QVA GRAVIA DECIDENTIA
ACCELERANTVR.
&longs;ub &longs;igno Pacis.
ART. I.
Scribendi Occa&longs;io.
las
tas, R. P. Cazræus Societatis
Rector &longs;crip&longs;it ad ip&longs;um
tam circa cætera de Motu con&longs;cripta, quàm circa di&longs;putata &longs;pe
ciatim de Motu Terra attributo. Itaque Author ad illum re&longs;
crip&longs;it eâ Epi&longs;tolâ, quæ heic babetur ordine tertia, quàmque pri
mam legere &longs;i libet, licet, imò & non Quia verò
R. P. cætera inter obiecerat, non fui&longs;&longs;e Authorem probatu
rum
cidentia accelerantur, &longs;i commi&longs;&longs;um à
animaduerti&longs;&longs;et; & Author responderat &longs;e nec potui&longs;&longs;e nec
dum po&longs;&longs;e Paralogi&longs;mum vllum videre; ac optare adeò,
vt R. P. tum illum retegeret, tum proportionem quam crede
ret e&longs;&longs;e veriorem manife&longs;taret; idcircò R. P. con&longs;crip&longs;it, edi
ditque nuper Epistolam aliam hocce Titulo,
tia accelerationis motus in naturali de&longs;cen&longs;u grauium
determinantur; aduer&longs;us nuper excogitatam à
Galilei Florentino Philo&longs;opho, ac Mathe matico de
eodem motu P&longs;eudo &longs;cientiam.
ad quam heic primùm Respondetur.1. in 3.
ART. II. III. IV. V.
Status Controuer&longs;iæ.
accipere liceat primum quoddam spatium, vt vnam orgyiam;
& habe re pro momento, &longs;eu tempore primo illud quod effluit,
donec lapis per hanc orgyiam decidit: & pro gradu celeritatis
primo eam celeritatem, quæ in fine primi huius temporis acqui
&longs;ita e&longs;t: An inquam, acceptis deinceps æqualibus &longs;patijs, tempo
ribus, & gradibus, cen&longs;eri debeat lapis motu&longs;-ve ip&longs;ius tum
acqui&longs;u&longs;&longs;e duos celeritatis gradus, cùm e&longs;t &longs;uperata &longs;ecunda
orgyia, licet &longs;ecundum tempus nondum totum effluxerit, ac
pari modo treis, cùm tertia, quatuor cum quarta, &c. adeò vt
&longs;emper velocitates &longs;e habeant &longs;ieut &longs;patia, quòd R. P. conten
dit: An potiùs cen&longs;eride beat
dus, cùm effluxit &longs;ecundum tempus, licet plura spatia, quàm
duo &longs;uperata &longs;int: ac pari modo treis, cùm tertium, quatuor, adeò vt &longs;emper velocitates &longs;e habeant &longs;icut
tempora; quæ e&longs;t Galilei &longs;ententia. Ex qua aliunde &longs;equitur,
vt temporibus æqualibus &longs;patia &longs;uperentur iuxta numeros ab
vnitate impareis: ita vt &longs;i primo tempore lapis decidat per
vnam orgyiam, decidat &longs;ecundo per treis, tertio per quinque,
quarto per &longs;eptem, &c. atque idcircò spatia in fine cuiu&longs;que
temporis à principio v&longs;que aggregata habeant &longs;e &longs;icut quadra
ta temporum; hoc e&longs;t, vt spatia &longs;uperata &longs;int in fine vnius
in fine quatuor &longs;exdecim, &c. Quæ omnia liceat repræ&longs;entare
in maiu&longs;culo quodam Triangulo, cuius lateribus, ac ba&longs;i in par
teis æqualeis diui&longs;is, interducti&longs;que lineis aream di&longs;pe&longs;centibus
in minores, mutuò æqualeis, &longs;imilei&longs;que triangulos, partes
vtriu&longs;vis lateris (incipiendo ab apice) habeantur pro tempori
bus; ba&longs;es triangulorum ip&longs;is respondentium pro gradibus ce
leritatis; & intercepta triangula, ip&longs;orumve areæ pro spatiis. Vide & totius Epi&longs;tolæ &longs;iue Di&longs;&longs;ertationis &longs;eriem.
3. in 9.
ART. VI. VII. VIII.
De Motus æquabiliter
accelerati definitione.
lis grauibus decidentibus competit) illum,
dens, temporibus æqualibus æqualia celeritatis mo
menta acquirit.
tiùs definiendum cum vulgari &longs;ententia illum,
bus &longs;patiis æqualia celeritatis augmenta acqu
quam ex Galilei definitione præclarè intelligitur accelerationis
æquabilitas: prout incre&longs;
latera memorati Trianguli ab apice v&longs;que in ba&longs;im incre&longs;cen
& hæc linea ideò incre&longs;cit æquabiliter, quòd &longs;ecundum parteis
laterum æqualeis (per quas dictum e&longs;t repræ&longs;entari tempora)
additamenta continuò æqualia acquirat.
tem R. Patri probata, nihil tale potest intelligi: cùm nulla
facta temporis mentione, & &longs;umptis partibus lateris trianguli
pro spatiis, & interceptis triangulis pro celeritatis gradibus,
con&longs;tet, &longs;i totidem &longs;emper addantur triangula, quot lateris par
tes, creatum iri triangulum totalem, cuius area inæquabili&longs;
&longs;imè ab apice in ba&longs;im incre&longs;cat.9. in 14.
ART. IX. X. XI. XII.
De Paralogi&longs;mo,
qui Galileo Definitionem &longs;puriam impugnan
ti obiicitur.
Patri probatam,
quòd &longs;i velocitates e&longs;&longs;ent, vt emen&longs;a &longs;patia, atque idcircò
&longs;patium v. c. duplum percurreretur velocitate dupla illius, qua
dimidium: &longs;equeretur duplum, & dimidium, &longs;eu totum, &
partem, eodem, aut æquali tempore percurri. Nempe &longs;eu
motus æquabilis, &longs;eu acceleratus æquabiliter &longs;it, non potest ce
leritas e&longs;&longs;e dupla per duplum &longs;patij, quin ea ex&longs;i&longs;tente vbique
dupla, duplæ partes percurrantur quibu&longs;libet temporibus, &longs;ic
que perueniatur eodem tempore ad dupli, & ad dimidij finem. Contendit R. P. committi heic Paralogi&longs;mum: & nullam
tamen rationem profert, quàm quæ continetur his verbis,
Si graue de&longs;cendens per AB, tempus quodcum
que in&longs;umat, putà quadrantem; ac deinde BC
ip&longs;i AB æquale dimidio quadrante percurrat:
quis neget in C duplam haberi velocitatem eius,
quæ fuit in B? & tamen idem graue totam AC,
& dimidium eius AB non percurreret.
nihil aliud, quàm rem controuer&longs;am &longs;upponit, habetque
pro principio: videlicet &longs;ecundam partem percurri di
midio temporis, quo primam. Atque id quidem præter Incom
modum ex po&longs;itione hac con&longs;equens, quòd cùm oporteat pari
modo percurri partem tertiam dimidio temporis, quo &longs;ecun
dam; quartam, quo tertiam, &c. debeat cum effluxu temporis
&longs;ecundi percurri spatium infinitum: quatenus omnia illa di
midiorum dimidia, &longs;iue fragmenta temporis non po&longs;&longs;unt
aliquid) ni&longs;i priùs omnia, hoc e&longs;t infinita, fuerint numerata.
A. p. 14. in 21.
ART. XIII. XIV. XV. XVI. XVII.
XVIII. De Po&longs;tulato Galilei circa motum
&longs;uper æque-altis, non æque-inclinatis planis.
fieri, &longs;iue ad perpendiculum graue decidat, &longs;iue &longs;upra planum
inclinatum delabatur; candidè egit
Gradus velocitatis eiu&longs;dem mobilis &longs;uper diuer&longs;as pla
norum inclinationes acqui&longs;itos tum e&longs;&longs;e æqualeis, cùm
eorumdem planorum eleuationes ponuntur æquales:
demon&longs;trationem attulerit) &longs;edvt eatenus probabile, quatenus
deductæ ex eo conclu&longs;iones cum experientia con&longs;entirent. Id
tamen R. P. exagitat, vti & confirmationem, non incongruè
alioquin petitam ex pendulis, quæ longioribus, breuioribu&longs;que
filis illigata, & ex eadem tamen altitudine vibrari permi&longs;&longs;a, ad
eandem proximè a&longs;&longs;urgant, &longs;icque debeant omnia parem impe
tum (&longs;eu velocitatem) de&longs;cendendo acquirere: vtcumque per
arcus inæqualeis procurrant. Neque verò etiam R. P. licet
difficilia obiiciat, proptereà infirmat
bus Author habet aliqua &longs;imilia) ad probandum grauia tam
decidentia, quàm delabentia conficere primo tempore vnum &longs;pa
tium, &longs;ecundo tria, tertio quinque, &c.21. in 32
ART. XIX. XX. XXI. XXII.
De
Experimento circa ictum, impetumve grauium
cadentium, ad explorandum impetu&longs;-ne, vt
&longs;patium incre&longs;cat.
maiore impetu e&longs;&longs;e, vehementiu&longs;que percutere, ac tantam e&longs;&longs;e
velocitatem, quantus impetus, & percußio est: non ideò tamen
con&longs;tat vllis (qualia R. P. dicit in quolibetgraui clara, facilia,
indubitata) experimentis, graue decidens ex altitudine dupl
duplò fortiùs percutere, triplò ex tripla, quadruplò ex quadru
pla, &c. Quin-etiam &longs;unt Experimenta, quæimpetum, per
cußionemque non e&longs;&longs;e duplò maiorem in&longs;inuant, ni&longs;i ex altitu
dinequadrupla; triplò, ni&longs;i ex nonupla; quadruplò, ni&longs;i ex &longs;e
decupla. Huiu&longs;cemodi &longs;untilla de Aqua cylindrico va&longs;e con
tenta; cuius duplum non ex&longs;ilit tempore æquali, ni&longs;i altitudo
quadrupla &longs;it; nec triplum, ni&longs;i nonupla; quadruplum, ni&longs;i &longs;e
decupla: & de Chorda ten&longs;a, cuius vibratæ itus, reditu&longs;que
dupli non &longs;unt, ni&longs;i quadruplo pondere tendatur; tripli, ni&longs;i
nonuplo; quadrupli, ni&longs;i &longs;edecuplo: ac rursùs de Pen&longs;ilibus,
quorum vibrationes ad perpendiculum peruenientes non acqui
runt impetum duplum, ni&longs;i altitudo de&longs;cen&longs;us &longs;it quadrupla,
triplum, ni&longs;i nonupla, quadruplum, ni&longs;i &longs;edecupla, &c.
A p. 32. in 41.
ART. XXIII. XXIV. XXV. XXVI. XXVII.
XXVIII. De Experimento in Bilance facto, ac
aliud reuerâ probante, quàm velocitates e&longs;&longs;e
&longs;icut &longs;patia.
spatium incre&longs;cere; &longs;ed speciatim quoque illud, quod edixit,
diametrum cuiu&longs;libet globi ita e&longs;&longs;e præci&longs;am impetus illius
men&longs;uram, vt ex altitudine duarum diametrorum præcisè, per
cutiat duplò fortiùs: ex altitudine trium triplo: ex altitudine
quatuor quadruplò, &c. Iußit autem Experimentum in Bi
lance peragi, qua ruè &longs;u&longs;pen&longs;a, & alterâ lancium per aërem
liberâ, alterâ &longs;uffulia, & pondere exæquatâ cum libera, glo
bóque &longs;imùl, &longs;i deinceps, inquit, dimittatur globus in liberam
ex vna &longs;ui diametro, is percußionis impetu attollet &longs;uffuliam
cùm &longs;uper-addito præci è vno &longs;ui pondere; &longs;i ex duabus, cum
&longs;upper-addito duplo: &longs;i ex tribus, cum triplo: &longs;i ex quatuor,
cum quadruplo. Et permirum tamen id Experimentum de
prehendi fal&longs;um; quatenus dimi&longs;&longs;us globus ex altitudine dia
metri vnius, non modò attollit cum altera lance (eo, quo dictum
e&longs;t, modo exæquata) ponderis tantumdem, quanto ip&longs;e e&longs;t, ve
rùm etiam
aliunde attollit non modò ex diametro vna altitudinis, verùm
etiam ex diametri &longs;emi&longs;&longs;e, imo ex quadrante, imò ex octante,
imò & ex vncia. Quin-etiam eius ponderis, quod eleuat &longs;um
mum ex diametro vna, duplum eleuat non ex diametris dua
bus, &longs;ed ex quatuor: triplum non ex tribus, &longs;ed ex
nouem: quadruplum non ex quatuor, &longs;ed ex &longs;edecim: adeò
proinde vt proprio R. P. experimento eius &longs;ententia euertatur,
&Adde &, &longs;i velocitatis gradus
pro ratione diametrorum cre&longs;cerent, euenturum, vt dimißis ex
eadem altitudine duobus globis ex eadem materia, quorum
vnus e&longs;&longs;et diametro decies maiore, quàm alius, minor caderet
decuplo velociùs, ac decuplò citiùs perueniret in terram, quàm
mator; cùm experientia tamen doceat cadere æque-velociter,
Ari&longs;toteles cen&longs;eat cadere maiorem velociùs, & peruenire
citiùs.
ART. XXIX. XXX. XXXI XXXII. XXXIII.
De Tempore, quo R. P. colligit parteis &longs;patij
&longs;ingulas decur&longs;um non iri.
(&longs;eu quod nul um e&longs;&longs;et) pro vero habuerit. & illam Motus
æquabiliter accelerati definitionem a&longs;&longs;ump&longs;erit, quæ traditur
nulla temporis mentione:
tem, &longs;eu accelerationem, maximéque æquabilem, intelligi, &longs;ine
comparatione ad tempus. Et quia &longs;upponendo velocitates
acquiri, vt spatiæ, manife&longs;tè &longs;equitur, vt &longs;ecundum æquale
spatium decurratur dimidio temporis, quo primum; tertium
triente, quartum quadrante, &c. (quippe tempore &longs;emper
ex&longs;i&longs;tente ad velocitatem incre&longs;centem &longs;ubmultiplo) cum heic
tamen con&longs;equantur incommoda varia, ac illud speciatim,
quod acceleratio fieret, vt difformiter. &longs;ic in ratione plu&longs;quam
tripla: ideò o&longs;tendit quidem R.
fieri non po&longs;&longs;e vt decurrantur &longs;patia temporibus huiu&longs;modi;
&longs;ed
&longs;equitur ex eapo&longs;itione, quod velocitates &longs;e habeant vt &longs;patia.
A p. 13. in 63.
ART. XXXIV. XXXV. XXXVI. XXXVII.
XXXVIII. De Tempore, quo R. P. colligit
&longs;ingulas parteis decur&longs;um iri.
&longs;ur&longs;um eiu&longs;dem primæ partis dimiaium, trientem, quauran
tem, & vniuersè tot fragmenta, quot &longs;unt inferiùs partes
æquales; ac tum contendit, quanto tempore dimidium inferius
primæ partis percurritur, tanto deinceps partem &longs;ecundam
æqualem percurri; quanto triens, tanto tertiam; quanto qua
drans, tanto quartam, &c. adeò proinde, vt in inferiore pri
mæ partis dimidio contineantur &longs;igillatim omnia tempora, qui
bus omnes &longs;uper&longs;tites æquales partes percurruntur. Attamen
abs re, & omninô gratis negligit &longs;uperius dimidium, nullam
que eius rationem habet; à cuius tamen initio, non fine, motus
incipit, & per quod iam acceleratur, cùm pauciores parteis, Gratis
fata omnium partium inferiorum alligat: nam & quòd vult
&longs;ecundam partem e&longs;&longs;e huius dimidij duplam, atque ideo e&longs;&longs;e
velocitatem duplam, & tempus æquale: nihil aliud; quàm
quæ&longs;itum petit. Aliunde autem variis argumentis conficitur,
vt a&longs;&longs;umpto quocumque primo tempore, tam inferius dimidium,
quàm &longs;ecunda pars tempore breuiore, breuioreque in infinitum
percurrantur (&longs;ubdiui&longs;o nempe priore dimidio in duo alia, &
rur&longs;us priore in alia, &c.) vt
&longs;ecunda pars percurrantur dimidio temporis, quo integra pri
ma: vt tempus per &longs;ecundam partem &longs;e&longs;qui alterum &longs;it, non
duplum ad illud, quo percurritur inferius dimidium: vt tam
prima pars &longs;ola, quàm prima, & &longs;ecunda &longs;imùl, hoc e&longs;t pars,
& totum eodem, aut æquali percurrantur tempore; atque id
genus cætera, quæ proportione etiam obiici in trientem, qua
drantem, fragmentaque alia a&longs;&longs;umptæ primæ partis po&longs;&longs;unt.
A p. 63. in 72.
ART. XXXIX. XL. XLI. XLII.
De Ratione continuò dupla, qua &longs;patia de
curri temporibus æqualibus R. P. contendit.
parte prima &longs;ubdiui&longs;a in duo dimidia; a&longs;&longs;umit R. P. illud
quo inferius
tempore æquali &longs;ecundo percurri partem &longs;ecundam, quæ est
nempe dupla illius dimidij: ac tertio parteis tertiam, & quar
tam, quæ iunctim &longs;unt duplum &longs;ecundæ: & quarto quintam,
&longs;extam, &longs;eptimam, octauam, quæ iunctim &longs;unt duplum tertiæ,
& quartæ; & quinto octo &longs;uccedenteis, &longs;exto &longs;equenteis &longs;ex
decim: atque ita porrò in ratione continuò dupla. At verò
heic quoque abs re præteritur primum primæ partis dimidium:
& maximè cùm requiratur, quæ accelerationis &longs;it ratio non
à medio v&longs;que primæ partis, &longs;ed ab eius v&longs;que initio. Peruer
tit etiam R. P. Arithmeticam progreßionem, qua &longs;uperiùs
&longs;tatuens velocitates e&longs;&longs;e, vt &longs;patia, voluit vni parti integræ, non
eius dimidio competere vnum celeritatis gradum, duobus
duos, &c. Conficitur rur&longs;us heic quoque, vt totum, & pars
eodem tempore percurrantur; vt non ampliùs, quàm triens, &
quadrans exæquentur toti; vt item &longs;olæ partes quinta, &longs;exta,
&longs;eptima, octaua; atque ita de reliquis. Comficitur quoque, vt
decurrantur &longs;patia non modò in ratione dupla, &longs;ed etiam in
tripla, quadrupla, &c. Denique & illud inde &longs;equitur,
quod iam ante obiectum est; vt primo nimirùm tempore per
acto, effluere &longs;ecundum æquale non poßit, quin decur&longs;um fuerit
spatium infinitum.72. in 79.
ART. XLIII. XLIV.
De Tempore,
quo globum ferreum ca&longs;urum ex Luna in
Terram contendit.
C
ræ milliaria Jtalica
proportione à &longs;e instituta decur&longs;um iri id spatium à globo fer
reo è Luna dimi&longs;&longs;o intra horas
tinuò dupla, decur&longs;um iri id spatium intra minuta non omninò
duo.
perientia, qua cùm constet globum non conficere amplius vno
&longs;emi-minuto, quàm milliare vnum altitudinis; & &longs;eruata
etiam acceleratione in ratione dupla, non poßit &longs;ecundo &longs;emi
minuto, ni&longs;i duo conficere: tertio, ni&longs;i quatuor: quarto, ni&longs;iocto:
manife&longs;tum fit ex ijs aggregatis non po&longs;&longs;e intra duo minuta
confici milliaria plu&longs;quam quindecim. Quàm ingenti verò
di&longs;crimine hic numerus abe&longs;t à milliaribus
ijs potiùs, quæ ille vult intra duo minuta integra percurri,
1677721
bent primo &longs;emi-minuto percurri
&longs;ecundo
quintis: & quarto79. in 82.
ART. XLV. XLVI. XLVII.
De Tem
pore per primas parteis ob&longs;eruatione determi
nando; pauca de cau&longs;&longs;a Phy&longs;ica, déque lap&longs;u
circa cam admi&longs;&longs;o.
I
percurruntur: ac alios ideò prouocat, vt rem experiantur in
turri pedes ducentos alta (vtcumque ip&longs;e præ cæteris videatur
fui&longs;&longs;e experturus) ac non videtur
ex ob&longs;eruatis proprijs &longs;ufficienter refellere: dum ait duntaxat,
e&longs;&longs;e verendum, ne cùm in alijs magnoperè errauerit, heic quo
que &longs;it hallucinatus. Quippe neque o&longs;ten&longs;um e&longs;t erra&longs;&longs;e ip&longs;um
in alijs, neque heic habet aliquid non experientiæ con&longs;onum,
maximéque illud effatum,
libet &longs;patia &longs;umantur, tempora ip&longs;orum fore inter &longs;e,
vt alterum eorum ad &longs;patium medium proportionale
inter ip&longs;a:
tim tempore & &longs;ecunda pars, & duo primæ dimidia percur
rantur, determinare. Excu&longs;atione, dilationeque v
circa cau&longs;&longs;am Phy&longs;icam, de qua vide batur ip&longs;e titutus feci&longs;&longs;e
aliquid sperandum. Circa hanc cau&longs;&longs;am lap&longs;us admi&longs;&longs;us in
EpistolisMotu impre&longs;&longs;o:
gradus velocitatis facti æquales spatijs &longs;unt; & intercepta
triangula, de quibus &longs;uprà, a&longs;&longs;umpta &longs;unt non modò pro &longs;pa
tijs, verùm etiam pro gradibus; pro quibus a&longs;&longs;umendæ potiùs
triangulorum ba&longs;es fuerunt.82. in 96.
exaggerat; non oblitus etiam quantum condoluerit, habitam ab
Authore fui&longs;&longs;e
beneuolentiæ &longs;ignificatione.86. in 88.
ART. I.
Scribendi Occa&longs;io.
edi non improbauit, &longs;i modò attexeretur alia, quam &longs;ubinde
&longs;crip&longs;it, in&longs;crip&longs;itque
nis.
veritatem maiori iam luce illu&longs;tratam aperire, & ab errore
vindicatam exhibere; ac aliunde queritur frequens ea &longs;ibi af
fingi quæ nec dixerit, nec ex traditis à &longs;e principijs potuerint
deduci; idcircò &longs;ic edi vi&longs;um e&longs;t Vindicias, vt Exceptio inter
&longs;eratur, ad explorandum quî fieri poßit, vt veritatem &longs;ic il
lu&longs;tratam, vindicatamque Author non videat, & ad eluen
dum labem illam, qua ad&longs;pergi per&longs;en&longs;it &longs;e, ob affictionem to
ties obiectam.89. in 93.
ART. II. III. IV. V.
De Statu Controuer&longs;iæ.
Epi&longs;tolam, in quam &longs;uperior con&longs;cripta e&longs;t; ideò vt Status
controuer&longs;iæ luculentior fiat, ac &longs;imùl appareat, qualis
&longs;tratio hæc &longs;it; placet ip&longs;am eruere ex eius totius Epistolæ textu,
ac reducere, analy&longs;i facta, in hypotheticum Syllogi&longs;mum, qui
e&longs;&longs;e poßit huiu&longs;modi.
acqui&longs;itæ &longs;e habent vt emen&longs;a &longs;patia, nece&longs;&longs;e e&longs;t &longs;patia decurri
temporibus æqualibus in ratione continuò dupla:
&longs;patia decurri temporibus æqualibus in ratione continuò
dupla.
initium ab A&longs;&longs;umptionis confirmatione, dum in
di&longs;putatum e&longs;t; tumgradus ad eiu&longs;dem-met A&longs;&longs;umptionis pro
bationem factus, dum palmare illud Bilancis Experimentum
e&longs;t narratum; ac tandem ventum ad probandum con&longs;equutio
nem Propo&longs;itionis, dum explicitus est conatus circa Rationem
&longs;patiorum duplam, quæ eadem conclu&longs;io fuit Demon&longs;trationis.
A p 93. in 97.
AD ART. VI. VII. VIII.
De Motus
æquabiliter accelerati Definitione.
Neque enim po&longs;&longs;unt velocitatis gradus per triangulorum re
præ&longs;entari ba&longs;eis, &longs;i per parteis laterum repræ&longs;ententur &longs;patia,
vt R. P. vult; tum quòd nulla habita temporis mentione
t
&longs;itus aut perire debeat, aut nihil agere, neque poßit duplum
illius, qui acquiritur; tum quòd &longs;it futurum vt &longs;ecundo tempo
re octo penè spatia primo æqualia percurrantur. Confundit
R. P. Vniformitatem cum Proportione, dum progreßiones
G
vult: ac in eadem rursùs incidit Incommoda, dum in difformi
Triangulo vult iteratò spatia per laterum parteis, potiu&longs;quàm
per triangulos interceptos repræ&longs;entari.97. in 1. 0.
AD ART. IX. X. XI. XII.
De Paralogi&longs;mo,
qui Galileo Definitionem &longs;puriam impugnan
ti obiicitur.
Paralogi&longs;mum
o&longs;tendere: &longs;ed fru&longs;trà nihilominùs; cùm &longs;eu varios &longs;en&longs;us
di&longs;tinguat, &longs;eu propo&longs;itiones retexat, &longs;eu con&longs;equutionem ex
pendat, nihil aliud rursùs, quàm quæ&longs;itum, &longs;eu principium (vt
fuerat illi
quidpiam vult, mutato nomine, concludat. Haud iure verò
conqueritur &longs;ibi affingi, quòd dixerit, &longs;patio in duas parteis
æqualeis diui&longs;o, po&longs;teriorem percurri dimidio temporis, quo prio
rem (vnde illatum e&longs;t
&longs;ecundum tempus percurrendo) cùm relata ip&longs;ißima illius ver
ba fuerint (de quadrante nempe, & dimidio quadrantis) ac, vt
po&longs;&longs;et Paralogi&longs;mi Galileum conuincere, non fuerit alio prin
cipio v&longs;us. Denique, &longs;i Paralogi&longs;mus à
o&longs;tenditur R. P. alio loco aut nihil conclu&longs;i&longs;&longs;e, aut apertißimè
in eundem Paralogi&longs;mum incidi&longs;&longs;e.110. 136.
AD ART. XIII. XIV. XV. XVI. XVII.
XVIII. De Po&longs;tulato Galilei circa motum
&longs;uper æque-altis, non æque-inclinatis planis.
G
lius hactenus fal&longs;itatis conuicta &longs;unt; pote&longs;tque adeò eius do
ctrina potiore iure cen&longs;eri Scientia, vt quæ experientiæ con
&longs;entanea &longs;it, quàm ea, quæ à R. P. traditur, vt quæ experien
tiæ repugnet, ac fundata &longs;it in Experimento, quod fal&longs;um de-Si planum, vt minùs decliue, ita etiam prolixius
&longs;it, potest profectò prolixitas paruitatem incrementorum
velocitatis &longs;ic compen&longs;are, vt acqui&longs;ita in fine motus veloci
tas &longs;itnihilo minor. Quod e&longs;t allatum de pendulis exemplum
&longs;emper congruit: & ex quatuor pendulis, quæ prolixitate
&longs;int, primum vnius præcisè pedis, &longs;ecundum quatuor, tertium
nouem, quartum &longs;edecim: peragit reuerâ, con&longs;tanterque pri
mum vibrationes quatuor, eodem tempore, quo &longs;ecundum
peragit treis, & tertium duas, & quartum vnam: &longs;i modò
quidem 136. in 141.
AD ART. XIX. XX. XXI. XXII.
De Experimentis circa ictum, impetumve gra
uium cadentium, ad explorandum, impetu&longs;
ne, vt &longs;patium incre&longs;cat.
fuit iactatum peragi ea po&longs;&longs;e in grauibus quibu&longs;libet; tamet&longs;i
ne in vno quidem peragere fuerit conce&longs;&longs;um. Allata tria ex
perimenta qua&longs;i &longs;upparia ad &longs;uadendum non incre&longs;cere impe
tum, velocitatemve &longs;icut spatia, &longs;ed &longs;icut spatiorum radices,
attinent omninô ad rem; ac illud speciatim de Aqua ef
fluente ex va&longs;e cylindrico, quatenus &longs;umma aqua in foramen
decidens, non magis à &longs;ibi &longs;ubiecta, præeunteque impeditur,
quàm &longs;i per aërem caderet; quòd illa &longs;emper pari cum ip&longs;a
velocitate &longs;e&longs;e &longs;ubducat, anteceden&longs;que nihil officiat.
A. p. 141. in 146.
AD ART. XXIII. XXIV. XXV. XXVI. XXVII.
XXVIII. De Experimento in Bilance facto, ac
&longs;icut &longs;patia.
tum fal&longs;itatis conuictum e&longs;t: mirum videri profectò potest,
quamobrum R. P. venditare pergat pro Demon&longs;tratione ra
tiocinium, quod fuerit eo Experimento duntaxat &longs;uffultum; ac
potißimùm prouocando ad vberiorem experientiam, qua con
trouer&longs;ia dirimatur; qua&longs;i verò &longs;inondum &longs;it dirempta contro
uer&longs;ia, eius Demon&longs;tratio interim cohæreat? Fru&longs;trà iam &longs;ol
licitus e&longs;t de non a&longs;&longs;umendo &longs;upra æquilibrium exce&longs;&longs;u; cùm
agno&longs;cat iam quàm vanè v&longs;urpet diametrum globi pro men
&longs;ura præci&longs;a altitudinum, ex quibus totidem pondera at
tollantur. Incommodum illud de globo diametri decuplò mi
noris, & decuplò citius ca&longs;uro ex eadem altitudine, obiectum
legitimè fuit, & R. P. eximere &longs;e ab illo nequicquam tenta
uit.146. in 157.
AD ART. XXIX. XXX. XXXI. XXXII. XXXIII.
De Tempore, quo R.P. colligit parteis &longs;patij
&longs;ingulas decur&longs;um non iri.
tradenda motus æquabiliter accelerati definitione. Affictum
nihil fuit R. P. inter vrgendum incommoda; quæ &longs;i variata
interdum &longs;int, in cau&longs;&longs;a fuit variatio principiorum, quibus
ille e&longs;t v&longs;us. Nihil iteratò demon&longs;trat: verum aut ex fal&longs;is
concludit; aut in
committit; aut prætereà inuoluit &longs;e multiplici contradictione. Quæ&longs;tio ne que e&longs;t, neque fuit, an ostenderit (quod fuit conce&longs;
&longs;um) non po&longs;&longs;e partem spatij &longs;ecundam decurri dimidio tem-&longs;ed an o&longs;tenderit ad
uer&longs;us &longs;eip&longs;um; vt pote ex cuius principio, po&longs;itioneve illud
&longs;equatur. Nequicquam conatur capita ab&longs;urda &longs;ibi obiecta
retorquere; qua&longs;i &longs;it perinde &longs;eu &longs;patium, &longs;eu tempus cum
velocitate conferat; & ad hominem cum argumentatur, in
limine ip&longs;o aberrat, dici vt putà id &longs;upponens, quod minimè
dicitur, & tempus cum velocitate &longs;ecus conferri, quàm con
fertur. Tota gloriatio con&longs;equens nihil habet, quod inuidea
tur; & dum ait impugnationem &longs;ui ratiocinij, non po&longs;&longs;e, vt
inanem, ac vanam, inuenire plau&longs;um, ni&longs;i apud minùs peritos;
&longs;atis e&longs;t prouocare illum vt proferat vel vnicum, cui &longs;uam
&longs;ententiam per&longs;uadeat, peritum.157. in 181.
ART. XXXIV. XXXV. XXXVI. XXXVII.
XXXVIII. De Tempore, quo R.P. colligit
&longs;ingulas parteis decur&longs;um iri.
dam partem e&longs;&longs;e duplam velocitatis per dimidium inferius pri
mæ, quàm quia &longs;patium, duplum e&longs;t: neque hanc con&longs;equutio
nem vllo modo probauit; &longs;ed ex eo &longs;olùm &longs;uppo&longs;uit, quod ve
locitates &longs;icut spatia &longs;int, quæ est iterata principij petitio: cùm
hoc ip&longs;um &longs;it, quod controuertitur, neque vllatenus inueniatur
o&longs;ten&longs;um; ni&longs;i ex fal&longs;o illo circa Bilancem experimento. Ex
varijs obiectionibus vna est delecta, cui re&longs;ponderetur, propter
errorem calami, quo in immen&longs;a, importunaque literarum
farragine litera vna irrep&longs;it pro alia. Beatus e&longs;t R.
Author e&longs;&longs;e non videatur ingre&longs;&longs;us in controuer&longs;iæ pene tralia,
quique eum æquè à dictis &longs;uis, atque à natura penitiùs inspi
ciunda arce at. Tempus minutorum &longs;ex attributum primæ
qui tamet&longs;i alicubi non probet ex ijs &longs;ex minutis quatuor priori
dimidio, & duo po&longs;teriori attribui: id tamen tum ex varijs
eius principijs deducitur: tum recipit Author deducturum &longs;e
eadem, & plura incommoda, ex quacumque alia di&longs;tributione
eius numeri, aut alterius à R. P. facienda: &longs;i modò &longs;emper
velocitates habere &longs;e vt spatia &longs;upponat.181. in 191.
ART. XXXIX. XL. XLI. XLII.
De Ratione continuò dupla, qua &longs;patia de
curri temporibus æqualibus R. P. contendit.
à primæ partis medio, non ab ip&longs;o eius principio; & maximè
quidem, cùm aliunde velit velocitates e&longs;&longs;e vt spatia, spatiive
parteis, quarum vna &longs;it tota prima, non dimidium primæ: ac
in&longs;ignes prætereà &longs;uboriantur difficultates ex eo, quòd dum
ad obiecta de &longs;ubdiui&longs;ione prioris dimidij in alia, aliaque dimi
dia re&longs;pondet, standum ait alicubi, quòd diui&longs;io e&longs;&longs;e in Phy
&longs;icas parteis infinita non valeat, & ibi tamen standum, vbi
tot partes adhûc &longs;uper&longs;unt, vt ex ijs ratio accelerati motus
perfectè intelligatur. Quippe cùm inter cætera a&longs;&longs;umpto
ca&longs;u ex Luna, Sole, aut Firmamento, & a&longs;&longs;umpta particula
prima Phy&longs;icè diuidua, in qua reperiri debeant dimidium
inferius, ac in ip&longs;o triens, quadrans, & tot fragmenta cætera,
quot &longs;unt partes ip&longs;i primæ æquales in toto illo &longs;patio, quotque
etiam di&longs;tingui poßunt in &longs;uperiore dimidio; incredibilis &longs;it
partium numerus, per quas in priore dimidio contentas opor
teat motum peragi, priu&longs;quam incipiat accelerari; & in qui
bus tamen con&longs;i&longs;tendum &longs;it, quòd diui&longs;io vlteriùs fieri in duo
telligatur. Quæ&longs;tio heic iterùm non e&longs;t, an velocitas per
&longs;ecundam partem &longs;it præcisè dupla velocitatis per primam: &longs;ed
an id &longs;equatur (vt & ab&longs;urda quædam alia) ex R. P. prin
cipijs. Refugit R. P. prouocationem ad calculos, nec incom
moda clariùs pateant, ac illud speciatim, quod obiectum e&longs;t
ex triente, & quadrante non componi integrum: neque item
ex partibus quinta, &longs;exta, &longs;eptima, octaua. Irrito cona
mine rationem duplam, vt &longs;olam congruam excu&longs;are adniti
tur, eò quòd ip&longs;a quoque &longs;eip&longs;am euertat, quoties tempora a&longs;
&longs;umuntur maiora, vel minora dato, quæ &longs;int ip&longs;a quoque inter
&longs;e æqualia: &longs;iquidem ea quoque deberent in eadem ratione
respondere spatijs: quod tamen non fit: vt in allato à R. P.
exemplo de ca&longs;u globi ex Luna mon&longs;tratur.191. in 208.
AD ART. XLIII. XLIV.
De Tempore,
quo globum ferreum ca&longs;urum ex Luna in
Terram contendit.
cùm R. P. fateatur non po&longs;&longs;e illam rapiditatem, quam priùs
a&longs;&longs;eruerat, in&longs;anam e&longs;&longs;e adeò, vt globus id &longs;patium minutis
non omninô duobus percurrat: tamet&longs;i lenire rem &longs;tudet, dum
naturam quidem id exigere, &longs;ed medij tamen conditionem
obstare ait.208. in 209.
AD ART. XLV. XLVI. XLVII.
De
quodam lap&longs;u emendando circa cau&longs;&longs;am Phy
&longs;icam accelerati grauium motus.
e&longs;&longs;e cau&longs;&longs;am initij motus, & &longs;olùm medium, putà aërem e&longs;&longs;e
cau&longs;&longs;am accelerationis, quatenus à fronte re&longs;iliens, & à tergo
claudem, graue vrget; cùm alioquin &longs;ola grauitate agente, &longs;i
bique &longs;imili manente, vt in vacuo, de&longs;cen&longs;us foret vniformis,
&longs;imili&longs;que &longs;ui per&longs;eueraturus: idcircò an&longs;a & accepta, & in
hunc locum dimi&longs;&longs;a e&longs;t adiiciendi quidpiam de Phy&longs;ica cau&longs;&longs;a. Nam primùm quidem paulò fu&longs;iùs deducitur lap&longs;us indicatus
ad calcem &longs;uperioris Epistolæ: declarando videlicet, quo pro
gre&longs;&longs;u tentatum fui&longs;&longs;et in Epi&longs;tolis
motore tran&longs;lato
lerentur iuxta progreßionem numerorum imparium ab vnita
te incœptorum; & quemadmodum talis cau&longs;&longs;a fui&longs;&longs;et agnita
tum primo momento &longs;ola attractrix Terræ vis, quæ imprime
ret &longs;ingularem ictum: tum &longs;ecundo, & reliquis tam eadem
attractrix, quàm aër à tergo &longs;uccedens, in&longs;tan&longs;que, adeò vt
quolibet momento duo qua&longs;i ictus imprimerentur: &longs;icque &
primo momento vnus acquireretur velocitatis gradus, quo &longs;u
peraretur vnum &longs;patium: &longs;equente autem quolibet &longs;uper-ad
derentur duo, e&longs;&longs;entque proinde tres, quinque, &longs;eptem, &c. quibus spatia totidem con&longs;equenter &longs;uperarentur: vnde &
con&longs;entaneum foret velocitates e&longs;&longs;e, vt spatia, quæ proinde &longs;i
mul repræ&longs;entari deberent per illas triangulorum areas: quod
animaduer&longs;um e&longs;t repugnare. Deinde verò o&longs;tenditur,
quamobrem cùm cau&longs;&longs;a vnica &longs;ufficiat, iuxta antè expo&longs;ita
(&longs;upponitur autem videri non e&longs;&longs;e ip&longs;am aliam, quàm ip&longs;am
vim Terræ tractricem) o&longs;tenditur, inquam, vtramque à
R. P.
putà aër, ad accelerationem nihil confert, quin-etiam potiùs
&longs;olus accelerationis &longs;it cau&longs;&longs;a: grauitas verò, &longs;eu qualitas graui
in&longs;ita, & ab attractione di&longs;tincta, nulla e&longs;t: neque proinde po
te&longs;t motum &longs;eu in &longs;patio vacuo, &longs;eu in aëre, (vt &longs;i &longs;olus aër in
vniuer&longs;o e&longs;&longs;et) præ&longs;tare.
AD ART. XLVIII.
De Re&longs;pon&longs;ionis
Conclu&longs;ione.
anteponere veritatem. Fuit in
ret lituras, aut etiam rem totam &longs;upprimi iuberet. Non capitur
quamobrem cen&longs;eat &longs;e veritatem iam illu&longs;tratam, & ab er
rore vindicatam exhibere: ac &longs;peret tamen, vt ex correcto
fal&longs;o &longs;uo Experimento veritas deinceps certiùs inueniatur. Ip&longs;e
fuit
cui tamen nihil aut re&longs;pon&longs;um, aut oppo&longs;itum &longs;altem, fui&longs;&longs;et,
&longs;i is fui&longs;&longs;et creditus, qui ip&longs;a rei nouitate, quod iam ait, per
celleretur, tanquam nemine alio hactenus inuento, qui in eius
a&longs;&longs;ertionibus, ac decretis pugnam aliquam, contrarietatemque
aut inuenißet, aut obiecißet. Quare & e&longs;&longs;e &longs;ecurus pote&longs;t
iri deinceps nihil inqui&longs;itum in ea, quæ &longs;e dicit habere
ob&longs;curiora, incertioraque; fore autem, vt &longs;olitum affectum,
venerationemque &longs;emper experiatur.
ART. I.
Scribendi Occa&longs;io
Notandum &longs;olùm, Epistolas
Motu impre&longs;&longs;o à motore tran&longs;lato,
velut Apologia, ea occa&longs;ione fui&longs;&longs;e con&longs;criptas, quòd fides
ægrè habita fui&longs;&longs;et Experimentis ab Authore factis, ad&longs;truen
do illi Theoremati,
feratur, motus omneis no&longs;tros, rerumque à nobis mo
bilium, perinde fieri, apparereque, ac &longs;i illud quie&longs;ceret.
perinde atque quie&longs;cente, proiectus &longs;ursùm lapis &longs;ecundum
mali longitudinem, tueretur &longs;emper tam a&longs;cendendo, quàm
ex&longs;cendendo eandem a malo di&longs;tantiam; & dimi&longs;&longs;us è carche
&longs;io ad pternam, ita caderet, vt neque ex parte puppis de&longs;ere
retur, neque ex parte proræ attingeretur à malo. Quòd pi
la exprora in puppim, expuppi in proram proiecta, pari im
petu ferri appareret, parque &longs;patium conficeret; & neque tar
diùs perueniret ad collu&longs;orem, tamet&longs;i aufugientem, qui ad
proram: neque citiùs ad alium, tamet&longs;i occurrentem, qui ad
puppim, donec volaret per aërem. Quòd è curru, aut equo
citißimè abrepto, perinde ac quie&longs;cente, proiectæ &longs;ursùm res in
ip&longs;am manum reciderent: dimi&longs;&longs;æ cadere apparerent &longs;ecun
dum perpendiculum; emi&longs;&longs;æ prorsùm, retror&longs;úmque, nec pro
piùs, nec longiùs caderent in terram. Quòd dimi&longs;&longs;a pila
ab incedente, currenteve per complanatum locum, antro
&longs;emper procurreret; pari vi antrorsùm, retror&longs;úmque proie
cta, pariabe&longs;&longs;et, dum à motu ce&longs;&longs;aret, à proiectore di&longs;tantia; &
nunc ad perpendiculum caderet, nunc proiectorem etiam &longs;eque
retur; prout adactio manus retrorsúm e&longs;&longs;et velocior, æquè ve
lox, aut minùs velox, quàm corporis prorsùm. Jtaque horum
aliorumque Experimentorum explicandæ caußæ de&longs;tinata fue
rat Epi&longs;tola Prior; ac fuerant ideò variæ de Motu attingendæ
difficultates. Fuerat & Po&longs;terior speciatim con&longs;cripta decla
randæ inanitati rationis illius, quæ aduer&longs;us A&longs;&longs;ertores motus
Telluris peti &longs;oleret ex eo, quòd &longs;agitta &longs;ursùm euibrata è
puppi, dum nauis moueretur, non in puppim recideret, &longs;ed in
aquam à tergo puppis, quæ interim &longs;ubducta foret: ac fuerat
con&longs;equenter o&longs;ten&longs;a imbecillitas aliarum rationum complu
rium, quæ &longs;olent ij&longs;demobiici. Præstita, inquam, hæc fue
rant; cùm R. P. Epi&longs;tolis vi&longs;is, ea ex vtraque impugnauit,
quæ potißimùm di&longs;plicuerunt.227. in 228.
ART. II. III. IIII.
Nondum ob&longs;eruatum,
qui Galileo obiicitur, Paralogi&longs;mum: &, Neu
tram duarum virium à Motore tran&longs;lato im
pre&longs;&longs;arum imminui ab alterutra.
est, &longs;uperque in Epi&longs;tolis &longs;uperioribus adnotatum. Quod &longs;u
perest: cùm mota, v. c. naui, lapis ex ea proiicitur &longs;ursùm; is
apparet quidem tam proiectori, quàm omnibus, qui in naui
&longs;unt, a&longs;cendere, de&longs;cenderéque &longs;ecundum perpendiculum: &longs;ed
reuerâ tamen a&longs;cendit, de&longs;cenditque obliquè (vti & apparet
quie&longs;centibus in littore) de&longs;cribit nempe lineam curuam, quam
dicunt parabolicam: cau&longs;&longs;aque e&longs;t, quia manus proiiciens vt
cumque &longs;ursùm moueri appareat, reuerâ tamen mouetur obli
què, deflexa nempe à motu nauis, qui illam, dum attollitur,
dum horizontem. Et quoniam Author dixerat,
pellentem mobile &longs;ursùm, non modò non de&longs;trui, &longs;ed
ne vlla quidem ratione imminui à vi depellente in la
tus (
pari vi, naui quie&longs;cente, pro: iceretur à manu: vti neque mi
nùs in latus, quàm &longs;i immota manu veheretur &longs;olo motu nauis)
Idcircò R. P. i&longs;tud improbans, obiicit, quod e&longs;&longs;e apud peritos
Effatum ait,
diuer&longs;as parteis actis, tantò &longs;egniùs deferri in vnum
terminum, quantò fortiùs in alterum tendit.
hoc e&longs;&longs;e poßit verum, donec mobili iam &longs;eparato à motore &longs;u
peruenit vis, quæ ip&longs;um deflectat: fal&longs;um e&longs;t tamen, &longs;i nihil
noui à proiectore v&longs;que interueniat, in quo & vis ip&longs;ius pro
pria, & vis corporis ip&longs;um transferentis in vnam coïerint, quæ
tantùm &longs;it alterutrâ fortior, quantùm altera fortis e&longs;t; vt in
exemplo allato con&longs;tat, in quo quicquid e&longs;t motus &longs;ur&longs;um, à ma
nu est; quicquid motus prorsùm, à naui; & quod dee&longs;t virtuti
manus propriæ ad proiiciendum non minus altum &longs;ecundum li
neam curuam, quàm &longs;ecundum rectam, &longs;uppletur à vi tran&longs;
latitia nauis; vti & quod deest naui ad adigendum non mi
nus pror&longs;um &longs;ecundum curua, quàm &longs;ecundum rectam,
&longs;uppletur à vi proiectitia manus. Habentur & alia de Ex
perimentis.228. in 235.
ART. V. VI. VII.
Po&longs;&longs;e varias Sectas
veritatis &longs;tudio tentari: ac, Po&longs;&longs;e animalis ince&longs;
&longs;um præ &longs;altatione; & globi volutionem præ
adactione, dici naturalem.
perimentorum
eruditis, pij&longs;que minus placiturum: verùm, &longs;alua modò maneat
pietas, nihil e&longs;t, quod vetet philo&longs;ophari liberè, nullique Sectæ
addictum e&longs;&longs;e Displicet illi con&longs;equenter dici ince&longs;&longs;um ani
malis præ &longs;altatione naturalem: &longs;ed non apparet quid &longs;it in
congruum, quatenus motus naturalis notio e&longs;t, vt sponte, aut
&longs;ine repugnantia &longs;iat; violenti, vt præter naturam, &longs;eu cum
aliqua repugnantia. Displicet & globi volutionem &longs;upræ
planum dici naturalem præ adactione eiu&longs;dem per aërem: &longs;ed
con&longs;tat &longs;atis globum e&longs;&longs;e &longs;uapte natura comparatum, vt volua
tur potiùs &longs;upra planum (quod ni&longs;i aliunde deficeret, euaderet
motus vt æquabilis, &longs;ic perpetuus) quàm vt per aërem adiga
tur (per quem aliunde inæquabiliter, & motu &longs;tatim finiendo
trans fertur.) Vt prætereatur e&longs;&longs;e hæc omnia Ari&longs;toteli con&longs;ona,
quem coryphæum R.P.
235, in 240.
ART. VIII. IX. X.
Incredibilem fore
motus corporum decidentium &longs;egnitiem, &longs;i vt
incipit, ita pergeret; &, Non &longs;olùm acceleratio
nem, &longs;ed ip&longs;um quoque initium motus e&longs;&longs;e à
principio externo.
potiùs, quàm naturalem: nam quamuis accelerationem e&longs;&longs;e
violentam non deneget: ob de&longs;cen&longs;um tamen, &longs;eu &longs;implicem
motum, cui illa &longs;uperuenit, contendit e&longs;&longs;e potius dicendum ca
&longs;umlapidis naturalem. Sed
motu &longs;en&longs;ibile e&longs;t, ex acceleratione e&longs;t, ac ne millies quidem
mille&longs;ima eius pars ad &longs;implicem motum, de&longs;cen&longs;umve &longs;pectat:
con&longs;tat, &longs;i à potiore parte denominatio facienda &longs;it, dicendum
motu naturalem. Quàm parùm autem cen&longs;endum &longs;it, quod
ex &longs;implici motu e&longs;t, ex eo probatur, quòd &longs;i qualis incipit mo
tus quo momento primo e&longs;t adhûc ab acceleratione liber, talis
per&longs;eueraret per duarum
pro primo momento, vno minuto ex ijs, quæ decima vocant, non
dum e&longs;&longs;et planè peractus po&longs;t annos
&longs;i occœpi&longs;&longs;et illo motu ab v&longs;que initio Mundi cadere, perfeci&longs;&longs;et
iam &longs;eptimam vnam digiti partem. Deinde, cùm illud vio
lentum dicatur, cuius principium extra e&longs;t; etiam de&longs;cen&longs;us, &longs;eu
&longs;implex motus e&longs;&longs;e comprobatur à principio externo, nempe à
virtute attractrice Terræ (credebatur tuncpo&longs;&longs;e quoque aër à
tergo impellere) tum quia lapis &longs;eu intra vacuum (vbi nihil
cum Mundo, Terráque adeò communicaret, ac perinde illi fo
ret, &longs;eu e&longs;&longs;et, &longs;eu non e&longs;&longs;et Mundus) &longs;euintra aërem infinitum
(&longs;i &longs;olus præter ip&longs;um foret) talem motum nullum haberet:
tum quia quæ res &longs;unt inten&longs;ionis capaces, à qua cau&longs;&longs;a habent
gradus reliquos, ab ea nanci&longs;cuntur & primum; atque adeò,
vti dum calefit aqua, non cæteri gradus ab externo &longs;unt, pri
mus ab interno principio, &longs;ed omnes ab externo &longs;unt: ita dum
lapis deorsùm mouetur, non cæteræ motus partes ab externa
cau&longs;&longs;a, & prima ab interna &longs;unt; verùm &longs;unt omnes ab ex
terna.240. in 246.
ART. XI. XII. XIII. XIV.
Terram grauia
attrahere; &, Quid illi contingeret, &longs;i ver&longs;us
Lunam dimoueretur? Quid lapidi, &longs;i intra for
nicem ad centrum Terræ con&longs;titucretur?
expo&longs;itam: Ad illud, quod quærit R. P. quid ip&longs;i Terræ con-Dicitur e&longs;&longs;e probabi
le, fore, vt vbicumque Terra con&longs;titueretur, illeic quie&longs;ceret
eo modo, quo corpus eiu&longs;ce materiæ, vt aquæ &longs;ub pari mole
æquiponderet, vbicumque in imo, in &longs;ummo, in medio, aut vbi
uis intra aquam &longs;tatuatur, con&longs;i&longs;tit. Nimirùm, quòd Terra
&longs;ecundum &longs;i totam neque grauis &longs;it, neque leuis; & talis affe
ctio partium propria &longs;it, prout à tota di&longs;trahuntur: quódque in
Mundo spherico ex&longs;i&longs;tente, medium quidem, & extremum
&longs;it, non item infimum, & &longs;ummum; ac ta is conditio &longs;it
Terræ, globorumque Mundi cæterorum propria, propter
eandem partium di&longs;tractionem, & retractionem, quæ &longs;igillatim
cum speciali cuiu&longs;que centro comparatur. Non probatur etiam
aliunde Terram e&longs;&longs;e in Mundi medio; cùm etiam oppo&longs;itum
arguant excentrici &longs;iderum motus: neque veri&longs;imile e&longs;t, &longs;i
Terra abduceretur in verticem Antipodum, vbi &longs;uper
ficies, cui in&longs;i&longs;timus, excederet punctum, in quo fui&longs;&longs;et centrum,
nos ibi hæ&longs;uros: aut abreptos vlteriùs, eò auolaturos, &longs;eu po
tiùs ca&longs;uros. Ad aliud, quod quærit, quid eueniret lapidi, &longs;i
intra cauernam in meditullio Terræ excauatam, oppletamque
aqua, aut aëre constitueretur? Dicitur probabile e&longs;&longs;e, &longs;i Terra
quidem qua&longs;i magnes &longs;it, qui &longs;uis qua&longs;i radijs emißis attrahat
terrena: euenturum, vt lapis ineam cauernæ partem feratur, è
qua radij plures, confertiore&longs;que affluxerint; &, &longs;i &longs;upponan
tur ex æquo vndequàque affluere, fore, vtin medio &longs;u&longs;pen&longs;us Vnde &, quod rogat, cur lapis in puteum dimi&longs;&longs;us
fundum petat, non latera? Cau&longs;&longs;a e&longs;t in promptu, quòd plu
res, den&longs;iore&longs;que radij exparte fundi, ad quam e&longs;t tota Terræ
moles, adueniant, quàm ex parte vlla laterum aduenire
poßint.
ART. XV. XVI. XVII. XVIII. XIX. XX.
Et Magnetem ferrum, & Terram grauia trahe
reper in&longs;en&longs;ilia organula: &, Cur attractio pro
pe Terram non &longs;it &longs;en&longs;ibilior, quàm procùl.
tem non trabere &longs;ine organulis corporeis contendit: neque non
agit &longs;eriò, dum hamulos, catenula&longs;que, quatenus patitur imbe
cillitas, fingit. Dum ait R.
ri, quàm quòd Magnes, & ferrum &longs;ponte naturæ incitata in
mutuos amplexus accurrant; id eleganter quidem, &longs;ed non ita
vt res vocibus &longs;ubiecta intelligi poßit: quomodo &longs;cilicet vtrum
uis, ac &longs;peciatim ferrum inanime, ac inarticulatum, incitet
&longs;eip&longs;um, & nullare à Magnete emi&longs;&longs;a, diuinet tamen, quando
e&longs;t propè, & metiatur vireis, ac &longs;patium, è quo ver&longs;us ip&longs;um
in&longs;iliat. Neque verò dicere pote&longs;t emitti à Magnete quali
litatem quandam, quæ &longs;it merum accidens: cùm exinde diffi
cultatum inextricabilium &longs;eges &longs;ubna&longs;catur. Quod cau&longs;&longs;atur
videri oculis, nec palpari manibus poßint. Iniuriâ traducit Au
thorem R. P. qua&longs;i proptereà neget po&longs;&longs;e
qualitatem, qualem de&longs;cribit imprimere:
à Deo &longs;it, quicquid Magneti
impre&longs;&longs;um. Quod obiicit verò, vt ferrum à Magnete fortiùs è
propinquo, quàm, è longinquo trahitur, non &longs;ic ob&longs;eruari
trahi à terra lapidem, quatenus magis non ponderat, nec ve
locius initio cadit ad ba&longs;in turris, quàm ad fastigium: Patet
cau&longs;&longs;am e&longs;&longs;e, non quòd di&longs;crimen aliquod non &longs;it: &longs;ed quòd
euadere &longs;en&longs;ibile non poßit, quou&longs;que lapis ponderetur, inci
piatve cadere ex tanta altitudine, quæ non minorem habeat
trahitur, ad molem Magnetis.254. in 267.
ART. XXI. XXII. XXIII. XXIV. XXV.
Non e&longs;&longs;e Atomorum minùs, quàm Ari&longs;toteleæ
Materiæ tolerabilem in Religione po&longs;itionem.
ratione, calore, frigore, & cæteris rebus naturalibus iuxtæ
Atomorum &longs;uppo&longs;itionem dicta &longs;unt, ad &longs;tatum &longs;upernatura
lem: ac præ&longs;ertim cùm Atomi nihil aliud fint, quàm prima
Materies, quæ &longs;i prout a&longs;&longs;erta e&longs;t ab Ari&longs;totele, toleretur, a&longs;
&longs;umendo &longs;olùm, quòd à Deo creata &longs;it: tolerari &longs;anè poßint
Atomi, prout a&longs;&longs;eruntur non modò ab
&longs;ed etiam ab alijs, ac nominatim à Platone (qui cum illi&longs;-ne
iure ex&longs;ulet, vt R. P. loquitur, à Regno Philo&longs;ophico, con&longs;u
lendi Patres) a&longs;&longs;umendo &longs;olummodò, fui&longs;&longs;e illas à Deo creatas. Satis e&longs;&longs;e vult R. P. &longs;i dicamus halitus calidos, &c.
à corpori
bus exhalari: at non illi inepti, qui requirunt prætereà ex qui
bu&longs; nam corpu&longs;culis texantur i&longs;ti halitus, vt modum actionis
ip&longs;orum condi&longs;cant: quod & Plato po&longs;t alios fecit, & Demo
critus speciatim &longs;ic e&longs;t ex&longs;equutus, vt ideò Platoni ab Ari&longs;totele
præ&longs;eratur, & à Cicerone, Plutarcho, alij&longs;que mirè commen
detur. Exclamat R. P. conclamatum fore de Formis &longs;ub
&longs;tantialibus, &longs;iortus, & interitus nihil aliud &longs;int, quàm locales
quædam Atomorum motiones: exclamat, inquam, vt videtur,
ob Rationalem animam: cùm tamen, vt generali Effato de for
mis è materia educibilibus adhibetur exceptio Rationalis ani
mæ, &longs;ic adhiberi poßit Effato de accidentalibus: ac ip&longs;a Anima
aliunde &longs;it propriè futura &longs;ubstantia, quatenus &longs;ub&longs;i&longs;tit per
&longs;uam &longs;ub&longs;tantialem entitatem distinctam à materia, dicere
communis &longs;ententia non poßit. Quærit & quò &longs;int abitura
&longs;anctiora Religionis no&longs;træ my&longs;teria: idque, vt videtur, ob
mysterium augu&longs;tißimum Tran&longs;ub&longs;tantiationis: cùm tamen,
vt iuxta Ari&longs;toielea &longs;ententiam ex&longs;i&longs;tentia &longs;ub&longs;tantiæ &longs;ine
accidentibus, aut accidentium &longs;ine &longs;ub&longs;tantia defenditur vir
tute naturæ impoßibilis, &longs;ed poßibilis virtute diuina: eodem
modo, ac ij&longs;dem verbis iuxta Democriticam defendatur.267. in 276.
ART. XXVI. XXVII. XXVIII.
Actum
e&longs;&longs;e de Motu Teriæ, proponendo, non a&longs;&longs;e
rendo; &, Ferant ne magis Sacræ literæ Ter
ram in centro, quàm extra centrum circum
uolui.
C
tran&longs;lato
tum Telluris petitur vulgò argumentum ex &longs;agitta &longs;ursùm è
naui emi&longs;&longs;a, neque innauim recidente; nullum, inquam, prout
&longs;icuti mota naui, omnes motus &longs;iue nautarum, &longs;iue rerum,
quas ip&longs;i mouent, perinde fiunt, apparentque, ac &longs;i nauis quie&longs;
ceret, mi&longs;&longs;aque adeò &longs;ursùm &longs;agitta in
emi&longs;&longs;a, partem recidit: ita &longs;i Terram ver&longs;us ortum moueri
&longs;uppo&longs;uerimus, omnes motus no&longs;tri, rerumque à nobis mobi
lium, perinde fient, apparebuntque, ae &longs;i Terra quie&longs;ceret. lapisque adeò &longs;ursùm proiectus, in eundem Terræ recidet lo
cum, è quo proiectus fuerit;
rem, eiu&longs;que manum, &longs;uperaddit, intercedente manu, tantum
impetus lapidi, quantum oportet, vt &longs;uperet mundanum
proiectio, interim peruadit; eodem modo, quo nauis transferens
&longs;uperaddit &longs;agittæ, intercedente arcu, tantum roboris, quantum
e&longs;t nece&longs;&longs;e, vt &longs;uperet aëreum &longs;patium æquale illi, quod peruadit
interim eanauis pars, è qua facta emißio: Cùm, inquam, de
duci id po&longs;&longs;et; Author reipsâ ita deduxit po&longs;teriore Epi&longs;tola, vt
admonuerit quærendam ergo, ad impugnandum Terræ motum,
rationem veri&longs;imiliorem. Et quia poterat responderi alias
iam multas e&longs;&longs;e inuentas: ideò illas, e&longs;&longs;e o&longs;tendit magna ex parte
haud magis firmas. Iam R. P. hoc non fert, ac &longs;uperiore
ratione euer&longs;a, indignatur fui&longs;&longs;e cæteras convul&longs;as: qua&longs;i aut
eas expendere præoccupando non licuerit, aut &longs;it, cur magis,
quàm &longs;uperior vocari in examen non poßint, nec debeant. Et
traducit quidem Authorem R. P. qua&longs;i a&longs;&longs;eruerit moueri Ter
ram non diurna modò reuolutione circa axem proprium, verùm
etiam annuo motu circa Solem: vnde & ait tolerabilius fui&longs;&longs;e,
etiam per &longs;acras Literas, &longs;i a&longs;&longs;ertus fui&longs;&longs;et diurnus dumtaxat. Attamen, neque a&longs;&longs;erendo, &longs;ed proponendo &longs;olummodò de mo
tu Terræ actum e&longs;t; neque ea loca Scripturæ &longs;acræ, quæ aduer
&longs;us motum Terræ obiiciuntur, comperiuntur minùs aduer
&longs;us diurnum, quàm aduer&longs;us annuum e&longs;&longs;e comparata; neque
non præclare addit R. P. debere no&longs;tram Philo&longs;ophiam fidei
Chri&longs;tianæ e&longs;&longs;e con&longs;onam; &longs;ed &longs;upere&longs;t no&longs;&longs;e quid &longs;it di&longs;&longs;onum;
cùm non statim quicquid videtur repugnare Literis &longs;acris id
circò reuerà repugnat, vt rectè o&longs;tendit D. Augu&longs;tinus ad
uer&longs;us eos, qui dicunt cælum Sphæricum, cùm Scriptura dicat
exten&longs;um, vt pellem. A p.
276. in 281.
ART. XXIX. XXX. XXXI.
De Con
&longs;equutionibus ex Terra Planetis inter&longs;ita
improbatione.
O
Si moueri Terram inter Planetas per
&longs;ua&longs;um &longs;it, creditum quoque iri ip&longs;am e&longs;&longs;e
alijs
nem
nam, quæ docet A&longs;tra non ad hominum, aliarumve rerum ha
bitationem e&longs;&longs;e facta, &longs;ed vt illuminent, fœcundentque Terram. Verùm legitimas non e&longs;&longs;e huiu&longs;modi con&longs;equutiones, declara
tur, Tum ex eo, quòd o&longs;tenditur pari ratione deduci ea&longs;dem ex
placitis alijs, quæ à viris pijs, eruditi&longs;que defenduntur (cuiu&longs;
modi &longs;unt illa de rotunditate Terræ; de Luna eclip&longs;in patiente
ob Terram, vt Terrapatitur ob Lunam; déque ip&longs;ius &longs;uperfi
cie montibus, & conuallibus, terrenæ in&longs;tar interstincta: de
Terræ exilitate comparatè ad Stellas; aéque Luna adhûc lon
gè exiliore, quæ præ illis tamen habetur in magnis luminari
bus, atque ita de cæteris) Tum ex eò, quòd o&longs;tenditur, quàm
malè cohæreant cum Antecedente, ex quo deducuntur. Quod
autem
ctam ait à
profitetur Author &longs;e vel &longs;ola fama, ac non expectata promul
gatione legitima, ad id complectendum induci.281 in 288.
ART. XXXII. XXXIII. XXXIV.
Sit
ne ab&longs;urdum reputare Orbem magnum (&longs;eu
cœlum Solis) e&longs;&longs;e qua&longs;i punctum comparatum
ad Firmamentum; & Solem qua&longs;i vnam Fixa-
quantum Sol motus circa Terram; atque adeò quantum cælum
Solis e&longs;t, tantum erit & cælum
bem magnum.
nicani a&longs;&longs;umunt tam immanem e&longs;&longs;e Fixarum à nobis di&longs;tan
tiam, vt &longs;i
tus, nobis heic remanentibus, &longs;it appariturus nobis qua&longs;i pun
ctum: nimirùm ex hoc &longs;equitur,
&longs;i puncta, fore hoc orbe non minores. Ac Author quidem
habet diuer&longs;a, quod Stellæ &longs;unt, & quod apparent, vt dicendum
illicò e&longs;t: interim autem illi re&longs;pondent, cùm ea &longs;it Fixarum
di&longs;tantia, vt nulla ob&longs;eruatio &longs;it, qua definire illam liceat, &
ab omnibus merègratis, próque lubitu maior, aut minor a&longs;&longs;u
matur (nemine putà aliam rationem, quàm propriam &longs;iue opi
nionem, &longs;iue voluntatem habente) ideò tam po&longs;&longs;e &longs;e maiorem,
quàm alios minorem eam a&longs;&longs;umere: imò & tantò magis, quantò
exinde fit commendatior tum concinnitas, tum maiestas operum
Dei. Quod ve
vnam quampiam Fixarum, & Fixas e&longs;&longs;e qua&longs;i totidem
iubent illi attendere, veliuxta ip&longs;am communem &longs;ententiam
(quæ tam propè admouet Fixas) &longs;i Sol recedat, quantum Fixæ,
Fixæ accedant, quantum
& vna Fixarum, qua&longs;i
ART. XXXIV. XXXV. XXXVI. XXXVII.
Po&longs;&longs;e Solem è Fixis non minorem, quàm Or
bem magnum apparere: & veros omnium Stel
larum di&longs;cos in vnum compo&longs;itos vix apparen
ti di&longs;co vnius mediocris Stellæ exæquatum iri.
vi&longs;a di&longs;tinguere licet di&longs;cum apparentem à vero; cùm ille po&longs;
&longs;it e&longs;&longs;e pedalis, i&longs;te (hoc e&longs;t flammulæ facies &longs;ecundum diame
trum tran&longs;uer&longs;am) &longs;emidigitali non maior; ita in
non videntur, ni&longs;i per tenebras nocturnas, di&longs;tinguendi haud
dubiè &longs;unt di&longs;ci apparentes à veris. Itaque, &longs;i apparentes qui
dem
is triplò maior euaderet, quàm
tem pari modo in vnum di&longs;culi veri coaptarentur, is non maior
euaderet, quàm vniusEt
accepto harum
uerâ ampliùs) &longs;upra horizontem appareat; di&longs;ci quidem appa
rentes conficerent di&longs;cum ad
non Ex quo efficitur, vt mirum non &longs;it, fi
di&longs;cos. Heinc autem responderi pote&longs;t ad id, quod R.
cit de
di&longs;tantiam spectato; qua&longs;i nimirùm con&longs;titutus in ip&longs;o
magni centro, aut qua&longs;i centrum eius ex&longs;i&longs;tens, non poßit tantus
apparere, quantus ip&longs;emet
futurum, vt
foret exilißimus, apparens tamen tantus e&longs;&longs;et, qui totum ip&longs;um
O
claratur pleniùs exemplo flammulæ per noctem conspectæ.
A p. 293. in 301.
ART. XXXVIII. XXXIX.
Hùc accom
modari non potui&longs;&longs;e cau&longs;&longs;am, quæ redditur
vulgò, quare
mam, ita per parteis halituo&longs;as è flamma procedenteis vehe
menter illuminari, vt ab oculo computetur in vnam flammam
continuam: id tum repugnat (quatenus & nullum inter flam
mam veram, &longs;puriamque apparet di&longs;crimen; &, &longs;ivera flam
ma occultetur &longs;ola, nulla apparet &longs;puria; &, &longs;i verâ flammâ
præter foramen visâ, aër occultetur, &longs;puria nibilominùs appa
ret) tum aliunde accommodari nec Lunæ potest, nec ip&longs;is
lis, quarum &longs;pecies noctu magnoperè incre&longs;cit. Quamobrem
fuit longè commodiùs repetere cau&longs;&longs;am ex affectione oculi, pu
pillæ nempe dilatatione, & impreßione retinæ facta, donec ocu
lus in tenebris degit. Quippe cau&longs;&longs;a hæc non no&longs;tris modò flam
mis, & tam Lunæ, quàm
ip&longs;i
tus. Videlicet tunc paradoxum non erit, videri noctu
&longs;eu oculum videntem
facto, conspectóque qua&longs;i vna quapiam
A p. 301. in 306.
ART. XL. XLI. XLII.
Qua mente, & qua
tenus ex motu Terræ æ&longs;tus Maris deductus; &,
Po&longs;&longs;e exinde explicari varietates, quæ tam per
Æquinoctia, & Sol&longs;titia, quàm per Nouilunia,
& Plenilunia contingunt.
& de ip&longs;o Maris æ&longs;tu, quatenus e&longs;t vi&longs;us cum hac motus Ter
ræ hypothe&longs;i congruere; maximè verò quatenus aqua bis die
tim fluit, ac refluit, vt bis contingit in motu Terræ inæqualitas,
propter commi&longs;tionem diurni, & annui, respectu partis eiu&longs;
dem Terræ, qua, vt va&longs;e, contenta aqua, dum inæquali ductuQuòd porrò &longs;icut
Iupiter &longs;uos &longs;atellites &longs;ibi circumducens, dum interim vnà cum
ip&longs;is motu duodecenni transfertur per
vnà cum ip&longs;is totale quodam mobile; ita Terra Lunam &longs;ibi
circumducens, dum interim vnà cum ip&longs;a transfertur motu an
nuo per Zodiacum, vnum aliquod mobile totale cum ip&longs;a cen
&longs;eatur:
emittere quo&longs;dam veluti magneticos radios, quibus
bi circumducat, ac &longs;peciatim hoc mobile (Terram videlicet cum
Luna) Efficietur, vt quia hoc mobile pendebit à
veluti plumbum à clauo per filum; efficietur, inquam, vt, Quem
admodum plumbum &longs;egniùs vibratur, &longs;i infra appendatur
tur
Jta Terra per
tunc propter Lunam veluti infernè appen&longs;am prolixius euadat
qua&longs;i pen&longs;ile; & per Nouilunium velociùs, quòd tunc Luna ve
luti &longs;upernè impendens acceleret nonnihil motum. Quare &
exinde &longs;uperuenit quædam tam in
lunio inæqualitas, ob
quadraturas æ&longs;tuo&longs;iùs. Quòd autem prætereà hi fluxus, re
fluxu&longs;que intendantur ip&longs;is Sol&longs;titiorum,
temporibus; cau&longs;&longs;a e&longs;&longs;e pote&longs;t &longs;uperueniens tertia inæqualitas,
ob prolixiores, breuiore&longs;que diurni motus arcus (parallelos &longs;em
per æquatori acceptos) per Zodiacum; atque ita quidem, vt cùm
in
uer&longs;us motui annuo &longs;ecundum
vt æstus &longs;int per
A p. 306. in 313.
Po&longs;&longs;e & varietates alias ad locorum &longs;itus; &
acce&longs;&longs;us retardationem, quæ dietim fit, ad mo
tum Lunæ men&longs;truum, quatenus e&longs;t idem cum
diurno Telluris, referri.
&longs;eruatur, eadem affluxus, & refluxus in litoribus Maris de
prehenditur; &longs;icque ad varios littorum &longs;itus referri po&longs;&longs;unt di
uer&longs;itates, quæ mox memoratis generalibus accidentibus &longs;uper
ueniunt; vt vel exemplo nauiculæ, cui &longs;imiles in&longs;int inæqualita
tes, intelligi potest. Quòd autem affluxus ad littora fiat
diebus &longs;ingulis vnà propò horà (&longs;eu quatuor horæ quintis) tar
diùs, ex eo e&longs;&longs;e pote&longs;t, quòd cùm, vt iam dictum, Terra, & Lu
na vnum totale mobile &longs;int, & Terra &longs;uo motu diurno &longs;ic Lu
nam circum-rapiat, vt Luna tamen non penitùs, ob di&longs;tantiam,
ob&longs;ecundando, circulum vnum non ab&longs;oluat, ni&longs;i intra men&longs;em;
ac die bus proinde &longs;ingulis integra propè hora tardiùs ad meri
dianum perueniat, è quo pridie cum aliqua Terræ parte di&longs;ce&longs;
&longs;erit, Idcircò affluxus non præcisè redeat, cùm ip&longs;a eadem
ræpars ad meridianum eumdem redit, &longs;ed cùm redit Luna, quæ
est mobilis totalis qua&longs;i complementum. Epistolæ conclu&longs;io.
A p. 313. in 318.
1. l. 17. lege
6. l. 4.
1. p.
6. l. 5.
1 l. 17.
p. 3 l. 2
293. l. 10. lege
242. 13.
octingenties. 430. 25.
255. 17. collinees, 256 28. voce non.
270.
24. An&longs;toteleæ &longs;ententiæ. 285, 2 ad hoc.
QVA GRAVIA DECIDENTIA
ACCELERANTVR.
& religio&longs;ißimo, doctißimoque Viro,
PETRO CAZRÆO
natus es ad me dare, ac publici iuris &longs;imul
facere
naturali determinatur.
Agnoui verò imprimis illam &longs;in
gularem beneuolentiam, qua perrexi&longs;ti ob&longs;tringere
me, quæque e&longs;t &longs;anè tota ad tuam bonitatis eximiæ
indolem accepta ferenda. Promptum deinde fuit
memini&longs;&longs;e eruditæ Epi&longs;tolæ, qua ante duos annos ea
&longs;ignifica&longs;ti, quæ in meis illis,
tran&longs;lato,
dentium ea ratione accelerari, vt &longs;uperata &longs;patia temporibus
æqualibus, numerorum imparium progreßionem imitarentur.
Commemini etiam, cùm fui&longs;&longs;em conatus facere &longs;atis
in cæteris, expetii&longs;&longs;e me, vt quia neque Paralogi&longs;mum,
quem in Galileo cau&longs;abaris, animaduerti&longs;&longs;em, neque
experientia, aut ratio mon&longs;tra&longs;&longs;et quidpiam oppo&longs;i
tum;
gere, tum inuentam illam à te progre&longs;&longs;ionem me edo
cere. Volui&longs;ti id porrò nunc
&longs;tare, ac me vel ex eo deuinxi&longs;ti, quòd euulgare Medi
tationes de motu præclaras aggre&longs;&longs;us, hanc e&longs;&longs;e pri
mam volueris, quam non creditori profectò, qualem
me habes, per&longs;olueres; &longs;ed debitori, qualem me potiùs
ingenuè fateor, oppignerares. Heinc e&longs;t, cur licet ni
hil in me &longs;it, quod qua&longs;i par pari rependam; adnitar
tamen, quantum licet, te&longs;tari gratitudinem, eandem
tecum rem meditatus, ac eas dubitandi rationes, quæ
mihi &longs;e&longs;e inter legendum vltrò obtulere, reponens. Quippe lógè ab&longs;um abeo, quem tu me e&longs;&longs;e pro tua illa
rara comitate volui&longs;ti, dum decreui&longs;ti
ius Demon&longs;trationis. Is nimirùm &longs;um, qui aliud
nihil valeam, quàm difficultates qua&longs;dam excitare, ac
tibimet proponere, qui in hi&longs;ce rebus & diuti&longs;&longs;imè, &
curio&longs;i&longs;&longs;imè ver&longs;atus, ip&longs;as explanare facillimè po&longs;&longs;is. Interim autem non &longs;ubuereor, ne tamet&longs;i videarabs te
di&longs;&longs;entire, neque illicò manus dare, tu idcircò mihi &longs;u
cen&longs;eas: cùm ea &longs;is humanitate, eo in veritatem affe
ctu, vt non po&longs;&longs;is in me candorem, quem ego in te
probem, improbare.
II.
Principio verò, vt experiar, num rem &longs;atis ca
piam, de qua agitur; Quæri, ecce, mihi videtur,
ratione, &longs;eu proportione celeritas rerum decidentium incre&longs;cæt?
Videlicet &longs;upponimusrem nimis-quàm notam,
ne, quàm in medio; & in medio, quàm in ip&longs;o princi
pio. Supponimus rur&longs;us hanc velocitatem ita conti
nuò incre&longs;cere, vt ab ip&longs;o v&longs;que in&longs;tanti, quo mobile à
quiete recedit, illius motus magis, magi&longs;que continen
ter acceleretur; &longs;eu incrementa velocitatis plura &longs;em
per, ac plura vniformiter præacqui&longs;itis &longs;uper-addan
tur. Supponimus tertiò i&longs;thæc incrementa compa
rari po&longs;&longs;e aut cum partibus temporis, quæ vno tenore
&longs;uccedunt, aut cum partibus &longs;patij, quæ plures, plure&longs;
que continenter per curruntur. Supponimus quartò
po&longs;&longs;e accipi, &longs;iue de&longs;ignari primum quoddam tem
pus, vt minutum horæ &longs;ecundùm, &longs;iue interuallum in
ter duas pul&longs;ationes arteriæ, cui con&longs;equentia tempora
æqualia po&longs;&longs;int de&longs;ignari; adeò vt totum illud tem
pus, quod in decidendo mobile in&longs;umit, in plureis hu
iu&longs;cemodi æqualeis parteis di&longs;tinguatur. Supponimus
quintò po&longs;&longs;e accipi, &longs;iue de&longs;ignari primùm quoddam
&longs;patium, quod tempore nempe primo percurratur, vt
putà orgyiam, aut aliam men&longs;uram, cui aliæ æquales
po&longs;&longs;int accipi, in con&longs;equente &longs;patio, adeò vt totu illud
&longs;patium, quod à mobili decidente peiuaditur, intelli
gatur e&longs;&longs;e in plureis huiu&longs;modi parteis diui&longs;um. Sup
ponimus demùm po&longs;&longs;e accipi, &longs;iue de&longs;ignari velocita-
eiu&longs;dem primi temporis, & cui per con&longs;equentem
motum æquales aliæ &longs;uper-addantur, vt &longs;olent gra
dus gradibus in capacibus inten&longs;ionis qualitatibus &longs;u
per-addi; adeò vt, quæ velocitas in fine motus e&longs;t ac
qui&longs;ita, ac inten&longs;i&longs;&longs;ima e&longs;t, e&longs;&longs;e coalita cen&longs;eatur ex om
nibus velocitatibus, &longs;iue gradibus, qui per&longs;euerante
motu acqui&longs;iti fuerint, ijque inter&longs;e, &
æquales. Hi&longs;ce autem &longs;uppo&longs;itis, quia partes tempo
ris æquales, quæ primæ &longs;uccedunt, pauciores &longs;unt nu
mero, quàm quæ &longs;patij partes æquales decurruntur
po&longs;t primam; & qui velocitatis gradus acquiruntur
po&longs;t primum, ac &longs;unt veluti incrementa &longs;upperaddita,
comparari po&longs;&longs;unt, vt iam dictum e&longs;t, aut cum parti
bus æqualibus temporis, aut cum partibus æqualibus
&longs;patij; ideò difficultas, &longs;eu quæ&longs;tionis &longs;tatus is videtur
poti&longs;&longs;imùm,
acquirantur; quot &longs;tuunt partes temporis: an potiùs, quot spa
tij partes percurruntur?
requiritur,
habeant?
III.
&longs;e quemadmodum &longs;patia; &longs;eu, vt tot gradus velocitatis
æquales primo acquirantur, quot &longs;unt partes æquales
&longs;patij, quæ po&longs;t primum, primoque gradu &longs;uperatum
decurruntur. Siquidem toto &longs;patio diui&longs;o in decem
v. c. orgyias; qualis, quantu&longs;que e&longs;t velocitatis gra
dus in fine primæ orgviæ acqui&longs;itus, taleis, tanto&longs;que
vis acqui&longs;itos in fine &longs;ecundæ duos, in fine tertiæ treis,
in fine quartæ quatuor, & ita deinceps, quov&longs;que in At Galileus vult potiùs &longs;e ve
locitates habere &longs;icut tempora; &longs;iue gradus velocitatis
æqualeis primo tot acquiri, quot temporis partes pri
mæ æquales po&longs;t ip&longs;am fluunt. Addit verò &longs;patij par
teis continuò acquiri per parteis temporis æqualeis, ea
&longs;erie continua, qua numeri impares ab vnitate pro
grediuntur; adeò vt &longs;i primo momento, &longs;eu prima
æquali parte temporis mobile deciderit per vnam or
gyiam, decidat &longs;ecundo per treis, tertio per quinque,
quarto per &longs;eptem, ac ita deinceps. Addit rur&longs;us, quia
numeros &longs;ic progredienteis aggregando, quadrati con
tinuò numeri creantur; heinc fieri, vt &longs;i primo &longs;patio
illa continuò aggregentur, quæ æqualia æqualibus
percurruntur temporibus, &longs;patia tunc &longs;e habeant &longs;icut
quadrata temporum; hoc e&longs;t, vt quemadmodum pri
mo tempore e&longs;t &longs;uperatum vnum &longs;patium, &longs;ecundo
tempore &longs;int &longs;uperata quatuor, tertiò nouem, quaito
&longs;exdecim, & &longs;ic con&longs;equenter. Hæc autem melius in
telligi, declararique non valeant, quàm productis ex
eodem puncto duabus rectis lineis angulum in ip&longs;o
creantibus, ac in parteis quotcumque æqualeis diui&longs;is,
interducti&longs;que rectis lineis tum inter re&longs;pondentia
&longs;ingula heincinde diui&longs;ionis puncta, tum à quouis hu
iu&longs;modi in vtraque linea puncto &longs;ecundùm ductum
alteri lineæ parallelum. Tale e&longs;t &longs;chema, quod exhi
bui ad calcem prioris mearum illarum Epi&longs;tolarum,
quodque &longs;i heic iam repetiero, ac paulò accuratiùs, ob
factan. illam, de qua po&longs;teà, æquiuocationem, expo
&longs;uero, erit forta&longs;&longs;is operæ pretium.
IIII.
Itaque illud heic apponendo, vides primùm
heinc inde in parteis æqualeis, ad puncta D, E, F, G, H,
I, K, L (po&longs;&longs;ent autem in longè plureis continuatæ di
uidi) vt lineæ ductæ cùm inter ip&longs;a puncta, tùm ex ip&longs;is
in puncta M, N, O, totum &longs;patium KAL di&longs;pe&longs;cant
in triangula inter
&longs;e &longs;imilia, ac pror
sù æqualia. Cùm
po&longs;&longs;imus porto
habere punctum
A pro initio tem
poris, pro initio
&longs;patij, pro initio
velocitatis, quæ
tria heic in motu
&longs;pectantur, ac vna
cùm ip&longs;o inci
piunt; Po&longs;&longs;umus imprimis habere parteis æqualeis al
terutrius, aut vtriu&longs;que lineæ AB, AC pro partibus,
&longs;iue momentis æqualibus temporis ab initio fluentis,
adeòproinde, vt AE, v. g. repræ&longs;entet
tum, EG &longs;ecundum, GI: tertium, IL quartum. Po&longs;&longs;umus &longs;ecundò habere æqualia illa triangula pro
æqualibus &longs;patij partibus, quæ ab initio percurrun
tur; adeò vt ductâ &longs;eor&longs;im lineâ PQ ca&longs;um refe
rente per orgyias &longs;exdecim, Triangulum ADE
repræ&longs;entet primam orgyiam PR, quæ primò mo
mento percurritur; tria proxima, treis orgyias RS,
quæ &longs;ecundo; quinque &longs;equentia quinque orgyias
ST, quæ tertiò; & &longs;eptem &longs;uccedentia &longs;eptem or-Con&longs;tat autem exinde &longs;patia
aggregata ita &longs;e habere, &longs;icut quadrata tempo
rum; quandò ADE triangulum (&longs;patiumve
PR) e&longs;t vnum; quemadmodum quadratum
ip&longs;ius AE, hoc e&longs;t temporis vnius, e&longs;t vnum; &
aggregatum AFG (&longs;eu PS) e&longs;t quatuor; quem
admodum quadratum AG, duorum, e&longs;t qua
tuor; & aggregatum AHI (&longs;eu PT) e&longs;t nouem;
quemadmodum quadratum AI trium, e&longs;t no
uem; & aggregatum AKL (&longs;eu PQ) e&longs;t &longs;ex
decim; quemadmodum quadratum AL qua
tuor, e&longs;t &longs;exdecim. Po&longs;&longs;umus tertiò habere li
neam DE, pro primo gradu velocitatis acqui
&longs;itæ in fine primi temporis: quatenus, vt pri
mùm tempus AE non e&longs;t indiuiduum, &longs;ed in
tot in&longs;tantia, &longs;eu temporula pote&longs;t diuidi, quot
&longs;unt puncta, particulæve in ip&longs;a AE (aut AD)
ita neque gradus velocitatis indiuiduus e&longs;t, &longs;eu
vno in&longs;tanti, acqui&longs;itus totus; &longs;ed ab v&longs;que ini
tio per totum primum tempus incre&longs;cit, ac re
præ&longs;entari pote&longs;t per tot lineas, quot po&longs;&longs;unt
parallelæ duci ip&longs;i DE inter puncta linearum
AD, & AE; adeò vt quemadmodum illæ lineæ
continuo incre&longs;cunt à puncto A in lineam DE, &longs;ic
velocitas à principio motus continuò incre&longs;cat, & re
præ&longs;entata, qualis e&longs;t in interceptis primi temporis in
&longs;tantibus, per interceptas lineas, repræ&longs;entetur qualis
e&longs;t in vltimo in&longs;tanti eiu&longs;dem primi temporis, per
ip&longs;am DE inter vltima ductam puncta. Et quia ve
locitas deinceps incre&longs;cere pergens, repræ&longs;entari rur-
ductas inter omnia puncta &longs;uccedentia re&longs;iduarum
linearum DB, & EC, heinc efficitur, vt linea FG re
præ&longs;entet velocitatem acqui&longs;itam in fine &longs;ecundi mo
menti: linea HI acqui&longs;itam in fine tertij, & linea KL
acqui&longs;itam in fine quarti. Con&longs;tat verò inde, vt ve
locitates &longs;e habeant &longs;icut tempora; cùm ob triangulos
anguli communis, & parallelarum ba&longs;ium, notum &longs;it
e&longs;&longs;e vt DE ad EA, ita FG ad GA, HI ad IA, & KL
ad LA. Atque hæc quidem, vt clariùs con&longs;tet, qua
de re inter nos agatur.
V. Iam, Tu initio argumentum Di&longs;&longs;ertationis ita
partiris, vt duo præ&longs;tanda tibi proponas. Vnum,
que demon&longs;tres ea, quæ ab ip&longs;o de acceleratione Motus in na
turali de&longs;cen&longs;u grauium Libro &longs;ecundo nouæ &longs;cientiæ, &
toto Dialogo tertio dicta &longs;unt, non modò &longs;u&longs;picionibus meris,
vixque probabilibus coniecturis niti, &longs;ed ex principijs etiam
apertè fal&longs;is, euidentibu&longs;que paralogi&longs;mis omnia concludi; ex
quo con&longs;equens &longs;it, nouam illam &longs;cientiam euane&longs;cere, quam
ingenio&longs;o quidem, & plau&longs;ibili, &longs;ed inani tamen, & ca&longs;&longs;o
apparatu nobis Alterum,
G
&longs;ubstituas, rationemque, modum, ac men&longs;uram acceleratio
nis eiu&longs;dem in naturali de&longs;cen&longs;u grauium ex euidentibus, at
que indubitatis experientiis demonstres. Circa priùs de
inde caput, duo &longs;unt, in quibus occuparis; nam impe
tis
Galileo traditam: &
bus velocitatis, qui acquiruntur à mobili, dùm &longs;uper Circa po&longs;terius ex&longs;equeris
tria: Nam
Bilancem excogita&longs;ti;
inde accelerationis
gre&longs;&longs;ionem, qua &longs;uperantur &longs;patia temporibus æqua
libus, imitari progre&longs;&longs;ionem non numerorum impa
rium, &longs;ed rationis continuò duplæ, quam & exprimis
in de&longs;cen&longs;u globi à Luna v&longs;que in centrum terræ. Hæc
e&longs;t igitur Di&longs;&longs;ertationis &longs;umma.
