus Alverniæ, nullam fidem habendam e&longs;&longs;e duco; cujus enim fidei homo
&longs;it, omnes catholici probè norunt. Sed demus, ita e&longs;&longs;e, non tamen inde
concluditur, præfatum Cylindrorum æquilibrium, cùm alia cau&longs;a & ra
tio e&longs;&longs;e po&longs;&longs;it; nempe in alti&longs;&longs;imis montibus, præ&longs;ertim &longs;i in acumina
tum verticem attollantur, non verò &longs;i in va&longs;tas planities explicentur,
vel &longs;en&longs;im a&longs;&longs;urgant, leniore ac molliore clivo, in alti&longs;&longs;imis; inquam, mon-Igitur plus ine&longs;t materiæ
dilatabilis corporibus liquidis prædicto aëri expositis; quid mirum ergo,
&longs;i ten&longs;io facilior e&longs;t, multa enim faciliùs tenditur, quàm modica; præterea
fieri potuit, vt aliquid aëris in tubum irrep&longs;erit; fatetur enim præfatus Au
tor, quamvis alioquin hoc experimentum &longs;æpiùs probaverit, vna dumtaxat
vice à fi&longs;tula aëra exula&longs;&longs;e: ille autem aër purior faciliùs comprimi & di
latari pote&longs;t: Hinc ij, qui de rebus Americæ &longs;crip&longs;erunt, te&longs;tantur, in ver
tice cuju&longs;dam montis, auram ita tenuem e&longs;&longs;e, vt re&longs;pirationi vix &longs;erviat;
in his, vt vides, nulla e&longs;t difficultas.
Nulla &longs;anè; &longs;ed cur quæ&longs;o &longs;egmentum IC toties alitudinem
mutat, nulla temporum habita ratione? aliquando enim cum Thermome
tro convenit, ita vt fervente æ&longs;tu &longs;ub&longs;idat, & &longs;æviente bruma a&longs;&longs;urgat, aliàs
omnino &longs;ecus accidit; vnde hoc quæ&longs;o, Antime?
In alia hypothe&longs;i hoc nullo modo explicari pote&longs;t, in no&longs;tra
facilè explicatur; nempe pro diver&longs;a ratione auræ purioris, &longs;eu defæcatio
nis, cui &longs;cilicet materiæ dilatabilis plus ine&longs;t, varia e&longs;t &longs;egmenti extantis al
titudo; quò enim plùs ine&longs;t prædictæ materiæ, minor e&longs;t, quo minùs, major,
vt patet ex dictis; plùs autem, vel minùs ine&longs;t, pro diver&longs;o ventorum, ha
lituum & effluviorum appul&longs;u: porrò diver&longs;æ &longs;unt combinationes, vt vo
cant majoris &longs;cilicet, & minoris quantitatis hujus materiæ; itemque caloris
& frigoris ambientis; vnde fieri pote&longs;t, vt vnum ab alio minuatur vel au
geatur. V.g.major quantitas illius materiæ, cum majore caloris vi acceden
te conjuncta, brevius &longs;egmentum extantis Mercurij facit; reliquæ combina
tiones facilè fieri po&longs;&longs;unt, quare vltro illas omitto, ne &longs;im fortè prolixior.
Quid autem cen&longs;es de illa ob&longs;ervatione, quam præfatus Au
tor indicat, & de qua Venetiis &longs;criptum e&longs;t, &longs;cilicet æ&longs;tu cre&longs;cente, &longs;egmen
tum extantis Mercurij decre&longs;cere, cre&longs;cere verò æ&longs;tu decre&longs;cente, an fortè
aliquid de illa proba&longs;ti?
