<?xml version="1.0"?>
<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" >
<archimedes xmlns:xlink="http://www.w3.org/1999/xlink">      <info>
	<author>Varro, Michel</author>
	<title>De motu tractatus</title>
	<date>1584</date>
	<place>Geneva</place>
	<translator/>
	<lang>la</lang>
	<cvs_file>varro_demot_044_la_1584.xml</cvs_file>
	<cvs_version/>
	<locator>044.xml</locator>
</info>      <text><front><section> <pb xlink:href="044/01/001.jpg"/>
<p type="head"><s>TERRA <lb/>
MACHINIS MOTA <lb/>
DISSERTATIONES <lb/>
GEOMETRICAE, MECHANICAE <lb/>
PHYSICAE, HYDROSTATICAE <lb/>
In quibus <lb/>
Machinarum Coniugatarum uires inter &longs;e comparantur: <lb/>
Multiplici Noua Methodo Terrae magnitudo et <lb/>
Grauitas inue&longs;tigatur: ARCHIMEDES <lb/>
terrae motionem &longs;pondens ab arrogantia <lb/>
&longs;u&longs;picione uindicatur. <lb/></s>
<s>AVTHORE <lb/>
PAVLO CASATO <lb/>
E SOCIETATE IESV. <lb/></s>
<s>ROMAE. <lb/></s>
<s>Ex Typographia Ignatij de Lazaris.</s><s>M.DC.LVIII.<lb/></s>
<s>SVPERIORVM PERMISSV.<lb/></s></p>
<pb xlink:href="044/01/002.jpg"/><pb xlink:href="044/01/003.jpg" id="p.0001"/><p type="head">


<s>ILLVSTRI ET IN <lb/>
PRIMIS GENEROSO DOMINO, <lb/>
DOMINO CAROLO BARONI <lb/>
Azerotin, Name&longs;tij Ro&longs;icij <lb/>
Brandei&longs;ij Domino, <lb/>
MICH. VARRO. S. P. D.<!-- KEEP S--></s></p><p type="main">


<s><emph type="italics"/>CVM ab Ineunte &aelig;tate in Ma&shy;<lb/>
thematicis me exercui&longs;&longs;em, &longs;em&shy;<lb/>
per animo meo in h&aelig;&longs;it hoc de&longs;ide&shy;<lb/>
rium, vt qu&aelig; de Archimede Syra&shy;<lb/>
cu&longs;ano referuntur, ea &amp; ratione <lb/>
demon&longs;trare &amp; experimento comprobare po&longs;&longs;em. <lb/>
</s><s>Cumque multa in eo genere meditatus e&longs;&longs;em, po&longs;t&shy;<lb/>
quam ad iuris ciuilis &longs;tudium tran&longs;ii, ac tandem <lb/>
ad Rempub. <!-- REMOVE S-->nunquam mihi tantum otii contigit, <lb/>
vt ea in ordinem redigere potuerim. </s><s>At cum pau&shy;<lb/>
cis retr&ograve; annis &longs;atis longam peregrinationem per <lb/>
Sarmatiam &longs;u&longs;cepi&longs;&longs;em, e&longs;&longs;etque vacuus curis a-<emph.end type="italics"/>