VI.
Vt ordine autem de &longs;ingulis dicam, & à
Priore capite incipiam,
originem cæterorum
celerati Motus definitionem in&longs;tituerit, Motum æquabiliter
acceleratum dico eum, qui à quiete recedens temporibus æqua
libus æqualia celeritatis momenta acquirat. Rem autem
putas eius momenti, vt dicas
definitionem adulterinam e&longs;&longs;e, ac fal&longs;am; & quicquid
toto illo Libro de eodem motu accelerato, &longs;atis alioquin
ingeniosè
Improbas &longs;ubinde, quòd
certa, ac euidenti confirmauerit, &longs;ed ab eius tantum &longs;im
plicitate motibus naturalibus maximè congruente; à per
fecta cum demon&longs;tratis à &longs;e theorematibus con&longs;en&longs;ione; &
ab aperta, vt ip&longs;e quidem fidenter a&longs;&longs;erat, receptæ vulgò
definitionis ab&longs;urditate. Tum verò circa &longs;implicitatem
perpendere &longs;olùm me iubes, an non &longs;implicior &longs;it
definitio, quæ à cæteris vulgò v&longs;urpatur, dum Mo
tum æquabiliter acceleratum eum potiùs e&longs;&longs;e a&longs;&longs;e-
acquirit. Circa con&longs;en&longs;ionem autem &longs;olùm, bucis,
cinnè cohæreant;
e&longs;&longs;e paralogi&longs;mum, quo ille vulgarem, moxque re
latam definitionem ab&longs;urditatis apertæ damna
uit.
VII Ego intereà, optime Vir, neque video De
&longs;initionem a Galileo in&longs;titutam à te directè impu
gnari, fal&longs;itati&longs;ve vllius conuinci; neque agno&longs;co quî
magis vera, congruaque potuerit in&longs;titui. Quippe
memini&longs;&longs;e, aut potiùs adnota&longs;&longs;e diligenter oportet
agi heic de motu æquabiliter accelerato, &longs;iue cuius
celeritas continenter, vniformiterque incre&longs;cat, ne
que vllum &longs;it momentum con&longs;equentis temporis, in
quo motus non &longs;it velocior, quàm in quovis antece
dente, & in quo non eadem ratione ip&longs;a velocitas
augeatur. Fieri id porrò e&longs;t manife&longs;tum ex ijs, quæ
deducta iam &longs;unt; &longs;i æqualibus temporibus æqualia
celeritatis momenta, &longs;eu incrementa acquirantur. Nam vt repetamus &longs;uperiorem figuram, nemo dicat
celeritatem vniformiter incre&longs;centem po&longs;&longs;e meliùs
repræ&longs;entari, quàm diductione crurum anguli, linea
rumve AB, AC, quatenus complectuntur &longs;pa
tium, quod à puncto A magis continenter, vni
formiterque cre&longs;cere non po&longs;&longs;it: ac aliunde angu
lus BAC apertior, aut conductior (prout finge
tur maior, aut minor velocitas) valet v&longs;urpari. Vt autem rem magis ob oculos ponam; duco ec
ce lineam VX, per ip&longs;um apicem A, quæ cum li-
leis, & &longs;eruatâ eorum
dem angulorum men
&longs;urâ, ita fluere conci
piatur, vt totum &longs;pa
tium BAC peruadat. Tunc enim manife
&longs;tum e&longs;t portiones
huius lineæ continuò
veluti re&longs;ectas, inter
cepta&longs;que à lineis AB,
AC, cre&longs;cere &longs;emper,
&longs;eu maiores, maiore&longs;
que vniformiter e&longs;&longs;e; ac non portiones &longs;emel inter
ceptas perire, &longs;ed ip&longs;is permanentibus nouas, nouaf
que heinc inde continenter &longs;uper-acquiri. Cùm
verò etiam gradus velocitatis con&longs;imiliter cre&longs;cant,
&longs;iue maiores, maiore&longs;que vniformiter euadant, ac
&longs;emel acqui&longs;iti non pereant, &longs;ed ip&longs;is &longs;uper&longs;titibus,
per&longs;euerantibu&longs;que noua, atque noua momenta, &longs;iue
incrementa velocitatis &longs;uper-addantur; &longs;upere&longs;t, vt
quemadmodum linearum illarum incrementa fiunt,
&longs;ic fiant quoque velocitatum. Notum e&longs;t autem.
vt
acceptis partibus æqualibus lineæ AC, verbi cau&longs;sâ,
incrementa earum portionum, &longs;iue linearum paralle
larum interceptarum, acquirantur &longs;emper æqualia
&longs;ub æqualibus illis partibus. Nam, vt &longs;ub AE ac
qui&longs;ita e&longs;t linea DE, ita &longs;ub EG, acquiritur æqua
lis alia; cùm ip&longs;a FG &longs;it dupla ip&longs;ius DE; & &longs;ub
GI iterum alia; cùm ip&longs;a HI &longs;it eiu&longs;dem tripla; &
drupla; atque ita porrò, &longs;eu vlteriùs pergas, &longs;eu
alia puncta intra ea&longs;dem parteis lineæ AC, alia&longs;
que parallelas commemoratis interceptas, &longs;ingula&longs;
que &longs;uis punctis re&longs;pondenteis, accipias. Quare &
a&longs;&longs;umptis partibus æqualibus temporis per parteis
æqualeis lineæ AC repræ&longs;entatis,
&longs;eu incrementa velocitatis per parallelas repræ&longs;entatæ,
æqualia acquiri &longs;ub huiu&longs;modi partibus; adeò vt
qualis gradus velocitatis acqui&longs;itus e&longs;t in fine primi
temporis vnus, talis alius, hoc e&longs;t æqualis, &longs;it ip&longs;i &longs;uper
acqui&longs;itus in fine &longs;ecundi, ac &longs;int iam duo; & iterum
æqualis alius in fine tertij, ac &longs;in: iam tres; & rursùs
alius in fine quarti, ac &longs;int iam quatuor; atque ita de
cæteris, &longs;iue con&longs;equentibus, &longs;iue inter&longs;umptis.
VIII.
Sic itaque mihi videtur Motus æquabili
ter, hoc e&longs;t continenter, vniformiterque acceleratus
perquàm appo&longs;itè definiri is,
temporibus æqualibus æqualia celeritatis momenta
mentave)
po&longs;&longs;e ip&longs;um alia ratione concipi, aut de&longs;cribi talem. Nam quod &longs;pectat quidem ad illam à te laudatam
definitionem, qua motus æquabiliter acceleratus de&longs;
cribitur is,
menta acquirit:
exinde licear acceleratum æquabiliter motum? E&longs;to
enim &longs;patium percurrendum v. c. linea AB in par
teis æqualeis diui&longs;a ad puncta C, D, E, F, G, I, K. Decidat mobile ex A; & in C fine primæ partis ac
qui&longs;ierit primum velocitatis gradum; in D autem
duo iam &longs;int: in E tertium, quo
iuncto ad duos &longs;uperiores, per
&longs;euerantei&longs;que &longs;int tres; in F
quartum, & ita porrò, quo
v&longs;que in B acqui&longs;ierit nonum,
quo iuncto cum octo antece
dentibus &longs;int nouem. Iam cùm
quilibet horum graduum la
titudinem quandam habeat;
neque enim e&longs;t magis indiui&longs;i
bilis, aut ex indiui&longs;ibilibus
con&longs;tans, quàm pars AC, CD,
DE, quælibet-ve alia: ac idcir
cò ip&longs;e quoque incre&longs;cat æqua
biliter, vnoque tenore: repræ&longs;entetur primus gradus
per triangulum ALC, vt pote à puncto, &longs;eu angulo
A ad ba&longs;in LC æquabiliter, vnóque tenore cre&longs;cen
tem. Aptentur deinde ad CD duo triangula æqua
lia tum inter &longs;e, tum cum ip&longs;o ALC,
repræ&longs;entet illum, qui &longs;ecundò acquiritur, LCM au
tem primò aqui&longs;itum, ac per&longs;euerantem. Nihil e&longs;t
opus, vt de&longs;ude
velocitatem æquabiliter, eodemve tenore ex C in D,
quo incœperat, perrexeratque v&longs;que in D; vt feci&longs;&longs;et
enim, oporteret de&longs;criptum e&longs;&longs;e non quadrangulum
LD con&longs;tans ex duobus triangulis; &longs;ed trapezion CN
con&longs;titutum ex tribus. Eadem autem ratione mani
fe&longs;tum e&longs;t, &longs;i ad DE aptentur tria triangula, defutura
duo; &longs;i ad EF quatuor, defutura tria, & ita deinceps,
octo; vt proinde intelligamus totidem dce&longs;&longs;e ad acce
lerationis æquabilitatem velocitatis gradus, quot nu
merare licet triangulos ad læuam è regione cuiu&longs;que
partis, complendo &longs;ummam triangulorum APB. Con&longs;tare ergo videtur Motum æquabiliter accelera
tum definiti non po&longs;&longs;e illum,
æqualia celeritatis augmenta acquirat;
definitionem à Galileo traditam e&longs;&longs;e meritò præfe
rendam.
impugnanti obiicitur.
IX.
Ac tu id quidem non fers; &longs;ed ais,
&longs;atis non po&longs;&longs;e, quomodo
ingenij receptam communi con&longs;en&longs;u motus accelerati defini
tionem non modò fal&longs;am, atque impoßibilem exi&longs;timauerit;
&longs;ed patenti quoque, ip&longs;i&longs;que tyronibus obuio paralogi&longs;mo
eiu&longs;dem fal&longs;itatem palam, atque euidenter demon&longs;tra&longs;&longs;e adeò
prafidenter a&longs;&longs;eruerit; & quod ampliùs e&longs;t, etiam viru non
ineruditis per&longs;ua&longs;erit. Tum autem pergis,
miSi acceleratio motus,
bus &longs;patiis æqualia &longs;umeret velocitatu ineremema, e&longs;&longs;ent
&longs;ine dubio velocitates inter &longs;e, vt emen&longs;a spatia: At quoite&longs;. cúmque velocitates inter &longs;e &longs;unt vt emen&longs;a &longs;patia, debent
nece&longs;&longs;ariò ea spatia aut eodem, aut æquali tempore percur
ri. Si igitur velocitas acqui&longs;ita per totam AC eam
rationem habeat ad velocitatem acqui&longs;itam per AB, quam
quo spatium AB ab&longs;oluitur. Jmpoßibile est au
tem, vt corpus graue de&longs;cendens per AC eodem,
aut æquali tempore percurrat totam AC, quo per
currit partem eius AB, ni&longs;i motus fiat in instanti. Tam impoßibile e&longs;t igitur, vt velocitates in de&longs;cen&longs;u
grauium inter &longs;e &longs;int, vt emen&longs;a &longs;patia (ac proinde,
vt etiam æqualibus &longs;patiis cre&longs;cant æqualiter) quàm
impoßibile e&longs;t motum illum fieri in instanti. Pergis &longs;ub
inde,
ac Mathematicorum fidem! istudEt
tamen mirum quantum Galileus de hac, vt putat, &longs;ubtili,
clara, euidenti, ac Mathematica demon&longs;tratione &longs;ibi applauSed
illud multò adhûc mirabiùus, quod Lynceus Philo&longs;ophus, ac
Mathematicus, Lynceorumque princeps in tam aperta
luce cæcutiat, & vir eius nominis tam facilè deludatur.
X.
Ego verò, ô optime, ac religio&longs;&longs;ime Vir, quo
me cen&longs;u putem iri habitum, qui non &longs;im ex viris
non ineruditis, & eandem tamen cum Galileo opi
nionem per&longs;ua&longs;us &longs;im, ac perinde cæcutiam, perinde
deludar? Etenim cùm meam quæ&longs;is fidem, fatcor
ingenüè me non videre quem in eo notas Paralogi&longs;
mum; ac videri mihi nece&longs;&longs;ariò deduci, fore, vt &longs;i ve
locitas per totam AC acquiratur dupla illius, quæ
acquiritur per totam AB, ip&longs;a AC eodem, aut æqua
li tempore, quo AB percurratur. Rem certe in
hunc modum concipio. Intelligatur AC diui&longs;a in
duodecim parteis æqualcis, ac proinde eius dimidium
duo mobilia, quorum vnum di&longs;cedat ex A
ver&longs;us C, eodem momento, quo aliud ex D
ver&longs;us E. Notum e&longs;t, &longs;i vtrumque quidem
ferretur non accelerato, &longs;ed æquabili motu,
euenturum e&longs;&longs;e, vt velocitate illius ex&longs;i&longs;tente
dupla ad velocitatem i&longs;tius, illud perueniret
in C eodem momento, quo i&longs;tud in E; quo
niam &longs;patium ab illo &longs;uperatum foret vbi
que ad &longs;patium ab i&longs;to &longs;uperatum duplum, hoc e&longs;t,
forent ab illo &longs;uperatæ duæ partes, cùm ab i&longs;to vna;
ab illo quatuor, cùm ab hoc duæ, &c. quatenus &longs;pa
tia &longs;e haberent vbique vt velocitates, hoc e&longs;t veloci
tas per totam AC e&longs;&longs;et vbique dupla velocitatis per
totam DE. At verò, quoniam heic agitur de motu
non æquabili, &longs;ed continenter accelerato; ita de&longs;cen
dant rur&longs;us mobilia eodem tempore, vnum ab A,
aliud à D, vt &longs;uccrefcentibus continuò velocitatis gra
dibus, illud perueniendo in C acqui&longs;ierit duodecim,
hoc perueniendo in E &longs;ex: Quæ&longs;o quid impediat,
quo minùs illud perueniat in C eodem tempore, quo
i&longs;tud in E? Nam di&longs;crimen e&longs;t quidem inter mo
tum acceleratum, & æquabilem, quòd in æquabili
partes &longs;patiorum æquales percurrantur æqualibus
temporibus, vt &longs;ingulæ partes lineæ DE &longs;ingulis mi
nutis, & geminæ partes lineæ AC minutis item &longs;in
gulis; in accelerato non item: At in eo tamen motus
conueniunt, quòd vbique velocitas per totam AC
dupla &longs;it velocitatis per totam DE; & qua ratione
plures, plure&longs;que ex &longs;ingulis partibus lineæ DE
quoque plures, plure&longs;que ex geminatis lineæ AC. Ex hoc autem &longs;it, vt quemadmodum in æquabili mo
tu, DE percurreb
&longs;ex, ob geminas parteis i&longs;tius corre&longs;pondenteis &longs;ingu
lis illius, ita in accelerato, &longs;i DE percurratur tribus
minutis, AC percurratur &longs;imiliter tribus; quòd dum
primo minuto percurritur pars illius vna, percurran
tur i&longs;tius duæ, ob ge minam velocitatem; & ob ean
dem cau&longs;&longs;am, dum &longs;ecundo minuto percurruntur
illius duæ, percurrantur i&longs;tius quatuor, dum tertio
demùm illius tres, percurrantur i&longs;tius &longs;ex. Nim rùm
non alia ratione dici po&longs;&longs;ent habere &longs;e velocitates vt
&longs;patia: neque velocitas per totam AC dupla e&longs;&longs;et ve
locitatis per totam DE E&longs;to deinde vnicum mobile,
quod decedens ab A, tendat ver&longs;us C, & &longs;it rursùs
velocitas per totam AC dupla velocitatis per totam
AB, patet idem prorsùs dicendum de AC, re&longs;pectu
AB, quod dictum fuit de eadem re&longs;pectu DE. Nam
in æquabili quidem motu oporteret mobile percur
rere &longs;imul, &longs;eu primo minuto primam, & &longs;ecundam
parteis; &longs;ecundo &longs;ecundam, & quartam; ac ita porrò
quov&longs;que &longs;exto, percurreret, &longs;eu attingeret &longs;imul
&longs;extam, atque duo &longs;ecimam. In accelerato verò
e&longs;t nece&longs;&longs;e, vt percurrat &longs;imul vnam, & duas in pri
mo; duas, & quatuor in &longs;ecundo; treis, & &longs;ex in tertio;
atque adeò totam AB, & totam AC tempore eo
dem. Atque ego quidem rem itaconcipio.
XI Verum tu &longs;i m&longs;tas,
gi&longs;mi a&longs;&longs;umptio in motu vniformi, ac perpetuò &longs;ibi æquali
nece&longs;&longs;aria e&longs;t, & non vno modo tantum, &longs;ed pluribus in
telligi potest, quo modo velocitates &longs;int inter &longs;e, vt emen&longs;a
&longs;patia: licet eadem &longs;patia neque eodem, neque æquali tem
pore percurrantur. Pergis autem,
drantem; ac deinde BC ip&longs;i AB æquale, dimidio
quadrante percurrat; quis neget in
beri velocitatem eius, quæ fuit in B? & tamen
idem graue totam AC, & dimidium eius AB
non percurreret. Et hæc e&longs;t quidem tota tua ad
conuincendum paralogi&longs;mi Galileum proba
tio, ob quam continenter hæc verba &longs;ubiun
gis:
ratiocinatio merus Paralogi&longs;mus id óque nullo modo, vt ip&longs;e
gloriatur communem, &longs;anioremque aliorum &longs;en&longs;um erroris
reuincit, qui in naturali grauium de&longs;cen&longs;u volunt æqualibus
spatijs æqualia velocitatis momenta acquiri. An verò pa
tietur tua bonitas, &longs;i dicam po&longs;&longs;e cuipiam videri, e&longs;&longs;e
te potiùs, qui hoc loco incidas in paralogi&longs;mum? Ni
mirum videris &longs;ic argumentari, vt id, quod contro
uertitur, a&longs;&longs;umas pro principio, dum nihil aliud, quàm
&longs;upponis &longs;patium AB, percurri duplo temporis, quo
&longs;patium BC; & velocitatem in C, e&longs;&longs;e duplam eius,
quæ fuit in B; quæ ip&longs;a tamen e&longs;t controuer&longs;ia. Et
cùm &longs;oluenda e&longs;&longs;et ratio, qua conficitur fore, vt AC
percurratur eodem, aut æquali tempore, quo &longs;patium
AB, nihil aliud, quam conclu&longs;ionem negas, fore di
cendo, vt idem graue totam AC, & dimidium eius
AB eodem tempore non percurreret. Teneri certè
&longs;olutionemque, cùm &longs;i i&longs;ta quidem methodus &longs;uffi
ciat, nihil e&longs;&longs;e videatur facilius, quàm paralogi&longs;mi ar
guere vniuer&longs;um Euclidem. Et agno&longs;co quidem te
&longs;upponere tanquam rem nimis euidentem, totum
&longs;patium AC prolixiore tempore, quàm eius partem
AB percurri: &longs;ed cùm Galileus non neget e&longs;&longs;e illud
tempus prolixius, imò tale e&longs;&longs;e reuerâ &longs;upponat; ab
incommodo tamen arguit, probando prolixius non
fore, &longs;i velocitas acqui&longs;ita per totam AC dupla defen
datur illius, quæ acquiritur per totam AB: vnde &
videtur omnmò obiecta ratio fui&longs;&longs;e &longs;oluenda. Agno&longs;co
etiam te heinc moueri, quòd non &longs;atis appareat ratio,
cur &longs;i ex A in B acquiratur vnus velocitatis gradus,
acquiri alius ex B in C, per&longs;euerante primo, non
valeat. Sed cau&longs;&longs;a nimirùm intelligitur non modò
ex dictis in vulgarem definitionem; verùm etiam
maximè ex incommodo, in quod aliunde incidis,
dum con&longs;equenter loquens, vis &longs;patium BC percurri
dimidio temporis, quo AB; vt putà, quod AB vnico
gradu velocitatis BC, gemino percurratur.
XII. Nam, vt illud paucis deducam, &longs;equitur
exinde, vt tempore dato, quo decur&longs;a &longs;emel fuerit
pars AB, tempus aliud ip&longs;i æquale attingi nulla ra
tione valeat, ni&longs;i &longs;uperato &longs;patio infinito. Intelliga
tur enim linea AC infinitè producta, diui&longs;aque in
parteis CD, DF, EF, &c. ip&longs;is AB & BC
æqualeis. Qua ratione tu vis tempus, quo percurri
tur AB, e&longs;&longs;e duplum temporis, quo percurritur BC
velis oportet tempus id, quo percurritur BC e&longs;&longs;e
duplum eius, quo DE, & i&longs;tud illius, quo EF,
& &longs;ic deinceps; neque enim maior vnius,
quàm alterius e&longs;t ratio; ac in accelerato poti&longs;
&longs;imù n æquabiliter motu, de quo præ&longs;ertim
quæ&longs;tio heic e&longs;t. Quare & velis etiam opor
tet, vt cùm tempus, quo percurritur BC, &longs;it
dimidium temporis, quo percurritur AB; illud,
quo percurritur CD, &longs;it quadrans eiu&longs;dem
primi temporis; illud, quo DE, octans; quo
EF, pars decima &longs;exta; quo FG, trige&longs;ima &longs;e
cunda; quo GH &longs;exage&longs;ima quarta, &c. Por
rò hæc omnia tempora &longs;imul iuncta nunquam
æquabuntur primo tempori, quo decur&longs;um
fuerit AB (quandò procedentes hoc modo
fractiones relinquunt &longs;emper ex integro, to
tove quidpiam inexhau&longs;tum) ni&longs;i lineam, &longs;eu
&longs;patium infinitum admi&longs;eris, & parteis æqua
leis in eo infinitas, quæ infinitis analogis (&longs;eu
dimidiorum dimidiis in tempore ip&longs;o, aut
æquali, quo AB percurritur) contineri intel
lectis, re&longs;pondeant. Adderem heic etiam
incommodum aliud de &longs;patijs incre&longs;centibus,
& in fine cuiu&longs;libet æqualis temporis numerandis
&longs;ecundum rationem non modò duplam, verùm etiam
triplam, & ampliùs: &longs;ed res erit po&longs;teà vberiùs dicen
da. Adderem rursùs alia quoque, vt Quòd &longs;equere
tur lineam proiectorum, & illam &longs;peciatim, quæ de&longs;
cribitur à lapide &longs;ur&longs;um, & &longs;ecundum mali altitudi
nem, dum nauis mouetur, proiecto, non e&longs;&longs;e Parabo-
tum a&longs;cendendo con&longs;umi; ac proinde lapidem illum
neque peruenturum ad mali carche&longs;ium, neque reca
&longs;urum in pedem eiu&longs;dem: verùm i&longs;ta aut colliguntur
ex ijs, quæ &longs;unt dicta in Epi&longs;tolis, aut in promptu
&longs;unt, facileque occurrunt. Et de Definitione huc
v&longs;que.
æquè inclinatis planis.
XIII.
In&longs;ectaris &longs;ecundo loco, tanquam aliam
erroris cau&longs;&longs;am, Quod Galileus &longs;ibi dari, & gratis
concedi, inquis, po&longs;tulat,
mobilis &longs;uper diuer&longs;as planorum inclinationes acqui&longs;itos tunc
e&longs;&longs;e æqualeis, cùm eorumdem planorum eleuationes ponuntur
citatis ab eodem globo (exem
pli gratia) per plana CA, &
CD de&longs;cendente, in punctis
A, & D acqui&longs;itos, e&longs;&longs;e inter &longs;e
æqualeis, quòd æqualem, vel potiùs eandem eleua
tionem habeant, videlicet BC.
tum,
&longs;ufficiente experientia confirmatum; imò cùm rationes etiam
non de&longs;int, quibus oppo&longs;itum probabilius reddatur (nempe
gradus velocitatis per longius planum acqui&longs;itos gradi
per breuius planum acqui&longs;itis e&longs;&longs;e minores) id à Galileo non
peti, &longs;ed debuerat demon&longs;trari cùm præ&longs;ertim maxima pars
&longs;ub&longs;equentium theorematum hoc vnico postu ato nitantur. Quid enim certi ex incertis concludi pote&longs;t.
aut ex principie,
demonstrari?
exigimus, &longs;u&longs;piciones, ac veri&longs;imilitudines nulla ratione ad
mittimus,
inferuntur theoremata, &longs;uis illis principiis certiora, aut eui
dentiora e&longs;&longs;e non po&longs;&longs;unt, & nominatim &longs;olemne illud, &
quod totius &longs;cientiæ à Galileo excogitatæ firmamentum est,
spatia &longs;cilicet æqualibus temporibus emen&longs;a eam inter &longs;e
rationem ob&longs;eruare, quæ est inter numeros omneis impareis
continua &longs;erie ab vnitate procedenteis (quamvis aliunde
fal&longs;um demon&longs;trari non po&longs;&longs;et) neque ex præ&longs;uppo&longs;itis illis
principiis euidenter, neque aliunde &longs;ufficienter conclude
retur.
XIV.
Hoc autem loco non video primùm, quì
reprchendendus Galileus &longs;it, &longs;i quam propo&longs;itionem
non demon&longs;tratam, &longs;ed veri&longs;imilem &longs;olùm habuit,
non vt demon&longs;tratam, &longs;ed vt veri&longs;imilem duntaxat
exhibuit. Candidè nimirùm videtur egi&longs;&longs;e, neque
exegi&longs;&longs;e à Lectoribus, vt maiorem, quàm ip&longs;e Po&longs;tu
lato fidem haberent; &longs;ed illos potius qua&longs;i monui&longs;&longs;e,
ne ip&longs;um concederent, ni&longs;i deinceps agno&longs;cerent
con&longs;tabilitum variis ex eo deductis conclu&longs;ionibus,
quæ cum experientia planè con&longs;entirent. Deinde
cùm in &longs;cientijs, ac demon&longs;trationibus attinent bus
ad Mathe&longs;in puram, mera euidentia, non &longs;ola &longs;u&longs;pi
cio, aut veri&longs;imilitudo admittenda &longs;it: in &longs;cientijs ta
men Phy&longs;icis, ac mi&longs;ta Mathe&longs;i, quacumque &longs;e&longs;e Phy
&longs;ica, hoc e&longs;t caligo humanæ mentis in rebus natura
libus inue&longs;tigandis, ingerit; fœlices &longs;imus, &longs;i non Vnde
& videtur po&longs;&longs;e Po&longs;tulatum, &longs;i veri&longs;imile modò &longs;it, ac
neque ratione, neque experientia vlla oppugnetur, ad
mitti ad &longs;cientiam, quæ vtcúmque perfecta ab&longs;olutè
non &longs;it, eiu&longs;modi tamen &longs;it, cuius &longs;it humana imbe
cillitas capax. Ad hæc, addam-ne fui&longs;&longs;e rem mihi
quodammodò &longs;tupendam, acce&longs;&longs;i&longs;&longs;e ca&longs;u ad me i&longs;ta
con&longs;cribentem, nobili&longs;&longs;imum Senatorem Petrum
Calcauium virum omninò promouendis bonis arti
bus comparatum, puræque cum-primis Mathe&longs;eos
&longs;tudio&longs;i&longs;&longs;imum; ac vi&longs;a mihi præ manibus tua Di&longs;&longs;er
tatione, argumentóque cognito, innui&longs;&longs;e tran&longs;mi&longs;
&longs;um in hanc vrbem exemplum editi nuperrimè Libri
ab Euangeli&longs;ta Torricellio, qui Galilei &longs;ucce&longs;&longs;or exi
mius demon&longs;trauerit in eo i&longs;tud Po&longs;tulatum? Præ
tereo autem, vt copiâ illius videndi &longs;tatim impetratâ,
deprehenderim rem confectam quinque propo&longs;itio
nibus, ac Præmi&longs;&longs;o illo,
iuncta ex &longs;e moueri, ni&longs;i centrum commune grauitatis ip&longs;o
rum de&longs;cendat. Videlicet prima Propo&longs;itio e&longs;t,
G
eleuationem habentibus, con&longs;tituta: &longs;i eandem inter &longs;e ratio
nem homologè habeant, quam habent planorum longitudi
nes, habere æqualia momenta. Secunda,
æqualia fuerint, habere momenta in ratione reciproca longi
tud num eorumdem planorum. Tertia,
momenta e&longs;&longs;e in ratione homologa cum perpendiculis par
tium æqualium eorumdem planorum. Quarta,
la
dem planorum. Quinta autem e&longs;t ip&longs;um Po&longs;tulatum
mobilis &longs;uper diuer&longs;as planorum inclinationes acqui&longs;itos tunc
e&longs;&longs;e æqualeis, cùm eorumdem planorum eleuationes &ecedil;quales
&longs;unt.
XV. Verùm, ne ad alia excurram, quàm quæ
ip&longs;emet ex Galileo commemoras, improbas ec
perimentum, quo ille e&longs;t conatus h
a&longs;&longs;erere, quodque ad&longs;cripta figura &longs;ic refers E
tribus, aut quatuor digitis à pariete remoto &longs;u&longs;pendatur, &longs;it
que AB, De&longs;criptaque in pariete recta CD horizonti
parallela, globus B à perpendiculari eductus v&longs;que ad alti
tudinem rectæ CD manu altollatur, nempe ad C; indeque
liberè dimittatur. Tum globus idem in uit
&longs;olùm de&longs;cendet ad punctum B, &longs;ed eodem impetu vlteriùs
v&longs;que ad D, aut proximè ad illud, a&longs;cendet.
globus idem è puncto E &longs;uspendatur, & item ad altitudinem
pari modo ad eandem rectam CD, aut proximè ad eam
con&longs;cendet ver&longs;us H. Jmò, &longs;i ex F &longs;u&longs;pen&longs;us attollatur ad
I, inde feretur, v&longs;que ad K. Per diuer&longs;os igitur illos arcus
decidens globus, &longs;emper ad æqualem altitudinem con&longs;cendit. Ergo è quolibet de&longs;cen&longs;u æqualem acquirit impetum; ni&longs;i
enim e&longs;&longs;et impetus æqualis, globum ad æqualem altitudinem
non attolleret. Quid ni igitur idem quoque faciat globus,
&longs;i per plana CB, GB, IB de&longs;cendat?
etiam e&longs;t globum per illa, aut &longs;imilia plana decidentem, æqua
lem tali de&longs;cen&longs;u impetum, ac proinde æqualem quoque ve
locitatis gradum acquirere. Subinde autem, vt o&longs;ten
das quàm hæc &longs;int incerta, incohæcentia, &c.
mis quidem ne&longs;cio,
ratione &longs;u&longs;pen&longs;i, ac librati alitùs in Etruria, quàm in Gal
lia a&longs;&longs;urgant; at heic neque tam propè ad horizontalem li
neam, neque per diuer&longs;os arcus ad eam æqualiter accedunt. Nempe filo pedum quatuor cum dimidio &longs;u&longs;pen&longs;us globus ad
lineam horizontalem tribus infra centum pedibus
propiùs quàm duobus digitis nunquam acceßit. At centro
nouem tantum digitis &longs;upra lineam horizontalem accepto,
filóque duorum pedum con&longs;tituto, iam globus ad lineam ho
rizontalem vno digito, quàm anteà propiùs acceßit. Vbi
verò centrum &longs;eptem infra lineam horizontalem digitis a&longs;
&longs;umptum est, vix ad quatuor à linea horizontali digitos
globus a&longs;cendit. Concludis idcircò his verbis,
igitur fide
&longs;um, ac per quo&longs;cumque arcus librarum, ad æqualem &longs;em
per altitudinem a&longs;&longs;urgere? aut quomodo ex re adeò euiden
ter fal&longs;a petere au&longs;us e&longs;t testim
XVI.
Imprimis porrò non retices ip&longs;e dictum
e&longs;&longs;e à Galileo demi&longs;&longs;um ex C globum a&longs;cen&longs;urum
ctum ab illo a&longs;&longs;eueranter a&longs;&longs;urrecturum globum
ad eandem altitudinem, aut veritatis te&longs;timonium
ex re fal&longs;a ab ip&longs;o peti; qua&longs;i intellexerit globum a&longs;
&longs;equi altitudinem exqui&longs;itè, &longs;eu præcisè eandem. Et
certè non modò dixit ip&longs;e
turum interuallum quoddam perexiguum;
&longs;am attigit, ob quam ita fiat; referens eam putà ad
impedimentum partim aëris, partim fili; de quo vtro
que heic dicerem, ni&longs;i iam dictum &longs;atis copiosè in
Epi&longs;tolis memoratis foret. Deinde, quód globus ad
horizontalem lineam propiùs ad H, remotiùs ad
Ka&longs;cendat, quàm ad ip&longs;um D; videri pote&longs;t cau&longs;&longs;a
per&longs;picua, neque infringere vim experimenti. Nam
quod &longs;pectat quidem ad H, res ideò contin git, quòd
quoties clauus defigitur inter A, & horizontalem
lineam, breuitas tum fili, tum &longs;pati
arcus de&longs;cribitur, minùs præ&longs;tet impedimenti: vnde
& abfui&longs;&longs;et globus adhûc propiùs, &longs;i fui&longs;&longs;et clauus
infra E defixus, vti & longiùs, &longs;i &longs;upra ip&longs;um Quod
verò ad K, res minùs e&longs;t mira; quòd quoties clauus
defigitur infra horizontalem lineam, dimi&longs;&longs;us ex I
globus non per totum arcum IB decidat, &longs;ed per
inferiorem &longs;olùm eius partem, in quam perpendicu
lariter cadit; vnde & minùs adhûc, minu&longs;que re&longs;i
lii&longs;&longs;et, &longs;i defixi&longs;&longs;es clauum inferiùs, quou&longs;que globus
non potui&longs;&longs;et ad lineam attolli; veluti & magis, ma
gi&longs;que, &longs;i &longs;uperiùs, quou&longs;que clauo defixo in linea, Ex quo effici
tur, vt cùm res propriè attendenda non &longs;it, vbi cla
uus infra lineam defigitur, quòd tunc libratio &longs;implex
non &longs;it, &longs;ed mi&longs;tio duorum motuum, quorum im
petus &longs;e mutuò retundunt; &longs;it verò propriè atten
tenda, cùm clauo &longs;upra lineam defixo, vibrationis
motus &longs;implex e&longs;t; ideò non &longs;it exi&longs;timandum illam
qualemcumque interuallorum inæqualitatem in
terturbare negotium; ac poti&longs;&longs;imùm quidem, cùm
ip&longs;a ordinata &longs;int, ac eandem inter &longs;e, quàm fili, &
arcus prolixitates proportionem &longs;eruent. Ad hæc,
id videtur præ&longs;ertim e&longs;&longs;e ob&longs;eruatione dignum in
his pendu orum vibrationibus, quòd, Si quatuor di
&longs;tinctos g obos quatuor di&longs;tinctis filis &longs;ic appendas,
vt primi longitudo &longs;it vnius, v. c. pedis, &longs;ecundi qua
tuor, tertij nouem, quarti &longs;exdecim; experturus &longs;is,
vbi omnes dimi&longs;&longs;i &longs;imul fuerint, quartum perfectu
rum vnam vibrationem eodem tempore, quo ter
tius interim perfecerit duas, &longs;ecundus treis, & primus
quatuor. Scilicet exinde intelligitur, tum pendulo
rum vibrationes tantò &longs;egnius fieri, quantò earum
arcus planiores, &longs;iue inclinatiores &longs;unt; tum inclina
tiones arcuum men&longs;uratas &longs;ecundum varias perpen
diculi, &longs;eu fili longitudines, habere &longs;e perinde vt qua
drata temporum, ac vibrationes habere &longs;e recipro
vt ip&longs;as radices; &longs;icque rem eximiè quadrare ad &longs;u
periùs expo&longs;itam motus æquabilis rationem; tum
globum quartum non acquirere impetum ad eleua
tionem nece&longs;&longs;arium, ni&longs;i tempore duplo tertij, tri
plo &longs;ecundi, quadruplo primi; ac e&longs;&longs;e quidem im-
tempore impetus exprimitur à quarto &longs;emel, exprimi
à tert
XVII.
Quod attinet autem ad comparationem
arcuum CB, GB, IB, cum ip&longs;is planis punctim
notatis inter extrema eadem; tu &longs;ic in&longs;tas, vt licet
totum id e&longs;&longs;e verum concederetur, quod dicitur de
impetu globi per diuer&longs;os arcus librati, vrgeas
e&longs;&longs;e rationem, aut meritò &longs;altem videri po&longs;&longs;e aliam,
cendentis globi per diuer&longs;a plana. G
quis,
& eatenus &longs;olum eius de&longs;cen&longs;us interturbatur, quatenus à
recto, & perpendiculari cur&longs;u ad circularem cogitur, at
que adducitur: at præter impedimentum ex varia plano
rum inclinatione, adhûc maius, dum globus etiam magis
à perpendiculari de&longs;cen&longs;u di&longs;trahitur; tantò minoribus in
&longs;uper momentis globus per planum de&longs;cendit, quan ò mi
nùs accliue fuerit, vt facilè omnibus notum e&longs;t. Verùm
non video quî id concludas; quatenùs non a&longs;&longs;umis
planum, quantò minùs decliue e&longs;t, tantò e&longs;&longs;e quo
que prolixius. Etenim notum quidem e&longs;t acquiri
minores velocitatis gradus in minus decliui, quod
&longs;it decliuiori æquale, at, &longs;i vt minùs decliue, ita etiam
prolixius &longs;it, notum quoque e&longs;t velocitatem in fine
illius quæ&longs;itam e&longs;&longs;e po&longs;&longs;e æqualem velocitati in fine
decliuioris acqui&longs;itæ, prolixitate nempe de&longs;cen&longs;us par
uitatem incrementorum velocitatis compen&longs;ante. Interim autem æqualitas impetus in B acqui&longs;iti, &longs;iue
per arcum, &longs;iue per planum contingat globi delap&longs;io,
ex eo videtur con&longs;equi, quòd &longs;ilum &longs;upernè globum
ret infernè, & &longs;ine filo arcus marmoreus, aut
perfectè po
beretur. Atque id quidem tantò magis, quantò idem
Galileus o&longs;tendit arcum CB, & planum CB eodem,
&longs;eu æquali tempore percurri; ac pari modo arcum,
& planum GB, & porrò arcum quemlibet non ma
iorem quadrante cum plano vnà terminato. Quin
etiam cùm o&longs;tenderit percurrere globum eodem, &longs;eu
æquali tempore quoduis planum inter quodlib
cumferentiæ circuli punctum, & infimum punctum,
quale e&longs;t heic B, con&longs;titutum, vt putà &longs;emper exæ
quato illi tempori, quo percurritur diameter circuli
eiu&longs;dem perpendicularis; elicitur quoque exinde, vbi
ea omnia plana fuerint in eandem reducta altitudi
nem, diuer&longs;a quidem tempora fore, &longs;ed impetum
nihilominùs parem. Atque eadem quidem o&longs;tendit
præ larus vir Ioannes Bapti&longs;ta Balianus Genuen&longs;is,
edito hac dere libello, qui eodem ip&longs;o anno, quo Ga
lilei Liber prodijt, argumento &longs;umpto ab ip&longs;is pen
dulorum vibrationibus: &longs;ed, vt præmonui, nihil e&longs;t
nece&longs;&longs;e maiorem Galilei Po&longs;tulato a&longs;&longs;erere fidem,
quàm ip&longs;e a&longs;&longs;ertam voluerit; dum eatenùs &longs;olùm
adhibendam petijt, quatenus deductæ ex eo conclu
&longs;iones cum experientia con&longs;entirent.
XVIII.
Id prætereo, quod &longs;ub
globi ad eandem altitudinem, non &longs;atis rectè colli
gi impetus æqualitatem; quoniam id aduer&longs;
recitandæ tuæ rationi, atque experientiæ: vti & dum
cau&longs;&longs;am petis ex eo,
deatur:
quam nihil obiicis, inter breuitatem, & decliu
tem &longs;patij; tum familiari experientiæ de rebus deor
sùm impactis, quæ impetu pari deicctæ tantò emer
gunt altiùs, quantò incidentia e&longs;t magis perpendi
cularis. Attingo ergo potiùs id, quod &longs;upere&longs;t,
dum id &longs;ugillas, quod Galileus &longs;e e&longs;&longs;e &longs;æpiùs exper
tum ait,
globum æneum per excauatum in longiore tigillo alueolum,
in quacumque tigilli &longs;upra horizontem eleuatione de&longs;cenden
tem, perpetuò tantum præcisè temporis in de&longs;cen&longs;u per pri
mum totius percurrendi spatij quadrantem, quantum in
trium reliquorum decur&longs;u in&longs;ump&longs;i&longs;&longs;e: ex quo &longs;ine dubio con
&longs;equens e&longs;&longs;et, &longs;patia æqualibus temporibus decur&longs;a in ea
e&longs;&longs;e ratione, quæ reperitur inter numeros impareis ab vnita
te procedenteis. Nimirùm, vt o&longs;tendas ea, quæ ex i&longs;tis
qua&longs;i principiis con&longs;equuntur, aut inferuntur, e&longs;&longs;e ip
&longs;is certiora, aut cuidentiora non po&longs;&longs;e:
erroribus obnoxium e&longs;t, & exploratu adcò difficile, vt nihil
inde certi concludi po&longs;&longs;e videatur. Enimverò, vtcum
que experiundi modus difficilis &longs;it, obnoxiu&longs;que er
roribus; non idcircò tamen experimentum conuin
citur fal&longs;um. Tuum certè illud de Libra, cui totus
po&longs;teà inniteris, quot quæ&longs;o, vel te deducente, er
roribus obnoxium e&longs;t? quàm exploratu difficile?
&
ip&longs;um tamen fal&longs;um non habes? Cùm profectò illo
te&longs;tetur &longs;e &longs;altem centies rem explora&longs;&longs;e, & experi
mentum &longs;emper ita &longs;ucce&longs;&longs;i&longs;&longs;e, vt vix vlla vnquam
differentiola interce&longs;&longs;erit; videri pote&longs;t non e&longs;&longs;e tua
ties &longs;altem, accurati&longs;&longs;imè expertum, ac ip&longs;am fal&longs;am
deprehendi&longs;&longs;e: aut rationem certè congruam afferas,
qua impo&longs;libilem demon&longs;tres. Et tamen, neque te
vel &longs;emel ip&longs;am explora&longs;&longs;e, fal&longs;amque comperi&longs;&longs;e di
cis, neque vllam rationem profers: &longs;ed cau&longs;aris &longs;olum
modo explorandi difficultatem; quam & repetis,
dum po&longs;tquam retuli&longs;ti tempora ab illo notata, no
tatis nempe, expen&longs;i&longs;que ponderibus aquæ, quæ è
clep&longs;ydra interim fluxi&longs;&longs;et:
videt, quàm hic ob&longs;eruandi modus incertus &longs;it, & quàm
difficile, ne dicam impoßibile, tempus vtriu&longs;que illius de&longs;
cen&longs;us ad exactam men&longs;uram exigere, vel eo maximè no
mine, quòd in tanta celeritate initia, & fines horum mo
tuum &longs;atis præcisè aduerti, notarique po&longs;&longs;e non videantur.
Sed nihil e&longs;t opus in&longs;i&longs;tam ad arguendum id non
&longs;ufficere; ni&longs;i aliunde aut resfactu impo&longs;&longs;ibilis de
mon&longs;tretur; aut ob&longs;eruator probetur fui&longs;&longs;e malæ fidei,
ac indiligens, & difficultates præcauere ne&longs;cius. Ad
derem quemadmodum ip&longs;e rem explorare fuerim
conatus, tum dimi&longs;&longs;o per aërem globo, tum dela
bente globulo per tubulos vitreos etiam orgyiis dua
bus longiores, facto&longs;que nunc magis, nunc minùs de
cliueis, & adnotatis partibus æquis tum ad parietem,
&longs;ecundum quem globus decideret, tum ad vtram
que oram alueoli in tigno excauati, & tubulum quem
que continentis; ac &longs;imul adhibitis &longs;ociis, qui adno
tarent &longs;inguli parteis &longs;ingulas, quæ interim pertran
&longs;irentur, dum ip&longs;e temporis momenta nunc pul&longs;atio
nibus arteriæ, nunc itibus, reditibu&longs;que penduli di-
tim a&longs;&longs;ignatis &longs;igni&longs;icarem: verùm memini rem ad te
per&longs;criptam; & circa hæc nimius iam &longs;um.
tium, ad explorandum impetus-ne vt &longs;patium incre&longs;cat.
XIX.
Venio igitur ad Po&longs;terius caput, &longs;ecun
damue partem tuæ Di&longs;&longs;ertationis; in qua &longs;cilicet re
cepi&longs;ti te veram, ac certam de Motu accelerato &longs;cien
tiam fal&longs;æ, ac incertæ Galileanæ &longs;ub&longs;tituturum; & in
qua profe&longs;&longs;us te iterùm omnia, quæ ab illo con&longs;cri
pta &longs;unt, fal&longs;a, ac inania e&longs;&longs;e demon&longs;traturum; prouo
cas me primum ad
tamet&longs;i ego tenuitatis con&longs;cius per&longs;onam Arbitri, lu
dici&longs;que, quam mihi humani&longs;&longs;imè iteratò defers, re
cu&longs;o; iteratò profe&longs;&longs;us nihil aliud à me, quàm rationes
qua&longs;dam dubitandi ex&longs;pectari po&longs;&longs;e. Et
dem experientia petitur,
aut graue aliud corpus quodcumque per aërem sponte natu
ræ deorsùm cadit, ac percutit. Indubitatum enim e&longs;t,
pergis,
ci&longs;e percutientis corporis e&longs;&longs;e velocitatem, quantus impetus,
quantaque ip&longs;a percußio fuerit. Impetus enim omnis, &
percußio ex velocitate est; imò impetus ip&longs;e velocitas est,
nulloque hæc abinuicem di&longs;crimine dirimuntur, vt meritò, pro
inde, qua ratione accre&longs;cit velocitas, eadem impetus, & per
cußio augeantur. Hactenus nihil e&longs;t, quod non probem.
Pro&longs;equeris autem:
graue quodcumque ex qualibet altitudine per aërem cadens,
& percutiens, vt libet, perpetuò ex altitudine dupla duplo
quadruplóue fortiùs percutere: velocitas igitur quoque ex
altitudine dupla, duplò maior e&longs;t, & tripla, aut quadrupla,
&longs;i tripla, quadrupláue altitudo &longs;uerit: ac proinde velocitas,
spatiis æqualibus, non autem æqualibus temporibus, æqualia
momenta acquirit. Quæ&longs;o verò heic patere, religio&longs;i&longs;
&longs;imè Vir, me meam te&longs;tari h
quod tu a&longs;&longs;umis,
prorsùs experientiâ con&longs;tat; neque tu vllam &longs;pecia
lem affers, ex qua res, vt tibi, ita mihi con&longs;tet. Ac
deducis quidem deinceps, qua&longs;i &longs;ecundam experien
tiam, id, quod in Libra expertus es: &longs;ed interim circa
hanc primam, cæcutio planè, neque agno&longs;co, qui
rem facilè exploraris. Et explora&longs;&longs;e tamen quis hæ
reat, quandò i&longs;thæc &longs;ubi
lileus, nullo (vt credibile e&longs;t) facto ip&longs;ius periculo, tanquam
fal&longs;am, atque impoßibilem, eodem paralogi&longs;mo re-
ceptam, & ex eadem experientia &longs;ine dubio dedu
ctam, conatus e&longs;t reuellere. Si ex altitudine dupla,
inquit, duplò maior percußio e&longs;t, vt puta ex A du
pla eius, quæ ex B, erit & velocitas dupla. At
velocitas dupla e&longs;&longs;e non pote&longs;t, ni&longs;i graue, æquali,
imò eodem tempore, totum spatium AC, & di
midium eius AB percurrat, quod tamen e&longs;t impoßibile. Nec percußio igitur, nec velocitas dupla e&longs;t, ex altitudine
dupla Do
obuta, & facili adeò turpiter delu&longs;um e&longs;&longs;e; mirorque item
vehementer tales, támque apertos eius errores, non modò à
nenune hactenus e&longs;&longs;e reprehen&longs;os, &longs;ed tanquam prima
Quandò, inquam, hæc &longs;ubiicis, nemo profectò fa
cilè hæreat, qum ip&longs;e, expertus, illa videris, quæ
neque Galileus, neque alij viderunt.
XX.
Quod meattinet; cùm lapidem video ex vna,
ex duabus, ex tribus, ex quatuor orgyiis cadentem in
terram; agno&longs;co quidem e&longs;&longs;e ictum, atque idcircò
quàm ex vna, ex tribus, quàm ex duabus, ex quatuor
quàm ex tribus; verùm e&longs;&longs;e duplò præcisè maiorem
ex duabus, quàm ex vna, triplò ex tribus, quadruplò
ex quatuor, nulla penitùs ratione agno&longs;co. Neque
enim po&longs;&longs;um id di&longs;picere ex cauitate in terram facta,
aut penetratione in ip&longs;am; quoniam neque lapis du
plò profundiùs cauat, penetratque ex dupla altitudine,
aut triplò ex tripla; neque cognitus e&longs;t aut gradus
re&longs;i&longs;tentiæ, quo talis terra obnititur; aut progre&longs;&longs;us,
quo cre&longs;cit re&longs;i&longs;tentia, dum quò inferiùs tenditur,
eò partes terræ minùs &longs;eu deor&longs;um, &longs;eu in latera ce
dere, compelli, ac &longs;ubire po&longs;&longs;unt: vt habita proinde
ratione huius re&longs;i&longs;tentiæ, colligere valeam id, quod
ad duplam penetrationem ex altitudine dupla dce&longs;t,
non aliunde e&longs;&longs;e, quàm ex huiu&longs;modi re&longs;i&longs;tentia. Sic
cùm video fi&longs;tucam in palum delap&longs;am ex &longs;implici,
dupla, aut tripla altitudine: quandoquidem neque
video palum defigi profundiùs in terram, duplo qui
dem ex dupla, aut triplò ex tripla altitudine; neque
per&longs;pectum habeo quo gradu, in qualibet profundi
tatis parte ip&longs;i vrgenti re&longs;i&longs;tatur; aduerto quidem
maiorem ictum, maioremque impetum, ac veloci-
que ex tripla, quàm ex dupla, &c. At e&longs;&longs;e illam du
plo præcisè maiorem ex dupla, triplò ex tripla, &c. nulla penitùs ratione per&longs;picio.
Sic, dum graue
quoduis ex dupla, triplaue altitudine decidens rem
&longs;ubiectam commouet, contundit, confringit: Sic, dum
cadens in cuneum &longs;cindendo ligno accommodatum,
ip&longs;um compellit, adigit, figit: Sic, dum cadens in ip
&longs;am manum, aliámue partem corporis, ip&longs;am vrget,
deprimit, lædit: Sic, dum alia huiu&longs;modi diuer&longs;imo
dè peraguntur; maiorem quidem &longs;emper ictum, &longs;ine
impetum, ac velocitatem ex altiore ca&longs;u fieri nullus
hæreo; at ex ca&longs;u duplò altiore duplò maiorem fieri,
triplò ex triplo, &c. qui di&longs;cernam prorsùs non habeo.
Quocirca bea&longs;&longs;es me valdè, &longs;i experientiam, aut &longs;al
tem modum experiundi &longs;ubindica&longs;&longs;es; cùm dicas &
rem experientiâ in graui quocumque facilè con&longs;tare;
& Galileum, cætero&longs;que eruditos viros coniicis &longs;ic
fui&longs;&longs;e &longs;ocordeis, vt nullum ip&longs;ius periculum fecerint;
feci&longs;&longs;e autem eos, qui vulgarem definitionem accele
rati motus tradiderunt primi.
XXI.
Addo videri po&longs;&longs;e me non ab&longs;que ratio
ne hacce de re ambigere; & coniicere ictum, percu&longs;
&longs;ionemque, atque idcircò impetum, velocitatemque
maiorem duplò non haberi, ni&longs;i ex altitudine qua
drupla; triplum, ni&longs;i ex nonupla; quadruplum, ni&longs;i
ex &longs;exdecupla, atque ita porrò iuxta numerorum qua
dratorum &longs;eriem. Nam Primò, &longs;it vas cylindricum
erectum, & continens aquam ad certam altitudi
nem, exempli cau&longs;sâ vnius pedis: Certum e&longs;t aquam
te (& ab ip&longs;a quidem &longs;uperficie) vt per&longs;picuum fit vel
ex vehementia, qua ex&longs;ilire deprehenditur, forami
ne ad ba&longs;in aperto. Aperiatur ergo foramen, & &longs;u
perfusâ leniter aquâ, ita vt contineatur &longs;emper ad
eandem altitudinem, excipiatur aqua, quæ interim
effluet, dato tempore, v. c. &longs;extantis minuti, ac &longs;it
illius men&longs;ura certa, exempli gratiâ, congius. Vt
deinde tempore eodem, & per idem foramen ex&longs;i
liant duo congij, & aqua proinde &longs;it duplò compre&longs;
&longs;ior, ad quam nam v&longs;que altitudinem adaugendus
erit, complendu&longs;ve cylindrus? Ad duplam-ne &longs;olum?
Non &longs;anè, &longs;ed omninò ad
Et vt ex&longs;iliant
tres, ad triplam-ne? Haud-quaquam profectò, &longs;ed
ad nonuplam. Et vt ex&longs;iliant quatuor, ad quadru
plam ne? Minimè gentium, &longs;ed ad &longs;exdecuplam.
Quin
poterit etiam aliunde res facillimo negotio notari, &longs;i
repleto &longs;iue ad labium, &longs;iue ad certam v&longs;que altitudi
nem cylindro, & aperto foramine, totáque aqua vno
tenore, nullamque refundendo effluente, notentur in
va&longs;e aquæ decrementa æqualibus temporibus facta. Quippe &longs;i interuallum vltimi decrementi fuerit vnius
v. c. pedis, erit interuallum penultimi trium, ante
penultimi quinque, antecedentis &longs;eptem, ac ita &longs;em
per procedendo per &longs;uccedenteis impareis: vnde & &longs;i
primi temporis initio fuerit altitudo pedum &longs;exde
cim, erit initio &longs;ecundi nouem, tertij quatuor, quar
ti vnius. Cùm ex&longs;ilitio verò aquæ continenter fiat
ex continente impetu, quo à &longs;uper&longs;tante vigetur, &
impetus i&longs;te nihil differat à continente velocitate,
An-non planum e&longs;t intelligere impetum, ac velocita
tem duplò maiorem fieri non ex altitudine dupla,
&longs;ed penitùs ex quadrupla; triplo non ex tripla, &longs;ed ex
nonupla, & ita deinceps? Secundò, &longs;i alligatus vno
&longs;ui extremo ad parietem funis prælongus, altero ex
tremo dependeat ex fulcro, ac appen&longs;o pondere certo,
v. c. vnius libræ, ten&longs;ione &longs;it leni inter ip&longs;a extrema:
verò digitis verò, ita abducatur, vt vltro citróque horizon
taliter vibretur, &longs;eu eat, ac redeat certo tempore (erunt
autem itus, reditu&longs;que omnes æqui-temporanei, &longs;eu
tam primi, quam vltimi, tam longi, quàm breues
eiu&longs;dem prorsù, durationis) &longs;itque tempus tantum,
quantum inter&longs;titium ab vna artenæ pul&longs;atione ad
aliam Vt fiat funis duplò inten&longs;ior, & itus, reditu&longs;
que ip&longs;ius euadant duplò velociores, hoc e&longs;t æquali
tempore duo; quantum, putas, erit ponderis adden
dum? An duplum?
Non; &longs;ed quadruplum.
Et vt
fiat triplo, &longs;intque adeo itus reditu&longs;que eodem tem
pore triplò velociores, &longs;eu plures: an triplum dum
taxat' Nequaquam, verum nonuplum. Et vt qua
druplò, an quadruplum? Haud certè, &longs;ed &longs;exdecu
plum. Cùm pondera porro æqualia primo &longs;uperad
dita &longs;e perinde habeant ad creandum hanc velocita
tem, ac partes æquales altitudinis, per quas pondus
demittitur: An non intelligi rursùs licet, quemadmo
dum velocitas non acquiritur duplò maior ex dupli
cato pondere, &longs;ed planè ex quadruplicato; ita duplam
quoque non ex duplicata altitudine, &longs;ed ex quadru
plicata acquiri?
XXII.
E&longs;t etiam Tertiò heic repetendum, quod
iam antè dixi de globis ad fila appen&longs;is, & liberè ire,
redireque permi&longs;&longs;is. Videlicet globus appen&longs;us ex
vno v. c. pede, dup ò quidem plureis vibrationes per
agit, quam appen&longs;us ad quatuor, triplo, quàm ap
pen&longs;us ad nouem, quadruplo, quàm appen&longs;us ad &longs;ex
decim; &longs;ed interim tamen &longs;ecundus &longs;patium conficit
dup ò maius, quàm primus, tertius triplò, quartus
quadruplò eodem tempore; ac velocitas interim ac
qui&longs;ita, impetu&longs;que ad perpendiculum expre&longs;&longs;us, non
vt &longs;patium pertran&longs;itum, &longs;ed vt tempus elap&longs;um &longs;e
habet. Ego certè rem &longs;ic intelligo.
Sit linea per
pendicularis AB in pariete ducta, diui&longs;aque in &longs;ex
decim pedes; ac &longs;int appen&longs;i quatuor globi, vnus
ad primum, alius ad quartum, tertius ad nonum,
po&longs;tremus ad decimum&longs;extum. Siquidem tamet&longs;i
debeant, ne inter mouendum &longs;e&longs;e interturbent: om
neis tamen &longs;chemate vno repræ&longs;entari nihil prohibet. Ducantur heinc inde duæ lineæ angulum &longs;tatuentes
in A, qui à perpendiculo bi&longs;ecctur, &longs;intque v. c. IA,
KA; & centro A; agantur inter illas arcus CD ad
mum
&longs;extum-decimum; qui &longs;imiles proinde erunt, pares
videlicet portiones &longs;uotum cuiu&longs;que circulorum eo
dem angulo men&longs;uratæ. Ducantur & &longs;ubten&longs;æ ar
cuum; & adnotentur qua&longs;i &longs;agittæ, &longs;eu appellati &longs;inus
ver&longs;i, lineæ nimirùm LM, NO, PQ, RB; cùm
&longs;int altitudines, quibus globi delabuntur ex linea AI
(vbi ad illam abducti, ex ea dimittuntur) in ip&longs;um
perpendiculum; primus putà ex C in M, &longs;ecundus
ex E in O, tertius ex G in Q, quartus ex I in B. Abducantur proinde globi ad memoratam lineam
AI, vt &longs;uas, exinde dimi&longs;&longs;i, vibrationes peragant, ad
lineam AK, aut quam-proximè terminandas. Nam &
quamuis quilibet globus, &longs;eu longiùs, &longs;eu breuiùs di
mi&longs;&longs;us, & &longs;eu moueri incipiat, &longs;eu de&longs;inat, vibrationes
omneis æqui-temporaneas &longs;ortiatur, temporibu&longs;ve
paribus perficiat; proportio tamen &longs;emper e&longs;t, quoties
&longs;ub æquali, eodemue angulo accipiuntur. Dimittan
tur & globi &longs;imul, ac peruenire concipiantur ad v&longs;
que perpendiculum. Quoniam tunc vt filum AO
quadruplum e&longs;t fili AM, & filum AQ nonuplum,
filum AB &longs;exdecuplum; ita altitudo NO dupla e&longs;t
altitudinis LM, & altitudo PQ nonupla, altitudo
RB &longs;exdecupla; quo pacto interuallum quoque per-
tium GQ nonuplum, &longs;patium IB &longs;exdecuplum: Id
circò, cùm aliunde ob&longs;eruemus tempus, quo globus
&longs;ecundus peruenit ad O, e&longs;&longs;e duplum temporis, quo
primus peruenit ad M, & tempus, quo tertius ad Q,
triplum; tempus, quo quartus ad B, quadruplum; Id
circò, inquam, intelligimus, impetum, &longs;eu velocita
tem, quæ acquiritur ex E, aut N in O, & ex G, aut
P in
ad velocitatem acqui&longs;itam ex C, aut L, in M, qua
&longs;e habet impetus, &longs;eu velocitas, quæ acquiritur ex A
in O, in Q, in B, ad velocitatem acqui&longs;itam ex A in
M; &longs;eu comparando oppo&longs;itè, vt illam ad illam, &longs;ic
i&longs;tam ad i&longs;tam. Hoc autem habito, quoniam im
petus, &longs;eu velocitas acqui&longs;ita ex E in O non e&longs;t ac
qui&longs;itæ ex C in M quadrupla, &longs;ed dupla; & acqui&longs;ita
qui&longs;ita ex I in B, non &longs;exdecupla, &longs;ed quadrupla e&longs;t:
quatenus quidem experiundo ob&longs;eruare licuit, con
&longs;titutam pilam &longs;upra planum libellatum, appo&longs;itum
que ad M, ad O, ad Q, ad B, dum percuteretur, pro
pellereturque à globis incurrentibus, a&longs;&longs;equi velocita
tem, excurrereque, non iuxta numeros quadratos,
quales &longs;unt &longs;patiorum CM, EO, GQ, IB; &longs;ed iuxta
radices ip&longs;orum, qualia &longs;unt & tempora, vnum, duo,
tria, quatuor. Quamobrem & fuit iteratò procliue
intelligere percu&longs;&longs;ionem quoque à re &longs;ecundum per
pendiculum cadente factam, &longs;equi rationem non
quadratorum, &longs;eu &longs;patiorum, &longs;ed radicum, &longs;eu tem
porum; atque ita, quò cadens graue vehementiùs
feriat duplò, triplò, quadruplò, cadere debere ex al
titudine non duplò, triplò quadruplò; verùm, quadru
plò, nonuplò, atque &longs;exdecuplò maiore.
quàm velocitates e&longs;&longs;e &longs;icut spatia.
XXIII. Verumtamen, hi&longs;ce dimi&longs;&longs;is, acceden
dum e&longs;t ad &longs;ecundam, peculiaremve experientiam,
cui totam &longs;cientiam &longs;uper-ex&longs;truis, & de qua in hunc
modum præfaris.
rientiam, cum fœnore etiam exhibeam, adiungam & aliam,
à nullo mortalium hactenus ob&longs;eruatam, quæ & priorem
perfectißimè includat, & non rationem &longs;olùm, quâ celeritas
in naturali de&longs;cen&longs;u grauium augetur, &longs;ed eiu&longs;dem quoque
celeritatis pene incredibilem modum, ac men&longs;uram, exacti&longs;- Pergis declarando ecqua illa &longs;ie
tuiu&longs;cumque materiæ, ex vnius diametri altitudine cadens,
duplum &longs;ui ponderis, hoc e&longs;t, præter pondus quod &longs;ine im
petu in æquilibrio retineret, aliud &longs;ibi æquale attollat; &
ex altitudine duarum diametrorum, triplum; ex tribus dia
metris, quadruplum; & ita deinceps: adeo vt ex quauis
altitudine cadens, &longs;emper (vltra æquilibrium) toties pro
prium pondus multiplieatum attollat, quot in tota, vnde
cadit, altitudine diametri continentur. Subiicis, rem exag
gerando,
pote &longs;implicißimam, capacißimàmque, natura &longs;ingulariter
amare videtur, men&longs;uram, ac modum, tam velocitatis
motus in de&longs;cen&longs;u grauium, quàm virtutis eius motricis,
quæ in eadem velocitate continetur, &longs;uâ nobis diametro exhi
beat: adeo vt ex decem, aut centum diametrorum altitudine
decidens, eum acquirat impetum, qui attollendis decem, aut
centum &longs;imilibus globis, in altera lance impo&longs;itis, &longs;ufficere
poßit, &longs;i materiæ conditio id patiatur. Addis & quid
ip&longs;e ob&longs;eruaueris.
beum vnius vnciæ, ex altitudine &longs;ex pedum, &longs;iue dia
metrorum centum quatuordecim cadentem, vncias toti
dem vltra æquilibrium, hoc est, libras &longs;eptem, &
vncias tres in altera lance impo&longs;itas, &longs;uo impetu eleua&longs;&longs;e,
non &longs;ine ingenti eorum qui præ&longs;entes aderant admiratione,
ac stupore. Tum & hæc habes.
diametris experiri placuerit, non admodùm magna opus
erit diligentia: at &longs;i è maiore altitudine idem tentare pla
cuerit, tum in hac, vt in cæteris Phy&longs;icis experientiis,
modis occurrendum erit; vt ne fortè ex conditione materiæ
effectus impediatur, nó&longs;que ex errore, aut ex ignorantia, id
impoßibile arbitremur, quod &longs;olius materiæ vitio, ac defectu,
in certis circum&longs;tantiis minùs ex animi &longs;ententia &longs;uccedit.
Paginas de
inceps ali
quot in&longs;umis,
vt ea incom
moda de&longs;cri
bas, & mo
dum, quo il
lis occurra
tur, tradas;
depicta &longs;cili
cet Bilanco,
quæ ip&longs;i&longs;&longs;i
ma heic ap
pingitur, agi
na putà im
mobili, & al
tera lancium
&longs;u&longs;pen&longs;a in
aëre, altera
&longs;upra men
&longs;am CD qui
e&longs;cente, cum
impo&longs;ito pondere, ac &longs;peculatore ad&longs;tante, qui ad
quamque vel minimam eius elationem attendat (id
que dum globus manu H dimi&longs;&longs;us incidit in alterius
re&longs;pondet con&longs;imilis F) ac in&longs;uper vtraque lance ca
tenulis ferreis à &longs;capo AB per intermedios circulos,
triangulo&longs;-ve, dependente. Denique autem &longs;ubiun
gis,
lus,
con&longs;tet (quod quilibet &longs;ine tanto apparatu, tantáque diligen
tia facillimè experiri potest) globum quemcumque, ex vnius
diametri altitudine, po&longs;&longs;e (vltra æquilibrium) pondus &longs;ibi
æquale, & ex duabus diametris duplum pondus attollere.
Prætereo autem demon&longs;trationem non alio nixam
fundamento, quàm ipsâ experientiâ à te &longs;uppo&longs;itâ;
prætereoque item, quod iterùm &longs;ubdis,
pari certitudine constare, quod antè dictum e&longs;t, nihil ad pro
po&longs;itionis veritatem, atque euidentiam opus e&longs;&longs;e, vt ex al
tiore di&longs;tantia, tantóque apparatu experientia inquiratur,
quæ ex aliquot diametrorum altitudine plu&longs;quam abundè;
ac facillimè habeatur.
XXIV.
Et tale e&longs;t quidem tuum experimentum.
Ego autem, humani&longs;&longs;ime Vir, grati&longs;&longs;imo primùm
animo complector liberali&longs;&longs;imum erga me affectum;
ac deinde etiam tibi gratulor, quod primus morta
lium excogitâris quemadmodum negotium vi&longs;um
difficile reuocari ad trutinam po&longs;&longs;et. Nempe quan
tumvis res non videatur pro tua &longs;tare &longs;ententia; fuit
tamen tua &longs;olertia dignum, id in mentem inducere,
vnde examen improbum, quacumque ex parte huiu&longs;
modi foret, po&longs;&longs;et ca&longs;tigari. Ac &longs;i res quidem &longs;ic &longs;e
haberet, vt enarrati abs te videtur, reputari po&longs;&longs;et
penitus confecta; nullumque e&longs;&longs;et dubium, quin
quam veram &longs;ub&longs;titueres iure: at res potius ita &longs;e ha
bet, meo quidem iudicio, vt Galileanam confirmare,
euertere tuam omninò videatur. Ecquid-nam verò,
inquies, Tu igitur meus amicus mihi referenti non
credis; ac virum me habes malæ fidei, dum hæres, id
ne verum &longs;it, quod ip&longs;e me fui&longs;&longs;e expertum enarro? Ab&longs;it hoc à me, optime virorum, qui habeo te po
tiùs plenum fidei, & &longs;ummo candore, finceri&longs;&longs;ima
que &longs;inceritate vi&longs;a narrantem. Sed patietur &longs;anè
&longs;inceritas tua, vt, quod &longs;upere&longs;t, &longs;i quid erroneum
videbitur, culpam coniiciam aut in quidpiam non
&longs;atis fortè animaduer&longs;um, vt omnes &longs;umus homines;
aut, &longs;i malis, etiam in illos, quorum operâ v&longs;us fueris,
quibu&longs;ve referentibus cen&longs;ueris pro tua bonitate non
e&longs;&longs;e negandum a&longs;&longs;en&longs;um. Itaque cùm tua verba
relegens, deprehendam te nihil aliud tibi, tanquam
ob&longs;eruatum à te vindicare; quàm illud, quod iam re
tuli,
altitudine &longs;ex pedum, &longs;iue diametrorum centum quatuorde
cim cadentem, vncias totidem vltra æquilibrium, hoc e&longs;t li
bras &longs;eptem, & vncias treis in altera lance impo&longs;itas &longs;uo
impetu eleua&longs;&longs;e. Itemque illud, quod po&longs;teà impedi
menta memorans,
edoctus &longs;um, qui adhibita omni indu&longs;tria globum vnius vn
ciæ ex altitudine &longs;ex pedum in lancem &longs;ubiectam, viginti
quinque, aut triginta vicibus dimittens, ter &longs;olùm centrum
attingere, & pondus perfectè attollere potui.
quam, ita deprehendam, non cau&longs;or tuam fidem,
quam cum per&longs;ua&longs;ione aliqua non vera (re familiari Cùm ad
dis autem prætereà generale e&longs;&longs;e, vt pro numero dia
metrorum, quibus idem globus dimi&longs;&longs;us abfuerit à
lance, pondera cleuet &longs;uo paria; qua&longs;i cùm id præ
&longs;titerit in certo quodam numero, non valeat citra
illum plureis, vltrà pauciores eleuare; hoc e&longs;t, quod
peto mihi condones, vt dicere liceat, in veritatis gra
tiam, te aut &longs;atis non attendi&longs;&longs;e, aut alijs etiam ni
miùm credidi&longs;&longs;e.
XXV.
Vt &longs;altem liceat quid-nam mihi contige
rit, commemorare; Tu &longs;æpe adeò repetii&longs;ti non e&longs;&longs;e
magno apparatu, magnaque diligentia opus ad
peragendum experimentum, vt ni&longs;i argumentis &longs;u
perioribus fui&longs;&longs;em oppo&longs;itum per&longs;ua&longs;us, vix induxi&longs;
&longs;em in animum (nihil &longs;cilicet hæ&longs;itans, imò hæ&longs;itan
di pudore &longs;uffu&longs;us) periculum facere vllum. Feci
tamen, & ip&longs;a præ&longs;ertim à te inculcata facilitate in
uitatus; vnde & obuiam primò Bilancen, qua numu
larius &longs;olebat nuper monetæ argenteæ &longs;ummam ali
quot librarum Marcarum non-numeratam appen
dere, probaréque, a&longs;&longs;umendam duxi. Quoniam ve
rò tu a&longs;&longs;erebas
quilibet cuiu&longs;cumque materiæ ex vnius diametri altitudine
cadens, pondus attollat &longs;ibi æquale, præter illud, quod in &ecedil;qui
librio &longs;ine impetu retineret,ideo &longs;ufficere putaui, &longs;i
globum marmoreum, quem habebam præ manibus,
duorum cum &longs;extante digitorum pedis Pari&longs;ini dia
metro, ac vnciarum proximè decem, Libræ itidem
Pari&longs;inæ pondere, ad experiundum v&longs;urparem. Ap
paratis ergo ponderibus variis, quæ ex æquo cum
tam (à &longs;uppo&longs;ita nempe tabula) duplum eiu&longs;ce pon
deris, hoc e&longs;t vncias prope viginti; ac &longs;ubinde elatum
globum vna &longs;ui diametro &longs;upra fundum alterius lan
cis con&longs;tantis in aëre, placidè in ip&longs;am dimi&longs;i. Tum
autem verum quidem fuit attolli ex ip&longs;ius ca&longs;u op
po&longs;itam lancem cum ponderis duplo; at quia vidi
interim ip&longs;am &longs;upra expectatam attolli altitudinem,
idcircò &longs;tatim duo intellexi, alterum po&longs;&longs;e idem pon
dus ex altitudine minore, alterum po&longs;&longs;e ex ip&longs;a ea
dem, pondus adhûc maius attolli. Et aduocatis cer
tè amicis, qui ad lancis elationem, emotionemve à
tabula, me globum dimittente, attenderent, aut me
attendente globum ip&longs;i dimitterent, res ita &longs;ucce&longs;&longs;it,
vt lanx &longs;u&longs;tentata cum duplo eodem pondere elata
fuerit dimi&longs;&longs;o globo non modo ex diametro vna,
verùm ex dimidio etiam diametri, etiam ex triente,
quadrante, &longs;extante, octante, dextante; ac vice ver&longs;a,
vt dimi&longs;&longs;o globo ex eadem vnius diametri altitudi
ne, elata lanx fuerit cum impo&longs;ito pondere, non
modo duplo, &longs;ed etiam triplo, quadruplo, quin
tuplo, & ampliùs. Experiri etiam con&longs;equenter lu
buit, an &longs;altem globus decidens ex duplo altitudinis
(diametrorum &longs;cilicte duarum) eleuaret duplum eius
ponderis, quod &longs;ummum mox extulerat; &longs;ed longè
&longs;anè abfuit; ac magis adhûc, vt ex triplo triplum, ex
quadruplo quadruplum.
XXVI.
Quandoquidem verò ip&longs;e globum plum
beum vnius vnciæ v&longs;urpâras; ideò talem quoque
v&longs;urpandum cen&longs;ui, plumbeum &longs;cilicet, ac vnius
continere digiti be&longs;&longs;em, ac idcircò partem Pari&longs;ini
pedis decimam-octauam. Cæterùm idem mihi eue
nit, quod circa globum marmorum; impo&longs;itis enim
in lance &longs;uffulta duabus vncijs, extulit eas globus
&longs;en&longs;ibiliter non ex altitudine modo diametri vnius,
&longs;ed ex dimidio etiam eiu&longs;dem, etiam ex triente, qua
drante, &longs;extante, octante, dextante, imò, & ex vncia,
duodecimáve diametri parte. Ac rur&longs;us ex eadem
diametri vnius altitudine, non duas modò extulit
vncias, verùm etiam treis, etiam quatuor, quinque,
&longs;ex, &longs;eptem, dua&longs;que drachmas in&longs;uper, quadrantem
ve vnius vnciæ. Et cùm experiri iterum placuerit,
an duplum huius ponderis eleuaretur ex ca&longs;u globi
à duplo altitudinis, triplumque ex ca&longs;u à triplo, &c. deprehendi dimi&longs;&longs;o globo ex diametris duabus alti
tudinis, attolli non duplum, hoc e&longs;t, vncias quatuor
decim cum &longs;emi&longs;&longs;e; &longs;ed vncias &longs;olummodò nouem,
cum be&longs;&longs;e, aut dodrante duntaxat. Quo pacto de
inceps ex diametro tertia extulit non triplum, hoc
e&longs;t viginti vnam vncias cum dodrante; &longs;ed vncias
&longs;olummodò duodecim, ac ferè dimidium; & ex dia
metro quarta extulit, non quadruplum, hoc e&longs;t vn
cias viginti nouem; &longs;ed duplum &longs;olùm, hoc e&longs;t vn
cias quatuordecim, atque &longs;emi&longs;&longs;em. Prætereo au
tem, quemadmodum, vt extulit dumtaxat duplum ex
diametris quatuor, &longs;ic etiam deinceps extulerit &longs;olum
modò triplum ex diametris nouem, & quadruplum,
ex &longs;exdecim. Adnoto iam &longs;olùm, licui&longs;&longs;e ex i&longs;tis in
telligere, po&longs;&longs;e tuam hanc experientiam meritò vocari
ita e&longs;&longs;e à natura comparatum, vt illius diameter &longs;it
men&longs;ura præci&longs;a velocitatis, &longs;eu impetus, quem inter
cadendum acquirit; ea &longs;cilicet lege, vt cadens ex dia
metro vna in liberam lancem, attollat &longs;uffultam, &
præter æquilibrium, ponderis tantumdem, non iti
dem amplius (veluti etiam neque minus, &longs;i minor
fuerit altitudo) ac deinceps &longs;ic progredi, vt ex dua
bus diametris attollat præcisè duplum, ex tribus tri
plum, ex quatuor quadruplum, ex decem decuplum,
ex centum centuplum, atque ita porrò.
XXVII.
At quor&longs;um ergo contigit, inquies, vt
dimi&longs;&longs;us vncialis globus ex altitudine diametrorum
centum, & quatuordecim, vncias totidem eleuârit? Ego profectò id præcisè diuinare non valeo; quan
doquidem tu nullam &longs;eriem ob&longs;eruationum appo
&longs;ui&longs;ti, neque expre&longs;&longs;i&longs;ti quid contigerit, &longs;i quid for
ta&longs;&longs;is expertus es citra, vltrave numerum illum. Nam,
&longs;i &longs;altem commemora&longs;&longs;es ecquid tibi euenerit dimit
tenti globum ex altitudine diametrorum aut centum;
aut octoginta, aut quinquaginta, &c. liceret forta&longs;
&longs;is rem coniicere; at tale nihil recita&longs;ti, neque expli
cui&longs;ti quali pondere, pedeve v&longs;us fueris; cùm &longs;i Pa
ri&longs;ino quidem, videri po&longs;&longs;is hallucinatus quinta, aut
&longs;exta ponderis parte; quatenus globi diameter fuit
tibi duntaxat decima-nona pedis pars, quam ego de
prehendi decimam-octauam. Vtcumque fuerit; ex ijs,
quæ &longs;unt à me ob&longs;eruata, deducitur, quò diametri
&longs;iunt multiplicatiores, eò &longs;ingulas &longs;uper-additas at
tollere minus &longs;uper-additi ponderis; quandò ex &longs;ed res &longs;emper ita decre&longs;cit, vt ex tribus &longs;olùm pri
mam con&longs;equentibus eleuetur tantumdem, ex quin
que aliis rursùs tantumdem, ex &longs;eptem aliis &longs;imili
ter, ac rut&longs;us ex nouem, & ita deinceps. Deducitur
prætereà ex incre&longs;cente numero diametrorum, & de
cre&longs;cente numero additorum ponderum, perueniri
demùm ad æqualitatem; ita &longs;cilicet, vt &longs;it diametro
rum, ponderumque numerus par, quo &longs;uperato &longs;it
deinceps minor ponderum, maior diametrorum. Et
quia talis numerus incipiendo v. c. à duodecima v&longs;
que parte diametri, è qua fuere duæ vnciæ eleuatæ,
reperitur e&longs;&longs;e proximè quinquaginta; & incipiendo à
diametro integra, è qua eleuari vi&longs;æ &longs;unt vnciæ &longs;ep
tem cum quadrante, reperitur e&longs;&longs;e itidem quinqua
ginta: idcircò videmur po&longs;&longs;e dicere, &longs;i dimittatur
globus vnam pendens vnciam, ex altitudine diame
trorum &longs;uarum quinquaginta, fore vt parem nume
rum vnciarum attollat; tamet&longs;i citra hunc numerum,
&longs;it diametrorum numerus minor, vltrà maior nu
mero vnciarum. Vides igitur contingere po&longs;&longs;e, vt
aliquo ca&longs;u diametrorum numerus ponderum nume
ro exæquetur; neque licere tamen inferre e&longs;&longs;e vbi
que diametrorum numerum numero ponderum
æqualem. Ac &longs;i res quidem tibi contigi&longs;&longs;et circiter
quinquage&longs;imam, aut &longs;exage&longs;imam diametrum, foret
mihi, vt vides, re&longs;pon&longs;io in promptu; quandò verò
numerus i&longs;tum &longs;uperat duplò circiter; ac is e&longs;t aliunde,
è quo eleuari non debuerint, ni&longs;i vnciæ &longs;eptuaginta
quatuor; vnde exce&longs;&longs;us e&longs;t circiter trientis: idcircò par
vi&longs;uro, an, &longs;i quid impo&longs;uit circa vnam, paucula&longs;ve
diametros, non aliquid etiam potuerit imponere cir
ca tam multas. Mihi certè hactenùs non licuit pe
riculum facere, qui Bilancem neque maiorem, neque
exqui&longs;itiorem ea, de qua iam dixi, v&longs;urpaui. Vnde
neque velim numeros à me de&longs;criptos ita habeas,
qua&longs;i &longs;crupulosè, præci&longs;eve definiti fuerint; cùm &longs;atis
e&longs;&longs;e duxerim, &longs;i præter-propter veri forent, po&longs;&longs;em
que intelligere &longs;equi illos haud-dubiè aliam, quàm à
te præ&longs;criptam rationem.
XXVIII.
Nihil verò nece&longs;&longs;e e&longs;t dicam circa id,
quod ais,
prium e&longs;&longs;e voluit, vt eius diameter præci&longs;a e&longs;&longs;et men&longs;ura
illius altitudinis, ex qua &longs;uo nutu cadens, æquale &longs;ibi pon
dus attolleret; ac proinde, &c. in cæteris tamen etiam
corporibus idem quoque &longs;eruata proportione accidere; vt &longs;i ex
quacumque di&longs;tantia æquale &longs;ibi pondus attollant, ex eadem
di&longs;tantia duplicata duplicatum, & ex triplicata
attollant, atque ita con&longs;equenter, ob eandem rationem; cui
rationi ip&longs;a quoque experientia &longs;uffragetur, &c. hac ta
men differentia, quòd in globis, diameter altitudines præ
cisè definiat, vnde pondus ip&longs;orum multiplicetur, in cæteris
figuris non item; &longs;ed in illis altitudines diametris ip&longs;arum
&longs;int minores; ratio verò po&longs;tulet vt vniuer&longs;im in figuris om
nibus tales altitudines diametro &longs;phæræ eiu&longs;dem molis, ac
ponderis inueniantur æquales. Nihil, inquam, e&longs;t opus
vt ad i&longs;tud dicam; cùm neque &longs;uffragari experien
tiam videam, neque ip&longs;e globus, quicum corpora
aliarum figurarum confers, habeat pro men&longs;ura præ-
&longs;ibi pondus attollat, &longs;uam diametrum; &longs;ed potiùs duo
decimam circiter &longs;uæ diametri partem; neque aliun
de eadem diameter præcisè definiat altitudines, vnde
pondus, &longs;eu impetus multiplicetur, euadatque tri
plus ex tripla, quadruplus ex quadrupla, &c. &longs;ed id
potiù faciat progre&longs;&longs;io numerorum imparium, qua
dratorumve, ad quos terminantur. Addo autem
videri mihi rem e&longs;&longs;e dignam con&longs;ideratu, quæ acci
deret circa globos, &longs;i velocitatis, &longs;iue impetus acqui
&longs;iti gradus men&longs;urandi e&longs;&longs;ent penes &longs;ingulas diame
tros, quæ men&longs;urarent &longs;ingulorum ca&longs;us. Sunto
enim globi, v.c. duo ex eadem materia, quorum
vnus &longs;it diametro decies maiore, quàm alius, & di
mittatur vterque ex eadem altitudine. Tunc, quia mi
nor decidet per diametros decuplò plureis, quàm ma
ior, fiet, vt attollat pondera &longs;ibi æqualia decuplò
multipliciora, quàm attollat, maior ex &longs;ibi æqualibus;
Quare & &longs;equetur, vt per idem &longs;patium feratur de
cuplò citiùs, temporeve decies breuiore perueniat
ad lancem, quàm maior. Hoc autem con&longs;tat, quàm
fal&longs;um &longs;it; cùm &longs;i globorum alteruter deberet velo
ciùs moueri, & peruenire citiùs, is non &longs;ine quadam
veri&longs;imilitudine deberet potiùs e&longs;&longs;e maior (quandò
& Ari&longs;toteles per&longs;ua&longs;us id fuit, & toti penè mundo
hactenus per&longs;ua&longs;it) ac doceat tamen experientia duo
pondera eiu&longs;dem materiæ, inæquabili&longs;&longs;ima licet, ve
luti vnum vnius vnciæ, alterum verò librarum cen
tum, ex eadem cadentia altitudine, cadere eadem
velocitate, ac momento eodem peruenire in terram.
exemplo repetito de pen&longs;ilibus, nihil referat, quod
cumque pondus filo appendas, vt celeritate eadem
vibrationes fiant; ideò enim pen&longs;ile centum libra
rum non vibratur velociùs, quàm pen&longs;ile vnius vn
ciæ, quoniam altitudo, ex qua vtrumque cadit, ea
dem e&longs;t, men&longs;urata nempe, eadem portione perpen
di uli, quemadmodum e&longs;t ante declaratum: cùm
celeritas aliunde &longs;tatim augeatur vel minuatur, ac fi
lum breuius fit, vel prolixius. Et hactenus quidem
de tua Experientia.
decur&longs;um non iri.
XXIX.
Sequitur iam Secundum membrum Po
&longs;terioris capitis, quod tibi fuit præcipus &longs;copus. Videlicet ita concludis.
que euidenter con&longs;tat, celeritatem motus in naturali grauium
de&longs;cen&longs;u per aërem, &longs;eclu&longs;is externis impedimentis, vniformi
&longs;emper incremento augeri, & in spatijs æqualibus cre&longs;cere
æqualiter: ita &longs;cilicet, vt ex dupla di&longs;tantia, celeritas dupla,
& ex tripla di&longs;tantia, celeritas tripla, atque ita deinceps,
eadem ratione, maior &longs;emper celeritas habeatur: ni&longs;i fortè
eò v&longs;que iam progre&longs;&longs;a e&longs;&longs;et celeritas, vt nec celeriùs
uidi, nec citiùs rarefieri, & accurrere ad replendum va
cuum naturaliter po&longs;&longs;et. Et po&longs;teà:
lud etiam con&longs;tat, quàm non rectè
motus æquabiliter accelerati definitionem eam reiecerit, qua
motus eiu&longs;modi is dicitur; qui spatijs æqualibus, æqualia cele
ritatis augmenta acquirit; & quàm o&longs;citanter idem halluci-
tione, eiu&longs;dem &longs;e fal&longs;itatem, impoßibilitatémque o&longs;tendi&longs;&longs;e,
tam facilè &longs;ibi, atque incon&longs;uliè per&longs;ua&longs;it: cùm aperta iam,
indubitatáque experientiâ con&longs;tet, in naturali grauium de&longs;
cen&longs;u, æqualibus spatijs, æqualia celeritatis augmenta perpe
tuò acquiri, &longs;emperque velocitates, emen&longs;aque ab initio mo
tus spatia, in eadem ratione reperiri. Ad i&longs;ta verò vides
profectò quid &longs;it iam promptum re&longs;pondere; cùm
tantum abe&longs;t, vt aperta indubitatáque experientia de
finitionem illam vulgarem, aut incrementa velocitatis
pro ip&longs;a &longs;patiorum ratione &longs;tabiliat, quin illam potiùs
planè euertat, & Galileanum ita confirmet, vt mani
fe&longs;tò exinde con&longs;tet incrementa velocitatis acquiri
duntaxat æqualia æqualibus temporibus; acqui&longs;ita
verò, &longs;eu &longs;uperata &longs;patia e&longs;&longs;e vt ip&longs;orum temporum
quadrata. Ex quo fit, vt allatis illis antè argumen
tis, quibus permouebar, vt coniicerem percu&longs;&longs;ionem,
atque idcircò impetum, velocitatémque rei deciden
tis maiorem duplò non haberi, ni&longs;i ex altitudine qua
drupla, triplum, ni&longs;i ex nonupla, quadruplum, ni&longs;i ex
&longs;exdecupla, i&longs;tud iam nouum acce&longs;&longs;erit. quatenus ob
&longs;eruatum e&longs;t duplum ponderis ex vnius diametri alti
tudine elati non efferri ex dupla, &longs;ed ex quadrupla;
triplum non ex tripla, &longs;ed ex nonupla; quadruplum
non ex quadrupla, &longs;ed ex &longs;exdecupla duntaxat. Sunt
autem tibi habendæ gratiæ, qui pro tua &longs;olertia eò
re&longs;pexeris, vnde argumentum adeò cuidens ducere
tur; ip&longs;eque debes ex eo lætari, quòd tamet&longs;i expe
rimentum præconceptæ à te opinioni non faueat;
conferat nihilominùs ad veritatis illu&longs;trationem.
XXX.