Si Mercurij extantis &longs;egmentum à Cylindro aëris &longs;u&longs;tineretur,
hoc reverà accidere deberet, iuxta illam no&longs;tram hypothe&longs;im, quam in &longs;u
periore congre&longs;&longs;u fusè &longs;atis tradidimus, vt patet; &longs;ed cùm prædictum &longs;e
gmentum ab aëris Cylindro non &longs;u&longs;tineatur, vt &longs;upra o&longs;ten&longs;um e&longs;t, æ&longs;tus
maris ad rem hanc nihil facit: vbi autem hæc inaudij, probavi rem accura
ti&longs;&longs;imè, &longs;ervata fi&longs;tula in &longs;itu perpendiculari BD eum &longs;egmento extantis
Mercurij CI, per totos ferè 30. dies, ob&longs;ervavi multam mutationem altitu
dinis; nam Mercurius aliquando &longs;upra C a&longs;&longs;urgere,
mihi, alii&longs;que, quibus o&longs;tendi, &longs;æpè ac &longs;æpiùs vi&longs;us e&longs;t, nunquam tamen
æ&longs;tus maris leges &longs;ervavit, &longs;ive diurnas, ita vt momento &longs;ummi æ&longs;tus, quo
Luna e&longs;t in Meridiano, &longs;ub&longs;ideret, & momento &longs;ummi rece&longs;&longs;us, &longs;eu reflu
xus, Luna &longs;cilicet Meridianum &longs;extæ horæ occupante, a&longs;&longs;urgeret; &longs;ive leges
men&longs;truas, ita vt in Plenilunio & Novilunio &longs;ub&longs;ideret, in Quadraturis a&longs;
&longs;urgeret: Idem Florentiæ & Liburni ob&longs;ervatum fuit, vt à viro &longs;umma fi
de digno accepi; quare non e&longs;t, quod multùm curemus de prædicta illa ob
&longs;ervatione, quæ cum certis experimentis minimè con&longs;entit; quare, ne tem
pus teramus, profer quæ&longs;o, &longs;i quid fortè re&longs;tat.
Ve&longs;tri Pari&longs;ien&longs;es aliquid jactant, quod tibi fortè nonnihil
negotij face&longs;&longs;at; Sit enim vas ABD, in quod in
fundatur Mercurius, &longs;it fi&longs;tula CP,
aperta in P, latiore foramine, & aliud vas HKNL
ampullæ in&longs;it, recto &longs;itu, vt vides; in&longs;eratur fi&longs;tula
OI, admotoque pre&longs;sè digito in C, infundatur
per O Mercurius, donec tum vas HN, tum fi&longs;tu
la CP, tum ampulla, tum fi&longs;tula IO impleantur;
tum &longs;uilla ve&longs;ica probè ob&longs;truantur, debito &longs;ci
licet tempore, foramina P & O, itemque perexi
guus canaliculus R ; his
&longs;ubducatur digitus ex C, Mercurius ruit deor&longs;um
ex vtraque fi&longs;tula, ita vt totum extans &longs;egmen
tum NO vacuum Mercurio maneat, extetque &longs;e
gmentum FT Mercurio plenum, altum ferè pe
des duos &
&longs;ica R foramen aperias, & tantulum aëris &longs;ub
eat, &longs;ub&longs;idit illico Mercurius infra T, in fi&longs;tula
CP, a&longs;&longs;urgitque &longs;upra in fi&longs;tula IO, quia &longs;cilicet,
inquiunt, aër qui &longs;ubiit, premit &longs;uperficiem Mer
curij TV, & LN, vnde vtramque deprimi ne
ce&longs;&longs;e e&longs;t, &longs;ed LN deprimi non pote&longs;t, ni&longs;i Mercurius &longs;upra LN, in fi&longs;tula
IO a&longs;cendat.
aëris qui &longs;ubit, adeò compre&longs;&longs;um manere, vt vtramque illam Mercurij &longs;u
perficiem deprimat; in no&longs;tra hypothe&longs;i longè faciliùs res i&longs;ta explicatur;
nempe cùm po&longs;t Mercurij de&longs;cen&longs;um, tum in PV, tum in NO,