<pb xlink:href="044/01/004.jpg" /><emph type="italics"/>nimus, atque ad earum rerum meditationem me <lb/>
impelleret genius meus, c&oelig;pi aliquid de his &longs;cribe&shy;<lb/>
re, quantum ip&longs;e iter faciendo meo marte a&longs;&longs;equi <lb/>
potui cum libris de&longs;tituerer. </s><s>Scriptum illud cum <lb/>
in maxim&egrave; ardua &amp; diffic&igrave;li contemplatione ver<lb/>
&longs;etur, nec ab eo tempore ex quo ad&longs;olitas occupa&shy;<lb/>
tiones redii ei extremam manum apponere mihi <lb/>
licuerit, decreueram inter priuatas meas mu&longs;as <lb/>
a&longs;&longs;eruare Verebar enim vulgi <expan abbr="iudici&utilde;">iudicium</expan>, (cuius <expan abbr="ta-m&etilde;">ta&shy;<lb/>
men</expan> rationem viro politico <expan abbr="habend&atilde;">habendam</expan> e&longs;&longs;e cen&longs;eo) ne&shy;<lb/>
que &longs;olum vulgi, verum etiam <expan abbr="eor&utilde;">eorum</expan> qui doctorum <lb/>
nomine gaudent, cum inaudita qu&aelig;dam interdum <lb/>
qu&aelig;que ab eorum opinione recedere <expan abbr="vide&atilde;tur">videantur</expan> at&shy;<lb/>
tingam. </s><s><expan abbr="Cupieb&atilde;">Cupiebam</expan> etiam in eo argumento vlteri&ugrave;s <lb/>
progredi, ant&egrave; quam quidquam ederem, atque ea <lb/>
qu&aelig; in meis aduer&longs;ariis ea de re &longs;par&longs;a habeo, iis <lb/>
qu&aelig; <expan abbr="conge&longs;&longs;er&atilde;">conge&longs;&longs;eram</expan> &longs;ubiicere, vt iu&longs;tum <expan abbr="volum&etilde;">volumen</expan> fieret.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="italics"/>Po&longs;tquam ver&ograve; te di&longs;ce&longs;&longs;um ex hac nostra ci&shy;<lb/>
uitate parare intellexi, in qua dum ver&longs;atus es. <lb/>
</s><s>non &longs;ol&ugrave;m ei <expan abbr="ornam&etilde;to">ornamento</expan> fui&longs;ti, &longs;ed etiam optimos <lb/>
quo&longs;que virtutum tuarum admiratione tibi con&shy;<lb/>
ciliasti: mihi ver&ograve; peculiariter innumera beneuo-<emph.end type="italics"/>


<pb xlink:href="044/01/005.jpg" /><emph type="italics"/>lenti&aelig; &longs;igna exhibui&longs;ti, non potui tantum virum, <lb/>
me&iacute;que <expan abbr="am&atilde;tem">amantem</expan> &longs;ine aliquo munere aut<emph.end type="italics"/> <foreign lang="greek">mnhmosu/nw|</foreign><lb/>
<emph type="italics"/>dimittere. </s><s>Itaque libellum hunc tibi dicare, &amp; <lb/>
&longs;ub tuo nomine in publicum edere &longs;tatui. </s><s>Squalli&shy;<lb/>
dus quidem prodit, &amp; rudis, mole etiam perexi&shy;<lb/>
guus: &longs;plendidius aliquid &amp; magis elaboratum <lb/>
postularet tua dignitas. </s><s>Atqui ea e&longs;t argumenti <lb/>
illius magnitudo, vt in eo aliquid volui&longs;&longs;e &longs;atis <lb/>
&longs;it. </s><s>Militare &longs;an&egrave; munus e&longs;t, e&oacute;que nomine tibi <lb/>
conueniens: &longs;i quis enim hac cognitione in&longs;tructus <lb/>
fuerit, non min&ugrave;s ea in re bellica vti poterit, <lb/>
quam Archimedes in Syracu&longs;is defendendis <lb/>
aduer&longs;us Marcum Marcellum v&longs;us est. </s><s>E&aacute;&shy;<lb/>
que mirari de&longs;inet qu&aelig; de eo Plutarchus nar&shy;<lb/>
rat. </s><s>Id lucidius <expan abbr="dem&otilde;&longs;trare">demon&longs;trare</expan> potui&longs;&longs;em, &longs;i mihi h&aelig;c <lb/>
vlterius per&longs;equendi otium fui&longs;&longs;et: Jeiuna enim <lb/>
per &longs;e videntur, ni&longs;i quis &longs;uccum qui &longs;ub corti&shy;<lb/>
ce latet, eliciat. </s><s>Malui tamen hoc veluti pro&shy;<lb/>
gymna&longs;mate alios quibus plus est otii &amp; in&shy;<lb/>
genii ad eiu&longs;modi inqui&longs;itionem hortari &amp; ac&shy;<lb/>
cendere, qu&agrave;m pr&aelig;claram illam cognitio&shy;<lb/>
nem diutius &longs;epultam relinquere cum ne-<emph.end type="italics"/>