Pro&longs;equeris deinde &longs;ic.
motus in naturali de&longs;cen&longs;u grauium, non modò ad locum, &longs;ed
ad tempus quoque re&longs;pectum includat, iamque de altero
&longs;it, qua videlicet ratione, celeritas &longs;patijs æqualibus augea
tur; vt ne quid ad perfectam motus accelerati notitiam de
&longs;it, nece&longs;&longs;arium e&longs;t, vt de &longs;patiis quoque, quæ temporibus
æqualibus percurruntur, quam inter &longs;e rationem ob&longs;eruent,
reliqua di&longs;putatione inquiramus, & ex ii&longs;dem quoque expe
rientiis definiamus. Hoc iam loco, optimè Vir, agno&longs;
cere potes originem mali. Nempe labes tota vide
tur ex definitione vulgari contracta, quatenus ratio
nem incre&longs;centis celeritatis ita cum &longs;patio comparat,
vt nullam interim in&longs;tituat comparationem cum tem
pore, &longs;ine quo tamen neque celeritas, neque acce
leratio intelligi pote&longs;t. Non modò certè Ari&longs;toteles,
verùm etiam communis &longs;en&longs;us id Velox definit,
paucum multò conficit;
attendatur &longs;olùm penes &longs;patia, debere &longs;emper id
mobile, quod decem percurrerit &longs;tadia, dici moueri
celeriter, & &longs;emper id, quod vnicum percurrerit, tar
dè; cùm contingere tamen po&longs;&longs;it, vt quod percurrit
vnicum, moueatur decuplo velocius, quàm illud,
quod percurrit decem. Ex quo fit, vt cùm celeri
tas nihil &longs;it aliud, quàm pa&longs;&longs;io motus; intelligatur
quidem motus ab&longs;olutè &longs;umptus ex relatione ad &longs;pa
tium, cùm & definiatur progre&longs;&longs;io è loco in locum
(nulla mentione temporis) & duo loca &longs;ine &longs;patio
interiecto non accipiantur; at celeritas non intelli
gatur &longs;ine relatione ad tempus, & illud quidem breue
alium pote&longs;t. Fit etiam proinde, vt idem dicendum
de acceleratione &longs;it; quippe acceleratio duo &longs;altem
tempora de&longs;ignat, in quorum vno celeriter, in alio
celeriùs mobile feratur; ac intelligimus aliunde tem
poribus illis æqualibus &longs;umptis, pauciores &longs;patij par
teis priore, plureis po&longs;teriore percurri. Et adnitere
facere per&longs;pectum, quidnam acceleratio &longs;it, nulla men
tione temporis; ac perno&longs;ces rem impo&longs;&longs;ibilem factu
e&longs;&longs;e. Vtcumque enim plureis, plurei&longs;que &longs;patij par
teis memores
quenter, &longs;ucceßiuè,
tineant, non magis accelerationem, quàm &longs;implicem
celeritatem, aut potiu&longs;-quam motum &longs;impliciter &longs;pe
ctatum de&longs;cribes. Quanquam nihil e&longs;t opus id vr
geam, cùm tu pro confe&longs;&longs;o iam habeas; profe&longs;&longs;us
nempe
ad locum, &longs;ed ad tempus quoque re&longs;pectum includere:
mirari &longs;olùm quis po&longs;&longs;it, agno&longs;cere te in celeritate
duplicem re&longs;pectum, & velle tamen alterum, ip&longs;um
que præcipuum in tradenda definitione accelerati mo
tus exclu&longs;um; ac inuehi in Galileum, qui inclu&longs;um
voluerit. Nam & licet, veluti tu re&longs;pectum ad tem
pus prætermi&longs;&longs;um fers, &longs;ic ille re&longs;pectum ad locum
prætermitti po&longs;&longs;e cen&longs;uerit: excu&longs;ari pote&longs;t, quòd qui
motum dicit, locum etiam dicat, quemadmodum
mox attigi; & cùm foret &longs;olùm de celeritate &longs;uperue
niento quæ&longs;tio, ideò nugationem deuitans, illam per
re&longs;pectum ad tempus, &longs;ine quo intelligi nequeat, pu
XXXI.
Subdis con&longs;equenter;
fiat, primùm occurrendum est errori, qui facilè obrepere
potest, &longs;i quæ de cele itatis augmento in &longs;patiis æqualibus
antè demonstrata &longs;unt, minùs accuratè perpendantur. Cùm
enim ex &longs;uperioribus iam euidenter con&longs;tet, in naturali gra
uium de&longs;cen&longs;u, &longs;emper ex dupla di&longs;tantia, celeritatem ha
beri duplam; & ex tripla distantia, triplam; atque ita
deinceps, eadem ratione celeritatem augeri: nihil procliuius
e&longs;&longs;e potest, quàm vt quis exi&longs;timet, accelerationem
fieri per &longs;ubdiui&longs;ionem primi cuiu&longs;libet temporis, in paricis
&longs;emper minores, pro multitudine, & ratione &longs;patiorum æqua
lium, quæ motu decurruntur; ita videlicet, vt pars &longs;ecunda
spatij, ab&longs;oluatur dimidia parte temporis, quo prima pars
decur&longs;a est; & tertia pars &longs;patij, tertia parte eiu&longs;dem primi
temporis percurratur, & ita de cæteris: maximè cùm in hac
etiam hypothe&longs;i, &longs;patia & velocitates in eadem e&longs;&longs;e ratione,
& quod con&longs;equens e&longs;t, ex impeta quoque decidentium corpo
rum hac ratione inuariato, iidem omnes, quos experientia
docet effectus haberi, primo a&longs;pectu videantur. Heic pro
fectò rur&longs;us mirari tuam &longs;agacitatem par e&longs;t, qua
tenus eam non fugit error qui ex po&longs;itione à te a&longs;
&longs;erta con&longs;equitur; tamet&longs;i ip&longs;e non con&longs;equi ex iis,
quæ &longs;ubiicis, contendas. Me quod attinet, is e&longs;t
ip&longs;emet, quem deduxi aliàs aduer&longs;us Michaelem
Varronem, qui primus, quod &longs;ciam, eandem po&longs;itio
nem ante annos plus minùs &longs;exaginta defendit; de
clarando ex ea id incommodi inter cætera con&longs;equi,
vt, quemadmodum antè in&longs;inuaui, &longs;patia acqui&longs;ita
in &longs;ine æqualis cuiu&longs;libet temporis numeranda &longs;int,
vt difformiter, &longs;ic in plu&longs;quàm tripla ratione. Vt
&longs;aque linea, quam ip&longs;e v&longs;urpas, AB, & &longs;up
po&longs;ito tempore minutorum &longs;ex, quo &longs;uppo
nis AD primam partem percurri; Con&longs;tat
omninò, &longs;i &longs;ecunda æqualis pars DE per
curratur velocitate dupla ad illam, qua per
curritur AD, non in&longs;umi plus temporis in
percurrenda parte &longs;ecunda, quàm dimidium
eius, quod fuerit in&longs;umptum in prima (cùm
hac ratione tempora velocitatum &longs;ubmultipla
&longs;int) atque ita, &longs;i prima pars &longs;uperata fuerit mi
nutis &longs;ex, percurri &longs;ecundam dimidio, &longs;eu mi
nutis tribus. Eadem autem ratione &longs;i tertia
æqualis EF percurratur tripla, nece&longs;&longs;e e&longs;t
percurratur temporis triente, &longs;eu minutis duo
bus; ac eodem modo quarta FG quadrante,
&longs;eu &longs;e&longs;quiminuto, & quinta GH quinta par
te temporis, &longs;eu minuto vno cum &longs;ecundis duodecim;
ac &longs;exta HB, &longs;extante, &longs;eu minuto vno, & ita deinceps. Atque ego quidem hûc v&longs;que nullum video paralo
gi&longs;mum. Quamobrem re&longs;tat, vt di&longs;quiratur, quot
nam æqualia &longs;patia, parte&longs;ve &longs;patii æquales tem
poribus primum con&longs;equentibus, ip&longs;ique æqualibus
percurrantur. Porrò cùm ad id perno&longs;cendum, ni
hil oporteat aliud, quàm iungere &longs;imul varia hæc
fragmenta primi temporis, hoc e&longs;t dimidium, trien
tem, quadrantem, & porrò parteis quintam, &longs;extam,
&longs;eptimam, &c. deprehendimus in ip&longs;o fine quarti
&longs;patij, ex iunctis &longs;imul dimidio, triente & quadrante,
confectum e&longs;&longs;e &longs;ecundum tempus, &longs;eu iteratò minuta Ac pari ratio
ne in fine vndecimi &longs;patij, ex &longs;uper-adiunctis parti
bus quinta, &longs;exta, &longs;eptima, octaua, nona, decima,
vndecima, confectum e&longs;&longs;e tertium tempus, &longs;eu ite
rum minuta &longs;ex, cum &longs;uperante vna &longs;exage&longs;ima par
te. Et in fine &longs;patij trige&longs;imi primi, ex &longs;uperadiun
ctis duodecima, decimatertia, &c. confectum quar
tum, &longs;eu &longs;ex minuta, cum &longs;uperante parte circiter
quadrage&longs;ima. Et in fine octoge&longs;imi quarti, ex &longs;u
peradiunctis trige&longs;ima &longs;ecunda, trige&longs;ima tertia, &c. confectum quintum, &longs;eu &longs;ex minuta, cum &longs;uperante
vna parte proximè nonage&longs;ima, atque ita deinceps. Vnde licet aduertere, fore vt &longs;patia ea ratione incre&longs;
cant, quæ a&longs;&longs;umptis quibu&longs;libet æqualibus tempori
bus deprehendatur excedere, & difformiter quidem,
&longs;eu inæquabiliter, triplam; quippe procedendo per
hos numeros, vnum, quatuor, vndecim, triginta
octoginta quatuor, &c. &longs;icque lapide decidente pri
mo momento per vnam v. c. orgyiam, fore vt &longs;ecun
do æquali momento decidendo per treis, in tertio
per &longs;eptem, in quarto per viginti, in quinto per quin
quaginta duas, deciderit in fine quinti, orgyiis octo
ginta quatuor, ac breui res &longs;it abitura in immen&longs;um,
&longs;ecu&longs;que quàm docet ip&longs;a experientia, iuxta quam
orgyiiæ in fine quinti momenti &longs;uperatæ, colliguntur
plures e&longs;&longs;e non debere, quàm viginti quinque.
XXXII.
Demon&longs;tras ip&longs;e alia ratione (&longs;ed nimi
rùm aduer&longs;um te) non fieri accelerationem pro &longs;ub
diui&longs;ione i&longs;ta temporis.
motus per eam primi temporis &longs;ubdiui&longs;ionem fieret, de qua
deberet, hoc e&longs;t dimidia parte primi temporis; & pars ter
tia EF duobus minutis, nempe tertia parte eiu&longs;aem primi
temporis, & ita de cæteris. Quamobrem verò id non
fieret; cùm &longs;uppo&longs;ito tuo illo principio de velocita
tibus &longs;e&longs;e habentibus vt &longs;patijs, & nullus &longs;it paralo
gi&longs;mus, & res &longs;ponte &longs;ua &longs;e prodat, neque videatur
euerti po&longs;&longs;e, abs te, vt mox tentas euertere, ni&longs;i tua
ip&longs;ius euertas principia, & fal&longs;itatem prodens con&longs;e
quentis, quod tamen ex tuis principiis tam nece&longs;&longs;a
riò deducitur, videaris etiam prodere fal&longs;itatem ante
cedentis? Pergis itaque,
intelligimus, diui&longs;a bifariam parte AD in S, & parte
item DE &longs;imiliter in X. Tunc enim ob eandem ratio
nem nece&longs;&longs;e fuerit, vt pars SD percurratur in dimidio
eius temporis, quo pars AS decurritur; & DX in ter
tia parte, itemque XE in quarta parte eiu&longs;dem temporis,
vt manife&longs;tum e&longs;t. Quor&longs;um verò id nece&longs;&longs;e non fue
rit; cùm eadem &longs;it ratio dimidij ad dimidium, quæ
totius ad totum, & nulla &longs;it ob&longs;eruatio, aut ratio, ex
qua aliud inferatur potiùs de partibus AD, DE, EF,
&c. quàm de partibus AS, SD, DX, &c.
aut de
quibu&longs;libet minoribus, dummodò &longs;int omnes inter
&longs;e æquales? Pergis iterum, C
totam AD minutis &longs;ex pertran&longs;iri, nece&longs;&longs;e erit, vt decur
&longs;us per AS quatuor minuta, & de&longs;cen&longs;us per SD duo
tantum minuta in&longs;umat: vt &longs;cilicet ea ratione tempus de&longs;
cen&longs;us per SD &longs;it dimidia pars temporis in de&longs;cen&longs;u per AS
in&longs;umpti; ideoque etiam pars DX minuti.
parte temporis AS; & pars XE minuto vno, &longs;iue
&longs;us per totam DE minutis Quid ni
verò id quoque nece&longs;&longs;e non &longs;it, ex&longs;i&longs;tente &longs;emper
eadem ratione dimidiorum ad dimidia, quæ toto
rum ad tota? At
dem partem non ni&longs;i tribus minutis decurri. Id verò &longs;anè
non &longs;uppo&longs;ui&longs;ti, vt aliquid gratis conce&longs;&longs;um; &longs;ed vt
aliquid nece&longs;&longs;ariò cum tuis principiis cohærens. Quare & fit quidem, vt euincas rem e&longs;&longs;e impo&longs;&longs;ibi
lem, percurri partem DE dimidio eius temporis, quo
percurritur AD; &longs;ed euincas tamen aduer&longs;us teip&longs;um;
cùm ex hoc rursùs efficiatur, vt motu æquabiliter ac
celerato ex A in E, non fuerint in E acqui&longs;iti duo
celeritatis gradus, quemadmodum in D fuit acqui&longs;i
tus vnus, &longs;i mobile quidem per totam DE non &longs;it
motum duplò velocius, quàm per totam DA; atque
idcircò in dimidio temporis, durationeve minuto
rum trium. Fit etiam, vt quando concludis,
hanc igitur primi temporis &longs;ubdiui&longs;ionem, accelerationem
motus in de&longs;cen&longs;u grauium &longs;atis exactè non explicari;
po&longs;&longs;it, neque explicari per tuam illam po&longs;itionem,
cum qua hæc &longs;ubdiui&longs;io indiuiduè connexa e&longs;t, &
à qua illam auertere, ob contradictionem con&longs;equen
tem conatus, nihil aliud videris, quàm, quod vulgò
aiunt, incommodum per incommodum &longs;oluere.
XXXIII.
Prætextu &longs;ubinde quæ&longs;ito vlterioris
dæ po&longs;teà à te progre&longs;&longs;ionis motus per parteis tem
poris æqualeis &longs;ecundum rationem continenter du
plam. Nam,
nimirùm non trium, non duorum cum triente, vt
priùs, &longs;ed minutorum præcisè duorum) id autem &longs;ic
probas.
&longs;imiliter AE dupla &longs;it ip&longs;ius AD, nece&longs;&longs;e e&longs;t, vt velocitas
in D dupla &longs;it velocitatis in
modo dupla reperiatur velocitatis in D; imò, vt velocitas
etiam quæcumque in quovis puncto inter D, & E con&longs;titu
to de&longs;ignabilis perpetuò dupla &longs;it velocitatis alterius inter S,
& D etiam aßignabilis, vt facilè quilibet per &longs;e intelligere
pote&longs;t. Sumpto enim puncto quocumque inter D, & E,
ex empli gratiâ T, diui&longs;oque bifariam interuallo AT, &longs;ectio
nece&longs;&longs;ario cadet inter D, &Et quia erit
AT dupla ip&longs;ius AV, erit etiam velocitas in T dupla ve
locitatis in V, & ita in cæteris punctis, quæ de&longs;ignari po&longs;&longs;unt
inter D, & E. Quare per totum interuallum DE velocitas
erit dupla velocitatis per totum spatium
lum DE duplum e&longs;t interualli
terualla nempe
Quo loco admitto imprimis, vt nouum incommo
dum, eandem partem DE, quæ probata e&longs;t primùm
percurri debere ex tuo principio minutis tribus, ac
deinde minutis duobus cum triente, probari iam per
curri debere minutis duobus. Quippe nihil e&longs;t, quod
magis prodat fal&longs;itatem principii, quàm tot repu
gnantium, atque ab&longs;urdorum capitum deductio. Neque verò heic adhûc finis; quandò alia innumera
pari ratione con&longs;equentur. Nam &longs;i, v.c.
AS bifa
riam &longs;ecetur in P, conficietur eodem tuo ratiocinio,
vt PS percurratur eodem tempore, quo SD, atque Et quia &longs;eruatâ analogià
PS percurri debet vno minuto cum triente, efficie
tur, vt non modò SD, verùm ip&longs;a quoque DE per
curratur rursùs non duobus minutis, &longs;ed vno&longs;olùm
cum triente; atque ita bifariam &longs;ecando, diminuendo
que in infinitum. Adnoto deinde non tran&longs;ire te
vltrà comparationem partis DE cum parte SD, ne
que comparare ip&longs;am cum parte PS, vt mox factum
e&longs;t, & fieri po&longs;&longs;e nihil prohibet; cùm nulla &longs;it ratio,
ob
con&longs;i&longs;tatur; verùm a&longs;&longs;umere te &longs;olum, id
ab&longs;oluitur interuallum
&longs;uperior
tione vniformis e&longs;&longs;et;
de&longs;ignatam
quo interuallum
tempore breuiore ab&longs;olui. Adnoto, inquam, vt appareat,
cui fundamento &longs;uper-ex&longs;truas quicquid deinceps
ædificas, &longs;upponens nimirùm vt ratum principium
(quod obiter, & aliud agendo &longs;tabilieris) æqualita
tem temporis, quo pars SD, & ip&longs;ius dupla DE per
curruntur.
XXXIV.
Etenim illicò &longs;ic habes;
& eadem pror&longs;us ratione aliud demonstratur, quod ingentis,
atque admirabilis paradoxi loco non immeritò fortaßis habe
ri poßit, nempe &longs;i spatium, per quod corpus graue quod
cumque de&longs;cendit, in parteis quotlibet æqualeis diui&longs;um intel
ligatur, & primæ, ac &longs;upremæ partis etiam de&longs;ignetur
piendo diui&longs;iones i&longs;tas omneis ab infimo eiu&longs;dem primæ par
tis puncto, donec totidem de&longs;ignatæ &longs;int, quo
partes æquales acceptæ fuerint: tum &longs;ingulæ partes buiu&longs;mo
di æquales tanto præcisè tempore à corpore graui
gæ, ac respondentes in &longs;uprema parte
riore eius dimidio)
cur&longs;æ fuerint. Rem con&longs;equenter ita declaras;
S
corpus graue de&longs;cendat, in parteis exempli gratiâ
&longs;ex æqualeis diui&longs;um in
que, ac &longs;upremæ partis
cto
de tertia
&longs;exta
dens per
cundam partem
tis
æquali tempore partem
& tertiam prim&ecedil; partis, nempe
pore de&longs;cendente tran&longs;curri, & ita de c&ecedil;teris. Tunc
autem pergis.
partis posterior dimidia pars tran&longs;ini&longs;&longs;a fuerit, iam
paulò antè o&longs;ten&longs;um est, nec maiore negotio idem
de c&ecedil;teris quoque partibus concludetur. Sumpto
enim
XXXV.
Verùm priu&longs;quàm gradus ad
cæteras fiat, con&longs;i&longs;tendum e&longs;t in hac prima; cùm O&longs;ten
&longs;um e&longs;&longs;e ais tempus, quo percurritur CD, æquale e&longs;&longs;e
tempori, quo decur&longs;um fuerit HC: &longs;eu, ne confun
damus, & rem explicemus, qua&longs;i repetendam ex &longs;u
periore &longs;chemate, o&longs;ten&longs;um e&longs;&longs;e ais id tempus, quo
percurritur DE, æquale e&longs;&longs;e tempori, quo de
cur&longs;um fuerit SD. At primò, in&longs;inuatum iam
e&longs;t id e&longs;&longs;e impo&longs;&longs;ibile; cùm quo iure ip&longs;e bi
&longs;ecui&longs;ti primam partem AD in S, liceat bi
&longs;ecare primum dimidium AS in P; & rursùs
primum horum dimidiorum in duo alia, &
primum i&longs;torum in duo, & ita porrò quoties
libuerit: Iuxta tuum verò ratiocinium, &longs;e qua
tur tempus, quo percurritur SD, e&longs;&longs;e æqua
le tempori, quo decur&longs;um fuerit PS, quate
nus, vt velocitas per totam DE e&longs;t dupla ve
locitatis per totam SD, quemadmodum in
teruallum duplum e&longs;t; ita velocitas per totam
SD dupla e&longs;t velocitatis per totam PS, &longs;icut
interuallum e&longs;t itidem duplum; Hoc autem
po&longs;ito, vlteriùs &longs;equatur tempus per SD, atque
idcircò per DE ip&longs;i æquale, e&longs;&longs;e non iam minuto
rum duorum, vt o&longs;tendi&longs;ti, &longs;ed minuti vnius cum
triente; vt pote coæquatum tempori per PS, quod
tam e&longs;&longs;e debet triens quatuor minutorum (quibus
te triens minutorum &longs;ex (quibus percurritur AD)
cùm id tamen factuimpo&longs;&longs;ibile &longs;it, repugnantia putà
inuoluens, ac tantò magis, quantò ex vlterioribus
&longs;ubdiui&longs;ionibus probari pote&longs;t eandem DE percurri
proximè quinquaginta tribus; & rursùs proximè
octodecim, & rursùs &longs;ex, &c. Deinde, cùm ad id
o&longs;tendendum v&longs;us fueris ea ratione, quòd nece&longs;&longs;e &longs;it,
tatem in E duplam velocitatis in D, &longs;icuti
pla ip&longs;ius
quitur exinde, vt tam tota DE, quàm tota SD per
curratur non triente, &longs;ed dimidio temporis, quo tota
AD: cùm vbicumque e&longs;t velocitatis duplum, vbi &longs;it
dimidium temporis duntaxat, neque tu id infregeris,
&longs;ed incommodum &longs;olùm attuleris, quod cùm euertat
con&longs;equutionem de &longs;ubdiui&longs;ione primi temporis, &longs;up
po&longs;itionem quoque euertit de velocitate dupla in du
plo &longs;patii, tripla in triplo, &c. vt aliquoties e&longs;t incul
catum. Nam & quod po&longs;teà a&longs;&longs;umis tempus per
SD, atque adeò DE e&longs;&longs;e breuius, quàm dimidium
eius, quo tran&longs;curritur AD, id facis quidem rectè,
verumtamen iure non tuo; quippe id facis &longs;olùm me
tu eius incommodi, quod præ&longs;en&longs;iti po&longs;&longs;e vrgeri de
motus acceleratione vniformiter, continenterque in
cre&longs;cente: cùm id alioquin & repugnet tuæ &longs;uppo&longs;i
tioni de velocitate dupla in duplo &longs;patio, tripla in
triplo, &c. & euertat demon&longs;trationem ip&longs;am, ad
quam iam recurris, cùm o&longs;ten&longs;um ais tempus, quo
percurritur &longs;ecunda pars, æquale e&longs;&longs;e tempori, quo
tran&longs;mittitur dimidium po&longs;terius, &longs;eu inferius primæ:
neque enim id fuit o&longs;ten&longs;um alio ratiocinio, quam
quod ip&longs;emet &longs;tatim pernega&longs;ti.
XXXVI.
Attamen &longs;upponatur etiam tua huiu&longs;-
quo percurritur DE &longs;e&longs;quialterum &longs;it, non verò æqua
le illi tempori, quo percurritur SD. Cum velocita
tes enim &longs;int per te, vt &longs;patia; ac aliunde &longs;it manife
&longs;tum, vbi e&longs;t duplum velocitatis, ibi dimidium e&longs;&longs;e
temporis, vbi triplum trientem, atque ita&longs;emper in ra
tione &longs;ubmultipla; &longs;i &longs;it primò vt AE ad AD, ita
AD ad AS; erit igitur diuidendo vt AS ad SD, ita
AD, ad DE; ac deinde, &longs;i &longs;it AS tempus minuto
rum quatuor, & SD minutorum duorum; Erit igitur
tempus AD quidem minutorum &longs;ex, & DE minuto
rum trium, atque adeò &longs;e&longs;qui-alterum, non æquale
tempori SD. Sequitur iterùm, vt non &longs;ecùs, quàm
Galileus ratiocineris, dum Paralogi&longs;mi illum arguis. Siquidem ex tuo quoque ratiocinio euineitur, vt to
ta AE eodem tempore, quo ip&longs;a AD, quæ pars eius
e&longs;t, percurratur. Nam &longs;i vt AE ad AD, ita DE ad
SD; ergo vt DE tempus ad SC tempus, ita AE tem
pus ad AD tempus: Atqui DE tempus per te e&longs;t
æquale tempori SD; igitur AE tempus æquale erit
AD tempori; hoc e&longs;t totum, & pars percurrentur
tempore æquali, aut eodem. Sequitur prætereà, vt
quia quælibet magnitudo etiam ip&longs;a diameter Mundi
tam e&longs;t dupla &longs;ui dimidij, quàm AE e&longs;t ip&longs;ius AD, &
tam in fine dupli e&longs;t velocitas dupla, quam in fine
dimidij dimidia; ideò etiam diameter Mundi ita &longs;e
ad &longs;emidiametrum habeat, vt DE ad SD; quare &
quemadmodum DE percurritur eodem tempore, quo
SD, duobus videlicet minutis; ita etiam Mundi &longs;emi
diameter debeat eodem tempore, &longs;eu duobus minutis Quippe & tamet&longs;i partes &longs;int incompara
biliter plures in &longs;emidiametro Mundi, quàm in &longs;pa
tiolo DE, &longs;unt tamen gradus velocitatis incompara
biliter etiam plures, ac proportione totidem; vt tem
pora &longs;ubmultipla illis &longs;uperandis &longs;ufficere valeant. Vt
breue faciam, erroris origo ex eo profluxi&longs;&longs;e videtur,
quòd merè gratis con&longs;titeris in parte AD, eiu&longs;que
dimidio inferiore SD; & rem perinde habueris, ac &longs;i
dimidium &longs;uperius AS diuidi perinde non po&longs;&longs;et, ne
que haberet &longs;peciatim dimidium eadem ratione, qua
habet AD. Proptereà enim accepi&longs;ti &longs;olùm omnia
de&longs;ignabilia punctaper totam DE, in quibus veloci
tas e&longs;&longs;et dupla velocitatis in totidem punctis per to
tam SD; neque reputa&longs;ti pergendum, vt haberes
eodem tenore puncta de&longs;ignabilia per totam SD, in
quibus velocitas e&longs;&longs;et dupla velocitatis in totidem
punctis de&longs;ignabilibus per totam PS, atque ita in in
finitum; vt prorsùs nece&longs;&longs;arium e&longs;t ex tua ip&longs;ius &longs;up
po&longs;itione. Quanquam res vberiùs cogno&longs;cenda e&longs;t
circa cæteras, quas de&longs;cribis parteis.
XXXVII.
Vt enim probes (re&longs;umpto iam recen
tiore &longs;chemate) tempus per tertiam partem DE æqua
le e&longs;&longs;e tempori per trientem primæ partis IC,
inquis, CN
treis parteis æqualeis
tas in
e&longs;t tripla. Cumque ob eandem cau&longs;&longs;am velocitas quoque in
IC;
quartam partem EF æquale e&longs;&longs;e tempori per
KC quadrantem primæ,
ui&longs;a bifariàm
DP
teis quatuor æqualeis
que velocitas in
tota
quoque in
velocitatis in
EF
KC, Sequitur,
dem autem etiam ratio e&longs;t cæterarum omnium par
tium, vt facilè quilibet ex i&longs;tis per &longs;e intelliget. Con
cludis,
que graue de&longs;cendit, ea, qua dictum e&longs;t, ratione diui
&longs;um intelligatur, &longs;ingulæ partes huiu&longs;modi æquales tanto
præcisè tempore à corpore graui de&longs;cendente percur
rentur, quantò partes ip&longs;is analogæ ac re&longs;pondentes
in &longs;uprema parte
gnatæ ab eodem corpore graui decur&longs;æ fuerint, vt est
propo&longs;itum. Prætereo autem, quod &longs;ubinde de
claras te ad&longs;crip&longs;i&longs;&longs;e fini cuiu&longs;que &longs;ex partium
numerum integrum, incipiendo ab vnitate,
ad de&longs;ignandum velocitatis gradus illeic acqui&longs;itos, &
ex æquo factos cum decur&longs;is partibus; ad&longs;crip&longs;i&longs;&longs;e au
tem mediis interuallis &longs;ecundæ, & &longs;equentium partium
fractos numeros, ad de&longs;ignandum tempora, &longs;iue fra
ctiones temporis primi, quibus vnumquodque &longs;pa-
XXXVIII.
Videris itaque imprimis haud abs re
dixi&longs;&longs;e
po&longs;terius primæ partis dimidium, vt &longs;calam Prototy
picam, cuius gradibus coæquetur, exqui&longs;itéque men
&longs;uretur cæterarum omnium con&longs;equentium duratio;
tamet&longs;i illud e&longs;&longs;e po&longs;&longs;it parte digiti mille&longs;ima minus,
& i&longs;tarum aggeries, quanta e&longs;t tota &longs;emidiameter
mundi. Non &longs;anè, quod negem dari lineas, alia&longs;que
magnitudines, in quibus arcana prorsùs admiranda,
& quæ nemo vnquam &longs;u&longs;picatus fui&longs;&longs;et, detegantur à
Geometris: &longs;ed quod videri iure po&longs;&longs;it penitus incre
dibile alliga&longs;&longs;e potius naturam ip&longs;a qua&longs;i fat&adot; cætera
rum partiumip&longs;i po&longs;teriori, quàm prioridimidio; imò
& non tam toti ip&longs;i dimidio, quàm infimo illius pun
cto, à quo triens, quadrans, cæteræ fractiones debeant
&longs;upputari. Ecquod-nam e&longs;&longs;e enim pote&longs;t illius pri
uilegium; aut quid-nam admi&longs;&longs;um à priore dimidio
e&longs;t, vt eo excidi&longs;&longs;e, & pro nihilo reputari iure cen&longs;ea
tur? Quid habere
decie&longs;que, & centies mille&longs;ima pars
dimidio; non habere autem cum illo priore, à quo to
tus motus dependet; non cùm cæteris partibus perinde
&longs;uccedentibus; non &longs;altem cum vicinis, quibu&longs;cum
proximè cohæret? Deinde, ne hac in re hæream, ea
dem prorsùs incommoda ex triente pro tertia parte,
ex quadrante pro quarta, atque ita de cæteris, quæ ex
ip&longs;o dimidio pro &longs;ecunda con&longs;equuntur. Nam, vt
rem circa ip&longs;um trientem, partemque tertiam &longs;olùm
atringam, Sicuti primùm totam AC in treis diui&longs;i&longs;ti
di pote&longs;t in trienteis treis, quorum po&longs;tremus &longs;it QH;
& vt facis tempus per IC minuti vnius cum triente;
cùm &longs;it nempe triens minutorum quatuor, &longs;iue duo
rum bes; ita facere licet tempus per QH quadragin
ta &longs;ecundorum, cùm &longs;it triens minutorum duorum,
&longs;iue bes vnius minuti. Cùm autem hoc modo QH
&longs;e habeat ad IC, vt IC, ad ND; & CA non minùs &longs;it
tripla ip&longs;ius AQ, quàm DA ip&longs;ius AI, vtráque nem
pe pari modo, quo EA ip&longs;ius AC; adeò vt velocitati
bus ob rationem triplam exæquatis, &longs;ic ego po&longs;&longs;im
concludere QH &longs;e habere ad IC, vt tu concludis IC
&longs;e habere ad DE, &longs;equitur, vt, quia concludis tempora
per IC, & DE e&longs;&longs;e æqualia; tempora quoque per QH,
& IC æqualia &longs;int, ac proinde tempus per IC &longs;it iam
non vnius minuti cum be&longs;&longs;e, &longs;ed dimidium minuti
cum &longs;extante; & qua ratione hoc &longs;equitur, &longs;equetur vt
a&longs;&longs;umpto dimidio ip&longs;ius AH, ac ita &longs;umptis in infini
tum dimidiorum dimidiis, quæ per trienteis diuidan
tur, futurum, vt ip&longs;a IC minore &longs;emper, ac minore in
in&longs;initum tempore, quàm ip&longs;e admi&longs;eris, cen&longs;eatur per
curri. Sic ex eo, quod vis velocitatem in E e&longs;&longs;e tri
plam velocitatis in C; & velocitatem in D triplam
velocitatis in I, pro ratione nempe &longs;patiorum, Sequi
tur vt tam tota DE, quàm tota IC percurrantur non
iam vno minuto cum triente, &longs;ed omninò duobus
minutis, trienteve minutorum &longs;ex, quibus percurritur
AC: cùm vbicumque e&longs;t velocitatis triplum, ibi ma
nife&longs;tò non &longs;it nec ampliùs nec minùs, quàm tempo
ris triens. Sic incidis rursùs in eum, quem e&longs;&longs;e cau&longs;-
Nam &longs;i vt AE ad;
AC ita DE ad IC; ergo vt DE tempus ad IC tempus,
ita AE tempus ad AC tempus; atqui tempus DE per
te e&longs;t æquale tempori IC; ergo AE tempus tempori
AC æquale erit; hoc e&longs;t pars, & totum æquali tempo
re percurrentur. Sic quia totum quodlibet ita &longs;e habet
ad &longs;ui trientem, & velocitas in fine totius ad velocita
tem in fine trientis, vt &longs;e habet magnitudo, & veloci
tas AE comparata ad AC: &longs;equitur, vt etiam pari mo
do &longs;e habeat, quo DE comparata ad IC; quare &
quemadmodum DE triens ip&longs;ius AE eodem tempo
re percurritur, quo IC: ita diametri mundi triens eo
dem tempore percurratur. Neque enim dicas maio
rem e&longs;&longs;e connexionem ip&longs;ius DE, quàm trientis dia
metri mundi cum ip&longs;a IC; nam vis ratiocinij e&longs;t &longs;o
lùm in comparatione totius ad trientem; & aliunde
quot &longs;unt plures partes in triente diametri mundi,
quàm in triente &longs;patij DE: totidem &longs;unt etiam veloci
tates plures, quibus tempore eodem &longs;uperetur, atque
ita de cæteris.
æqualibus R. P. concludit.
XXXIX.
Supere&longs;t po&longs;tremum, &longs;iue tertium mem
brum, de Ratione continuò dupla, qua pertran&longs;iri
&longs;patia temporibus continuò æqualibus infers. Primùm
autem, vbi adnota&longs;ti non po&longs;&longs;e quidem ex deductio
ne à te mox facta,
poris graue ex aßignata altitudine de&longs;cendens in toto de&longs;
cen&longs;u in&longs;umat, ni&longs;i di&longs;tinctè etiam cogno&longs;eatur tempus de&longs;-
pero &longs;chemate)
at cognitis, aut præ&longs;uppo&longs;itis temporibus illis, facilè deinceps
totum tempus totius de&longs;cen&longs;us per quamcumque de&longs;ignatam
altitudinem determinari:
rum recipis. Tum &longs;upponens me ex&longs;pectare
diutiùs, quid &longs;is dicturus de
bent &longs;patia æquali tempore emen&longs;a,
verò æqualibus temporibus &longs;patia decurri maiora
&longs;emper, ac maiora in Ratione dupla. Diui&longs;o enim
spatio
parteis quotcumque æqualeis iniam
osten&longs;um est partem &longs;ecundam
tis dimidiam partem inferiorem
percurri; & ob eam quidem cau&longs;&longs;am, quòd, vt pars
CD
totam
&longs;imili ratione etiam efficitur, velocitatem per totam
DF
totam
Æ
eademque omninò ratio e&longs;t ip&longs;arum
perantium; vt &longs;atis manife&longs;tum e&longs;t.
æqualibus temporibus emen&longs;a, & velocitates ii&longs;dem
temporibus æqualibus acqui&longs;itæ &longs;emper augentur in
continua ratione dupla.
XL. Cæterùm, cùm i&longs;te habeatur qua&longs;i
prouentus quidam eximius totius tuæ Di&longs;&longs;ertationis;
agendum cogitaueris de primo dimidio AN. Vide
licet rationem duplam, progre&longs;&longs;ionemque à puncto
N ita inchoas, vt &longs;i motus inciperer, ac vniformiter
quidem, non à puncto A, &longs;ed à puncto N. An dices
fortè po&longs;&longs;e AN ita bi&longs;ecari, vt motus, & ratio, pro
gre&longs;&longs;ioque illius incipiat à puncto inter A, & N me
dio? Sed bi&longs;eca, vt voles, eadem erit ruina.
Bi&longs;eca
rursùs, iterumque, & porrò v&longs;que in infinitum; atta
men &longs;emper &longs;upererit pars, à cuius medio, non autem
ab A fieri incœptio cogitetur; adeò vt prorsùs perinde
&longs;it con&longs;i&longs;tere in dimidio AN. Cùm autem dicturus
prætereà non &longs;is fieri &longs;olùm quoddam qua&longs;i tyroci
nium, &longs;eu præludium ex A in N, ac motum deinde,
& rationem, progre&longs;&longs;ionemque incipere &longs;eriò ab N;
cùm non &longs;is, in quam, id dicturus, vt pote, qui motum
admittas à primo v&longs;que &longs;ui momento accelerari vni
formiter; ac &longs;upponas etiam, vbi tempus per AC mi
nutorum &longs;ex fuerit, tempus per AN futurum minuto
rum quatuor; quæ&longs;o te, ecquis modus e&longs;t progre&longs;&longs;io
nis ex A in N? Nam ab A quidem incipiens motus
acceleratur continuò, & progre&longs;&longs;u accelerationis in
alterato tran&longs;it per N, ac pergit vlterius, nec dicere
licet quid illi &longs;peciale contingat in N, quod in alio
quovis puncto non contingat. An non ergo, &longs;i tem
poribus æqualibus &longs;patia decurruntur in ratione du
pla; debet omninò &longs;patium AN percurti tempore
æquali cum &longs;patio con&longs;equente duplo, vt putà ip&longs;o
NS? Id autem cùm pror&longs;us ita e&longs;&longs;e debeat, qui fit, vt
per te etiam triplum percurratur &longs;patium, putà ND?
tempus per NC, & CD, vtrumque, ex te, minutorum
duorum, &longs;tatuitur coniunctim minutorum quatuor. Ecquo ergo modo &longs;anari id putas?
Patere rursùs mi
rari me, quor&longs;um ablegandam cen&longs;ueris progre&longs;&longs;io
nem illam arithmeticam, qua velocitates &longs;e, vt &longs;patia
habent, & quam &longs;ternendam, vt fundamentum ædifi
cij totius cen&longs;ui&longs;ti? Ecce enim, cùm velles gradus ce
leritatis ita di&longs;tribui, vt in D e&longs;&longs;ent duo gradus, quo
rum vnus e&longs;&longs;et acqui&longs;itus ab A in C, & alius ip&longs;i æqua
lis acqui&longs;itus à C in D; vis iam à C in D talem gra
dum acquiri, qualis acquiritur ab N in C; quando
quidem CD tanto tempore, quanto NC, cuius e&longs;t
dupla, percurritur. Ex quo rur&longs;us con&longs;equitur, vt ve
locitates per AC, & NC acqui&longs;itæ &longs;int prorsùs æqua
les; ac proinde, vt AC, & NC hoc e&longs;t totum, & pars
eodem tempore percurrantur; ac &longs;patium CD non
percurratur modò eodem tempore, quo NC, &longs;ed
etiam eodem, quo AC; quæ iterùm ne&longs;cio &longs;anari quá
valeant.
XLI.
Patere in&longs;uper, vt requiram, &longs;ub&longs;it-ne tibi
ratio, quamobrem diuisâ lineâ AB in parteis æqua
leis, deligere po&longs;&longs;is dimidium NC, &i pergendo pro
portione dupla dicere, vt NC ad CD, ita CD ad
DF, & DF ad FK, &c. dicere autem perinde non
liceat, vt AC ad CE, ita CE ad EI, & EI ad &longs;ui du
plam? Dicere certè accipiendum e&longs;&longs;e po&longs;terius pri
mæ partis dimidium, quòd contineatur in eo men
&longs;ura cæterarum partium con&longs;equentium, videtur e&longs;&longs;e
dicere gratis, ip&longs;amque petere quæ&longs;tionem; ac aliunde
neralem cùm &longs;tatuas, incipere vndelibet licet, & nullo
quidem ex puncto magis &longs;ecundum naturam, quàm
ex puncto A. Dic enim, amabò, &longs;i qui&longs;piam perno&longs;&longs;e
rationem exoptet, qua decidens graue progrediatur
ab A in B, & tu o&longs;ten&longs;urus ita exordiaris, Vt NC ad
CD, ita CD ad DF, &c. putas te illi facturum
&longs;atis, ac tibi obiectum non iri quæ&longs;tionem e&longs;&longs;e, non
de progre&longs;&longs;u ab N &longs;olùm, &longs;ed de progre&longs;&longs;u ab v&longs;que
A, de quo &longs;i nolles dicere, nihil dicere foret præ&longs;tabi
lius? Patere quin etiam, vt rogitem te, quî ea expedi
re, quæ à te deinceps &longs;ubiunguntur, valeas? Compa
rans enim tempora, quibus partes omnes prim
quentes percurruntur, cum temporibus, quibus vis
fragmenta po&longs;terioris illius dimidij &longs;igillatim &longs;umpta
percurri, i&longs;thæc habes verba,
terualli media pars inferior ab&longs;oluitur, & quo duæ &longs;equen
tes partes, nempe
itemque illud, quo quatuor &longs;equentes
&longs;equentes octo
teræ con&longs;equenter, &longs;eor&longs;im tamen, & &longs;ucceßiuè ab&longs;olueren
tur. Quæ&longs;o te verò, quî id fieri, quod hac ratione
deducis valeat? A&longs;&longs;ume enim integrum tempus, quod
cúmque volueris, vt ad illud referas qua&longs;cúmque heic
enumeras parteis, & peruidebis ratio-ne dupla id ip
&longs;um, quod moliris, ab&longs;oluat. E&longs;to v. c. tempus per
AC triginta &longs;ex, vt triens, &longs;eu tempus, quod tribuis
po&longs;teriori dimidio, quodque primum facis, &longs;it duode
cim; cùm &longs;ubinde &longs;patium æquale dimidio, cui d
tum &longs;it tempus 6. ideò duplices, vt pro &longs;ecundo &longs;patio
duo tempora duorum &longs;equentium interuallorum, vi
delicet trientem 4, & quadrantem 3, ac habebis non
duodecim, hoc e&longs;t tempus æquale primo, &longs;ed &longs;eptem
illius duodecimas dumtaxat; aut &longs;i duplices, etiam duo
decimas quatuordecim. Adde pari modo quatuor
tempora quatuor aliorum interuallorum, hoc e&longs;t par
teis 5, 6, 7, 8, & habebis iterùm non duodecim, &longs;ed
vix ampliùs quàm duodecimas &longs;eptem, cum &longs;emi&longs;&longs;e;
aut &longs;i duplices, etiam quidpiam amplius, quàm duode
cimas quin lecim. Adde & quæ octo &longs;equuntur inter
uallorum con&longs;equentium; & habebis rursùs non duo
decim, &longs;ed duodecimas non omninò octo: aut &longs;i
duplices, etiam duodecimas ferè &longs;exdecim. Imò &
adde &longs;exdecim, quæ interuallorum &longs;uccedentium &longs;unt,
& vix habebis ampliùs, quàm duodecimas octo:
aut &longs;i duplices, etiam aliquid amplius quàm duodeci
mas &longs;exdecim. Adde & quæ &longs;unt triginta duorum
proximorum, & habebis &longs;olùm duodecimas non om
ninò octo cum triente: aut &longs;i duplices, etiam duodeci
mas &longs;exdecim cum proximè be&longs;&longs;e, atque ita de cæteris. Ex quo profecto &longs;it, vt videas nulla ratione cohærere,
quam &longs;ube&longs;&longs;e exi&longs;tima&longs;ti, æqualitatem temporum cum
ratione dupla &longs;patiorum.
XLII. Denique, vt alia præteream, quæ tuo ex ra
tiocinio, dum rationem duplam &longs;tabilire conaris, con
&longs;equuntur incommoda; Sequitur ecce vt &longs;tabilias
non modò duplam, &longs;ed etiam triplam, quadruplam,
decuplam, & quamlibet aliam. Nam vt de tripla &longs;o
lùm dicam (cùm in cæteris idem iuris &longs;it) ac non
quod &longs;patium e&longs;t triplum, æquali tempore percurri, ac
ita rationem incipere triplam, deberéque eodem pro
gredi tenore ex D in T ip&longs;ius ND triplam, & ita
deinceps; ne id, inquam, repetam: accipiatur non NC,
&longs;ed XC infimus triens primæ partis. Vis tu tempora
XC, & DE e&longs;&longs;e æqualia, quoniam XC e&longs;t triens ip
&longs;ius DE, eo modo, quo vis tempora per NC, & CD,
e&longs;&longs;e æqualia; quoniam NC e&longs;t dimidium ip&longs;ius CD:
Quare, vt, a&longs;&longs;umendo partem analogam ip&longs;i NC, vt
putà CD, progrederis deinceps in ratione dupla CD,
DF, FK, &c. ita a&longs;&longs;umendo partem analogam ip&longs;i
XC, progredi deinceps licebit in ratione tripla DE,
EH, HB, &c. Sequitur quoque te recidi&longs;&longs;e in illud
ip&longs;um incommodum, quod deduxi antè aduer&longs;us
eandem rationem duplam: nempe, vt debeas admit
tere, peracto primo tempore in percurrendo aliquo
&longs;patio, percurri deinceps debere &longs;patia omninò infini
ta, priu&longs;quam finis temporis alterius æqualis adueniat. Quippe, &longs;i vt tu bi&longs;ecui&longs;ti partem primam AC in N,
ita cæteræ bi&longs;centur in S, V, &c. Quemadmodum
tempus NC fit per te dimidium temporis AN, ita
tempus CS erit dimidium temporis NC, & tempus
SD dimidium temporis CS, &c. Et vtcumque con
tendas iam, incipiendum e&longs;&longs;e non à puncto A, &longs;ed à
puncto N: idem nihilominùs &longs;equetur. Nam rema
nente eadem bi&longs;ectiore partium, ac habentibus, &longs;e
dimidiis eadem ratione, qua habent tota; cùm &longs;i ex
N in C certus velocitatis gradus acquiratur, is &longs;it dein
de in S duplus, ac pari ratione e&longs;&longs;e debeat in D qua-quòd vt geminatur à pri
mo interuallo in &longs;ecundum, &longs;ic geminati debeat à &longs;e
cundo in tertium, à tertio in quartum, &c. ideò tem
pora fient &longs;emper dimidiorum dimidia. Vnde eueniet,
vt peracto tempore primo, procedatur &longs;olùm con&longs;e
quenter per eiu&longs;dem dimidium, quadrantem, octan
tem, & fractiones cæteras nunquam ip&longs;i toti, ni&longs;i
tran&longs;actis &longs;patiis infinitis, exæquandas.
Terram contendit.
XLIII.
Cùm tibi &longs;ubinde in animo e&longs;&longs;et &longs;pecimen
quoddam in&longs;igne dare huiu&longs;ce tuæ rationis duplæ,
ca&longs;um delegi&longs;ti globi ferrei ex Luna v&longs;que in centrum
Terræ. Ac primùm quidem adnotas &longs;equi ex tua illa
ratione, G
quàm à
corpus graue quodcumque &longs;ex temporibus, exempli gratiâ,
inter &longs;e æqualibus de&longs;cendens, non ni&longs;i triginta &longs;ex interualla
æqualia percurrat; po&longs;ita aliunde acceleratione motus
æqualibus temporibus in ratione dupla, demon&longs;tratum
dicis
temporibus de&longs;cendens in terualla non tantum triginta &longs;ex,
&longs;ed &longs;exaginta tria decurrat. Verùm hac in re non e&longs;t
immoiandum, neque exaggeranda e&longs;t exorbitatio,
qua facta progre&longs;&longs;io in ratione dupla, vtcumque initio
moderata &longs;it, & progre&longs;&longs;ionem &longs;ecundum &longs;eriem nu
merorum imparium proximè circum&longs;tat;
omneis metas probabilitatis prætergreditur, cùm res
&longs;tatim pateat in ip&longs;o de ca&longs;u ex Luna exemplo. Ecce
trum terræ milliaria 196000. ratiocinatur globum
ferreum è Luna dimi&longs;&longs;um peruenturum ad centrum
Terræ intra horas 3. & minuta 22. cum &longs;ecundis 4.
quatenus ex ob&longs;eruatione ab eo peracta decidit ini
tio, intra &longs;ecunda quinque, centum cubitis; ac perre
cturus e&longs;t deinceps iuxta progre&longs;&longs;ionem ab eo a&longs;&longs;i
gnatam: idcircò tu illa milliaria diuidens in pedes
980000000 (quanquam Galileus non pedes v&longs;urpa
uit, &longs;ed cubitos, quorum numerus foret 588000000)
& numerum reducens in pedum centena 9800000,
a&longs;&longs;umis 100 pedes (a&longs;&longs;ump&longs;it ille ex ob&longs;eruatione 100
cubitos, qui continent pedes (166 2/3)) pro &longs;patio, quod
percurritur quinque &longs;ecundis, &longs;eu tempore vno, qua
lia &longs;unt duodecim in vno minuto, & 24 in duobus mi
nutis: ac tum extendendo 24. hæc tempora, tribuis
primo 100, &longs;ecundo 200, tertio 400, quarto 800, at
que ita ingeminando, quov&longs;que vige&longs;imo quarto tri
buas 838860800: & colligis po&longs;tea omnium &longs;um
mam 1677721500, numerum videlicet pedum, qui
percurruntur intra duo minuta. Et quia illi &longs;unt pedes
longè plures, quàm in prædicto &longs;patio à Luna ad cen
trum teriæ a&longs;&longs;ignentur, concludis fore, vt
bus in eo de&longs;cen&longs;u à Luna v&longs;que ad
horæ minuta, &longs;iue trige&longs;imam vnius horæ partem non in&longs;u
meret:
ter vtrumque calculum inueniatur.
XLIIII.
Ego autem & video &longs;anè, & quantum
a&longs;&longs;equor, debet globus ferreus cadere per te à Luna in
centrum aut vno minuto, & quinquaginta &longs;eptem
cudis quinquaginta quatuor, quatenus videris debui&longs;
&longs;e v&longs;urpare cubitos. Verum neque video, neque a&longs;&longs;e
quor pernicitatem vllam tantam, qua decidens graue
tempore tam breui percurrat tam immane &longs;patium,
quale continere admittis ducenta milliarium, prope
modum millia. Certè, cùm attendo globum tormen
tarium è machina quapiam maiore explo&longs;um vertica
liter, vno circiter pò&longs;t minuto repetitam terram attin
gere, & vix tamen, ex &longs;upputatis ob&longs;eruationibus variis,
pertigi&longs;&longs;e ad vnum milliare altitudinis, ex qua v&longs;que
recidens dimidium eius temporis, &longs;eu &longs;emi-minutum
in&longs;ump&longs;erit: (&longs;æpe enim &longs;æpiùs ob&longs;eruauimus e&longs;&longs;e re
rum grauium &longs;ur&longs;um proiectarum de&longs;cen&longs;um æqui
temporaneum a&longs;cen&longs;ui) cùm ad i&longs;tud, inquam, at
tendo, con&longs;ideróque &longs;imul globum per hoc milliare
decidere eadem illa velocitate, qua inciperet cadere à
Luna; a&longs;&longs;equor quidem euenturum, vt ex Luna deci
dens, & iuxta progre&longs;&longs;ionem Arithmeticam numero
rum ab vnitate imparium incedens, decideret altero
&longs;emi-minuto milliaribus tribus, tertio quinque, &
quarto &longs;eptem; adeò vt, &longs;ub finem &longs;ecundi minuti de
prehenderetur decidi&longs;&longs;e milliaribus &longs;exdecim, &longs;eu
iuxta Galileum, nouemdecim, cum vna quinta millia
ris parte: At quid-nam hoc e&longs;t ad milliarium ducenta
millia comparatum? Quanquam & iuxta illam tuam,
Geometricamve rationem duplam, po&longs;&longs;et res prope
verum haberi, quod ad milliaria illa prima, ac minuta
duo prima attinet, &longs;i diceremus eundem globum de
cur&longs;urum primo &longs;emi-minuto milliare vnum, &longs;ecundo
vides, vt duobus minutis milliaria non decideret plu&longs;
quam quindecim; cùm a
ducatur, vt primo &longs;emi-minuto decidere velis globum
milliaribus &longs;ex cum fere triente; &longs;ecundo milliaribus
quadringentis, ac tribus, & vna quinta milliaris parte,
tertio vicies quinquies mille octingentis quatuor, cum
dodrante; & quarto totis milliarium myriadibus cem
tum &longs;extaginta quinque; ac in&longs;uper mille quingentis
&longs;eptem, cum vna quinta; totidem enim ex tua &longs;erie, ac
&longs;umma pedum colliguntur. Quæ admonere &longs;anè po
tui&longs;&longs;e videntur, quàm incredibilem admitteres rem,
dum concluderes, & ad marginem exprimeres
globus ferreus à Lunæ concauo ad centrum de&longs;cendens, &longs;er
uata temporibus æqualibus acceleratione in ratione dupla, in
toto de&longs;cen&longs;u duo vnius horæ minuta prima integre non in
&longs;umeret.
pauca de cau&longs;&longs;a Phy&longs;ica, deque lap&longs;u circa eam admi&longs;&longs;o.
XLV.
Videris deinde fidem liberare circa id,
quod facturum te receperas de tempore determinan
do, quo duo illa primæ partis percurruntur dimidia;
vt quo habito di&longs;tinctè deinde præ i&longs;um tempus cog
no&longs;ceremus, quo decidens graue de&longs;ignatum &longs;patium
&longs;uo de&longs;cen&longs;u percurteret. Dicis autem primò, G
quidem id fidenter promittere, dum ait &longs;e iteratis &longs;æpiùs ac
diligenter experient is ob&longs;erua&longs;&longs;e globum ferreum ex altitud ne
cubitorum centum decidentem quinque &longs;ecundis horæ minutis
totum illud &longs;patium decurri&longs;&longs;e: verùm, cùm idem non minùs
e&longs;&longs;e spatia &ecedil;qualibus temporibus emen&longs;a eam inter &longs;e ratio
nem ob&longs;eruare, quæ inter numeros omneis impareis ab vni
tate continua &longs;erie procedenteis inuenitur; & in hac tamen
po&longs;teriore ob&longs;eruatione vehementer errauerit, magnoperè
verendum e&longs;&longs;e, ne in priore quoque non minùs hallucinatus
&longs;it. Dicis deinde,
prima quælibet pars de&longs;ignati spatij tran&longs;mittitur, ni&longs;i tem
pus quoque cogno&longs;catur, quo pars &longs;equens priori æqualis, vel
duæ medietates prim&ecedil; &longs;eor&longs;im decurruntur; quod tamen
exactè determinare,
cau&longs;&longs;as iam &longs;æpiùs adductas. Et quænam quidem fue
rint huiu&longs;modi cau&longs;&longs;æ non commemini; &longs;ed interim
tamen candorem commendo, quo dicis Tertiò,
cúmque diligentia adhibita nihil habere potui&longs;&longs;e, in quo in
tellectus conquie&longs;ceret:
fœliciùs a&longs;&longs;equi po&longs;&longs;e confidat,
eligat, puta
præcisè minorem, pedum videlicet centum; & ex vtraque
altitudine, tempus de&longs;cen&longs;us exactißimè inquirat; tum mino
re tempore, ex maiore &longs;ubducto, re&longs;iduum daturum tempus
de&longs;cen&longs;us per turris maioris centum pedes infimos: tempus
verò illud minus, quo idem corpus ex &longs;ola centum pedum al
titudine de&longs;cendet, &ecedil;quale tempori futurum, quo ex maiori
quoque altitudine, per centum pedes &longs;uperiores de&longs;cenderit.
XLVI.
Ad primum porrò quod attinet; videtur
&longs;anè non &longs;atis idonea refutatio experimenti, quod
ille te&longs;tatur &longs;e &longs;æpiùs, ac diligenter peregi&longs;&longs;e, ni&longs;i te&longs;te
ris temetip&longs;um idem tenta&longs;&longs;e, peregi&longs;&longs;eque, ac fui&longs;&longs;e
rem &longs;ecùs à te ob&longs;eruatam, fal&longs;itati&longs;que adeò con-Quod enim e&longs;&longs;e verendum ais, ne halluci
natus fuerit, hoc &longs;atis profectò non e&longs;t; & quòd argu
mento e&longs;t tibi error vehemens, quem admi&longs;i&longs;&longs;e illum
ais, circa progre&longs;&longs;ionem iuxta &longs;eriem numerorum im
parium; declaratum iam antè e&longs;t, vt ea quoque ip&longs;a in
re non fuerit erroris conuictus; imò & &longs;uffragium
etiam tulerit cùm ex aliis experimentis, tum etiam ex
tuo, hoc e&longs;t in Bilance peracto. Ad &longs;ecundum quod
&longs;pectat, determinauit ille, quo præcisè tempore &longs;ecun
da &longs;patij pars, ac dimidium primæ, & quævis alia per
curreretur, ex a&longs;&longs;ignato tempore, quo pars prima de
curritur. O&longs;tendit nimirum ex &longs;uis principijs,
lationis principio duo quælibet spatia &longs;umantur, tempora
ip&longs;orum fore inter &longs;e, vt alterum eorum ad spatium medium
proportionale inter ip&longs;a. Adeò vt, &longs;i inter AB pri
mam partem, & AC aggregatum primæ cum
&longs;ecunda inuenias mediam proportionalem AD,
tempus ca&longs;us per AB, ad tempus ca&longs;us per AC,
futurum &longs;it vt AB, ad AD. Nimirùm id
con&longs;equitur ex eo, quòd &longs;patia &longs;int inter &longs;e
in duplicata temporum ratione; &longs;eu vt quadra
ta temporum; quódque &longs;it per&longs;picuum ratio
nem &longs;patij AC ad &longs;patium AB e&longs;&longs;e duplam
rationis AC, ad AD, &longs;eu eandem, quam ha
bent quadrata AC, & AD. Ex quo fiet, vt cùm AB
&longs;upponas e&longs;&longs;e &longs;ex minutorum, AC compobetur mi
nutorum octo, & 29. &longs;ecundorum proximè; ac proin
de tempus per BC &longs;it minutorum duorum, & viginti
nouem proximè &longs;ecundorum. Eadem autem ratione
diui&longs;a bifariam prima parte in E, & accepta AF media
per primum dimidium AE minutorum 4, & &longs;e cun
dorum 14
rius dimidium FB minuti 1, at &longs;ecundorum 45 Ad
Tertium nihil e&longs;t, quod dicam, quandò nihil determi
nas, &longs;ed prouocas
alio exoptes. Ac videbatur quidem id
te præ&longs;ertim ex&longs;pectandum, cùm profitereris
&longs;cientiam,
ac potentia accelerationis motus in naturali de&longs;cen&longs;u grauium
determinaretur:
Galileo p&longs;eudo-&longs;cientiam
hac in re e&longs;&longs;e importunus; addoque &longs;olùm, vbi id ex
perimentum peractum fuerit, &longs;ucce&longs;&longs;eritque, certum
me propemodum e&longs;&longs;e, ex ijs, quæ hactenus peregi ip&longs;i
valdè affinibus, elicitum exinde iri, quod opinionem
fulciar, non tuam, &longs;ed ex Galileo hactenus expre&longs;&longs;am.
XLVII.
Iam ad finem properans,
li&longs;que &longs;it cau&longs;&longs;a accelerationis in naturali de&longs;cen&longs;u grauium:
cur corpora, &longs;altem, quæ eiu&longs;dem figuræ, & homogenea &longs;int,
cuiu&longs;cumque, & quantumlibet in&ecedil;qualis ponderis illa fuerint,
deorsùm nihilominùs &ecedil;quali celeritate de&longs;cendant: aliàque
eiu&longs;mo li, qu&ecedil; tibi quidem in promptu &longs;int, & alio loco, ac
tempore opportuniùs forta&longs;&longs;e proferenda in publicum: &longs;ed in
terim h&ecedil;c pr&ecedil;libanda puta&longs;&longs;e, qu&ecedil; non mo ò ad reuincendos
G
nam accelerati motus naturam aperiendam nece&longs;&longs;aria vide
rentur. Quo rursùs loco, nihil e&longs;t, quod addam, neque
cur importunè rogem, quamobrem non cen&longs;ueris
ac duabus præ&longs;ertim heic commemoratis; cùm id fe
cerit maximè &longs;perandum, qui titulus e&longs;t
&longs;tratioScilicet tibi liberum fuit ex&longs;pecta
re tempus, quoddam opportunius; ac mihi &longs;anè op
pidò nimiùm pro tua comitate tribui&longs;ti, cùm faciens
editionis &longs;pem, id futurum inter&longs;erui&longs;ti,
cognoueris i&longs;ta viris eruditis, mihique imprimis minimè di&longs;
plicui&longs;&longs;e. Ac intelligo quidem non fui&longs;&longs;e cur tibi pla
cerent, quæ de ii&longs;dem quæ&longs;tionibus in priore mearum
illarum Epi&longs;tolarum commentus &longs;um, ac cætera inter,
quod adnixus fui explicare Phy&longs;icam cau&longs;&longs;am, ob
quam cadens graue primo momento per vnam or
gyiam, cadit in &longs;ecundo per treis, in tertio per quin
que, &c. Verùm ratio iam nulla &longs;ube&longs;t, quorsùm aut
quicquam repetam, aut obiectionem, &longs;i quampiam es
propo&longs;iturus præoccupem; cùm paratus aliunde &longs;im
& manus dare, & habere gratiam, quam maximam
voueo, meliora docenti. Agno&longs;co interim, me in&longs;igni
quadam incuria illa confcrip&longs;i&longs;&longs;e, quæ leguntur poti&longs;
&longs;imùm à calce paginæ &longs;eptuage&longs;imæ ad caput &longs;exage
&longs;imæ tertiæ, vbi figuram explicans, quam ab initio hûc
retuli, ip&longs;os velocitatis gradus &longs;ic feci ex pari cum par
tibus &longs;patij, vt per eo&longs;dem triangulos repræ&longs;entatos
a&longs;&longs;ump&longs;erim; cùm debuerim potiùs per ip&longs;as triangu
lorum veluti ba&longs;eis parallelas repræ&longs;entare.
XLVIII.
Po&longs;tremò anacephalæo&longs;i concludens;
vides, & euidenter agno&longs;cis, quàm non rectè
tum æquabiliter acceleratum eum e&longs;&longs;e definierit, qui æqualibus
clarius iam tibi &longs;it, eumdem motum, æqualibus temporibus, non
&ecedil;qualia, &longs;ed maiora &longs;emper, ac maiora recipere celeritatis aug
menta, in continua ratione dupla. Vides item, & pari eui
dentiâ per&longs;picis, non minus erra&longs;&longs;e
&ecedil;qualibus temporibus emen&longs;a, eam inter &longs;e rationem ob
&longs;eruare voluit, quæ inter numeros omnis imparis ab vnitate
procedenteis reperitur; cùm eadem quoque spatia, clarè ac
manife
ac maiora percurri, in eadem continua ratione dupla. Vides
porrò, ac penè palpas, quàm vana, atque inanis &longs;it noua illa,
& tantopere ab ip&longs;o
p&longs;eudo &longs;cientia: cùm non ni&longs;i fal&longs;is, atque erroneis principiis
innitatur; & quam non immeritò ante annos duos mihi di&longs;
plicuerit, quòd tu quoque ii&longs;dem illis principiis nounullam fi
dem adhiberes.
a&longs;&longs;en&longs;um pr&ecedil;beas, re&longs;titutam &longs;cilicet motus accelerati defini
tionem & ab iniu&longs;ta Galilei oppugnatione vindicatam. Ha
bes & veram, germanàmque in naturali de&longs;cen&longs;u grauium
accelerationis rationem, tam in temporibus, quàm in &longs;patijs
&ecedil;qualibus con&longs;ideratam. Habes denique eam quoque ratio
nem, qu&ecedil; inter spatia &ecedil;qualibus temporibus emen&longs;a reperi
tur, indubitatis experientiis, certis, euidentibú&longs;que rationibus
demon&longs;tratam. Qu&ecedil; &longs;i, vt &longs;pero, tibi accepta, probataque fue
rint, non exiguum huius oper&ecedil; pretium me con&longs;ecutum e&longs;&longs;e
arbitrabor. Ad hæc verò omnia, Optime virorum,
nihil regerere in animo e&longs;t: cùm illa &longs;atis, &longs;uperque
&longs;int, quæ circa &longs;ingula edi&longs;&longs;erui. E&longs;t &longs;olùm, quòd
gratias agam vberes, pro in&longs;igni illo affectu, quem
ante duos annos in me te&longs;tari dignatus es, quemque
quam meam &longs;pera&longs;ti comprobationem. Quòd &longs;i
videaris &longs;pe excidi&longs;&longs;e, dum reprobantem potiùs, quàm
approbantem habes me: at non excidi&longs;ti profectò,
cùm & &longs;pera&longs;tia ffarite tui reuerent
amanti&longs;&longs;imum virum; & me eum volui&longs;ti, vt interpre
tor, qui aliunde ius amicitiæ &longs;eruans illibati&longs;&longs;imum,
tibi, in veritatis gratiam, non erube&longs;cerem repugnare. Et quàm, putas, &longs;æpe expetij po&longs;&longs;e tibi &longs;ub&longs;cribere, vt
foret non affectum magis, quàm opinionum con&longs;pi
ratio; verùm ip&longs;emet iudex eris, vbi meas nugas per
volveris, an-non &longs;altem di&longs;&longs;en&longs;erim cum aliqua &longs;pecie
probabilitatis. Sic certe habe, fore me &longs;emper com
parati&longs;&longs;imum a&longs;&longs;entiendo, &longs;i quandò maior mihi ex
te &longs;imilitudo veri affulgeat, qui &longs;um interim, &longs;i quis
alius, comparati&longs;&longs;imus ob&longs;equendo. Vale, Pari&longs;ijs,
Eidib. Mart. M. DC. XLV.
QVOD non improbâris, oprimè CASRÆE,
mandari typis meam Re&longs;pon&longs;ionem, &longs;eu
qualecumque Iudicium de tua illa Demon
&longs;tratione, circa accelerationem grauium
decidentium, cuius autographum ad te mi&longs;i, &longs;i modo
Vindicias, quas intercedente eodem nobili Senatore,
& amico &longs;ingulari, Franci&longs;co Luillerio, dedi&longs;ti ad me,
iuberem attexi: Ecce non alia conditione Typogra
pho annui, dum meam opellam exigeret, quàm vt
tuam &longs;imul accipiens, tuo de&longs;iderio faceret &longs;atis. V&longs;us
&longs;um autem ea licentia, quam abs te factam memini,
committendi etiam Re&longs;pon&longs;ionem ad Epi&longs;tolam il
lam tuam, cuius aliquoties à te facta mentio; idque
tam in tuo, quàm in meo contextu, pro tuo arbitratu,
variatis perpaucis: & quod Vindicias attinet, omi-
tum cen&longs;eres Exceptione vti (Notis &longs;cilicet interpo&longs;itis,
quibus controuer&longs;ia fieret explicatior (ac tum inte
gram facere Lectori adiudicationem. Cùm certè, quòd
&longs;pectat ad me, tuæ Demon&longs;trationis vim non per
&longs;enti&longs;cam, ac tu, tamet&longs;i iam agno&longs;cas id Experimen
tum, cui, vt fundamento, innixam fecoras, collabi,
con&longs;cribis tamen, peti&longs;que Vindicias, aiens
mihi veritatem maiori iam luce illu&longs;tratam aperire, &
quam quæ&longs;iui, optauique, ab errore vindicatam exhibere:
incumbit &longs;anè nece&longs;&longs;itas, inquirendi quid illud &longs;it,
quod ob&longs;tet mihi tantoperè, ne tua Demon&longs;tratione
mouear; quove modo &longs;im adeò hebes, vt ne in tanta
quidem luce po&longs;itam à te veritatem videam. Quin
etiam, cùm à capite ad calcem, quod aiunt, queraris,
&longs;upponere me extuis principiis, quæ ex illis non de
ducantur, ac affingere tibi quædam, quæ te imperitiæ
coarguant; teneor vel ex hoc maximè ad intertexen
dum velut Apologiam; vt cùm nihil habeam veritate,
&longs;inceritatéque antiquius, ac nihil minùs volüerim,
aut admittere quidpiam fal&longs;um, aut tibi quicquam
imponere; deuoueam, &longs;i quid tale mihi imprudenti
exciderit, aut &longs;altem declarem quid potuerit me ad id
efferendum mouere. Nam vides alioquin habitum
me iri malæ fidei, improbumque virum, qualem non
haberi (Deum immortalem) quantum magis mea
intere&longs;t, quàm imperitum non reputari! Quanquam
ego &longs;anè longè &longs;emper abfui, vt imperitiam in te
cau&longs;arer, cuius magnam potiùs peritiam, virtutem
que reuereor; &longs;ed animo &longs;olùm præconcepi, fore, vt
impatienter ferres, &longs;i in i&longs;ta tanta caligine rerum, di
cereris non in&longs;pexi&longs;&longs;e attentè &longs;atis aliquid, enuncians
videlicet ea, ex quibus quæpiam incommoda con&longs;e
qui deprehenderentur. No&longs;ti etiam, quantum &longs;udâ
rim, vt in&longs;inuatione lenire id po&longs;&longs;em; ac &longs;peciatim
quantum laboris inter cætera &longs;u&longs;tinuerim, cùm articu
lo xxiv. o&longs;tendenda tibi fuit fal&longs;itas tui illius Experi
menti. Quin-etiam tamet&longs;i in hi&longs;ce Vindiciis conti
nuo veluti in&longs;ultu dicas pa&longs;&longs;im
care, decipi, &longs;uppo&longs;itionibus tantum fal&longs;is vti; præoccupato
animo, & non intelligentem e&longs;&longs;e; non e&longs;&longs;e in buius controuer
&longs;iæ ingre&longs;&longs;um penetralia; non penitiùs dicta à te, ip&longs;amque
naturam rei inspexi&longs;&longs;e,
nia tibi lubens condono, partim con&longs;cius meæ imbe
cillitatis, partim contentus libertatem Lectoribus per
mittere, vt diiudicent quicquid id e&longs;t rei. Quod atti
net autem ad ea, quæ toties tibi à me affingi, impo
nique exaggeras, æquum e&longs;t profectò, vt eam inficias,
ac eam labem, qua &longs;entio me ad&longs;pergi, pro viribus
eluam. Facio verò id etiam vel eo nomine maximè
inuitus, quòd ea mouenda iterùm &longs;int, quæ di&longs;plicui&longs;
&longs;e tibi videntur; &longs;ed nece&longs;&longs;itatem ip&longs;e hanc feci&longs;ti, ni&longs;i
contendi&longs;ti, vt me proderem, non rudem quidem, ac
ineptum, quorum nominum non puderet me; &longs;ed pro
fligatæ con&longs;cientiæ, & nullius candoris virum, qualis,
Deo propitio, neque &longs;im, neque vt habear, pati po&longs;&longs;im. Sed ecce demùm tuas Vindicias, cum ne minimo qui
dem vllo &longs;en&longs;us, vocumque detrimento; vtcum que &longs;e
ponerem volens ho&longs;ce titulos, quibus me exornas,
&longs;ic ingenuè profiteor.
dralis Eccle&longs;iæ Dinien&longs;is Præpo&longs;itum dignißimum.
de Motu accelerato ante paucas hebdomadas ad te direxi,
Respon&longs;ionem tuam, eamque accuratè, ac diligenter per
legi. In qua &longs;anè non po&longs;&longs;um non probare quam-maximè
diligentiam, ac &longs;agacitatem tuam, in eius Experientiæ exa
mine, quæ totius Epistolæ fundamentum, & occa&longs;io etiam
fuit: ea quippe fœlicitate rem perfeci&longs;ti, vt meritò tibi gra
tiæ habendæ &longs;int, quòd ea demùm per&longs;pexeris, ex quibus mul
tò certiùs tota de motu accelerato controuer&longs;ia dirimatur. Qua in re, cùm partem mihi quoque nonnullam fœlicitatis
huius facis, vt qui viam, ac methodum nouam ad illu&longs;tra
tionem tandiù de&longs;ideratæ veritatis certißimam, clarißimam
que exhibuerim, id pro ingenita tibi humanitate, con&longs;ueta
que vrbanitate facis.
ac meæ Epistolæ argumento &longs;olertiam tuam, atque indu&longs;triam
pro innata animi mei ingenuitate vehementer probem, &
amicè deo&longs;culer, in cæteris tamen capitibus nec à me, nec
(opinor) à cæteris, obtinere poteris approbationem; in ijs
maxime, in quibus postr
mihi affingis, quæ nec mea &longs;int, nec ex meis legitimè de
duci poßint: vt &longs;cilicet ex iis, tanquam datis, ab&longs;urdam de
cretorum meorum omnium pugnam, & tanquam di&longs;&longs;en&longs;io-
cludas, quam ne rudioribus quidem harum rerum tyronibus
obuceres; & in iis tamentam pertinaci in&longs;tas indu&longs;tria, tan
taque vehementia depugnas, imò toties eadem multis pa
ginis, & maiore tuæ Epi&longs;tolæ parte inculcas, vt apud minùs
harum rerum peritos qui tuaplurimùm authoritate mouebun
tur, videri poßim mortalium omnium imperitißimus. Et
&longs;anè, &longs;i id iure faceres, & ea dicerem, quæ mihi affingis,
aut eadem ex meis ceu verbis, ceu principiis legitima illatio
ne concluderes; haberes quidem pro mea ingenuitate confi
tenrem reum; &longs;ed &ecedil;terno quoque me &longs;ilentio addicerem, qui
etiam num hac ætate tam pueriliter balbutirem. Sed cùm
euidens, persp
&longs;ibi omni ex parte perfect ßimè non cohæreat; patieris pro
tua humanitate, Vir prudentißime, vt qua potero breuitate
tibi primùm, ac deinde cæteris, in iis pr&ecedil;&longs;ertim rebus &longs;atis
faciam, qu&ecedil; minus &longs;ibi coh&ecedil;rere putaueris; vbi primùm pau
ca quædam etiam examinauero, quæ pro
adducis.
Hæc tua e&longs;t Præfatio, ob quam dicendorum quic
quam præoccupare nihil e&longs;t nece&longs;&longs;e; cùm repetiturus
eadem omnia &longs;is. Quia verò deinceps Articulos &longs;ingu
los Epi&longs;tolæ meæ, &longs;iue Re&longs;pon&longs;ionis, ad Demon&longs;tratio
nem tuam, numeris di&longs;er
à primis.
De Statu Controuer&longs;iæ.
numerum
occupetur, nihil adhùc e&longs;t, in quo di&longs;&longs;entiamus.
Dicere vis &longs;anè circa explicandum vtriu&longs;que opi
nionis modum quatenus etiam opinionem, quam tu
defendis ita expo&longs;ui, vt ip&longs;e cam exponeres (tamet&longs;i
po&longs;teà me non ingre&longs;&longs;um in penetralia controuer&longs;iæ
dicas) alioquin enim circa rem ip&longs;am planum e&longs;t,
quantum di&longs;&longs;entiamus; cùm tu gradus velocitatis in
acceleratione grauium decidentium acqui&longs;itæ habere
&longs;e velis vt tran&longs;acta &longs;patia, non vt tempora; ego vnà
cum Galileo &longs;e vt tran&longs;acta tempora, non verò vt
&longs;patia habere opiner: ac tu defendas &longs;patia æqualibus
temporibus in dupla continuò ratione percurri; ego
&longs;patia decurri cen&longs;eam æqualibus temporibus iuxta
progre&longs;&longs;ionem numerorum imparium ab vnitate in
cœptorum. Porrò quia ad illu&longs;trationem totius
controuer&longs;iæ de&longs;iderari adhùc videtur ratio illius Ti
tuli, quo fuit libellus à te in&longs;criptus,
tio, qua ratio, men&longs;ura, modus, ac potentia accelerationis mo
tus in naturali de&longs;cen&longs;u grauium determinantur, Aduer&longs;us
nuper excogitatam à Galileo
ac Mathematico de eodem motu P&longs;eudo &longs;cientiam
dem non pauci tuo libro
quamobrem tu illum Demon&longs;trationem indigita&longs;&longs;es,
quod non &longs;atis per&longs;picerent, qua forma con&longs;tare De
mon&longs;tratio po&longs;&longs;et) ideò videtur operæ-pretium rem
heic &longs;upplere; ac tantò magis, quantò iam etiam titu
lus e&longs;t tuus, Itaque,
vt Demon&longs;trationem, quantum quidem a&longs;&longs;equor, toto
ex opere eliciam, ea videtur huiu&longs;modi.
acqui&longs;it&ecedil; &longs;e habent, vt emen&longs;a &longs;patia, nece&longs;&longs;e e&longs;t spatia
acqui&longs;it&ecedil; &longs;e habent vt emen&longs;a spatia:
spatia decurri æqualibus temporibus in ratione continuò du
pla.
Propo&longs;itionis con&longs;equutio probatur.
in fine primæ partis vnus velocitatis gradus acqui&longs;itus &longs;it, in
fine &longs;ecundi acqui&longs;iti &longs;int duo, in fine tertij tres, & ita dein
ceps; oportet tempus, quo percurritur &longs;ecunda pars, æquale e&longs;&longs;e
tempori, quo percurritur dimidium inferius primæ partis,
quòd velocitas per illam acqui&longs;ita &longs;it dupla velocitatis acqui
&longs;itæ per hoc, vti & spatium duplum e&longs;t; ac deinde tempus,
quo percurruntur tertia, & quarta (tempus, inquam, aliun
de æquale tempori, quo &longs;igillatim percurrerentur triens,
& quadrans infimi eiu&longs;dem primæ partis) e&longs;&longs;e &longs;imiliter
æquale, quòd vt ambarum &longs;patium duplum e&longs;t &longs;patij &longs;ecun
dæ, ita dupla velocitas acqui&longs;ita per illas &longs;it: & iterùm tem
pus, quo percurruntur quinta, &longs;exta, &longs;eptima, octaua, pari
ratione e&longs;&longs;e æquale, quod vt &longs;patium illarum iunctim spatij
&longs;ecundæ, & tertiæ e&longs;t duplum, &longs;ic dupla velocitas &longs;it; atque ita
de cæteris:
tates acqui&longs;itæ &longs;e habent vt emen&longs;a &longs;patia; nece&longs;&longs;e e&longs;t spatia
decurri temporibus æqualibus in ratione continuò dupla.
A&longs;&longs;umptio autem ita probatur.
quilibet a&longs;&longs;umatur, & Bilanx ita &longs;uspendatut, vt lance al
tera &longs;u&longs;tentata cum impo&longs;ito tanto pondere, quantum ip&longs;ius
per aërem libera impo&longs;ito æquilibrium faciat) globus dein
ceps dimittatur in ip&longs;am lancem liberam: fore, vt dimi&longs;&longs;us
ex &longs;uæ vnius diametri altitudine globus attollat &longs;uo impetu
non modò lancem &longs;u&longs;tentatam cum æqualibrij pondere, &longs;ed
vnum pondus prætereà, &longs;uo itidem ponderi æquale, præcisè:
& dimi&longs;&longs;us ex duarum diametrorum altitudine, duo attollat
pondera, hoc e&longs;t duplum &longs;ui ponderis præcisè, & ex trium
altitudine, treis, &longs;eu triplum, &c.
tus, imò impetus velocitas &longs;it; habent &longs;e velocitates in motu
accelerato grauium decidentium acqui&longs;itæ vt emen&longs;a &longs;pa
tia.
Confirmatur A&longs;&longs;umptio aduer&longs;us Galileum.
tum illum, qui à quiete recedens æqualibus temporibus æqua
lia celeritatis momenta acquirit; & paralogi&longs;ticè probat mo
tum æquabiliter acceleratum non e&longs;&longs;e eum, qui æqualibus &longs;pa
tiis æqualia celeritatis augmenta acquirit (quandò id arguit
ex eo, quod totum, & pars eodem, aut æquali tempore per
currerentur: cùm tamen con&longs;tet dimidium tempore breuiore
percurri, quàm duplum) ac tum gratis &longs;ibi po&longs;tulat concedi
gradus velocitatis eiu&longs;dem mobilis &longs;uper diuer&longs;as planorum
inclinationes acqui&longs;itos tunc e&longs;&longs;e æqualeis, cùm eorumdem pla
norum eleuationes ponuntur æquales
falsò a&longs;&longs;umit globum filo nunc longiore, nunc breuiore &longs;u&longs;pen
&longs;um, & ex eadem altitudine per inæqualeis arcus vibratum,
a&longs;&longs;urgere &longs;emper ad eandem altitudinem.
Ac talis quidem formari pote&longs;t, vt mihi videtur,
tua Demon&longs;tratio, quantum, vt dixi, elicitur ex operis
ma; ordine licet retrogrado, ob analy&longs;in, qua fuit re
texendus. Videlicet initium facis ab A&longs;&longs;umptionis
Confirmatione, dum prima parte operisin refutando
Galileo es totus; pro&longs;equeris deinde probando ean
dem A&longs;&longs;umptionem tuo Experimento, dum ip&longs;um
copiosè deducis, & exaggeras; ae tandem probas, vt
con&longs;equens Propo&longs;itionis deducatur ex po&longs;ito ante
cedente, dum &longs;tabilire fusè conaris illam &longs;patiorum
Rationem duplam; quæ etiam Conclu&longs;io e&longs;t De
mon&longs;trationis. Nihil verò nece&longs;&longs;e heic e&longs;t adnotare
quemadmodum non modò A&longs;&longs;umptio &longs;it fal&longs;a; &longs;ed
etiam Propo&longs;itionis con&longs;equutio &longs;it nulla: cùm hoc &longs;it
totius controuer&longs;iæ opus. Itaque hac luce præmi&longs;&longs;a,
& tuum contextum, vt in&longs;equamur, initium facia
mus ab ip&longs;a A&longs;&longs;umptionis confirmatione.
De Motus
æquabiliter accelerari Definitione.
tam à
tum quòd eam quoque rationem,
receptam accelerati motus definitionem ab&longs;urditatis arguit,
paralogi&longs;mum e&longs;&longs;e contendam. Jdeoque numero
lilei definitionem inde numeris omnibus perfectam e&longs;&longs;e conclu
dis, quòd eà &longs;eruatâ rectè vniformis acceleratio intelligatur. At imprimis istud non reprehendo; &longs;ed quòd &longs;uam illam
definitionem nouam nec &longs;ufficienter, nec ea, qua par e&longs;&longs;et,
ratione confirmauerit.
Ni&longs;i tu illud reprehendis; non videbaris ergo dicere
institutam. Quòd fueris autem cau&longs;atus ip&longs;um
illam Definitionem experientia certa, ac euidenti non con
firma&longs;&longs;e;
tiore
&longs;emper e&longs;&longs;e repetas
qui Galileus certè eam non vt receptam, communemque
impugnauit, &longs;ed vt eam, quæ po&longs;&longs;et fortè ab aliquo ex
cogitari. Verumtamen id obiter.
ratio haberi pote&longs;t, vt &longs;tatim con&longs;tabit: Satis-ne igitur Gali
lei definitio inde perfecta concluditur, quòd eà &longs;eruatâ vnifor
mis acceleratio habeatur?
Ita profectò, &longs;i per eam con&longs;tet, quid &longs;it motum
accelerari, & accelerari æquabiliter; neque id vulgari,
&longs;iue potiùs tua, de qua dicis mox con&longs;titurum, perinde
præ&longs;tetur.
mentem, acceleratio illa
motus habeatur, iu
bes concipere duas li
neas
A,
anguli apicem
dentem
duabus angulos vtrim
que æqualeis con&longs;tituentem: hanc, &longs;eruatâ &longs;emper eadem
tem concipi postulas, vt etiam intelligamus partem inter
lineas
vt notatis in
GI, IL,
haberi æqualia aduertamus. Nempe vt
ip&longs;ius
IH
ita deinceps. Ex quibus ita concludis:
partibus æqualibus temporis per parteis æqualeis lineæ
AC repræ&longs;entatis, notum e&longs;t momenta, &longs;eu incremen
ta velocitatis per parallelas repræ&longs;entatæ æqualia ac
quiri &longs;ub huiu&longs;modi partibus.
&longs;ed recordare verißimè quoque à te dictum numero
ctum
pro initio spatij, & (vt item addis) pro initio velocitatis.
Recordor; &longs;ed adnoto &longs;imul habui&longs;&longs;e me punctum
A, pro initio temporis quidem æquabiliter &longs;luentis,
prout comparatur ad lineam AC (aut AB) in parteis
æqualeis diui&longs;am; pro initio verò &longs;patij in longum de
currendi, prout comparatur ad aream AKL in trian
gulos æqualeis di&longs;tinctam; ac pro initio velocitatis
continenter acquirendæ, prout comparatur cum linea
parteis æqualeis continuò ad&longs;ci&longs;cente, quov&longs;que cœ
pta à puncto A, euadat KL.
& parteis æqualeis
æqualibus temporis; concipe etiam vicißim idem punctum
mentaQuo po&longs;ito, tam
per parallelasæqualia
&longs;ub huiu&longs;modi partibus acquiri. Cùm igitur in vtraque
hypothe&longs;i eadem omninò velocitatis acceleratio habeatur, cur
prior à te constituta perfectam omnibus numeris
finitionem o&longs;tendat; vulgatam autem defi utionem po&longs;terior
hypothe&longs;is pari ratione perfectam non euincat?
Cau&longs;&longs;am in&longs;inuaui tum mox, tum verbis illis, quæ
præmi&longs;eram,
genter oportet agi heic de motu æquabiliter accelerato, &longs;iue
cuius celeritas continenter, vniformiterque incre&longs;cat, neque
vllum &longs;it momentum con&longs;equentis temporis, in quo motus non
&longs;it velocior, quàm in quouis antecedente, & in quo non eadem
ratione ip&longs;a velocitas augeatur. Nempe memini
ris,
eo egi&longs;ti, admonendo fui&longs;&longs;e originem mali, quòd in
definitione vulgari, &longs;eu tua nulla e&longs;&longs;et facta
poris, &longs;ine quo tamen neque celeritas, neque accele
ratio (& maximè quidem vniformis) intelligi po&longs;&longs;it. Obieci illeic,
debere &longs;emper id mobile, quod decem percurrerit &longs;tadia, dici
moueri celeriter, & &longs;emper id, quod vnicum percurrerit, tar
dè, cum contingere tamen poßit, vt quod percurrit vnicum,
moueatur decuplò velociùs, quàm illud, quod percurrit decem.
Addo heic &longs;olùm; &longs;i AC &longs;it &longs;patium, & mobile di&longs;ce
dens ab A acceleretur v&longs;que ad E per parteis integri
minuti; & motu non interrupto accelerari pergat ab
E in G, &longs;ed per parteis integræ horæ; ac rursùs motu
non interrupto accelerari pergat à G in I, &longs;ed per par
teis integri &longs;ecundi; rur&longs;u&longs;que etiam non interrupto
tegri die
e&longs;&longs;e vn formem? Et ecce ea tamen futura e&longs;t continens;
ac ip&longs;i gradus velocitatis repræ&longs;entati iuxta te paralle
lis ED, GF, IH, LK, cum interceptis omnibus, ha
bituri &longs;unt inter &longs;e, eandem rationem, quam ip&longs;æ par
tes &longs;pati, repræ entatæ iuxta te partibus lineæ AC. Quòd &longs;i id reputes ab&longs;urdum; ab&longs;urdum quoque vi
deri debet metiri accelerationem, ac vniformem po
ti&longs;&longs;imùm, penes &longs;patium, non penes tempus: atque
idcircò lineam AC comparatam ad eas parallelas pro
velocitatibus habitas, non pro tempore, &longs;ed pro &longs;patio
habere.
Enim verò, vt expre&longs;&longs;iùs dicam quamobrem lineæ
DE, FG, & parallelæ cæteræ accipi non po&longs;&longs;int pro
gradibus velocitatis, &longs;i partes lineæ AC accipiantur pro
&longs;patij, non pro temporis partibus, ac &longs;imul in&longs;inuem
quid di&longs;criminis circa repræ&longs;entationem per eandem
figuram, inter vtramque hypothe&longs;in &longs;it, rem ecce
paucis ita deduco. Si DE &longs;it velocitatis gradus, qui per
additamenta continua à puncto A &longs;ecundum trian
gulum ADC, acqui&longs;itus &longs;it, dum mobile AE percur
rit; quæro quî euadat hic gradus, vbi deinceps mobi
le pergendo decurrit EG? An per
Non &longs;ane: quoniam alioquin mobili perueniente ex
A in G non reperiretur acqui&longs;itus in G, ni&longs;i vnus velo
citatis gradus; quatenus etiam per te, &longs;eu ex vulgari de
finitione, additamenta ex E in G æqualia &longs;unt addita
mentis ex A in E, nec pote&longs;t proinde ab v&longs;que E ac
qui&longs;itus e&longs;&longs;e, ni&longs;i gradus vnus, v. c. FP æqualis ip&longs;i DE Et quamvis tu &longs;is inferiùs di
cturus velocitatem acqui&longs;itam ex E in G duplam e&longs;&longs;e
acqui&longs;itæ in E (nempe dum &longs;tatuis primum gradum
acquiri à &longs;olo medio ip&longs;ius AE) & &longs;ic velle debeas
gradum acqui&longs;itum in E, &longs;eu DE perire; quoniam re
periri in G, ni&longs;i duos gradus non vis: cùm &longs;i acqui&longs;itus
in E remaneret, futuri e&longs;&longs;ent tres: vide nihilominùs
quid hoc loco &longs;equatur. Nam &longs;i pereunte gradu DE,
duo gradus, quos vis reperiri in G, vt puta FP, &
PG, acquirendi &longs;int per &longs;olum &longs;patium EG, factis vi
delicet augmentis &longs;ecundum triangulum, qui ducta
linea ex E in F &longs;it EFG, nece&longs;&longs;e e&longs;t, accelerationis
æquabilitas interrumpatur pror&longs;us in E; & cùm ibi
acceleratio ad &longs;uum redierit principium, non &longs;it dein
ceps futura tanta, quanta fuerit in E, ni&longs;i in medio
&longs;patij EG. Itaque gradus velocitatis DE acqui&longs;itus
ex A in E non perit, &longs;ed manet; & cum mobile pro
inde peruenit ad G, talis gradus euadit PG, ac illi ad
iunctus reperitur FP acqui&longs;itus interim per augmen
ta facta &longs;ecundum triangulum DFP.
Quæro deinde, an gradus velocitatis DE manens,
dum mobile percurrit EG, otio&longs;us &longs;it, an aliquid agat? Non dices &longs;anè otio&longs;um e&longs;&longs;e; alioquin enim mobile
tempore nihilo breuiore perueniret ex E in G, quàm
ex A in E, vt putà tran&longs;latum æquali &longs;olùm velocita
te. Igitur agit aliquid.
Requiro, quantum?
hoc e&longs;t,
Si concipiamus mobile, po&longs;tquàm peruenit ad E, non
accipere amplius vlla augmenta, qualia acquiri dixi
mus &longs;ecundum triangulum DFP, &longs;ed moueri &longs;olùm
æquabiliter velocitate acqui&longs;ita DE: requiro quanto An dices
&longs;olùm quanto tempore peruenerit ex A in E? Atqui,
vt faceret, oporteret velocitatem non totam permane
re, &longs;ed &longs;en&longs;im deminur, vt &longs;i deminutio fieret &longs;ecun
dum triangulum DPE: quippe hoc &longs;olùm modo
tempus po&longs;&longs;et æquale fieri, dum nimirum velocitas &longs;ie
decre&longs;ceret ad v&longs;que P, vt ab v&longs;que A reciprotè incre
ui&longs;&longs;et. Quo ca&longs;u neque mobile æquabiliter moue
retur; neque peruenienti in G &longs;upere&longs;&longs;et ampliùs vlla
velocitas: neque proinde, &longs;i velocitate hac decre&longs;cente
intelligamus acquiri velocitatem &longs;ecundum triangu
lum DFP, acqui&longs;ita erit in G velocitas alia, quàm FP
ip&longs;ius DE æqualis, non dupla. Igitur mobile percur
rens EG velocitate &longs;ola DE percurreret ip&longs;um tem
pore breuiore, quàm percurri&longs;&longs;et AE. Quanto igitur?
Omninò dimidio.
Siquidem cùm velocitas DE non
foret deminuta, &longs;ed mobili perueniente ad G, reperi
retur adhùc integra, vt puta effecta PG, ideò vim
&longs;uam exprimeret &longs;ecundum totum quadrangulum
DG, hoc e&longs;t &longs;ecundum duos triangulos triangulo
ADE &longs;igillatim æqualeis; &longs;icque velocitas bis illud po&longs;
&longs;et &longs;ecundum quadrangulum DG, quod po&longs;&longs;et &longs;emel
ret duplò citius (quod e&longs;t dimidium temporis) ex E in
G velocitate DE manente eadem, quam ex A in E,
velocitate eadem DE incre&longs;cente à nihilo &longs;ui. Atque
ex hoc e&longs;t, quare adnotem, gradum, qui acquiritur, &
gradum, qui manet, e&longs;&longs;e inæqualeis; ac manentem di
ci po&longs;&longs;e duplò maiorem, quatenùs e&longs;t duplò poten
tior, &longs;eu duplo fortiùs ampliú&longs;que agens.
Intelligamus iam, dum mobile percutrit EG, &
velocitas DE manens promouetur &longs;ecundum qua
drangulum DG, quov&longs;que euadat PG, nouum in
terim velocitatis gradum acquiri &longs;ecundum triangu
lum DFP, quov&longs;que euadat FP: nece&longs;&longs;e e&longs;t prorsùs
ob nouam velocitatem additam percurri EG tempore. breuiore, quàm &longs;it dimidium temporis, quo decur&longs;um.
fuerit AE. Quanto-nam ergo?
Sanètriente.
Nam vt
velocitas &longs;ecundum quadrangulum DG, dupla ve
locitatis &longs;ecundum triangulum ADE diminuit tem
pus ad dimidium; ita velocitas &longs;ecundum trapezion
DFGE, triplum eiu&longs;dem trianguli, diminuit ad v&longs;
que trientem: Adeò vt, &longs;i tempus, quo decur&longs;um
fuerit AE, &longs;upponatur, vt à te fit, minutorum v. c. &longs;ex,
tempus, quo decurretur EG, futurum &longs;it minutorum
duorum. Cæterùm præter iam obiecta alibi incom
moda, tum illud quoque heinc &longs;equitur, Quòd &longs;i
EG &longs;ecunda pars &longs;patij percurratur triente eius tem
poris, quo decur&longs;a fuerit prima AE, futurum &longs;it, vt
tempore &longs;ecundo percurrantur partes non modò &longs;e
cunda, &longs;ed etiam tertia, quarta, quinta, &longs;exta, &longs;eptima,
& penè octaua; quandò qua ratione &longs;ecundum &longs;pa
tium percurritur triente, eadem tertium percurretur
quinta eiu&longs;dem temporis parte; quartum &longs;eptima,
quintum nona, &longs;extum vndecima, &longs;eptimum decima
tertia, octauum quintadecima, & hæc fragmenta &longs;i
mùl iuncta vnum integrum proximè conficient. Hoc autem fal&longs;um qu dem e&longs;t, & tu ip&longs;e longè abes,
vt fatearis &longs;ed vides tamen, vt fuerit ex ea po&longs;itione
deductam, qua vis parteis lineæ AC e&longs;&longs;e parteis &longs;patij,
Vides ergo quantum repugnet po&longs;itio huiu&longs;modi;
ac peruidere &longs;imul potes, quantum inter&longs;it di&longs;eriminis
inter hypothe&longs;in vtramque. Nam in ea quidem,
quam &longs;equor, cùm partes lineæ AC, fiant partes
temporis, linea DE optimè repræ&longs;entat velocitatem
aqui&longs;itam in fi
timè repræ&longs;entat vnum &longs;patium, dum ea acquiritur,
tran&longs;actum: FG verò optimè repræ&longs;entat velocita
tem acqui&longs;itam in fine &longs;ecundi; & &longs;imul trapezion
DFGE optimè repræ&longs;entat tribus triangulis tria &longs;pa
tia peracta, quorum vnum debeatur gradui FP, prout
interim acquifito, & alij duo gradui PG, prout per
&longs;eueranti ab v&longs;que puncto E. At in ea, quam tu &longs;e
queris, neque habes, quò referas tempus, cuius etiam
tua definitio non meminit
partes æquali tempore percurrantur, illarum di&longs;tin
ctionem habes, vt ad eas referas gradus inæqualeis ve
locitatis. Addo autem, quædam præclarè ex mea
hypothe&longs;i intelligi, quibus nihil &longs;imile ex tua. Veluti
Primò, Quemadmodum omnes velocitatis gradus
&longs;emel acqui&longs;iti inuariati maneant, & &longs;ingulis tempo
ribus æquipolleant con&longs;tanter duobus gradibus, hoc
e&longs;t duobus &longs;patijs æqualibus primo percurrendis &longs;uf
ficiant; vt de&longs;ignatur continua &longs;erie quadrangulo
rum æqualium, DG, PI, QL, itemque FQ,
RM, &c. Deinde, Quemadmodum primo tempore
vnicum &longs;patium percurratur, quatenus vnicus e&longs;t gra
dus, qui acquiritur, & nullus interim, qui permaneat:
In &longs;ecundo autem &longs;int tria, quorum vnum quidem per
per&longs;euerantem: In tertio quinque, quorum vnum per
tunc acqui&longs;itum, & ex alijs quatuor, duo per primum,
duo per &longs;ecundum per&longs;eueranteis: In quarto &longs;eptem,
quorum vnum itidem per tunc acqui&longs;itum, & ex alijs,
duo per primum, duo per &longs;ecundum, duo per tertium
per&longs;eueranteis, atque ita de cæteris. Ad hæc, Quem
admodum proinde æqualibus temporibus æqualia
fiant additamenta, &longs;eu æquales gradus velocitatis ac
quirantur, & interim tamen decur&longs;us &longs;patiorum &longs;ecun
dum &longs;eriem numerorum ab vnitate incœptorum
fiat.
nece&longs;&longs;arium e&longs;t, vt acqui&longs;ita æqualibus temporibus velocitatis
incrementa æqualia &longs;int (vt paßim &longs;upponere videris) &longs;ed
&longs;atis e&longs;t, &longs;i continuò maiora in quacumque ratione
trica acquirantur: cùm notum &longs;it omnibus progreßiones
Geometricas non minùs vniformeis e&longs;&longs;e, quàm Arithmeticas. Ex quibus planè efficitur, definitionem accelerati motus
quamcúmque inde veram, perfectamque non probari, quòd
ea ratione concepta &longs;it, qua vniformis acceleratio exprima
tur.
Id, quod dicis videri me &longs;upponere, reuerâ &longs;uppo
no: & quod ais
non minùs e&longs;&longs;e vniformeis, quàm Arithmeticas,
tem notum non e&longs;t (
neque capio id, quod ais,
nem &longs;atis e&longs;&longs;e, &longs;i incrementa velocitatis continuò maiora in
quacumque ratione Geometrica acquirantur. Sed nempe
videris tu mihi
mitatem:
identitatis, ob vnum, eundemque tenorem, in vna,
atque eademre;
dinis relatio, quæ in rebus alioquin diuer&longs;is, &longs;iue di&longs;&longs;i
tis reperiatur. Ex hoc quippe e&longs;t, cur dicatur inter
fontem, & radicem, non
&longs;e: & in colore pennarum cycni, non
ne Geometrica rationem vnius ad quàtuor, quatuor ad
&longs;exdecim, &longs;exdecim ad &longs;exaginta quatuor, dicamus
e&longs;&longs;e
gre&longs;&longs;ione Arithmetica vnius duorum, trium, quatuor,
vel duorum, quatuor, &longs;ex, octo; vel trium &longs;ex, nouem,
duodecim, &c.
dicamus. Heinc igitur e&longs;t, quorsùm videar non iniu
riâ &longs;upponere accelerationem motus, vt
æquabilis &longs;it, debere Arithmetica progre&longs;&longs;ione ince
dere, & ea quidem &longs;ecundum impareis ab vnitate nu
meros, putà vnum, tria, quinque, &longs;eptem, &c. a&longs;&longs;um
pta; cùm tu, licet Geometricarum &longs;im plici&longs;&longs;imam, du
plam nempe, elegeris reperire in ea vniformitatem,
&longs;eu æquabilitatem non po&longs;&longs;is: &, &longs;i reperire velis ali
quam, Arithmeticam v&longs;urpare cogaris, eam nempe,
quæ &longs;ecundum vnitates e&longs;t, veluti dum ais gradus ve
locitatis &longs;ic acquiri, vt &longs;int in fine primi &longs;patij vnus, in
&longs;ine &longs;ecundi duo, in fine tertij tres, &c. Quamobrem
autem dicas definitionem, de qua agitur,
fectamque non probari, quòd ea ratione concepta &longs;it, qua
re&longs;pexeris; cùm videam heic agi de motu, cuius vni
formis &longs;it acceleratio.
accelerati motus definitionem inde numero
das, quòd ea ratione concepta &longs;it, qua vniformis acceleratio
non exprimatur. Modò enim vtdisti puncto
&longs;patij con&longs;tituto, cuius partes æquales æqualibus &longs;egmentis
EG, GI, IL
quampiam, &longs;ed eandem planè velocitatis accelerationem ha
beri: vt iam ampliùs inquirere tibi non liceat, quomodo ex
vulgata motus accelerati definitione, qua
æqualibus &longs;patijs æqualia velocitatis augmenta acqui
rat, Iam
enim habes concipi pror&longs;us eodem modo, quo tu illum con-
lilei definitione. Nam quòd eodem
numero
gulo
tum minoribus triangulis inter pa
rallelascon&longs;titutis metiendum putas, non
rectè id facis. Vt enim velocitas
acqui&longs;ita per &longs;patium
tur per lineam
qui&longs;ita in
DN:
de cæteris. Cur enim celeritatis
augmenta hoc loco triangulis, in &longs;uperiore autem figuraConstat autem lineas
EQ, vniformi augmento accre&longs;cere, & e&longs;&longs;e, vt
CL, Non
rectè igitur cen&longs;es augmentum velocitatis vniforme e&longs;&longs;e non
po&longs;&longs;e, &longs;i spatijs æqualibus cre&longs;cat æqualiter, & tota illa noui
istius trianguli difformis &longs;tructura sponte corruit.
Heic idem dicendum, quod & paulò antè, quate
nus parteis lineæ AB contendis habendas pro parti
bus &longs;patij, quæ comparentur cum parallelis habitis
pro gradibus velocitatis, nulla habita temporis ratio
ne. Quod autem quæris,
menta triangulis in &longs;uperiore autem figura lineis metienda
edixerim?
tu duos gradus NM, & MD, v. c. æqualeis facias,
qua&longs;i acqui&longs;itos ex L, & C, &longs;ecundum duos triangulos
LNM, & CMD (tamet&longs;i inæquales &longs;int, & MD ex
LC manente factus, duobus æquiualeat) ideò quem
defectum exprimere non licuit lineâ ND, exprimere
placuerit trapezio LD. Nimirùm, cùm velocitas
ND creetur partim ex LC, promota in MD &longs;ecun
dum quadrangulum, partim ex additamentis ip&longs;i fa
ctis &longs;ecundum triangulum LNM; tu ex velocitate hac
detrahis integrum triangulum LMC: &longs;icque ex tri
bus &longs;uper&longs;unt tantum partes velocitatis duæ, quas vt
&longs;imul iunct is repræ&longs;entarem, triangulum à te factum
inde quadrangulo, locum ip&longs;um trianguli tran&longs;lati re
liqui inanem. Fandem autem ob cau&longs;&longs;am relicti &longs;unt
duo trianguli manes ad ordinem tertium tres ad quar
tum, &c. Exindeque e&longs;t, cur
pterea cius &longs;tructura, quatenus e&longs;t tuis decretis confor
mis, &longs;ponte corruat. Addam-ne, cùm lineâ AC
b
deductis articulo XXXV, & &longs;equentibus progre&longs;&longs;ionem
tuam illam duplum incipere ab S, & mobile tam citò
peruenire ex C in D, quàm ex S in C, &longs;icque ob
duplum &longs;patium velocitatem acqui&longs;itam in D e&longs;&longs;e du
plam velocitatis acqui&longs;itæ in C, atque adeò e&longs;&longs;e ad il
lam vt lineam DN ad lineam CL: addam-ne in
quam, & triangulum &longs;ieri exinde adhuc deformius,
& comparationem hanc tuam peruerti, cùm adeò
fal&longs;um &longs;it dicere, vt SC, ad CL, ita SD ad DN? An
non vel ex hoc capite agno&longs;cere potes, a&longs;&longs;umptis li
neis CL, DN, & parallelis cæteris pro incrementis
velocitatis, non licere vniformitatem, æquabilitatem
ve accelerationis tueri?
De Paralogi&longs;mo, qui
Galileo Definitionem &longs;puriam impugnanti
obiicitur.
communem aliorum de&longs;truere conatus es, aggrederis numero
x. eam rationem, qua idem Galileus communiorem motus
vniformiter accelerati definitionem ab&longs;urditatis arguit, à
paralogi&longs;mo excu&longs;are: &longs;ed fru&longs;tra huius cau&longs;&longs;æ pairocinium
&longs;u&longs;cipis, cùm nec eam obtinere, nec &longs;atis plau&longs;ibiliter eam de
fendere poßis. Hæc porrò e&longs;t Si accelera
tio motus in de&longs;cen&longs;u grauium æqualibus &longs;patiis,
æqualia &longs;umeret velocitatis incrementa, e&longs;&longs;ent velo-
inter &longs;e &longs;unt, vt emen&longs;a &longs;patia, debent nece&longs;&longs;ariò ea
&longs;patia aut eodem, aut æquali tempore percurri. Si igi
tur velocitas acqui&longs;ita per totam AC, eam rationem
habeat ad velocitatem acqui&longs;itam per AB,
quam &longs;patium AC, ad &longs;patium AB, nece&longs;&longs;e e&longs;t,
vt totum &longs;patium AC eodem, aut æquali tem
pore decurratur, quo &longs;patium AB ab&longs;oluitur. Impo&longs;&longs;ibile e&longs;t autem, vt corpus de&longs;cendens per
AC, eodem, aut æquali tempore percurrat to
tam AC, quo percurrit partem eius AB, ni&longs;i mo
tus fiat in in&longs;tanti. Tam impo&longs;&longs;ibile e&longs;t igitur,
vt velocitates in de&longs;cen&longs;u grauium inter &longs;e &longs;int, vt
emen&longs;a &longs;patia, quàm impo&longs;&longs;ibile e&longs;t motum illum fie
ri in in&longs;tanti.
contendis e&longs;&longs;e veram Demon&longs;trationem. Vitium ego tan
quam intelligenti breuiùs fortè indicaui: at præoccupato cer
tè aliunde animo, non &longs;ufficienter illud detexi. Exactiùs igi
tur (vt po&longs;tulas) &longs;ingulas huius Ratiocinationis propo&longs;itiones
hoc loco perpendemus. Prima h&ecedil;c e&longs;t,
in de&longs;cen&longs;u grauium æqualibus &longs;patiis æqualia &longs;umeret
velocitatis incrementa, e&longs;&longs;ent velocitates inter &longs;e, vt
emen&longs;a &longs;patia.
e&longs;&longs;e videtur? Duplicem enim patitur, & quidem valdè di
uer&longs;um, quorum alter verus, alter fal&longs;us &longs;it; & ni&longs;i po&longs;teriore
hoc &longs;en&longs;u illam po&longs;t
hil. Prior &longs;en&longs;us i&longs;te e&longs;t, Si acceleratio motus in de&longs;cen&longs;u
grauium æqualibus spatiis æqualia &longs;umat velocitatis augmen
ta; nece&longs;&longs;e e&longs;t, vt hæc eadem augmenta quibu&longs;libet spatij
partibus acqui&longs;ita eandem inter &longs;erationem ob&longs;eruent, quàmSi
enim intriangulo æqualia spatia de&longs;ignentur& in
e&longs;t duos gradus, ad quos acceleratio perueni&longs;&longs;e
ponitur in
tum in
tur terminare celeritatis augmentum, e&longs;&longs;e ad
gradum vnum ip&longs;ius
&longs;en&longs;u, &longs;i primam illam
ac nece&longs;&longs;aria, &longs;ed A&longs;&longs;umptio, quæ &longs;ub&longs;umitur, fal&longs;a e&longs;&longs;et at
que impoßibilis; nempe hæc. At quoties velocitates inter
&longs;e &longs;unt vt emen&longs;a &longs;patia (
bent nece&longs;&longs;ariò ea &longs;patia aut eodem, aut æquali tem
pore percurri:
cinatio corruit. Sed alius item e&longs;&longs;e pote&longs;t primæ illius Propo
&longs;itionis &longs;en&longs;us, vt &longs;eilicet quoties acceleratio velocitatis in de&longs;
cen&longs;u grauium æqualibus &longs;patiis æqualia incrementa acquirit,
integræ velocitates &longs;ecundum &longs;e totas, & qua&longs;libet &longs;ui parteis
analogas aeceptæ, & con&longs;iderata, & non tantum acqui&longs;itæ
partibus &longs;patii æqualibus incrementa, eam ab initio ad finem
inter &longs;e rationem ob&longs;eruent, quam emen&longs;a &longs;patia. Qui &longs;en
&longs;us à priore longè diuer&longs;us est, & à te non intenditur modò;
&longs;ed di&longs;tinctè quoque eodem numero x. exprimitur.
Ais enim.
Rem certè in hunc modum concipio. Intelligatur
AC, diui&longs;a in duodecim parteis æqualeis, ac proinde
eius dimidium AB, &longs;eu ip&longs;i æqualeis DE in
que primùm duo mobilia, quorum vnum de&longs;cendat
ver&longs;us E; notum e&longs;t, &longs;i vtrumque quidem fer
retur non accelerato, &longs;ed æquabili motu,
euenturum e&longs;&longs;e, vt velocitate illius ex&longs;i&longs;tente
dupla ad velocitatem i&longs;tius, illud perueniret
in C, eodem momento, quo i&longs;tud in E;
quoniam &longs;patium ab illo &longs;uperatum foret
vbique ad &longs;patium ab i&longs;to &longs;uperatum, du
plum; hoc e&longs;t, forent ab illo &longs;uperatæ duæ
partes, cùm ab i&longs;to vna: ab illo quatuor, cùm ab hoc
duæ, &c. quatenus &longs;patia &longs;e haberent vbique, vt velo
citates; hoc e&longs;t, velocitas per totam AC, e&longs;&longs;et vbique
dupla velocitatis per totam DE. At verò, quoniam
heic agitur de motu non æquabili, &longs;ed continenter
accelerato; ita di&longs;cedant rursùs mobilia eodem tem
pore, vnum ab A, aliud à D, vt &longs;uccre&longs;centibus conti
nuò velocitatis gradibus, illud perueniendo in C, ac
qui&longs;ierit duodecim, hoc perueniendo in E, &longs;ex:
interrogas,
in C, eodem tempore, quo i&longs;tud in E?
pondeo, nihil certè impedire, &longs;i tales e&longs;&longs;ent, quales de&longs;cribis
velocitate: taleis autem &longs;ine dubio de&longs;cribis, qualeis in prima
illaAt hoc &longs;en&longs;u hypo
thetica illa Galilei propo&longs;itio fal&longs;a e&longs;t, euidenterque impoßi
bilis: cùm nulla prorsùs ratione con&longs;equens inferi poßit ex
antecedente. Hoc enim e&longs;t Antecedens,
locitatis in de&longs;cen&longs;u grauium per totam AC, ita con
tinua &longs;ucce&longs;&longs;ione cre&longs;cit, vt primùm in B acqui&longs;itus
&longs;upponatur vnus aliquis velocitatis gradus; & vlteriùs
procedente motu, & continuò incre&longs;cente celeritate,
certè e&longs;t antecedens, & nihil aliud aiunt ij, qui à
&longs;urditatis arguuntur. Iam ergo vide, vtrum ex hoc antece
dente, rectè tuum illud, & Galilei Con&longs;equens inferatur:
velocitas de&longs;cen&longs;us per totam AC ab initio ad finem,
& &longs;ecundum qua&longs;libet eius parteis con&longs;iderata, perpe
tuò dupla e&longs;t eius velocitatis, qua idem graue per AB
de&longs;cendit.
res, &longs;iue vt &longs;eparatam, qualis e&longs;t
cen&longs;us per
&longs;ui-ip&longs;ius, nec velocitatis per
&longs;ed planè eadem, aut æqualis omninò est. Nempe volumus,
& nece&longs;&longs;ariò exigimus (quod ip&longs;a quoque rei natura po&longs;tu
lat) vt motus, qui per totam
per æqualem
velocitate progrediatur per totam
ueniatur eius, qua fuit in
& communis aliorum &longs;uppo&longs;itio e&longs;t, & primæ propo&longs;itionis à
G
potiùs aduer&longs;us Chimeras, & Tragalaphos depugnet. At
ex eo antecedente tuumillud, &
ria illatione non priùs inferetur, quàm aliud quodlibet ex
vero fal&longs;um eruatur. Prima igitur
&longs;en&longs;u, quo ab ip&longs;o v&longs;urpatur, & à te intelligitur, fal&longs;a e&longs;t,
atque impoßibilis; ideóque tota eius ratiocinatio, non demon
&longs;tratio, &longs;ed merus Paralogi&longs;mus e&longs;t.
An videri potes operosè quidem, &longs;ed nequicquam
tamen explicare conatum, vt Paralogi&longs;mum o&longs;tendas,
quem quanta moderatione potueram non fui&longs;&longs;e à te
fortè liceret mihi dicere, videri po&longs;&longs;e cuipiam, te eum
potiùs e&longs;&longs;e, qui incideres in Paralogi&longs;mum? Quippe
huiu&longs;modi de re &longs;ola hæc verba habueras, quæ non
pigebit repetere,
pus quodcumque in&longs;umat, puta quadrantem: ac deinde BC
ip&longs;i AB æquale, dimidio quadrante percurrat: quis neget in
C
idem graue totam AC, & dimidium eius AB eodem tem
pore non percurreret. Scilicet i&longs;thæc ip&longs;a &longs;unt, ob quæ
ego dixerim, videri te
a&longs;&longs;umere:
târis me
nunc autem, quia contigit &longs;ecus, & &longs;altem virum
præoccupatum
que dicendam. Age itaque tu adeò humanus, vt te hu
ius meæ hebetudinis, præoccupationi&longs;que mi&longs;e
reat, patere &longs;altem lentè incedam, viamque pertentem;
&longs;i quà po&longs;&longs;im te con&longs;equi. Cùm tu quæ pauca Gali
leus hac de re habet, reduxeris ad &longs;yllogi&longs;ticam quan
dam formam; videtur mihi po&longs;&longs;e non incommodè, vt
res di&longs;tinctiùs percipiatur, ea fieri A&longs;&longs;umptio, quæ tibi
Propo&longs;itio e&longs;t, ea Propo&longs;itio, quæ A&longs;&longs;umptio, & Syllo
gi&longs;mus proinde &longs;ic in&longs;titui.
bent nece&longs;&longs;ariò ea spatia aut eodem, aut æquali tempore per
curri.
&longs;patiis æqualia &longs;umeret velocitatis incrementa, e&longs;&longs;ent velocita
tes inter &longs;e, vtemen&longs;a spatia.
bus spatiis æqualia &longs;umeret velocitatis incrementa, deberent
nece&longs;&longs;ariò ea &longs;patia aut eodem, aut æquali tempore percurri.
Tu Propo&longs;itionem (nomine A&longs;&longs;umptionis)
ac impoßibilem
quo dicendum con&longs;equenter) nam alio quidem, quem
diuer&longs;um ais, & Galileo, mihique tribuis, admittere
verum, nece&longs;&longs;ariumque cogeris, ob meum illud ratio
cinium, cuius aliquam recita&longs;ti partem. Nihil verò
ex eo repeto; cùm nemo non &longs;tatim peruideat po&longs;&longs;e
Propo&longs;itionem accipi in duplici ca&longs;u, Vno, &longs;i motus
non acceleratus, &longs;ed æquabilis &longs;it; Altero, &longs;i acceleratus,
&longs;ed æquabili tamen progre&longs;&longs;ione. Si primo enim,
&longs;int duo mobilia, quorum alterum &longs;it velocius, & per
currere debeat &longs;patium duplò longius, quod &longs;it, verbi
cau&longs;sâ, duo &longs;tadia; manife&longs;tum e&longs;t duo ab illo &longs;tadia,
& vnum ab alio, eodem, aut æquali tempore percurri. Sin verò &longs;ecundo, duo mobilia &longs;int, quorum motus
continenter &longs;ic acceleretur, vt celeritas vnius &longs;it conti
nenter, &longs;eu tempore toto, aut ei&longs;dem &longs;altem partibus
celeritatis alterius dupla, & &longs;patium percurrendum &longs;it
&longs;imiliter duplum, veluti rursùs duo &longs;tadia: manife&longs;tum
iterum e&longs;t, duo ab illo &longs;tadia, & vnum ab alio, eodem,
aut æquali tempore percurri. Ac Propo&longs;itionem qui
dem ego &longs;ic&longs;tabilio. Re&longs;tat, vt tu proponas ca&longs;um,
qui exceptionem faciat, ac non e&longs;&longs;e veram vniuersè
demon&longs;tres. Porrò nullum habes, præter tuum &longs;en
&longs;um, &longs;eu ip&longs;am quæ&longs;tionem, atque conclu&longs;ionem, de
qua controuer&longs;iam Galileo facis; neque vllum tibi ad
eum conuincendum argumentum &longs;uppetit, quàm ip&longs;a
verbis illis, quæ paulò antè recitaui, tum ex illis, quæ
habesiam, fa&longs;ioribus quidem, &longs;ed ei&longs;dem tamen. Quia
verò tu ad A&longs;&longs;umptionem (Propo&longs;itionis nomine) hæc
refers; age quid id &longs;it peruideamus.
A&longs;&longs;umptio e&longs;t,
uium æqualibus &longs;patiis æqualia &longs;umeret velocitatis incremen
ta, e&longs;&longs;ent velocitates inter &longs;e, vt emen&longs;a spatia. Tu illam
explanaturus duplicem ip&longs;i &longs;en&longs;um attribuis.
quidem i&longs;te est,
uium æqualibus &longs;patijs æqualia &longs;umat velocitatis augmenta,
nece&longs;&longs;e est, vt hæc eadem augmenta quibu&longs;libet spatij parti
bus acqui&longs;ita, eandem inter &longs;e rationem ob&longs;eruent, quàm
emen&longs;a &longs;patia. At ego non &longs;um Oedipus, pote&longs;que ip&longs;e
cau&longs;&longs;ari te non affari intelligentem: &longs;iquidem non ita
&longs;um &longs;olers, vt per&longs;picere valeam, quid diuer&longs;itatis, aut
explanationis, &longs;en&longs;us hic, quem facis &longs;pecialem,
contineat. Po&longs;terior,
tio velocitatis in de&longs;cen&longs;u grauium æqualibus spatiis æqualia
incrementa acquirit, integræ velocitates &longs;ecundum &longs;e totas, &
qua&longs;libet &longs;ui parteis analogas acceptæ, & con&longs;ideratæ, & non
tantum acqui&longs;ita partibus &longs;patii æqualibus incrementa, ea
ab initio ad finem inter &longs;e rationem ob&longs;eruent, quam emen&longs;a
&longs;patia.
non tantum acqui&longs;ita partibus spatii æqualibus incrementa,
quod ad priorem &longs;en&longs;um attinens, cen&longs;ui&longs;ti hui
&longs;erendumSed vtcumque &longs;it; cùm tu &longs;en&longs;um hunc eun
dem cum eo facias, quem ais à me exprimi di&longs;tinctè; ea
de cau&longs;&longs;a ip&longs;um in confe&longs;&longs;o habeo. Iam cùm &longs;it A&longs;
&longs;umptio hypothetica, & duas proinde parteis
tu &longs;ic vtramque à conditione (vt Dialectici loquuntur)
ab&longs;oluis, vt priorem &longs;en&longs;um antecedenti tribuas, &
po&longs;ter orem con&longs;equenti; ac po&longs;tquàm antecedens ex
pre&longs;&longs;i&longs;ti in linea (expre&longs;&longs;um priùs in triangulo, dum ex
plicares priorem &longs;en&longs;um) arguas non inferri ex eo legi
timè con&longs;equens, expre&longs;&longs;um iuxta po&longs;teriorem. Tu
igitur tale facis Antecedens.
mùm in B acqui&longs;itus &longs;upponatur vnus aliquis ve
locitatis gradus, & vlteriùs procedente motu, &
continuò incre&longs;cente celeritate duo iam in C velo
citatis gradus habeantur.
Ac tum, po&longs;tquàm dixi&longs;ti illos, quià Ga
lile o arguuntur, nihil aliud dicere, videre
me iubes, vtrum ex tali Antecedente, rectè inferatur
tale Con&longs;equens.
nem, & &longs;ecundum qua&longs;libet eius parteis con&longs;iderata perpetuò
dupla e&longs;t eius velocitatis, qua idem graue per AB de&longs;cen
dit.
Itaque, cùm neges &longs;equelam, vt aiunt, hypotheticæ
A&longs;&longs;umptionis, & in illa cardo negotij ver&longs;etur, Ad
moneo dumtaxat circa Antecedens videri loco
tatis,
in&longs;erere, aut &longs;altem debere iam &longs;upponere aduerbium
ligatur huiu&longs;modi.
acqui&longs;itus &longs;upponatur vnus aliquis velocitatis gradus, & vl
terius procedente motu, & continuò incre&longs;cente æquabiliter
celeritate, duo iam in C velocitatis gradus habeantur.
Quippe heic agitur de Motu, cuius acceleratio fiat,
&longs;eu celeritas, velocitas-ve incre&longs;cat &longs;ucce&longs;&longs;ione conti
nua, non quacumque, &longs;ed æquabili. Nam illa qui
dem acceleratio, quam antè obiiciebam po&longs;&longs;e accipi,
primò &longs;ecundum parteis minuti, deinde &longs;ecundum
parteis horæ, tum &longs;ecundum parteis &longs;ecundi, tandem
inquam, acceleratio continua &longs;ucce&longs;&longs;ione fieret, atta
men difformi, inæquabili, qualemque ip&longs;e non es ad
mi&longs;&longs;urus, cùm ab initio v&longs;que controuer&longs;iæ &longs;tatueris
definiti
spatijs æqualia celeritatis augmenta acquirat. Circa Con&longs;e
quens, moneo &longs;olùm te aut debui&longs;&longs;e in&longs;erere, aut iam
debere &longs;upponere mentionem partium
qua&longs;i nimirùm e&longs;&longs;e debeat, aut &longs;altem intelligi huiu&longs;
modi Con&longs;equens.
nem, & &longs;ecundum qua&longs;libet eius parteis con&longs;iderata perpetuò
dupla e&longs;t velocitatis de&longs;cen&longs;us eiu&longs;dem mobilis per totam AB
ab initio ad finem, & &longs;ecundum qua&longs;libet eius parteis, parti
bus ip&longs;ius AC analogas, con&longs;ideratæ.
Id &longs;cilicet ip&longs;e iam edixeras po&longs;teriorem exprimens
&longs;en&longs;um; & per&longs;picuum e&longs;t inæqualeis lineas, quæ ac-
&longs;e deinceps illegitimè comparari &longs;ecundum parteis,
&longs;i facto æquali partium numero non prima vnius ad
primam alterius, &longs;ed ad decimam referatur, & vniuersè
quælibet ad quamlibet ordinis non &longs;ui.
Hi&longs;ce præmi&longs;&longs;is, videndum e&longs;t, quo iure tu&longs;eque
lam neges, & mon&longs;tres con&longs;equens non rectè, ac para
logi&longs;ticè inferri ex antecedente. Nam nece&longs;&longs;itas qui
dem inferendi ex eo manife&longs;ta e&longs;t, quod Acceleratio
fieri, aut velocitas cre&longs;cere non po&longs;&longs;it æquabiliter per
totam AC, neque &longs;imiliter per totam AB, quin &longs;i ve
locitas in C dupla &longs;it velocitatis in B, quælibet partes
analogæ acceptæ per totam AC, duplæ &longs;int ad analo
gas per totam AB: atque ita, quin velocitas mobilis
de&longs;cendentis per AC &longs;it perpetuò dupla velocitatis
eiu&longs;dem mobilis de&longs;cendentis per AB. Quod &longs;anè
adeò e&longs;t manife&longs;tum, vt neip&longs;e quidem negare id po
tueris, po&longs;tquàm ob&longs;erua&longs;ti comparatam primùm à
me lineam AC diui&longs;am in duodecim parteis cum
linea AC diui&longs;a in &longs;ex, tanquam cum &longs;eparata, exi&longs;ten
teque, intelligentiæ cau&longs;sâ DE, ac &longs;ubinde intellexi
&longs;ti e&longs;&longs;e omninò nece&longs;&longs;arium, vt idem mobile, &longs;i velo
eitatem in B, &longs;implam, in C verò duplam acquirat,
reperiatur &longs;imul in fine primæ, & in fine &longs;ecundæ
duodenarum partium; in fine tertiæ, & in fine &longs;extæ;
in fine &longs;extæ, & in fine duodecimæ; propter analogiam
&longs;implicium partium lineæ AB, & duplicium lineæ AC.
Ecquid-nam ergo iuris iam habes, vt perneges con&longs;e
quutionem? Scilicet his verbis illud explicas,
AC,
nec velocitatis per
eadem aut æqualis omninò e&longs;t.
Hui tamen! &longs;iccine exactius, magi&longs;que
&longs;ufficienter mihi Paralogi&longs;mum iam de
tegis, & proptereáne ægrè fers te mihi
(
uiùs ratiocinationis Galileanæ vitium?
&longs;ui ip&longs;ius, nec velocitatis per
Enimverò, non quæritur, vtrum reipsâ dupla &longs;it, &longs;ed
an duplam e&longs;&longs;e tuo ex principio con&longs;equatur. Nam
noui quidem ego fal&longs;um e&longs;&longs;e Con&longs;equens; &longs;ed verè ta
men con&longs;equi ex Antecedente, admi&longs;&longs;o o&longs;tendo. Dicis
ne a&longs;&longs;umo quidem, &longs;ed &longs;olum con&longs;equi demon&longs;tro, vt
cumque po&longs;tquàm id demon&longs;traui, &longs;ub&longs;umere deinde
po&longs;&longs;im, vt o&longs;tendam te tibi repugnare, quòd
ris AC, & AB inæqualibus percurri temporibus, prin
cipium tamen id defendas, ex quo fateri &longs;imul cogaris
eodem, aut æquali tempore percurri. Itaque cùm
heic non agatur de veritate Con&longs;equentis, &longs;ed de ne
ce&longs;&longs;itate, qua con&longs;equitur, ac tu deberes o&longs;tendere
nece&longs;&longs;ariò non con&longs;equi, & declarare in quo peceá
rim, inferendo fore velocitatem per totam AC du
plam velocitatis per totam AB, nihil aliud habes, Quod perinde e&longs;t, ac &longs;i te ponen
te illud Antecedens,
con&longs;equutionem, illam ex eo probem,
careat:
compul&longs;us ad id probandum, nihil tamen aliud
quàm hoc dicas,
a&longs;&longs;umis, &longs;ed planè &longs;en&longs;u præditus e&longs;t. Videlicet quæ&longs;tio
non erit de veritate Con&longs;equentis, nam ego quoque
Platonem &longs;en&longs;u carere fal&longs;um reputabo: &longs;ed de nece&longs;
&longs;itate con&longs;equutionis, quam tu infirmare deberes, ne
euerteret tuum Antecedens; neque ego falsò a&longs;&longs;u
mam, carere Platonem &longs;en&longs;u, qui ne a&longs;&longs;umam quidem:
&longs;ed nece&longs;&longs;ariò &longs;olummodò, & vt conclu&longs;ionem dedu
cam; tamet&longs;i
contradicere tibi ip&longs;i, tanquam coactum a&longs;&longs;erere Pla
tonem &longs;en&longs;u de&longs;titui, quem a&longs;&longs;eras præditum &longs;en&longs;u.
Pergis porrò,
ip&longs;a quoque rei natura po&longs;tulat) vt motus, qui per totam
AC,
planè velocitate incipiat, & eadem velocitate progrediatur,
per totam
augeatur, vt tandem in
B,
exigis, vt
ad C, &longs;iue de&longs;iturus in B,
& progrediatur v&longs;que ad B,
ip&longs;a quoque rei natura (vtcumque po&longs;teà cau&longs;&longs;eris me
non in&longs;pexi&longs;&longs;e illam penitiùs.) Quod autem vis, &
exigis, vt velocitas ex B ita augeatur, vt tandem in
C dupla inueniatur eius, quæ fuit in B, idip&longs;um iam
e&longs;t, quod o&longs;ten&longs;um e&longs;t tantùm auer&longs;ari Naturam, Quam
obrem, non &longs;ufficit tibi, vt velis, atque exigas velo
citat
vt illud, &longs;i po&longs;lit, o&longs;tendas. Quomodo verò id vnquam
po&longs;&longs;is, ni&longs;i volendo, & exigendo, vt quod quæritur,
tibi concedatur, atque adeò petendo, vt loquuntur,
principium? Idip&longs;um e&longs;t, quod te feci&longs;&longs;e, circa relata
verba, obieci articulo XI. & quod tamen iam repetis
con&longs;tanter. Quippe eò quoque te iam adegit, quem
exi&longs;tima&longs;ti te po&longs;&longs;e di&longs;tinguere priorem &longs;en&longs;um, à
po&longs;teriore valde diuer&longs;um. Nam po&longs;tquàm dixi&longs;ti
verba tua &longs;equuntur,
æqualia spatia de&longs;ignentur& in
gradus, & in
&longs;tum e&longs;t d
ueni&longs;&longs;e ponitur in
acqui&longs;itum in
tium. AD. Deprehendere enim &longs;tatim
licet, quemadmodum idip&longs;um &longs;upponas, quod pror
sùs controuertitur: nempe in E e&longs;&longs;e duos gradus, vbi
vnus fuerit in D. Ni&longs;i verò hoc e&longs;t; quid nam tandem
e&longs;t, quod dicunt petere principium? Subinnueram
ego articulo eodem id mouere te, quòd velocitas ac
qui&longs;ita in C (re&longs;umendo nempelineam ABC) &longs;it re
uerâ maior, quàm acqui&longs;ita in B; &longs;ed tu attendere
nolui&longs;ti ex eo, quòd &longs;it maior, non &longs;equi tamen e&longs;&longs;e
duplam; ratus &longs;cilicet te penitiùs in&longs;pexi&longs;&longs;e rei natu
ram, ac eo principio &longs;emper abductus, de quo tota e&longs;t
gulo, lineæ ba&longs;i parallelæ repræ&longs;entare gradus veloci
tates valeant, &longs;i partes cruris alterutrius ip&longs;is re&longs;pon
dentes repræ&longs;entent &longs;patia; non aduertendo, quî i&longs;ti
gradus inæquales &longs;int, & à &longs;eip&longs;is differant, dum
acquiruntur, & dum manent; & quid incommodi ex
hac repræ&longs;entatione trahatur. Videtur &longs;altem occa&longs;io
dubitandi fieri debui&longs;&longs;e, po&longs;tquàm admonitus à me,
fal&longs;um deprehendi&longs;ti id Experimentum, cui &longs;oli in
nixus, prounciâras velocitatem duplam e&longs;&longs;e ex du
pla altitudine; ac &longs;altem ob&longs;erua&longs;ti globum cadentem
ex A in C, hoc e&longs;t ex altitudine duarum
&longs;ui diametrorum, non eleuare cum oppo&longs;ita
lance duplum eius ponderis, quod eleuat ex
A in B, hoc e&longs;t ex altitudine vnius: &longs;ed res e&longs;t
po&longs;teà fu&longs;iùs dicenda. Heic &longs;olùm moneo,
quod &longs;ubdis
tionem e&longs;&longs;e primæ Propo&longs;itionis
&longs;umptionis) G
tuam, aliorumque &longs;uppo&longs;itionem, ip&longs;amque fal&longs;am,
ac impo&longs;&longs;ibilem; &longs;ed à Galileo tamen hypotheticè &longs;o
lùm v&longs;urpari, & Antecedens fieri, vt quid ex ea incom
modi nece&longs;&longs;ariò &longs;equatur, demon&longs;tret. Vnde &
quod ais,
vides quonam &longs;en&longs;u accipiendum &longs;it; & quod &longs;upere&longs;t,
ip&longs;e iam agno&longs;cis, an eius rationem
gi&longs;mum
tuus,
ac penitùs agno&longs;cit,Tunc ex tuis, & Galilei principijs facilè agno&longs;ces velocita
tem in E, hoc e&longs;t in fine &longs;ecundi temporis acqui&longs;itans, veloci
tatHoc autem con&longs;tituto, tuis ego, &
armis ita aduer&longs;um te in&longs;urgo.
Et verò opperior.
libus acqui&longs;ita eam inter &longs;e rationem ob&longs;erua
rent, quam tempora, nece&longs;&longs;ariò ip&longs;æ quoque
velocitates perpetuò e&longs;&longs;ent inter &longs;e, vt tempora,
e&longs;&longs;etque, exempli gratiâ, velocitas duobus temporibus æquali
bus acqui&longs;ita velocitatis primo tempore acqui&longs;itæ dupla.
Scilicet i&longs;ta tibi e&longs;t hypothetica Propo&longs;itio.
A&longs;&longs;um
tio &longs;equitur.
vt eodem, aut æquali tempore à velocitate dupla &longs;patium
decurratur duplum eius, quod percurritur à velocitate &longs;ubdu
pla.
Conclu&longs;ionem &longs;ubtices; nam quod &longs;equitur e&longs;t
qua&longs;i Sub&longs;umptum. Quæ&longs;o te verò, ecquam nam
po&longs;&longs;es exinde deducere, con&longs;tante Syllogi&longs;mo ex ter
minis quatuor; neque tertio termino, vt decuit in hy
pothe&longs;i, vnà cum Propo&longs;itionis aut antecedente, aut
con&longs;equente a&longs;&longs;umpto. Huiu&longs;modi enim videtur
fui&longs;&longs;e debere A&longs;&longs;umptio.
tis incrementa temporibus æqualibus acqui&longs;ita eam inter &longs;e
rationem ob&longs;eruant, quam tempora.
Ac tum Conclu&longs;io fui&longs;&longs;et.
ip&longs;æ quóque velocitates perpetuò e&longs;&longs;ent inter &longs;e, vt tempora,
e&longs;&longs;etque, exempli gratiâ, velocitas duobus temporibus acqui&longs;i
ta velocitatis primo tempore acqui&longs;itæ dupla.
Agno&longs;cis autem ecquid nam aduer&longs;um me heinc
concludatur. Sed de A&longs;&longs;umptione tamen tua,
habenda e&longs;&longs;et legitima, vt dicam, ea, vt po&longs;&longs;it quadam
tenus cum propo&longs;itione cohærere, nece&longs;&longs;e e&longs;t ita &longs;up
pleatur.
&longs;ita
e&longs;t, vt eodem, aut æquali tempore
rum temporum)
plum eius, quod percurritur
mo)
Tunc autem addo e&longs;&longs;e nece&longs;&longs;e, vt percurratur &longs;pa
tium non modo duplum, &longs;ed & quadruplum primi: &longs;i
velocitas quidem acqui&longs;ita æquabiliter fuerit (qualis
illa e&longs;t, qua de agimus) quatenus dum &longs;ecundus veloci
tatis gradus tempore &longs;ecundo acquiritur, & per ip&longs;um
par &longs;patium illi, quod decur&longs;um fuit tempore primo,
percurritur, percurruntur &longs;imùl duo alia per gradum
velocitatis primo tempore acqui&longs;itum, ac in vigore
per&longs;euerantem, veluti iam antè declaratum e&longs;t. Sed
ecce Sub&longs;umis.
tur à velocitate &longs;ubdupla primo illo toto tempore acqui&longs;ita,
eodem tempore &longs;imul percurretur &longs;patium PN &longs;patii PM
duplum à velocitate dupla toto tempore AE acqui&longs;ita.
Cùm
a&longs;&longs;umis? Nam in A&longs;&longs;umptione quidem non
di&longs;tinxeras v
aut æquale acciperes, & procliue fuit, vt
acciperes re&longs;pectu duplæ, cui re&longs;ponderent
duo tempora, &longs;iue, vt expre&longs;&longs;i, aggregatum
temporum duorum, vnde & &longs;ub&longs;umendum
fuit.
curratur à velocitate &longs;ubdupla, futurum vt toto
tempore AE
duorum)
Quo ca&longs;u rursùs addo futurum, vt non modò du
plum, &longs;ed etiam quadruplum percurratur.
spatium PN, & eius dimidium PM, quod e&longs;t impoßibile,
ni&longs;i motus fieret in in&longs;tanti.
e&longs;t,
curratur duobus, & dimidium PM illorum primo, &longs;e
quitur quidem, &longs;ed addendum, percurri in&longs;uper alia
duo &longs;patia: quæ duo aliis iuncta, motu, qui fiat &longs;uc
ce&longs;&longs;iue, non in Enimverò, vt Sub
&longs;umptum tuo &longs;en&longs;u probes, & te perinde, atque me,
mutatis &longs;o ùm terminis, ratiocinari planum facias, hi&longs;
ce verbis pro&longs;equeris.
piam alio &longs;patio
mobilia, quorum vnum per
cipiat velocitate dupla, quo alterum per
momentis continuò partes spatii
rantur, quàm &longs;int partes &longs;patii
dem momentis &longs;ubdupla velocitate decurruntur. Quo igi
tur tempore mobile lentius &longs;patium
eodem alterum mobile duplò velocius &longs;patium
ab&longs;oluerit. Et quoniam, te iudice, alia ratio non e&longs;t, &longs;iue spa
tium
dem coniunctum &longs;upponatur, nece&longs;&longs;arium planè fuerit, vt
etiam ab vno, eodemque mobili, vno, eodemque tempore to
tum spatium
quod certum est e&longs;&longs;e impoßibile, ni&longs;i motus fieret in in&longs;tanti. Hæc ratiocinatio, variatis tantum terminis, de quibus contro
uer&longs;ia e&longs;t, tota (vt vides) tua est.
Imò, non tantum meam agno&longs;co, &longs;ed inuariatis
etiam terminis, & qualem omninò aduer&longs;um te dedu
xi, agno&longs;co; adeò vt mirer ip&longs;um te, illam aduer&longs;um
te comparatam, non variatis terminis retorquere in
me, &longs;ed mutato nomine, v&longs;urpare aduer&longs;us teip&longs;um. Nam, vt mutares terminos, de quibus, vt ais, contro.
uer&longs;ia e&longs;t, debueras idip&longs;um, quod ego ratiocinando
habui pro
re,
quòd velocitas exæquetur à me quidem
verò Sic autem accepta linea PM pro tempo
re AD, & PN pro tempore AB, pro&longs;equi potu
hoc modo.
piam alio tempore
duo mobilia, quorum vnum per
velocitate &longs;ubdupla; tum nece&longs;&longs;e fuerit, vt quibu&longs;libet &longs;pa
tij partibus continuò momenta temporis
percurrantur, quam &longs;int momenta temporis
aliò mobili ii&longs;dem partibus &longs;ubdupla velocitate decurruntur. Quo igitur spatio mobile lentius tempus
velocius tempusEt quo
niam te iudice alia ratio non est, &longs;iue tempus
RO,
&longs;iue eidem coniunctum &longs;upponatur: nece&longs;&longs;arium
planè fuerit, vt etiam ab vno, eodemque mobili,
vno eodemque &longs;patio totum tempus
eius dimidium
e&longs;t e&longs;&longs;e impoßibile, ni&longs;i motus fieret in puncto.
Hoc &longs;anè modo fui&longs;&longs;es ratiocinatus
tum terminis,
ce&longs;&longs;itatem vi&longs;us fui&longs;&longs;es. Nunc autem, cùm terminos
controuer&longs;os non varies, ac nihil concludas aduer&longs;um
me, &longs;ed illud omninò, atque eodem modo, quod e&longs;t
aduer&longs;us te conclu&longs;um: e&longs;t planè cur mirer &longs;ic captare
te ex teip&longs;o triumphum. Nam & cum alioquin ita
habes.
controuer&longs;ia e&longs;t, tota, vt vides, tua e&longs;t; quam &longs;i vt legitimam
admittis, tuis ip&longs;e plagis conclu&longs;us es: &longs;in autem reiicis, & ab
&longs;urdamagno&longs;cis, non rectè facis, dum nullo modo dißimilem,
tanquam demon&longs;trationem defendis, & hanc eius loco tibi
repo&longs;itam Paralogi&longs;mum iam e&longs;&longs;e, & non ni&longs;i eadem diftin
ctione di&longs;&longs;ol
Cùm, inquam, &longs;ic habes, per&longs;picis omninò, quo
iure me dicas iis plagis conclu&longs;um, quibus tu potiùs à
me irretitus teip&longs;um implicueris magis: aut-quàm
meritò Paralogi&longs;mum cen&longs;eas, quod ratiocinium priùs
probâris, & nunc tanti putaueris, vt tuum inde ratio
cinum duxeris e&longs;&longs;e confirmandum. Et pergis qui
dem,
æqualia velocitatis augmenta acquiri, eaque eandem inter &longs;e
rationem &longs;eruare, quam æqualia&longs;iue spatia, &longs;iue tempora ob
&longs;eruant; & aliud velocitates ip&longs;as integras &longs;ecundum &longs;e totas,
& &longs;ingulas earum parteis analogas ab initio ad finem totius
motus inter &longs;e comparatas, in eadem e&longs;&longs;e ratione, quæ inter
æqualia &longs;iue tempora, &longs;iue spatia emen&longs;a reperiatur. Pri
mum illud verum e&longs;&longs;e nihil repugnat, at &longs;ecundum istud fal
&longs;um, & impoßibile est; quod &longs;i rectè
Paralogi&longs;mum nobis pro demon&longs;tratione non obtru&longs;i&longs;&longs;et.
Verumtamen, ne confunde quæ&longs;o tempora cum
&longs;patiis; cum ais aliud e&longs;&longs;e
poribus, &c. Siquidem & facta ratiocinatione nihil
conclu&longs;i&longs;ti contra tempora, vt te puta&longs;ti concludere;
&longs;ed &longs;olùm contra &longs;patia, quatenus à me fuerant impe
tita: & tempora aliunde cum velocitatibus comparata
nullam agno&longs;cunt di&longs;tinctionem, qualem te putas in
uehere: cùm & totæ velocitates, & ip&longs;arum partes, &longs;eu
augmenta eandem &longs;emper proportionem cum tempo
ribus, partibu&longs;que corum analogis &longs;eruent. Quin
etiam, quod &longs;pectat ad &longs;patia, declaratum iam e&longs;t,
quàm irrito conamine &longs;ic di&longs;tinguas, quatenus de mo
tu non quomodocumque, &longs;ed æquabiliter accelerato
leus non aduerterit fal&longs;um, ac impo&longs;&longs;ibile e&longs;&longs;e, quod
&longs;ecundum ais, hoc e&longs;t,
quidem i&longs;tud e&longs;&longs;e fal&longs;um, impo&longs;&longs;ibileque non modò
aduertit, &longs;ed etiam o&longs;tendit, quod tu recu&longs;as aduertere,
con&longs;equi ex ea, quam tu &longs;equeris, opinione. Recu&longs;as,
inquam, & ita habes, qua&longs;i idip&longs;um pro principio vero,
atque nece&longs;&longs;ario à &longs;e credito v&longs;urpauerit; ac interim
fui&longs;&longs;e ab eo Paralogi&longs;mum obtru&longs;um ais, quem nuilla
tenus o&longs;tendi&longs;ti, & prof
Paralogi&longs;mum.
minùs fal&longs;am, atque impoßibilem numero xi. in fine mihi af
fingis; dum ais m
con&longs;equenter loquentem, velle in de&longs;cen&longs;u per totum spatium
AC bifariam diui&longs;um in B, partem BC tran&longs;curri
qua fal&longs;a &longs;uppo&longs;itione, &longs;equenti numero vnum In
commodum, & ad finem Respon&longs;ionis tuæ alia plura
longè ab&longs;urdißima deducis, quæ tanquam con&longs;ectaria
ex meis principiis, ac decretis nece&longs;&longs;ariò illata mihi
obiectas.
mus, eius examen in commodiorem locum re&longs;erua
bimus.
Cùm tu Caput magni momenti per&longs;tringas adeò
obiter; non po&longs;&longs;um ego non &longs;altem duo, aut tria quæ
dam adnotare. Quî enim Imprimis intactum præ
teream, quod
ac impo&longs;ßibilem, dum aio te ad vulgatam motus definitionem
con&longs;equenter loquentem, velle in de&longs;cen&longs;u per totum &longs;patium
dimidio eius temporis, quo percurritur AB?
&longs;o tuam fidem, an tua, an alterius fuerint, quæ &longs;unt iam
&longs;uperiùs verba recitata? Su&longs;ceperas ip&longs;e o
in illa Galilei A&longs;&longs;umptione Paralogi&longs;mum, & præmi
&longs;eras,
quomodo velocitates &longs;int inter &longs;e, vt emen&longs;a spatia; licet
eadem spatia, neque eodem, neque æquali tempore percur
rantur:
ris id præ&longs;taret, atque idcircò
gi&longs;mi conuinceret, i&longs;thæc met &longs;ub
graue de&longs;cendens per AB, tempus quodcumque in&longs;umat, putà
quadrantem; ac deinde BC ip&longs;i AB æquale dimidio qua
drante percurrat; quis neget in
tem eius, quæ fuit in B? Et tamen idem graue totam AC,
& dimidium eius AB eodem tempore non percurreret.
Subinde autem qua&longs;i re ab&longs;olutè cófecta pro&longs;equutus
es,
merus Paralogi&longs;mus. Quæ&longs;o ergo te, quid tibi affinxi?
Agno&longs;cis tua verba, an non?
&longs;am, ac impoßibilem?
impo&longs;&longs;ibilem agno&longs;eas; at tunc &longs;altem veram, atque
nece&longs;&longs;ariam habui&longs;ti, cùm illa &longs;ola v&longs;us fueris ad o&longs;ten
dendum Paralogi&longs;mum. Nam &longs;i fal&longs;am quidem tunc
quoque, ac impo&longs;&longs;ibilem habui&longs;ti, quomodo proba&longs;ti
id, quod intendEt, &longs;i &longs;en&longs;i&longs;ti po&longs;&longs;e eam tibi, tan
quam fal&longs;am, ac impo&longs;&longs;ibilem negari, quanam proui
dentia ip&longs;am communiAn o&longs;ten&longs;urus Paralogi&longs;
mum, volui&longs;ti &longs;ponte te exhibere paralogi&longs;tam ridi
culum, vt puta non alio principio, quam fal&longs;o, atque
ms, cùm te tamen tantopere o&longs;tenta&longs;&longs;es, reperireris
Sed qualemcumque habueris: &longs;altem ego &longs;um bona fi
de v&longs;us, neque affinxi quicquam tibi; cùm non aliam
tibi Propo&longs;itionem tribuerm, ni&longs;i, quam tu ip&longs;e pro
principio ad conuincendum Galileum v&longs;urpaueris,
quamque iam etiam fal&longs;am, impo&longs;&longs;ibilemque dicere
non po&longs;&longs;is, quin arguas te nihil confeci&longs;&longs;e, &longs;ed ope
ram planè lu&longs;i&longs;&longs;e, in Galileum cùm in&longs;ulta&longs;ti: ac per
peram fui&longs;&longs;e glortatum its verbis,
lilei fal&longs;a e&longs;t, & tota eius ratiocinatio merus Paralogi&longs;mus.
An dices Propo&longs;itionem fui&longs;&longs;e conditionalem? Si di
cas, eadem e&longs;t ruina. Siquidem facta conditionis ap
po&longs;itione, &longs;uppo&longs;itio aut vera tibi, ac nece&longs;&longs;aria, aut
fal&longs;a, ac impo&longs;&longs;ibilis fuit. Si prius, vides contradictio
nem, qua fal&longs;am iam, ac impo&longs;&longs;ibilem agno&longs;cis; &longs;i po
&longs;teriùs, vides ludibrium, cui te fui&longs;ti expo&longs;iturus. An
dices te po&longs;teà cen&longs;ui&longs;&longs;e difficile determinatu e&longs;&longs;e,
quod tempus per primam, quod per &longs;ecundam de&longs;
cen&longs;us partem in&longs;umatur; ac ideò cœni&longs;&longs;e compara
tionem non ab v&longs;que initio, &longs;ed ab ip&longs;o &longs;olùm me
dio primæ partis? Si dicas, declaras te quidem &longs;ubdu
bita&longs;&longs;e po&longs;tmodùm, an hoc fortè principium non e&longs;&longs;et
verum, nece&longs;&longs;ariumque: &longs;ed concedendum e&longs;t inte
rim, te, cùm ip&longs;um heic v&longs;urpa&longs;ti, aut non habui&longs;&longs;e ip
&longs;um fal&longs;um, ac impo&longs;&longs;ibile; aut vltrò voluiffe exhibere
te Sophi&longs;ten planè ex&longs;ibilandum: quod ab&longs;it tamen vt
cen&longs;eam. Vtcumque &longs;it, &longs;altem ego nihil affinxi.
De
inde, quod dixerim
vulgatem loq
ne habentibus, vbicumque a&longs;&longs;umpto æquali &longs;patio
v
& plan
dem depu
BC percurratur octante, &longs;eu dimidio quadrantis. Po
deducere
to
principiis, ac decretis
gendi vel deuiter, ob examen propo&longs;itionis re&longs;erua
tum in commodioreSed vtcumque &longs;it, re
puta
exiqua
ha
to Paralogi&longs;mo, & comperiaris non &longs;atisfeci&longs;&longs;e, cùm In ommodum ite
tan
quam con&longs;equens ex tuo decreto cum hac propo&longs;i
tione congruo, de &longs;patiis emen&longs;is, temporibus æqua
libus, in ratione continuò dupla.
Priu&longs;quam hæc de Paralogi&longs;mo, quem Galileo ob
ieci&longs;ti, dimi
culis XXXVI, & XXXVIII. fui&longs;&longs;e tenon &longs;ecus ratiocina-
ralogi&longs;mum admi&longs;erit, incidi&longs;&longs;e te, recidi&longs;&longs;eque
in cundem: ac o&longs;tendere vel ex ea &longs;ola ratiocina
tione tua, quæ relata e&longs;t articulo XXXIII. quemad
modum ex tuis principiis demon&longs;trare liceat,
velocitates &longs;icut &longs;patia &longs;int,
eodem, aut æquali tempore percurrantur.
ergo, quæ illeic, lineâ, ideò probas
locitatem in
tatem inCùm & aliunde,
citas per totam
SD; quatenus
&longs;patii, quod &longs;it item incœptum ab
inter
re, aut &longs;ic licere argumentari.
tas à
Igitur,
velocitas, ab A in D dupla e&longs;t velocitatis ab A in
Et &longs;imiliter,
quia velocitas ab
Ac rur&longs;us, quia vt velocitas per totam DE dupla
e&longs;t velocitatis per totam SD, ita velocitas per totam
SD debet e&longs;&longs;e dupla velocitatis per totam PS, & ve
locitas per totam PS, velocitatis per aliud vlterius di
midium, acita porrò, quantum licebit &longs;ubdiuidere ad
v&longs;que punctum A, &longs;icque demum velocitas per totam
locitas per totam AD velocitatis per totam AS; Dico
aut te nihil concludere, aut &longs;ic licere ratiocinari.
Si
citas per totam
Igitur,
velocitas per totam
Et &longs;imiliter, AE
qui velocitas per totam
tam
Quo, & non aliomodo Galileus, & ego ratiocina
ti &longs;umus. Adderem concludi eodem planè modo, per
curri AF triplum, AG quadruplum, &c. tempore eo
dem, quo eandem AD; verùm res deductu perfacilis
e&longs;t, iuxta ea quæ pari ratione deducis &longs;equentibus
articulis; & e&longs;t iam aliunde tempori parcendum.
De
Po&longs;tulato Galilei, Circa motum &longs;uper æque altis,
non æquè inclinatis planis.
in quo cùm initio, at
que in fine
&longs;e euidens, aut ex euidentibus demon&longs;tratum, cum eodem
lileo agno&longs;cis, candide omninò facis: &longs;ed id planè &longs;ufficit, vt
cætera quoque, quæ ab eodem Galileo ex illo Po&longs;tulato inferun
tur, veri&longs;imilia tantum, & minimè demon&longs;trata cen&longs;eantur:
eumque proinde nobis de motu accelerato, non &longs;cientiam (vt
eam vocat) &longs;ed opinionem tantum tradidi&longs;&longs;e, quod &longs;olùm con
cludo.
At concludere &longs;imùl debes, aut in ip&longs;a Scientiæ
voce
cùm &longs;e nouam &longs;cientiam inuchere profe&longs;&longs;us e&longs;t; licere
adhûc minùs tibi, qui illam P&longs;eudo-&longs;cientiam vocans,
profiteris te veram, ac certam in eius locum &longs;ub&longs;ti
tuere; quatenus tradita ab illo experimentis innititur,
quæ nullius hactenus fal&longs;itatis conuicta &longs;int; tua iis
&longs;uffulcitur, quæ conuicta &longs;int nullius e&longs;&longs;e veritatis.
viderim) partim vera, partim fal&longs;a, aut &longs;altem incerta e&longs;&longs;e
non dubito. Duas certè eius Propo&longs;itiones primas ego quo
que de globis euidenter demonstro; at quomodo ex prioribus
illis duabus Propo&longs;itionibus po&longs;teriores inferantur, &longs;atis non
video, ni&longs;iCùm enim globi
pondere æquales
F
(
momenta ad de&longs;cen&longs;um
retineant in reciproca,
& permutata ratione planorum, ob eamque cau&longs;&longs;am momen
ta ip&longs;ius
CA;
cioribus momentis deor&longs;um voluitur, & magis à motu perpen
diculari di&longs;trahitur, eundem nihilominus gradum velocitatis
acquirere inNam quod
ais tarditatem motus spatij longitudine compen&longs;ari, conie
ctando quidem a&longs;&longs;eris; at (quod ad Po&longs;tulati per &longs;e, & ex
terminis minimè euidentis nece&longs;&longs;arium e&longs;&longs;et) nulla id ratione
demonstras.
Quod de Propo&longs;itionibus Torricellij ais, cogno&longs;ces
tiones. Quod autem ais
demon&longs;trando tarditatem motus &longs;patij longitudine compen&longs;ari
dixi&longs;&longs;e:
non coniect
tendente
clinata pareis velocitatis gradus in fine decen&longs;us non acquirere;
ac non demon&longs;trante, &longs;ed dumtaxat notum dicente,
quantò minus accliue fuerit:
id concluderes, quatenùs non a&longs;&longs;umeres planum, quantò mi
nùs accliue e&longs;t, tantò e&longs;&longs;e quoque prolixius. Etenim notum
quidem e&longs;&longs;e acquiri minores velocitatis gradus in minùs de
cliui, quod &longs;it decliutori æquale: at &longs;i, vt minus decliue, ita
etiam prolixius &longs;it, notum quoque e&longs;&longs;e velocitatem in fine illius
quæ&longs;itam e&longs;&longs;e po&longs;&longs;e æqualem velocitati in fine decliuioris ac
qui&longs;itæ, prolixitate nempe de&longs;cen&longs;us paruitatem incremento
rum velocitatis compen&longs;ante Pro&longs;equeris.
xvi & xvii.
adducis, ve
experimentum
æqualem altitudinem a&longs;cen&longs;u defenda
contendo, pendula eiu&longs;modi neque ad eandem, vnde ip&longs;a demi&longs;
&longs;a &longs;unt, altitudinem a&longs;cendere, neque ad æqualem &longs;emper, &longs;i
ex punctis ad lineam horizontalem diuer&longs;imodè comparatis,
&longs;uspendantur; huiu&longs;que etiam rei, ac diuer&longs;itatis cau&longs;&longs;as, at
que impedimenta inquiris, quæ &longs;i abe&longs;&longs;ent, tum eadem pendu
la ad æqualem perpetuò altitudinem præcisè con&longs;cen&longs;ura
diuinas, non autem demon&longs;tras.
At beatus &longs;um &longs;altem, &longs;i non ab&longs;que aliqua, & cui
nih lrefragetur, veri&longs;imili ratione, diuinem.
militudines, aut &longs;u&longs;piciones.
Tu verò & optimè facis, & beatior me longè es, &longs;i
demon&longs;trationes adinuenias, nec ea amplexeris, quæ
apertè fal&longs;a cùm &longs;int, ne veri&longs;imilitudinis quidem, aut
&longs;u&longs;picionis nomen mereantur.
quatuor distinctis filis &longs;ic appen&longs;os, vt primi longitudo &longs;it
vnius pedis, &longs;ecundi quatuor, tertij nouem, quarti &longs;exdecim:
ai&longs;que eos, &longs;i ex quapiam altitudine &longs;imul dimittantur, &longs;uas
inter &longs;e vibrationes ita componere, vt dum quartus globus
vnam perficiet, tertius duas, &longs;ecundus treis, & primus quatuor
ab&longs;oluat. Hæc, inquam, & quæ inde colligis, nec certiora
&longs;unt, nec exactiùs cum experientia congruunt, quàm ea, qui
bus confirmandis a&longs;&longs;umpta &longs;unt. Et&longs;i enim in paucis ali
quibus vibrationibus ea ratio vtcúmque ob&longs;eruari videatur;
breut tamen interrumpitur, vt &longs;æpius à me experientia
combrobatum est; cuius etiam rationem indicat, qui noua
G
que &longs;e expertum e&longs;&longs;e a&longs;&longs;erit, vibrationes omneis eiu&longs;dem pen
duli æquali tempore perpetuò non ab&longs;olui: quod tamen nece&longs;
&longs;arium e&longs;&longs;et, vt con&longs;en&longs;us ille vibrationum diutiùs perma
neret.
Illud de Pendulis experimentum ita certum e&longs;t, vt
fal&longs;um nunquam deprehenderim, quoties a&longs;&longs;umun
tur, & quandiù manent longitudinum exqui&longs;itè ea
rumdem. Nam quia non ponderis, &longs;ed longitudinis
variatio vibrationum celeritatem, aut tarditatem va
riat, ideò ni&longs;i quatuor illa pendula a&longs;&longs;umantur exqui
&longs;itè longitudinum præ&longs;criptarum, fiet &longs;en&longs;im, vt quod
cæteris, vibrationum euariet, aut accelerando, &longs;i vel
tantillum breuius æquo fuerit, aut retardando, &longs;i tan
tillum prolixius. Et aliunde quia filum, ni&longs;i metalli
cum &longs;it, diducitur &longs;en&longs;im, prolixiu&longs;que euadit, dum
partim tortum detorquetur, partim pondere pertra
ctum tenuatur; idcircò inde quoque fit, vt ni&longs;i cauea
tur, ne fiat variatio, longitudinis, vibrationes, quæ per
initia con&longs;onanter inter &longs;e fiebant, decre&longs;cant &longs;en&longs;im,
ac denique di&longs;crepare deprehendantur. Heinc &longs;emper
mihi con&longs;titit, quod pendulum primò di&longs;crepare acce
lerando animaduerti, fui&longs;&longs;e aliquantulum æquo bre
uius; quod remorando, aliquantò prolixius: vt pro
inde non mirer & tibi; & authori,
&longs;am fui&longs;&longs;e aliquam vibrationum incon&longs;tantiam, & in
æqualitatem. Cæterùm res ip&longs;a in &longs;e e&longs;t omninò cer
ta: & vel ex eo, quod deprehendi&longs;ti vibrationes &longs;al
tem peraliquod tempus ita con&longs;onare, vt pendulum
&longs;exdecim pedum vibrationem &longs;emel dumtaxat perage
ret, dum pendulum nouem, perageret bis, pendulum
quatuor, ter: pendulum vnius, quater; potui&longs;ti intelli
gere, quàm hæc egregiè congruant cum iis, quibus
confirmandis fuere v&longs;urpata; cum tu interim tale nihil
in tuæ &longs;ententiæ confirmationem profere po&longs;&longs;is.
non &longs;atis àme refelli, aut erroris
argui ea experimenta, quibus
in de&longs;cen&longs;u grauium tam per aërem, quàm per plana quælibet
inclinata confirmat: nihil
experiundi modum di&longs;&longs;iciNimirum eo loco id &longs;olùm efficere volui, vt quilibet intellige-
experimento its erroribus obnoxio v&longs;us fuerit, qui nullâ dili
gentiâ vitaripo&longs;&longs;e videantur. Satis autem eadem illa expe
rimenta erroris po&longs;tmodùm reuincenda videbantur, &longs;i longé
aliam accelerationis rationem in de&longs;cen&longs;u grauium interuenire
demon&longs;trarem.
Non repugna&longs;&longs;em, &longs;i demon&longs;tra&longs;&longs;es; at demon&longs;tra&longs;
&longs;e non con&longs;titit.
De
Experimentis circaictum; impetum-ve grauium
cadentium; ad explorandum impetu&longs;-ne, vt
&longs;patium incre&longs;cat.
rientia confirmem, quod experientià con&longs;tare affirmo, nempe
Corpus graue quodcumque ex qualibet altitudine per
aërem cadens, & percutiens vt libet, perpetuò ex alti
tudine dupla duplò ampliùs, & ex tripla, quadruplave
di&longs;tantia, triplò, quadruploque fortiùs percutere.
comprobari po&longs;&longs;e, quo idip&longs;um po&longs;tmodum o&longs;ten&longs;urus eram in
globo. Non fuit igitur cum operæ, ac temporis iactura du
plex ingerenda Experientia, vbi plu&longs;quam abundè &longs;ufficere
potuit vnica.
Hactenus de Confirmatione tuæ illius A&longs;&longs;umptio
nis, quam &longs;uperiùs retulimus, vbi de Controuer&longs;iæ
Statu. Sequitur videamus quid habeas de impugna
ta Probatione, ad quam &longs;pectabat Primum membrum
Po&longs;terioris partis Operis totius. Quippe ratus te euer
ti&longs;&longs;e funditus Galilei &longs;cientiam, ac profe&longs;&longs;us te illi
initium ab ip&longs;a Experientia, tanquam à germano eius
fundamento. Quandoquidem porrò his me affatus
verbis fueras,
facileis, atque indubitatas Experientias prouoco, & in ijs ar
bitrum te, ac iudicem habere vehementer gaudeo. Prima peti
tur ex impetu, quo globus, aut graue aliud corpus quodcumque
per
Quis heic loci non ex&longs;pecta&longs;&longs;et plu&longs;quàm vnicam
perientiamQuis exi&longs;tima&longs;&longs;et te ex vnica facere primam,
& &longs;ecundam? Quis non credidi&longs;&longs;et à te, ni&longs;i omneis, ni&longs;i
plurimas, &longs;altem plureis vnâ peractas, ob illud,
graue quodcumque?
facilè experientiâ
qualibet altitudine per
&c.
tiam, præter vnicam in Bilance factam, in quam glo
bus cadens, & percutiens, neque e&longs;t corpus graue
quodcumque, neque vt-libet cadit, percutitque. Sed
nimirùm tu talem Fxperientiam, tamet&longs;i foret vnica,
tanti faciendam e&longs;&longs;e cen&longs;ui&longs;ti, vt e&longs;&longs;et in&longs;tar omnium,
ac veritatem &longs;ic demon&longs;traret, vt facit ver non vna
hirundo. Et, &longs;i talem quidem ip&longs;am inueni&longs;&longs;em, qua
lem &longs;perandam feceras,
verbo vno vt dicam,
aliam te importunè rogitarem; fui&longs;&longs;et illa enim abun
dè, & &longs;atis. Nunc autem, cùm eam longè &longs;ecus &longs;e ha
bere compererim, & tu ip&longs;e non au&longs;is ampliùs, qua
lem priùs diuendere, &longs;icuti mox videndum e&longs;t; quis
non aliam mecum abs te expetii&longs;&longs;et?
xxi.
& xxii.
adiicis,
fru&longs;trà &longs;unt: cùm ex iis etiam vltrò datis, nihil aduer&longs;us in&longs;i
nuatam à nobis Experientiam, aut omninò contra nos (ob
Exemplorum, quibus vteris, dißimilitudinem) concludas.
neres, non fuit, & prætextu Exemplorum, quæ articulis
XXI, & XXII. habentur, di&longs;&longs;imulare vi&longs;um e&longs;t, quæ op
po&longs;ui XX. circa varia Experimenta. Siquidem illa in eo
recen&longs;ui, quæ tu videbaris potui&longs;&longs;e præ&longs;ertim intelli
gere, cùm diceres
quocumque;
rares quemadmodum con&longs;taret tibi grauia ex altitu
dine dupla decidentia impetus e&longs;&longs;e duplò maioris, tri
plò ex tripla, &c. Tu verò, cùm quid re&longs;ponderes (aut
dic &longs;altem, quomodo po&longs;&longs;im id interpretari) non &longs;up
peteret, factum &longs;atis e&longs;&longs;e puta&longs;ti, &longs;i ea diceres
Sed fru&longs;trà fuerint, quatenus ex te fru&longs;trà requi&longs;iui quæ
laterent te; at non fuere fru&longs;trà, vt o&longs;tenderem, te non
debui&longs;&longs;e id, quod in te minimè e&longs;&longs;et, o&longs;tentare. Certè
enim iam non potui&longs;ti illud, quod mox, prætexere,
excitatæ difficultates
operam, tempu&longs;que in iis impendi&longs;&longs;es. Quanquam &
nulla vnquam pote&longs;tin rebus huiu&longs;cemodi diligentia
e&longs;&longs;e &longs;uperflua; ip&longs;eque te&longs;tor fui&longs;&longs;e te, quod &longs;pectat ad
me, ampliùs præ&longs;titurum paucis quibu&longs;dam ver&longs;ibus
explicantibus vnicum, de quo con&longs;taret, Experimen
tum; quàm opere toto, toti&longs;que ratiociniis; ac in eo
&longs;um &longs;emper, vt &longs;i vel deinceps proferre po&longs;&longs;is vnicum,
deuoueam, flammi&longs;que addicam. Quippe fiu&longs;trà &longs;int
mille ratiocinia, &longs;i vel vnicum refragetur Experimen
tum; vt fru&longs;tra &longs;omniemus monteis aureos, qui abeant
&longs;tatim vel minima expergefactione in fumum. Quod
ad ea &longs;pectat, quæ habeo &longs;equentibus articulis, tu
Exempla dicis, vt po&longs;&longs;is di&longs;&longs;imilitudinem cau&longs;&longs;ari; cùm
Experimenta &longs;int, quæ ad rem attineant, ac &longs;upparia
&longs;altem &longs;int iis, quibus controuer&longs;ia dirimenda videa
tur.
Nam, ne
de Primo;
momento &longs;ubducatur ba&longs;is, totum aquæ contentæ cy
lindrum &longs;tatim effluxurum, eo modo, quo &longs;tatim elabe
retur cylindrus marmoreus, aut quiuis alius &longs;olidus, &longs;i
eodem va&longs;e contineretur. Vt autem in cylindro mar
moreo cadente non velociùs de&longs;cendit pars &longs;uprema,
quàm infima, aut intermedia quælibet, quòd omnes
ex æquo ferantur deor&longs;um, & par conficiant &longs;patium,
pariterque accelerentur; ita concipimus in aqueo non
velociùs de&longs;cendere partem &longs;upremam, quàm infi
mam, aut quamlibet mediam, &longs;ed parem e&longs;&longs;e omnium
de&longs;cen&longs;um, omniumque accelerationem; atque id
circò perinde e&longs;&longs;e &longs;upremæ parti aquæ, &longs;iue aqua &longs;ub
&longs;it, &longs;iue nulla &longs;it: quatenus quæ &longs;ube&longs;t, tantum præce
dendo aufugit, quantum ip&longs;a pote&longs;t con&longs;equendo in
&longs;tare: ac fieri proinde, vt &longs;uprema aqua ad ba&longs;in dela
bens, tanto de&longs;cendat tempore, quanto &longs;i ex eadem
altitudine per aërem delaberetur. Iam, cùm exiguum
folùm foramen ad ip&longs;am ba&longs;in aperitur, idem propor-Nam &longs;i&longs;olus quidem e&longs;&longs;et cylindiulus
aquæ re&longs;pondens ip&longs;i foramini, manife&longs;tum e&longs;t ip&longs;um
perinde effluxurum, ac totum cylindrum ba&longs;i tota
aperta. Quoniam verò talis cylindrulus copio&longs;iore
aqua ambitur, non ideò quidem minùs effluit, &longs;ed
efficitur, vt dum pars &longs;uprema antecedenteis con&longs;equi
tur, circum&longs;tantes aquæ &longs;upremæ partes in ip&longs;ius lo
cum propter fluxilitatem &longs;ubeant, ac pari modo, con
tinente
nimirum, alii&longs;que inde&longs;inenter &longs;ub&longs;titutis, ab ip&longs;a v&longs;que
&longs;uperficie, quæ idcircò &longs;emper complanata appareat,
quov&longs;que &longs;ub effluxus finem excauetur, dum quæ &longs;u
pere&longs;t aqua parcior e&longs;t, quàm vt perinde facilè, abun
deque confluere po&longs;&longs;it. Itáque etiam foramine aper
to, aqua &longs;umma in locum ba&longs;eos, ip&longs;umve foramen
tanta velocitate cadit, quanta per aërem caderet; ac
licet proinde de eiusimpetu ex effluxu non &longs;ecus iudi
care, quàm ex ip&longs;o ca&longs;u; vt pote cùm effluendo cadat,
& cadendo effluat; ac pari &longs;emper tempore ex &longs;ummo
ad imum perueniat. Vide igitur an Exemplum di&longs;&longs;i
mile &longs;it, & non potiùs Experimentum (&longs;uppar mini
mùm) illiu&longs;met rei, de qua agitur: & quia quæritur, an
impetus exprimatur duplex ex altitudine dupla, an ex
quadrupla, i&longs;tud verò experimentum (&longs;eu exemplum
mavis) duplum probat ex altitudine quadrupla, non
dupla; agno&longs;ce quo iure dicas quæ habentur memo
ratis articulis
aduer&longs;us in&longs;inuatam à te experientiam, aut omninò contra
te, ob exemplorum, quibus vtor, dißimilitudinem concludere.
XXVIII. De Experimento in Bilance facto, ac
aliud reuerâ probante, quàm velocitates
e&longs;&longs;e &longs;icut &longs;patia.
caput attingis, cùm Experientiam de globo per aërem deciden
te examinas. Jngenuè enim fatendum e&longs;t, in mentem mibi
nunquam incidi&longs;&longs;e, vt inquirerem, an globus ex vnius dia
metri altitudine decidens, po&longs;&longs;et vltra æquilibrium, & pondus
&longs;ibi æquale ampliùs aliquid attollere.
Commendanda &longs;anè ingenua confe&longs;&longs;io (quan
quam addendum fui&longs;&longs;e videtur,
mentem, vt inquireres,
metri altitudine decidens, po&longs;&longs;et vltra æquilibrium, & pondus
&longs;ibi æquale, ampliùs aliquid attollere:
idem æquilibrium, & pondus &longs;ibi æquale ex dimidio, quadran
te, octante, & penè dicam ex vncia altitudinis &longs;uæ diametr
attolleret;
in vtramque partem aberrâris tantopere) Commen
dandumid, inquam; &longs;ed cùm i&longs;tud &longs;it, vt præclarè ais,
fuit, quo res controuer&longs;a determinaretur,
turqueVnum,
cur adeò &longs;olemniter prouoca&longs;&longs;es me
indubitatas Experientias,
rent, ac Demon&longs;trationem tuam, &longs;cientiamque totam
con&longs;tabilirent: cùm ecce habens vnicam, videri iis
po&longs;&longs;es, qui rerum amantes verbis non capiuntur, ita
o&longs;citanter illam peregi&longs;&longs;e, vt nihil e&longs;&longs;et minùs, quàm Profectò ni&longs;i v&longs;us fui&longs;&longs;es voce
ci&longs;ionis,
&longs;es opinione præoccupatus, ac præ illius a more, volui&longs;
&longs;e non opinionem experientiæ, &longs;ed experientiam
opinioni accom modare: Nunc autem non video, cur
tot paginis, tantoque apparatu in&longs;titeris (etiam tot
cautiones adhibendas iis, qui rem experiri &longs;crupulo
&longs;iùs vellent, præ&longs;cribens) vt te expertum crederemus,
vt eius diameter præci&longs;a e&longs;&longs;et men&longs;ura illius altitudinis, ex
qua, &c.
ras differentiam, quòd in globis diameter altitudines præcis è
definiat, vnde pondus, &c. Alterum, cur huiu&longs;imodi Ex
perimento deprehen&longs;o fal&longs;o; hoc e&longs;t, cùm verùm iam
non &longs;it, vt contenderas,
quodcumque ex qualibet altitudine per aërem cadens, &
percutiens vt libet, perpetuò ex altitudine dupla dupla præcisè
ampliùs, & ex tripla, quadruplave di&longs;tantia, triplò, qua
druplove fortiùs percutere;
num eam Ratiocinationem habere, imò & acriter
tueri pro Phy&longs;ica Demon&longs;tratione, quam non alij
fundamento, quàm huic vnico Experimento &longs;uper
ex&longs;truxeris? Hoc &longs;anè e&longs;t, quod mihi videtur faten
dum &longs;imùl ingenuè fui&longs;&longs;e, ac parcendum &longs;imùl labo
ri, quo æque te exerceres, ac me, quemque declinare
potucras, &longs;i neque meam Re&longs;pon&longs;ionem, neque tuas
Vindicias e&longs;&longs;e cuulgandas cen&longs;ui&longs;&longs;es; cùm alioquin
iam de&longs;titutus omni argumento, quo Demon&longs;tra
tionem &longs;uffulcias, ludere videaris omnem operam, dum
operosè adeò in ea propugnanda de&longs;udas.
rùm, ne accuratior illa tua experientia neutiquam tuæ parti
&longs;uffragetur; quamuis dicas com nodè ad
accidi&longs;&longs;e, vt globus non-ni&longs;i ex quatuor diametrorum altitu
dine decidens attollere potuerit duplum eius ponderis, quod ex
vnius diametri eleuatione &longs;ummum extulerat; &longs;icut nec tri
plum, ni&longs;i ex altitudine diametrorum nouem, &c. Ego enim
tuo exemplo inductus, cùm idem tentare item voluerim; ne
que globum ex vnius diametri altitudine, &longs;uum pondus toties
multiplicatum attollere comperi; neque ad duplicatum, tri
plicatumque pondus eleuandum, ad tantam altitudinem attolli
debui&longs;&longs;e. V&longs;us &longs;um quidem bilance obuia, & fortaßis non ita
exacta, & globo Porphyretico vnciæReperi autem hunc globum repetita aliquoties operatione ex
vnius diametri altitudine eleuare &longs;olùm vncias
an vitio bilancis acciderit, vt maius pondus non extulerit) at
idem globus duplum illius ponderis, ex diametris tribus, tri
plum ex quinque, quadruplum ex &longs;eptem, quintuplum ex
nouem &longs;ustulit; interruptus autem nihil vlteriùs tentare po
tui. Ex his autem adhûc vides (quod totius controuer&longs;iæ ca
put e&longs;t) æqualibus spatiis æqualia acquiri velocitatis aug
menta. Hanc ego tamen operationem tibi tanquam exactam
non propono, quia necdum mihi per otium licuit eam adhi
bere diligentiam, quamres huius momenti pro &longs;uo merito po
&longs;tulat: &longs;ed vt te quoque ad exactam illius rei experientiam
inuitem; ex qua tota de motu accelerato controuer&longs;ia diri
menda videatur.