<pb xlink:href="044/01/006.jpg" />
<emph type="italics"/>minem hodie animaduertam qui ei in&longs;udet, <lb/>
neque mihi &longs;pes vlla affulgeat diuturni otii, cuius <lb/>
ope in hoc &longs;tadio pergere po&szlig;im: Qu&ograve;d &longs;i fort&egrave; <lb/>
mihi aliquando contingat, riuos plurimos ex his <lb/>
fontibus me educturum; <expan abbr="c&otilde;fido">confido</expan>; quibus multum <lb/>
<expan abbr="c&otilde;modit&agrave;tis">commodit&agrave;tis</expan> rebus humanis accedat. </s><s>Qu&aelig; enim <lb/>
hic traduntur, ad motus omnes atque ad omnis ge<lb/>
neris virium comparationes accommodari po&longs;&shy;<lb/>
&longs;unt ad fines propo&longs;itos a&longs;&longs;equendos. </s><s>Quod qu&agrave;m <lb/>
lat&egrave; pateat, dici non pote&longs;t. </s><s>E&longs;t enim eorum v&longs;us <lb/>
non &longs;ol&ugrave;m in mechanicis, in quibus tamen e&longs;t ma <lb/>
ximus, &longs;ed etiam in politicis &amp; &oelig;conomicis: &longs;unt <lb/>
enim in illis motus, &longs;unt vires &amp; re&longs;istenti&aelig;. </s><s>In <lb/>
arte medica &amp; reliquis phy&longs;ices partibus pra&shy;<lb/>
cticis, quantus &longs;it, nemo fando exprimere po&szlig;it. <lb/>
</s><s>Quia vero ea qu&aelig; praxim docent gratiora &longs;unt <lb/>
ip&longs;a contemplatione, &amp; cau&longs;&aelig; propter effecta in&shy;<lb/>
quirantur,<emph.end type="italics"/> <foreign lang="greek">*a)lfh/stas</foreign> <emph type="italics"/>omnes hortor vt quod ego in&shy;<lb/>
numeris aliis cur is implicitus addere non po&longs;&shy;<lb/>
&longs;um, ip&longs;i addant. </s><s>Abundat nunc Europa pr&aelig;&shy;<lb/>
&longs;tantibus ingeniis, &longs;i M&oelig;cenates ade&longs;&longs;ent. <lb/>
</s><s>Ea autem qu&aelig; pr&aelig;ter h&aelig;c meditatus &longs;um, ac fer-<emph.end type="italics"/><pb xlink:href="044/01/007.jpg" />
<emph type="italics"/>m&egrave; parata habeo, h&aelig;c &longs;unt. </s><s>Tractatus de iactu. <lb/>
</s><s>De continuitate eiu&longs;que &longs;olutione. </s><s>De <expan abbr="c&otilde;den&longs;a-tione">conden&longs;a&shy;<lb/>
tione</expan> &amp; rarefactione earumque cau&longs;is &amp; effecti&shy;<lb/>
bus: <expan abbr="It&etilde;">Item</expan> in Mechanicis, tractatus de variis ma&shy;<lb/>
chinis ad motus <expan abbr="ci&etilde;dos">ciendos</expan>, ac de perfecti&szlig;im&aelig; cuiu&longs;&shy;<lb/>
que ad id quod propo&longs;itum fuerit moliendum in&shy;<lb/>
ue&longs;tigatione. </s><s>Nonnulla <expan abbr="eti&atilde;">etiam</expan> de <expan abbr="Rerumpublicar&utilde;">Rerumpublicarum</expan> <lb/>
motu tum interno <expan abbr="t&utilde;">tum</expan> externo notaui, qu&aelig; <expan abbr="eod&etilde;">eodem</expan> or&shy;<lb/>
dine tradere optarem: quorum omnium principia <lb/>
hic &longs;i quis diligenter animaduertat tradita &longs;unt. <lb/>
</s><s>Si quis mihi in his <expan abbr="palm&atilde;">palmam</expan> pr&aelig;ripuerit, meque an&shy;<lb/>
teuerterit ei maximas gratias agam. </s><s>Sunt tamen <lb/>
inter h&aelig;c qu&aelig;dam qu&aelig; vulg&ograve; pandere nephas est. <lb/>
</s><s>Itaque theori&aelig; magis in&longs;i&longs;tendum puto, in qua &longs;i <lb/>
quis exercitatus fuerit, nullo negotio illam in opus <lb/>
educere poterit, idque &longs;ine periculo fiet, cum vul&shy;<lb/>
go non pateat. </s><s>Alioqui <expan abbr="pericul&utilde;">periculum</expan> e&longs;t, ne &longs;i particu&shy;<lb/>
laria tradantur iis contenti homines, vt fieri &longs;olet <lb/>
vniuer&longs;alem cognitionem &amp; cau&longs;arum inqui&longs;i&shy;<lb/>
tionem negligant, pereatque &longs;cientia. </s><s>Eaque de <lb/>
cau&longs;a nihil quicquam de his qu&aelig; fecerat Archi-<emph.end type="italics"/>