Po&longs;trema hæc verba, quàm e&longs;&longs;ent te digna; ni&longs;i
aliunde Demon&longs;trationem, quod mox obiiciebam, ita
propugnares, ac&longs;i foret iam controuer&longs;ia à te dirempta
&longs;cito me iterum expertum, ac adhibitos mihi fui&longs;&longs;e ad
iutores in&longs;igni peritia, & in experiundo &longs;edulitate, ac
diligentia claros Petrum Petitum, & Danielem
Auberium Maurerium; ac nihil tamen vnquam mihi,
quale tu narras, contigi&longs;&longs;e. Nam v&longs;urpatis globis
duobus altero plumbeo vnius vnciæ, altero ligneo
drachmæ vnius cum triente, fuit &longs;emper eadem proxi
mè ratio, quam in Re&longs;pon&longs;ione iam de&longs;crip&longs;i, exhibita;
& cùm aberratum ab ea &longs;en&longs;ibiliùs e&longs;t, ecce quid Plumbeus,
cùm ex diametro vna extuli&longs;&longs;et vncias 7, dr. 1: extu
lit deinceps ex tribus 11, 3: ex quinque 14, 2: ex &longs;eptem
16, 3: ex nouem 17, 6: cùm iuxta tuam ob&longs;eruationem
efferre debui&longs;&longs;et ex tribus 14, 2: ex quinque 21, 3: ex
&longs;eptem 28, 4: ex nouem 35. 5. Ligneus,
vna extuli&longs;&longs;et drachmas quindecim, extulit deinceps
ex tribus 24, ex quinque 30, ex &longs;eptem 36, ex
nouem 41: Cùm debui&longs;&longs;et per te efferre ex tribus 30,
ex quinque 45, ex &longs;eptem 60: ex nouem 75. Immane
quanto di&longs;crimine! Et non cau&longs;&longs;or quidem proptereà
cuam fidem; &longs;ed e&longs;t cur demirer profitentem te
ac certam &longs;cientiam
indubia
nihil fueris; ac non au&longs;is hanc operationem, tanquam
certam proponere, partim Bilancis incu&longs;ans vitium,
quæ exacta fortè non fuerit, partim quampiam occu
pationem, quæ te ob&longs;eruantem interruperit. Profe
ctò enim Tu, &longs;i quis alius, certus e&longs;&longs;e huius rei debui&longs;ti;
vt qui non modò fueris profe&longs;&longs;us te certam de ip&longs;a
&longs;trationis, qua feceris certam, Vindicias con&longs;cribas. Non moror item, quòd po&longs;tquàm mihi fœlicitati cui
piam verti&longs;ti,
tu non inq
non tam fui&longs;&longs;e fœlicitas, quàm non-nihil maior circa
rem non raram, neque inex&longs;pectatam atter
moror, inquam, quòd temperâris aduer&longs;atiuâ,
reor:
me dem, non e&longs;&longs;e quamobrem de me, deque Galileo
verearis, quatenus dixi
ca&longs;um ex altitudine quadrupla, neque triplum ante ca&longs;um ex
nonupla, &c.
præ&longs;tare perinde te, refragante Experientiâ, &longs;pon&longs;orem
non po&longs;&longs;is.
Non in&longs;to demùm quanto oporteat te tuæ &longs;on
tentiæ amore teneri, qui etiam quæ&longs;ieris ex qualicum
que illo progre&longs;&longs;u remedium, quò iubere po&longs;&longs;es
viderem,
foret) æqualibus spatiis æqualia acquiri velocitatis augmen
ta:
dum vidi&longs;&longs;e, vti ex facta gemina comparatione clarum
e&longs;t; tu, mendo&longs;o etiam progre&longs;&longs;u, tanquam vero &longs;up
po&longs;ito, id videre me iubeas, quod ne ip&longs;e quidem aut
videas, aut videre po&longs;&longs;is. Siquidem, vt videres, opor
teret quemadmodum velocitas acqui&longs;ita ex &longs;patio, al
titudineve diametri vnius, exprimitur eleuatione pon
deris vnciarum 5, dr. 2: ita acqui&longs;itam ex &longs;patio duplo,
&longs;iue ex altitudine diametrorum duntaxat duarum,
exprimi eleuatione dupli ponderis, vnciarum videlicet 4; & ex triplo, &longs;iue ex altitudine diam etrorum
trium, eleuatione tripli, &longs;eu 6, cùm tu ta
men videas eleuari duplum, &longs;iue vncias 10, dr. 4, non
ex &longs;patio duplo, &longs;ed ex triplo, ex quo eleuari oporteret
non duplum, &longs;ed triplum, &longs;euvncias 15, dr. 6. Idip&longs;um
dico de cæteris ad v&longs;que altitudinem diam etrorum
nouem, ex qua attolli oporteret ponderis nonuplum,
&longs;eu vncias 47, dr. 2, non, vt ais, quintuplum &longs;olùm, &longs;eu
vncias 26, dr. 2. An placuit tibi progre&longs;&longs;us ille per nume
ros impareis, vnum, tria, quinque, &longs;eptem, nouem, quo
rum &longs;untinter &longs;e interualla æqualia? Atqui oporteret
hoc ca&longs;u ex diametro vna nihil attolli ponderis, ac &longs;u
peratis deinde duabus diametris, attolli pondus &longs;im
plum, &longs;iue vncias 5, dr. 2, & &longs;uperatis adhûc duabus du
plum, & adhûc duabus triplum, &c: cùm tu velis ta
men ex altitudine nulla, qua&longs;i cyphra, ad altitudinem
v&longs;que integræ diametri, qua&longs;i vnius, attolli pondus &longs;im
plum, &longs;eu vncias 5, dr. 2, adeò proinde, vt &longs;i per &longs;patia
æqualia
vt po&longs;t primam diametrum, cui velocitatem attollen
tem &longs;implum attribuis, accipias &longs;ecundam, cui attol
lentem duplum attribuas, &c. Dicerem id fortè placui&longs;&longs;e,
quòd exi&longs;timâris videri vtcumque congruere cum eo,
quod defendispo&longs;teà, primum primæ partis dimidium,
qua&longs;i pro nihilo haberi, ac numerandum motum dun
taxat ab initio v&longs;que &longs;ecundi dimidii, & pergendum
per
bet duo dimidia contineat. Verum, vt taceam notum
e&longs;&longs;e, quàm parùm cohærenter id fieret, nihil e&longs;t cur
tempus in coniectando teram, cùm etiam pigeat terere
altitudine eleuati, non e&longs;&longs;e in &longs;equentibus operationibus acci
piendum duplum, triplum, quadruplum, &c. &longs;ed &longs;olius exce&longs;
&longs;us vltra æquilibrium a&longs;&longs;umendum e&longs;&longs;e duplum, triplum, qua
druplum, &c. quærimus enim accelerationis, ac velocitatis
effectum, ad quem non pertinet æquilibrium.
Nequicquam profectò &longs;ollicitus es.
Vtcumque enim
exi&longs;timâris id e&longs;&longs;e
nio, vt ex totidem diametris totidem præcisè eleuaren
tur pondera, præter æquilibrium, globo paria: nunc ta
men, cùm videas nihil e&longs;&longs;e nece&longs;&longs;e ad&longs;tringi, neque ad
diametrum, neque ad pondus (imò neque ad figuram
globi, &longs;i modò corpus eiu&longs;modi &longs;it, quod lancem ex
æquo circa medium afficiat) &longs;ed liberum e&longs;&longs;e quamli
bet altitudinem pro prima a&longs;&longs;umere, & quodlibet pon
dus, quod &longs;ummum ex ea attolletur pro pondere pri
mo: con&longs;tat tale pondus, quodcum que illud &longs;it, &
æquilibrio quidem comprehen&longs;o, germanam e&longs;&longs;e men
&longs;uram eius impetus, qui exprimitur ex ca&longs;u à tali altitu
dine; cùm &longs;i aliquid addatur tali ponderi, impetus &longs;it
minor, &longs;i detrahatur aliquid, etiam ex æquilibrio, &longs;it
maior. Quanquam & &longs;i per&longs;tes putare detrahendum
e&longs;&longs;e
quamobrem ip&longs;e proptereà lucratus aliquid videaris,
cùm eo detracto tam ex primo, quàm cæteris ponderi
bus, quæ pondera &longs;uperfutura, &longs;unt pari progre&longs;&longs;ione
&longs;int con&longs;equutura. Nam in exemplo quidem tuo, v g.
&longs;eu numeros 5.2, 10.4, 15.6, 21, 26.2, detracto æqui
librio, &longs;eu comprehen&longs;o habeas (quod tibi forta&longs;&longs;is
quinarii numeri cum quadrante, &longs;eu dr. 2; vt putà, &longs;eu
dicas 4.2, 9.4, 14.6, 20, 25.2: &longs;eu 6.2, 11.4, 16.6, 22, 27.2.
Sed res e&longs;t per &longs;e &longs;atis manife&longs;ta.
diligentiam tuam, ac &longs;olertiam vehementer probem, & exa
ctiorem adhûc à te ex&longs;pectem; perinde probare non po&longs;&longs;um
quæ &longs;equuntur reliqua: & primùm quod ais numero xxviii. fore, vt &longs;i penes globorum diametros men&longs;urandæ e&longs;&longs;ent eo
rum velocitates, demißi ex eadem altitudine globi duo eiu&longs;
dem materiæ, &longs;ed mole inæquales, pari celeritate non de&longs;cen
derent. Ponis autem exempli gratiâ duos globos, quorum
vnus &longs;it diametro decies maiore, quàm alter, & minorem
hunc dicis decuplò velociùs altero moueri. Sed &longs;agacitas tua
hoc loco non aduertit primùm, à maiore globo vnius diametri
de&longs;cen&longs;u tantum velocitatis acquiri, quantum à minore globo
decem diametrorum de&longs;cen&longs;u acquiritur: nihilque omninò re
ferre, &longs;i è duabus velocitatibus inter &longs;e æqualibus altera plu
reis in parteis &longs;ubdiuidatur, quæ &longs;imùl iunctæ alteram exæ
quent; &longs;icut nec ratio acceleratæ velocitatis per quodlibet
spatium variabitur, &longs;i partes eiu&longs;dem &longs;patij æquales ab vno
minores de&longs;ignentur, ab altero maiores. Deinde, illud etiam
non aduertit, vt &longs;i penes spatii parteis æqualeis in quacumque
ratione acceptas, accelerationis velocitas men&longs;uretur, futurum
omninò &longs;it, vt perinde eorumdem globorum diametris ea
dem quoque accelerationis velocitas men&longs;uretur; præ&longs;ertim &longs;i
diametri (vt in propo&longs;ito exemplo) &longs;upponantur commen&longs;u
rabiles; quod & ex ip&longs;a rei natura, & ex proximè adducto
eius exemplo, qui &longs;patium quodlibet, per quod fieret de&longs;cen&longs;us,
nunc maiores in parteis diuideret, nunc in minores, euidenterNon rectè igitur concludis globos eiu&longs;dem
naturæ, &longs;ed mole inæqualeis, inæquali velocitate de&longs;cen&longs;uros,
&longs;i penes eorum diametros expenderentur eorum velocitates.
Quoniam igitur me tam parùm e&longs;&longs;e per&longs;picacem,
&longs;agacemque, arguis, vt quod dixi de duobus globis
non aduerterim; age di&longs;quiramus, tua-ne per&longs;picacia,
& &longs;agacitas aduerterit &longs;atis eam, quam in&longs;titui&longs;ti ani
maduer&longs;ionem. Ego quidem &longs;oleo in rebus, quæ di
cuntur graues, grauitatem duplicem (duplexve pon
dus) di&longs;tinguere. Vnam appello Simplicem, eam nem
pe, quæ conuenit rei etiam quie&longs;centi: vt putà qualem
habet lapis, dum immotus terram &longs;uppo&longs;itam pre
mit, aut claua immota &longs;uppo&longs;itum cuneum. Alteram
Adiectitiam voco, eam putâ, quæ rei ex motu accele
rato aduenit, & de&longs;inente motu euane&longs;cit; qualem &longs;ci
licet habet lapis, prout ex alto decidit, aut claua, prout
tum decidit, tum robu&longs;ta quoque impingitur manu. Cùm verò &longs;implex grauitas men&longs;ura adiectitiæ &longs;it, qua
tenus pro exce&longs;&longs;u grauitatis &longs;implicis, quo vnum cor
pus &longs;uperat aliud, exce&longs;&longs;us quoque e&longs;t adiectitiæ, &longs;i
vtrumque quidem ex eadem decidat altitudine: ideò
&longs;implici grauitate duorum corporum pondere inæqua
lium data, habeo adiectitiam vtriu&longs;que ex pari ca&longs;u
acqui&longs;itam, in eadem ratione, proportioneve, qua &longs;im
plicem: Adeò vt, &longs;i &longs;implex vnius &longs;it librarum decem,
& alterius centum; vbi adiectitia prioris fuerit centum,
po&longs;terioris futura &longs;it mille. Et quia grauitas vtriu&longs;que
adiectitia ex effectu, &longs;eu percu&longs;&longs;ione in rem &longs;ubiectam
facta cogno&longs;citur: ideò rem attendo penes percu&longs;&longs;io
nem, quatenus ip&longs;a notior e&longs;t, faciléque intelligitur,
fuerit, notam quoque eam fore, quæ fict per alterum:
adeò vt &longs;i, exempli gratiâ, prius corpus in vnam bi
lancis lancem decidens eam percu&longs;&longs;ionem faciat, qua
altera cum pondere centum librarum attollatur, deci
dens po&longs;terius eam facturum &longs;it, qua attollatur cum
pondere librarum mille. Iam, cùm tua verba fuerint,
quantàque ip&longs;a percußio fuerit: impetum enim omnem, &
percußionem ex velocitate e&longs;&longs;e, imò impetum ip&longs;um velocita
tem e&longs;&longs;e nullóque hæc ab inuicem di&longs;crimine dirimi: vt me
ritò proinde quaratione accre&longs;cit velocitas, eadem impetus, &
percußio augeantur:
corporum illorum in fine motus ita &longs;e habere, vt &longs;i à
priore acqui&longs;iti &longs;int decem gradus velocitatis, quibus
pondus decem librarum adauctum &longs;it v&longs;que ad cen
tum, acqui&longs;iti etiam fuerint decem gradus à po&longs;teriore,
quibus pondus centum librarum adauctum fuerit v&longs;
que ad mille. Et certè i&longs;ta graduum velocitatis æquali
tas in proportione partium grauitatis adie ctitiæ funda
ta, dici pote&longs;t cau&longs;&longs;a cur duo corpora pondere, &longs;iue
grauitate &longs;implici &longs;ummè inæqualia (vt &longs;i alterum pen
dat libras mille, alterum non ampliùs, quàm vnciam)
æquali cadant tempore; vnde & vici&longs;&longs;im arguantur
e&longs;&longs;e æqui-velocia.
Accedamus propiùs ad hypothe&longs;in.
O&longs;tendere
volui velocitatis gradus men&longs;urandos non e&longs;&longs;e, vt tu
a&longs;&longs;erebas, penes globorum diametros, quæ men&longs;ura
rent &longs;ingulos ca&longs;us.
caußâ, duo ex eadem materia, quorum vnus &longs;it diametro
altitudine: tunc, quia minor decidet per diametros decuplò
plureis, quàm mator, fiet, vt attollat pondera &longs;ibi æqualia
decuplò multipliciora, quàm attollat maior ex &longs;ibi æqualibus:
Quare & &longs;equitur, vtper idem &longs;patium feratur decuplò ve
lociùs, ac decuplò citiùs, temporeve decies breuiore perue
niat ad lancem, quàm maior: hoc autem con&longs;tat quàm fal&longs;um
&longs;it; cùm, &c. Con&longs;idera iam, an quid dicerem, non ad
uerterim. E&longs;to pondus maioris globi mille vnciarum,
& clatus globus vna &longs;ui diametro &longs;upra lancem, in eam
dimittatur; tum gradum velocitatis iuxta te acqui&longs;ie
rit, quo lancem percutiens alteram attollat cum pon
dere vnciarum mille, præter æquilibrium. E&longs;to pon
dus minoris, vnius, & dimittatur &longs;imiliter globus ex
vna &longs;ui diametro, tum etiam gradum velocitatis vnum
iuxta te acqui&longs;ierit, quo lancem vnam percutiens alte
ram attollet cum pondere vnius vnciæ vltra æquili
brium. Attollatur po&longs;teà, & dimittatur minor globus
ex &longs;ecunda &longs;ui diametro, tum velocitatis gradus acqui
&longs;ierit duos, quibus attollantur duæ vnciæ, ac pari modo
ex tertia diametro attollentur tres, ex quarta quatuor,
& &longs;ic deinceps, quov&longs;que ex decima, hoc e&longs;t ex altitu
dine, è qua dimi&longs;&longs;us fuerit maior globus, attollantur
decem. Itaque ex duobus illis globis ex eadem altitu
dine dimi&longs;&longs;is, percutiet minor lancem impetu decuplò
maiore, proportione &longs;ui ponderis, quàm maior &longs;ui re&longs;
pectu percutiat (cùm ille &longs;cilicet attollat decuplum &longs;ui
ponderis, i&longs;te attollat &longs;olùm tantumdem). Igitur &,
cùm impetus, ac velocitas idem &longs;int, erit velocitas mi
noris maior decuplò per illud &longs;patium, quàm maioris,
quàm maior percurret. Atque ego quidem &longs;ic ad rem
aduerti. Ais iam tu,
maiore globo vnius diametri de&longs;cen&longs;u tantum velocitatis ac
quiri, quantum à minore globo decem diametrorum de&longs;cen&longs;u
acquiritur. Verùm cùm ego aduerterim rem &longs;e reip&longs;a
ita habere: aduerti tamen &longs;imùl id aduer&longs;ari tuis de
cretis, vnde & tua &longs;agacitas aduerti&longs;&longs;e duntaxat vide
tur quid fieret, non verò quid ex propriis a&longs;&longs;ertionibus
&longs;equeretur. Pergis
locitatibus inter &longs;e æqualibus altera plureis in parteis &longs;ub
diuidatur. quæ &longs;imùl iunctæ alteri exæquentur, &longs;icut nec ratio
acceleratæ velocitates per quodlibet &longs;patium variabitur, &longs;ipar
tes eiu&longs;dem spatii æquales ab vno minores de&longs;ignentur, ab
alio maiores:
les &longs;int, vt illæ reuerâ per illud &longs;patium &longs;unt: &longs;ed pluri
mùm refert, &longs;i inæquales &longs;int, vt tuis ex decretis e&longs;&longs;e de
ducuntur, Quod deinde &longs;ubdis, diuer&longs;um non e&longs;t.
&longs;ingulas decur&longs;um non iri.
&longs;ine respectu ad tempus definitionem accelerati motus aut
inqui&longs;ierim, aut etiam con&longs;tituerim. Et&longs;i enim priùs accele
rationem motus cum partibus spatij, quàm cum partibus
temporis æqualibus contulerim, cùm tamen vtrumque abun
dè, ac diligenter eadem Epi&longs;tola factum à me cerneres; &longs;atis
iu&longs;tam huius repreben&longs;ionis an&longs;am accipere inde non potui&longs;ti.
vniformiter acceleratum potius definirem e&longs;&longs;e eum,
poribus æqualibus velocitatis augmenta in continua
ratione dupla reciperet:
ritatis incrementa partibus temporis æqnalibus tribueret,
procliue fuit, vt æqualia illa velocitatis augmenta statim &longs;pa
tij potiùs, quàm temporis partibus æqualibus attribuerentur. Sed hæc leuiora &longs;unt.
Dictum hucv&longs;que e&longs;t de tuæ Demon&longs;trationis A&longs;
&longs;umptione. Probare deinceps volui&longs;ti con&longs;equutionem
Propo&longs;itionis; veruntamen duo qua&longs;i membra huiu&longs;ce
Probationis fuerunt. Nam po&longs;tquàm ex tuo &longs;upe
riore Experimento collegi&longs;ti
tem acquiri duplam, ex tripla triplam, &c.
deinceps cen&longs;ui&longs;ti de Tempore, quòd
celeritas motus respectum includat:
declarare
cunda percurratur dimidio temporis, quo prima, tertia
triente, quarta quadrante, &c. vtcumque id videatur
&longs;equi ex ratione illa incre&longs;centis &longs;patiorum in&longs;tar ce
leritatis:
&longs;umpto ab inferiore primæ partis dimidio, quod cer
to tempore percurratur, &longs;ecunda, quæ eius dimidij &longs;it
dupla, percurratur pari tempore: tertia verò triente
eiu&longs;dem temporis, tanquam re&longs;pondens infimo eiu&longs;
dem primæ partis trienti: quarta quadrante, vt re&longs;
pondens quadranti, atque ita de cæteris; Ex quibus
&longs;ubinde &longs;equatur, vt quemadmodum pars &longs;ecunda
æquali tempore percurritur, &longs;ic percurrantur duæ &longs;i
mùl &longs;equentes; &longs;ic quatuor &longs;imùl &longs;uccedentes; &longs;ic Itaque dicendum e&longs;t prius de priore
capite. Interim
ne, &longs;it, an perperam factum, quod admonuerim
bui&longs;&longs;e temporis mentionem in definitione accelerati motus
omitti;
&longs;atis o&longs;tendit. Quod autem deinceps
acceleratum motum non minùs diligenter cum tempore, quàm
cum &longs;patio contuleris:
norem temporis rationem
&longs;patii (vt præteream potui&longs;&longs;e quoque haberi non
nihil maiorem, quatenus à me in&longs;inuatum e&longs;t) ac futu
ram deinceps fui&longs;&longs;e comparationem tam cum illo,
quàm cum i&longs;to cohærentiorem. Quod &longs;ubiicis
fortaßis volui&longs;&longs;e;
re volui&longs;&longs;em, &longs;i licui&longs;&longs;et quidem per te: &longs;ed nihil heic
in iis cardo controuer&longs;iæ vertitur: &longs;ed quòd &longs;it de ra
tione dupla temporibus æqualibus &longs;peciatim dicen
dum inferiùs.
xxxii.
xxxiii.
non &longs;olum contra expre&longs;&longs;am Epistolæ meæ &longs;ententiam,
&longs;ed contra euidentem quoque Demon&longs;trationis lucem velis à me
ea dici, quæ verbis expreßis nego, quæque fal&longs;a e&longs;&longs;e non tan
tum pronuncio, &longs;ed clarè etiam, atque euidenter demon&longs;tro: ex
ii&longs;que deinde, tanquam meis, ea mihi ab&longs;urda affingas, in
quæ nemo, quantumvis hebes impingat. Demon&longs;trare certé
debueras ea, quæ à me
tutis à me principiis nihilominus &longs;equi, antequam eadem, vt
mea decreta impeteres: imò id &longs;olum faciendum tibi fuerat,
vt me caußæ præuaricatorem euinceres, qui ea ip&longs;a fal&longs;a
dentique ratione inferrentur. Quid enim tibi opus fuit mul
tis paginis impugnare ea, quæ iam expugna&longs;&longs;em: & conqui&longs;i
tis vndique rationibus fal&longs;a o&longs;tendere, quæ fal&longs;a e&longs;&longs;e prior
agno&longs;cerem? Et tamen nihil e&longs;t in tota tua Epi&longs;tola aliud, in
quo acrius, animo&longs;iu&longs;que depugnes.
Quomodo quæ&longs;o, optimus, & non pe&longs;&longs;imus po
tiùs e&longs;&longs;em, &longs;i is quidem, quem tu me hoc articulo de
pingis, forem? Verùm, quia num tibi quid affinxerim:
num quædam à te reiecta vt fal&longs;a, ex tuis principiis &longs;e
qui non o&longs;tenderim; num po&longs;tquam tu quædam ex
pugna&longs;ti vt fal&longs;a, ego non tam illa, quàm ex illis vt
tuis, cætera &longs;uperfluè impugnauerim; quia, inquam
num i&longs;ta &longs;e verè, fal&longs;óve habeant, cogno&longs;cendum e&longs;t
ex ijs, quæ à te &longs;ubiiciuntur; idcircò nihil e&longs;t,
quod ad i&longs;ta regeri generatim debeat.
nem affingis, quam iam &longs;upra numero
& in hunc locum examinandam reieci. Vis enim,
& &longs;iue demon&longs;tratione,s&s&longs;ine vlla vel probabili ratione
ais, & qua&longs;i pro tuo iure &longs;upponis,
dens per &longs;patium AB in parteis quotlibet
æqualeis diui&longs;um, percurrere partem &longs;ecundam
DE, in dimidio eius temporis, quo percurritur
prior pars AD,
curri velocitate dupla eius velocitatis, qua tran&longs;
curritur AD.
Quàm falsò repetas hanc Propo&longs;itionem tibi
à me affictam, feci abundè manife&longs;tum, cùm id
obiter non &longs;um prætergre&longs;&longs;us, quod tu citato Quippe tuis verbis recitatis, & deducta occa&longs;ione, ob
quam illa texueras, demon&longs;tratum e&longs;t tuam fui&longs;&longs;e,
quam iam inficiaris, expre&longs;&longs;am &longs;ententiam; heincque
adeò probatum manet me non modò probabili, &longs;ed
conuincenti etiam ratione (ni&longs;i te velis Paralogi&longs;tam,
quod ab&longs;it vt cen&longs;eam, ridiculo&longs;i&longs;&longs;imum haberi) ac
non meo iure, &longs;ed ex tuis verbis hanc &longs;uppo&longs;itionem,
qua&longs;i tuam &longs;upponere, G
AB in parteis quotlibet æqualeis diui&longs;um, percurrere partem
&longs;ecundam DE
poris, quo percurritur prior pars AD
quod idem e&longs;t,
velocitatis, qua tran&longs;curritur AD. Sequitur.
ro tuæ Re&longs;pon&longs;ionis X. volueris velocitatem per totam AE
duplam e&longs;&longs;e velocitatis per primam partem AD, idque ex
meis quoque principiis nece&longs;&longs;arium e&longs;&longs;e a&longs;&longs;erueris: nunc, mutato
con&longs;ilio, velocitatem per &longs;olam partem DE velocitatis per
partem AD acqui&longs;itæ duplam e&longs;&longs;e contendas: & quidem, vt
ais, ex principiis item meis?
Quid cau&longs;&longs;æ &longs;it, quæris?
Non &longs;anè mutatio con&longs;ilij
in me; &longs;ed quæ fal&longs;orum principiorum, incommodo
rumque ex iis deductorum variatio in te ob&longs;eruatur. Nam quòd velis quidem velocitatem acqui&longs;itam in E
e&longs;&longs;e duplam velocitatis acqui&longs;itæ in D, vt &longs;patium AE,
&longs;patij AD duplum e&longs;t: contendo iam velocitatem, qua
percurritur DE, e&longs;&longs;e duplam eius, qua tran&longs;curritur AD,
&longs;eu, quæ acquiritur per AD: &, quòd tu contendas ab
A, v&longs;que ad E, augeri æquabiliter, idcircò &longs;um argu-
plam e&longs;&longs;e velocitatis per totam AD. Cùm hoc autem
&longs;uo iam loco demon&longs;tratum abundè &longs;it: ideò illud &longs;o
lùm, quod tu huius loci facis proprium, e&longs;t attenden
dum. Quæ&longs;o itaque; cùm velis in D acqui &longs;itum e&longs;&longs;e
vnum velocitatis gradum, & duos in E, an velis gradum
acqui&longs;itum in D, manere per ip&longs;am DE, ac e&longs;&longs;e vnum
ex iis duobus, qui acqui&longs;iti reperiuntur in E; an nolis? Si velis; igitur perip&longs;am DE &longs;unt duo gradus, vnus
nempe manens, & alius, qui interim acquiritur. Si no
lis; igitur oportet duos gradus, qui &longs;unt in E, acqui&longs;i
tos e&longs;&longs;e per &longs;olam DE. An-non ergo vtrovis modo
nece&longs;&longs;e e&longs;t velocitatem per &longs;olam DE, duplam e&longs;&longs;e
eius, quæ acquiritur per AD? Dilemma e&longs;t, neutrum
que e&longs;t membrum, circa quod liceat tergiuer&longs;ari. Nam
circa &longs;ecundum quidem, dicere nihil potes: cùm id
&longs;it tamen reuerâ tuum; quatenus, vt &longs;uperiùs quoque
adnotatum e&longs;t, vis velocitatem acqui&longs;itam per totam
DE, e&longs;&longs;e duplam acqui&longs;itæ in D, & acqui&longs;itam in D
perire: nam alioquin in E velocitas iam e&longs;&longs;et tripla, &longs;i
ue in E tres gradus e&longs;&longs;ent: cùm e&longs;&longs;e tu velis &longs;olùm duos,
& acqui&longs;itos quidem per &longs;olam DE. Circa primum
autem &longs;i forta&longs;&longs;is dicas manere quidem primum gra
dum, &longs;ed nihil agere; &longs;equetur &longs;olo &longs;ecundo gradu, qui
per DE acquiretur, agente, partem DE tempore ni
hilo breuiore tran&longs;curri, quàm ip&longs;am AD: cùm etiam
per te percurratur minùs, quam dimidio. Et, &longs;i dicas
agere: Aut ob &longs;ui con&longs;tantiam duplò aget ampliùs,
quàm per AD, vt &longs;uperiùs deduximus; & tunc incom
modum &longs;equetur, quod &longs;uprà quoque o&longs;ten&longs;um e&longs;t;
poris; & &longs;ecundum tempus integrum non effluet, ni&longs;i
&longs;ub partem &longs;patij octauam, quod tu vis effluere cum
ip&longs;a &longs;ecunda: Aut certè tantumdem; & tunc, quia etiam
tantumdem aget, qui gradus acquiretur per ip&longs;am
DE: recurret idip&longs;um, quod tu refugis; nempe partem
DE percurri velocitate dupla illius, qua decur&longs;a fuerit
AD.
principiis vlla ratione deducis: & vt priorem iam &longs;uprà fal
&longs;am euici; ita nunc i&longs;tam e&longs;&longs;e impoßibilem, hac ratione cui
denter demon&longs;tro.
Imò de Priore quidem apertè probaui; neque tu
quicquam aliud, quàm, vt aiunt, principium petii&longs;ti:
& cùm te iam dicis euici&longs;&longs;e eam fal&longs;am; notum e&longs;t quæ
&longs;tionem non e&longs;&longs;e, an fal&longs;am euiceris, &longs;ed an euiceris
non-tuam, &longs;eu ex tuis principiis minimè deductam. De
Po&longs;teriore etiam rem feci apertam; neque cùm ego
in&longs;titi nullum e&longs;&longs;e in mea argumentatione Paralo
gi&longs;mum, tu potui&longs;ti vllum o&longs;tendere: & cum iam &longs;u&longs;ci
pis demon&longs;trandum eam e&longs;&longs;e impo&longs;&longs;ibilem, minimè
attendis quæ&longs;tionem non e&longs;&longs;e, an impo&longs;&longs;ibilis &longs;it, &longs;ed
ex tuis ne deducta principiis.
que per spatium quodlibet, putà AB de&longs;cendens, æqualibus
temporibus spatia continuò maiora, ac maiora decurrat in con
tinua ratione dupla.
clu&longs;io e&longs;t; quæ & fal&longs;a e&longs;t, & non probabitur deinceps
à te, ni&longs;i ex ip&longs;i&longs;inet principiis, quæ vt fal&longs;a &longs;unt, ita Sed
tuum e&longs;to principium; quid inde?
ue de&longs;cendens percurrit &longs;ecundam partem DE, tantò præcisè
spatium duplò minus antè percurrerit; nempe SD, quod
&longs;upponitur dimidium &longs;uperioris spatij AD.
An-non agno&longs;cis circulum?
Neque enim alia ratio
ne probas &longs;patia continuò percurri in ratione dupla,
quàm quia &longs;upponis tanquam principium, partem DE
percurri tanto tempore, quantò dimidium SD. Sed
& hoc e&longs;to.
tempore percurrantur.
Imò impo&longs;&longs;ibile e&longs;t; tantum abe&longs;t, vt nece&longs;&longs;arium;
neque in te e&longs;t, vt nece&longs;&longs;itatem probes, ni&longs;i priùs o&longs;ten
deris velocitates e&longs;&longs;e vt &longs;patia, quod tantum abe&longs;t, vt
hactenus quidem præ&longs;titeris, quin potiùs præ&longs;tare co
natus, tuo in Bilance Experimento, ip&longs;o euentu fueris
delu&longs;us. Quanquam e&longs;to & i&longs;tud quoque.
AD, nece&longs;&longs;ariò breuius e&longs;t tempore, quo decurritur pars
&longs;uperior AS (alioquin motus per AD æquabilis e&longs;&longs;et, non
autem acceleratus, vt per &longs;e manife&longs;tum e&longs;t.)
Admitto id quidem, &longs;ed independenter ex tuis
principiis.
poris, quo decurritur AD, &longs;ed in tempore aliquantò breuiore.
Id quoque admitto; &longs;ed omninò ex aliis principiis,
quàm tuis.
maiore.
Et hoc admitto denique; verùm aliis prorsùs, quàm
tuis principiis per&longs;ua&longs;us.
Hem! quid profero?
Videlicet Primò tefal&longs;a v&longs;ur
pare principia, neque alia lege concludere ex ip&longs;is ve
rum, quàm &longs;i quis ex eo, quod a&longs;&longs;umat
e&longs;&longs;e in cælo,
e&longs;&longs;e in cælo. Secundò, committere te, vt vulgo aiunt, cir
culum, incidereve in Diallelum; vti obiter in&longs;inuatum
e&longs;t, & tota ex &longs;erie tui operis con&longs;tat. Tertiò, te noua
contradictione temetip&longs;um inuoluere, dum coactus vi
&longs;uperioris dilemmatis, dicere teneris velocitatem per
DE duplam e&longs;&longs;e velocitatis per AD, & nunc a&longs;&longs;umis,
aut te proba&longs;&longs;e contendis eandem velocitatem per
DE duplam e&longs;&longs;e velocitatis per SD, quod &longs;it &longs;olùm di
midium ip&longs;ius DE. Quartò te rursùs eâ implicari,
quòd cùm huc v&longs;que volueris acqui&longs;itos e&longs;&longs;e ab A in
E duos gradus, qui &longs;imùl iuncti &longs;int duplum illius, qui
acqui&longs;itus e&longs;t ex A in D; velis iam eo&longs;dem duos gra
dus e&longs;&longs;e duplum illius, qui &longs;olummodò &longs;it acqui&longs;itus
ex S in D. Quintò te idcircò omnia perturbare; qua
tenus quicquid hactenus dixi&longs;ti de &longs;patio in parteis
æqualeis diui&longs;o, & incipiendo quidem ab A, vt proba
res velocitates acqui&longs;itas e&longs;&longs;e vt &longs;patia; de &longs;patiis iam,
ac velocitatibus ita loqueris, vt &longs;i incipiendum &longs;it ab S,
neglecto pror&longs;us dimidio AS. Sextò, non re&longs;ponde
re te quæ&longs;tioni; quoniam quæ&longs;tio e&longs;t, non an veloci
tas per &longs;olam DE &longs;it dupla velocitatis per AD; &longs;ed an
nitum e&longs;t. Po&longs;tremò te vitiosè id o&longs;tendere, quatenus
a&longs;&longs;umis vnum ex tuis principiis, cum quo Propo&longs;itio
huiu&longs;modi non cohære&longs;cat: cùm id non &longs;ufficiat, ni&longs;i
o&longs;tendas; te aut non habere aliud principium, quàm
a&longs;&longs;umptum hoc: aut habere quidem, &longs;ed ex nullo ta
men ip&longs;orum illam con&longs;equi: aut habere iure eam de te
&longs;iduciam, vt impo&longs;&longs;ibile &longs;it te tibi contradicere, ac
non clarè per&longs;picere quid ex principio quolibet vel &longs;e
quatur, vel non &longs;equatur.
Quin imò quàm varias ob cau&longs;&longs;as cen&longs;eam reiicien
dam, tanquam &longs;puriam, habes.
ca&longs;u etiam aliàs facis) inde vel maximè mea decreta reuelli,
quòd ex iis adeò pugnantia concludantur.
Quamobrem verò id à me e&longs;&longs;e debuit inex&longs;pecta
tum; tibi præ&longs;ertim, viro &longs;apienti, cui nihil continge
re ex inopinato debet? An quia putâras non debere
me tua decreta expendere, &longs;ed in tua verba, qua&longs;i man
cipium domino addictum iurare? An quia volueras,
vt &longs;i quid fal&longs;um, aut repugnans occurreret, id non
tam lenirem, vt conatus &longs;um facere, quàm omninò di&longs;
&longs;imularem? An quia contenderas, vt quicquid id fo
ret, nihil aliud, quam plauderem, & nihil con&longs;cientiam
reueritus, creditæ mihi veritati remitterem nuncium, vt
tibi adularer? Horum nihil credo: &longs;ed tamen non &longs;a
tis per&longs;picio, quî id fecerim præter tuam &longs;pem; ni&longs;i
quòd i&longs;torum tuorum decretorum tanta per&longs;ua&longs;ione
certus fueris, vt quemadmodum eatenus incideras in
di&longs;&longs;et (&longs;ic enim po&longs;teà memoras) ita ego minimus
omnium, in quos po&longs;&longs;es incidere, impar pror&longs;us forem,
à quo quicquam tale deprehenderetur.
iure vtique diceres: at &longs;ine demonstratione, &longs;ine vlla veri&longs;imi
litudine id non &longs;emel tantum dicere, &longs;ed inculcare
in&longs;tare etiam acriùs, & tanquam de con&longs;tanti victoria trium
phare, vide an i&longs;tud &longs;it ingenitæ moderationis tuæ, atque etiam
dignitatis.
Imò, mi Cazræe, Tuip&longs;e, quo iure in me &longs;ic in&longs;ultes,
Vide. Iacturam fortè faciam vnius, aut alterius pagi
næ; &longs;ed nece&longs;&longs;itatem profectò imponis retexendi quid
piam ex ijs, ob quæ ita inueheris. Conquereris, quòd,
xerim, atque inculcârim tua decretainde maximè reuelli, quòd
adeò pugnantia exijs concludantur.
tanquam de con&longs;tanti victoria triumphârim, hoc e&longs;t,
ex&longs;ultabundus ge&longs;tierim, & qua&longs;i thra&longs;ofuerim gloria
tus; id vt à me alienum e&longs;t, ita Deo propitio, nu&longs;quam
deprehendes.) Itaque id-ne ab&longs;que iure, & &longs;ine vlla
demon&longs;tratione, aut veri&longs;imilitudine fecerim, perui
deamus. Verba tua fuerant vt retuli, articulo XXXI.
grauium de&longs;cen&longs;u &longs;emper ex dupla di&longs;tantia celeritatem haberi
duplam, & ex tripla di&longs;tantia triplam, atque ita deinceps ea
dem ratione celeritatem augeri; nihil procliuius e&longs;&longs;e potest,
quàm vt quis existimet accelerationem illam fieri per &longs;ubdi
ui&longs;ionem primi cuiu&longs;libet temporis in parteis &longs;emper minores,
pro multitudine, & ratione spatiorum æqualium, quæ motu
dimidia parte temporis, quo prima decur&longs;a e&longs;t: & tertia pars
&longs;patii tertia parte eiu&longs;dem primi temporis percurratur, & ita
de cæteris. Excepi ego,
&longs;agacitatem par e&longs;t, quatenùs eam non fugit error, qui ex po&longs;i
tione à te a&longs;&longs;erta con&longs;equitur, tamet&longs;i ip&longs;e non con&longs;equi, ex iis,
quæ &longs;equuntur, contendas. Duo heic fuerunt:
rorem e&longs;&longs;e, quòd &longs;ecundum &longs;patium æquale percurra
tur dimidio illius temporis, quo primum; tertium trien
te, quartum quadrante, atque ita de reliquis:
huiu&longs;modi errorem con&longs;equi ex tua pofitione, quòd
celeritates &longs;e habeant vt &longs;patia, atque adeò, quod ex
duplo di&longs;tantiæ celeritas habeatur dupla, ex triplo tri
pla, &c. Et
cùm tu e&longs;&longs;e errorem & confe&longs;&longs;us fueris, & aliquot
etiam argumentis o&longs;tenderis.
fuit, an nempe huiu&longs;modi error tuis ex principiis, &longs;eu
ex po&longs;itione mox memorata &longs;equeretur, an-non. Et,
&longs;i &longs;equeretur, an cùm deinceps & errorem o&longs;tenderes,
& ex eo admi&longs;&longs;o repugnantia deduceres, non reuerâ
o&longs;tenderes, ac deduceres aduer&longs;us teip&longs;um, vt cuius er
ror reuerâ e&longs;&longs;et, tanquam nece&longs;&longs;ariò deductus ex tuis
principiis.
Iam verò illum ex tuis principiis, &longs;eu propo&longs;itione
memorata &longs;equi, ex eo argumentatus &longs;um, quòd tem
pora e&longs;&longs;ent incre&longs;centium velocitatum &longs;ubmultiplicia:
adeò, vt quod &longs;patium æquale &longs;ecundum dupla velo
citate percurritur, dimidio temporis percurratur, quo
primum: & quod tertium tripla, triente; quod quar
tum quadrupla, quadrante, atque ita de cæteris.
paralogi&longs;mum:
&longs;ito deducere ab&longs;urditatem. Quæ&longs;o igitur, an meo
iure, & &longs;ine vlla, ni&longs;i demon&longs;tratione, &longs;altem veri&longs;imili
tudine dixerim hunc errorem ex tuis principiis deduci? Et cùm fuerim conte&longs;tatus in mea &longs;eu demon&longs;tratio
ne, &longs;eu veri&longs;imili ratione nullum &longs;ube&longs;&longs;e paralogi&longs;
mum; cur tu, &longs;i quempiam e&longs;&longs;e puta&longs;ti, verè &longs;ube&longs;&longs;e
non o&longs;tendi&longs;ti? Nam quòd fueris ratiocinatus ex con
clu&longs;ione illa
locitatem per &longs;ecundam partem non e&longs;&longs;e duplam ve
locitatis per primam, id non arguit illud non &longs;equi ex
alio tuo principio, ex quo aliunde etiam potuerit per
media quæpiam alia mendo&longs;a illa conclu&longs;io trahi: ac
poti&longs;&longs;imùm, cum &longs;it adeò verum, quod dicitur vulgò, Quam
obrem neque vllus exinde concludi pote&longs;t paralogi&longs;
mus; neque non con&longs;tat quàm variè tua ratiocinatio
peccet, quámque mea illa confiimetur ex confecto
dilemmate, quod repetere nihil e&longs;t nece&longs;&longs;e. Quæ&longs;o
etiam, potueri&longs;-ne paulò antè exaggerere
primùm demon&longs;trare ea, quæ à te tanquam fal&longs;a reiecta vi
de bam, ex con&longs;titutis à te principiis nihilominus &longs;equi, ante
quam eadem, vt tua decreta impeterem,Scilicet res
præ&longs;tita fuerat, & ita quidem, vt te inuita&longs;&longs;em, ad de
tegendum paralogi&longs;mum, &longs;i quem &longs;ube&longs;&longs;e exi&longs;timares. Mi&longs;&longs;um autem facio, vt non modo hoc præterm &longs;eris,
&longs;ed di&longs;&longs;imulâris etiam incommodum ex hac po&longs;itione
deductum de Progre&longs;&longs;ione illa &longs;patiorum plu&longs;quam
tripla eodem articulo &longs;upputata; ni&longs;i quod ad calcem
tanquam veræ progre&longs;&longs;ionis, quam vano labore re
qui&longs;ierim.
Ad duosarticulos &longs;equenteis, nempe XXXII, & XXXIII,
poti&longs;&longs;imùm &longs;pectat, quod rursùs es ante conque&longs;tus
contra euidentem quoque demon&longs;trationis lucem velle à te ea
dici, quæ verbis expreßis negas, quæque fal&longs;a e&longs;&longs;e non tantum
pronuncias, &longs;ed clare etiam, atque euidenter demon&longs;tras. At
quomodo quæ&longs;o dicere id potes; cùm ex iam dictis
quæ&longs;tio &longs;it duplex;
&longs;patium dimidio temporis, quo primum, tertium trien
re, &c. Tu verò &longs;ic me impetas, qua&longs;i litem tibi mouerim de
prima, non autem &longs;olùm de &longs;ecunda; & cùm deberes
ip&longs;e tueri errorem non &longs;equi ex tuis principiis, qua &longs;ola
de re agitur; o&longs;tendas &longs;olùm errorem e&longs;&longs;e; qua de re nu<ail;
la e&longs;t controuer&longs;ia? Heinc mihi initium articuli XXXII.
fuit,
non fieri accelerationem pro &longs;ubdiui&longs;ione i&longs;ta temporis:
recitata membratim tua demon&longs;tratione, a&longs;&longs;en&longs;i vbi
que te verè errorem, incommodumque concludere; ac
monui &longs;olùm con&longs;tanter, te concludere aduer&longs;us te
ip&longs;um, quatenus error, incommodumque ex tuis prin
cipiis con&longs;equeretur. An dicere igitur potes,
tra expre&longs;&longs;am &longs;ententiam, & demon&longs;trationem tuam velle
te ea dicere, quæ verbis expreßis pronuncias, &c.
modò noluerim, verùm ne cogitârim quidem. Sic
cùm articulo XXXIII. o&longs;tendi&longs;&longs;es rur&longs;us tuo modo, ex
comparatione &longs;ecundæ partis cum inferiore primæ di-
commodum: non repugnaui ego &longs;imiliter, quin tuo modo
o&longs;tendi&longs;&longs;es; imò & expre&longs;sè admi&longs;i incommodum,
qua&longs;i à te o&longs;ten&longs;um; & excepi &longs;olùm
gis principij fal&longs;itatem proderet, quàm tot repugnantium, at
que ab&longs;urdorum capitum deductio. An ergo etiam illeic
negaui te dicere quæ diceres, aut demon&longs;trare, quæ de
mon&longs;trares: & non potiùs &longs;emper in eo &longs;olùm fui, quòd
cognitus error à te in &longs;eip&longs;o, & in con&longs;equente multi
plici incommodo; non foret tamen per&longs;pectus in
cau&longs;&longs;a, &longs;eu in principio antecedente: eo modo, quo po
te&longs;t deformitas pueri agno&longs;ci, & probro haberi ab eo,
qui pote&longs;t non agno&longs;cere e&longs;&longs;e &longs;e illius
liare illud e&longs;t,
hæc &longs;atis, vt inde con&longs;ter, tua-ne fuerit iu&longs;ta quercla.
& eapropemodum omnia, quæ tam acriter nobis obiectas, &
tanquam ab&longs;urda tantopere in&longs;ectaris, tibi nobi&longs;cum e&longs;&longs;e
communia demon&longs;trem. Concipe in triangulo AB
in eius latere AC parteis æqualeis non iam& in
dum velocitatis, expre&longs;&longs;um linea
ex tuis, &
E
que velocitas in
D.
Quamobrem igitur aggre&longs;&longs;us ar
gumentari ad hominem, & demon
&longs;trare tanta volens aduer&longs;us Galileum,
ac me, in ip&longs;o limineaberras? Scilicet neque Galilei,
dum exprimi lineâ EH,
lum: &longs;iquidem tota linea EH non &longs;ecundum modò
gradum exprimit, acqui&longs;itum abv&longs;que D, verùm etiam
primum acqui&longs;itam ab v&longs;que A, ip&longs;umque iunctum
cum &longs;ecundo.
tam duplam e&longs;&longs;e velocitatis acqui&longs;itæ toto tempore AD?
Non; &longs;ed acqui&longs;itam toto tempore AE: ita vt tem
pore AD acquiratur vnus velocitatis gradus, & illo
per&longs;euerante, æquiualentéque duobus, quantum ad
&longs;patia &longs;uperanda tempore æquali attinet, acquiratur
interim alius &longs;uccedente tempore DE, qui cum eo
iunctus fiat aggregatum, quod &longs;it ip&longs;ius duplum, vt
deductum &longs;uperiùs e&longs;t.
æqualibus illis temporibus emen&longs;a inter &longs;e &longs;int, vt velocita
tes: acproinde vt spatium &longs;ecundo tempore
tii tempore
&longs;tatuit
me negaturum ignora&longs;&longs;e potes: cùm ab initio v&longs;que
controuer&longs;iæ, & à primis illis Re&longs;pon&longs;ionis articulis
non alia ratione exhibuerim opinionem intelligen
dam; adeò proinde, vt &longs;i ip&longs;e pro&longs;equi velles vlterius,
argumentando ad hominem, contentus e&longs;&longs;e non de
bueris &longs;ola hac interrogatione, & conce&longs;&longs;ionem &longs;up
ponere, quam iure à me non obtineres: &longs;ed &longs;uppo&longs;ita
negatione, vrgere in me aliquid, quod appo&longs;itum ad An verò po&longs;&longs;es iam vrgere dilemm
dem, quo ego in te v&longs;us &longs;um? Vt po&longs;&longs;is, ob&longs;tat pri
mùm, quòd ego &longs;ecundum membrum manife&longs;tò re&longs;
puam, cui tamen inhærere te ex ijs, quæ heic habes, in
telligi pote&longs;t: quódque circa primum videas admitte
re me, & manere primum gradum toto tempore DE;
& manendo non e&longs;&longs;e otio&longs;um, &longs;ed agere aliquid; &
agere duplum illius, qui interim acquiritur; & ex dupla
vnius, & &longs;implici alteriùs actione &longs;uperari tria &longs;patia:
ac tu non po&longs;&longs;is ex admi&longs;&longs;o à me triplo &longs;patio per tem
pus DE percurrendo, deducere incommodum vllum,
vt ego deduxi ex triente temporis, quo tu debes admit
tere DE pro &longs;patio &longs;umptum percurri. Ob&longs;tat &longs;e
cundò, quòd vt facias, mutare duntaxat terminos
oporteat: hoc e&longs;t, vbi ego tempus tu &longs;patium; vbi
ego &longs;patium tu tempus debeas dicere, vt factitatum
&longs;uperiùs e&longs;t, cùm retorquere conatus es, quod ego
obieceram, vt defenderem nullum fui&longs;&longs;e in Galileo
Paralogi&longs;mum. Scilicet confu&longs;io inde &longs;equitur, è
qua extricari non liceat, neque rem iam ten
to, vt tempori parcam; tamet&longs;i &longs;altem videretur circa
ea, quæ &longs;equuntur, tentanda. Adnoto ergo potius,
quod heic infers
pore
con&longs;equutionem; eò quòd a&longs;&longs;umas, vt rem conce&longs;&longs;am
duos gradus velocitatis, qui reperiuntur in tempore
DE, acquiri ambo per illud tempus: cùm tamen ego
velim vnum tantum acquiri, & alium e&longs;&longs;e permanen
tem, præ&longs;tantemque duplum illius, qui acquiritur:
adeò vt, coniuncta vtriu&longs;que actione acquiratur &longs;patij
At &longs;i
negaueris; maioremque agnoueris, quod in tuis, & Galilei
decretis admittere cogeris: cur tam acriter reprehendis in
nostris?
gem, &longs;i ma orem agno&longs;cam?
to tempore DE neque duplam, neque maiorem, &longs;ed
omninò æqualem illi, quæ acquiritur toto tempore
AD agno&longs;co. Indeque e&longs;t illa definitio motus æqua
biliter accelerati, quod,
acquirat velocitatis incrementa:
in meis, & Galilei decretis admittere cogor: ac iure
idcircò reprehendo in tuis, quód cogaris admittere ad
uer&longs;us propriam definitionem,
lia momenta velocitatis non acquiri.
qui&longs;ita perpendamus, cuiu&longs;nam alterius velocitatis &longs;it
æqualis?
Placet; quandò res cordi e&longs;t, & tantopere tibi pla
cet tuum illud de deducendo infra initium initio, ab
ip&longs;o putà S,
D
est velocitatis acqui&longs;itæ in
inter
alterius inter
dia inter
Concedo; hæc enim reuerâ in opinionem, quam
&longs;equor, quadrant, &longs;ecus ac in tuam, quæ tantoperè
auer&longs;atur progredi adhuc, promouendo comparatio
nem vltra S ver&longs;us A, ne initium magis ver&longs;us initium
promoueatur. Concedo, inquam, quatenus hæ omnes
velocitates ab A incipiunt, & eandem inter &longs;e ratio
nem, quam ip&longs;a tempora ob&longs;eruant.
ta toto tempore
acqui&longs;itæ toto tempore
Tamet&longs;i punctum, à quo incipiunt velocitates, iam
varies: concedo nihilominus, & neque id modò, &longs;ed
etiam velocitatem acqui&longs;itam tempore DE duplam
e&longs;&longs;e acqui&longs;itæ tempore AS, & tempore DK, & tem
pore KE. Nempe acqui&longs;ita tempore DE non e&longs;t tota
EH, vt falsò &longs;upponis, &longs;ed eius dimidium, quod pro
inde duplum e&longs;t non totius DG, quam falsò totam
acqui&longs;itam &longs;upponis ab S, in D, &longs;ed dimidij eius dun
taxat. Hoc autem cùm æquale &longs;it acqui&longs;itæ ab A in S,
à D in K, à K in E: ideò acqui&longs;ita à D in E, pari modo
e&longs;t earum omnium dupla.
Et quis, cui hoc dixit, acqui&longs;itam tempore DE, du
plam e&longs;&longs;e acqui&longs;itæ tempore AD, ni&longs;i ip&longs;e tibi?
atque eadem ratione, qua in no&longs;tra, velocitatem &longs;ecunda parte
DE
AD
dietate
Nego, Nam
in mea quidem, & Galilei &longs;ententia &longs;umendo has
parteis DE, AD, SD pro partibus
temporis, res e&longs;t nece&longs;&longs;aria; at in tua,
&longs;umendo ea&longs;dem pro partibus &longs;patij,
o&longs;ten&longs;um iam e&longs;t velocitatem per DE
debere e&longs;&longs;e duplam velocitatis per AD. Et o&longs;tendetur paulò pò&longs;t non probari
duplam velocitatis per SD, ni&longs;i ip&longs;um
met petendo principium.
locitatem tertio tempore
locitatis primo tempore acqui&longs;itæ triplam &longs;o
lùm non e&longs;&longs;e, &longs;ed triplo maiorem.
Nempe hoc placet ex abundanti: vide ergo perpe
tuum aduer&longs;us nos paralogi&longs;mum. Nam vt hactenùs
falsò &longs;uppo&longs;ui&longs;ti velle nos totam velocitatem EH, quæ
dupla e&longs;t velocitatis DG, acqui&longs;itam e&longs;&longs;e &longs;olo tempo
re DE, quam acqui&longs;itam tamen facimus toto tempore
AE, cùm ratiocinatio no&longs;tra con&longs;tans &longs;it, vt AD, ad
DG, ita AE ad EH; non autem vnquam, vt AD ad
DG, ita DE ad EH: vt hactenus, inquam, id falsò
&longs;uppo&longs;ui&longs;ti; &longs;ic falsò iam &longs;upponis velle nos totam ve
locitatem FI, quæ tripla e&longs;t eiu&longs;dem velocitatis DG,
acqui&longs;itam e&longs;&longs;e &longs;olo tempore EF, quam acqui&longs;itam &longs;ta
tuimus toto tempore AF: cùm con&longs;tanter dicamus, vt
AD, ad DG, ita AF ad FI; neque tu o&longs;tendere po&longs;
&longs;is dixi&longs;&longs;e vnquam nos, vt AD ad DG, ita EF ad FI.
in
ratione velocitas in
alia quælibet velocitas de&longs;ignabilis inter
per e&longs;t velocitatis alterius interTota
igitur velocitas toto tempore
tius velocitatis toto tempore
qui&longs;itæ &longs;ola parte primi temporis
e&longs;t, totius velocitatis toto tempore
notum e&longs;t.
Quid, negato fal&longs;o principio, notum per &longs;e &longs;it, aut
non &longs;it; con&longs;tat abundè ex iam dictis.
lud ip&longs;um, quod tantopere in no&longs;tra in&longs;ecturis.
Imò nihil minùs.
quam ab&longs;urda, & inter &longs;e pugnantia nobis obiicis, po&longs;&longs;e in
te pari modo, atque impetu retorqueri. Quid enim prohibet,
vt ego quoque velis, nolis, dicam coniunctum e&longs;&longs;e cum tuis
principiis nece&longs;&longs;ariò, vt velocitas acqui&longs;ita tempore
pla &longs;it velocitatis acqui&longs;itæ tempore
æqualia &longs;int, manifestum con&longs;equenter e&longs;&longs;e spatium &longs;ecundo
tempore emen&longs;um, spatij priore tempore emen&longs;i, e&longs;&longs;e præcisè
duplum; ac proinde ex
ribus æqualibus percurri (vt ego contendo) in continua ratione
dupla. Id enim ex ea &longs;uppo&longs;itione neceßarium est.
Cùm id totum &longs;it adò fal&longs;um, adeóque falsò &longs;uppo
&longs;itum, vt &longs;æpiùs iam o&longs;ten&longs;um e&longs;t: non e&longs;t quòd hanc
tibi gloriationem inuideam.
totum primum tempus
eius potiùs veiocitatis, quæ vltima primi illius temporis medie
tate, &longs;cu tempore
pugnantia loqui conte&longs;tabor.
Cùm hanc e&longs;&longs;e meam &longs;ententiam agno&longs;cas; ip&longs;am
debebas impetere, non &longs;puriam a&longs;&longs;ingens (vocem con
donabis, quandò tua e&longs;t) euidenter Nunc
verò &longs;altem cur non
tia loqui contestaris?
qui&longs;itam velocitatis toto primo tempore
præcisè duplam, &longs;ed dupla maiorem: tantò euidentiorem inde
concludam principiorum tuorum, ac decretorum ab&longs;urditatem,
ex quibus tam apertè pugnantia concludantur: cùm fieri non
poßit, vt velocitas acqui&longs;ita in
velocitatis toto tempore
Dicerem heic aliquid, ni&longs;i depugnares aduer&longs;us
tuam vmbram.
cùm tu rem ita e&longs;&longs;e, ac nece&longs;&longs;ariò admittendam e&longs;&longs;e contendas.
Scilicet?
&longs;eu velocitas æqualibus temporibus, &longs;eu &longs;patiis æqualibus æqua
biliter augeri &longs;upponatur, non modò non ab&longs;urdum, aut à recta
ratione abhorrens, &longs;ed prorsùs neceßarium eße, vt velocitas
tota &longs;ecunda parte temporis, aut spatii acqui&longs;ita, nunquam
&longs;it totius velocitatis tota prima parte acqui&longs;itæ præcisè dupla,
&longs;ed potiùs, vt totius velocitatis &longs;ola po&longs;trema medietate eiu&longs;-
reperiatur: & &longs;imiliter, vt tota velocitas tertia, aut quarta
parte, &c. acqui&longs;ita, tripla non &longs;it, aut quadrupla totius ve
locitatis per primam partem acqui&longs;itæ, &longs;ed eius præcisè veloci
tatis, quæ tertia, aut quarta parte inferiore eiu&longs;dem partis
primæ acqui&longs;ita fuerit. Itaque quicquid aduer&longs;us has pro
po&longs;itiones magna tuæ Respon&longs;ionis parte opponis, aut ex &longs;up
po&longs;itis earum contrariis colligis, ac concludis, vanum &longs;ine du
bio, atque inane e&longs;t; quamuis apud harum rerunt minùs pe
ritos plau&longs;um inuenire poßint, atque approbationem.
Cuius momenti i&longs;ta &longs;int, expendendum e&longs;t ex hacte
nus dictis. Moneo &longs;olùm breuiter quatuor, Primum,
velle te
acqui&longs;ita velocitatis incrementa exæquentur. Secun
dum, iniuriam à te &longs;emper fieri mi&longs;erando illi dimidio
partis primæ priori: vt cuius rationem
habeas. Tertium, no&longs;cendum e&longs;&longs;e deinceps quo fru
ctu volueris hæc præoccupata in gratiam eorum, quæ
&longs;unt dicenda circa articulos &longs;equenteis. Quartum, &longs;i
mihi proferre po&longs;&longs;is vel vnum
tentia &longs;tet, & apud quem plau&longs;um, approbationemque
inuenias, vltrò me in eandem &longs;ententiam iturum.
ab
&longs;urdum infers, & tangis: futurum &longs;cilicet,
vt tempore quocumque dato putà vno horæ minuto primo; quo
decur&longs;a &longs;upponatur de&longs;ignati &longs;patii pars quæcumque prima, vt
AD,
&longs;it, quàm ab eodem mobili decur&longs;um fuerit &longs;patium infinitum:
Cùm enim ab&longs;urdum hoc aliunde non concludas, ni&longs;i ex fal&longs;a
hypothe&longs;i, quòd &longs;patij pars &longs;ecunda dimidio primi temporis,
primi eiu&longs;dem temporis decurrantur: iamque ex tuis etiam
principiis, ea &longs;uppo&longs;itio fal&longs;a, & impoßibilis o&longs;ten&longs;a &longs;it:
euer&longs;o malè iacto fundamento, tota &longs;uperex&longs;tructa moles
corruit.
Conclu&longs;i ego illud ab&longs;urdum ex hypothe&longs;i fal&longs;a
quidem, &longs;ed non vt fal&longs;a, verùm vt tua; & tu o&longs;tendens
fal&longs;am &longs;eu ex tuis, &longs;eu ex meis principiis, lucratus nihil
es, lucraturus &longs;olùm, &longs;i o&longs;tendere non-tùam potui&longs;&longs;es. Itaque & &longs;emper monui, &
iterùm, nihil e&longs;&longs;e opus, vt e&longs;&longs;e probes fal&longs;um,
&longs;ecundam spatii percurri dimidio temporis, quo primam:
opus e&longs;&longs;e, vt o&longs;tendas id non e&longs;&longs;e tuum, hoc e&longs;t non ex
pre&longs;sè a&longs;&longs;umptum à te vt verum, nece&longs;&longs;ariumque prin
cipium, quo Paralogi&longs;mi Galileum argueres; & non
nece&longs;&longs;ariò con&longs;equi ex eo, quod defendis velocitates
&longs;e habere vt &longs;patia. Nempe hoc po&longs;terius
e&longs;t, quòd vt
dem, vt tam illud
les corruat. Quod interim putas ab&longs;urdum euer&longs;um,
non tantùm quatenus obiectum e&longs;t tibi articulo XII.
&longs;ed etiam quatenus obiicitur po&longs;teà articulo xlii. id
haud rectè putas. Siquidem illeic non conclu&longs;i ex
hac eadem hypothe&longs;i, &longs;ed ex alia itidem tua, qua nimi
rùm vis accelerationem non ab v&longs;que principio, &longs;ed à
medio v&longs;que duntaxat primæ partis inchoandam e&longs;&longs;e:
adeò vt cùm nihil ad hoc habeas, non &longs;it cur inuoluas
quod dixi articulo xij. cum eo, quod deinceps articulo
xlii. neque cur etiam illo ruente, i&longs;tud &longs;ic putes corrui
turum, vt ariete nouo non indigeat.
tiorumque &longs;ingulis temporibus percurrendorum progre&longs;&longs;um
&longs;crutaris. Quid enim veri, ac certi ex fal&longs;is legitimè con
cluderes?
Heic loci e&longs;t, in quo antè præmonui te loquutu
rum obiter de progre&longs;&longs;u per &longs;patia in ratione plu&longs;quam
tripla futuro æqualibus temporibus, quem ego qui
dem & &longs;crutarer, & mon&longs;trarem fal&longs;um, vt fal&longs;itatis
deberes o&longs;tendere eandem hypothe&longs;in non deduci ex
tuo principio, ne ip&longs;um quoque ip&longs;a eadem fal&longs;itate
inuolueres, ita loquereris de eo progre&longs;&longs;u, qua&longs;i ego
ip&longs;um vt verum ex fal&longs;a hypothe&longs;i vano labore per
&longs;crutarer. Vnde & iuuit tequærere,
ex fal&longs;is legitimè concluderem?
cludere ip&longs;um fal&longs;um: aut ne&longs;cires, quod tyrones no
runt, tam verum, quàm fal&longs;um po&longs;&longs;e legitimè concludi
ex fal&longs;is: ac &longs;peciatim demon&longs;trationem ducentem ad
incommodum (qualis mea fuit argumentatio) non alia
progredi ratione?
XXXVIII. De Tempore, quo R. P. colligit &longs;ingulas
parteis decur&longs;um iri.
xxxvi.
xxxvii.
ac xxxviii.
pro&longs;equeris, vt eam propo&longs;itionem refellas, qua
contendo velocitatem tota &longs;ecunda parte
præcisè duplam e&longs;&longs;e totius velocitatis per inferiorem primæ
per tertiam, & quartam partem, &c. acqui&longs;itam, exactè tri
plam e&longs;&longs;e, ant quadruplam non velocitatis, quæ per totam pri
mam partem
quæ tota tertia, aut quarta parte inferiore eiu&longs;dem primæ par
tis acqui&longs;ita fuerit. Nullum enim non moues lapidem, vt
hanc veritatem euertas, quam tamen paulò antè tuis pincipiu
innixam, & &longs;tabilitam agnouisti; & quam &longs;i vmquam
eucrteres, tuam quoque, ac
teres. Si enim velocitas &longs;ecundo tempore acqui&longs;ita velocitatis
primo tempore acqui&longs;itæ e&longs;&longs;et dupla, & fimiliter velocitas ter
tio, & quarto tempore acqui&longs;ita eiu&longs;dem velocitatis primæ tri
pla e&longs;&longs;et, & quadrupla, spatia temporibus illis æqualibus de
cur&longs;a in eademinter &longs;e e&longs;&longs;ent ratione: nempe in ratione dupla,
tripla, & quadrupla contra
Hæc iam attinent ad Secundum membrum proba
tionis præcipuæ, qua &longs;equelam propo&longs;itionis Demon
&longs;trationis tuæ confirmas. Mi&longs;&longs;um autem facio, quod
ais de mea, & Galilei &longs;ententia, quandò ex paulò antè
deductis adeò manife&longs;tè intelligitur, fore vt potiùs ma
ri flammam, & terram cælo commi&longs;ceas, quàm ex Ga
lilei contextu, aut mea Re&longs;pon&longs;ione id probes, quod
heic a&longs;&longs;eris, aut euincere valeas cuertere me agnitam à
me veritatem. Quod &longs;upere&longs;t autem cùm tua &longs;enten
tia tum ver&longs;ibus hi&longs;ce, tum hactenus toties repetita &longs;it,
plam e&longs;&longs;e totius velocitatis per inferiorem primæ partis medie
tatem Quæ&longs;ote primùm,
quomodo nam ip&longs;am hactenùs &longs;tabilii&longs;ti? Nam &longs;i
to rAn ergo
alia ratione probas, quam quæ habetur numero tuæ
Di&longs;&longs;ertationis XXXIV. pro &longs;ecunda parte comparata
cum primæ partis inferiore dimidio; & XXXVII. pro
quarta comparata cum triente: ac xxxviij. pro
quarta comparata cum quadrante? Non certe.
Ita
que quid id &longs;it videamus, ac circa partem &longs;peciatim &longs;e
cundam (cùm eadem &longs;it ratio proportione de cæteris)
nam & tamet&longs;i res videatur e&longs;&longs;e iam abundè confecta:
operætamen
A&longs;&longs;umptâ illeic lineâ AB, diui&longs;a in parteis æqua
leis AD, DE, &c. ac prima parte bi&longs;ecti in S,
expre&longs;&longs;a &longs;ententia hi&longs;ce verbis ex&longs;tat
Tum probatio hæc additur,
pla ponatur ip&longs;ius
ip&longs;ius
velocitatis in
pla reperiatur velocitatis in D. Deducis con&longs;e
quenter velocitatem per totam DE e&longs;&longs;e du
plam velocitatis per totam SD: &longs;ed quod caput
e&longs;t, peruideamus. Nece&longs;&longs;e dicis
D,
&longs;it ip&longs;iusQuomodo
ergo nece&longs;&longs;itatem huius con&longs;equutionis pro
bas? Nam hoc opus, hic labor e&longs;t.
Quomodò,
inquam, ex eo, quòd
AS,
velocitas in D dupla &longs;it velocitatis in S, & velocitas in
&longs;upponis ex eo vim habere,
tia &longs;int. Atqui hæc ip&longs;a e&longs;t controuer&longs;ia,
tes inter &longs;e &longs;icut &longs;patia &longs;int:
e&longs;t, probas, &longs;ed omninò principium petis, &longs;eu ip&longs;am
quæ&longs;tionem, remve controuer&longs;am pro principio a&longs;&longs;u
mis. An verò dices te proba&longs;&longs;e,
tia?Id enim nu&longs;quam de
prehendetur? An vbi volui&longs;ti arguere Galileum Pa
ralogi&longs;mi? At abundè iam
paralogi&longs;mo, cùm rur&longs;us nihil aliud, quàm principium
petieris: vt taceam te, &longs;i quid habui&longs;ti probationis, id
po&longs;teà nega&longs;&longs;e: quando nega&longs;ti
curratur quadrante, percurri &longs;ecundam dimidio quadrantis,
An vbi demùm protuli&longs;ti
tum?
ferre locum, in quo alia ratione probaueris
&longs;e habere vt spatia. Atqui & fal&longs;um deprehen&longs;um Ex
perimentum tuum e&longs;t; & quæ germana fuit Experien
tia fal&longs;um conuicit
spatia. Itaque ex his &longs;equitur, non modo nece&longs;&longs;e non
e&longs;&longs;e: &longs;ed fal&longs;um etiam, atque adeò prorsùs impo&longs;&longs;ibile,
vt
E, velocitatis in D.
Cùm ergo non modò probatum non &longs;it, &longs;ed fal
&longs;um quoque & impo&longs;&longs;ibile ip&longs;a Experientia &longs;uffra
gante o&longs;ten&longs;um,
rem primæ partis medietatem
Quæ&longs;o quî adhûc valeas talem &longs;ententiam defendere,
tendum hanc veritatem?
inde inferres,
æquale tempori, quo percurritur SD,
velocitatem, &longs;icuti &longs;patium duplum e&longs;t, huiu&longs;cemodi
lapides, & articulis quidem XXXV. ac XXXVI. moui, I.
fore, vt &longs;uppo&longs;ito tempore, quo percurritur SD,
minutorum v. c. duorum, idem &longs;patium SD,
percurreretur &longs;imùl minuto vno cum triente, &longs;iue &longs;e
cundis 80: ac rur&longs;us &longs;ecundis 53, ac iterum 18, iterumque
6, &c. II.
Cùm aliunde &longs;tatui&longs;&longs;es tempus per SD, bre
uius e&longs;&longs;e tempore per AS, fore tamen ip&longs;i æquale. III.
Tempus per DE non æquale fore, &longs;ed &longs;e&longs;quialterum
temporis per SD. IV. Futurum, vt aut concluderes ni
hil, aut vtereris paralogi&longs;mo, quo Galileum v&longs;um cau&longs;
&longs;areris. V. Fore, vt quæuis magnitudo, etiam &longs;emi
diameter Mundi, tantulo tempore, quantulo SD li
neola percurreretur. Quæ eadem rursus incommoda
proportione deducta &longs;unt circa partem tertiam com
paratam cum infimo eiu&longs;dem primæ partis triente, ar
ticulo XXXVIII. Quomodo porrò tu excepi&longs;ti, reieci&longs;ti
ve hos lapides? Scilicet hoc loco dixi&longs;&longs;e contentus,
mero xxxvi. ita à diui&longs;ione rationis argumentaris:
AE ad AD, ita AD ad AS: erit igitur diuidendo, vt
AS ad SD, ita AD ad AE.
non est à diui&longs;ione rationis: & quamuis, vt par e&longs;t, terminos
etiam di&longs;poneres, nihil hac ratione concluderes, ni&longs;i priùs &longs;up
poneres velocitatem per totam
Nempe ex quinque argumentis, quæ &longs;unt mox an
tè indigitata,
dicere) vitilitigares. Quippe
mo loco &longs;crip&longs;i AE pro DE, pro errore mentis habui&longs;ti. Qua&longs;i verò habere oculos oporteat, &
&longs;en&longs;um, quo &longs;cribere volui
Aut qua&longs;i in huiu&longs;inodi tanta literarum farragine, im
portunaque inculcatione, non vnam pro alia irrepere Et cùm volueris ip&longs;e po&longs;teà videri huma
nior, dum legens IC, adnota&longs;ti
(quanqùam dicere nolui HC, &longs;ed ND, tribus inte
gris ver&longs;ibus, ad illud v&longs;que,
fuere, ob idem initium, ca&longs;u prætermi&longs;&longs;is) cùm,
illeic humanior fueris, cur heic quoque e&longs;&longs;e nolui&longs;ti? Debui&longs;ti ergo potiùs re&longs;titutâ literâ D, o&longs;tendere me
impropriè loquutum, qua&longs;i ignorantem diui&longs;ionem
rationis e&longs;&longs;e
con&longs;equens, ad ip&longs;ummet con&longs;equens:
rationem differentiæ terminorum cum ip&longs;orum alterutro. Sed
ita nimirùm agere fuit cordi, vt dicere po&longs;&longs;es, quamuis
vt par e&longs;t, di&longs;ponerentur termini, nihil me hac ratione
conclu&longs;urum, ni&longs;i prius &longs;upponerem
tam
men fal&longs;um non ignorarem. Ego verò fal&longs;um
&longs;ed & tuum e&longs;&longs;e non ignoro: ac ne ex &longs;uperiùs dedu
ctis argumentum repetam, paucis o&longs;tendo nihil e&longs;&longs;e
hac &longs;uppo&longs;itione, aut omninò vlla tergiuer&longs;atione
opus. Ex verbis paulò antè ex tua di&longs;&longs;ertatione reci
tatis, negare non potes, quin hoc totum tuum &longs;it:
neges oportet ratiocinia Geometrica, aut fatearis le
gitimè diuidendo ita concludi,
tim expreßè a&longs;&longs;umis; ideóque nihil inde concludis: fru&longs;traque
in&longs;uper laboras, vt originem erroris inquiras, qui nullus e&longs;t,
ni&longs;i in fal&longs;is &longs;uppo&longs;itionibus tuis.
Cùm hypothe&longs;es fal&longs;æ, &longs;int; cuius tamen &longs;int, ad
uer&longs;us quem &longs;int, quem errorem creent, &longs;atis iam
apertum.
uer&longs;iæ penetralia ingre&longs;&longs;us non videris: cùm vbique ferè fal&longs;a,
atque ab hac tota materia perquàm aliena &longs;upponas; & vix
quicquam, ni&longs;i ex talibus &longs;uppo&longs;itionibus concludas. Tuma
ioribus, & melioribus occupatus, leuiora hæc neglexi&longs;&longs;e
videris.
Si hæc &longs;it ingenuitas tua; beatus es, qui ita de te, ita
de me &longs;entire po&longs;&longs;is: ac prouidere quid Lectores opi
naturi demùm &longs;int, vbi cùm te My&longs;ten, me propha
num habuetint, te per&longs;picacem, me hebetem, te dili
gentem, ac &longs;edulum, me o&longs;citantem, & agentem aliud:
requirent tamen vel vnam fal&longs;am hypothe&longs;in, quæ
mea &longs;it; & vel vnam periodum, in qua aliquid ab hac
tota materia tantillùm alienum &longs;upponam, aut di
cam.
quicquid concludis, ex du
plici fal&longs;a hypothe&longs;i &longs;imiliter concludis. Vna e&longs;t, quód ve
locitates totæ, atque integræ quibu&longs;libet partibus acqui&longs;itæ
eam inter &longs;e rationem ob&longs;eruent, quam partes ip&longs;
ip&longs;ius
&longs;uperiùs numero
Qaid euiceris, & cuiu&longs;-nam fuerit hypothe
&longs;is fal&longs;a, memini&longs;&longs;e potes.
ceßarium ducas qua&longs;cumque &longs;patij parteis vbicumque
de&longs;ignatas eodem tempore percurri, &longs;i eandem inter
&longs;e rationem ob&longs;eruent. Sic ex eo, quod dico
figura videlicet articuli XXXIV.) IC,
triplam
que partem
lui&longs;ti HC)
Cuius Suppo&longs;itio fal&longs;a fuerit; qua con&longs;equu
tione rem deduxerim; quid dicere voluerim:
citra nau&longs;eam iam repeti non pote&longs;t.
ip&longs;amque rei naturam penitiùs inspexi&longs;&longs;es.
Et heic quoque beatus es, qui me æquè à tuis
dictis, & ab ip&longs;a rei natura penitùs in&longs;piciunda ar
ceas.
paßim à numero Re&longs;pon&longs;ionis tuæ xxxiij mihi etiam affin
gas, qua&longs;i velim, ac &longs;tatuam primam partem AD &longs;ex
minutis, po&longs;tremam verò eius medietatem SD, ac &longs;ecun
dam partem DE minutis duobus percurri: cùm ne
que eo loco, quem numero illo xxxiij examinas, neque v&longs;piam
alibi quidquam tale dixerim; & po&longs;t modum numero xl.
à me con&longs;titui non po&longs;&longs;e, quòd non &longs;atis notum e&longs;&longs;et tempus,
quo &longs;patiumNumeris quidem priori
bus, ex aliorum, quos iam
primam partem spatij
medietatem
cipijs eos erroris reuincerem; at &longs;agacitas tua aliena cum meis
confundere non debuit, aut mihi tribuere, quod reprebendo in
cæteris. Vide, &longs;i lubet, Epi&longs;tolæ meæ numerum xxxiij.
in quo
&longs;olo partibus &longs;patijparteis qua&longs;dam temporis attribuo, ex mea
ne, an ex aliena &longs;ententia id pronunciem. Ex bac tamen fal&longs;a
&longs;uppo&longs;itione vix credibile e&longs;t, quam-multa mihi ab&longs;urda obii
cias, quamque multainter &longs;e, & cum meis decretis pugnantia
congeras: vno verbo, rem &longs;ic omnem in partem ver&longs;as, vt &longs;i à
me dicta e&longs;&longs;ent, quæ mihi affingis, meritò haberi po&longs;&longs;em om
nium hominum ineptißimus. Infinitus &longs;im, &longs;i aut recen&longs;ere
&longs;ingula, aut ijs &longs;igillatim &longs;atisfacere voluero, quæ ex adeò fal
&longs;a hypothe&longs;i mihi imponis: &longs;atius &longs;it &longs;emel dicere, à numeró
Re&longs;pon&longs;ionis tuæ xxx. ad finem, vix aliquid à te nobis obiici,
quòd eam hypothe&longs;in non &longs;upponat, quodque proinde ea &longs;emel
negata, tanquam euer&longs;o fundamento non corruat.
Miratus es?
At
merum &longs;ex minutorum Primæ parti attributorum vltrò
excogitauerim: ip&longs;e es, qui eum induxi&longs;ti citato illo
Epi&longs;tolæ, &longs;eu Demon&longs;trationis tuæ loco; ac nihil fuit
nece&longs;&longs;e, vt alium, quoties fuit aliquo exemplo vten
dum, &longs;ub&longs;tituerem.
ris difficile e&longs;&longs;e determinare tempus, quo primum pri
mæ partis dimidium, quo &longs;ecundum percurrerentur:
ego tamen, quòd ob&longs;eruarem habere te varia decreta,
tuis principiis con&longs;entaneum, & quoniam &longs;æpè opus
fuit exemplorum illu&longs;tratione, tempus illud &longs;emper
a&longs;&longs;ump&longs;i iuxta aliquod ex tuis principiis.
cùm ob&longs;eruâtim, quicquid ip&longs;e aduer&longs;us alios deduce
res partem &longs;ecundam non percurri dimidio temporis,
quo primam: id tamen fui&longs;&longs;e à te a&longs;&longs;umptum, tan
quam veram hypothe&longs;in, qua paralogi&longs;mi Galileum
conuinceres; & non potui&longs;&longs;e à te a&longs;&longs;umi, ni&longs;i reputan
do partem &longs;ecundam percurri dupla velocitate, &longs;iue
duobus gradibus, nulla agnita di&longs;tinctione inter ma
nentem, & acqui&longs;itum: idcircò, quia ex prima parte
duo faciebas dimidia, quorum prius ad po&longs;terius ean
dem rationem, quam pars prima ad &longs;ecundam tuere
tur; cen&longs;ui &longs;ex minuta à te primæ parti attributa ita di
&longs;tribuenda in hæc duo dimidia, vt priori quatuor, po
&longs;teriori duo congruerent.
te velle aliunde inferius primæ partis dimidium, & &longs;e
cundam partem æquali tempore percurri: vi&longs;um rursùs
e&longs;t deberi ex te duo minuta illi dimidio, tanquam
trientem temporis parti primæ attributi: quoniam
idem triens deberetur &longs;imiliter &longs;ecundæ parti, iuxta eam
ratiocinationem, quàm &longs;uperiùs fu&longs;iu&longs;culè circa arti
culum VIII. ex eo contexui, quód e&longs;&longs;e in fine primæ
partis vnum, in fine &longs;ecundæ duos gradus velocitatis
acqui&longs;itos cen&longs;eres.
ris ita factum e&longs;&longs;e à me; &longs;ed cur mireris te non vidi&longs;&longs;e id
e&longs;&longs;e cohærens cum principiis tuis, & à me licet admoni
tus, cen&longs;ueris tamen di&longs;&longs;imulandum. Nam quod di&longs;
putàris quidem aduer&longs;us alios, tempus per &longs;ecundam
&longs;en&longs;i con&longs;tanter te facere rectè; at &longs;emper quoque ad
monui te id di&longs;putare aduer&longs;us teip&longs;um: neque tu ocu
los ad hoc &longs;u&longs;tinui&longs;ti aduertere, & attendere, an aliquis
foret, quo id mon&longs;tra&longs;&longs;em, paralogi&longs;mus.
inde fit manife&longs;tum, multa me tibi obieci&longs;&longs;e ex fal&longs;a
hac &longs;uppo&longs;itione, non quia fal&longs;a, &longs;ed quia tua: neque
&longs;atis e&longs;&longs;e, vt eam neges, quò quicquid obieci,
euer&longs;o fundamento corruat,
das &longs;imùl tuam non e&longs;&longs;e (&longs;eu non e&longs;&longs;e ex tuis principiis
qua nece&longs;&longs;itate vi&longs;um e&longs;t, deductam) ac ideò non e&longs;&longs;e,
cur quov&longs;que illud
quod a&longs;&longs;umo, affingere, imponeréque. Addo
quod caput e&longs;t, fui&longs;&longs;e perinde mihi futurum, &longs;eu hanc
&longs;eu aliam di&longs;tributionem minutorum &longs;ex, aut cuiu&longs;li
bet temporis alterius, in ea dimidia a&longs;&longs;erui&longs;&longs;es: &longs;i modò
&longs;emper rationem &longs;patiorum, ac velocitatum &longs;uppone
ret eandem: quippe fac iam aliam qualemcumque
voles, quæ &longs;emper hanc tuam rationem &longs;upponat; &
ego recipio me eadem ab&longs;urda, ac fortè etiam alia lon
gè ab&longs;urdiora e&longs;&longs;e obiecturum.
De Ra
tione continuò dupla, qua &longs;patia decurri temporibus
æqualibus R. P. concludit.
& numero item xl.
Quid
nam cau&longs;&longs;æ e&longs;&longs;e poßit, cur Progreßionem accelerationis in
de&longs;cen&longs;u grauium non à primo &longs;patij decurrendi puncto
à puncto primi spatii medio
aliquas inquiratur. Nam, inquis,
tem AD, in S, bi&longs;ecare etiam potui&longs;ti partem AS, ac &longs;u
periores &longs;imilieer cæteras.
fuit alicubi, cùm diui&longs;io infinita e&longs;&longs;e non potuerit. Quid ni igitur
iam primùm, in ea parte con&longs;i&longs;tamus, ex qua totius motus ac
celerati ratio perfectè intelligatur? Sed ne putes tamen, &longs;i
pars &longs;uperior
infinitas in parteis, con&longs;equens proptereà e&longs;&longs;e, vt per illas par
teis omneis mente confictas acceleratio varietur: motus enim,
eiu&longs;que acceleratio effectus Phy&longs;icus est, qui proptereà (vt in
cæteris rebus Phy&longs;icis accidit) per parteis &longs;en&longs;ibileis, ea&longs;que
pro ratione ponderis, & re&longs;i&longs;tentiæ medij, maiores, aut mino
res metiendus videatur. Accedit, quòd tecum, & cum
lileo non &longs;entio corpus graue de&longs;cendens &longs;tatim à quiete, atque
in omnibus, ac &longs;ingulis indiui&longs;ibilibus momentis accelerare
motum.
medio e&longs;t; vnde de&longs;cen&longs;us in vacuo &longs;ui &longs;emper &longs;imilis, atque
vniformis ex&longs;i&longs;teret: &longs;icut tunc quoque tota cau&longs;&longs;a de&longs;cen&longs;us,
nempe grauitas, &longs;emper eadem, ac &longs;ui &longs;imilis per&longs;eueraret. Igitur, cùm graue quodcumque per aërem, aut aliud medium
de&longs;cendit, talis de&longs;cen&longs;us à &longs;olagrauitate inchoatur, etiam me
dio plus, aut minùs re&longs;i&longs;tente, prout ip&longs;um grauius, aut leuius
e&longs;t, & faciliùs, aut difficiliùs diuiditur: nec priùs acceleratur
motus de&longs;cendentis corporis, quàm à medij accurrentis, &longs;éque
à tergo claudentis motu, eóque iam notabili, medii re&longs;i&longs;tentia
&longs;upereretur, & grauitatis ni&longs;us, natiuaque velocitas Phy&longs;icè
augeatur: ad quod &longs;ine dubio requiritur pars temporis, ac spa
tii non Mathematicè minima, &longs;ed Phy&longs;icè notabilis, quæ cùm
pro grauium diuer&longs;itate, & varia re&longs;i&longs;tentia mediorum modò.
primo spatii percurrendi puncto minùs tutò inchoetur. Hæc
porrò, &longs;i cum tuis, ac
principiis certè Phy&longs;icis aptè congruunt. Sed reliqua breuiùs
percurramus.
Peruentum iam e&longs;t ad Ph&longs;iycæ tuæ Demon&longs;tratio
nis Conclu&longs;ionem: quæ quoniam e&longs;t eadem cum ip&longs;o
con&longs;equente Propo&longs;itionis, idcircò elicienda fuit vi
con&longs;equutionis qua illud dependet ab antecedente. Quod porrò notas quæ&longs;ii&longs;&longs;e me; quanto, amabò, iure
quæ&longs;iuii: cùm
motum æquabiliter acceleratum, qui æqualibus &longs;patiis
æqualia celeritatis augmenta acquireret; ac &longs;patia illa
æqualia &longs;emper & habui&longs;&longs;e, & &longs;ic expre&longs;&longs;i&longs;&longs;e per lineas
in parteis æqualeis diui&longs;as, vt e&longs;&longs;et in iis vna prima, vna
&longs;ecunda, &c. nunc autem rem &longs;ic perturbare, vt pars
prima vna æqualium non &longs;it; vt primum primæ dimi
dium pro nihilo &longs;it, vt reliquum pro tota &longs;it: vt motus
æquabiliter acceleratus non incipiat, cùm incipit; vt
incipiat, po&longs;tquam incepit, & alia id genus, quæ ob
iecta &longs;unt, quæque repetere iam piget? Cùm deduxe
rim verò incommoda varia ex eo, quòd liceat
dium
rum in duo alia, & &longs;ic con&longs;equenter: quid tu ad ea om
nia? Nempe
e&longs;&longs;e tandem alicubi &longs;tandum: cùm diui&longs;io e&longs;&longs;e infinita non po&longs;
&longs;it. Age itaque peruideamus quid hac re&longs;pon&longs;ione ef
ficias. Dicis
infinita non poßit:
que diui&longs;io finita non erit, ac partes &longs;upererunt, per Igitur tumerit nece&longs;
&longs;ariò &longs;tandum, cùm &longs;ic finita erit diui&longs;io, vt exhau&longs;tis
partibus, nulla ampliùs fieri &longs;ubdiui&longs;io po&longs;&longs;it. Quando
nam verò id continget? An-non cùm tota pars AD
tantula erit, & &longs;ic diui&longs;a in duo dimidia AS, & SD, vt
AS non habeat ampliùs duo dimidia, ac &longs;it indiui&longs;ibilis
pars? An-non proinde cùm l inea AD contexta erit
ex duobus punctis?
Prouidens tu quæ po&longs;&longs;ent exinde iure vrgeri in
commoda, præoccupa&longs;ti,
vt quid Phy&longs;icum, quod mente quidem, &longs;eu Mathematicè
diui&longs;ibile in parteis infinitas &longs;it: &longs;ed non ita tamen, vt accelera
tio variari &longs;ecundum eas poßit; quippe quæ effectus Phy&longs;i
cus cùm &longs;it, non-ni&longs;i per parteis &longs;en&longs;ibileis metienda videa
tur. Aequiuocatio e&longs;&longs;e quædam po&longs;&longs;et circa vocem
xeris parteis
rerum natura; nempe vt opponantur Mathematicis,
&longs;iue iis, quas mente confictas dixi&longs;ti. Nam &longs;i alioquin
diceres
naturam non e&longs;&longs;e metiendam in &longs;uis adeò &longs;ubtilibus
operationibus iuxta &longs;en&longs;us captum. Neque enim in
compingendo v. g. animalculo acari no&longs;trum &longs;en&longs;um
con&longs;ulit, qui ip&longs;um habet qua&longs;i punctum, &longs;iue rem vi&longs;u
minimam; &longs;ed &longs;eip&longs;am potiùs, prout illud texit ex
innumeris myriadibus partium infra omnem &longs;en&longs;us
acutiem ex&longs;i&longs;tentium, & nece&longs;&longs;ariarum tamen, vt rem
faciat per&longs;e mobilem, ac vegetationis, &longs;en&longs;us, appeti
tus capacem. Vt præteream &longs;en&longs;um haberi regulam
plu&longs;quàm Le&longs;biam, propter diuer&longs;itatem &longs;en&longs;uum acu-
po&longs;&longs;unt &longs;ubtiliora omnibus rebus antè perceptis per
cipere; & &longs;ine &longs;pe tamen, vt vnquam naturæ &longs;ubtilita
tem a&longs;&longs;equantur. Itaque, vt in hac di&longs;tinctione hærea
mus: tunc igitur erit finita diui&longs;io, &longs;eu
eam diui&longs;ionem, vltra
non liceat, cùm AS erit non Mathematicè quidem,
&longs;ed Phy&longs;icè tamen indiui&longs;ibilis: atqui &longs;i AS &longs;it Phy&longs;i
cè indiui&longs;ibilis: erit igitur & pars SD indiui&longs;ibilis, tan
quam ip&longs;i AS æqualis? An ergo, &longs;i pars SD &longs;it in
diui&longs;ibilis Phy&longs;icè, di&longs;tingues in ea trientem, quadran
tem, & cæteras Phy&longs;icas parteis iis temporibus percur
rendas, quæ men&longs;uræ &longs;int con&longs;equentium, hoc e&longs;t ip&longs;i
AD æqualium? Cùm non po&longs;&longs;is: vide quàm fru&longs;trà
eò confugeris, vt
nita non poßit.
Hanc iterùm difficultatem qua&longs;i præ&longs;entiens, præ
uenien&longs;que,
&longs;i&longs;tamus, ex qua totius motus accelerati ratio perfectè intelli
gatur?
hoc vt con&longs;i&longs;tamus, quov&longs;que ad eam diui&longs;ionem per
uenerimus, ex qua partes AS, & SD &longs;int duo puncta
Phy&longs;ica, &longs;eu duæ Phy&longs;icè indiui&longs;ibiles partes: &longs;ed in illa
&longs;tandum, in qua tam AS, quàm SD con&longs;tent adhùc ex
tot Phy&longs;icis partibus,
fectè intelligatur. At imprimis, &longs;i ita &longs;it, fru&longs;trà ergo
dicis alicubi &longs;tandum,
cùm etiam diui&longs;ione ex&longs;i&longs;tente non infinita, progredi
adhûc vlteriùs liceat: atque idcircò vigent adhûc in
commoda omnia, quæ obiecta &longs;unt: quandò pote&longs;t Deinde, cùm in dimidio SD, tot requiris parteis, vt
nam quæ&longs;o &longs;unt, quas requiris? An aliquot pauculas,
v. c. &longs;ex, quas nempe recen&longs;es, dum rationem motus
accelerati explicas per trientem, quadrantem, per quin
tam, perque &longs;extam parteis tantum? Sanè vel ne&longs;ciens
tot requiris, vt innumerabiles &longs;int; & tum ab&longs;is longi&longs;
&longs;imè ab eo, vt cau&longs;&longs;eris &longs;tandum, quòd
non poßit,
con&longs;i&longs;tendum &longs;it: tum etiam ab eo, vt ex cognitis par
tibus Rem vt experiamur, ac
cipiamus, ecce, ca&longs;um globi ferrei (quod tuum po&longs;teà
exemplum e&longs;t) ex cælo Lunæ in centrum terræ: atque
in ip&longs;o talem partem,
mus.
nium partium i&longs;ti primæ æqualium &longs;it æqualis duratio
totidem minutiorum partium &longs;igillatim acceptarum
in inferiore eius dimidio: ergo inferius eius dimidium
diui&longs;ibile e&longs;t in tot parteis, non Mathematicas, men
teve confictas, &longs;ed Phy&longs;icas, &longs;iue in ip&longs;a rerum natura
ex&longs;i&longs;tenteis, quot partes &longs;unt à cælo Lunæ, v&longs;que in
centrum terræ, ip&longs;i AD æquales. Hæ verò partes quot
nam &longs;unt? Certè, cùm a&longs;&longs;umendo pedes (vt facis) pro
Galilei cubitis, admittas à Luna in centrum nonagies
octies mille myriadas pedum: oportebit, etiam &longs;i pri
mam partem AD, non minorem pede habeas, vt di
cas dimidium illius inferius, &longs;eu &longs;emi-pedem totidem
pati diui&longs;iones, & continere totidem parteis Phy&longs;icas
non mente confictas. Quid verò &longs;i acceperis partem
vi&longs;u perceptibilis &longs;it, &longs;ed micro&longs;copicis etiam vitris, ex
quam plurimis texi ob&longs;eruetur: an non tribus additis
cyphris,
mytiadum partium? Quid &longs;i ca&longs;us foret ex Sole, vicies
&longs;altem di&longs;tantiore, quam Luna? Quid &longs;i ex firmamen
to di&longs;tantiore &longs;altem ducenties quinquagies? Tantam
igitur partium multitudinem e&longs;&longs;e vis in inferiore di
midio SD, vt ratio motus accelerati po&longs;&longs;it perfctè
intelligi: tantam, in &longs;uperiore AS, vt cen&longs;eamus illam
non po&longs;&longs;e vlteriùs in duo &longs;ubdiuidi dimidia. Vide&longs;-ne
ergo quàm procùl ab&longs;it à diui&longs;ionum fine ea pars,
qua iam primùm,
Subiicis,
de&longs;cendens, statim à quiete, atque in omnibus, ac &longs;ingulis mo
mentis accelerare motum. Quot ergo putas momenta,
&longs;eu Phy&longs;icas temporis parteis ab&longs;que acceleratione
tran&longs;iri? Tot certè, quot &longs;unt innumerabiles illæ par
tes, quæ &longs;unt
midio di&longs;tinctæ: neque enim illæ, ni&longs;i &longs;ucce&longs;&longs;iuè, & vna
po&longs;t aliam, atque adeò di&longs;tinctis temporis partibus per
curruntur. Vide igitur per quot parteis, & per quot
momenta temporis di&longs;tincta inefficacem facias cau&longs;
&longs;am Phy&longs;icam, quam aduocas &longs;tatim. Videlicet
&longs;am accelerationis
neque enim prius accelerari motum à grauitate inchoatum,
quàm à medii accurrentis, &longs;eque à tergo claudentis motu, eó
que iam notabili re&longs;i&longs;tentia &longs;uperetur. Quo loco rursùs
æquiuocatio in nomine
ligis aut naturæ, aut nobis. Et nobis quidem
alligetur; & priu&longs;quam no&longs;tra per&longs;picacia
quam valeat, natura iam tran&longs;ierit per innumerabi
leis parteis. Si ergo naturæ; quæro quot partes in mo
tu nece&longs;&longs;ariæ &longs;int, vt natura progre&longs;&longs;a e&longs;&longs;e
reputetur? An-non &longs;altem myrias deberet e&longs;&longs;e &longs;atis?
An-non &longs;altem decem, centum, & mille myriades?
An
non &longs;altem
mille myriades myriadum? Stupendum i&longs;ta non e&longs;&longs;e
&longs;atis, &longs;ed deinceps adhûc multiplicanda e&longs;&longs;e,
numerus
ficaxpo&longs;&longs;it. Sed de hac quidem Phy&longs;ica cau&longs;&longs;a dicen
dum erit inferiùs: quæro heic &longs;olùm, an putes aërem
&longs;e&longs;e à tergo claudere, cùm iam &longs;uperatur, vel &longs;tatim ac
&longs;uperata à fronte e&longs;t pars &longs;patij prima, vnaque ex illis
innumerabilibus, an non? Si dicas &longs;e non claudere;
igitur &longs;patium illud à tergo vacuum remanet; quod
non es &longs;anè admi&longs;&longs;urus. Si &longs;e claudere, ergo cum &longs;e
claudendo agat (neque enim alia ratione putas hanc
cau&longs;&longs;am agere) ab ea v&longs;que parte agit aliquid: ergo ab
initio v&longs;que grauitatem iuuat: ergo & motum accele
rat: ergo ex&longs;pectandæ non &longs;unt tam innumerabiles
partes, vt motus notabilis &longs;it, & acceleratio incipiat. Quod
&longs;uperetur:
tate &longs;ola agente &longs;uperatam iam facias, priu&longs;quàm aër
aliquid agat, &longs;iue mobili iam promoto per totum &longs;upe
rius dimidium &longs;uperueniat, ac &longs;e&longs;e claudat. Vtcum
que autem e&longs;&longs;e debeat
platicè &longs;ubtilem determinationem in primæ partis me-Qua&longs;i non po&longs;&longs;it motus
medium, aut non-ni&longs;i paulò pò&longs;t medium? E&longs;t ne
aliquod argumentum, quo probes i&longs;tam tuam cau&longs;&longs;am
nihil omninò agere, nihil &longs;uperare re&longs;i&longs;tentiæ, per tot
illas partium &longs;patij, tempori&longs;que myriadas, quæ toti
priori dimidio tribuuntur, &longs;tatim autem ac mobile at
tigit primam po&longs;terioris, incipere & agere, & re&longs;i&longs;ten
tiam &longs;uperare?
tii non Mathematicè minima, &longs;ed Phy&longs;icè notabilis. Aduer
&longs;atiuam hanc non capio: cùm videretur debere pars
dici, aut
quicquid &longs;it, vis eam Phy&longs;icè notabilem e&longs;&longs;e; quid inde
concludis?
primo &longs;patii percurren li puncto non tutò inchoetur. Non
tutò inchoetur? Imò, vnde tutiùs inchoetur, quàm
vnde e&longs;t periculi nihil? Nam tibi quidem meritò ef
ficiuntur omnia &longs;u&longs;pecta, cùm viâ regiâ &longs;emel relictâ,
non valeas ecce, ni&longs;i per dumos, &longs;alebra&longs;que incedere;
at verò illis, qui viam tenent, &longs;imile nihil timendum e&longs;t. Sed nempe platicè a&longs;&longs;umenti, platicè perinde conclu
dendum fuit. Sperandum quippe fuerat, vt conclu
deres, cur ante primæ partis medium, &longs;eu alicubi per
totum prius dimidium, acceleratio non inchoaretur; at
tu intereà de medio, totove priore dimidio nihil: &longs;ed
&longs;olùm,
Quod autem addis,
non fortè conueniant, principiis certè Phy&longs;icis aptè congruere;
cedò &longs;olùm, Quibus?
quæris, cur
rationem accelerationis à primo spatii decurrendi puncto non
rùm, quod diui&longs;o, vt libet, in parteis æqualeis tempore, aut
&longs;patio, &longs;emper impoßibile &longs;it, vt velocitas &longs;ecundæ partis præ
cisè dupla &longs;it totius velocitatis per priorem partem acqui&longs;itæ:
quod ex tuis etiam principiis anteà numero
mon&longs;tratum e&longs;t.
Et &longs;æpe repetij, & repetere &longs;æpiùs cogis me, quæ
&longs;tionem non e&longs;&longs;e, an impo&longs;&longs;ibile &longs;it velocitatem per
&longs;ecundam partem e&longs;&longs;e præcisè duplam velocitatis per
primam: &longs;ed id-ne &longs;equatur ex admi&longs;&longs;o principio, quòd
velocitates vt &longs;patia &longs;e habeant. Ego enim &longs;emper id
&longs;equi conte&longs;tatus &longs;um: tu non &longs;equi proba&longs;ti nun
quam; & perinde &longs;emper procedis, ac &longs;i id habendum
e&longs;&longs;et nihili; quod ip&longs;um tamen e&longs;t rei caput. An, &
quomodo aliquid ex meis principijs demon&longs;traueris;
nihil e&longs;t quam obrem heic repetatur.
eo, quòd partes NC, & CD eodem tempore percurrun
tur, talem gradum velocitatis acquiri concludis ab N in
C, qualis acquiritur à C, in D: tunc enim velocitates e&longs;&longs;e
vt spatia nece&longs;&longs;e e&longs;t.
Quàm egregiè elaberis?
Ego enim cætera inter,
quæ non attigi&longs;ti, ex eo, quòd priùs admi&longs;i&longs;&longs;es, pro
pter progre&longs;&longs;ionem Arithmeticam, duorum graduum
acqui&longs;itorum in D, vnum acqui&longs;itum ab A, in C, alte
rum à C, in D, conclu&longs;i te velle velocitatem acqui&longs;i
tam ab N in C, e&longs;&longs;e æqualem acqui&longs;itæ à C, in D,
quandoquidem tum velles ip&longs;am CD tanto tempore,
quanto NC, cuius e&longs;&longs;et dupla, percurri. Et quia vi
deris non attendi&longs;&longs;e ad con&longs;equutionem, quæ &longs;atis
modò ea probetur. NC, & CD debent, per
te, e&longs;&longs;e æquales; quoniam vtraque, per te, de
bet e&longs;&longs;e æqualis lineæ AC: quare &, &longs;i æquali
percurrantur tempore, æquali percurrentur ve
locitate. Et de æqualitate quidem lineæ CD,
cum AC, non e&longs;t dubium; probo de NC, AC, &
NC eadem velocitate &longs;ecundum &longs;e totas per
curruntur, ex te; Ergo &longs;unt inter &longs;e æquales. Pro
batur antecedens. Ad velocitatem acqui&longs;itam
per totam AC, addita quæ acquiritur per CD,
facit velocitatem in D duplam velocitatis in
C; ad volocitatem acqui&longs;itam per totam NC,
addita quæ acquiritur per eandem CD, facit
itidem velocitatem in D, velocitatis in C du
plam; & vtrumque quidem per te. Igitur per te
AC, & NC, &longs;ecundum &longs;e totas velocitate ea
dem percurruntur; &longs;untque idcircò inter &longs;e
æquales. Tu ergo vim con&longs;equutionis ex inte
gro antecedente diffimulans, infers &longs;olùm ex
duplo &longs;patij, & temporis æqualitate, velocitates
e&longs;&longs;e vt &longs;patia: ac retices quod intere&longs;t, quodque
&longs;ubnotatum fuit, cùm &longs;ubiunxi,
velocitates per AC, & NC, acqui&longs;itæ &longs;int pror&longs;us
æquales: ac proinde vt AC, & NC, hoc est totum, &
pars eodem tempore percurrantur, &c. Sequitur.
etiam peccas; cùm, vt impugnes con&longs;titu
tam à me cæterarum partium toto spatio decurrendo de&longs;igna
tarum respectum ad analoga primæ partis &longs;egmenta, non &longs;o
lùm earumdem partium re&longs;pectum ad parteis temporis exigis,
tempora etiam illis ad&longs;cribis, quæ nullo modo ip&longs;is conuenire
non ignoras. Vis enim primi &longs;patij partem dimidiam dimidia
parte eius temporis percurri, quo totam primam partem ab
&longs;olui &longs;upponis; & tertiam partem tertia parte, quartam
quartaparte eiu&longs;dem temporis: cùm ex tuis, &
cipiis dimidia parte prima temporis, quarta pars tantum spatij
&longs;uperior decurratur, & reliqua dimidia parte temporis tres
inferiores &longs;patij quadrantes ab&longs;oluantur. Vide ergo quid ex
tam ab&longs;urda hypothe&longs;i concludere poßis.
Cùm nihil &longs;it, quod prodat magis decretorum
incohærentiam, quàm reductio ad calculos; ex eo e&longs;t,
cur poti&longs;&longs;imùm &longs;upputationes auer&longs;eris. Id autem hoc
loco præ&longs;ertim probatur. Admi&longs;i&longs;ti po&longs;&longs;e di&longs;tingui
in motu grauium decidentium plura æqualia tempora:
at cùm planum foret, vt &longs;patio diui&longs;o in parteis æqua
leis, primum tempus attribueretur primæ huiu&longs;cemodi
partium, ac deinde explicaretur quota eius temporis
parte percurrerentur cæteræ; & in qua ip&longs;arum &longs;ecun
dum tempus æquale de&longs;ineret, in qua tertium, &c. di
uerti&longs;ti nihilominus, & pro primo tempore accipien
dum volui&longs;ti id, quo decurreretur eiu&longs;dem primæ par
tis non prius, &longs;ed po&longs;terius dimidium; & tum volui&longs;ti
&longs;ecundam partem, quæ e&longs;&longs;et dupla huius dimidii, æqua
li cum eo tempore percurri: tum tertiam æquali cum
eo, quo triens eiu&longs;dem primæ partes infimus; quartam
æquali cum eo, quo quadrans, &c. tum
pus æquale primo e&longs;&longs;e id, quod debetur &longs;ecundæ parti
&longs;oli: tertium, quod tertiæ, & quartæ &longs;imùl: quartum,
quod quintæ, &longs;extæ, &longs;eptimæ, octauæ: quintum, quod
bus, atque ita porrò. Ego itaque o&longs;ten&longs;urus, vt hæc &longs;e
probè non haberent, cætera inter argumenta, rem ex
primendam numeris cen&longs;ui, ac a&longs;&longs;ump&longs;i
tempus, quod dimidio illi po&longs;teriori attribueres, veluti
a&longs;&longs;em, eiu&longs;que proinde parteis duodecim qua&longs;i vncias,
&longs;iue mauis minuta habui. Debueras tu procedere dein
ceps per parteis æqualeis huic dimidio: quo ca&longs;u &longs;e
cundæ parti fui&longs;&longs;ent attributa minuta &longs;ex, &longs;iue
&longs;iue triens (ob triplicatam) & quartæ tria, &longs;iue quadrans
(ob quadruplicatam) &c. & quia tamen duplum di
midij v&longs;urpandum e&longs;&longs;e vbique cen&longs;ui&longs;ti, vt partes &longs;e
cunda, tertia, quarta, &c. fierent vbique toti primæ
æquales: ideò effectum e&longs;t, vt &longs;ecundæ parti non dimi
dium, &longs;eu &longs;ex minuta, &longs;ed omninò tantumdem, &longs;eu duo
decim tribueris, & tertiæ be&longs;&longs;em, &longs;iue octo: quartæ di
midium, &longs;iue &longs;ex. Ip&longs;e proinde, vtcumque rationem
dupli prætermi&longs;erim (& quam tamen iam inter&longs;eren
dam cen&longs;ui) declarare volui, vt hæc tempora non con
gruerent &longs;patiis vtravis ratione a&longs;suptis. Et de &longs;ecundo
ueniret tempus primo æquale, &longs;eu minutorum duode
cim, at &longs;implici non ni&longs;i dimidium, &longs;eu minuta &longs;ex: de
fuccedentibus autem iuxta aggregationem tuam, ob id,
quòd neque &longs;implicibus, neque duplicibus conueniret
vnquam tempus æquale primo, &longs;eu minutorum duo
decim, &longs;ed vel in &longs;implicibus &longs;emper deficeret, vel in
duplicibus &longs;emper abundaret: cùm deberet tamen &longs;al
tem in duplicibus &longs;emper exæquari, vt exæquatum Quid tu ad i&longs;ta
igitur?
Dicis me,
temporis exigere, quas neque ego, neque alius qui&longs;quam aßi
gnare poßit: &longs;ed tempora etiam illis ad&longs;cribere, quæ nullo
modo ip&longs;is conuenire non ignorem. Verumtamen, quæ
&longs;tio non e&longs;t de eo, quod ego, aut alius præ&longs;tare po&longs;&longs;i
mus, aut non po&longs;&longs;imus, in a&longs;&longs;ignandis temporibus, quæ
partibus quibu&longs;que conueniant: quanquam Galileum
quidem imitatus, &longs;umpto quocumque tempore primæ
parti debito, a&longs;&longs;ignaui tempus, quod exigitur ad &longs;ecun
dam, & quod ad vtrumque primæ partis dimidium,
paratus idem prorsùs præ&longs;tare circa quælibet tempora,
quarumcum que voles partium cætetarum, iuxta gene
rale &longs;cilicet Effatum, quod articulo
retuli, & in quod nihil fuit, quod à te obiiceretur. Non item e&longs;t quæ&longs;tio, an tempora quæ partibus ad&longs;cri
bo, ip&longs;is nullo modo conuenire ignorem, an &longs;ciam (&longs;cio
enim e&longs;&longs;e longè alià, prout ex citato moxloco intelligi
pote&longs;t) &longs;ed an ea ad&longs;cribam iuxta tua principia. Quo
nam verò modo id non fieri probas?
poris percurri, quo totam primam partem, & tertiam
tertia, quartam quarta,Sperâram, vt aliò querela
tua vergeret. Quia enim iuxta ante-dicta defendis te
nolle dimidium inferius primæ partis percurri dimidio
eius temporis, quo &longs;uperius: procliue mihi videbatur,
vt querereris tibi affingi tempora à te pernegata. Sed
videlicet, animaduerti&longs;ti me commi&longs;i&longs;&longs;e tuæ libertati,
vt dares quodcumque demùm velles tempus pro infe-Vnde
& animi &longs;olùm gratiâ, & con&longs;onanter ad &longs;uperiora,
a&longs;&longs;ump&longs;i pro partis primæ tempore numerum trigin
ta &longs;ex, vt inferiori dimidio attribueretur numerus com
modi&longs;&longs;imus duodecim. Et &longs;anè heic non quærebatur,
quota portio e&longs;&longs;et hoc tempus temporis totius per pri
mam in&longs;umpti: &longs;ed &longs;olùm, quodcumque illud e&longs;&longs;et, ex
quibus &longs;ui partibus cen&longs;eri po&longs;&longs;et integrum, vt alia ip&longs;i
æqualia deinceps adnumerarentur. Quidnam verò e&longs;t,
quod &longs;ubiungis? I&longs;tud nimirùm:
lilei principiis dimidia parte primi temporis quarta pars tan
tum spatii &longs;uperior decurratur, & reliqua dimidia parte tem
poris tres inferiores spatii quadrantes ab&longs;oluantur. Sed
quæ&longs;tio heic non e&longs;t, quid Galileus, & ego &longs;entiamus:
ea de re enim &longs;atis iam con&longs;tat: verùm, an quod tibi
obiicio, &longs;it tuum, &longs;iue iuxta tua decreta, an non? Cùm
non fuerit, quod re&longs;ponderes, his tamen verbis con
clu&longs;i&longs;ti,
dere poßis. Ego verò,
the&longs;i tam ab&longs;urda, cum tua &longs;it, conclu&longs;erim, & ad conclu&longs;io
nem re&longs;ponde, &longs;i poßis. Pergis.
augmentum velocitatis in
ratione dupla con&longs;titutum impugnes, inter alia a&longs;&longs;umis pari
iure, ac modo &longs;tatui po&longs;&longs;e idem augmentum etiam procedere in
quacumque alia
drupla, in decupla &c. exemplumque profers in tripla.
Et pri
mùm quidem obiter mihi affingis, quòd velim partem AN,
& eius triplam ND eodem tempore percurri.
Ego verò nihil affinxi; &longs;ed idip&longs;um fuit, quod de
duxeram articulo XL. ea parte, quam non attigi&longs;ti:
torum, & CD illius dupla, &longs;imiliter minutorum
duorum, atque ideò tota ND, minutorum qua
tuor: forè vt AN ex tuis principiis minutorum
quatuor, & eius tripla ND, tempore eodem
percurrerentur.
parte
tem comparas cum tribus &longs;equentibus
eodem tempore, aut æquali cum tertia parte
tempore longiore percurruntur. At rectiùs cum ea
dem tertia parte
ua, & nona, nempe
tum &longs;patium decurrendum continua non e&longs;t, vt vides:
interrupta enim primùm e&longs;t inter
inde ab
à nona parte interrumperetur v&longs;que ad decimam octa
uam, & ita deinceps: progreßio autem in ratione dupla
&longs;ola per totum spatium continua e&longs;t.
Id &longs;atis peruidi, &longs;ed & &longs;imùl agnoui, quàm
opero&longs;o &longs;imùl,
i&longs;ta aduerteres; ea videlicet &longs;uperex&longs;truens la
ba&longs;centibus &longs;ponte fundamentis. Laba&longs;centibus,
inquam, primùm, quatenùs fal&longs;um e&longs;t, velocitates e&longs;&longs;e
inter &longs;e &longs;icut &longs;patia: quod tamen fuit tibi fundamen
tum primarium, ip&longs;umque eodem Experimento, quo
id &longs;tabilieras, euer&longs;um. Deinde quatenus nihil e&longs;&longs;e
videtur po&longs;&longs;e ab&longs;urdius, quàm primum primæ partis
dimidium nullo po&longs;&longs;e habere loco in progre&longs;&longs;ione
gre&longs;&longs;ionem
dij durationem quærere innumerabilium partium con
&longs;equent
tam malè cohæreant, vt quod commentum &longs;emel pla
cuerit, cohætere po&longs;&longs;e videatur. Tandem, quatenus
etiam iuxta progre&longs;&longs;ionem in ratione dupla, quam &longs;o
lam vis e&longs;&longs;e continuam, repugnes tibi nece&longs;&longs;e e&longs;t, cùm
indefinite aiens
iora &longs;emper, ac maiora in ratione dupla,
rationem euertas, quotie&longs;cumque a&longs;&longs;ump&longs;eris tempo
ra a&longs;&longs;umptis maiora, & ip&longs;a tamen inter &longs;e æqualia. Quippe cùm in tuo, v. c. de ca&longs;u ex Luna exem
plo a&longs;&longs;ump&longs;eris primo tempore decurri pedes 100, &longs;e
cundo 200, tertio 400, quarto 800, quinto 1600,
&longs;exto 3200, &c. con&longs;tat&longs;i deinceps duo tempora pri
ma pro vno a&longs;&longs;umas, duo &longs;equentia pro alio, duo
item &longs;equentia pro alio: aut &longs;i tria quidem prima pro
vno, tria &longs;uccedentia pro alio, &c. con&longs;tat, inquam,
fore omnia tempora inter &longs;e æqualia; & abfutura ta
men, quæ interim decurrentur &longs;patia, à ratione dupla:
cùm binis temporibus a&longs;&longs;umptis pro &longs;ingulis, futura
&longs;int &longs;patia in ratione quadrupla, vt putà primo tem
pore 300, &longs;ecundo 1200, tertio 4800: & a&longs;&longs;um
ptis ternis, futura &longs;int in ratione octupla, vt puta pri
mo tempore 700, &longs;ecundo 5600, tertio 44800,
atque ita de cæteris. Dicerem heic de Incommodo,
in quod te recidi&longs;&longs;e con&longs;equenter obieci,
ab&longs;oluendo tempore &longs;ecundo,
infinitis,Sed cùm tu nihil am
pliùs habeas, quàm quod te obiter attigi&longs;&longs;e memora
tum &longs;uperiùs e&longs;t; ideò nihil e&longs;t addendum ad ea, quæ in. Re&longs;pon&longs;ione leguntur.
De Tempore,
quo globum ferrcum ca&longs;urum ex Luna in
Terram contendit.
incredibilem putas
celeritatem, qua globus ferreus à Luna ad terram de&longs;cende
ret in continua ratione dupla: non &longs;ufficienter probat eam ex
natura rei tantam e&longs;&longs;e non debere: ac tecum ego quoque arbi
tror eam adeò immen&longs;am reipsâ e&longs;&longs;e non po&longs;&longs;e, quantumvis id
natura exigeret: quod medium tantam, adeóque celerem par
tium diui&longs;ionem, ac rarefactionem pati po&longs;&longs;e non videatur:
quod &longs;atis à me in&longs;inuatum non ignoras.
Peracta Conclu&longs;ione, fuit tibi, qua&longs;i illu&longs;tre quod
dam Exemplum prolixus huiu&longs;modi ca&longs;us, vt in ip
&longs;o exprimeres, quanta e&longs;&longs;etvis progre&longs;&longs;ionis in ratione
continuò dupla. Quòd ego porrò celeritatem, qua tu
&longs;tatui&longs;ti globum ferreum ca&longs;urum ex Luna in terram
minutis non omninò duobus, tantam non e&longs;&longs;e ex rei
natura, abundè &longs;atis probauerim: vel ex eo con&longs;tat,
quòd mon&longs;tratum &longs;it, eam non e&longs;&longs;e iuxta progre&longs;&longs;um,
quem natura in motu grauium decidentium in&longs;tituit:
& euer&longs;um &longs;it fundamentum, cui ip&longs;am &longs;uper&longs;truxeras,
ratio &longs;cilicet eadem &longs;patiorum, ac velocitatum; idque
non modò Experimentis aliis, &longs;ed illo etiam, quod à
te v&longs;urpatum, deprehen&longs;um e&longs;t, &longs;ecus &longs;e habere, & &longs;ecus Ne memorem rapiditatem,
qua ille globus ciendus foret, o&longs;ten&longs;am fui&longs;&longs;e adeò
manem, adeò, vt loquuntur, in&longs;anam, vt te etiam
iam cogat ad abnegationem &longs;ui: tamet&longs;i rem lenias,
dum naturam quidem id exigere, &longs;ed medij tamen
conditionem ob&longs;tare dicis.
De quodam
lap&longs;u emendando circa cau&longs;&longs;am Phy&longs;icam
accelerati grauium Motus.
Cum nihil habeas circa alios, qui heinc ad con
e&longs;u&longs;ionem v&longs;que inter&longs;eruntur, articulos, & ego in ip
&longs;is, occa&longs;ione Phy&longs;icæ cau&longs;&longs;æ, de qua te dicturum alio
loco, temporéque receperas, in&longs;inuâtim lap&longs;um, à quo
non &longs;atis caueram, in priore Epi&longs;tolatum de Motu im
pre&longs;&longs;o à motore tran&longs;lato (imò & in Epi&longs;tola ante duos
annos ad te data) eam ob rem heic locus erit opportu
nus, vt rem paulò fu&longs;iùs deducam, ac memetip&longs;um cor
rigam, dicturus &longs;imùl de Phy&longs;ica cau&longs;&longs;a, quam tu pla
cere tibi dixi&longs;ti in articulum XXXV. Itaque, cùm ego
demirarer illam accelerati motus progre&longs;&longs;ionem &longs;e
cundum &longs;eriem numerorum ab vnitate imparium, Ra
tiocinatus &longs;um imprimis, lapidem v.g. non habere ex
&longs;e huiu&longs;modi motum; quoniam &longs;i &longs;olus lapis non ex
&longs;i&longs;tente Mundo foret, aut aliàs in vacuo &longs;ic con&longs;titue
retur, vt nihil cum Mundo communicaret; non e&longs;&longs;et
prorsùs, quamobrem eò, quò iam mouetur tenderet;
vnde & conclu&longs;i cau&longs;&longs;am huiu&longs;modi motus e&longs;&longs;e debe
re extrin&longs;ecam, ip&longs;amque aut impellentem, aut attra-Secundò, vi&longs;um mihi
e&longs;t a&longs;&longs;umi po&longs;&longs;e aërem, qui infernè pre&longs;&longs;us, re&longs;ilien&longs;
que ad latera, in locum po&longs;terum &longs;uccederet, &longs;uperné
que in&longs;taret, pro cau&longs;&longs;a impellente; & magneticam Ter
ræ vim, quæ hamulorum, catenularumque in&longs;tar, in
fernè pelliceret, pro cau&longs;&longs;a trahente. Tertiò vi&longs;um e&longs;t
aërem non po&longs;&longs;e inchoare motum, quatenus &longs;i nulla
e&longs;&longs;et Terra, & &longs;olus aër in vniuer&longs;o, & ip&longs;e quidem in
finitè fu&longs;us, vnaque lapis intra ip&longs;um, tunc lapis in
hanc potiùs partem, quàm in aliam non moueretur:
quare & motum lapidis videri debere ab attractione
incipere, ac tum po&longs;&longs;e ab aëre &longs;uccedente adiutari. Quartò, cùm fui&longs;&longs;em ratiocinatus motum &longs;emel im
pre&longs;&longs;um futurum perpetuum, & æquabilem, ni&longs;i e&longs;&longs;et
cau&longs;&longs;a, quæ illum aut retundendo minueret, aut vrgen
do acceleraret; conclu&longs;i motum lapidis accelerari, quòd
&longs;tatim à prima attractione, & qua&longs;i po&longs;t primum
&longs;uccederent continuò ictus alij, qui impre&longs;&longs;ione facta,
manenteque facerent motum celeriorem. Quintò vi
&longs;um e&longs;t neque attractionem &longs;olam, neque impul&longs;io
nem &longs;olam, neque vllam aliam &longs;implicem cau&longs;&longs;am &longs;uf
ficere ad memoratam progre&longs;&longs;ionem: quia cùm hoc
modo ictus continenter facti progre&longs;&longs;uri e&longs;&longs;ent &longs;ecun
dum vnitatum &longs;eriem, con&longs;entaneum videbatur, vt &
velocitatis gradus acquirerentur, & &longs;patia quoque per
currerentur &longs;ecundum eandem &longs;eriem: &longs;icque in fine
cuiu&longs;que momenti &longs;patia aggregata non forent vt
quadrata temporum, vnum, quatuor, nouem, &longs;ex de
cim, & quadrata cætera; &longs;ed vt vnum tria, &longs;ex, decem,
& con&longs;equentia aggregata. Sextò vi&longs;um e&longs;t ergo
mo momento &longs;ola Terra vi attractice ageret, vnumque
ictum imprimeret: vnde & vnus gradus velocitatis im
primeretur, quo mobile certum &longs;uperaret &longs;patium: &longs;e
cundo autem momento tum Terra attrahere pergeret,
tum aër pellere inciperet; &longs;icque duo, ex duobus velut
ictibus, noui e&longs;&longs;ent velocitatis gradus, qui cum primo
manente e&longs;&longs;ent tres, vnde & tria &longs;patia primo æqualia
percurrerentur; & ita porrò continenter. Po&longs;tremò,
cùm mihi viderer cau&longs;&longs;am dicere, quamobrem &longs;patia
percurrerentur &longs;ecundum &longs;eriem numerorum ab vni
tate imparium, & aggregata &longs;patiorum e&longs;&longs;ent &longs;icut
quadrata temporum; rem totam &longs;ic expo&longs;ui, repetito
iam aliquoties triangulo, vt partes æquales alterutrius
cturum pro momentis, &longs;eu partibus æqualibus temporis
habens, intercepta
illa ip&longs;i triangula
per interductas li
neas partim ba&longs;i,
partim cruribus pa
rallelas creata, ha
beri po&longs;&longs;e &longs;imùl
cen&longs;uerim, & pro
partibus æquali
bus &longs;patij decur&longs;i;
& pro æqualibus
gradibus veloci
tatis acqui&longs;itæ.
Iam lap&longs;us fuit, quatenus proinde velocitates vt
&longs;patia habere &longs;e admi&longs;i imprudens. Quia enim non
qui&longs;itum ita integrum manere in &longs;ecundo, vt ad &longs;u
perandum duo &longs;patia valeret, ip&longs;umque ita habui, qua
&longs;i valeret &longs;olùm ad &longs;uperandum vnicum; ideò cùm vi
derem &longs;ecundo momento tria &longs;uperari &longs;patia, exi&longs;ti
maui facilè ita vnum &longs;uperari per gradum manentem,
vt duo alia deberent per duos alios, interim acqui&longs;itos
&longs;uperari. Pari autem ratione quinque &longs;patia tertio
&longs;uperari momento agno&longs;cens, &longs;ic putaui treis gradus
&longs;uperiores manere, vt &longs;ingula per &longs;ingulos &longs;uperaren
tur &longs;patia, ac interim acquirerentur duo alij, quibus
duo alia &longs;uperarentur: non &longs;atis attendens duos tan
tum gradus prius acqui&longs;itos, manentei&longs;que e&longs;&longs;e, quo
rum vtrique deberentur duo &longs;patia; &longs;icque ambobus
quatuor; ac nece&longs;&longs;arium rursùs e&longs;&longs;e vnicum duntaxat
acquiri, cui &longs;patium quintum deberetur. Pari etiam
ex &longs;patiis &longs;eptem quarto momento &longs;uperatis, quin que
retuli ad gradus quinque, quos habui iam acqui&longs;itos,
ac manenteis, & duo ad duos, qui acquirerentur in
tereà: non attendens ip&longs;os e&longs;&longs;e treis duntaxat, quorum
tamen &longs;ingulis deberentur duo &longs;patia; vnde & per illos
&longs;uperarentur &longs;ex, ac ideò e&longs;&longs;e &longs;olùm nece&longs;&longs;e, vt tum ite
rùm acquireretur vnicus, quo &longs;eptimum &longs;uperaretur;
atque ita de cæteris. Itaque, quam primùm animum
aduerti, di&longs;plicuit rem &longs;ic expo&longs;ui&longs;&longs;e, vt velocitates ita
&longs;e habere viderentur, quemadmodum &longs;patia, & non
modò &longs;patiorum, &longs;ed etiam velocitatum aggregata
perinde &longs;e habere, vt quadrata temporum: quod mi
hi quidem vi&longs;um e&longs;t ip&longs;i naturæ repugnare; &longs;ecundum
quam potiùs doberent velocitates e&longs;&longs;e quemadmo-
vt temporum (aut velocitatum proinde) quadrata. Quare & retento eodem Schemate, &longs;ic omnia con
gruere mihi vi&longs;a &longs;unt, vt partes illæ cturum æquales ro
præ&longs;entarent &longs;emper æqualeis parteis temporis: lineæ
verò parallelæ ex vno crute in aliud ductæ, & &longs;tatim
à prima in parteis æqualeis diui&longs;æ, gradus æqualeis ve
locitatis; intercepta autem illa, æqualiaque triangula,
æqualeis parteis &longs;patii; ac denique ex triangulis impari
numero &longs;ub vnoquoque
bina, & quadrangulos con&longs;tituentia triangula, repræ
&longs;entarent &longs;patia per gradus manenteis decur&longs;a; & quod
impar &longs;upere&longs;&longs;et, repræ&longs;entaret &longs;patium gradu interim
acqui&longs;ito decur&longs;um. Atque hoc quidem modo &longs;en
tentiam expre&longs;&longs;i partim in Re&longs;pon&longs;ione, partim etiam
&longs;uperiùs circa explicandum Controuer&longs;iæ &longs;tatum. Cæ
terùm vt animaduerti &longs;ingulos, non binos velocitatis
acquiri gradus; &longs;ic facile fuit animaduertere &longs;ingulos,
non binos quouis momento impingi ictus. Quam
obrem peruidi me in eo fru&longs;trà labora&longs;&longs;e, vt Phy&longs;i
cam cau&longs;&longs;am accelerati motus requirens, excogitarem
denique duas, quarum vna inchoaret motum, & pri
mo momento &longs;ola ageret, &longs;ingularemque ictum im
primeret: ac deinde in &longs;ecundo momento geminæ e&longs;
&longs;ent, quæ & &longs;imul agerent, & geminatis ictibus accele
rarent æquabiliter motum: quippe cùm non modò
non fuerit duplex cau&longs;&longs;a nece&longs;&longs;aria, &longs;ed ne potuerit
quidem e&longs;&longs;e, ni&longs;i vna. Quam-nam verò, putas, ex dua
bus retinui; quam-nam eliminandam cen&longs;ui? Scilicet
retinui attractricem Terræ, vt quæ po&longs;&longs;et &longs;ola non
rare æquabiliter: vt putà per gradus ab v&longs;que initio
tum manenteis, tum acqui&longs;itos, eo modo, quo decla
ratum e&longs;t. Abieci verò impellentem attributam aëri,
vt quæ non modò inefficax inchoando motui videre
tur, &longs;ed illius etiam promotioni, &longs;eu accelerationi offi
ciens; tantum abe&longs;t, vt ad ip&longs;am procurandam quic
quam conferret. Atque hæc quidem cau&longs;&longs;a e&longs;t, quam
obrem quidpiam videatur &longs;imùl de tua opinione di
cendum, quatenus partim con&longs;entit cum ea, quæ mihi
priùs animo in&longs;edit, partim di&longs;&longs;entit ab ea, quæ iam in
&longs;idet. Quippe, vt ego quidem priùs, &longs;ic tu agno&longs;cis du
plicem cau&longs;&longs;am; & vnam quidem penitùs candem,
aërem putà impellentem; alteram verò nomine diuer
&longs;am, &longs;ed effectu eandem, in&longs;itam putà grauitatem (cui
ego attractricem Terræ
tenus tu eam retinens, ip&longs;i quoque tribuis incœptio
nem motus. Cùm verò ip&longs;e &longs;olam iam attractricem
retineam, à qua continenter agente, & impre&longs;&longs;ione non
pereunte, acceleratio motus fiat; opinatis tu grauita
tem ad accelerationem nihil facere: &longs;ed inalteratam &longs;ic
per&longs;euerare, vt ex &longs;e motum vniformem, & æquabilem
faciat: &longs;olum autem aërem &longs;e&longs;e à tergo concludentem
e&longs;&longs;e accelerationis cau&longs;&longs;am. Heinc nempe &longs;uperiùs tua
hæc verba fuerunt.
de de&longs;cen&longs;us in vacuo &longs;ui &longs;emper &longs;imilis, atque vniformis
ex&longs;i&longs;teret: &longs;icut tunc quoque tota cau&longs;&longs;a de&longs;cen&longs;us, nempe graui
tas, &longs;emper eadem, ac &longs;ui &longs;imilis per &longs;eueraret. Itaque cùm
di&longs;&longs;en&longs;us &longs;it circa tuam vtramque cau&longs;&longs;am, ecce de
vtraque pauca hæc attingo.
Et ab Aëre quidem vt incipiam, non immanifc&longs;tum
videtur ip&longs;um nihil po&longs;&longs;e ad accelerationem conferre;
quin-etiam potiùs officere, tantum abe&longs;t, vt aër &longs;olus
&longs;it accelerationis cau&longs;&longs;a. Ip&longs;e certè cùm priùs illum in
aliquam partem admittens, varia energiæ ip&longs;ius argu
menta conqui&longs;iui (au&longs;us etiam ad cum ex parte referre
adactionem retrorsùm factam tormentariæ machinæ,
dum globus prorsùm exploditur; idque, vt iam reor,
iniutiâ, quòd potiùs ille totus effectus ad vnum ignem
pertineat) &longs;ubieci &longs;tatim eas rationes, ob quas meritò
de mea aëris a&longs;&longs;umptione dubitaretur. Vt verò iam
vel vnicam aduer&longs;um te heic repetam, quæ&longs;o ex te,
qui &longs;ieri valeat, vt lapidi deorsùm tendenti ad celeri
tatem aër conferat, non conferat tendenti &longs;ur&longs;um? Ni
mirùm vt aër lapide cadente infernè ab&longs;cedit, &longs;upernè
&longs;uccedit: &longs;ic &longs;ursùm adacto &longs;upernè ab&longs;cedit, infernè
&longs;uccedit, &, tuo verbo vt Non
ne ergo, &longs;i de&longs;cendendo iuuat aër impetum à grauitate
impre&longs;&longs;um: nece&longs;&longs;e e&longs;t, vt a&longs;cendendo iuuet impetum
impre&longs;&longs;um à manu? Et quia impetus à manu impre&longs;
&longs;us fortior illo e&longs;t, qui à grauitate imprimitur, &longs;iquidem
illum &longs;uperat, eóque ne quicquam re&longs;i&longs;tente, lapis ni
hilo min ùs ten dit &longs;ur&longs;um: quid e&longs;t, cur a&longs;cendendo non
magis, quam ex&longs;cendendo iuuet? Nonne clauditur
à tergo rapidiùs, &longs;tatim ac manum lapis de&longs;eruït, quàm
dum lapis initio cadit? Nonne &longs;altem deberet tune
accelerationis quidpiam facere, non verò pati diminu
tionem? Nonne & quandiù grauitate d
rioreque ex&longs;i&longs;tente, aër à tergo velociùs occurrit? Sed
& quæ&longs;o te, nonne ip&longs;e fateris re&longs;i&longs;tere aërem? Dixi&longs;ti
Phy&longs;icum, qui per parteis maiores, aut minores pro ratione
ponderis, & re&longs;i&longs;tentia medij metiendus videatur. Igitut
aër non tantum re&longs;i&longs;tit &longs;upernè, vt omnes admittunt,
&longs;ed etiam infernè, vt tu quoque admittis (& certè vi
detur tantò maior e&longs;&longs;e debere infernè re&longs;i&longs;tentia, quan
tò aër cra&longs;&longs;ior e&longs;t, & propter terram &longs;uppo&longs;itam diffici
liùs diffundi, ac dilabi pote&longs;t; &longs;ed hoc parùm e&longs;t.) Aut
ergo re&longs;i&longs;tentia aëris infernè e&longs;t maior, quàm impul&longs;io
&longs;upernè, aut æqualis, aut minor. Si dicas maiorem;
igitur motus rei cadentis non accelerationem ab aëre,
&longs;ed retardationem patietur. Si æqualem; igitur motus
non aceclSi mi
norem, igitur cum tota vis aëris &longs;upernè impellens &longs;it
ab ip&longs;a vi lapidis infernè aërem vtgentis, erit effectus
potentior cau&longs;&longs;a; & ex&longs;i&longs;tente aëre, qua&longs;i flagello, quo
lapis &longs;eip&longs;um qua&longs;i verberet, fiet flagelli adactio,
quam intentatio rapidior; &, vt verbo dicam, mouebi
tur aër velociùs à tergo, quàm refugiat à fronte; &longs;ic
que nece&longs;&longs;ariò relinquet locum in medio vacuum:
quod vt repugnat, &longs;ic clarum e&longs;t, non po&longs;se aerem ve
lociùs accedere, quàm ab&longs;cedat: cùm etiam ex &longs;e tantò
moueatur &longs;egniùs, quantò longiùs ab
uente. Ac vt præteream, &longs;i id dicas, idem prorsùs fo
re dicendum de aere, dum lapis &longs;eu &longs;ur&longs;um, &longs;eu alior
&longs;um compellitur: prætereo quoque non fore quam
obrem cau&longs;&longs;emur aerem &longs;uâ re&longs;i&longs;tentiâ retardare tan
tillum motum, cùm illum potiùs &longs;it promoturus; ne
que quamobrem concludamus aerem quicquam re
&longs;i&longs;tere, cùm nullum &longs;it re&longs;i&longs;tentiæ ip&longs;ius futurum indi-
quod frigefacere, quando calor e&longs;t ita potentior fri
gore, vt &longs;olus ip&longs;ius effectus &longs;entiatur. Sic non e&longs;t
quare iam excu&longs;es non po&longs;&longs;e globum ferreum ex Luna
eadentem moueri tam perniciter, quàm prædixeris,
ob conditionem medij, cùm re&longs;i&longs;tentia &longs;it &longs;emper ip&longs;a
impul&longs;ione futura minor. Et quod ais
neque tam celeriter diuidi, neque tam citò rarefieri, &
accurrere ad replendum vacuum naturaliter po&longs;&longs;e:
probat non minorem in re&longs;i&longs;tendo,
vim e&longs;&longs;e; cùm & vacuum ex eo metuendum à tergo
non &longs;it, quòd non aër immediate antrorsùm pul&longs;us ille
&longs;it, qui retrorsùm concluditur, verùm ille, qui priùs
ad latera pul&longs;us, & à &longs;uccedente compul&longs;us, eò iam ac
ce&longs;&longs;it. Ex his itaque, alii&longs;que id genus argumentis
fieri videtur, vt aër à tergo accurrens minùs po&longs;&longs;it ad
compellendum, quàm occurrens à fronte ad re&longs;i&longs;ten
dum: aut &longs;altem, vt compen&longs;atio fiat, & dici ad &longs;um
mum valeat, tantum aërem à tergo conclu&longs;um ad pel
lendum iuuare, quantum à fronte diui&longs;um ad proce
dendum re&longs;i&longs;tere. Vnde & efficiatur, vt aër non mo
dò non &longs;ola, &longs;ed ne vlla quidem cau&longs;&longs;a &longs;it accelera
tionis.
De Grauitate verò, quod &longs;it qualitas in&longs;ita, & ab
attractione di&longs;tincta, cuius effectus &longs;it motus deorsùm,
& ille quidem aëre, alióve quovis medio &longs;eclu&longs;o, &longs;em
per idem, &longs;imili&longs;ve &longs;ui, aut æquabilis, videtur mihi dici
non po&longs;&longs;e. Ac vt illa quidem præteream, quæ mox
&longs;unt de aëre, & nomine aëris vniuersè de medio dicta;
dicamus igitur de vacuo, in quo ais Nihil autem e&longs;t nece&longs;&longs;e admoneam, quod &longs;atis in Epi
&longs;tolis antè memoratis expre&longs;&longs;i: lapidi nempe, ex&longs;i&longs;tenti
in vacuo, perinde e&longs;&longs;e penitùs, ac &longs;i Mundus prorsùs
non foret: quippe ni&longs;i perinde foret, habere igitur de
beret colligationem quampiam cum Mundo, aliqua
ve parte ip&longs;ius, &longs;iue per contactum corporeum, &longs;iue per
defluxum, atque tran&longs;mi&longs;&longs;ionem aut aliquorum cor
pu&longs;culorum, aut qualitatum, accidentiumve, non &longs;ine
&longs;ubiecto corporeo, fulcien eque prætermeantium:
quo ca&longs;u non e&longs;&longs;et lapis in vacuo, &longs;ed in &longs;patio cor
poribus, &longs;ub&longs;tantiave corporea pleno. Quamobrem
nihil penitùs cum ip&longs;o Mundo communicans, perinde
&longs;e habere debet, ac &longs;i Mundus foret redactus in ni
hilum, aut procul in immen&longs;itatem imaginariorum
&longs;patiorum tran&longs;latus. Supponamus itaque Deum &longs;ic
feci&longs;&longs;e vacuam regionem hanc elementar
concauo Lunæ orbe ad Terræ v&longs;que &longs;uperficiem facta
&longs;it penitùs inanis, & lapis vno &longs;tadio &longs;upra &longs;uperfi
ciem Terræ con&longs;titutus. Interim verò dum lapis per &longs;e
æquabiliter de&longs;cendet, & vbi iam vnum, alterumve
qua potentia e&longs;t, &longs;ic emouere totum Mundum, & cum
ip&longs;o Terram in eadem &longs;emper di&longs;tantia cum cælo cir
cùm per&longs;euerantem, vt ip&longs;um circa lapidem, qua&longs;i cir
ca quoddam centrum circumducat, quov&longs;que per
acto circutionis dimidio ita illum &longs;i&longs;tat, vt Terra iam
&longs;it è regione loci, in quo fuerit, & lapis ip&longs;am habeat
ad oppo&longs;itam partem: quæro quid-nam tunc lapidi
cuenturum &longs;it? Si perrecturum moueri dicas, igitur
à centro non modò Terræ, verùm etiam Mundi r
det. Si dicas mutaturum viam, & petiturum ip&longs;am Ter
ram; ergo &longs;entiet Mundum mutatum, eo modo, quo
ferrum magnetem &longs;ibi circumductum? Ergo per quan
dam vim tran&longs;mi&longs;&longs;am, cuius interuentu cum Mundo
communicet, &longs;icque in puro vacuo non &longs;it: quod e&longs;t
contra &longs;uppo&longs;itionem. Si demùm con&longs;titurum dicas;
ergo carebit grauitate, qua & de&longs;cendat per vacuum,
& æquabiliter de&longs;cendat. Prætereo heic, quæ ad hanc
fententiam qua&longs;i con&longs;equenter edi&longs;&longs;erüi, cùm ante
duos annos re&longs;cribens ad te, declararem tum grauita
tem non e&longs;&longs;e qualitatem quandam ip&longs;i lapidi inhæren
tem: tum motum illum primum, quo lapis à quiete
recedit, quique deinceps acceleratur, non ab huiu&longs;mo
di grauitate, &longs;ed ab ip&longs;a terræ attractione e&longs;&longs;e: tum
&longs;i deinceps talis motus æquabilis per&longs;eueraret, fore, vt
primo momento, quo intelligeretur fieri, &longs;uppo&longs;ito
e&longs;&longs;e vno horæ minuto, ex ijs quæ decima vocant: vt
(inquam) lapis, &longs;iue per vacuum, &longs;iue per plenum mo
ueretur, non caderet ex laqueari ad tabulatum (hoc e&longs;t
orgyis duabus) ne per annorum quidem quinquagies
centena millia, aliaque huiu&longs;modi. Addo heic &longs;olùm
grauitatem, quæ aliquid agat in primo momento,
motum inchoando lapidem adigit deor&longs;um, aut agere
etiam aliquid in &longs;ecundo, & con&longs;equentium quolibet,
aut nihil. Po&longs;terius non dices, quoniam &longs;eclu&longs;o pri
mo momento grauitatem faceres otio&longs;am, ac nullam,
& lapis conquie&longs;ceret, neque po&longs;&longs;es dicere, quam
obrem ip&longs;i vno momento, non quolibet alio, in quo At &longs;i
dicas prius; aut impetus prima actione, & qualibet con
&longs;equente impre&longs;&longs;us euane&longs;cit, aut manet. Si euane&longs;cit,
ergo debet pari ratione euane&longs;cere, qui &longs;ecundo mo
mento, & con&longs;equente quolibet ab aëre imprimitur;
neque enim potior e&longs;t ratio de vna cau&longs;&longs;a, quàm de
alia (imò neque vlla ratio de vtravis e&longs;t; cùm & dici
non valeat quid perire impetum faciat, &, &longs;i quid di
catur, probaturum &longs;it, quicquid vnico ictu à nobis per
cellitur, eo &longs;olo momento, quo percellitur, moueri, ne
que vel tan tillum per&longs;euerare po&longs;&longs;e in motu, tanquam
impetu illicò pereunte) quare & aëre nequicquam
pellente per&longs;euerabit nihilominus con&longs;titutus à te
æquabilis motus. Sin manet: ergo impetus primi mo
menti additusimpetui &longs;ecundi, & quilibet anteceden
tes additi con&longs;equentibus motum efficient celeriorem. Itaque motus à grauitate &longs;ola non &longs;ic elicietur, vt &longs;it
&longs;emper &longs;ui &longs;imilis, atque vniformis; neque grauitas
&longs;emper eadem, &longs;imili&longs;que &longs;ui, & inalterata (hoc e&longs;t, quæ
à me &longs;implex dicta e&longs;t, &longs;ine appellata adiectitia) per
&longs;euerabit.
nece&longs;&longs;ariò pro me, & pro veritate re&longs;cribenda putaui; tum
vt, &longs;i fieri pote&longs;t, eam tibi, quam ignotam acrius impugnas,
veritatem, maiore luce illu&longs;tratam aperiam: tum vt, ne &longs;al
tem apud eos, qui Respon&longs;ionem tuam vi&longs;uri &longs;unt, adeò de
formis, & ab&longs;urdus appaream, quàm me deformem, & ab-Equidem mihi planè per&longs;uadeo, non alio
animo id à te factum, quàm &longs;tudio veritatis; &longs;ed quia tamen
aliter factum e&longs;t, quàm intenderes, spero tibi non ingratu
fore, &longs;i quam quæ&longs;iisti, atque opta&longs;ti veritatem, eam tibi ab
errore vindicatam exhibeam.
Ego verò, Religio&longs;&longs;ime Vir, ita habeo me, vt
exi&longs;timem licere per tuam æquitatem, habere ip&longs;am
tui cau&longs;&longs;am, à veritatis cau&longs;&longs;a &longs;eiunctam. Nam te
quidem &longs;emper eo loco habeo, vt reputem virum non
modò pii&longs;&longs;imum, optimumque, & mei amanti&longs;&longs;i
mum: &longs;ed etiam periti&longs;&longs;imum, &longs;olerti&longs;&longs;imum, &longs;tudio
&longs;i&longs;&longs;imum veritatis. Veritatem autem eo loco habeo,
vt Eius amore, qui &longs;eip&longs;um e&longs;&longs;e Veritatem dixit, &longs;an
cti&longs;&longs;imum reputem, ip&longs;am, quantum agno&longs;citur, nulli
rei non præhabere, & à conditione per&longs;ona (aliunde
licet cari&longs;&longs;imæ, ac venerabili&longs;&longs;imæ, quæ eius po&longs;&longs;e&longs;&longs;io
nem &longs;ibi vendicet) qua&longs;i &longs;epo&longs;itam &longs;pectare. Ac
tu quidem nunquam volui&longs;ti, opinor, vt quia plurimi
tuam virtutem, amicitiamque facerem: eapropter, &longs;i
quidquam tibi videretur, qua&longs;i tabulas vnà ob&longs;igna
rem; & in tuam iurans &longs;ententiam, quicquid diceres,
indubium haberem; tuaque permotus authoritate, non
hærerem, quin veritas planè, prorsúmque à te &longs;taret. Quare iniurium haud-quaquam fuit, habere te vnum
ex iis viris doctis, qui quapiam in re falli po&longs;&longs;int, &
cùm habeant &longs;e homines, alienum non putent à &longs;e, vt
errare po&longs;&longs;e, &longs;ic po&longs;&longs;e ab aliis &longs;ecus &longs;entientibus mone
ri. Ego itaque, non quòd &longs;im profe&longs;&longs;us e&longs;&longs;e eum m
qui docere te veritatem aliquam po&longs;&longs;em, &longs;ed quòd te
veritatem &longs;equi tuâ doctrinâ non e&longs;&longs;em per&longs;ua&longs;us,
berem. Vnde non mirari, quod ais, non po&longs;&longs;um,
te deformem, atque ab&longs;urdum à me effictum:
&longs;emper incubui vt de re dicens quod |opinarer, de te
reuerenter &longs;entirem. Sed nimirùm ex eo, quòd ip&longs;e
cau&longs;&longs;am tuam non aliam e&longs;&longs;e, quàm veritatis exi&longs;times,
videris id, quod de re dixi, ita accepi&longs;&longs;e de te, vt ex eo,
quod po&longs;&longs;it opinio deformis, atque ab&longs;urda apparere,
ip&longs;emet deformis, & ab&longs;urdus appareas; ac illa attingi
non debeat, ne ip&longs;e quoque attingaris. Quanquam
&, quæ&longs;o, apud quo&longs;nam effingere te, qualem putas,
volui? Videlicet apud te &longs;olùm, ad quem res e&longs;t pri
uatim mi&longs;&longs;a, & per quem &longs;tetit, vt aut qua&longs;cumque
velles lituras duceres: aut quicquid id e&longs;&longs;et, &longs;upprimi
iuberes. Cùm neutrum volueris, &longs;ed potiùs rem
euulgandam cen&longs;ueris, confi&longs;us, quod ais,
dicijs ignotam mihi, impugnatamque, & maiore iam luce
illu&longs;tratam veritatem aperire:
catam exhiberes:
reluctante con&longs;cientia, mancipiique more a&longs;&longs;entari,
applauderéque, annuendo e&longs;&longs;e mihi apertam, exhibi
tamque veritatem, quam nullam planè per&longs;picerem.
ratiore experientia globorum decidentium momenta expen
dens, nouam veritati lucem attuli&longs;ti: &longs;pem enim magnam in
de feci&longs;ti, futurum breui, vt huius lucis beneficio quæ&longs;itam
hactenus veritatem certiùs inueniamus: quam ego &longs;emper
vbicumque inuentam pari plau&longs;u excipiam, ead&ecedil;mque &longs;ua
uitate amplexabor.
Quæ&longs;o te verò, optime Vir, quomodò putes i&longs;ta
cum iis, quæ mox dixi&longs;ti, cohærere? Nam &longs;i ego qui
dem meâ experientiâ nouam veritati lucem attuli, quî
ergo tu mihi veritatem ignotam, ac maiori luce il
lu&longs;tratam aperui&longs;ti? An tuâ illâ experientiâ, cui mea
fuit oppo&longs;ita? At &longs;i mea quidem veritati lucem, tua
ip&longs;i tenebras fecit. An adhibito à te ratiocinio?
At cùm
id non fuerit aliunde, quàm ex iis tenebris deductum;
quomodo rem mihi aperuit, quæ coram allata à me
luce euanuit? Spem factam ais, vt huius lucis à me al
latæ beneficio veritatem quæ&longs;itam certiùs inueniamus. Et quomodo ergo tu &longs;ic eam habui&longs;ti, vt à me quæ&longs;i
tam mihi ab errore vindicatam iam exhibueris? An
forte, quia iuxta lucem à me allatam es ratiocinatus? Non &longs;anè: quin potiùs con&longs;titi&longs;ti &longs;emper in illis ii&longs;dem
tenebris, hoc e&longs;t hæ&longs;i&longs;ti &longs;emper principiis ex tua illa
fal&longs;a Experientia ductis. Ac laudabili&longs;&longs;imum quidem,
quod profiteris te veritatem, vbicumque inuenta fue
rit, perquàm grate, & cum plau&longs;u, &longs;uauitateque ample
xaturum: &longs;ed cùm &longs;it quidem quæ&longs;tio de ea, quam
profiteris &longs;imul te mihi aperui&longs;&longs;e, exhibui&longs;&longs;eque: quo
modo, amabò, vis i&longs;ta excipiam?
in illis deceptus es, quàm au&longs;picatò tibi, ac fœliciter illud
ceßit.
Ip&longs;e verò hebetem me neque ne&longs;cio, neque diffi
teor; at magno tamen de&longs;iderio acutè videndi non
careo. Vnde & cùm in cæteris rebus non &longs;im aliunde
ratiocinatus, quàm iuxta eam lucem, quæ per factam à
me experientiam allata e&longs;t, vellem o&longs;tenderes quid
ais, peruellem apertam deceptionem faceres, & aut fal
&longs;itatem principij, aut incohærentiam con&longs;equutionis
manife&longs;tares. Nam &longs;i mihi quidem id Experimentum,
de quo loqueris, au&longs;picatò, ac fœliciter ce&longs;&longs;it; non vi
deo huc v&longs;que quid-nam fuerit illi aut à me
aut à te con&longs;entaneum admi&longs;&longs;um.
incertis &longs;atis diù multumque ver&longs;atus fuerim, vnus tamen ha
ctenus inuentus es, qui meis in a&longs;&longs;ertionibus, ac decretis pu
gnam, contrarietatémque non dicam inuenerit, &longs;ed aliquando
etiam obiecerit: vt mirum tibi videri non debeat, &longs;i rei noui
tate percul&longs;us, ea, quæ à me in re apertiore decreta, & con&longs;ti
tuta &longs;unt, à tam fœda di&longs;&longs;en&longs;ione vindicanda putauerim.
At no&longs;ti certè me eum non e&longs;&longs;e, qui vltrò me a&longs;&longs;er
tionibus, decreti&longs;que tuis immi&longs;cuerim. Non eram ea
fœlicitate, vt vel te no&longs;&longs;em, vel nomen meum e&longs;&longs;e tibi
notum putarem, cùm ea fuit humanitas tua, vt me
prior interpellâris, & tum ea improbaueris, quæ con
&longs;cripta e&longs;&longs;ent à me: tum non modò priuatim, &longs;ed pu
blicè etiam te&longs;tatus dolorem, ob fidem à me principiis
fal&longs;is, erronei&longs;que adhibitam, tua vt certiora &longs;ub&longs;titue
ris,
&longs;en&longs;um. Neque id modò; verùm etiam con&longs;titui&longs;ti me
publicè eorum arbitrum, iudicemque: ac prouoca&longs;ti
adeò, vt quid videretur de ip&longs;is e&longs;&longs;e &longs;entiendum, &longs;igni
ficarem. Vtinam verò ip&longs;e me non ita &longs;ponte &longs;ollici
ta&longs;&longs;es; longi&longs;&longs;imè enim abfui&longs;&longs;em, ab omni tuorum
a&longs;&longs;ertorum, decretorumque inqui&longs;itione. Quippe
&longs;atis con&longs;cius, quàm-multa reprchendi in me valeant,
exi&longs;timans, vt qui&longs;que &longs;uo &longs;en&longs;u &longs;apiat, in eo &longs;olùm
&longs;um, vt &longs;i roger, quid &longs;entiam aliqua de re, illud ex
plicem bona fide. Vtinam &longs;altem incidi&longs;&longs;es in al
quo is haberi potui&longs;&longs;es, Qui gloriaretur &longs;e in hac tanta
& ob&longs;curitate naturæ, & imbecillitate humani ingenij,
habere decreta, atque a&longs;&longs;ertiones; nec duceret e&longs;&longs;e
abunde, &longs;i qua&longs;piam veri&longs;imiles coniecturas nanci&longs;
ceretur Qui con&longs;onantiæ decretorum, a&longs;&longs;ertionumque
&longs;ic foret certus, vt &longs;i à quopiam ob&longs;eruaretur, aut obii
ceretur pugna, contrarieta&longs;ve aliqua; tum qua&longs;i ad
rem in&longs;olentem &longs;tupore quodam percelleretur: Qui &longs;ic
videretur &longs;ibi comparatus, vt non quandoque dormi
tar
per&longs;picax, vt nihil rerum cum decretis &longs;eu cohæren
tium, &longs;eu repugnantium latere mentem vn quam po&longs;&longs;et:
Qui veluti &longs;tomachabundus notaret illum, à quo pri
mo interturbata fœlicitas eiu&longs;ce de &longs;e opinionis foret,
ac labor creatus mon&longs;trandi con&longs;tantem &longs;ui cum &longs;e ip
&longs;o con&longs;en&longs;um. Me quod attinet, tale nihil vnquam
&longs;entire aut potui, aut volui de re; ip&longs;e præ&longs;ertim &longs;atius
ducens viuere, quod aiunt, in diem, ac po&longs;&longs;e, &longs;i quid
manè &longs;en&longs;i, ip&longs;o ve&longs;pere recantare. Ac non requiro
quidem, quæ &longs;int illa ob&longs;curiora, magi&longs;que incerta, in
quibus ais tua decreta tantam tueri con&longs;tantiam; quan
dò videor tibi ne in huius quidem longè clarioris,
certiori&longs;que de Motu controuer&longs;iæ ingre&longs;&longs;us penetra
lia; te&longs;tor tamen me longè e&longs;&longs;e, vt in illa vnquam in
quiram, qui etiam, i&longs;ta quod attinet, &longs;i forte præmo
nui&longs;&longs;es me, quid rei tibi cordi foret, non adulatus
neque quicquam re&longs;crip &longs;i&longs;&longs;em, ne videri po&longs;&longs;em quam
tu heic appellas fœdam di&longs;&longs;en&longs;ionem (qua&longs;i diceres
Camarinam) mouere.
aut pro veritate inter nos pugna, & contentio interce&longs;&longs;erit,
&longs;umma tamen, vt spero, per&longs;euerabit &longs;emper animorum
con&longs;en&longs;io, nec minùs vnquam futurus &longs;um Tuus ad omnia
PETRVS CAZRÆVS.
M. DC. XLV.
Ego verò &longs;anctè affirmo, nihil me vnquam remi&longs;
&longs;urum neque de &longs;umma veneratione, qua te pro&longs;e
quor, neque de &longs;incero affectu, quo toto ex corde &longs;um
Tuus. Vale.
Pari&longs;ijs, Non. Maij, M. DC. XLV.
EPISTOLA TERTIA,
QVAM, TAMETSI TEMPORE
primam, vi&longs;um e&longs;t tamen po&longs;t-ponere, quòd
præter argumentum cum &longs;uperioribus com
mune, contineat etiam explicationem plu
rium aliarum difficultatum, quæ fuerant in
Epi&longs;tolas,
lato,
& Religiv&longs;ißimo, Doctißimóque Viro,
PETRO CAZRÆO,
EXIMIA profectò humanitas tua, vt im
perâris tibi patientiam percurrendi, co
gno&longs;cendique quicquid illud fuit mearum
ineptiarum; méque &longs;imul adeò &longs;olerti, ele
gantique di&longs;qui&longs;itione cohone&longs;tandum cen&longs;ueris. Et
dies quidem &longs;unt aliquot, ex quo illam cum literis no-
&longs;ed vix iam demùm ruente men&longs;e aggredior quid
piam re&longs;cribere; quòd nunc &longs;olùm inualetudo, quæ me
per dies complurcis habuit, vacare &longs;criptioni non-nihil
permittat. Te&longs;tatus &longs;um nuper reuerendis illis, opti
mi&longs;que Patribus Furnerio, & Burdino, cùm dignati
fui&longs;&longs;ent inui&longs;ere me, & &longs;uaui&longs;&longs;ima de tua virtute inci
di&longs;&longs;etmentio, quantum ægrè ferrem non licere mihi
aliquid &longs;tatim reponere: nempe tu magis me deuinxi
&longs;ti, quàm vt omninò po&longs;&longs;im, aut debeam videri tacen
do ingratus. Quare & nunc occupationes, quibus
aliunde incumbentibus vrgeri me &longs;entio, &longs;epono, ni
hilique earum detrimentum habeo; &longs;imodò i&longs;to erga
te merito officio defungar. Cogito porrò aliquid cir
ca &longs;ingula capita
&longs;atis gratam habui&longs;&longs;e, aut obiter &longs;olùm legi&longs;&longs;e eam vi
dear: tum vt rationem reddere, quam depo&longs;cere vi&longs;us
es, di&longs;tinctiorem &longs;imul, & pleniorem po&longs;&longs;im.
& Neutram duarum virium à Motore tran&longs;lato
impre&longs;&longs;arum imminui ab alterutra.
II.
Cùm tu igitur duas illas
tran&longs;lato
men; po&longs;tquàm exhibui&longs;ti in&longs;ignia &longs;ingularis bene
uolentiæ, & comitatis te&longs;timonia: tum explicare ag
gre&longs;&longs;us es, quæ improba&longs;ti circa Priorem. Imprimis
verò, quòd comprobârim illud Galilei decretum,
tate impares,
adduxi&longs;&longs;em, per&longs;pecturum fui&longs;&longs;e & fal&longs;um, & Paralogi&longs;mo
euidente confirmatum. Ego verò neque inficior hallu
cinari potui&longs;&longs;e me; neque me habeo adeò &longs;olertem, vt
Paralogi&longs;mum à te in&longs;inuatum etiamnùm pervideam. Peruelle proinde ip&longs;um o&longs;tendi&longs;&longs;es, atque adeò &longs;ubin
dica&longs;&longs;es, qua ergo alia proportione accelerationem de
cidentium fieri, aut experiundo notaueris, aut deduxe
ris demon&longs;trando. Certè non &longs;atis intelligo quam
obrem cen&longs;ueris,
referre ad meum in&longs;titutum:
quæ &longs;uppo&longs;ita à me e&longs;t, fru&longs;trà e&longs;t tota ratiocinatio. Quod ad experientiam porrò attinet, ob&longs;eruationes à
Galileo recitatas prætereo: ad meas quod &longs;pectat, quot
quot mihi licuit, & quantum licuit peragere, illam pro
portionem &longs;emper exhibuerunt. Poti&longs;&longs;imæ fuere, cùm
rem præ&longs;titi, adnotatis &longs;patiis, tam in prolixiore &longs;ex
decim orgyis pariete, quàm in tubo vitreo inclinato
prolixiore duabus; ac &longs;ociis &longs;imul adhibitis, quorum
&longs;inguli ad &longs;ingula &longs;patia, eorumque notas attenderent,
vt tam decidente globo
bente per tubum, dicere po&longs;&longs;ent, ecquo momento ex
numeratis (& alta voce pronunciatis) æqualibus, glo
bus pertran&longs;iret vnamquamque notam. Nempe ex
inde con&longs;titit, quale &longs;patium fui&longs;&longs;et primo momento
&longs;uperatum vnum, talia deinceps &longs;uperata fui&longs;&longs;e &longs;ecundo
momento tria, tertio quinque, quarto &longs;eptem: adeò vt
illa aggregando reperirentur &longs;uperata in fine primi
momenti vnum, in fine &longs;ecundi quatuor, in fine tertij
&longs;patiorum &longs;e vt temporum quadrata haberent. Quod
ad rationem; quia nondum per&longs;pexi, quem ip&longs;e te ais
per&longs;pexi&longs;&longs;e Paralogi&longs;mum: ideo
quou&longs;que eximias lucubrationes vulgaueris, quas pol
liceris aduer&longs;us ea, quæ à Galileo de Motu edi&longs;&longs;eruntur
Dialogo tertio.
III. Deinde, cùm ip&longs;e elicio,
&longs;ur&longs;um, non modò non de&longs;trui, &longs;ed ne vlla quidem ratione im
minui à vi impellente in latus,
fidem apud harum rerum peritos, apud quos receptum e&longs;t, Mo
bile quodcumque duobus motibus in diuer&longs;as partes actum,
tantò &longs;egniùs deferri in vnum terminum, quantò fortiùs is
alterum tendit. Ego verò, cui cordi e&longs;t, non tam peri
tis quid per&longs;uadere, quàm addi&longs;cere ab ijs aliquid; id
expeto &longs;olùm, vt per&longs;picuè doceant, quod po&longs;&longs;im ca
pere per&longs;picuè. Et, quod &longs;pectat quidem ad tuum
Effatum, &longs;i dum Mobile reipsâ mouetur, di&longs;iunctum
que e&longs;t à motore, veluti lapis per aërem, &longs;uperueniat
vis aliqua, vt venti, aut manus, quæ ip&longs;um deflectat:
agno&longs;co eo ca&longs;u vim primò impre&longs;&longs;am imminutum iri,
& mobile, ad quem terminum de&longs;tinabatur, non per
uenturum. At &longs;i noui nihil interueniat ab ip&longs;o v&longs;que
proiectore, in quo & visip&longs;ius propria, & vis corporis
ip&longs;um transferentis in vnam coierint: non video quî
debeat recipi Effatum; cùm mobile non tam agatur
duabus viribus, quarum vna alteri ob&longs;tet, quàm vnâ,
eáque &longs;ic compo&longs;itâ, vt ad vnicum terminum, &longs;cilicet
obliquum, contendat. Neque enim manus, dum à
naui transfertur, lapidem reuerâ &longs;ur&longs;um proiicit (vt-
proiicit reuerà obliquè, quatenus & ip&longs;a obliquè mo
uetur, dum agi &longs;ur&longs;um creditur, deflexa putà à motu
nauis. Et quia proinde vis propria manus, & tran&longs;la
titia nauis &longs;ibi non repugnant, &longs;ed &longs;e&longs;e veluti inten
dunt, vnam que totalem, fortioremque, quàm &longs;i &longs;igilla
tim e&longs;&longs;ent, con&longs;tituunt: heinc fieri videtur, vt &longs;e &longs;e non
de&longs;truant, &longs;ed vna euadant, quæ tantum &longs;it alterutrâ
fortior, quantum altera fortis e&longs;t. Quare & cùm lapis
non tendat directè &longs;ur&longs;um, vt &longs;i à &longs;ola manu proiicere
tur: neque directe &longs;ecundùm horizontem, vt &longs;i vehere
tur, agereturve à &longs;olanaui; verùm feratur motu mi&longs;to,
obliquóve, & de&longs;cribat per aërem, qua&longs;i arcum (&longs;iue
potiùs lineam, quam dicunt parabolicam) cuius chorda,
&longs;eu ba&longs;is &longs;ecundum horizontem e&longs;&longs;e intelligatur; & &longs;a
gitta, &longs;eu axis &longs;ecundum perpendiculum (prout medium
e&longs;t inter a&longs;cen&longs;um, & de&longs;cen&longs;um) Exinde e&longs;t, cur lapis
neque minùs altùm, quàm &longs;i à &longs;ola manu proiiceretur,
perueniat: neque minus ptorsùm, quàm &longs;i à &longs;ola agere
tur naui, quatenus prolixitas lineæ e&longs;t quidem maior,
quàm &longs;implex a&longs;cen&longs;us, de&longs;cen&longs;u&longs;que ad perpendicu
lum; &longs;ed ad hoc vim &longs;uppletimpre&longs;&longs;io à naui: & pro
lixior quoque, quàm &longs;implex &longs;ecundum horizontem
progre&longs;&longs;io; &longs;ed ad hoc vim &longs;upplet impre&longs;&longs;io à manu. Idem verò dicendum e&longs;t de &longs;emi parabolica linea: vt
dum lapis è carche&longs;io non proiectus, &longs;ed dimi&longs;&longs;us, ad
pternam perinde cadit, vt &longs;i nauis quie&longs;ceret: &longs;iqui
dem ip&longs;i grauitati lapidem adacturæ &longs;ecundùm perpen
diculum, accedit vis nauis, qua manus dimittens inte
rim transfertur, quæque tantumdem impetus addit,
quàm perpendiculi, maiorem. Heinc mirabilis quidem
e&longs;t ea, quam obiicis,
etiam, aut centuplò contractiorum, apertiorumque æqui tem
poranea de&longs;criptio:
minore, & maiore vi, quæ alteri, vt per axem, perpendi
culumve duntaxat acturæ, &longs;uperadditur. Et
quidem ratio,
tran&longs;mitteretur ad eandem altitudinem, aut di&longs;tantiam in pro
iectoris quiete, aut motu, eodem tempore. &longs;i foret ab eadem vis
&longs;ed con&longs;tat vim non e&longs;&longs;e eandem, quatenus proiectoro
moto e&longs;t tantumdem adauctior, quanta e&longs;t ip&longs;a vis
tranferentis. Ad illud quod habes de
&longs;i illud quidem vniforme &longs;it, nihil videtur prorsùs ob
&longs;tare, quatenus tantum proiicienti, transferentique,
quantum proiectili re&longs;i&longs;tit, pergitve potiùs re&longs;i&longs;tere:
quod idem dicendum de vento, &longs;i &longs;ecundùm eundem
nauis cur&longs;um, & æquabilisfuerit: &longs;in verò aut medium
inæquabile &longs;it, aut ventus obliquus, vel variabilis, at
que ade ò &longs;it inæquabilis re&longs;i&longs;tentia; tunc videtur pro
fectò po&longs;&longs;e non-nihil de&longs;ci&longs;cere à parabolico &longs;uo cur&longs;u,
& à termino, in quem contendebat: &longs;ed nempe hic ip&longs;e
e&longs;t ca&longs;us, de &longs;uperueniente vi, ob quam dixi po&longs;&longs;e Effa
tum admitti.
IV.
Quòd
primis e&longs;t, quod vel tuo iu&longs;&longs;u peragi ab Equite pote&longs;t. Si is enim pluribus lapillis ad manum a&longs;&longs;umptis, &
manu ita proten&longs;a, vt &longs;it in perpendiculo, quod pedem
proximè præter-radat, lapillum vnum primò dïmittat
quie&longs;cente equo; tum alium equo pedetentim, & pa&longs;&longs;u
ac po&longs;teà alium moderatè currente; denique & alium
præteruolante tum ocyùs, tum ocy&longs;&longs;imè: eueniet &longs;anè,
vt lapilli omnes præter-radant &longs;emper eandem pedis
partem, omne&longs;que appareant ip&longs;i equiti ad perpendi
culum cadere: & quia tamen omnes eiu&longs;modi ca&longs;us,
præter illum, qui qua&longs;i axis equo quie&longs;cente factus fue
rit, &longs;emiparabolicæ erunt lineæ, eæque &longs;emper tantò
apertiores, quantò tran&longs;latio fuerit velocior: fiet, vt &longs;i
ip&longs;e è regione fueris, illa&longs;que adnotaueris, de&longs;ideraturus
non &longs;is luculentiora Poteris verò ip&longs;e quo
que &longs;imile quidpiam experiri, &longs;i pilam manu &longs;u&longs;tentâ
ris, ac dimi&longs;eris, dum per aulam, aut pergulam nunc len
to pa&longs;&longs;u, nunc concitato, nunc etiam currendo incedes. Nam vt pila tibi &longs;emper apparebit ad perpendiculum
cadere: ita agno&longs;ces ab ea de&longs;cribi &longs;emiparabolen nunc
contractam, nunc apertam, nunc apertiorem. Quod
con&longs;equenter verò depo&longs;cis
& &longs;ecundum mali nunc quie&longs;centis, nunc moti longitudinem
areu-bali&longs;ta emi&longs;&longs;o:
fimus recipiam me, cum fauente Numine in Prouin
ciam rediero, & ad mare acce&longs;&longs;ero, rem in tui gratiam
præ&longs;titurum. Intereà verò res probari vel tuo iu&longs;&longs;u
poterit, &longs;i qui&longs;piam è curru prope parietem quie&longs;cente,
& arcu-bali&longs;tâ lateri currus illigatâ emittat &longs;ur&longs;um glo
bulum; ac deinde curru præter eundem parietem, quan
tacumque voles pernicitate abrepto, globulum iterum
emittat, & &longs;it alius quis è regione, qui vtroque ca&longs;u
adnotet altitudinem, ad quam v&longs;que globulus pertin
get. Spondere enim au&longs;im haud inæqualem altitu-
multa experimenta haud ab&longs;imilia. Dico autem arcu
bali&longs;tam e&longs;&longs;e debere illigatam; quoniam &longs;i manu con
tineatur, poterit linea directionis aut perpendicularis
non e&longs;&longs;e, aut &longs;i à perpendiculari deflexerit, non per
inde vno, atque alio ca&longs;u deflecti: ob quam eandem
cau&longs;&longs;am agi currus debet per complanati&longs;&longs;imum lo
cum; ne, &longs;i &longs;ub&longs;ultârit, linea illa nutet. Prætereo au
tem, &longs;i tot illis, quæ conge&longs;&longs;i, experimentis quæ&longs;itam
fidem aliquam putes primatio illi Theoremati,
corpus, cui innitimur, transferatur, motus omneis no&longs;tros, re
rumque à nobis mobilium perinde fieri, appareréque, ac &longs;i il
lud quie&longs;ceret:
nem, &longs;eu moueatur, &longs;eu quie&longs;cat motor, qui id emi&longs;erit pari
vi;
ri modo haud apparerent. Quanquam & Paradoxum
dicis ob id &longs;olùm, quòd res prima fronte adeò admi
rabilis &longs;it, vt ni&longs;i quis expertus fuerit, fidem facilè ha
bere non po&longs;&longs;it. Quòd denique tibi hæret &longs;crupulus
ram, & in eam directe emi&longs;&longs;us, parem percußionis effectum
&longs;ortiri po&longs;&longs;e non videatur,
experimento e&longs;t Quan quam ego quidem, vt
fatear, &longs;atis hucu&longs;que fœlix non fui, vt rem pi&longs;toleto,
mo&longs;quetóque explorare volens, ob&longs;eruare potuerim
ca&longs;um (adeò pernix efficitur recidentis prope terram
motus: adeó que difficile e&longs;t declinationem tantulam
à perpendiculo cauere, quæ in altitudine tanta para
bolen creet cum di&longs;tentione crurum in&longs;igni, & ver&longs;us
ip&longs;am locus ca&longs;us inquiratur; ne etiam cau&longs;er ventum,
agitationemve &longs;uperioris aëris) ac fortè etiam Gali
leus eatenus hæ&longs;it hac de re; quatenus ip&longs;e paris fuit
inter experiundum infœlicitatis.
malis ince&longs;&longs;um præ &longs;altatione, & globi volutionem
præ adactione, dici naturalem.
V.
Seligis con&longs;equenter nonnulla, quæ dicis
nimia facilitate admittere, quæque viris eruditis, ac pijs minùs
placitura videantur. Quo &longs;anè loco, &longs;i aliquid ex ijs, quæ
admitto, pietati repugnet, id prorsùs deuoueo; vt
quod imprudenti, neque repugnantiam intelligenti
&longs;e&longs;e obtrudat; agno&longs;cóque te &longs;ummopere lenem, dum
quid dicis: quanquam quid tale hactenus, mihi acci
derit, non peruideo. Ad cætera, quæ merè &longs;ùnt na
turalia, quod attinet; non nego quidem ea me phi
lo&longs;ophari libertate, vt non vni alicui Sectæ erudito
rum, vt vocas, hære&longs;cam: &longs;ed &longs;i quid alij aut dicant,
aut dicere po&longs;&longs;e videantur, quod magis probabile &longs;it,
id veluti magis probabile &longs;equar: at quoniam &longs;olo
veritatis amore ita comparor, non e&longs;t, cur verear,
quid nimis. Neque verò is &longs;um, qui Platonis, Ari&longs;tote
li&longs;que (aut &longs;i quos putas e&longs;&longs;e illis eruditiores) &longs;annis
mouear: ac præ&longs;ertim, cùm ip&longs;i me voce, factóque do
cuerint,
tiquius. Non &longs;anè, quòd ego proptereà &longs;equi me
&longs;itear: &longs;ed quòd omnibus exploratis, & &longs;equutus id,
quod &longs;imilitudinem maiorem cum ip&longs;a habere mihi
vi&longs;um e&longs;t, tum videar mihi cumulatè eo defunctus of
ficio, quod exigit ip&longs;a eius reuerentia. Ex quo pro
inde &longs;it, vt &longs;i illi quidem, quos eruditos intelligis, ip
&longs;am veritatem facerent apertam, nemo me citiùs non
pedibus modò, &longs;ed manibus quoque, & corpore toto
iret, prorueretque in eorum &longs;ententiam: verùm quia
dum &longs;uis inhærent principiis, nihilo nobis veritatem
reuclatiorem faciunt: quid di&longs;pliceat, &longs;i à me aliæ, at
que aliæ pul&longs;entur fores? Aut nunquam enim veritas
(intelligo veram, proximamque cau&longs;&longs;am operum na
turæ cuiuis occurrentium) innote&longs;cet hominibus, quod
mihi penè per&longs;ua&longs;um e&longs;t; aut non vna e&longs;t via ad eius
rece&longs;&longs;um hactenus incompertum, tentanda. Quod
ad me &longs;pectat, agno&longs;co &longs;atis nihil aliud me, quàm
balbutire; longéque ab&longs;um, vt ex meis nugis
aliquam aut quæram, aut &longs;perem; tuque es nimis bo
nus, dum &longs;upponis me aliquam adeptum, qui nullam
promereor. Non &longs;um verò tamen ita &longs;crupulo&longs;us,
quin exigentibus amicis, propalatas aliquas faciam; ac
eo fine poti&longs;&longs;imùm, vt eruditos excitem, ad quidpiam
melius commini&longs;cendum.
VI.