<pb xlink:href="044/01/008.jpg" />
<emph type="italics"/>medes &longs;criptum relinquere voluit. </s><s><expan abbr="Exi&longs;tim&atilde;s">Exi&longs;timans</expan> eos <lb/>
qui in iis qu&aelig;<emph.end type="italics"/> <foreign lang="greek">qewrhtikw=s</foreign> <emph type="italics"/>tradiderat, diligentem ope&shy;<lb/>
ram ponere <expan abbr="vell&etilde;t">vellent</expan>, mult&ograve; maiora quoties opus fo&shy;<lb/>
ret pr&aelig;&longs;tituros. </s><s>Equidem mihi per&longs;uadeo non de&shy;<lb/>
futuros qui varia iudicia de hoc no&longs;tro &longs;cripto fe&shy;<lb/>
rant &amp; qua&longs;i nouum athletam in aren&agrave;m pro&shy;<lb/>
deuntem mirentur. </s><s>Quibus vno verbo re&longs;pon&shy;<lb/>
&longs;um volo, me nullius vnquam in verba ma&shy;<lb/>
gistri iura&longs;&longs;e, &longs;ed liberrim&egrave; &longs;emper philo&longs;o&shy;<lb/>
phatum e&longs;&longs;e: ita vt etiam in principia ab aliis <lb/>
&longs;tatuta animaduertere mihi licere putauerim. <lb/>
</s><s>Quod e&ograve; liberi&ugrave;s feci, po&longs;tquam magnam <expan abbr="part&etilde;">partem</expan> <lb/>
vulgo receptarum opinionum fal&longs;am e&longs;&longs;e re ip&longs;a <lb/>
deprehendi. </s><s>Omnibus placuero, &longs;i tibi placuero. </s><s>Si <lb/>
quid in his ob&longs;curius fuerit, habes <expan abbr="clari&szlig;im&utilde;">clari&szlig;imum</expan> vi&shy;<lb/>
rum Wence&longs;laum lauinium tuum, ab&longs;tru&longs;ioris <lb/>
philo&longs;ophi&aelig; indagatorem <expan abbr="&longs;umm&utilde;">&longs;ummum</expan>, qui tibi omnia <lb/>
explicabit. </s><s>Hoc igitur <expan abbr="munu&longs;cul&utilde;">munu&longs;culum</expan> vt &longs;erena <expan abbr="fr&otilde;-te">fron&shy;<lb/>
te</expan> &longs;u&longs;cipias rogo. </s><s>Vale. <!-- KEEP S--></s><s>V I. <!-- KEEP S--></s><s>K al. <!-- REMOVE S-->Jun. <!-- REMOVE S-->Anno <lb/>
Christi Domini<emph.end type="italics"/> M. D. LXXXIV. <!-- KEEP S--></s>



</p></section><pb xlink:href="044/01/009.jpg" pagenum="1"/><section><p type="head">

<s>M. VARRONIS DE <lb/>
MOTV TRACTATVS.<!-- KEEP S--></s></p></section></front><body><chap><p type="head">

<s><emph type="italics"/>PROBLEMA.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">

<s><emph type="italics"/>Data vi datum pondus mouere.<emph.end type="italics"/></s></p><p type="main">

<s>Hoc problema prima quidem <lb/>
fronte mirabile videtur, vt &longs;cilicet <lb/>
pondus vel maximum viribus ta&shy;<lb/>
men minimis, vt puta &longs;i dicas vnius <lb/>
hominis, vel etiam imbecillioris a&shy;<lb/>
licuius animalis viribus totum ter&shy;<lb/>
r&aelig; globum loco moueri po&longs;&longs;e. </s><s>Quod Archimedem <lb/>
Syracu&longs;anum iacta&longs;&longs;e referunt hoc dicto, <foreign lang="greek">do\s pou= stw=| <lb/>
ta\n ga\n kinw=|. </foreign></s><s>Si quis tamen in Geometrico puluere <lb/>
ver&longs;atus fuerit, pre&longs;ertim ver&ograve; in iis qu&aelig; ab ip&longs;o in <lb/>
&longs;uo <foreign lang="greek">i)soropikw=n</foreign> libello <expan abbr="trad&utilde;tur">traduntur</expan>. </s><s>Illud c&aelig;ter&aacute;que eiu&longs;&shy;<lb/>
modi, ludicra Geometri&aelig;, vt &amp; ip&longs;e facere &longs;olitus di<lb/>
citur, appellabit. </s><s>Ex huius autem problematis expli<lb/>
catione, omnium machinarum qu&ecedil; ad motus cien&shy;<lb/>
dos excogitari po&longs;&longs;unt, ratio pendet. </s><s>Et&longs;i ver&ograve; <expan abbr="tot&utilde;">totum</expan> <lb/>
Geometrica demon&longs;tratione expediri po&longs;&longs;it, quo&shy;


<pb xlink:href="044/01/010.jpg" pagenum="2"/>niam tamen h&ecedil;c con&longs;ideratio, qu&aelig; Gr&aelig;cis <foreign lang="greek">staqmikh\</foreign> di<lb/>
citur Geometri&aelig; tant&ugrave;m e&longs;t <foreign lang="greek">u(pa/llhlos</foreign> mixta &longs;cili&shy;<lb/>
cet ex phy&longs;ica &amp; Geometrica eo qu&ograve;d illius &longs;ubie&shy;<lb/>
ctum &longs;it motus. </s><s>Ide&ograve; paul&ograve; cra&longs;&longs;iori Minerua &amp; <lb/>
pr&aelig;ter Geometricam &longs;implicitatem <foreign lang="greek">fusikw=s</foreign> etiam <lb/>
tractanda e&longs;t: alioqui Archimedicis demon&longs;tratio&shy;<lb/>
nibus &longs;tandum e&longs;&longs;et, qu&aelig; in eo manc&aelig; &longs;unt, qu&ograve;d il&shy;<lb/>
l&aelig; propo&longs;itiones qu&aelig; ex phy&longs;icis peti debent, inde&shy;<lb/>
mon&longs;trat&aelig; manent, nec explicantur, &longs;ed pro confe&longs;&shy;<lb/>
&longs;is principiorum loco po&longs;tulantur. </s><s>Eas igitur, qua&shy;<lb/>
tenus ad huius problematis explicationem faciunt, <lb/>
hic di&longs;cutiemus. </s><s>Neque enim Euclidis <expan abbr="libr&utilde;">librum</expan> de gra&shy;<lb/>
ui &amp; leui, in quo hoc argumentum per&longs;equi volui&longs;&shy;<lb/>
&longs;e videtur, integrum habemus. </s><s>Ari&longs;toteles ver&ograve; in <lb/>
eo quod ab ip&longs;o &longs;criptum extat de Mechanicis fra&shy;<lb/>
gmento pr&ecedil;ter &longs;uum morem, c&ugrave;m alio qui in omni&shy;<lb/>
bus exacti&longs;&longs;imus &longs;it, hanc qu&aelig;&longs;tionem poti&ugrave;s nota&shy;<lb/>
uit qu&agrave;m explicuit in &longs;exto &amp; &longs;eptimo phy&longs;icorum <lb/>
libro multa pr&aelig;termi&longs;it. </s><s>Vt igitur ad rem aggredia&shy;<lb/>
mur, prim&ugrave;m voces, quibus vtendum e&longs;t, definie&shy;<lb/>
mus, vt intelligatur quo &longs;en&longs;u eas accipiamus. </s></p><p type="head">