Improbas primùm quod dixerim,
animalis præ &longs;altatione naturalem:
tum opinor, litigare de nomine. Vides me circa mo
tus rerum concretarum &longs;ic di&longs;tinxi&longs;&longs;e, vt reputârim
quemlibet motum aliqua ratione e&longs;&longs;e naturalem, ali
qua ratione violentum: ac id proinde nec de Ince&longs;&longs;u,
po&longs;teà aduertere quandam in Ince&longs;&longs;u violentiam ex
la&longs;&longs;itudine demon&longs;traram. Vides aliunde me illeic
loci nihil aliud requirere, quàm commodam quan
dam v&longs;urpationem nominum, qua &longs;i quis aliam attu
lerit commodiorem, &longs;im complexurus. Et quia is mo
tus mihi e&longs;t vi&longs;us dici po&longs;&longs;e
aut &longs;ine repugnantia; is
aut cum aliqua repugnantia: heinc e&longs;t, cur
turalem
tionem violentam,Non quod Ince&longs;&longs;us quoque non fiat cum repugnantia
aliqua, propter ip&longs;um pondus membrorum: aut Salta
tio non fiat &longs;ponte, &longs;iue ab eodem principio interno,
hoc e&longs;t anima: &longs;ed quòd neque Ince&longs;&longs;us fiat cum &longs;en&longs;i
bili adeò repugnantia, tantoque connixu ad eam &longs;u
perandam, vt Saltatio; neque Saltatio &longs;it perinde &longs;pon
tanea, incogitatáque, ac ip&longs;e Ince&longs;&longs;us; vt proinde cum
vterque motus aliqua ratione naturalis &longs;it, aliqua ra
tione violentus; Ince&longs;&longs;us tamen magis naturalis &longs;it, &
Saltatio magis violenta; cùm & id probetur ex eo,
quòd Ince&longs;&longs;us &longs;it incomparabiliter æquabilior, durabi
lior, minu&longs;que fatigans, quàm ip&longs;a Saltatio. Neque
verò &longs;i ad eos ip&longs;os, quos tu in&longs;inüas, eruditos prouo
care lubuerit, non potero memet tueri Principis eo
rum authoritate, qui etiam in ijs, quæ à &longs;e mouentur,
cuiu&longs;modi &longs;unt animalia, motus alios
alios
tionum, modorumque, fieri agno&longs;cit. Quod autem
concludis
violentum:
quæ dixi, cen&longs;ere &longs;um vi&longs;us; tamet&longs;i cen&longs;ens illum præ
i&longs;to e&longs;&longs;e maximè naturalem, i&longs;tum præ illo maximè
violentum, dixi videri illum mihi cen&longs;eri po&longs;&longs;e natu
ralem, i&longs;tum cen&longs;eri po&longs;&longs;e violentum, vtrumque nem
pe
VII.
Idem porrò dicendum e&longs;t circa id, quod miraris Neque enim dixi il
lam e&longs;&longs;e ab&longs;olutè naturalem, qua&longs;i nullo modo ab alio
&longs;it: &longs;ed &longs;olùm comparatione motus, quo globus per
aërem tran&longs;adigitur, quique &longs;it præ&longs;ertim dicendus
violentus. Scilicet globus, quà globus e&longs;t, &longs;eu ex figuræ
&longs;uæ natura, ad volutionem e&longs;t comparatus, imò com
parati&longs;&longs;imus; volutionem, inquam, quæ peragitur non
modò in loco, &longs;eu &longs;upra axem &longs;u&longs;tentantem, vt Ari&longs;to
teles admittit: &longs;ed maximè etiam per locum, &longs;eu &longs;u
pra planum horizontale, quod & &longs;u&longs;tentat, & nihil
re&longs;i&longs;tit; cùm aliunde tamen ex eodem Ari&longs;totele, nul
lum &longs;it corpus globo ineptius ad motum Heinc proinde &longs;it, vt de globo &longs;upra planum con&longs;titu
to liceat dicere, illum ad motum &longs;upra planum, &longs;eu ad
volutionem ita propendere, vt minimo pul&longs;u, ac ve
luti nutu talem motum &longs;ubeat, ip&longs;oque ita afficiatur,
vt depo&longs;iturus illum nunquam &longs;it, ni&longs;i planum defece
rit, aut facta aliunde fuerit re&longs;i&longs;tentia. Ni&longs;i verò ille
motus non e&longs;t dicendus maximè &longs;ecundum mobilis
naturam, qui &longs;emel inditus, &longs;it ex &longs;e perpetuus, ac præ
tereà æquabilis, vniu&longs;que tenoris?
natura effectiuè procedat. Sed quid-ni ille quoque di
catur, qui ab externo e&longs;t, effectiuéque ab alio e&longs;t; &longs;i mo
dò
rò contra illam &longs;it; & qua&longs;i fiat, quod dicitur,
o)t
fateris cum Ari&longs;totele motum rerum grauium e&longs;&longs;e na
turalem, quem ille tamen vult ab externo, non ab in
terno e&longs;&longs;e principio? Et nonne proinde eius verba
&longs;unt,
dem naturâ, alia verò prater naturam moueri?
uerti quidem, imò expre&longs;sè dixi,
&longs;um tendere, alias &longs;ur&longs;um:
cere cen&longs;ui ad æquabilitatem motus; vt dum globus
non ampliùs &longs;ur&longs;um, quàm deorsùm, nec deorsùm,
quàm &longs;ursùm fertur, motusinterim ab&longs;que vlla aut ac
celeratione, aut retardatione per&longs;eueret. Quod inter
&longs;eris verò
con&longs;equenter fuerit,
formis, &longs;eu naturis;
nam incommodi &longs;it: cùm & graues Doctores &longs;int, qui
motrices illas Ari&longs;totelis Intelligentias re&longs;puant; &
Ari&longs;toteles ip&longs;e, non modò fateatur moueri cælum à
&longs;eip&longs;o, &longs;cilicet tanquam
adeò habens in &longs;e motus &longs;ui principium: &longs;ed etiam
contendat Separatam &longs;ub&longs;tantiam non mouere cælum
vt Efficientem, &longs;ed vt Finem, ac
tur,
mouere. Atque id quidem, vt præteream, commodius
tuo globi &longs;upra planum ex facto &longs;emel vno impul&longs;u,
a&longs;&longs;erat quis cælum continuò, æquabiliterque moueri,
quia in &longs;ui à Deo creatione eam impul&longs;ionem acce
perit, qua cœptus tunc motus etiam-num perduret.
vt incipit, ita pergeret: & Non &longs;olùm accelerationem,
&longs;ed ip&longs;um quoque initium motus e&longs;&longs;e à principio
externo.
VIII.
Dicis po&longs;teà,
dant accelerationem e&longs;&longs;e violentam, &longs;i illam, vt quid &longs;uper
ueniens, mente &longs;ecernamus ab ip&longs;o de&longs;cen&longs;u. Non e&longs;t porrò
cur dubites, quin ip&longs;e quoque mente &longs;ecernam motum
illum &longs;implicem, quo lapis fertur deor&longs;um, quemque
tu de&longs;cen&longs;um appellas, ab omnibus, qui &longs;uperueniunt,
giadibus accelerationis. Quippe id abunde expre&longs;&longs;i,
cùm dixi
bilem, &longs;ed imperceptibilem tamen, ob incredibilem &longs;egnitiem.
Non e&longs;t proinde etiam, cur hæreas, quin illum e&longs;&longs;e na
turalem, & &longs;ine reluctatione agno&longs;cam; quippe qui
eum faciam, quantum e&longs;t ex &longs;e, æquabilem, perpetuum,
ac talem, qui &longs;it imprimendus etiam lapidi ex&longs;i&longs;tenti
in vacuo, vbi mobile nullam habet ad motum repu
gnantiam, quocumque ver&longs;um tandem agatur: verum
quòd eiu&longs;modi motus cen&longs;eri naturalis po&longs;&longs;it, non id
circò cen&longs;eo ca&longs;um lapidis habendum e&longs;&longs;e naturalem. Quoniam tamet&longs;i talis motus in hoc ca&longs;u interueniat,
euane&longs;cit tamen, &longs;iue nullus e&longs;t, re&longs;pectu accelerationis,
& quam ip&longs;e quoque fateris violentam. Atque vt per&longs;
picuè appareat cuius momenti &longs;it ille motus, &longs;iue, vt
tu vocas, de&longs;cen&longs;us, ab acceleratione &longs;ecretus, & cum
ip&longs;a tamen comparatus; age Experiamur, &, exempli
gratiâ, altitudin m accipiamus non immanem
&longs;ed qualem &longs;olùm vulgò v&longs;urpant inter tabulatum, &
laquear, duarum videlicet orgyiarum. Huiu&longs;modi e&longs;t
altitudo, quam lapis decidens peruadit vno minuto
horæ &longs;ecundo. Cùm acceleratio verò &longs;it intra hoc
tempus, & à primo v&longs;que momento continua, intelli
gamus id tempus diuidi in tertia, quarta, quinta, &
porrò ad v&longs;que horæ decima; vt licet vnum decimum
&longs;ubdiuidi vlteriùs po&longs;&longs;it in vndecima, duodecima, &, vt
volunt, in infinitum, in decimo tamen vno con&longs;i&longs;ta
mus, tanquam minimo temporis, &longs;eu primo momen
to, quo lapis ita decidit, decidereve incipit, vt à &longs;tatim
&longs;uperuentura acceleratione &longs;it liber. Erunt proin
de in vno minuto horæ &longs;ecundo minuta decima
167961600000000. Quoniam autem lapistotis i&longs;tis
decimis &longs;ucce&longs;&longs;iue fluentibus percurrit &longs;ucce&longs;&longs;iuè &longs;pa
tium duarum orgyiarum, illiu&longs;ve particulas; ideò cùm
iuxta memoratam, ob&longs;eruatamque proportionem, &longs;pa
tia &longs;int inter&longs;e vt quadrata temporum, intelligi opor
tebit di&longs;tingui &longs;patij particulas 3821109907456
0000000000000000. Exinde verò &longs;ict, vt cùm pri
mo momento lapis non percurrat ni&longs;i vnam huiu&longs;mo
di particularum, nece&longs;&longs;e &longs;it, vt acceleratione &longs;eclu&longs;a, &
non percurrendo quolibet con&longs;e quentium momento
rum, plu&longs;quam vnam particulam, totidem a&longs;&longs;ignentur
&longs;unt particulæ &longs;patij memoratæ. Reducamus itaque
huiu&longs;cemodi decima minuta in prima, in horas, in dies,
in annos; procreabuntur certè anni Iuliani, &longs;eu quales
nobis v&longs;ui &longs;unt 5322381, cum vno ferè anno prætereà. Igitur hic erit numerus annorum, quo demùm exacto
lapis ex laqueari ad tabulatum petueniet. Heinc, &longs;i
inter varianteis Chronologorum opiniones, &longs;uppona
mus Mundum fui&longs;&longs;e conditumà &longs;ex mille annis; vides,
vt &longs;i lapis ab initio Mundi occœpi&longs;&longs;et cadere, non
dum cecidi&longs;&longs;et temporibus no&longs;tris vna &longs;eptima parte
digiti; vtque oporteret ad
hûc
quàm durauerit hactenus. Qu&ecedil;&longs;o te ergo cuius &longs;it pretij
huiu&longs;modi motus, quo intra &longs;ex
non po&longs;&longs;it pars &longs;eptima digiti, re&longs;pectu accelerationis,
qua vno horæ &longs;ecundo percurruntur digiti centum
quadraginta quatuor? Quid verò, &longs;i acciperemus
pro momento primo non momentum horæ
&longs;ed cente&longs;imum, &longs;ed mille&longs;imum; quàm multæ myria
des durationum Mundi nece&longs;&longs;ariæ forent, ptin&longs;quàm
illo motu digitus vnus peruaderetur? Sed ne eò v&longs;que
rem deducam, quæ&longs;o te&longs;olùm, tamet&longs;i is motus con
cedatur & naturalis, & à principio intrin&longs;eco; cùm in
&longs;en&longs;ibilis tamen &longs;it non modò intra vnum minutum
&longs;ecundum, &longs;ed etiam intra centum annos, quibus totis
apparere non po&longs;&longs;it cente&longs;ima parte digiti promotior:
quæ&longs;o te, inquam, an-non ca&longs;us lapidis valeat potiùs
denominari ab acceleratione violentus, quàm ab illo
naturalis; cùm quicquid &longs;en&longs;ibile habet, ab acceleratio. ne obtineat.
IX.
Heinc igitur, quando ais,
accelerationem violentam concedant, non verò de&longs;cen&longs;um, ni&longs;i
hunc ab eius acceleratione mente, vt dictum e&longs;t, &longs;eiunctum à
principio externo, & contra naturæ inclinationem procedere
euidentiùs o&longs;tendam:
dam de&longs;cen&longs;um fieri contra naturæ inclinationem, qui
exi&longs;timo illum fieri &longs;ine naturæ reluctatione. Deinde
&longs;atis mihi tribui, cùm acceleratio e&longs;&longs;e violenta conce
ditur; quippe motus &longs;olus, qui e&longs;t ab acceleratione, &longs;iue
à cau&longs;&longs;a accelerante, &longs;en&longs;ibilis e&longs;t, atque adeò &longs;olus, de
quo con&longs;entaneum &longs;it requirere, naturali&longs;-ne &longs;it, an
violentus; cùm alioquin motum, &longs;eu de&longs;cen&longs;um illum
re&longs;iduum, qui per&longs;æcula integra fieri non po&longs;&longs;it &longs;en&longs;i
bilis, nemo perinde &longs;it curaturus. Tertio requi&longs;ii&longs;&longs;e
me illum, vt e&longs;&longs;et principium, à quo acceleratio incipe
ret, fieretque radix proportionis, qua acceleratio in
cre&longs;cit. Quòd autem illum e&longs;&longs;e putârim ab externo
principio, cau&longs;&longs;a fuit imprimis, quia animaduert, &longs;i
Deus vacuum fecerit locum intra regionem aëris, in
quem nihil prorsùs neque ex aëre, neque ex Terra, ne
que aliunde penetret, ac lapis in eius medio collocetui;
futurum non e&longs;&longs;e, curlapis ver&longs;us vllam partem mouea
tur, magis quàm motus fui&longs;&longs;et, &longs;i illum Deus in eodem
loco ante conditum Mundum con&longs;titui&longs;&longs;et, aut mo
uendus e&longs;&longs;et, &longs;i deinceps totus circa eum Mundus de
&longs;trueretur. Nempe, quia nihil penitùs cum toto Mun
do communicaret, perinde illi penitùs foret, &longs;eu e&longs;&longs;et,
&longs;eu non e&longs;&longs;et Mundus. Et quia aliunde animaduerti
futurum, vt &longs;i Deus circum creârit, re&longs;titueritve aërem,
lapis tum moueatur, feraturque ver&longs;us Terram, potius
huiu&longs;modi motus principium e&longs;&longs;e debere vel in aëre, à
quo quam-ptimùm lapis fuerit contactus, cœperit mo
ueri; vel in Terra, ver&longs;us quam, non aliò in&longs;titutus mo
tus fuerit; non verò in lapide ip&longs;o, qui quandiù &longs;olus
fuerit, nihilque externum ad ip&longs;um appulerit, ip&longs;umve
contigerit, eo motu caruerit. Rur&longs;us autem, quia ani
maduerti, &longs;i nihil v&longs;quàm rerum e&longs;&longs;et, præter aërem, ac
in aëre lapidem, non fore cur lapis in hanc potiùs par
tem, quàm in aliam quamlibet ferretur; idcircò con
clu&longs;i, cùm lapis cœperit ver&longs;us
primam motus cau&longs;&longs;am ab ip&longs;a Terra procedere; vnde
& attracticem vim in ip&longs;a Terra e&longs;&longs;e conce&longs;&longs;i. Et quòd
talis vis e&longs;&longs;e non po&longs;&longs;it procùl actuo&longs;a, propè otio&longs;a;
ideò ex illius actione continente in lapidem, collegi
e&longs;&longs;e nece&longs;&longs;arium inuale&longs;cere impetum, &longs;eu accelerari in
lapide motum. Quoniam verò peruidere &longs;um vi&longs;us ex
&longs;ola hac attractione non po&longs;&longs;e explicari proportionem
eiu&longs;ce accelerationis; & aliunde reputaui aërem, tamet
&longs;i non po&longs;&longs;it fieri cau&longs;&longs;a initij motus, po&longs;&longs;e nihilomi
nus motum &longs;emel cœptum iuuare, ac veluti prouchere;
idcircò illum quoque adhibui, & ex eius vi impul&longs;iua,
cum attractrice terræ coniuncta compo&longs;ui cau&longs;&longs;am
proportionis integram, quo legi&longs;ti modo. Hæc re
peto autem, vt tibi in&longs;inuem, quamobrem non modò
accelerationem, &longs;ed ip&longs;um quoque motum, &longs;iue pri
mum initium motus, qui à te dicitur de&longs;cen&longs;us, e&longs;&longs;e à
principio externo cen&longs;uerim.
X.
Ratio aliunde mihi fuit, quòd nihil videretur
magis con&longs;entaneum, quàm motum foueri, incremen-
ver&longs;a habere initium ab eadem cau&longs;&longs;a, à qua fomentum,
incrementumque acceperit. Quippe ob&longs;eruaui natu
ram &longs;ic in cæteris comparatam, vt qua ratione progre&longs;
&longs;um parat, eadem exordium faciat; ac habui planè in
congruum tam imbecillum facere internum rei princi
pium, vt motum incipiat, qui per totannorum myria
das &longs;it in&longs;en&longs;ibilis futurus, indigeatque &longs;emper externo
motore, qui acceleret, ac perficiat, & vno quidem pro
pè momento. Heinc verò e&longs;t, cur, vt dum aqua igni
admota incale&longs;cit, non quærimus cau&longs;&longs;am inten&longs;ionis,
&longs;eu
primi gradus in aqua; &longs;ed tam primum gradum, quàm
cæteros ad &longs;olum ignem referimus: ita dum lapis inua
le&longs;cit, acceleraturve in motu, non videatur accelera
tionis, &longs;iue partium motus requirenda cau&longs;&longs;a externa; &
initij, &longs;eu primæ illius particulæ motus, interna, hoc e&longs;t
in ip&longs;o lapide: &longs;ed tam pars prima, quàm cæteræ refe
rendæ videantur ad externam cau&longs;&longs;am. V&longs;urpo autem
aquam in exemplum; quoniam vt illa ex &longs;e calore de&longs;ti
tuitur, &longs;ic lapis ex&longs;e caret motu, quemadmodum in
telligitur ex po&longs;ito ca&longs;u, quòd in vacuo, ac non ex&longs;i&longs;ten
te præ&longs;ertim Mundo, con&longs;titutus &longs;it; &longs;ecus profectò, ac
animal, quod habet in &longs;e &longs;ui motus principium. Quo
&longs;anè loco non parùm &longs;u&longs;pexi Ari&longs;totelem, cùm cen&longs;uit
corpus graue moueri deorsùm
ac inter cæteras rationes, ob quas
&longs;eco, illam attulit, quod graue alioquin foret anima
tum; Ne
que verò aut non habebis Ari&longs;totelem inter erudi
tos; aut dices illum fui&longs;&longs;e de &longs;ola acceleratione loquu
tum; aut probabis &longs;ic di&longs;tinxi&longs;&longs;e, vt omninò cen&longs;uerit
non e&longs;&longs;e de&longs;cen&longs;um à principio externo. An ille &longs;atis
commodè cau&longs;&longs;am externam a&longs;&longs;ignârit, non e&longs;t cur
hoc loco di&longs;cutiam; abundè e&longs;t, &longs;i ip&longs;e quoque, dum
cau&longs;&longs;am externam con&longs;tituo, illum non modò non
refragantem, &longs;ed &longs;uffragantem etiam habeam. Nam
quando cæteri quidem eruditi declarauerint, quæ-nam
alia &longs;it accelerationis, proportioni&longs;que illius cau&longs;&longs;a; &
eandem cau&longs;&longs;am, quæ motum acceleret, non facere illi
initium, exigique omninò aliam, e&longs;&longs;eque illam intrin
&longs;ecam; tunc erit &longs;anè cur diffidam non meis modò nu
gamentis, &longs;ed placitis etiam tanti Coryphæi.
&longs;us Lunam dimoueretur; Quid lapidi, &longs;i intra fornicem,
ad centrum Terræ, con&longs;titueretur.
XI.
Cau&longs;&longs;aris deinde,
propria natura, &longs;ed à Terra diffu&longs;is circumquáque corpu&longs;culis
illecta, atque etiam illigata deor&longs;um trahi per&longs;uadeam.
Sed facio nimirùm, Vir docti&longs;&longs;ime, ac religio&longs;i&longs;&longs;ime,
quòd dum in perue&longs;tigatione cau&longs;&longs;arum naturalium
ver&longs;or, nu&longs;quam non caligo mihi offundatur; atque
idcircò tanquam incedens in den&longs;i&longs;&longs;imis tenebris, nihil
non palpitem, nihil non moueam, nullam non tentem
&longs;emitam, &longs;i fortè in aliquam &longs;peciem vel tenui&longs;&longs;imæ
luculæ emergam. Dicis
hoc e&longs;t non ioco, &longs;ed vt eruditi, quæ magis &longs;eria habue
rint, doceant. Neque enim e&longs;t, cur exi&longs;times i&longs;tis me
nugis ita hærere, vt ip&longs;as qua&longs;i veritatem ip&longs;i&longs;&longs;imam
habeam, aut colam, &longs;ed cùm totus Mundus &longs;it nuga
rum plenus, & videre videar nugas quoque e&longs;&longs;e, quæ
vulgò habentur &longs;eria maximè; &longs;upere&longs;&longs;e exi&longs;timo, vt
eas nugas deligam, quæ e&longs;&longs;e minùs nugæ videantur. Quæris,
&longs;um moueri naturâ?
tum, quod mox antè repetij. Deinde, vnde colligis
inficiari me moueri lapidem naturâ? Quippe & mo
ueri illum cen&longs;eo non reluctante interna natura; &
quam externam adh
to naturæ. Ad-hæc, non ignoras, quàm nihil &longs;it ne
ce&longs;&longs;e Philo&longs;ophiam excolere, &longs;iad grauiores difficulta
tes dicere &longs;ufficiat aliquid moueri, aut fieri naturâ. Non
quòd eò tandem, quæ humana e&longs;t imbecillitas, perue
niendum non &longs;it; &longs;ed quòd dum nobis non datur vltrà,
aliquò tenus prodire &longs;it. Rursùs, dum natura interna
mouet, agitve aliquid, id ni&longs;i certis organis, agendique
modo &longs;peciali non præ&longs;tat: an verò quis modus is &longs;it,
quæ hæc organa, docent nos ip&longs;i Eruditi? In de&longs;cen&longs;u
quidem rerum grauium dicunt grauitatem e&longs;&longs;e orga
num, & modum agendi expre&longs;&longs;ionem grauitatis: &longs;ed
amabo te, quid hæc grauitas? Et quid nam præ&longs;tat
lapidi con&longs;tituto in vacuo? Et, quorsum concipitur
tanta in ingenti lapide; cum &longs;eclu&longs;a tamen cau&longs;&longs;a exter
na accelerante, & violenta, incapax &longs;it, quæ per cen
tum annos moueat deorsùm lapidem per vnius digiti Et, cur grauitas eò maior fit quò
lapis fit acceleratior? Et, qui fieri pote&longs;t, vt grauitas
dicatur e&longs;&longs;e organum internæ naturæ, ac effectiuum
motus deorsùm cùm grauitas tota, & motus totu ob
&longs;eruabilis procedat à cau&longs;&longs;a externa? Heinc dum re
quiris,
Sanè vel hoc vnum di
tis.
vehementioribus eius commotionibus, à qua alia Tellure in
pri&longs;tinum locum retrahitur?
accepi Terram v&longs;quam &longs;ic contremui&longs;&longs;e, &longs;eu vehemen
tem adeò illius commotionem fui&longs;&longs;e, vt mota loco tota
fuerit (ni&longs;i fortè tremorem illum, qui contigit Chri&longs;to
patiente, &longs;ed pr&ecedil;ter naturæ tamen ordinem, intellexeris)
tuque ip&longs;e &longs;tatim pò&longs;t dicis
nullis Quare
Terræ tremores particulares e&longs;&longs;e videantur; quæ Terræ
vis retrahit glebas, retrahet etiam maiores parteis, quæ
aliqua vehementiore &longs;ucce&longs;&longs;ione fuerint commotæ.
XII.
Quæris con&longs;equenter,
gelica vi à propria &longs;ede dimota ver&longs;us Lunam aliquot
milliaribus attolleretur; illeic-ne sponte naturæ con&longs;i
steret, an ad pri&longs;tinum potiùs locum reuerteretur?
vis tu heic &longs;anè fieri controuer&longs;iam de loco Telluris in
Mundo, quod ad motum, quietemve &longs;pectat: quare
& Re&longs;pon&longs;ionem prætereo, quæ fieri po&longs;&longs;et iuxta illos,
qui moueri Terram contendunt, quique &longs;peciatim
d
ventive re&longs;lantis,
à rapida illa circumuolutione; e&longs;&longs;eque penitùs ad illam Dico ergo po
tiùs probabile e&longs;&longs;e, fore, vt eo ca&longs;u Tellus quie&longs;cat, vbi
cum que Deus, Angelu&longs;ve con&longs;tituerit ip&longs;am. Scilicet
concipio quicquid e&longs;t &longs;patiorum non modò intra cir
cuitum Lunæ, &longs;ed etiam intra ambitum, concamera
tionemve &longs;iue Firmamenti, &longs;iue etiam Mundi, e&longs;&longs;e li
berum, ac &longs;altem quod &longs;pectatad totam regionem Pla
netariam, nullam dari &longs;oliditatem earum, quæ tredun
tur, Sphærarum cæle&longs;tium. Sunt certè tum rationes
aliæ, tum maximè Pha&longs;es ill&ecedil; Veneris, quæ ip&longs;am nunc
vltra, nunc citra Solem e&longs;&longs;e conuincunt. Et po&longs;&longs;et
quidem totum hoc &longs;patium intra Mundi ambitum
concipi inane, ni&longs;i quà globi Siderum, ac Telluris &longs;unt,
& quatenus radij &longs;iderum variè
giri placet quam vulgò Atheream auram nuncupant;
&longs;ub&longs;tantiam nempe tenui&longs;&longs;imam, & aëre hoc no&longs;tro
incomparabiliter &longs;ubtiliorem, quæ pari modo diffu&longs;a
&longs;it, totumque &longs;patium occupet, ni&longs;i qui ijdem globi
&longs;unt; etiam Telluris, cuius aër, & aqua &longs;unt tenuiores,
fluidiores, ac exteriores Concipio aliunde,
quod legi&longs;ti fu&longs;iùs deductum in Epi&longs;tolis, non Tellu
rem magis, quàm Siderum vllum, e&longs;&longs;e ex &longs;e grauem,
aut leuem: &longs;ed grauitatem, ac leuitatem e&longs;&longs;e affectio
nes partium proprias, quatenus partes &longs;unt, & à &longs;uo
toto di&longs;trahi quadam tenùs po&longs;&longs;unt: quo eodem mo
do partes Lunæ, & cuiu&longs;vis Mundani globi e&longs;&longs;e po&longs;
&longs;unt graues, aut leues ab&longs;que grauitate, aut leuitate to
tius. Quare & po&longs;&longs;e quidem dici e&longs;&longs;e aliquid &longs;upe
riùs, & inferiùs, &longs;ursùm, & deorsùm, re&longs;pectu partium
cuiu&longs;que globi, & comparatè ad animal, cuius illæ, &
torum ip&longs;orum globorum, & &longs;eclu&longs;o animalis &longs;itu, à
quo nihil præter relationem, denominationemve ex
trin&longs;ecam habent, nihil e&longs;&longs;e reuerâ &longs;uperius, aut in
ferius, &longs;ursum, aut deorsùm. Et &longs;ecus quidem Ari&longs;tote
les; &longs;ed non &longs;ecus Plato, qui cùm agno&longs;cat e&longs;&longs;e in
Mundo extremum, & medium; contendit tamen non
ideò debere aut extremum &longs;upremum, aut medium
in&longs;imum cen&longs;eri. Heinc proinde dico, & vnumquem
que Siderum globum in ea parte Mundani &longs;patij,
quam Deus ab initio ip&longs;i præ&longs;crip&longs;it, circumgyrari, &
globum Telluris inea parte Mundani &longs;patii quie&longs;cere,
in qua Deus ip&longs;um initio con&longs;tituit. Rem ita e&longs;&longs;e in
telligo, vt&longs;i quis plureis apparet globos ex ea materia,
quæ &longs;ub pari mole, fiue ambitu tantum ponderet, quan
tum aqua, & ip&longs;os in aqua quie&longs;cente con&longs;tituat. Qui
libet enim eorum globorum, vbicumque fuerit con&longs;ti
tutus, ibi conquie&longs;cet; & neque ex &longs;ummo imum
petet, neque ex imo &longs;ummum; neque ex vtrouis ex
tremo medium; neque ex medio vtrumvis extre
mum; neque ex medio, extremove locum interce
ptum; neque exloco intercepto medium, aut extre
mum. Et &longs;i &longs;ingas Dædalum, Architam, aut al um
arti&longs;icem adeò ingenio&longs;um, vt vno eorum alicubi in
tra aquam con&longs;tituto efficere po&longs;&longs;it alios
&longs;eu varios illis circa ip&longs;um obeundos motus indere;
ij globi peragent &longs;uos motus quamcumque ad partem
in&longs;tituti fuerint: nempe &longs;eu prope &longs;uperficiem, &longs;eu
prope fundum; &longs;eu &longs;ub medium, &longs;eu prope medium,
&longs;eu procùl à medio: &longs;cilicet tam ille, quàm i&longs;ti, ob ip&longs;am
leues, vt auolent.
XIII.
Subinde ergo comparo cum immoto globo
Tellurem, cum circum-ductis Sidera; & dico, &longs;icut glo
bus ille emoueri pote&longs;t à loco, in quo e&longs;t, & promoue
ri ver&longs;us alium; &longs;ic po&longs;&longs;e ip&longs;am quoque Tellurem emo
ueri à loco, in quo e&longs;t, & promoueri ver&longs;us Lunam;
addoque, vt globus ille in quocumque alio aquæ loco
reponatur, in eo pari modo quie&longs;cet, neque priorem
repetet: &longs;ic & Tellurem, in quocumque loco con&longs;titu
ta fuerit, in eo man&longs;uram, nec pri&longs;tinum repetituram. Et dicis tu quidem
dico
in Mundo locum, & Terram ip&longs;um occupare: cùm &longs;u
perum tamen, & inferum comparatè &longs;olùm ad nos, &
re&longs;pectu globi, quem inhabitamus, videatur e&longs;&longs;e acci
piendum. Ex hoc certè intelligo, tran&longs;latà Terrâ ver&longs;us
Lunam ad Antipodas ex&longs;i&longs;tentem, nos non propterea
auolaturos in derelictum à Terra locum; vt neque
etiam Antipodas, tran&longs;latâ Terra ver&longs;us Lunam factam
nobis ad verticem: &longs;ed & illos, & nos perinde in ea
dem antiqua &longs;ede ver&longs;aturos, tanquam &longs;imùl tran&longs;lato
Terræ centro, re&longs;pectu cuius, & comparatè ad &longs;itum
capitis, pedumque no&longs;trorum, cen&longs;ebimur &longs;emper a&longs;
cendere, & de&longs;cendere, &longs;iue locum &longs;ur&longs;um, deor&longs;um
que habere; non autem &longs;impliciter re&longs;pectu loci, in
quo Terra aut erit, aut fuerit, & qui &longs;eu centrum Mun
di &longs;it, &longs;eu non &longs;it, nihil ad a&longs;cen&longs;um, aut de&longs;cen&longs;um
&longs;acit. Prætereo autem nullum e&longs;&longs;e argumentum
extra comprobetur; & vel ip&longs;um motum Planetarum
excentricum videri planè conuincere non e&longs;&longs;e Terram
con&longs;titutam in centro &longs;patiorum, motuúmque cæle
&longs;tium. Nam probare quidem Firmamenti, &longs;uperio
ri&longs;ve cæli motum concentricum e&longs;&longs;e, potiu&longs;quàm ex
centricum, ingenij humani viribus e&longs;t maius. Acnoui
quidem quas rationes Ari&longs;toteles, Ptolomæus, & alij
proferunt: &longs;ed nihil e&longs;t nece&longs;&longs;e heic o&longs;tendere, quàm
illæ &longs;int inefficaces. Dum igitur quæris,
con&longs;i&longs;teret?Et, dum præoc
cupas, Præ
occupas quoque, cur ita nunc &longs;uum locum affectet, vt
nullis concu&longs;&longs;a motibus ab eo dimoueri valeat? Sed
affectat, quia nutui Conditoris ob&longs;equitur; & in &longs;ta
tione collocata, eam non de&longs;erit, &longs;ed tuetur. Non va
let autem dimoueri vllis concu&longs;&longs;a motibus; quia om
nes, quos &longs;upponis, motus partium ip&longs;ius propriarum,
cohærentiumque &longs;unt, neque illam &longs;ecundum &longs;e totam
mouere loco magis po&longs;&longs;unt, quàm animal totum Pul
&longs;atio vnius arteriæ. Et &longs;unto alicubi magni Terræ
motus; ij tamen ad Terræ molem comparati, tale
quid vix &longs;unt, qualis e&longs;t in nobis pul&longs;atio arteriæ vege
tior, &longs;i quà in nobis pu&longs;tula cum apo&longs;temate intume&longs;
cit. Addendum e&longs;t porrò, cùm Mundi &longs;apienti&longs;&longs;i
mas Artifex omneis eius parteis ita con&longs;tituerit, vt nullo
e&longs;&longs;e loco, aut &longs;itu inter &longs;e commodiore po&longs;&longs;int: idcir
cò &longs;i contendas Terram &longs;uum locum repetituram, vt
in quo magis congruè Vniuer&longs;i re&longs;pectu &longs;it; fore, vt il
lum repetat, non tum propria vi, &longs;eu grauitate in&longs;ita,
cupârit, compul&longs;a; eo modo, quo trabs, &longs;i deprimatur
in fundum maris, &longs;uperficiem repetet, non &longs;anè vi
propria, &longs;eu leuitate ingenita: &longs;ed compul&longs;a ab aqua,
cuius occupauerit locum.
XIV.
Quod &longs;pectat ad aliam fictionem, &longs;ecundum
quam me interrogas,
Terræ meditullio concamerata cauerna fiat, & aqua, aëreve
oppleatur: lapis verò con&longs;tituatur, non in eius, Terræque
centro, &longs;ed loco inter centrum, & fornicem medio?
breuiter, probabile e&longs;&longs;e, vt &longs;i Terra &longs;it qua&longs;i Magnes,
tractorios radios quoquo versùm, ac in illam etiam
cauernam diffundens; fore vt lapis attrahatur ver&longs;us
eam fornicis partem, è qua ad ip&longs;um radij plures, vni
tiore&longs;que peruenerint; &, &longs;i &longs;upponas peruenire ex
æquo, ac vndelibet, fore, vt illeic inter æquas vndique
vireis contineatur, eo modo, quo fabula e&longs;t Moham
medis &longs;epulcrum &longs;u&longs;pendi. Sed, &longs;i lapidem quidem
attrahi contingat ad proximum: fornicem,
inquis,
ctus, attractu&longs;que ad putei latera non adhære&longs;cit?
e&longs;t, quia plures, vnitiore&longs;que radij è maiore Terræ
mole, quæ e&longs;t ver&longs;us centrum, concurrunt in lapidem,
quàm ad eum accurrant ex ip&longs;is putei lateribus.
ip&longs;amet Terra,
ret, leuioraque inde corpora expelleret?
&longs;upponas qua vi excauatus fornix fuerit, eadem po&longs;teà
ip&longs;um abrumpi; ego quidem non video, qua id ratione
dicere po&longs;&longs;i
fornices rumpi, vt aqua, aut aër inde abigantur, & quæ
ip&longs;um ferantur. Subdis,
&longs;i placet, Terrâin arenulas redactà, eam non confluxuram ad
centrum?
&longs;unt monteis, aliaque Terræ loca di&longs;rumpi, inque are
nulas redigi, vt compleant &longs;uppo&longs;itas &longs;pecus, crypta&longs;
que aut aqua, aut aëre plenas: idque, ni&longs;i fortè, vt dixi,
&longs;upponas eandem vim deterere Terram in arenulas,
quæ excauárit fornicem; quo ca&longs;u, quæ e&longs;&longs;et in arenu
lis &longs;uper&longs;tes magnetica vis &longs;ic eas mutuò pelliceret, vt &
in crypten confluerent, & aquam, aëremve inde abi
gerent; &longs;i modò &longs;uppo&longs;ueris quoque rimas, exitumve
patere. Pergis adhûc,
ab alio corpore attracta, &longs;ed &longs;ponte naturæ, & à principio
interno, atque innato. Verumtamen confluere po&longs;&longs;ent
attractæ à &longs;einuicem, vt & iam confluunt ferri ramen
ta, quæ magneticam combiberunt vim. Concludis,
C
dicatur?
menta, ex quibus liceat aliquid veri&longs;imilius coniectari.
&longs;en&longs;ilia organula; &,
&longs;it &longs;en&longs;ibilior, quam procùl.
XV.
In&longs;ectaris deinde Magneticam illam, &longs;eu
attractricem Terræ vim; opinari&longs;que
dum inui&longs;ibileis vncinos, harpagones, chelas, funei&longs;que ten&longs;os,
& tractorios fingo. Sed quod me quidem attinet, non
diuendo &longs;anè ha&longs;ce meas commentationes, &longs;eu vt antè
bium; at &longs;impliciùs ago, quàm vt rideam; quippe me
potiùs mi&longs;eret natiuæ imbecillitatis, cùm nihil ha
beam præclarius, quo meam, aut alterius &longs;ciendi auidi
tatem pa&longs;cam. Obiicis,
vulgò dictam attractionem in exemplum adducam; quòd
Magnes, & &longs;errum non &longs;ictis illis meis hurpagonibus, aut
inui&longs;ibilibus catenis, qua&longs;i vi adducta; &longs;ed vtrumque &longs;ponte
naturæ incitata in mutuos amplexus accurrant. Id verò
&longs;anè per-eleganter; &longs;ed quid mihi facias, qui &longs;im ita
hebes, vt vim vocibus &longs;ubiectam non capiam. Dicis
effectus e&longs;t, de cuius cau&longs;&longs;a ambigitur. Cau&longs;&longs;am ergo
interiicis, At cùm hæc vi
deatur e&longs;&longs;e generalis, inarti&longs;iciali&longs;que Re&longs;pon&longs;io, qua
ad omnia vtimur, quorum cau&longs;&longs;as ignoramus; non vi
deo profectò, quò tu, Vir acuti&longs;&longs;imus, collincees. Quippe
velle te dicere nihil aliud, quàm quod e&longs;t vulgò in ore
omnium,
fit; quia hoc natura ip&longs;a &longs;cit,
in animum non induco. Hæc certè e&longs;t cau&longs;&longs;a, cur
dixerim antè valere iubendam omnem Philo&longs;ophiam,
ac omnem præ&longs;ertim cau&longs;&longs;arum
darum deponendam curam; &longs;i huiu&longs;cemodi Re&longs;pon&longs;io
videatur po&longs;&longs;e &longs;ufficere. Ac e&longs;t quidem eò denique, vt
etiam dixi, perueniendum: &longs;ed &longs;unt interim tamen va
rij gradus cau&longs;&longs;arum in&longs;trum entariarum, de quibus
cùm dicere non liceat quemadmodum à natura, vt à
princip
natæ, addictæque ip&longs;i naturæ; licet tamen requirere
vel in ip&longs;is explorandis, &longs;icubi fortè &longs;ecundum gradus
aliquos occurrant, incumbere debet. Et cùm videa
mus &longs;anè alios e&longs;&longs;e alijs &longs;agaciores, ip&longs;aque naturæ ar
cana (arcana profecto) &longs;tudio&longs;iùs rimanteis; tamet&longs;i
detur nemini penetrare in adyta; fatendum e&longs;t tamen,
cùm omnes in ve&longs;tibulo hæ&longs;erint, fieri in ip&longs;o ve&longs;tibu
lo alios aliis promotiores.
XVI. Iam, cùm dicis
tari:
tionem? An non, vt fiat incitatio, e&longs;&longs;e alia pars inci
tans, & alia incitata debet? Idem certè mouere &longs;eip&longs;um,
ni&longs;i parteis habeat mouentem, & motam, cùm iis, quos
tu vocas Eruditos, aduer&longs;atur; tum communi etiam no
tioni repugnat, cui Ari&longs;toteles inhærens, impo&longs;&longs;ibilo
e&longs;&longs;e cen&longs;et, vt id &longs;eip&longs;um moueat, quod e&longs;t Non
ne verò &longs;unt huius generis tam Magnes, quàm Ferrum? De altero ergo vt &longs;olùm loquamur, quænam in Ferro
parsincitans? Et quid illam mouet vt incitet aliam?
Et, quonam motus genere illam in citat?
Pul&longs;u-ne, an
tractu, an alio? Ac &longs;i poneres quidem &longs;peciem animæ:
po&longs;&longs;et illa forta&longs;&longs;is vti interno quodam &longs;piritu ad cien
dum reliquam ma&longs;&longs;am: &longs;ed tu animam nempe impro
bas. Quónam ergo modo pote&longs;t concipi incitare &longs;e
ip&longs;um Ferrum, vt accurrat, a&longs;cendat, de&longs;cendat, viam
flectat, prout illi magnes appo&longs;itus fuerit? Facit
inquis: ego de voce ne conte&longs;tor; &longs;ed ea &longs;altem maius,
ampliu&longs;que aliquid de&longs;ignat, quàm
& cùm excludat principium extrin&longs;ecum, intrin&longs;ecum
quod pellat, & aliud vtique, quàm &longs;eip&longs;um: ni&longs;i fortè
ex accidenti. Id ergo quæritur, quod-nam &longs;it: &, cùm
&longs;it quid à ma&longs;&longs;a tota indi&longs;cinctum, neque vt in mem
bris animalium fit, commi&longs;&longs;urâ vllâ dearticulatum,
quomodo moueri ip&longs;ummet occipiat (quippe nihil; &longs;i
&longs;it immotum, mouere pote&longs;t Phy&longs;ice) quomodo mo
ueat aliud? quomodo totam incitet ma&longs;&longs;am?
Dices
quidem fortè, illud e&longs;&longs;e formam, quæ vt &longs;eipsâ vnitur
materiæ, ita &longs;eipsâ, ab&longs;que vllo intercedente organo
mouere po&longs;&longs;it materiam; vnde & totius ma&longs;&longs;æ, &longs;eu Fer
ri con&longs;equatur motus: verùm vtcumque heinc explice
tur motus Ferri, quà graue e&longs;t, & deor&longs;um tendit; illi
tamen motus, flexu&longs;que in quamcumque partem fuerit
Magnes appo&longs;itus, non videntur po&longs;&longs;e intelligi ex &longs;ola
applicatione formæ ad materiam, ni&longs;i & illa anima &longs;it,
& tum vireis, tum articulos flexanimcis habeat, vt quæ
dam variorum motuum organa; quæ nulla tamen de
prehenduntur. Sed hæc vt præteream; cùm videamus
Ferrum non ex quacumque di&longs;tantia in amplexum
Magnetis accurrere, &longs;ed accurrere &longs;olum, v. c. ab vno
palmo; quo modo vis intelligamus incitari ferrum
&longs;ponte naturæ in di&longs;tantia palmi, non in di&longs;tantia cubi
ti? An in di&longs;tantia cubiti &longs;uæ &longs;pontis non e&longs;t?
An na
tura caret? An lu&longs;cio&longs;um e&longs;t, neque pote&longs;t Magnetem
agno&longs;cere, ni&longs;i intra di&longs;tantiam palmi? Rides vncinos,
harpagones, chelas, &longs;imiliave organula, quæ ego opi
nor ex magnete emitti, quibu&longs;que in palmi di&longs;tantia
confertioribus, atque adeò validioribus, quàm ad di
&longs;tantiam cubiti exi&longs;timo illeinc, non heine pertrahi ad
quónam modo fieri hanc incitationem, cum tanto
propinqui, & remoti delectu capis? Et homo quidem
ad hominis amplexum &longs;e&longs;e incitat, quia e&longs;t animatus,
quia videt illum, quia &longs;pecie ab illo recepta agno&longs;cit:
at in Ferro nihil tale habes; cùm videaris tamen in ip&longs;o
præclarius quidpiam agno&longs;cere, quàm &longs;implex quæ
dam cognitio &longs;it, videlicet Diuinationem. Etenim
nece&longs;&longs;e e&longs;t prorsùs diuinare Ferrum, quandò Magnes
propè, quando procùl &longs;it, vt vireis metiatur, ac delige
re valeat, è quánam di&longs;tantia in ip&longs;um in&longs;iliat.
XVII.
An dices Magnetem emittere ex &longs;e non cor
pu&longs;cula quidem aliqua, quæ &longs;int qua&longs;i vncinuli, chor
dulæ tractoriæ, &c. &longs;ed vim, &longs;eu qualitatem quan
dam, quæ &longs;it merum accidens, quæque vbi ad Ferrum
peruenerit, tum ip&longs;um Ferrum veluti &longs;entiat, &longs;e&longs;eque
ip&longs;um excitet ad accurrendum ver&longs;us Magnetem? Si
dicas, admittes profectò in Ferro &longs;en&longs;um aliquem, &
aliud quidpiam exiges, quàm &longs;pontaneam incitatio
nem; cau&longs;&longs;am nimirùm extrin&longs;ecam, à qua principium
internum moueatur, & quæ proinde motus Ferri pri
marium dici principium debeat. Sed & de i&longs;ta quali
tate, &longs;eu virtute accidentaria, quanta diffi ultatum &longs;e
ges? Seu enim &longs;olitaria, & ab&longs;que &longs;ubiecto moueatur
per &longs;patium; &longs;eu de &longs;ubiecto in &longs;ubiectum per varias
parteis aëris, alteriu&longs;ve corporis migret; &longs;eu propaga
tione, hoc e&longs;t, corruptione vnius, & productione al
terius &longs;ucce&longs;&longs;iuè facta in palmaris &longs;patij infinitis pun
ctis (aut particulis mauis) innouetur: agno&longs;cis quàm
multa ab&longs;urda &longs;equantur: & vtcúmque tandem i&longs;tam
modum energiæillius exprimere valeat? Et, cùm non
dicas Ferri molem ab ea pertrahi; qua ratione tamen,
corpus cùm non &longs;it, tangere Ferri corpus pote&longs;t? Nam
tangi quidem Ferrum ab aëre, corporeve alio, in quo
ip&longs;a qualitas &longs;it, id fiebat iam ante: & corpus huiu&longs;ce
modi non fit illius organum, neque ab illa afficitur,
moueturve, vt coagat, nouoque modo Ferrum contin
gat, ac ip&longs;um veluti admoneat. Sed &, cùm contactus
nudus fuerit; quonam modo exinde &longs;iet &longs;pontanea illa
incitatio? Certè, vt iam dictis hoc addam, vbi Ferrum
&longs;uppo&longs;itum ad imminentem Magnetem fertur, non
videtur concipi po&longs;&longs;e qua ratione &longs;e euehat, & non à
Magnete trahatur. Nam animal quidem excitare &longs;e&longs;e
ad conten dendum &longs;ursùm pote&longs;t; quoniam ob mem
brorum articulationem pote&longs;t Terram premere, à qua
re&longs;i&longs;tente velut reflectatur, vt fiat re&longs;ilitio; at Ferrum
tale nihil facit, imò nec pote&longs;t facere: quare & hoc ip
&longs;um argumento e&longs;t, quòd non &longs;ui concitatione, &longs;ed
Magnetis tractione abripiatur &longs;ursùm. Et &longs;u&longs;pendatur
manibus homo, &longs;u&longs;pendatur Ferrum, ita vt vtrique &longs;it
&longs;olus aër &longs;uppo&longs;itus: non &longs;aliet &longs;anè &longs;ur&longs;um homo, ne
que ad amicum &longs;upere-ex&longs;tantem accurret, ni&longs;i amicus
eum traxerit. quî po&longs;&longs;it iure potiore Ferrum ad &longs;uper
ex&longs;tantem Magnetem, ni&longs;i traxent ip&longs;um Magnes? An
&longs;uæ &longs;pontis magis e&longs;t, pote&longs;tque magis agere &longs;ponte? An cùm homo pedibus pul&longs;et, prematque fru&longs;trà aë
rem, Ferrum id præ&longs;tat appo&longs;itè magis? Si non capia
mus igitur quomodò &longs;eu homo, &longs;eu Ferrum incitare
po&longs;&longs;it &longs;eip&longs;um, & Ferrum certè magis, quàm homo,
nixum, &longs;ine quo non videtur fieri po&longs;&longs;e incitatio: quid
e&longs;t, cur, vt homo, dum &longs;ur&longs;um effertur, arguit e&longs;&longs;e à
quo trahatur, non &longs;ic Ferrum arguat, dum &longs;ursùm ef
fertur? Ac dum homo quidem trahitur ab homine,
communis e&longs;t notio, debere id fieri aut manu demi&longs;&longs;a,
aut chorda, aut vncino, aut alio &longs;imili in&longs;trumento:
cur & dum Ferrum à Magnete; putemus id fieri ab&longs;que
organo vllo intercepto?
XVIII. Sugillas, quòd hæc organa dicuntur à me Sed nempe, &longs;i &longs;en&longs;ilia e&longs;&longs;ent, in ijs di&longs;qui
rendis non laboraremus. Quod in&longs;en&longs;ilia verò dican
tur, non ideò tamen nulla &longs;unt; magi&longs;quam nulli non
&longs;unt vitales, animale&longs;que &longs;piritus, qui licet in&longs;en&longs;iles
&longs;int, cau&longs;&longs;æ &longs;unt tamen tot motuum, quos in animali
bus ob&longs;eruamus. Sed nihil &longs;anè nece&longs;&longs;e e&longs;t inductio
nem texam innumerarum rerum in&longs;en&longs;ilium, oculi&longs;ve
imperceptarum, quas tamen & dari, & vehementibus
motibus præditas e&longs;&longs;e ambigat nemo. Nihil etiam
nece&longs;&longs;e e&longs;t, vt argumenta congeram, quibus huiu&longs;ce
modi rescontexi ex corpu&longs;culis in&longs;en&longs;ibilibus quidem,
&longs;ed præditis nihilominùs &longs;pecialibus figuris, probem. Nihil prætereà, vt vrgeam ex attractionis effectu ar
gui, organa illa in&longs;en&longs;ilia debere analoga e&longs;&longs;e, aut &longs;i
mile quidpiam habere cum ijs, quibus attractiones
&longs;en&longs;ibiliùs fiunt; quòd à &longs;en&longs;ibilioribus ad in&longs;en&longs;ibilio
ra procedendo &longs;eruari videamus analogiam: quódque
mens humana non capiat attractionem fieri, & ratione
quadam cum his &longs;en&longs;ibilibus analoga non fieri. Ni
hil, inquam, nece&longs;&longs;e e&longs;t, vt hæc, & &longs;imilia quædam
non ea ratione, quæ &longs;it mihi facta per&longs;picua. Dicis,
à Ferro. At tu ludere, opinor, non vis ab æquiuoco:
qua&longs;i ego heic aliud appellem in&longs;en&longs;ibile, quàm quod
præ &longs;ui exilitate eiu&longs;modi e&longs;t, vt nec videri oculis, nec
palpari manibus po&longs;&longs;it? Hoc certè modo ip&longs;as quo
que, quas vocant &longs;pecies intentionaleis, in&longs;en&longs;ibileis
dicimus; quatenus adeò &longs;ubtiles &longs;unt, vt videri ip&longs;æ ab
oculo nequeant. Vnde & &longs;icut i&longs;tæ &longs;pecies, licet alio
quin in&longs;en&longs;iles, oculum tamen donec e&longs;t animatus, ita
afficiunt, vt per ip&longs;as oculus videat, &longs;entiat, percipiat
ip&longs;a obiecta: &longs;ic re&longs;pondere po&longs;&longs;et Thales, &longs;i Ferrum
quidem animatum &longs;it, quantumvis ea vincula &longs;int ip&longs;i
ferro in&longs;en&longs;ibilia, ita tamen Ferrum ab iis affici, vt per
ip&longs;a &longs;entiat, percipiatque Magnetem. Verba tua de
inde &longs;unt;
bus, ne &longs;ur&longs;um auoles, Terræ alligatum te cen&longs;es?
me voce qua&longs;i cen&longs;oria cen&longs;ui&longs;ti e&longs;&longs;e admonendum, vt
in memet de&longs;cenderem. Accipio, & hoc &longs;olùm dico,
non magis &longs;entire me catenas, quibus trahor tamen;
quàm oculus &longs;pecies memoratas, dum videt tamen. Rogas con&longs;equenter,
Ferrum ad Magnetem, cæteraque corpora ad electrica, &longs;ine
&longs;en&longs;u concurrere non poßint?
po&longs;itum habes.
XIX. Pergis,
bus omnibus à &longs;apientißimo earum opifice indita naturalis
inclinatio ad con&longs;eruationem, perfectionemque propriam; ad
de, &longs;i veles, ad con&longs;eruandum vniuer&longs;i ordinem, vt opus non Sed, Vir religio&longs;i&longs;&longs;ime,
inter nos non ambigitur, &longs;it-ne naturalis inclinatio
hi&longs;ce rebus ab Opifice &longs;apienti&longs;&longs;imo indita; quippe
quali&longs;cumque ea &longs;it, tam ego illam e&longs;&longs;e à Deo agno&longs;
co, & fateor, quam tu: &longs;ed hoc &longs;olùm ambigitur, qua
lis nimirùm illa &longs;it? An non repugnantia?
An quid
po&longs;itiuum? An mera di&longs;po&longs;itio?
An quidpiam &longs;ub
&longs;tantiæ adiunctum? An externa affectio?
An interna
propen&longs;io? Et, &longs;i &longs;it propen&longs;io, &longs;iue expre&longs;&longs;io, impul
&longs;io, actus eiu&longs;dem qua&longs;i ponderis; quæ &longs;it ponderis
huiu&longs;ce conditio? Qua id ratione &longs;e ex&longs;erat, vt fiat
propendentia? Et, &longs;i &longs;it &longs;olùm propendentia, quomo
do ab illa non &longs;it &longs;olus ca&longs;us? Quomodo etiam actio?
Quomodo non &longs;ine delectu?
cæteraque id genus alia,
quæ no&longs;&longs;e foret operæ-pretium. Quare non debes
mea figmenta &longs;ic accipere, qua&longs;iego ip&longs;a in locum in
ditæ à Deo inclinationis obtendam. Enimverò illa
v&longs;urpo, qua&longs;i qua&longs;dam hypothe&longs;eis, quibus coner,
quatenus po&longs;&longs;um, intelligere, atque explicare indu
&longs;triam admirabilem, qua &longs;apienti&longs;&longs;imus Opifex voluit
&longs;ua hæc opera proprias ex&longs;erere actiones. Atque id
quidem eadem ratione, qua A&longs;tronomi, dum hypo
the&longs;eis, &longs;eu mavis fig menta in cælum inducunt. Ne
que enim ad eas confugiunt, qua&longs;i motum cælo, aut &longs;i
deribus fui&longs;&longs;e à Deo inditum negent; &longs;ed, vt illo &longs;uppo
&longs;ito, intelligant, ac explicent quomodo huiu&longs;modi
motus fieri po&longs;&longs;it tam multiplex, tam con&longs;onans, tam
regularis. Ac fortè tu quidem &longs;apienter, cùm innuis
debere &longs;ufficere nobis, &longs;i circa rerum contemplatio
nem, cogno&longs;camus de illis, quòd &longs;int: neque fingendas
beant, quomodo agant, &c. &longs;ed, vt antè dixi, ratio
nem non video; quando exinde &longs;equitur, vt vniuer&longs;am
eliminare Philo&longs;ophiam oporteat. Et vide, vt me con
&longs;equenter traducas.
proiectilibus inclinationem (voca motum, voca impetum, aut
aliter, vt volueris) imprimere talem poßis, quæ recedentibus à
te ij&longs;dem proiectilibus, diutiùs in illis per&longs;eueret; & in quam
cumque partem de&longs;tinaueris, eadem deferat, atque impellat,
imò quæ obuio etiam, impedimento non &longs;tatim tota de&longs;truatur,
&longs;ed aliam in partem proiectilia abducat, vt in reflexione tu
ip&longs;e contendis: eri&longs;-ne tam parum æquus rerum arbiter, vt à
&longs;apientißimo, ac præpotente Vniuer&longs;i Conditore rebus quibu&longs;
libet inclinationem longè perfectiorem imprimi po&longs;&longs;e addu
bites?
haberem; & comparatus præ&longs;ertim ad Authorem
meum; coram quo non modò factus &longs;um tanquam
nihilum, &longs;ed &longs;um etiam nihilo minus. Ac rursùs, vt &longs;i
ego negarem quicquid e&longs;t inclinationis, aut virium in
rebus naturæ, id debere Deo Optimo Maximo acce
ptum referri: ac denique, vt &longs;i quæ&longs;tio e&longs;&longs;et, po&longs;&longs;it-ne
Deus imprimere inclinationes aliquas rebus, & non
potius quale&longs;-nam &longs;int inclinationes à Deo impre&longs;&longs;æ;
quemadmodum dictum iam e&longs;t. Pergis,
te impre&longs;&longs;am e&longs;&longs;e eiu&longs;modi, quæ varijs impedimentis &longs;i&longs;ti qui
dem poßit, &longs;ed non de&longs;trui, aut etiam minui; an non &longs;ublato
impedimento motum redintegraret?
figmenta, quor&longs;um po&longs;tulas, vt illa adaugeam? Ne
que enim vim po&longs;&longs;e &longs;i&longs;ti, quin &longs;imùl de&longs;truatur, pro
babile puto.
uibus reipsâ inditam non e&longs;&longs;e concludas. Sed quamobrem
talem non habeam, ac eam præ&longs;ertim, quæ grauibus
indita e&longs;t; tum in ip&longs;is Epi&longs;tolis, tum in iis, quæ hacte
nus deduxi, inculcatum &longs;atis. Vnde & cùm &longs;ic rogas,
figmenta recurris?
qualis &longs;it, quam detrectem; & cur veritatis amore nul
lum non moueam lapidem, vt &longs;altem, &longs;i qua eius vm
bra, aut &longs;imilitudo occurrat, experiar. Et non latet me
quidem quàm multis difficultatibus omnia inuoluan
tur: &longs;ed hoc ip&longs;um e&longs;t, ob quod mea inania figmenta
non di&longs;&longs;imulo, vi&longs;urus an &longs;int, qui pleniora faciant. Sa
nè vbi ex intellecta tuo modo inclinatione declaratum
fuerit, non &longs;olùm quî &longs;aluari valeant præmi&longs;&longs;a illa in
commoda; &longs;ed etiam, qua ratione fiat, vt res grauis de
cidens, nulla &longs;uperaddita inclinatione, acceleretur, &
grauior, quàm fuerit initio, euadat, inclinatiorque
proinde fiat, ac eâ quidem, qua ob&longs;eruatur, propor
tione, non alia: & rursùs, vnde-nam contingat, cur
Saxum pondo
quàm lapis duellaris: &longs;ecus ac Ari&longs;toteles tuo illo
principio inductus opinatus fuit, cæteraque &longs;imilia;
tum non detrectabo, &longs;ed exo&longs;culabor, complectar,
tuebor, & valere longè iubebo non &longs;olùm quæ inania
&longs;unt, &longs;ed quæ plena etiam figm enta.
XX.
Rem con&longs;equenter adoriris, &,
quis,
rium e&longs;&longs;et, vt quo Terræ viciniora e&longs;&longs;ent, eò fortiùs ab ea
traherentur, vt in Ferro, ac Magnete euidenter contingit.
in re graui attractionem &longs;implicem à compo&longs;ita, &longs;eu
adiectitia, aëris
re nempe e&longs;t grauitas &longs;implex, quæ lapidi competit,
vbicumque &longs;it, & dum accipitur extra morum: ex po
&longs;teriore compo&longs;ita, quæ eidem lapidi, dum mouetur,
competit, & tanto quidem maior, quantò fuerit mo
tus vehementior. Deinde dico, debere quidem attra
ctionem &longs;implicem e&longs;&longs;e fortiorem propè, quàm procùl:
verùm di&longs;crimen in&longs;en&longs;ile e&longs;&longs;e, nec po&longs;&longs;e agno&longs;ci, ni&longs;i
in di&longs;tantia, intercapedineve multorum milliarium. Vt
enim, cùm &longs;it vniuersè verum tractionem ferri à Ma
gnete e&longs;&longs;e fortiorem propè, quàm procùl, inob&longs;erua
bile tamen e&longs;t di&longs;crimen, ni&longs;i interualla attractionis
per palmos, aut &longs;altem digitos &longs;umantur; quandò &longs;i a&longs;
&longs;umas per mille&longs;imas, aut cente&longs;imas, imò decimas
parteis digiti, nulla e&longs;t diligentia, qua interno&longs;ci quid
quam po&longs;&longs;it: ita cùm verum fuerit trahi à Terra lapi
dem tantò potentiùs, quantò propinquiùs, tantò debi
liùs, quantò remotiùs; ob&longs;eruari quidem poterit di&longs;
crimen, &longs;i interualla accipias tanta, quanta, exempli
gratiâ, e&longs;t, ip&longs;iu&longs;met Terræ &longs;emidiameter: at &longs;i accipias
interuallum, quod &longs;emi-diametro minus &longs;it, non
e&longs;t, cur po&longs;&longs;e fieri di&longs;crimen &longs;en&longs;ibile &longs;peres. Nempe,
&longs;i Terram admi&longs;eris e&longs;&longs;e Magnetem quemdam ingen
tem, vides profectò, &longs;i vel ad ip&longs;am v&longs;que Lunam,
Terræ virtutem extenderis, virtutem Magnetis longè
&longs;en&longs;ibiliùs per digitos decre&longs;cere, quàm Telluris virtus
per &longs;emidiametros decre&longs;cat: quippe cùm nullum Ma
gnetem videas, qui attrahat ferrum è tot digitis, quot
interponi. Vnde & cùm infers,
graue quodcumque iuxta Terram &longs;uspen&longs;um, aut ip&longs;i etiam
Terræ in&longs;i&longs;tens maius exhibere pondus, quàm longiùs à Terræ
&longs;uspen&longs;um: itemque per centum pedes Terræ vicinos velociùs
de&longs;cendere, quàm per totidem alios pedes à Terra remotiores:
Dico, ne, &longs;i turrim quidem habueris tribus, pluribú&longs;ve
milliaribus altam, exhiberi po&longs;&longs;e pondus maius ad
pedem turris, quàm ad fa&longs;tigium, quoniam decremen
tum attractionis (& con&longs;equenter grauitatis) quod &longs;e
cundum altitudinem turris fiet, erit longè in&longs;en&longs;ibi
lius, quàm &longs;it decrementum virtutis Magnetis per mil
le&longs;imam partem digiti. Res &longs;e perinde habet, vt &longs;i ac
ce&longs;&longs;eris ad Nam
verum quidem e&longs;t apparentem arboris magnitudinem
continenter incre&longs;cere; at non proptereà vbi fueris,
vno, duobus, tribus, imò pluribus pa&longs;&longs;ibus promotior,
ob&longs;eruabile erit aliquod di&longs;crimen magnitudinis in
cre&longs;centis. Atque eadem quidem erit cau&longs;&longs;a, quare
acceptis pedibus altitudinis aliquot, &longs;iue ad fa&longs;tigium,
&longs;iue ad medium, &longs;iue ad pedem turris, lapis eos vbivis
æquè velociter percurrat; quoniam & &longs;implex attractio
erit ad &longs;en&longs;um eadem; & compo&longs;ita pari modo ad ac
celerationem conducet. Heinc &, cùm paucis inter
po&longs;itis in eandem &longs;ententiam concludis,
tur grauia Magneticè deorsùm à Terra non trahi:
hoc euidens fiat, euidens priùs fieri debere, attractio
nem ferri à Magnete &longs;en&longs;ibiliorem e&longs;&longs;e vna digiti mil
le&longs;ima parte prope ip&longs;um Magnetem, quàm duabus. Quippe &longs;eruanda proportio e&longs;t inter attrahentia, attra
cta, & interualla attractionis.
tolerabilem in Religione Po&longs;itionem.
XXI.
Quæ &longs;elegi&longs;ti prætereà, tanquam
litate admi&longs;&longs;a à me,
nem attinentia; ea continentur verbis illis, quibus repe
tis me dixi&longs;&longs;e, O
decrementum, omnemque alterationem, qua calor, frigus, hu
mor, &longs;iccitas; itemque color, odor, &longs;apor, & qualitates aliæ
gignuntur, nihil videri e&longs;&longs;e aliud, præter motiones localeis, qui
bus rerum principia, tenuißima licet, atque in&longs;en&longs;ibilia, variè
inter &longs;e concernuntur, excernuntur, accedunt, ab&longs;cedunt,
tran&longs;ponuntur,Ego verò, ob&longs;tupui &longs;anè hæc, quæ
&longs;unt merè Phy&longs;ica, & ad &longs;tatum purè naturalem atti
nent, tran&longs;ducta abste fui&longs;&longs;e in Theologiam, ac &longs;tatum
&longs;upernaturalem. Quippe oportet non i&longs;ta modò atro
lapillo &longs;ubnotare, &longs;ed etiam quicquid dici pote&longs;t ab
vniuer&longs;is Phy&longs;icis, &longs;i nihil planè dicendum e&longs;t, quod
pari ratione non po&longs;&longs;it tran&longs;duci, parique modo acci
pi; vt &longs;i nihil di&longs;tinguendum foret inter id, quod fit
&longs;olis naturæ viribus, & id, quod fit, fierive pote&longs;t &longs;uper
naturali virtute. Cau&longs;&longs;aris primùm,
& Epicuri Atomos tanto iam tempore à Regno Philo&longs;ophico
merito &longs;uo ex&longs;ulanteis, & tot iam &longs;æculorum, ac &longs;apientum
omnium præiudicio damnatas reuocare ab ex&longs;ilio, iterumque
in Academiam retrudere moliar. At ego nihil molior,
méque eum non habeo, qui retrudere, reuocareve ali
quid valeam: &longs;ed quia veritatis de&longs;iderio teneor, & il
lam tamen (&longs;eu hebetudo, &longs;eu infœlicitas mea e&longs;t) non
reperio in Philo&longs;ophico, quod tu dicis, Regno; idcircò
o&longs;tendere quædam ve&longs;tigia propiora, ac tutiora po&longs;
&longs;int. Et Epicuro quidem, vt pote iuniori, te&longs;timonium
dicere Ari&longs;toteles non potuit; &longs;ed Democrito tamen
dixit, cùm cum non commendauit modò, &longs;ed prætulit
etiam Platoni, quem aliunde Sancti Patres Ari&longs;toteli
ip&longs;i prætulerunt: quantumcumque ip&longs;e deinde recla
mantibus Patribus,
rit, ex&longs;ulante &longs;imùl cum aliis Platone. Ac meritó
ne, an immeritò Atomi cum iis ex&longs;ulent (
Platone dico, cumque aliis, pr&ecedil;ter Demoeritum, & Epi
curum, viris &longs;apienti&longs;&longs;imis, qui ip&longs;i quoque illas &longs;ub
aliis a&longs;&longs;erüere nominibus) non e&longs;t heic di&longs;&longs;erendi lo
cus. Hoc &longs;olùm dico, videri po&longs;&longs;e a&longs;&longs;ertores Atomo
rum nihil magis pecca&longs;&longs;e, quàm ip&longs;e peccârit Ari&longs;tote
les, quòd e&longs;&longs;e dixit Materiam primam. Siquidem ip&longs;is
Atomi nihil aliud &longs;unt, quàm prima Materies, ex qua
primitùs omnia componuntur, in quam vltimò omnia
re&longs;oluuntur; tamet&longs;i in eo à Materia Ari&longs;totelica diffi
deat, quòd &longs;it quid (&longs;cilicet
quòd quanta, quòd qualis (hoc e&longs;t figurata) quòd
prædita motu. Quòd &longs;i illi quidem Atomos fecerunt
æternas, ac ingenitas; an-non Ari&longs;toteles quoque &longs;uam
illam Materiam æternam, ac ingenitam fecit? Ft, &longs;i
nihilominùs Materia Ari&longs;totelis retinetur, quatenus à
Deo producta (&longs;ecus ac illi vi&longs;um fuit) initio Mundi
a&longs;&longs;eritur: quid retinere Atomos vetat, quatenus pro
ductæ à Deo (&longs;ecus ac i&longs;tis placuit) initio Mundi a&longs;&longs;e
runtur? Æqua certè conditio e&longs;t; neque, &longs;i quis
cautione admittat e&longs;&longs;e Atomos, videtur e&longs;&longs;e illi magis,
XXII.
Et &longs;tatim quidem pò&longs;t admones,
litus calidos, frigidos, humidos, odoratos, ac &longs;apidos, è
plæri&longs;que corporibus ex&longs;piratos, velle vniuer&longs;im quo dictum e&longs;t
modo, de in&longs;en&longs;ibilibus corporibus ratiocinari, non videri e&longs;&longs;e
&longs;apientiæ, ac eruditionis meæ. Verùm, cùm id ego acci
piam, vt in&longs;ignem quandam tuæ erga me beneuolen
tiæ te&longs;tationem (nimirùm, cùm ego neque &longs;apiens &longs;im,
neque audire eruditus merear, volui&longs;ti tamen his voci
bus, pro tua bonitate, lenire cen&longs;uram) quod &longs;upere&longs;t,
non video &longs;anè, cur res &longs;pectata Phy&longs;icè à &longs;apientiæ
&longs;tudio aliena cen&longs;eatur. Quantum vis enim tu &longs;ecus
putes, dum contendis &longs;ufficere, &longs;i quis halitus calidos,
alió&longs;que ex&longs;pirari dicat: non ideo tamen improban
dum, &longs;i quis requirat prætereà è quibus principiis qui&longs;
que halitus &longs;it &longs;ingulariter contextus: &longs;i dicere proinde
po&longs;&longs;it, qualia requirantur principia, vt calidus, non
alius &longs;it; quomodo actionem eliciat, vt calefacere cen
&longs;eatur; quid imprimat rei patienti, vt dicatur illam ca
lefacere; aliaque id genus complura. Certè, vt præ
teream quos apud Platonem Socrates habet inter Sa
pienteis, Empedoclem, Heraclitum, Protagoram,
omnei&longs;que, præter Parmenidem, antiquiores (etiam
Homerum, & Epicharmum) quo&longs;que declarat fui&longs;&longs;e
ratione con&longs;imili philo&longs;ophatos, ac præcipuè dum
qualitates, cæteraque, nihil e&longs;&longs;e aliud, quàm motiones
exi&longs;timârunt: vt illos, inquam, præteream, &, vt de vno
Democrito, de quo iam dixi aliquid, loquar; Ecce, ne
Ari&longs;toteles quidem, licet in hi&longs;ce Elementis, qualitati
bu&longs;que vulgaribus con&longs;titerit, de&longs;ipere illum putauit;
fuerit, nihilque, quantum potuit, intactum præterm &longs;erit,Non e&longs;t verò etiam De
mocritus de&longs;ipere Plutarcho vi&longs;us, cùm ip&longs;um vnà, ac
Platonem Ari&longs;toteli ex eo prætulit,
& grauitatis inquirentes, non in ip&longs;is terra, & igne &longs;pecula
tionem finierint, &longs;ed ad ip&longs;a v&longs;que principia &longs;ola mente contem
plabilia, ea, quæ &longs;en&longs;ibilia &longs;unt, deducentes, fuerint ad v&longs;que
minima, & qua&longs;i &longs;emina, Non item M. Tullio, cuius verba &longs;unt:
loquar de Democrito? Quem cum eo conferre po&longs;&longs;um, non modò
ingenij magnitudine, &longs;ed etiam animi? Qui ita&longs;it au&longs;us ordiri:
Hæc loquor de vniuer&longs;o. Nihil excepit, de quo non profitea
tur. Quid enim e&longs;&longs;e potest extra vniuer&longs;a?
Quis hunc Phi
lo&longs;ophum non anteponat
inferioris ætatis, qui mihi cum illo collati, quintæ claßis viden
tur?
ne Laëitius, & cæteri habent. Nimirùm hæc pauca
&longs;unt &longs;atis; cum & tu prætereà ad alia re&longs;picias.
XXIII.
Ecce enim in&longs;tas (& humaniter &longs;anè)
meam &longs;agacitatem fugiat, quò tandem v&longs;que &longs;emel inducta
hæcper&longs;ua&longs;io proce&longs;&longs;ura videatur?
putas vlteriùs, quàm quò pote&longs;t procedere Ari&longs;toteleæ
per&longs;ua&longs;io.
dentur, præter localeis atomorum, vel
dicis)
tiones, de Formis &longs;ub&longs;tantialibus conclamatum e&longs;t. Et non
adiicis quidem quid incommodi con&longs;equatur, &longs;i eò v&longs;
que proce&longs;&longs;um fuerit: &longs;ed coniector tamen in&longs;inuare
mam v&longs;que rationalem procedatur. At vides &longs;anè
periculum pari ratione deuitatum iri, qua & deuitatur
in Ari&longs;toteleis &longs;cholis. Nam, vt generali Effato de
formis educibilibus ex Materia, adhibetur exceptio
Rationalis animæ, ex nihilo à Deo creatæ: ita generali
Effato de formis accidentalibus, eadem eiu&longs;dem Ani
mæ, vt à Deo &longs;imiliter creatæ adhibebitur; & vel ex eo
ip&longs;a Anima &longs;ub&longs;tantia e&longs;&longs;e comprobabitur, &longs;ecùs ac
formæ cæteræ, quòd &longs;ub&longs;i&longs;tat ip&longs;a per &longs;e: cæteræ verò
non &longs;ub&longs;i&longs;tant. Quid, quòd cæteræ non modò non
&longs;ub&longs;i&longs;tunt, &longs;ed neque dici quidem pote&longs;t, quid, aut vnde
habeant, vt &longs;ub&longs;tantiæ dicantur, ac &longs;int, & di&longs;tinctæ
quidem ab ip&longs;a materia; quandò &longs;uam illam &longs;ub&longs;tan
tialem &longs;uíque
ex quo fieri non admittuntur: neque ab ip&longs;a materia,
ex &longs;ub&longs;tantiali cuius entitate detrahi nihil volunt, quod
in formam abeat: adeò proinde, vt commentum inex
plicabile &longs;it, quòd interim Formas educi ex materia, il
liu&longs;ve potentia dicunt. Nam & quòd eò adiguntur, vt
explicent Formam educi ex materia, nihil e&longs;&longs;e aliud,
quàm fieri in materia, & dependenter ab illa; tum di
cunt prorsùs aliud, quàm quid &longs;it educi, &longs;iue extrò tra
his; tum non declarant vnde habeat e&longs;&longs;e, &longs;uamve enti
tatem hæc formæ &longs;ub&longs;tantia, quæ iam e&longs;t, & antè non
erat; quandò id totum non denotat ex quo facta, &longs;iue
vnde accepta &longs;it i&longs;ta realis entitas, quæ neque materia
&longs;it, neque vlla portio ip&longs;ius (cùm ob ip&longs;am eductam,
materia non cen&longs;eatur aliquid reale, &longs;eu entitatem vl
lam realem priùs habitam ami&longs;i&longs;&longs;e) & ip&longs;a proinde
dum in quo con&longs;i&longs;tat, dici, concipique non pote&longs;t. Quid etiam, quòd ip&longs;e Ari&longs;toteles &longs;ententiam &longs;uam ita
expo&longs;uit, Græcique eius Interpretes illam nobis &longs;ic tra
diderunt, vt planè videatur non alias, quàm acciden
taleis formas cognoui&longs;&longs;e? Accidentaleis, inquam,
prout accidens &longs;ub&longs;tantiæ opponitur, non e&longs;&longs;entiæ:
nam alioquin tam materiam, quàm formam, quàm
compo&longs;itum, eo e&longs;&longs;e &longs;en&longs;u
rentiam, quam genus, quam &longs;peciem
prædicati. Sed hæc iam dicenda pluribus non &longs;unt; ac
videndum potiùs, quod &longs;pecialiùs in&longs;tas; dum pergis
telis &longs;ententia.
XXIV.
quibus calor, frigus, humor, &longs;iccitas, itemque color, odor, &longs;apor,
& qualitates aliæ gignuntur, nihil e&longs;&longs;e aliud videntur, præter
localeis tenuißimorum corporum motiones: formæ igitur acci
dentariæ nullæ &longs;unt, mulióque minùs inueniri, & e&longs;&longs;e po&longs;&longs;unt
ab omni &longs;ub&longs;tantia &longs;eparatæ. Quid &longs;anctioribus igitur no
&longs;træ Religionis my&longs;teriis fiet?
timendum,
e&longs;&longs;e &longs;upponantur, & &longs;peciali &longs;olùm explicentur modo. Suusigni &longs;eruatur calor: &longs;uum frigus glaciei: &longs;uus &longs;apor
melli: &longs;uus odor ro&longs;æ: &longs;uus tympano &longs;onus: &longs;uus can
dor niui; &longs;ua lux Soli, &c. Cùm ex vulgari autem &longs;en
tentia explicari nequeat, in quónam con&longs;i&longs;tat energia,
& modus agendi illius eiu&longs;dem caloris, frigoris, &longs;aporis,
cæterarumque qualitatum; tentatur, an id declarari
ex tali hypothe&longs;i valeat. Neque verò ip&longs;e quoque
e&longs;&longs;e motionem quandam localem; &longs;altem agno&longs;eit al
terationem ab&longs;que motione locali non e&longs;&longs;e. Quòd
verò proptereà
quutus)
tia &longs;eparatæ non valeant:
non colligas pari modo ex Ari&longs;totelea &longs;ententia? Et, &longs;i
cùm Ari&longs;toteles manife&longs;tè faciat, qualitates, &longs;iue acci
dentaleis formas, in&longs;eparabileis à &longs;ub&longs;tantia, id admit
titur, quatenus &longs;olis viribus naturæ &longs;pectatis e&longs;t verum;
reiicitur autem, quatenus &longs;pectata Authoris naturæ
potentia e&longs;t fal&longs;um: quid e&longs;t, cur eædem qualitates, alio
licet modo, quàm Ari&longs;toteleo expo&longs;itæ, dici non va
leant ex&longs;i&longs;tere po&longs;&longs;e &longs;eparatæ à &longs;ub&longs;tantia, non na
turali quidem, &longs;ed diuina tamen virtute? Neque
enim e&longs;t, cur exi&longs;times calorem, v.g quà e&longs;t calor,
formaliterve, vt loquuntur, accipitur, e&longs;&longs;e ip&longs;a&longs;met ato
mos, atomorumve &longs;ub&longs;tantiam; vt neque idem calor
in &longs;ententia vulgari, ignis e&longs;t, eiu&longs;ve &longs;ub&longs;tantia. Quip
pe, vt in communi &longs;ententia calor e&longs;t formaliter quæ
dam qualitas &longs;ub&longs;tantiæ ignis attributa, quatenus eius
e&longs;t naturæ, vt calefacere, &longs;eu certo modo afficere corpo
ra &longs;ibi admota po&longs;&longs;it: ita etiam erit qualitas atomorum
&longs;ub&longs;tantiæ conueniens, quatenus &longs;ui motu, penetratio
neque in aliquod corpus, ip&longs;um di&longs;gregant, ex&longs;oluunt
que; & animatum &longs;ifuerit, non &longs;ine &longs;en&longs;u aliquo &longs;pe
ciali ip&longs;ius id faciunt. Quare & licet vi naturæ non
po&longs;&longs;it talis qualitas &longs;ine talibus e&longs;&longs;e atomis, ip&longs;arumve
&longs;ub&longs;tantia, eo modo, quo dices e&longs;&longs;e eandem ab&longs;que
igne, eiu&longs;ve &longs;ub&longs;tantia non po&longs;&longs;e, quatenus in neutra
&longs;olùm calidum: diuinitùs tamen
atomorumve &longs;ub&longs;tantia poterit, quam tu e&longs;&longs;e dices ab&longs;
que igne, illiu&longs;ve &longs;ub&longs;tantia po&longs;&longs;e. Et ratio e&longs;t, quia
vtrouis modo eadem e&longs;t &longs;ub&longs;tantia, à qua &longs;eparabilis
calor vi diuina defenditur; di&longs;crimenque &longs;olummodò
e&longs;t, quod tu dicas &longs;olùm &longs;ub&longs;tantiam, illi addant talem
&longs;ub&longs;tantiam, e&longs;&longs;e ex atomis contextam: quæ &longs;anè po&longs;i
tio ad &longs;eparabilitatem, in&longs;eparabilitatemve acciden
tium nec iuuat, nec nocet.
XXV.
Cùm idem verò proportione de cæteris dici
qualitatibus, &longs;iue accidentibus valeat; nihilo &longs;ecùs de
fendetur, explicabiturve augu&longs;ti&longs;&longs;imum Tran&longs;ub&longs;tan
tiationis my&longs;terium, &longs;i qualitates corporeas dependere
dixerimus ex &longs;ub&longs;tantia corporis, quæ ex atomis com
ponatur: quàm &longs;i dependere &longs;olùm vniuersè dicamus
ex &longs;ub&longs;tantia corporis; quatenus &longs;ub&longs;tantia corporea,
quæcumque ea &longs;it, componitur &longs;emper ex partibus,
particuli&longs;que, quas quomodocumque appelles (prout
variè &longs;ubdiuidendo aut infinitè pergere, aut peruenire
tandem ad atomos, &longs;eu indiuiduas licet) nihil penitùs
ad rem inter&longs;it. Videlicet vtrovis modo defendetur
Deum con&longs;eruare qualitates, &longs;iue accidentia, & Sacra
mentaleis &longs;pecies, &longs;epo&longs;itis, de&longs;tructi&longs;ve principiis, &longs;eu
partibus, mavis, &longs;ub&longs;tantialis compo&longs;itionis tam pa
nis, quàm vini; & in &longs;epo&longs;itæ, de&longs;tructæve &longs;ub&longs;tantiæ
locum, ac &longs;ub ij&longs;dem qualitatibus, accidentibus, aut
&longs;peciebus, &longs;ub&longs;tituere, collocareve &longs;ub&longs;tantiam glorio
&longs;i&longs;&longs;imam Corporis & Sanguinis Chri&longs;ti. Heinc proinde
quando requiris,
gari, & quæ haberi &longs;olet Ari&longs;totelea &longs;ententia, Vt toto
nempe corde, atque ore credamus, atque profiteamur
quicquid credendum, profitendumque Sacro &longs;ancta,
Catholica, Apo&longs;tolica, & Romana Eccle&longs;ia p
Vt non modò Epicurum, & Democritum; &longs;ed Ari&longs;to
telem quoque, & Platonem, & alios omneis flocci
faciamus, quoties proferent aliquid, quod &longs;it à &longs;acra
Fide alienum: Vt ip&longs;um naturale lumen nihili duca
mus, præ fidei lumine; & quicquid ab eo mon&longs;tratur,
damnemus, &longs;i i&longs;tud mon&longs;tret oppo&longs;itum: Vt defen da
mus non e&longs;&longs;e apud Deum impo&longs;&longs;ibile omne verbum;
& quod &longs;peciatim attinetad &longs;eparabilitatem, exi&longs;ten
tiamque aut &longs;ub&longs;tantiæ &longs;ine accidentibus, aut acciden
tium &longs;ine &longs;ub&longs;tantia, demus Deum aliquid po&longs;&longs;e, quod
nos fateamur inue&longs;tigare non po&longs;&longs;e, cuiu&longs;que tota ra
tio &longs;it ip&longs;a potentia facientis. Habes quid putem de
bere fieri, & quod &longs;anguinis effu&longs;ione propugnare pa
ratus &longs;im. Quod me deinde admones,
Deum immortalem, ne mei nominis authoritate, infirmiori
bus quidem errandi, cæteris verò præconceptam de ingenij mei,
ac iudicij &longs;agacitate opinionem imminuendi præbeam occa&longs;io
nem:Siquidem, quamvis
longè ab&longs;im, vt vllam mei nominis authoritatem e&longs;&longs;e
agno&longs;cam, & hoc eulogium &longs;ingulari tuæ humanitati
totum debeam: quamvis etiam mihi nihil &longs;it curan
dum, ne minuatur de me opinio, quæ merito meo e&longs;&longs;e
nulla pote&longs;t: attamen, quod caues, ne infirmioribus er
randi occa&longs;ionem præbeam; rem caues mihi planè
cauendam, & pro qua me tibi ob&longs;trictum pro&longs;iteor:
ne vlla vnquam, vel minima errandi occa&longs;io à me &longs;ug
geratur.
Ferant-ne magis Sacræ literæ Tellurem in centro,
quàm extra centrum circumuolui.
XXVI.
Venio nunc ad ea, quæ habes in &longs;ecundam
Epi&longs;tolam. Memoras imprimis, quod initio dixi,
videri infirmum reddi argumentum, quo &longs;olemus vulgò quie
tem a&longs;&longs;erere globo Telluris. Et po&longs;tquàm addidi&longs;ti,
à me dictum,
ciem moueri haud dubiè Tellurem: &longs;ed &longs;olùm vt in&longs;inuem
conquirendam e&longs;&longs;e rationem veri&longs;imiliorem:Si &longs;copus i&longs;te tuus est, collima&longs;ti: pluribus
opus non e&longs;t; adeptoque iam fine fru&longs;trà, ac inutiliter labo
ras. Sed ohe! humanitas tua adeóne euadit &longs;euera, vt
&longs;cribenti ad amicum ex&longs;patiari non liceat, nec præoc
cupare, &longs;i quid ille fortè aut requi&longs;iturus, aut quomo
documque habiturus e&longs;&longs;e iucundum videatur? An-non
&longs;pecialis, vt Dialogorum, &longs;ic Epi&longs;tolarum e&longs;t mos; &
ille quidem non qualis e&longs;&longs;e angu&longs;ta &longs;olet &longs;emita, &longs;ed po
tiùs qualis regia via, imò & qualis apertus campus? Alia
&longs;anè &longs;unt genera &longs;cribendi, quæ pro cuiu&longs;que in&longs;tituto
certis legibus, qua&longs;i frænis, atque catenis compe&longs;cun
tur; at genus Epi&longs;tolicum &longs;olutum, liberumque e&longs;t; &
cùm liceat in cæteris variè per vices digredi; facere in
Epi&longs;tolis etiam
poris ferenda; quanquam & tuum affectum probo,
dum &longs;ollicitus es, ne fru&longs;trà pretio&longs;am adeò rem de
teram. Rogas con&longs;equenter, S
quid rei &longs;it, quòd plurimorum &longs;imilium conglobatione præmi&longs;&longs;a
&longs;ic interrogem:
lius, probabilius, magis con&longs;entaneum, moueri Terram ver&longs;us
ortum, ac totam Mundi machinam, &longs;ideraque omnia &longs;alutare
ex ordine; quàm totam illam machinam, totque, & tanta &longs;i
dera circum ip&longs;am ire, eamque &longs;alutare?
quod tantopere vrgeo, atque exaggero, maiora ex Solis, fixa
rumque, quàm ex Telluris motu ab &longs;urda &longs;equi, atque incom
moda?
C
dam, vulgatum illud aliorum Philo&longs;ophorum à proiectilium
motu petitum argumentum infirmum e&longs;&longs;e, atque inualidum?
Tandem &, C
tu tam prolixam, nec ad prædictum finem nece&longs;&longs;ariam adiun
gam disputationem, in qua non modò Copernicanorum argu
menta omnia, & rationes qua po&longs;&longs;um, & valeo dicendi facul
tate
confirmare, &longs;ed aliorum quoque obiectiones infirmare pari &longs;tu
dio, & contentione moliar?