<s>DEFINITIO I.<!-- KEEP S--></s></p><p type="main">

<s>Vis dicitur agendi aut agenti re&longs;i&longs;tendi <expan abbr="pot&etilde;tia">potentia</expan>, <lb/>
pr&aelig;&longs;ertim ver&ograve; mouendi &amp; mouenti re&longs;i&longs;tendi. </s></p><p type="head">

<s>II.<!-- KEEP S--></s></p><p type="main">

<s>Vis &longs;ubiectum dicitur id quod vis mouet, vel 


<pb xlink:href="044/01/011.jpg" pagenum="3"/>quod &agrave; vi mouetur. </s></p><p type="main">

<s>H&icirc;c non agimus de vi primaria qu&aelig; virium o&shy;<lb/>
mnium principium e&longs;t, mou&eacute;tque omnia, nec <expan abbr="tam&etilde;">tamen</expan> <lb/>
mouetur, &longs;ed de ea, qu&ecedil; dum mouet, <expan abbr="eti&atilde;">etiam</expan> cum &longs;ub&shy;<lb/>
iecto, cui ine&longs;t, mouetur. </s></p><p type="main">

<s>Subiecta ver&ograve; qu&aelig; nullam vim habent, nec mo&shy;<lb/>
uentur, nec mouenti <expan abbr="re&longs;i&longs;t&utilde;t">re&longs;i&longs;tunt</expan>: &longs;i qua ver&ograve; vis illis ac&shy;<lb/>
cedat, tum ab ea &longs;e moueri patiuntur. </s></p><p type="main">

<s>Et&longs;i autem plura &longs;int virium genera, tot &longs;cilicet, <lb/>
quot &longs;unt in rerum natura contrariorum, actionem <lb/>
&amp; pa&longs;&longs;ionem recipientium, vt leue graue, rarum <expan abbr="d&etilde;-&longs;um">den&shy;<lb/>
&longs;um</expan>, plenum vacuum, durum molle, &amp; c&aelig;tera eiu&longs;&shy;<lb/>
modi, quoniam tamen ea omnia h&icirc;c per&longs;equi no&longs;tri <lb/>
non e&longs;t in&longs;tituti, c&ugrave;m de ea tant&ugrave;m qua motus fit a&shy;<lb/>
gere &longs;tatuerimus. </s></p><p type="head">

<s>III.<!-- KEEP S--></s></p><p type="main">

<s>C&ugrave;m de motu h&icirc;c agemus motum ad locum, <lb/>
quem Gr&aelig;ci <foreign lang="greek">fora\n</foreign> vocant, intelligi volumus. </s></p><p type="head">

<s>IIII.<!-- KEEP S--></s></p><p type="main">

<s>Linea autem recta qu&aelig; e&longs;t ab eo loco &agrave; quo mo&shy;<lb/>
tus fieri incipit ad illum ad quem tendit. </s><s>Illius vis <lb/>
qu&aelig; motum efficit, nutus dicetur. </s></p><p type="main">

<s><expan abbr="Ead&etilde;">Eadem</expan> ver&ograve; linea <expan abbr="c&otilde;&longs;iderata">con&longs;iderata</expan> &agrave; loco ad <expan abbr="qu&etilde;">quem</expan> <expan abbr="t&etilde;dit">tendit</expan> vis <lb/>
ad <expan abbr="ill&utilde;">illum</expan> &agrave; quo motus fieri incipit, contra <expan abbr="nut&utilde;">nutum</expan> dicitur. </s></p><p type="main">

<s>Itidem &amp; omnes illi parallel&aelig;. </s></p><p type="main">

<s>Qu&aelig; ver&ograve; line&aelig; vel rect&aelig;, vel curu&aelig;, nutus <expan abbr="line&atilde;">lineam</expan> 


<pb xlink:href="044/01/012.jpg" pagenum="4"/>ad angulos in&aelig;quales &longs;ecant, ill&aelig; obliqu&egrave; nutum <lb/>
ver&longs;us, vel contra nutum ferri <expan abbr="dic&utilde;tur">dicuntur</expan>, habita ratio&shy;<lb/>
ne partium, quas &longs;pectant. </s></p><p type="main">

<s>Plurim&ugrave;m autem &agrave; &longs;itu corporis humani deno&shy;<lb/>
minationem accipiunt ill&aelig; partes, vt &longs;ur&longs;um, deor&shy;<lb/>
&longs;um, dextror&longs;um, &longs;ini&longs;tror&longs;um, ant&egrave; vel pon&egrave; di&shy;<lb/>
cantur. </s><s>Qu&aelig; ver&ograve; line&aelig;, nutus lineam ad angulos <lb/>
rectos &longs;ecant, neque ver&longs;us nutum, neque contra <lb/>
nutum ferri dicuntur, &longs;ed &aelig;qu&egrave; di&longs;tant &agrave; loco natu&shy;<lb/>
rali. </s></p></chap><chap><p type="head">

<s><emph type="italics"/>Virium diui&longs;io.<emph.end type="italics"/></s></p><p type="main">

<s>Vis autem omnis aut naturalis e&longs;t, aut non natu&shy;<lb/>
ralis, aut mixta. </s><s>Naturalis vis e&longs;t, qua res qu&aelig;libet <lb/>
natura &longs;ua mouetur, aut mouenti re&longs;i&longs;tit habita ra&shy;<lb/>
tione tum loci &longs;ui naturalis, tum etiam &longs;itus &longs;uarum <lb/>
partium. </s><s>Non naturalis e&longs;t qu&aelig; nec ratione loci &longs;ui <lb/>
naturalis, nec &longs;itus partium mouet. </s><s>E&longs;t autem h&aelig;c <lb/>
duplex, fortuita &longs;cilicet &amp; voluntaria: illa vt vis ven&shy;<lb/>
torum &amp; &longs;pirituum intellectu carentium, h&aelig;c vt a&shy;<lb/>
nimalium &amp; &longs;pirituum intelligentium &amp; &longs;imilium. <lb/>
</s><s>Mixta dicitur, qu&aelig; partim naturalis e&longs;t, partim non <lb/>
naturalis. </s></p><p type="main">

<s>Locus autem naturalis cuiu&longs;que rei e&longs;t, in quo <lb/>
exi&longs;tens ip&longs;a quie&longs;cit, &amp; &longs;i inde remota &longs;it, vis ei &agrave; na<lb/>
tura in&longs;ita eam illuc impellit. </s><s>Huius ver&ograve; motus aut <lb/>
quietis cau&longs;&longs;a nulla alia a&longs;&longs;ignari pote&longs;t pr&aelig;ter pri-


<pb xlink:href="044/01/013.jpg" pagenum="5"/>mam illam rerum omnium conditricem, qu&ecedil;, ne o&shy;<lb/>
mnia in omnibus e&longs;&longs;ent &longs;ingulis partibus vniuer&longs;i <lb/>
&longs;ingula loca attribuit circa qu&aelig; conglobantur, &amp; i&shy;<lb/>
bi h&aelig;rent. </s><s>Quicquid enim terreum e&longs;t, in terr&aelig; glo&shy;<lb/>
bum <expan abbr="c&otilde;fluxit">confluxit</expan>. </s><s>Ita quicquid &longs;oli homogenes in Solis <lb/>
corpus, lunaria omnia in lunam, &amp; &longs;ic de c&aelig;teris cor<lb/>
poribus vniuer&longs;i. </s><s>Singul&aelig; autem eorum partes &longs;uis <lb/>
totis adh&aelig;rent, nec inde &longs;ponte <expan abbr="mou&etilde;tur">mouentur</expan>: &longs;i ver&ograve; in&shy;<lb/>
de mot&aelig; fuerint, e&ograve; redire nituntur. </s><s>Quod enim in <lb/>
terra fieri videmus, idem &amp; in reliquis corporibus v&shy;<lb/>
niuer&longs;i fieri dicere po&longs;&longs;umus, &longs;cilicet quod vnita cir<lb/>
ca locum &longs;uum naturalem maneant: &longs;i enim partes <lb/>
eorum &longs;ponte &longs;epararentur, &amp; vi ab ip&longs;is &longs;eparat&aelig; <lb/>
ad locum &longs;uum non redirent, &longs;tatim tota di&longs;&longs;olue&shy;<lb/>
rentur. </s></p><p type="main">