&longs;am iam recita&longs;ti illis verbis, quibus me id &longs;olùm dixi
facere,
liorem. Atqui conuicta illa ratione ex proiectilibus
de&longs;umpta quie&longs;cendum fuit, nec aliæ mouendæ: Ve
rùm aliæ quoque vi&longs;æ &longs;unt mouen dæ; nequeid omninò
abs re, atque incohærenter factum. Quia enim iure
obiici potuit, fru&longs;trà in&longs;inüari à me conquirendas e&longs;&longs;e
tæ fuerint; ideò vi&longs;us &longs;um non debere cæteras intactas
prætermittere, vt o&longs;tenderem quatenus eas quoque ar
bitrarer e&longs;&longs;e infirmas. Exi&longs;timaui autem, &longs;i licuit eam
&longs;uffodere, quæ qua&longs;i murus aheneus erat, & quam tu
t
hibere quò minùs cæteræ &longs;altem mediocri ar
uiolatiores manerent: aut magis extra aleam, vt vel
non po&longs;&longs;ent, vel non deberent parem experiri Quod autem &longs;imùl interrogaui, aut exaggeraui
aliquid in Copernicanorum gratiam; id egi, vt difficul
tates vberiùs innote&longs;cerent, patefaceremque quibus
argumentis, cuique rationum oppo&longs;itarum probabili
tati occurrendum &longs;it, &longs;i quis aduer&longs;us Copernicanos
præ&longs;tare voluerit rationem inuictam. Et quæris,
nato a&longs;&longs;erendam, propugnandamque a&longs;&longs;ump&longs;i&longs;&longs;em?
&longs;anè ampliùs facturus fui, qui neid quidem fui a&longs;&longs;um
pturus. Alios, qui a&longs;&longs;umunt, vberiore quadam, atque
concinniore methodo vides agere: ego quidvis com
memoraui breuiter, ac præpo&longs;terè; quippe vt &longs;e fors
obtulit, mentique, & manui properanti obiecit.
XXVIII. Sequitur,
ita inconueniens vi&longs;um iri, &longs;i cum Heraclide Pontico, &
Ecphanto Pythagoreo Terram in medio Vniuer&longs;i constitutam
quotidiano tantum motu circa proprium axem moueri conten
derem; &longs;ic enim concitatißimum illum Siderum motum, qui
plæri&longs;que
tollerem; ac &longs;atis moderatum, quo Sacris literis faciliùs &longs;atis-
quem proprium vocant, retinerem; atque in portento&longs;a, quæ ex
Copernici opinione &longs;equuntur, incommoda, atque ab&longs;urda non
inciderem. Heic verò tu me &longs;ic alloqueris, qua&longs;i ego
Philolai, aut Ari&longs;tarchi &longs;ententiam amplectar, & rem
proinde faciam minùs tolerabilem, quàm &longs;i &longs;equerer
hancà te Ego verò neque me illam ample
cti profiteor, neque i&longs;tam habeo tolerabiliorem, pro
pter eadem Scripturæ loca,
dasti Terram &longs;uper &longs;tabilitatem &longs;uam; Firmauit orbem Ter
ræ, qui non commouebitur:
Sol ne moueatur; Regre&longs;&longs;us e&longs;t Sol;
putas ex moderati, ac immoderati motus di&longs;tinctio
ne ab authoribus huius &longs;atisfieri: complana&longs;ti pe
nitus viam illius defen&longs;oribus, qui &longs;e tuebuntur, quòd
&longs;acra Scriptura dum patitur minus, non prohibeat ma
ius. Nec verò ip&longs;is di&longs;plicet modò concitati&longs;&longs;imus
ille motus, attributus vulgò primo mobili Sidera om
nia circum-rapienti; &longs;ed etiam inconcinnitas, qua ne
ce&longs;&longs;e e&longs;t Planetarum directiones, regre&longs;&longs;iones, &longs;tatio
nes, & non pauca alia ab Heraclide quoque, & Eephan
to &longs;aluentur. Quod autem &longs;pectat ad portento&longs;a, quæ
dicis ab&longs;urda, & incommoda; ip&longs;i nulla e&longs;&longs;e agno&longs;cunt:
vnde & ni&longs;i aduer&longs;am habeant &longs;acræ Scripturæ autho
ritatem, exi&longs;timant &longs;e prorsùs nihil intolerabile tueri. Sequitur adhûc,
phos tantum e&longs;&longs;e, &longs;ed etiam Chri&longs;tianos, Philo&longs;ophiamque
no&longs;tram nec debere, nec verò etiam po&longs;&longs;e à Chri&longs;tiana fide
di&longs;crepare. Id verò e&longs;t &longs;anè tua pietate dignum; ip&longs;eque
non modò a&longs;&longs;entior, verùm etiam palam profiteor, ac Id vnum &longs;upere&longs;t, vt no&longs;catur, quid Philo&longs;ophia
proferat à Chri&longs;tiana di&longs;crepans fide. Cùm enim Phi
lo&longs;ophia quam plurima doceat, quæ vera habentur, &
ab omnibus viris piis, atque Chri&longs;t anis admittuntur;
tamet&longs;i ip&longs;is refragari &longs;acræ Literæ apertè videan
tur; par e&longs;t profectò Literas &longs;acras eam pati interpreta
tionem, vt o&longs;tendi po&longs;&longs;it eas, cùm veræ &longs;int, veritati
non repugnare. Id autem D.
Augu&longs;tinus allato exem
plo præclarè in&longs;inüat; cùm difficultate propo&longs;ita,
modo non &longs;it
quod &longs;criptum est in libris no&longs;tris, Qui extendit cælum &longs;icut
Pellem?
illi dicunt; hoc enim verum e&longs;t, quod diuina dicit authoritas,
potiu&longs;quàm illud, quod humana infirmitas coniicit. Sed &longs;i
fortè talibus illi documentis probare potuerint, vt dubitari inde
non debeat; demon&longs;trandum est, hoc, quod apud nos est de Pelle
dictum, veris illis rationibus non e&longs;&longs;e contrarium. Et rursùs,
Quod &longs;i factum fuerit, non hoc habebat diuina Scriptura; &longs;ed
hoc &longs;en&longs;erat humana ignorantia. Haud-dubium proinde,
quin &longs;anctus Doctor, &longs;i in no&longs;tra incidi&longs;&longs;et tempora;
aut &longs;i eius temporibus fui&longs;&longs;et tota Terra, vt nuper e&longs;t
factum, circum-nauigata: tum agniturus Antipodas
fui&longs;&longs;et, tum ad humanam potiùs ignorantiam, quàm
ad Scripturæ diuinæ &longs;en&longs;um, præhabitam &longs;uam relatu
rus &longs;ententiam, quam vidi&longs;&longs;et certi&longs;&longs;ima experientiæ
veritate refelli. Quæ memoro &longs;olùm, vt intelligamus,
non quicquid Philo&longs;ophia docet, quod videatur prima
fronte à Literis &longs;acris e&longs;&longs;e di&longs;crepans, proptereà verè
di&longs;crepare.
que ignorata
XXIX.
Pergis con&longs;equenter,
tu fortè ip&longs;e &longs;entias, &longs;ed quid æ&longs;timaturi &longs;int plærique alij, qui
tua vel authoritate, vel rationibus inducti, &longs;ibi per&longs;ua&longs;erint
Telluris globum inter Planetas moueri.
vnum è Planetis &longs;ine dubio e&longs;&longs;e Terram, quæ cùm incolas ha
beat, procliue erit deinde etiam credere, in cæteris quoque Pla
netis, atque adeò in ip&longs;is item inerrantibus
dee&longs;&longs;e; & tantò quidem præstantiores, quantò reliqua Sidera
Terram magnitudine, & perfectione excedunt. Heinc
ne&longs;is in &longs;u&longs;picionem vocabitur, dum ait Terram ante reliqua
S
minarent Terram, temporaque, & annos metirentur. Inde
tota Verbi Incarnati œconomia, atque Euangelica veritas
&longs;u&longs;pecta reddetur; imò & tota fides
ponit, & docet
creaturarum habitationem, &longs;ed &longs;olùm, vt Terram &longs;ua luce
collustrent, fœcundentque, e&longs;&longs;e à Deo authore producta.
Verùm, religio&longs;i&longs;&longs;ime Vir, i&longs;ta imprimis in me non
quadrant, qui Telluris globum e&longs;&longs;e vnum ex Planetis,
aut moueri inter Planetas neque dico, neque defendo;
&longs;ed in eos potiùs, qui rem & &longs;entiunt, & profitentur &longs;ic
&longs;e habere. Neque verò aut ego vlla &longs;um authoritate,
qui &longs;i e&longs;&longs;em aliqua, ab&longs;it à me, vt vellem ip&longs;am placito
fal&longs;o patrocinari: aut rationes vllæ meæ &longs;unt, &longs;ed &longs;uo
rum dumtaxat authorum; quas quia opponere nobis
&longs;olent, dum no&longs;tras ip&longs;is obiicimus, ideò di&longs;&longs;imulare
vi&longs;um non e&longs;t, propter iam expo&longs;itam cau&longs;&longs;am. Deinde
quutiones fuerint, ablegandam igitur e&longs;&longs;e vniuer&longs;am
Phy&longs;icam, quatenusnullum e&longs;t placitum, ex quo dicere
non po&longs;&longs;imus, deduci po&longs;&longs;e ab aliquibus incommoda
non ab&longs;imilia. Ponatur enim, exempli cau&longs;&longs;a,
Terram sphæricam:
bilem circumquáque; & procliue fore credere Antipo
das. Inferetur, eos non potui&longs;&longs;e ab Adamo propagari;
atque idcircò Chri&longs;tum Dominum non e&longs;&longs;e eorum
Redemptorem. Nouum proinde Te&longs;tamentum in &longs;u&longs;
picionem vocatum iri, & totam Verbi Incarnati œco
nomiam, ac cætera his con&longs;entanea; vt prætereantur
portento&longs;a ab&longs;urda, & incommoda de hominibus,
ædificiis, arboribu&longs;que pen&longs;ilibus, quæ no&longs;ti obiecta
aliquando fui&longs;&longs;e. Ponatur &,
quemadmodum Terram; illuminari à Sole, obtenebre&longs;ceré
que, non &longs;ecùs, ac Terram; Eclip&longs;in pati propter Terram, vt
Terra patitur propter ip&longs;am; habere &longs;uperficiem perinde
maculo&longs;am, ac appareret habere
retur; habere monteis, valleis, planities, & alia id genus, eo
modo, quo Terram:
alteram Terram; ea&longs;dem in Luna, ac in Terra genera
tiones fieri; e&longs;&longs;e in ea incolas; & procliue fore etiam ho
mines credere, qui ex Adamo propagati non &longs;int,
à Chri&longs;to redempti.
quæ docet Lunam factam, vt illuminet Terram, non vt
ip&longs;am obtenebret, aut ab illa obtenebretur; vt incolas
habeat, &c. Ponatur
Firmamentum; & Stellarum minutulas e&longs;&longs;e decies octies, ma
iu&longs;culas verò centies octies maiores, quàm Terram; & con-
quàm Lunam; quamlibet i&longs;tarum plu&longs;quàm quater millies:
Concludetur igitur
& latam, vt po&longs;&longs;it meritò cum cæli altitudine compa
rari: cùm &longs;acræ tamen Literæ i&longs;ta interualla qua&longs;i ex
æquo habeant,
dero in infernum ades: &longs;i &longs;ump&longs;ero pennas meas, &c.
pectam
magna Luminaria, & Lunam e&longs;&longs;e alterum duorum,
quòd ip&longs;o quidem Sole &longs;it minus; at non tot Stellis, ac
præ&longs;ertim Procliue proinde fore
credere, e&longs;&longs;e igitur Stellarum orbeis Terra, ac Luna lon
gè præ&longs;tantiores; neque e&longs;&longs;e adeò &longs;epo&longs;itos, vt va&longs;tita
tes inutiles &longs;int, &longs;ed debere maiore ratione, & à præ
&longs;tantioribus inhabitari incolis; ac proinde, cùm tota
eorum lux ne tantum quidem in&longs;eruiat ad illuminan
dum Terram, & dimetiendum tempora, quantum in
&longs;eruit vna lux Lunæ: e&longs;&longs;e ergo illos à Deo in alium
v&longs;um conditos, &c. Denique ponatur quicquid vo
les aliud; & pari ratione opponetur po&longs;&longs;e his &longs;imilia
concludi; procliue e&longs;&longs;e ea credere; &longs;acrarum Literarum
fidem, totiu&longs;que Religionis fundamenta nutare.
XXX.
Quòd &longs;i, cum i&longs;ta nobis videantur deduci
po&longs;&longs;e ab aliquibus, non ideò minùs placita, quæ &longs;unt
memorata de rotunditate Terræ; de comparatione
Lunæ cum Terra; de Terræ, Lunæque exilitate, & am
plitudine Stellarum, à viris, qui reuerâ pij, & Chri&longs;tiani
&longs;int, defendantur; quatenus illæ con&longs;equutiones, vbi
præ&longs;ertim longiùs, & aduer&longs;us Fidem procedunt, im
probabiles &longs;unt, nulláque po&longs;&longs;unt aut ratione, aut ob-
tate con&longs;tituuntur, corruunt; fumu&longs;que cùm &longs;int, in
fumum excedunr: eadem de cau&longs;&longs;a dicent i&longs;ti, hæc, quæ
videntur po&longs;&longs;e deduci ab aliquibus, non debere ob&longs;ta
re, quò minùs placitum de motu Telluris inter Plane
tas con&longs;titutæ, à viris, qui reuerâ pij, & Chri&longs;tiani &longs;int,
defendatur. Nimirùm contendent, cùm Terra id
iuris habuerit, vt inter Planetas ver&longs;ata, heinc Vene
rem, Mercurium, Solem, illeinc Martem, Iouem, Satur
num, ac aliunde circum &longs;e Lunam proximè circumdu
ctam &longs;ortiatur; non idem iuris proptereà aliis Planetis
competere, quos propterillam Deus creârit. Neminem
proinde &longs;anæ mentis colligere po&longs;&longs;e e&longs;&longs;e aut in Luna,
aut in aliis Planetis, Stelli&longs;que fixis incolas, qui autho
mines &longs;int, aut &longs;imilitudinem cum hominibus habeant. quoniam, &longs;i non omnis tellus omnia fert; & Europa,
Americáque, Scythia, & Libya, quæ eiu&longs;dem globi
partes &longs;unt, diuer&longs;i&longs;&longs;ima proferunt; quantò æquius &longs;it
reputare, non po&longs;&longs;e eadem na&longs;ci, educari, degere in
Luna, atque cæteris, qui &longs;unt orbes planè diuer&longs;i? Si
quædam proinde oriantur, & intereant aut in Planetis
cæteris, aut in aliis Siderum globis, non po&longs;&longs;e illa e&longs;&longs;e
præ&longs;tantiora homine; quatenùs nihil e&longs;&longs;e pote&longs;t aut
ratione præclarius, aut &longs;upernaturalibus donis, quibus
ille &longs;olus donatur, diuinius. Cæterùm enim po&longs;&longs;e e&longs;&longs;e
corpora maiora, robu&longs;tiora, durabiliora, aut aliis qui
bu&longs;dam adiunctis perfectiora, quàm homines, id ne
negari quidem po&longs;&longs;e; cùm etiam in ip&longs;amet Terra mul
ta corpora id genus na&longs;cantur. Et non proptereà Ge
ne&longs;in in &longs;u&longs;picionem po&longs;&longs;e vocari; quoniam ea docet,
Stellas, vt Terram illuminent, &longs;intque in&longs;igna, & tem
pora; & non docet tamen Sidera ad hec &longs;olùm facta. Alioquin enim inferretur, e&longs;&longs;e quidem factum Solem,
vt illuminet Terram, &longs;ed non vt Lunam, aut Venerem,
quod Gene&longs;is tacet: &, Lunam e&longs;&longs;e quidem factam, vt
Terram illuminet; &longs;ed non vt (quod mox dictum e&longs;t)
tenebras in ip&longs;am inducat; nam & Gene&longs;is id non dicit. Vt prætereatur, &longs;i, quia Gene&longs;is aliud non declarat, ni
hil agitur aliud à Sideribus; non igitur Solem calefa
cere, vrere, fouere, &c. neque Lunam &longs;peciale impe
rium in res humidas exercere, in
medullas, & id genus &longs;imilia. Non item &longs;u&longs;pectam
reddi Verbi Incarnati œconomiam, veritatem Euan
gelicam, totam ip&longs;am fidem Chri&longs;tianam; quoniam ea
perinde illibata conferuatur; quatenus nullæ aliæ na
turæ rationales, & redemptionis, gratiæ, gloriæque &longs;u
pernaturalis capaces vlla ratione colligi po&longs;&longs;unt ex&longs;i
&longs;tere, præter homines in Terris degenteis; in quibus &longs;o
lis incarnatus Dei Vnigenitus vi&longs;us e&longs;t, & cum homi
nibus conuer&longs;atus. Neque verò cæteros globos, &longs;i in
ip&longs;is creaturæ quædam generantur, & corrumpuntur,
dici magis po&longs;&longs;e ab ijs habitari, quàm dicantur loca
Terræ de&longs;erta à &longs;axis, herbis, culicibus, cæteri&longs;que id
genus rebus; neque proptereà dici po&longs;&longs;e incolas habere,
qui &longs;int homines, aut cum hominibus comparandi. Nam &longs;upponere quidem, & docere Fidem &longs;acram, non
habitari Sidera ab aliis aut hominibus, aut naturis, quæ
pari modo vel ratiocinentur, vel participes &longs;int dono
rum &longs;upernaturalium: at non &longs;upponere, nec docere,
maculas quidem in Sole na&longs;ci, ac perire; non in cælo
reliquo Cometas, atque nouas Stellas. Nec porrò
&longs;acrum ip&longs;um Textum, cùm dicit Solem, & cætera Si
dera facta, vt Terram illuminent, negare prop tereà,
quin ip&longs;a aliude &longs;int in &longs;eip&longs;is, ac præter lucem aliquid;
& id genus alia, quæ tamen non dicit, vt nec cætera,
quæ no&longs;&longs;e nihil intere&longs;t ad &longs;upernaturalem &longs;alutem. Scilicet præclarè &longs;anctus ille Doctor,
&longs;ed Spiritum Dei, qui per ip&longs;os loquebatur, nolui&longs;&longs;e i&longs;ta docere
bomines, nulli ad &longs;alutem profutura. Eiu&longs;modi &longs;unt, alia
que affinia, quæ prædixi vereri me, ne illi fuerint re&longs;
pon&longs;uri.
XXXI. Subiicis,
publicum diuulgentur, & à viris præ&longs;ertim, qui &longs;ua authori
tate fidem facere videantur; & quàm non immeritò iam inde
à Copernici tempore Eccle&longs;ia &longs;emper huic &longs;e errori oppo&longs;ue
rit: eumque etiam nouißimè non
ais, &longs;ed &longs;upremum Eccle&longs;iæ caput Pontificio decreto in Galileo
damnauerit, & vt ne in posterùm verbo, aut &longs;cripto docere
tur, &longs;anctißimè prohibuerit. Heic non repeto, quod illi
tuebuntur, non &longs;equi ex ea, quam diuulgant, &longs;ententia
id, quod tu times, periculum. Tria potiùs dico.
Vnum,
me ab illis non &longs;tare, vel ex eo &longs;olo, quòd dicis eorum
opinionem haberi Eccle&longs;iæ &longs;u&longs;pectam. Videlicet ego
Eccle&longs;iæ alumnus, ita me totum ip&longs;i deuoueo, vt quic
quid illa improbat, ip&longs;e anathema conclamem. Alte
rum, fui&longs;&longs;e me in ea ver&longs;atum ignorantia, vt ne&longs;cie
rim hanc opinionem ab v&longs;que Copernici tempore Nam vi&longs;us &longs;um potiùs mihi agno
ui&longs;&longs;e aliquos eruditos viros, etiam Eccle&longs;iæ Proceres,
Scripturæ &longs;acræ Interpretes, & Religio&longs;os Doctores,
harum rerum intelligenteis, qui ab ip&longs;a v&longs;que ætate
Copernici illam probârint: ac fui&longs;&longs;e aliquid omninò
aut inqui&longs;itum, aut pronunciatum ante Galileum, me
penitùs latuit. Quòd enim &longs;emper aduer&longs;us ip&longs;am
&longs;peciales aliqui Scriptores loca quædam &longs;acræ Scriptu
ræ oppo&longs;uerint, id non magis vi&longs;um e&longs;t facere Eccle&longs;iæ
&longs;u&longs;pectam, quàm fecit &longs;u&longs;pectam opinionem de ro
tunditate cæli, quod ex D. v&longs;que Augu&longs;tino retulimus
iam obiici,
aëre, igne, æthereve circum Terram, & ver&longs;us cælum
fu&longs;o, id, quod ex D. v&longs;que Thoma obiectum e&longs;t,
extendit Aquilonem &longs;uper vacuum, & appendit Terram &longs;u
per nihilum:
rumve cæle&longs;tium, id, quod nemo non obiicit,
&longs;olidißimi qua&longs;i ære fu&longs;i,No&longs;ti &longs;i
quidem nullam e&longs;&longs;e ex huiu&longs;modi opinionibus (imò
neque ex omnibus, quas pij Doctores in Scholis tuen
tur) aduer&longs;us quàm loca Scripturæ aliqua proferri non
po&longs;&longs;int, aut &longs;oleant; cùm illæ tamen proptereà Eccle
&longs;iæ &longs;u&longs;pectæ non &longs;int. Po&longs;tremùm inaudii&longs;&longs;e me qui
dem latam fui&longs;&longs;e &longs;ententiam aduer&longs;us Galileum à Con
gregatione &longs;acra Cardinalium Inqui&longs;itioni præ&longs;iden
tium: at non accepi&longs;&longs;e perinde fui&longs;&longs;e decretum Ponti
ficium, atque generale con&longs;equenter factum. Et donec
quidem nihil aliud, quàm &longs;pecialis &longs;ententia fuit, dici
forta&longs;&longs;e potuit cau&longs;&longs;am ad Galileum &longs;olùm &longs;pectare,
aduer&longs;us quem e&longs;&longs;e potuerint &longs;peciales cau&longs;&longs;æ aliquæ, At ex quo Summum
Eccle&longs;iæ caput decretum, vt ais, interpo&longs;uit, non vi
deo quid-nam re&longs;pondere Copernicani Catholici
po&longs;&longs;int; ni&longs;i fortè &longs;ibi de eo non con&longs;tare, quov&longs;que
promulgatum fuerit, legitiméque iu&longs;&longs;um haberi tan
quam fidei articulum intemeratum. Quod me atti
net, me vel &longs;ola fama, habitáque fides tuis literis ita
mouet, vt non ex&longs;pectem promulgationem, &longs;ed &longs;tatim
pror&longs;us exo&longs;culer, & planè cæcâ, vt dicitur, obedien
tiâ ip&longs;um excipiam.
e&longs;&longs;e qua&longs;i punctum comparatum ad Firmamentum: Et,
S
totidem habere.
XXXII.
Miraris deinde,
S
ab&longs;urda quædam videatur inducere: cùm ip&longs;i infinita pro
pemodum ab&longs;urditatum portenta admittant; excolant
culicem, & elephantos deglutientes: ac notas me eorum tan
gere nonnulla, &longs;ed di&longs;plicere, quòd etiam excu&longs;em. Ego
verò ea non excu&longs;o; aut certè ea mihi mens e&longs;t, vt
non tam excu&longs;em, quàm proponam quod illi re&longs;
pondent; vt quæ nosip&longs;is obiicimus e&longs;&longs;e ab&longs;urda, non
e&longs;&longs;e per&longs;uadeant. Dicis,
Terræ circa
tur magnum illum
instar puncti respectu cæli obtinere. Et agno&longs;co &longs;anè.
prodigio&longs;æ molis admittenda &longs;int, vt earum &longs;emidiameter in
teriectam à Terræ centro ad
dat. Ego verò id, vt mihi videtur, non di&longs;&longs;imulo; quòd
&longs;i eleuare vi&longs;us &longs;um; id alienæ &longs;ententiæ fuit. Quan
quam me dixi&longs;&longs;e non commemini, Sidera inerrantia
Orbem magnum excedere; videlicet, potiu&longs; quàm
Solem, quem dixi quidem po&longs;&longs;e
ip&longs;i æqualem. Sed e&longs;to, vt dicis; quandò Copernicani
&longs;unt, qui illam magnitudinem tribuere Stellis non
erube&longs;cunt. Pro&longs;equeris,
ab omni ratione abhorrens non videtur, quid, amabò, iudica
bis ab&longs;urdum?
abnuo, &longs;ed ad&longs;tipulor; At quæ&longs;o te tamen, quid &longs;im
re&longs;pon&longs;urus, &longs;i cùm idem obiecero, illi ita exceperint? Tu id ab&longs;urdum, & ab omni ratione e&longs;&longs;e abhorrens
iudicas: & quam-nam tandem affers rationem? An-ne
quòd exinde Stellæ inerrantes molis &longs;int nimis prodi
gio&longs;æ? Ecquis verò tu, qui exi&longs;times e&longs;&longs;e aliquid nimium
in operibus immen&longs;i Authoris? Non videtur fui&longs;&longs;e
Deo cau&longs;&longs;a, cur eas tam va&longs;tas faceret: at fui&longs;ti-ne tu
eius con&longs;iliarius, vt penetra&longs;&longs;e putes te in omnia diui
næ Sapientiæ arcana? Non capis rationem tantæ va
&longs;titatis: an ergo quia tibi mens angu&longs;ta e&longs;t; ip&longs;a tanti
Opifices opera debent e&longs;&longs;e angu&longs;ta? Abhorrere à ratio
ne putas, vt aliquæ Stellæ &longs;int Sole maiores, ac tot præ
&longs;ertim vicibus: an-non es proinde illi &longs;imilis, qui vr
bem Romam &longs;imilem tuguriolis paucis putabat; tan
quam non capiens e&longs;&longs;e po&longs;&longs;e tot vicibus maiorem illa,
in quam &longs;olebant pa&longs;tores ouium teneros fœtus Et verò &longs;i fortè vixi&longs;&longs;es ante illud tempus,
quo Mathematici demon&longs;trârunt, aut &longs;altem dixerunt
e&longs;&longs;e Solem circiter centies &longs;eptuagies Terra maio
rem: quam igitur illud cen&longs;ui&longs;&longs;es ab omni ratione
abhorrens? Et cùm iam vides vulgò admitti id, quod
memoratum iam e&longs;t, e&longs;&longs;e Stellas fixas, quæ &longs;int centies
octies maiores, quàm Terra, & quater millies, quàm
ip&longs;a Luna: cur non id abhorrens à ratione putas? An
meliùs capis, ob quam rationem Deus illas fecerit tan
tas? An-non, &longs;i id, quod dicimus, tuo &longs;en&longs;u ab&longs;urdum
e&longs;t: &longs;ecundum magis, & minus &longs;olùm erit di&longs;crimen
ab&longs;urditatis? Habes-ne verò interim vllum omninò
argumentum, quo Stellas e&longs;&longs;e tantas &longs;ic probes, vt &longs;i
mùl probes aut non e&longs;&longs;e, aut non po&longs;&longs;e e&longs;&longs;e maiores? Non certè; &longs;ed penitùs gratis in ea con&longs;i&longs;tis magnitu
dine; neque e&longs;t tibi maior ratio quærendi ex nobis,
cur procedamus vlteriùs: quàm nobis quærendi ex te,
quamobrem con&longs;i&longs;tas citeriùs. Dicere ad &longs;ummum
potes, tibi &longs;ic videri; & quia &longs;ic videtur, nos à ratione
abhorrere: quid-ni & nobis pari iure dicere dete idem
liceat? Quanquam & nobis ratio e&longs;t, tum admiranda
concinnitas, quæ hac &longs;uppo&longs;ita amplitudine ob&longs;erua
tur; tum commendatio operum Dei, quæ tu, quantum
potes, extenuas, dum ea non maiora tuo captu facis. Quippe huiu&longs;modi amplitudo diuinæ potentiæ, &longs;a
pientiæ, & magni&longs;icentiæ con&longs;entanea e&longs;t: neque e&longs;t,
cur tu ab&longs;que vlla aut ob&longs;eruatione, aut ratione illam
contrahas, vel ab&longs;urdam putes. Quæ&longs;o te, inquam, Vir
Religio&longs;i&longs;&longs;ime, ecquid-nam illis dicturus &longs;im, cùm
hæc, & &longs;imilia reponent?
XXXIII. Subiicitur;
ex eadem Telluris circa Solem tran&longs;latione vlteriùs &longs;equuntur,
ab&longs;urda, à quibus tamen vt te expedias, fingis alia fortaßis
adhûc ab&longs;urdiora; vt, quòd illu&longs;triora illa, quæ in
apparent Sidera credi poßint vt mole maiora, &longs;ic etiam Sole
ip&longs;o longè lucidiora: adeò tibi facile e&longs;t tot, tamque ingenteis
in cælo pro tua voluntate verbo vnico creare Soleis. Ego ve
ro & heic quoque tibi ad&longs;tipulor. Sed dic, amabò,
etiam hoc loco, quid illis re&longs;pon&longs;urus &longs;im, cùm ip&longs;i &longs;ic
in&longs;titerint. Ludis, ac putas deludi nos?
De Solis voce
non agitur, quæ Fixis à vulgo non magis tribuetur,
quàm Lunæ vox tribuitur: tamet&longs;i nemo diffitea
tur, quin Fixæ &longs;int Luna maiores. Nempe quantæcúm
que eæ &longs;int; apparent tamen, donec è Terra &longs;pectan
tur, qua&longs;i punctula ad apparentem Solis, ac Lunæ ma
gnitudinem comparatæ Enimverò cùm heic agatur
de ea magnitudine, qua Stellæ &longs;ecundum &longs;e &longs;unt, &
qua apparerent, &longs;i tantumdem nobis admouerentur,
quantum Sol; ac de magnitudine etiam, qua Sol e&longs;t in
&longs;e, quáque appareret, &longs;i tantumdem à nobis remoue
retur, quantum Fixæ: puta&longs;-ne ludendo &longs;copum atti
gi&longs;ti? Non e&longs;to Sol, non &longs;unto Fixæ in tanta à Terris
di&longs;tantia, quanta à nobis a&longs;&longs;eritur: e&longs;to minima, & qua
lem Tycho po&longs;uit, nulla &longs;anè ob&longs;eruatione (quod ad
Fixas pr&ecedil;&longs;ertim &longs;pectat) verùm coniectatione mera,
meróque arbitrio inductus. Di&longs;&longs;idebit à Terra Sol,
cùm di&longs;&longs;ebit mediocriter, terrenis &longs;emidiametris mille
centum, & quinquaginta, & Fixæ quater-decies nulle. Finge igitur Solem quantu&longs;-quantus e&longs;t, tran&longs;latum
e&longs;&longs;e v&longs;que ad Fixas: cùm diameter eius apparens im-
di&longs;tantiam per di&longs;tantiam Solis à Terra, fiet quotiens
amplius, quàm duodecim. Et quia Solis diameter ap
paret iam nobis dimidij gradus, &longs;iue minutorum tri
ginta; &longs;equitur vt Sole inter Fixas ex&longs;i&longs;tente, eius dia
meter apparitura non &longs;it, ni&longs;i pars huius duodecima,
&longs;iue minutorum duorum cùm &longs;emi&longs;&longs;e. Porrò hac ea
dem diametro apparent vulgò quæ Stellæ &longs;unt magni
tudinis primæ, aut &longs;ecundæ. Igitur &longs;i Sol fuerit inter
Fixas con&longs;titutus, non apparebit maior, quàm vna Stel
larum. Et vice ver&longs;a, &longs;i qu&ecedil;libet earumdem Stellarum
fixarum con&longs;tituta fuerit vbi iam e&longs;t Sol, &longs;eu pari, qua
ille à nobis di&longs;tantia: apparebit nobis tanta, quantus
Sol; atque adeò omnes erunt qua&longs;i Soles. Quid &longs;i di
&longs;tantiam Fixarum augeas pro opinione Albategnij
Ptolemæo inhærentis, &longs;tatuenti&longs;que illam nouemde
cim millium &longs;emidiametrorum: an-non apparitura
fuerit Solis diameter infra duo minuta? Quid &longs;i adhûc
ampliùs, vt debere fieri probabile e&longs;t, nihilque repu
gnat? Verùm hoc &longs;ufficiat, vt intelligas non nos aut
ab&longs;urda tueri, aut ijs
&longs;ed te potiùs rem non aduertere, & fingere magis. Qua
re & cùm &longs;it Deusip&longs;e, qui tot in cælo ingenteis Soleis
pro &longs;ua voluntate, ac verbo vnico creauit: ne cau&longs;&longs;are
nos pro no&longs;tra voluntate, verbóque vno illos creare:
&longs;ed agno&longs;ce potiùs te eos pro tua voluntate, verbóque
vno de&longs;truere. Si illi, inquam, aduer&longs;um me hac
ratione in&longs;titerint; dic mihi, te quæ&longs;o, quid &longs;im re&longs;
pon&longs;urus?
apparere: &, Veros omnium
compo&longs;itos, vix apparenti di&longs;co vnius
mediocris Stellæ exæquatum iri.
XXXIV.
Subiungis verò;
fieri po&longs;&longs;e, vt Sol hic no&longs;ter, quamvis comparatione &longs;uperio
rum
men&longs;a tamen illa
appareat, ac tantæ etiam magnitudinis, quanta est tota regio
Planetaria
lucem eius vegetam, diffu&longs;o&longs;que ip&longs;ius radios, quibus oculus
afficiendus e&longs;&longs;et; eo modo, quo flamma candelæ noctu spectata
ignis ingens apparet. Id, inquam, ingenij tui admirabile qui
dem, &longs;ed incredibile figmentum e&longs;t, quod exemplo candelæ
comodè non probas. An porrò, cùm i&longs;tud videatur
tum incredibile;
quod cum i&longs;to connexum &longs;it, quodque, quantum con
iector, &longs;it incredibilius appariturum? Quantum, pu
tas, &longs;i omnes di&longs;ci mille & viginti duarum Stellarum
vulgò agnitarum &longs;imùl iungerentur, aggregarenturve
in vnum; quantum putas, inquam, totalem di&longs;cum
conficerent? An-non ingentem?
At ego opinor vix
tantum futurum, quantus apparet vel vnicus vnius
Stellæ, quæ &longs;it magnitudinis quartæ, di&longs;cus. Quale
nam, inquies, i&longs;tud e&longs;t, non figmentum iam, &longs;ed planè
delirium! Qualecumque &longs;it; accipe id tamen. Cùm
aliquando nocte &longs;erena iter facerem, &longs;ubiit animum
cogitatio, quî fieri po&longs;&longs;et, vt neque Lunâ, neque ma
iu&longs;culis Planetis collucentibus, &longs;ingula tamen circum-
legere paginam po&longs;&longs;em. Tum verò è ve&longs;tigio &longs;ubiit
me ingens admiratio, quî fieret, vt potiùs, &longs;i Stel
larum di&longs;ci tanti e&longs;&longs;ent, quanti e&longs;&longs;e perhiberentur, non
longè magis collucerent, nempe longè ampliùs, quàm
Luna: quippe cùm & Stellarum lux &longs;it lunari longè
viuidior; & di&longs;ci earum compo&longs;iti viderentur mihi
confecturi di&longs;cum lunari maiorem. Siquidem quam
vis di&longs;culi earum forent toto cælo di&longs;per&longs;i; videban
tur tamen tantumdem præ&longs;tare po&longs;&longs;e luminis re&longs;pectu
partis eiu&longs;dem Terræ ab hemi&longs;phærio toto re&longs;pectæ;
&longs;icut re&longs;pectu eiu&longs;dem aulæ tantumdem præ&longs;tant (aut
etiam ampliùs) candelæ variæ, ex quibus po&longs;teà fax
quædam ingens componitur. Rursùs itaque è ve&longs;ti
gio &longs;ubiit mentem recordatio ob&longs;eruatæ exilitatis tam
Planetarum, quàm Fixarum; ac cen&longs;ui ad illam refe
rendum e&longs;&longs;e, quòd Stellarum lux adeò debilis ad nos
perueniret. Quam-primùm diuerti ad ho&longs;pitium, in
quo fortè fortuna cælorum &longs;ehema reperi, continens
inter cætera, quot Stellæ e&longs;&longs;ent primæ magnitudinis,
quot &longs;ecundæ, quot tertiæ, & ad v&longs;que &longs;extam, ad
quam retuli ob&longs;curiores alias, quibus mille viginti
duarum ab&longs;oluitur numerus; continere non potui me,
quin ad calculos rem totam vocarem.
XXXV.
Ac primùm quidem &longs;upponendo e&longs;&longs;e Stel
larum diametros, cuiu&longs;modi vulgò apparent, explorare
lubuit quem di&longs;cum earum omnium di&longs;ci coniuncti
crearent. Attribuendo igitur Stellis primæ magnitu
dinis, dum profunda nocte &longs;pectantur, diametrum
minutorum trium; Stellis &longs;ecundæ diametrum duo-
mi&longs;&longs;is: quintæ vnius: &longs;extæ &longs;emi&longs;&longs;is: deduxi exinde &longs;in
gularum di&longs;culos: eo&longs;que in vnum componendo, com
parandóque ad di&longs;cum Solis, cuius diameter, vt iam
dictum e&longs;t, &longs;it dimidii gradus, &longs;iue minutorum triginta,
collegi debere ex iis di&longs;cum fieri, cuius diameter &longs;it
minutorum quinquaginta, & vnius; quique &longs;it proinde
ad di&longs;cum Solarem, vt ad nouem, viginti &longs;ex, &longs;eu pro
ximè triplus. Et quia tamen harum Stellarum, non
ni&longs;i dimidium horizonti con&longs;picuum e&longs;t; facile fuit
agno&longs;cere di&longs;cum ex i&longs;to dimidio e&longs;&longs;e Solaris &longs;e&longs;qui
alterum, &longs;iue exæquari Soli &longs;emel cum &longs;emi&longs;&longs;e. Quare
& deprehendi me non ab&longs;que ratione admiratum fui&longs;
&longs;e, quamobrem, &longs;i di&longs;ci Stellarum tanti &longs;int, quanti &
apparent, & e&longs;&longs;e dicuntur; Terra ex iis noctu non ma
gis re&longs;plendeat. Subinde verò, quia tantas non e&longs;&longs;e dia
metros Stellarum per&longs;pectum
etiam ducebam, quàm Galileus cen&longs;uerit, quòd in no
cturnis tenebris pupillæ
quàm &longs;uppo&longs;itum ab eo videretur) ideò explorare rem
placuit iuxta veriores diametros, quales videlicet appa
rent re&longs;ectâ non tam tele&longs;copio, quàm funiculo, aut ba
cillo tereti interpo&longs;ito, circumradiatione. Et ne videret
tamen mihi potiùs, quàm Galileo fidere: &longs;upponere
volui, quod is ob&longs;eruanit, Stellam magnitudinis pri
mæ e&longs;&longs;e diametri &longs;ecundorum quinque, &longs;iue tertiorum
trecentorum; & con&longs;equenter habere Stellam &longs;ecundæ
magnitudinis diametrum tertiorum ducentorum quin
quaginta: tertiæ ducentorum: quartæ centum quin
quaginta: quintæ centum: &longs;extæ quinquaginta. Hoc
in di&longs;cum vnum compo&longs;ui, ip&longs;umque ad di&longs;cum Solis
comparando, comperi non e&longs;&longs;e, ni&longs;i illius particulam
metro Solis ex&longs;i&longs;tente minutorum triginta, ratiocina
tus &longs;um diametrum di&longs;ci ex omnibus Stellis compo&longs;iti,
non e&longs;&longs;e maiorem vno minuto cum &longs;emi&longs;&longs;e; quantæ
vulgò e&longs;&longs;e apparet Stella magnitudinis quartæ. Quod
&longs;i dimidium detrahas, ob Stellas, quæ &longs;ub horizonte:
&longs;equitur di&longs;cum ex re&longs;iduis, non fore maiorem vna
octingente&longs;ima &longs;exage&longs;ima tertia di&longs;ci Solaris particu
la: ac eius diametrum futuram vnius proximè minuti
dumtaxat: hoc e&longs;t, quantæ e&longs;&longs;e apparet Stella magni
tudinis quintæ. Quare & ex hoc de&longs;ii admirari, quam
obrem lux omnium Stellarum &longs;upra horizontem lu
centium tam parum Terræ faciem illu&longs;trent; tuque ex
inde animaduertis quo progre&longs;&longs;u peruenerim ad in
credibile fig mentum.
XXXVI.
At verò, inquies, ecqui&longs;-nam capiat non
e&longs;&longs;e ingens totum maius tantulâ &longs;ui particulâ: &longs;eu tan
tam, quæ apparet lucem in omnibus Stellis &longs;upra hori
zontem coru&longs;cantibus, in exiguum adeò &longs;patium con
trahi, vt non &longs;it eo maius, quod à &longs;tellula magnitudinis
quintæ occupatur? Sed nimirùm con&longs;idera; &longs;i foret
Stella, quæ reuerâ e&longs;&longs;et diametro minuti vnius, fore, vt
lux eius &longs;pectata intra nocturnas tenebras appareret
oculo incompa biliter maior. Si enim quæ Stella e&longs;t
diametro &longs;olùm vnius &longs;ecundi cum be&longs;&longs;e: apparet ni
hilominùs diametro vnius minuti: &longs;anè, &longs;i proportio
nem admittas, ea apparitura erit diametro minutorum
Solem: quemadmodum, &longs;i aliunde fuerit vera diame
ter minutorum duorum, apparitura erit di&longs;co ad &longs;ola
rem plu&longs;quàm triplo: &longs;i trium, penè tredecuplo. At
quorsùm Stella, &longs;i vel tanta appareret, quantus e&longs;t Sol,
non tantum, quantum Sol luceret? Re&longs;pondeo; quia
illa lucis amplificatio re&longs;pectu oculi &longs;olùm ficret, &
non re&longs;pectu veri di&longs;ci, rerumve ab eo illuminatarum:
eo modo, quo flamma candelæ, dum &longs;eip&longs;a maior per
noctem videtur, non proptereà tamen aut &longs;e maior e&longs;t,
aut magis illu&longs;trat. Ex quo fit proinde, vt quemadmo
dum flamma candelæ quantò apparet maior, tantò
etiam ad&longs;pectus eius confu&longs;ior, & ob&longs;curior euadit, ne
que eminùs tantum illuminat, quantum &longs;i apparens
eius amplitudo tam &longs;plendida foret, quàm flammula
cominùs vi&longs;a: ita &longs;tellaris ille di&longs;cus quantò appare
ret maior, tantò foret etiam confu&longs;ior, ob&longs;curiorque
appariturus; atque idcircò Terræ faciem non perinde
illu&longs;traturus, ac &longs;i eminùs eo fulgore, quo & cominùs
appareret: ac proinde tantam dumtaxat in Terram
lucem effunderet, quantam iam effun dunt Stellæ &longs;epa
ratæ. Cæterùm huic di&longs;ci amplificationi fidem facit
vel ip&longs;a Venus, quæ vi&longs;a interdiù non maior, quàm
Stella quædam per-exigua, apparet tamen deinde in
tra tenebras diametri quintuplò, ac idcircò di&longs;ci vige
cuplò quintuplò maioris. Sed & fidem facit vberem
Mercurius, qui vi&longs;us e&longs;&longs;e circa maximas elongationes
minutorum trium, deprehen&longs;us tamen e&longs;t à me, cùm
e&longs;&longs;et proximè perigeius, ac in ip&longs;o di&longs;co Solari (vbi
imponere &longs;ua luce non potuit, &longs;pectata nempe eius
tele&longs;copium in ob&longs;cura &longs;cena referente) deprehen&longs;us,
inquam, e&longs;t triente minuti non maior; adeò vt cùm
e&longs;&longs;e apparet minutorum trium (quo tempore deberet
etiam aliquantò minor videri, quàm dum præcisè in
perigeio ver&longs;atur) di&longs;cus eius octogies &longs;emel, quàm
reuerâ &longs;it, amplificarior appareat. Fidem quoque
Iupiter, & Mars: qui cùm Acronychi illam Veneris
comparatione cum diametro Lunæ vix diametro e&longs;&longs;e
vnius minuti. At in&longs;tabis, hoc
omninò e&longs;&longs;e re&longs;pectu immanis illius, quod affingitur
&longs;tellis Fixis. Sed nempeid fieri videtur, quòd lux Pla
netarum mutuatitia &longs;it, & ab illorum &longs;uperficiebus de
bili&longs;&longs;ima reddita, ob di&longs;tractos Solareis radios (quippe
quatenus &longs;uperficies inæquabili&longs;&longs;imæ &longs;unt, & facies
habent aliò, alióque variè diuergenteis, vt de Luna
quidem manife&longs;tum e&longs;t, & coniicere de cæteris licet)
at ex oppo&longs;ito lux Fixarum videtur natiua, ac propria,
& Solaris in&longs;tar, vt puri&longs;&longs;ima, ita viuidi&longs;&longs;ima; adeò vt ab
exiguo di&longs;co (longè minore &longs;cilicet, quàm &longs;it Planeta
ris) procedens, tum fortiùs moueat oculum, tum cir
cumradiationem vberiorem pariat: tum apparentem
proptereà di&longs;cum amplificatiorem exhibeat. Argu
mento autem e&longs;&longs;e pote&longs;t, primùm continens illa &longs;cin
tillatio, qua radii Fixarum excurrunt, & quam Ari&longs;to
teles quoque ex motu non Stellæ, &longs;ed oculi e&longs;&longs;e conten
dit: ac deinde experimentum factum tele&longs;copio, quod
cætera cùm amplificet, Stellas tamen Fixas imminuit,
ob ip&longs;am nempe re&longs;ectionem radiorum excurrentium:
tionem Stellæ Fixæ exhibentur incomparabiliter mi
nores Planetis, habita ratione di&longs;corum apparentium:
&longs;cilicet, quòd ip&longs;arum radii & excurrant longè vberiùs,
& longè proinde ampliùs circum-radient.
XXXVII.
Atque hæc quidem omnia eo &longs;olùm fine
commemoro, vt innuam, Qua ratione Sol è Fixis &longs;pe
ctatus, tamet&longs;i &longs;uo di&longs;co exilis, appariturus tamen foret
luce adeò circum-diffu&longs;a, vt, tanquam &longs;patia in
gentia complens, apparenter exæquaretur, aut to
ti, aut &longs;altem in&longs;igni portioni regionis Planetariæ,
cuiu&longs;modi e&longs;t Orbis magnus, de quo fuit poti&longs;&longs;imùm
quæ&longs;tio. Et fac certè Solem non apparere maiorem,
quàm magnitudinis &longs;extæ Stellam: quia tunc vera dia
meter eius erit vno &longs;ecundo minor, hoc e&longs;t, ex iam di
ctis, tertiorum quinquaginta; orbis magni diameter
continebit ducenties, aut plus paulò certè, quinqua
ginta tertia (quippe totidem vicibus diametrum Solis
continet) efficietur, &longs;i ea reducas, vt Orbis magni dia
meter apparitura non &longs;it maior duobus minutis cum
dodrante, &longs;eu quàm appareat diameter Stellæ magni
tudinis primæ, aut &longs;ecundæ. Quòd &longs;i Stellarum dia
metri &longs;int adhûc minores, quàm Galileus cen&longs;uit, ob
in&longs;inuatam antè cau&longs;&longs;am; & magnitudinis &longs;extæ Stella
non &longs;it maior diametro, quàm &longs;extans &longs;ecundi, &longs;iue
decem tertia; efficietur eadem ratione, vt Orbis magni
diameter apparitura maior non &longs;it, quàm appareat dia
meter Stellæ magnitudinis &longs;extæ. Dices, profectò,
figmentum meum tantò magis incre&longs;cere, quantò hac
ratione veræ Stellarum diametri magis imminuuntur.
tantulo angulo, qui maior non &longs;it &longs;extante vnius &longs;e
cundi? Sed vide, quæ&longs;o, vt non dicam e&longs;&longs;e eam Stellam
vi&longs;ibilem &longs;ub huiu&longs;modi angulo: verùm eam Stellam,
quæ vi&longs;ibilis e&longs;t &longs;ub angulo &longs;emi&longs;&longs;is minuti, &longs;iue trigin
ta
non habere
liatam, &longs;extante &longs;ecundi maiorem. At hoc ip&longs;um quo
que e&longs;t, inquies, quod omni figmento e&longs;t maius, tam
minutulum punctulum ita po&longs;&longs;e circum-radiare, vt fu
turum aliàs planè incon&longs;picuum, effici vi&longs;ibile po&longs;&longs;it. Verùm, quid res &longs;it, vt percipi po&longs;&longs;it: e&longs;to candelæ flam
mula cra&longs;&longs;itudinis &longs;emidigitalis; ea poterit nocte ob
&longs;cura &longs;pectari à tribus pa&longs;&longs;uum millibus. Fac verò an
gulum, &longs;ub quo vi&longs;ibilis efficietur, non e&longs;&longs;e dimidio
minuti maiorem, ita vt flammula appareat, qua&longs;i ma
gnitudinis &longs;extæ Stella; quæ&longs;o te, quantus angulus erit,
qui ab ip&longs;ius flammulæ vera diametro &longs;ubtendetur? Profecto vix maior &longs;emi&longs;&longs;e &longs;ecundi.
Cùm in tribus
enim pa&longs;&longs;uum millibus &longs;int trecenta, & &longs;exaginta &longs;e
midigitorum millia: &longs;i, vt hic numerus &longs;e habet ad
vnum, ita centum millia, &longs;eu radium feceris ad aliud;
procreabuntur &longs;olum quinque decima octaua vnius,
&longs;eu tangens &longs;eptuncis vnius &longs;ecundi. Et minüe, &longs;i ve
lis, di&longs;tantiam ad ip&longs;um v&longs;que dimidium, vt &longs;i putes
eam flammulam videri dumtaxat à &longs;e&longs;qui milliari; tum
vera eius diameter angulum &longs;ubtendet &longs;ecundo vix
vno maiorem. An credidi&longs;&longs;es punctulum, quale e&longs;t
vnicum &longs;ecundum, aut &longs;ecundi etiam dimidium, ita
po&longs;&longs;e circum radiare, vt videri &longs;ub angulo triginta Iam igitur, cùm æquum &longs;it re
putare lucem Stellarum &longs;uperare &longs;ua puritate, &longs;uóque
&longs;plendore lucem flammulæ, fuligini cra&longs;&longs;æ, fumove
commi&longs;tæ, multis vicibus: po&longs;tulo dumtaxat, vt &longs;uperet
ter, &longs;i putes flammulam videri, quæ &longs;it angulo dimidij
&longs;ecundi; aut &longs;exies, &longs;i putes eam &longs;olùm, quæ &longs;it &longs;ecundi
integri. Nempe exinde efficietur, vt Stella vi&longs;ibilis &longs;it,
quæ vera diametro &longs;ubtendet non angulum modò
vnius &longs;ecundi, &longs;ed angulum etiam &longs;extantis &longs;ecundi. I&longs;ta
vberius non pro&longs;equor; ne cau&longs;&longs;eris non po&longs;&longs;e me meis
figmentis facere finem. Adnoto tamen; cùm ex iam
dictis, Stella magnitudinis &longs;extæ e&longs;&longs;e non debeat Sole
maior; ecquid-nam dicturus de figmento fui&longs;&longs;es, &longs;i
propo&longs;ui&longs;&longs;em cum Land&longs;bergio Stellam magnitudinis
&longs;extæ e&longs;&longs;e vicies quinquies ip&longs;o Orbe magno maiorem? Et ille tamen vi&longs;us e&longs;t &longs;ibi ex certis principiis demon
&longs;tra&longs;&longs;e omnia: quanquam illud &longs;altem non cauit, quod
circum-radiatio imponit circa magnitudinem veram:
quodque proinde diameter vna Stellæ magnitudinis
&longs;extæ e&longs;t longè minor quinque &longs;ecundis, &longs;ecùs quàm
ab illo &longs;uppo&longs;itmu e&longs;t.
quare flammæ noctu maiores appareant.
XXXVIII.
Ad te vt redeam, po&longs;tquàm præmi&longs;i&longs;ti,
pergis,
certam præ&longs;ertim di&longs;tantiam, &longs;emper auctior appareat: &longs;atis
certè tibi con&longs;tat Lunam, ac Martem, ip&longs;umque etiam Solem,
vbi verò longiùs à Terra remouentur, non maiores conspici,
&longs;ed apparere minores. Vnde ergo, quæ&longs;o te, colligis
immen&longs;a Siderum di&longs;tantia conspectum non modò maiorem
videndum, quàm nobis vicinioribus appareat, &longs;ed tantæ etiam
magnitudinis, vt regionem quoque Planetariam totam, atque
integram æquare videretur. Sed nimirùm, optime Vir,
cùm ip&longs;e cau&longs;&longs;am reticeas, cur candelæ flamma appa
reat per noctem adauctior; quòd &longs;agacitas illa tua, quan
tum coniicere par e&longs;t, difficultatem prouiderit, quæ ex
citari in vulgarem cau&longs;&longs;æ explicationem pote&longs;t; non
ea mihi tamen fuit prætermittenda, quæ e&longs;t probabi
li&longs;&longs;ima vi&longs;a, vt præoccupando declarare po&longs;&longs;em, quod
iam rogas me, vnde-nam putà colligam, Solem è Fixis
con&longs;pectum po&longs;&longs;e apparere æqualem regioni Planeta
riæ, &longs;icque maiorem, quàm heinc videri. Siquidem
conatus idem explicare ex cau&longs;&longs;a vulgò reddita, vi&longs;us
mihi ip&longs;i ridiculus &longs;um ob illius inanitatem. Ecce
enim dicere &longs;olent,
mentiâ illu&longs;trari ob halituo&longs;as qua&longs;dam parteis è flamma con
tinuò diffugienteis, vt computetur in eandem flammam, parti
bus videlicet illis factis ad&longs;pectabilibus ex&longs;i&longs;tenti oculo procùl,
& in minore lumine; cùm è vicino, ab eximio flammæ &longs;plen
dore occultentur. At quomodo probare valeant e&longs;&longs;e has
halituo&longs;as parteis illu&longs;trationis eius capaceis, vt totum
aëreum &longs;patium, in quo &longs;unt, efficiant non minùs illu
&longs;tre, quàm flammam? Nam non negabunt profectò
flammam e&longs;&longs;e centies, aut etiam millies &longs;plendidiorem
eo &longs;patio, quod ip&longs;am circum&longs;tat ad vnum, aut ad plu
reis palmos. Itaque dum procùl &longs;pectamus candelam,
vera e&longs;t flamma &longs;plendidius e&longs;&longs;e, ni&longs;i millecuplò, at cen
tuplò &longs;altem (imò, vt ampliùs largiar, &longs;altem decuplò)
quàm amplitudinem circum&longs;tantem: & nihilominùs
tota illa flamma apparet e&longs;&longs;e vniu&longs;modi, &longs;eu æquè lu
cida tam &longs;ub medium, quàm ad extrema. Quod aiunt
verò
lumine:
videtur? Quid ergo e&longs;t cau&longs;æ, cur luce illarum par
tiùm cominùs exili (imò ad ip&longs;um &longs;en&longs;um nulla) acci
piente
proportione
fit, &longs;iue ex Quod
autem dicunt,
cultari:
&longs;plendore, à quo habent, vt &longs;plendeant, ad&longs;pectabile&longs;
ve, vt contendunt, fiant. Nam quod vulgò quidem
etiam dicunt,
terare minus:
vtróque compo&longs;ito lumen inten&longs;ius: tamet&longs;i, quæ vi&longs;us
hebetudo e&longs;t, di&longs;cerni gradus non valeant, qui ab vtró
que conferuntur. Quòd in&longs;uper
maiore comparatum vi&longs;ibile fiat non propè, &longs;ed procùl:
probabile fieret, &longs;i &longs;pectato procul minore lucido, ma
ius abe&longs;&longs;et, nec iuxtim foret; at &longs;i vtrumque &longs;imùl vi
deatur, nece&longs;&longs;e e&longs;t, vt proportione debilitationis ob
&longs;patium &longs;eruata, tam procùl, quàm propè videri non
po&longs;&longs;it. Et quid heic contingat, experiri vis?
Iube oc
cultari præcisè flammulam candelæ non circum&longs;tans
&longs;patium: deberes adhûc videre &longs;patium perinde prorsùs
mam deficientem: at procùl &longs;anè erit, vt videas. Iube
aliunde occultari totum circum&longs;tans &longs;patium, adeò vt
&longs;ola flammula foramine facto libera videatur; deberet
tum ea flammula non maior videri, &longs;ed minor, pro ra
tione di&longs;tantiæ: & tamen procùl aberit, vt contractio
rem videas, & non maiorem potiùs, ac perinde prorsùs,
vt libero &longs;patio. Ni&longs;i verò i&longs;tud non arguit aliam fui&longs;&longs;e
tium circum&longs;tans diffugienteis, requirendam cau&longs;
&longs;am?
XXXIX.
Itaque aliam requi&longs;iui (affectionem
putà in pupilla, acretina) quæ vt effectui in candela ap
parenti congrueret, ita lucidis omnibus, quorum &longs;pe
cies noctu incre&longs;cit, accommodari congruè po&longs;&longs;et. Hu
iu&longs;modi maximè &longs;unt tam Luna, quàm Stellæ, &longs;eu
Errantes, &longs;eu
non &longs;emel ob&longs;eruauimus octaua propè &longs;ui parte noctu,
quàm interdiù maiorem: Veneris vero diametrum
multis maiorem vicibus; & Iouis con&longs;imiliter (quippe
qui fuerit etiam nobis &longs;æpenumerò ob&longs;eruatus inter
diù) con&longs;tatque vniuersè Stellas cæteras, cùm interdiù
&longs;int incon&longs;picuæ, in gruente tamen crepu&longs;culo æger
rimè primùm ob exilitatem videri, ac deinde magis,
magi&longs;que, dum &longs;en&longs;im grande&longs;cunt, vi&longs;ibileis fieri. Quæ&longs;o verò i&longs;ta-ne valeant ad halituo&longs;as aliquas par
teis, quæ vt à flamma, &longs;ic à Luna, Stelli&longs;que diffugiant,
referri; & non potiùs ad vberiorem tum pupillæ dila
tationem, tum impre&longs;&longs;ionem retinæ factam, donec
oculus in tenebris degit? At hæc tamen cau&longs;&longs;a, in-
Pote&longs;t-ne oculus in Solem re&longs;
pectans cen&longs;eri e&longs;&longs;e in tenebris? Pote&longs;t-ne Solem noctu
videre? Re&longs;pondeo po&longs;&longs;e haud-dubiè; neque id ha
bendum e&longs;&longs;e Paradoxum; quatenus id fore intelligi
tur, cùm oculus demùm eâ fuerit diftantiâ, è qua Sol
non maior, quàm vna Stellarum appareat, & è qua pro
inde non tenebras magis, quàm Stellarum vna di&longs;cu
tiat, neque oculum magis proinde per&longs;tringat. Ex quo
fit, vt dum ex me quæris,
illa di&longs;tantia non modò vi&longs;um iri maiorem, quàm appareat no
bis vicinioribus, &longs;ed etiam tantæ magnitudinis, vt toti regioni
Planetariæ exæquetur?
id quæras. Nam cùm ego quidem profitear vi&longs;um
iri Solem ex illa di&longs;tantia, qua&longs;i vnam aliquam Stel
lam heinc vbi degimus con&longs;pectam; neque dico &longs;anè,
neque colligo vi&longs;um iri nobis maiorem, quàm vici
nioribus iam videatur. Et tamet&longs;i dicam vi&longs;um iri tan
tum, quantum Orbem magnum, in&longs;ignemve portio
nem regionis Planetariæ; cau&longs;&longs;a e&longs;t, quia ex eadem
di&longs;tantia totus Orbis magnus non maiore appareret
amplitudine, quàm heinc appareat vna Stellarum cum
circumfu&longs;is corpu&longs;culo radiis. Tu verò &longs;ic interrogas,
vt &longs;i cen&longs;erem ex ea di&longs;tantia tum magnum Orbem
appariturum eiu&longs;dem, qua propè amplitudinis; tum
Solem non modò maiorem, quàm heinc con&longs;piciatur;
&longs;ed etiam quantus Orbis magnus ex Marte, v. g. aut
Ioue con&longs;piceretur, appariturum. Quòd verò &longs;ic in
terrogas, eo permotus argumento,
nam, ac Martem, ip&longs;umque etiam Solem quò propiùs acce
dunt ad nos, eò maiores con&longs;pici; quò longiùs ab&longs;cedunt,Etenim agitur
hoc loco de incremento in lucidis facto non ratione
di&longs;tantiæ, &longs;ed ratione ob&longs;curitatis. Neque enim re
quiritur, cur Mars v. g. dum e&longs;t perigeius, terri&longs;ve pro
pinquior, appareat maior, quàm apogeius, &longs;eu à terris
remotior, & in eodem quidem tenebrarum gradu: &longs;ed
cur in eadem propinquitate, aut in eadem remotione
maior, & minor appareat, prout in variis gradibus ob
&longs;curitatis con&longs;picitur; vt claro adhûc crepu&longs;culo, & no
cte iam facta profunda. Quare & ad hoc non ad il
lud &longs;imilitudo candelæ facit; & ad hoc, non verò ad
illud, quam cau&longs;&longs;am e&longs;&longs;e prætermittendam cen&longs;ui&longs;ti,
referenda fuit.
ctus: &, Po&longs;&longs;e exinde explicari varietates, quæ tam per
Æ
& Nouilunia contingunt.
XL.
Verba tua deinde &longs;unt,
affirmas
æ&longs;tum expo&longs;ui&longs;&longs;e, vt videatur denique cau&longs;&longs;am eius germa
nam adinueni&longs;&longs;e. Quàm bene e&longs;t verò, quod verbo
deatur
non tantum
mare! Certè, religio&longs;i&longs;&longs;ime Vir, &longs;i me bene no&longs;ti, lon
gi&longs;&longs;imè ab&longs;um, vt in hi&longs;ce rebus, aut &longs;imilibus quid
piam a&longs;&longs;eueranter dicam; tantum à me abe&longs;t, vt faciam Nam & tamet&longs;i con&longs;uetudo loquendi non
&longs;emper patiatur, vt caueam, ne a&longs;&longs;erere videar aliquid
id tamen &longs;emper te&longs;tatum volo, quæcumque mea
phra&longs;is &longs;it, eam mihi in&longs;idere mentem, vt nihil planè
tanquam verum, & indubitatum affirmem, &longs;iue plu&longs;
quàm probabile, veri&longs;imileve profitear. Quantò verò
magis hoc loco id volui; vbi &longs;ententiam non tam pro
priam, quàm alienam expo&longs;ui! Heinc & quæ dicere
iam pergo, non vt propugnans &longs;ententiam, quæ mihi
rata fixa &longs;it: &longs;ed tanquam tentans quid iuxta ip&longs;am &longs;it
vero &longs;imile, in&longs;inuo: & dum tu &longs;ubdis,
tarditate ingenij tui, an aliunde accidat, vt longè aliter, quàm
ego, hactenus hac in re &longs;en&longs;eris:
non me &longs;entire &longs;ecus, quàm te, quod ad rem ip&longs;am at
tinet; &longs;ed quod ad ea, quæ opinioni de motu Terræ
&longs;unt con&longs;entanea. Non e&longs;t profectò interim, cur vl
lam in te &longs;u&longs;piceris tarditatem ingenij: ego illam in
me recipio, qui agno&longs;co me non potui&longs;&longs;e ex tot opi
nionibus aliis, quæ hac de re circumferuntur, aliquam
deprehendere, quæ non videretur, quàm i&longs;ta nugacior. Gratum feci&longs;&longs;es, &longs;i in&longs;inua&longs;&longs;es ecquæ-nam tibi proba
tior foret: &longs;pes enim fui&longs;&longs;et quidpiam tua dignum &longs;o
lertia cogno&longs;cendi. Nam quod ais quidem G
cogi in &longs;ocietatem cau&longs;&longs;æ Lunam ad&longs;ci&longs;cere,
interpretari, qua&longs;i tu proptereà totum hunc effectum,
aut quæ &longs;unt certè
in Lunam. Vtcumque &longs;it, id me permouit, Tum,
quòd vi&longs;um fuerit admirabile, duplicem e&longs;&longs;e &longs;ingulis
diebus a quæ affluxum, & refluxum, vt duplex e&longs;t &longs;in
gulis diebus in motu Telluris inæqualitas (nempe
bili in celeritatem, &longs;emel ex eodem in tarditatem, prout
in ea motus diurnus, & annuus &longs;emel con&longs;pirant, &longs;emel
abnuunt). Tum quòd aliunde vi&longs;um fuerit non po&longs;&longs;e
aquam ob fluiditatem, & in cauitate Terræ continen
tiam, non &longs;ic fluere, & refluere, &longs;i contingeret ip&longs;am
Terram tanquam vas moueri, & inæqualiter moueri:
imò & non po&longs;&longs;e iteratò po&longs;teriore dici parte non ef
fluere, ac refluere proprio pondere; &longs;i &longs;emel priore ef
fluxerit, & refluxerit vi incre&longs;centis celeritatis. Licet
quippe omnium deinde huius motus circum&longs;tantia
rum non videretur perinde e&longs;&longs;e, aut fieri cau&longs;&longs;a explo
rata: non ideò tamen vi&longs;um e&longs;t generalem cau&longs;&longs;am e&longs;&longs;e
reiiciendam; &longs;ed quicquid e&longs;&longs;et difficultatis referen
dum e&longs;&longs;e ad difficultatem perueftigationis; & dum &longs;pes
e&longs;&longs;et, vt &longs;ingula di&longs;quirerentur &longs;crupulo&longs;iùs, ac inueni
rentur fœliciùs; e&longs;&longs;e videri magni ducendum, quòd
&longs;ecta e&longs;&longs;et veluti glacies, quam deterere &longs;olum &longs;uper
e&longs;&longs;et. Ac &longs;i fui&longs;&longs;et quidem aliqua opinio, quæ cau&longs;
&longs;am pari nece&longs;&longs;itate cum effectu &longs;uo coniunctam mon
&longs;tra&longs;&longs;et, illi primas potiùs tribuendas cen&longs;ui&longs;&longs;em; at,
quæ mea fuit tarditas, talem e&longs;&longs;e nullam per&longs;pexi.
XLI.
Succedunt hæc verba,
te non arbitror, etiam ex illis motibus cau&longs;&longs;am &longs;ufficientem
non reddi, cur circa
cæteris; cùm illis temporibus vix inæqualitas vlla in Telluris
motu appareat; & quæ minima in punctis
notatur, non &longs;ubitò, aut vna tantum die exoritur, &longs;ed paulla
tim, diuturnóque tempore accre&longs;cit: cùm æ&longs;tus illi tamen non
ita &longs;en&longs;im, & &longs;ucceßiuè v&longs;que ad aliquem maximum accre&longs;-
maiores item eo tempore æ&longs;tus fiant, quo Tellus in punctis
Æ
patitur: &longs;ed in plenilunio &longs;olùm proximè in&longs;equente. Et
fui&longs;ti tu &longs;anè arbitratu tuo in meam ignorantiam in
dulgens; qui etiam ignoro, quæ tu heic a&longs;&longs;umis. Nam
primùm quidem,
crementum; &longs;ed repentè maximos æstus in Plenilunio
noctium con&longs;equente contingere,
ob&longs;eruaui, neque ab alio quoquam accepi: cùm potiùs,
vt æ&longs;tus &longs;pectati per quadranteis men&longs;is, minimi circa
quadraturas, maximi circa &longs;yzygias, &longs;en&longs;im per inter
ceptos dies, & maximi ex minimis, & minimi ex ma
ximis euadunt; ita &longs;i &longs;pectentur per quadranteis anni,
audierim &longs;emper minimos fieri circa tempora inter
cardines tempe&longs;tatum media; maximos circa cardines
(ac præ&longs;ertim Æquinoctialeis) per tempora autem in
tercepta maximos &longs;en&longs;im ex minimis, minimos ex ma
ximis fieri: quantumcumque per aliquos dies ab&longs;que
apparente incremento, tam &longs;ub quadraturas, & &longs;yzy
gias, quàm &longs;ub Æquinoctia, Sol&longs;titiáque e&longs;&longs;e videan
tur. Deinde,
proximè, primúmve post Æquinoctium contingenti,
mihi &longs;eu iuxta propriam, &longs;eu iuxta alienam
tiam
lunio, quod & Plenilunio competere iuris; & neque
facto paulò ante Æquinoctium Plenilunio, ex&longs;pecte
tur ferè po&longs;t men&longs;em Plenilunium con&longs;equens, vt ma
ximi in eo &longs;int æ&longs;tus: neque non &longs;int æ&longs;tus maiores
Plenilunio, Nouilunióque ante Quòd
ip&longs;is æquinoctialibus punctis,
varietatem in ip&longs;is creat, neque &longs;ola e&longs;t, neque per dies
aliquot variatur &longs;en&longs;ibiliter: &longs;ed &longs;uperuenit illa cau&longs;&longs;a
alia, varietatis &longs;cilicet men&longs;truæ, quæ, quòd in Plenilu
niis, Nouilunii&longs;que potenti&longs;&longs;ima &longs;it: ideo illi coniuncta
æ&longs;tus maximè &longs;en&longs;ibileis creat. Quòd verò,
ficiens exinde reddatur, cur tunc æstus fiant adeò magni præ
cæteris:
vigeat: cùm aliàs in ip&longs;o Æquinoctio (ni&longs;i ca&longs;u quo
dam) vigor Plenilunij, Nouiluniive non &longs;it; aut in Ple
nilunio, Nouiluniove, vigor Æquinoctii. Quòd dicis
cau&longs;&longs;am minimam, quæ ad v&longs;que Æquinoctium paul
latim incre&longs;cat, ab illo paullatim decre&longs;cat: &longs;atis e&longs;t ta
men, vt coniuncta cau&longs;&longs;æ &longs;olitæ, hoc e&longs;t men&longs;truæ,
effectum intendat. Congruum certè e&longs;t, vt &longs;i vniuersè
motus diurnus æ&longs;tum creat, ob inæqualitatem &longs;ibi ex
motu annuo &longs;uperuenientem;
uenientem &longs;pecialem inæqualitatem ex ductu per Zo
diacum: quatenus vbi ille e&longs;t maximè obliquus, nempe
ad ip&longs;um Æquatorem, motus diurnus, qui e&longs;t &longs;emper
directè ad ortum, maximè reprimitur, hoc e&longs;t cohibe
tur, ne ver&longs;us ortum protendatur.
XLII. Pergis,
reddi, cur in Pleniluniis Mare vehementiùs æ&longs;tuet, quàm tem
poribus reliquis. Verùm imprimis nihil e&longs;t nece&longs;&longs;e
cau&longs;&longs;am reddere illius effectus, quem verum e&longs;&longs;e mini
mè con&longs;tet: &longs;anè enim quæcumque &longs;it aliquorum
opinio, ob&longs;eruata tamen non de&longs;unt, quæ probent
Europa
res. Deinde, vbi fuerit conce&longs;&longs;um, æ&longs;tuare vehementiùs
Mare Pleniluniorum temporibus; cau&longs;&longs;a ex illis moti
bus reddi poterit non prorsùs incongrua. Siquidem
vtcúmque huiu&longs;modi motus imaginarii &longs;int; &longs;i veri
tamen &longs;upponantur, declarari pote&longs;t ex illis, cur in
Pleniluniis inæqualitas &longs;en&longs;ibilior, fiat, quàm in No
uiluniis. Cùm enim Luna &longs;upponatur, qua&longs;i Terræ pe
di&longs;&longs;equa, & dum circumducitur illi motu men&longs;truo,
ip&longs;um interim motu annuo indiuiduè concomitans;
efficitur, vt qua&longs;i totale cum ip&longs;a mobile habeatur,
quod vna, atque eadem cau&longs;&longs;a motu annuo circum
ueheat: eo modo, quo Lunulas quatuor ip&longs;ius Iouis
pedi&longs;&longs;equas habere licet qua&longs;i vnum cumip&longs;o Ioue mo
bile, prout dum illi &longs;pecialibus circumducuntur perio
dis, cùm illo tamen indiuiduè mouentur per Zodia
cum, & ab eadem cau&longs;&longs;a motu illo duodecennali cir
cumferuntur. Quare & &longs;upponendo Solem e&longs;&longs;e ge
neralem motorem, qui &longs;ibi ip&longs;i circumductus eo mo
tu, quem Maculæ mon&longs;trant, Planetas omneis radiis
qua&longs;i magneticis circumrapiat, & propiores quidem
velociùs, remotiores &longs;egniùs ab&longs;oluere circuitus cogat:
nece&longs;&longs;e erit, vt Luna ex&longs;i&longs;tente oppo&longs;ita, &longs;icque di
&longs;tantiore à Sole, quàm Terra, mobile ex vtraque factum
abripiatur radio, qui &longs;it,
Solique propiore, prolixior. Et quia
qua&longs;i plumbum pen&longs;ile, quod vibratur &longs;egniùs, &longs;i ap
pendatur ip&longs;i plumbulum, propter quod euadat &longs;en&longs;i
le prolixius: idcircò oportet tunc Terra &longs;e motu annuo Ac &longs;i, cùm
Luna quidem e&longs;t Soli coniuncta, Terra eódem redu
ceretur, & radius vtramque abripiens efficeretur tan
tumdem breuior, nece&longs;&longs;e foretip&longs;am tantumdem cir
citer moueri celeriùs; eo modo quò plumbum, dum fi
lum contrahitur, breuiu&longs;que fit: at quia Terra &longs;emper
con&longs;i&longs;tente in eadem di&longs;tantia, Luna citrò acta, ip&longs;am
nihilo retrahit, neque radium breuiorem facit: eapro
pter non videtur motus tam accelerari &longs;en&longs;ibiliter, do
nec Luna coniungitur, quàm retardatur, dum opponi
tur Soli. Quia verò intereà Luna &longs;e&longs;e habet, qua&longs;i
plumbulum illigatum filo, à quo plumbum dependet;
eamobrem, vt tunc plumbulum facit vibrationes ali
quantulùm celeriores, quatenus & ip&longs;um dependens à
filo breuiore appetit vibrari celeriùs, &longs;icque eò facit, vt
plumbum referatur ocyus; ita pote&longs;t Luna præ&longs;tare, vt
Terra non-nihil acceleret cur&longs;um: quanquam hære
&longs;cendum in i&longs;tis non e&longs;t: &longs;ed adnotandum potiùs,
quod ais G
non eò &longs;pectare debere, qua&longs;i ille adci&longs;cat vllum è cæ
lo in&longs;luxum, &longs;iue occultam qualitatem, vti vulgò
faciunt, qui ad Lunam confugiunt; &longs;ed qua&longs;i a&longs;&longs;umpta
vniuersè motus Terræ inæqualitate, pro generali æ&longs;tus
cau&longs;&longs;a, cohærenter faciat, dum ex motu Terræ, prout
e&longs;t cum motu Lunæ indiuiduus, &longs;pecialem cau&longs;&longs;am re
petit &longs;pecialis inæqualitatis.
tardationem, quæ dietim fit, ad motum Lunæ men&longs;truum,
(quatenus e&longs;t idem cum diurno Telluris) referri.
XLIII.
Pergis adhûc;
cit animus, cùm ad ea, quæ aliter explicari nequeunt, vno
verbo re&longs;pondetur, hæc, & &longs;imilia ex particularibus locorum
affectionibus oriri. Porrò i&longs;tud non re&longs;pondetur, quod
&longs;pectat ad ea generaliora accidentia, quæ &longs;unt omnium
Marium, ac &longs;peciatim Indiæ, Europæque communia:
cuiu&longs;modi e&longs;t vehementia æ&longs;tus, tam in Sol&longs;titiis, &
Æquinoctiis, quàm in Nouiluniis, Plenilunii&longs;que in
ten&longs;ior: &longs;ed quod &longs;pectat ad accidentia, quæ locorum
Terræ particularium propria cùm &longs;int; quidni cau&longs;&longs;as
habere proprias ex particularibus locis po&longs;&longs;int? Vt
enim dum nauicula aquæ &longs;emi-plena &longs;upra lacum pla
cidum inæquabiliter mouetur, ip&longs;a aqua fluit, ac re
fluit vniformiter, pro vniformitate inæqualitatis, &longs;i
nauicula quidem in interiore circumductu vniformi
ter deflexa, politaque ex&longs;titerit; Pari modo, &longs;i totum
Mare vna quadam Terræ cauitate ab occa&longs;u in ortum
producta, æquabiliterque deflexa contineretur, illius
fluxus, atque refluxus vniformiter fieret, quod attinet
quidem ad illa generaliora accidentia. At quia, &longs;i na
uicula deflexionem lateralem habeat variis protubera
tionibus, depre&longs;&longs;ionibu&longs;que difformem; & ex fundo
ad &longs;uperficiem, &longs;iue etiam altiùs, a&longs;&longs;urgant varij &longs;tipi
tes tenuïores, cra&longs;&longs;iores, & ambitum quoque variè re
cedentem, extuberantemque habentes; ob&longs;eruabis
aquam, dum fluet, ac refluet, admirabileis pati varieta-
que aliò commodiùs has varietates referes, quàm ad
varietatèm, qua aqua tam ad latera, quàm ad medium
variè allap&longs;a interpedictur: Pari ratione, quoniam
Terra capacitatem illam &longs;uam varianti&longs;&longs;ima varietate,
ob promontoria, &longs;inus, freta, i&longs;thmos, in&longs;ulas, cher&longs;o
ne&longs;os, & alia id genus pa&longs;&longs;im occurrentia affectam
&longs;ortitur: nihil &longs;anè dici videtur commodiùs, quàm mi
rabilem illam varietatem, quæ in quotidiano fluxu, &
refluxu ad particulareis oras ob&longs;eruatur, referendam
e&longs;&longs;e ad varietatem ip&longs;arum orarum, &longs;iue littorum, tam
in continentibus, quàm in In&longs;ulis occurrentium. Ni
mirùm prout littora properantem aquam in ortum,
occa&longs;umve, &longs;iue è regione, &longs;iue obliquè excipiunt; &
&longs;iue directò accedentem, &longs;iue deflexione à littoribus
antecedentibus affectam; & &longs;ui &longs;itu &longs;iue directo, &longs;iue
flexuo&longs;o, &longs;inubu&longs;que, ac promontoriis magnis, paruis,
raris, crebris, regularibus, irregularibus interrupto; &
tractu &longs;iue longo, &longs;iue breui, &longs;iue &longs;ingulari, &longs;iue repeti
to; & fundo &longs;iue plano, &longs;iue prono, &longs;iue alueo&longs;o, &longs;iue
&longs;copulo&longs;o, &c. nece&longs;&longs;e e&longs;t aquam diuer&longs;i&longs;&longs;imos acci
pere motus. Quod certè in fluminum ripis ob&longs;eruare
in promptu e&longs;t, heic nempe aquam leniter, illeic rapidè
fluere; heic abire rectà, illeic torqueri in vortices; heic
vndulare, illeic &longs;pumare; & id genus &longs;imilia; idem pro
portione &longs;eruata con&longs;entaneum e&longs;t fieri, vti & reuerâ
ob&longs;eruatur fieri, in ip&longs;is littoribus Maris.
XLIIII.
Pergis denique;
an ip&longs;emet quotidianus maris æ&longs;tus duplex, &longs;atu ex quotidia
na Telluris motione explicetur. Nam cùm Tellus viginti
e&longs;t, vt quæ partes hoc momento celeriùs, tardiu&longs;ve moueri inci
piunt, iterùm po&longs;t horas viginti quatuor &longs;imili celeritate, aut
tarditate moueantur, vt manife&longs;tum e&longs;t. Si hæc igitur di
uer&longs;itas motus cau&longs;&longs;a e&longs;&longs;et quotidianorum æ&longs;tuum, deberent
præcisè po&longs;t horas viginti quatuor recurrere, cùm vnâ ferè
horâ quotidie tardiùs recurrant. Quò fit, vt &longs;ingulis men
&longs;ibus tunc mare maximè quie&longs;cat, cùm habita ratione motus
Telluris &longs;ummè feruere deberet; & contrà, tum vehementer
ferueat, cùm illud paccatè quie&longs;cere oporteret. Verùm vno
verbo in&longs;inuatum e&longs;t in Epi&longs;tolis naturam aquæ flui
dam ob&longs;tare, ne aqua circumferatur tam facilè, ac reli
qui globi compacta natura. Quippe cùm motus re
liqui globi non exqui&longs;itè obfecundet (&longs;cilicet, &longs;i ob
&longs;ecundaret, nullus æ&longs;tus ex&longs;i&longs;teret) ideò nece&longs;&longs;e e&longs;t
eius motum fieri non-nihil retardatiorem, & men&longs;urâ
quidem tarditatis acceptâ ex portione motus Lunæ
men&longs;trui addita diurno Telluris, quatenus ab ip&longs;o de
pendet, imò idem reipsâ e&longs;t. Quia enim, vt Sol &longs;ibi ip&longs;i
intra dies proximè viginti &longs;eptem circumductus Ter
ram vnà circumvehit, &longs;ed &longs;egniùs tamen in&longs;equentem,
& non-ni&longs;iintra annum ab&longs;oluentem circuitum, pro
pter diffu&longs;iores, pauciore&longs;que radios, qui cùm in Ve
nere, & Mercurio confertiores &longs;int, circuitus in ip&longs;is
faciunt celeriores: &longs;ic Terra &longs;ibi circumducta intra ho
ras viginti quatuor, Lunam circum &longs;e abripit, &longs;ed &longs;e
gniùs tamen ob&longs;equentem, & non-ni&longs;i intra men&longs;em,
ab&longs;oluentem circuitum, qui ab&longs;olueretur haud-dubiè
celeriùs, &longs;i confertiores radios exceptura, circum ferretur
propiùs: Ideò, vt motus Terræ annuus e&longs;t veluti com-
Solis, pote&longs;tque adeò non alius ab ip&longs;o Solis motu
cen&longs;eri: &longs;ic motus Lunæ men&longs;truus contextus intelli
gitur ex pluribus portionibus reuolutionum diurna
rum Telluris: pote&longs;tque adeò idem e&longs;&longs;e cum diurno
motu intelligi. Heinc autem fit, vt quia Terra, ac Lu
na pro vno totali mobili habentur (quod paulò antè
dictum e&longs;t) idcircò alteratio, quæ motui annuo adue
nit ex intermi&longs;tione diurni, non &longs;it præcisè accipienda
quatenus diurnus &longs;olius Terræ e&longs;t proprius, &longs;ed quate
nus e&longs;t ip&longs;i cum Luna communis. Et quia propter
hanc communionem efficitur, vt motus diurnus non
&longs;it integer accipiendus, ni&longs;i po&longs;tquàm non modò Ter
ra ex meridiano quopiam digre&longs;&longs;a ad eundem meridia
num redit, &longs;ed po&longs;tquàm ip&longs;a etiam Luna meridianum
eundem repetit: inde e&longs;t, cur Luna illum dietim repe
tente, vnâ prope hora, &longs;eu quatuor quintis horæ tar
diùs; cur, inquam, alteratio illa, atque adeò æ&longs;tus con
tingat dietim tanto tempore: quatuor &longs;cilicet horæ
quintis tardiùs. Prætereo autem, cùm Luna ad datum
meridianum eádem diei hora, ni&longs;i po&longs;t men&longs;em non
redeat, excur&longs;us tamen, & recur&longs;us maris eadem hora
po&longs;t dies quindecim in&longs;taurari; quòd ij geminentur
in dies &longs;ingulos, ac eadem hora eueniant, non
modò cùm Luna e&longs;t nobis in mendiano &longs;upra horizon
tem, &longs;ed etiam cùm infià, in meridiano Antipodum. Adeò proinde, vt dici po&longs;&longs;it, quemadmodum Luna
intra men&longs;em apparet reuolui circa Terram vna vice
minùs, quàm Sol; ita Mare affluere, & refluere duabus
vicibus minùs, quàm afflueret, ac reflueret, ab&longs;que illa Prætereo quoque hanc retardationem,
quatenus ex aquæ &longs;luore, lentoréque &longs;imùl dependet,
confirmari po&longs;&longs;e videri ex con&longs;imili retardatione aëris,
de qua in Epi&longs;tolis dictum; cùm ventus illo continuus,
& æquabilis ab ortu in occa&longs;um, quem experiuntur
nautæ in alto, non videatur po&longs;&longs;e explicari
quàm ex retardatione aëris, ob fluiditatem &longs;uam inca
pacis, qui con&longs;equatur præci&longs;e motum Telluris conti
nuum, & æquabilem ver&longs;us ortum. Quo modo quo
que dici po&longs;&longs;et reciprocatione cariturum Mare, futu
rum que motum eius in occa&longs;um continuum, & æqua
bilem, &longs;i Terræ qua&longs;i nucleus e&longs;&longs;et exqui&longs;itè rotundus,
maréque e&longs;&longs;et illi circumfu&longs;um, neque incurreret in
littora, ver&longs;us quæ elatum, effluere, reflueréque cogere
tur. Prætereò & id genus alia; cùm his denique &longs;it fa
ciendus modus.
XLV.
Itaque Finem iam tandem facio; agno&longs;cens
me reuerâ eum, quem debui, modum non tenui&longs;&longs;e. Et
con&longs;titueram quidem initio non-ni&longs;i pauca re&longs;ponde
re ad &longs;ingula præclaræ tuæ Di&longs;qui&longs;itionis capita: &longs;ed
ne&longs;cio, quo pacto abreptus, ita &longs;en&longs;im ab in&longs;tituto, in
cœptoque rece&longs;&longs;erim, vt eua&longs;erim denique in hanc,
quam vides, prolixitatem. Fortè, me quoque pecca&longs;&longs;e
putes aduer&longs;us leges vrbanitatis, cùm ab v&longs;que literis
datis nihil Re&longs;pon&longs;i habueris, ni&longs;i po&longs;t exactum iam
men&longs;em: at partim cau&longs;&longs;am initio dixi, partim ecce
propalàm facio, cùm tibi i&longs;tam quaternionum, folio
rumque &longs;eriem obiicio. Quicquid id &longs;it rei, Tu &longs;ic ac
cipe, qua&longs;i voluerim &longs;pontaneam
tionem te&longs;tatione con&longs;imili, & cum fœnore quo-Quod dignaris mihi ad calcem &longs;in
gularium ingenij tui parturitionum copiam offerre, id
nimiæ bonitatis e&longs;t, quam vt experiri non mereor, &longs;ic
&longs;ollicitare non au&longs;im. Operam tamen daturus &longs;um,
vt itinere i&longs;tâc in&longs;tituto, cùm Deo bene propitio in
Prouinciam breui regrediar, tum coràm agam quas de
beo gratias, tum coràm fiam particeps, quorum e&longs;&longs;e
videbitur communicatio non importuna. Si quid
&longs;upererit, cùm deinceps in Patria conquie&longs;cere dabitur,
beabis me, quicquid me voles. Tu intereà rogatus
perge, quod vltrò cœpi&longs;ti; hoc e&longs;t, ama me, & bene,
imò optimè Vale. Pari&longs;iis, VI. Eid. Decembris.
M. DC. XLII.
Senatori Diuionen&longs;i,
SErò Re&longs;pondeo; nam eccemen&longs;is, ex quo tuæ li
teræ datæ: &longs;ed in cau&longs;&longs;a fuit tum inualetudo, tum
prolixa Re&longs;pon&longs;io, cui hoc adtextum &longs;chediolum ha
bes. Eadem vtor excu&longs;atione erga religio&longs;i&longs;&longs;imum, ac
eruditi&longs;&longs;imum Patrem. Tu, tamet&longs;i ille, qua e&longs;t boni
tate, admi&longs;&longs;urus &longs;ponte eam e&longs;t; intercede nihilominùs,
vt admittat pleniore &longs;ponte. Operam verò imprimis
da, vt qui te authore amare me cœpit, me porrò, te
quoque promotore, amet. Nimirùm tantus ille e&longs;t
vir, vt maximi ducam eius amicitiam, & tibi, cui ip&longs;am
debeo &longs;olidam, me &longs;ummoperè ob&longs;trictum agno&longs;cam. Vale.
Pari&longs;iis, VI. Eid. Decemb. M. DC. XLII.
IVxta Priuilegium à Rege Chri&longs;tiani&longs;&longs;imo conce&longs;
&longs;um, cautum e&longs;t, ne quistoto Regnoimprimat, alibi
ve impre&longs;&longs;as diuendat PETRI GASSENDI
Proportione, qua grauia decidentia accelerantur, Epi&longs;tolas
treis,
Pari&longs;ien&longs;em, idque in decennium, &longs;ub &longs;olitis pœnis. Datum Pari&longs;iis 8. April.
1642. Signatum CEBERET.
[Errata not typed]