<s>Vis igitur illa in loco &longs;uo quie&longs;cendi grauitas di&shy;<lb/>
citur, cuius contrarium e&longs;t leuitas. </s><s>Res autem nulla <lb/>
per &longs;e leuis dicitur, &longs;ed <expan abbr="t&atilde;t&ugrave;m">tant&ugrave;m</expan> habita ratione alterius <lb/>
loci, qu&agrave;m &longs;ui naturalis: vt puta &longs;i pars aliqua Solis <lb/>
vi quapiam in terram inuecta e&longs;&longs;et, &longs;u&oacute;que arbitrio <lb/>
committeretur, illa &longs;tatim Solem peteret: ita &longs;i ter&shy;<lb/>
r&aelig; pars in Solem inuecta e&longs;&longs;et, &longs;u&oacute;que arbitrio com<lb/>
mitteretur, &longs;tatim &agrave; &longs;ole euolaret, &amp; &longs;e per c&aelig;lum <lb/>
terram ver&longs;us proriperet. </s><s>Vt igitur terr&aelig; partes in <lb/>
terra graues &longs;unt: &longs;ic Solis partes in &longs;ole graues &longs;unt: <lb/>
in terra ver&ograve; leues, terr&aelig; ver&ograve; partes in Sole leues 


<pb xlink:href="044/01/014.jpg" pagenum="6"/>&longs;unt. </s><s>Idem de c&aelig;teris corporibus vniuer&longs;i dici po&shy;<lb/>
te&longs;t. </s><s>Neque enim facili&ugrave;s ex globo lun&aelig; particulam <lb/>
ab&longs;trahas, qu&agrave;m ex terra glebam. </s></p><p type="main">

<s>Aer autem nullum proprium habet locum natu<lb/>
ralem, &longs;ed vbique e&longs;&longs;e pote&longs;t, c&ugrave;m rerum omnium <lb/>
locus vniuer&longs;alis e&longs;&longs;e videatur: de quo dubitari po&shy;<lb/>
te&longs;t an &longs;it infinitus, c&ugrave;m omnia contineat, &agrave; nulla re <lb/>
ver&ograve; totus comprehendatur, &longs;ed h&aelig;c di&longs;putatio non <lb/>
e&longs;t huius loci. </s></p><p type="main">

<s>Et&longs;i autem nullum proprium habet locum natu<lb/>
ralem, neque leuis aut grauis &longs;it: leuis tamen e&longs;&longs;e vi&shy;<lb/>
detur, c&ugrave;m grauis non &longs;it, nec &aelig;gr&egrave; &longs;e moueri patia&shy;<lb/>
tur. </s><s>Itaque &longs;i quo modo ita con&longs;titutus &longs;it, vt rem a&shy;<lb/>
liquam, qu&ograve; min&ugrave;s ad locum &longs;uum naturalem per&shy;<lb/>
uenire po&longs;&longs;it, impediat, tum per expre&longs;&longs;ionem &longs;eu <lb/>
<foreign lang="greek">e)/kqliyin</foreign>, ab ea eiicietur, in ei&uacute;&longs;que locum &longs;uccedet, <lb/>
vt fit in aqua, c&ugrave;m ei introducitur. </s><s>Qu&aelig; quidem <foreign lang="greek">e)/k&shy;<lb/>
qliyis</foreign> iis etiam accidit qu&aelig; loco naturali gaudent, <lb/>
c&ugrave;m &longs;e&longs;e mutu&ograve; impediunt, ne ad illum ferantur. <lb/>
</s><s>Pr&aelig;&longs;ertim ver&ograve; in liquidis locum habet, quorum <lb/>
partes facilius mouentur, qu&agrave;m rerum <expan abbr="coh&aelig;renti&utilde;">coh&aelig;rentium</expan> <lb/>
&amp; compactarum. </s><s>Inde accidit vt quicquid liquidis <lb/>
immergitur, tant&ograve; fiat in illis leuius qu&agrave;m grauius, <lb/>
e&longs;t moles eiu&longs;dem liquoris ip&longs;orum moli &aelig;qualis. <lb/>
</s><s>Sed h&aelig;c de loco naturali fu&longs;i&ugrave;s &agrave; nobis alibi medita&shy;<lb/>
ta, obiter h&icirc;c attigi&longs;&longs;e &longs;ufficiat, vt intelligatur quid 


<pb xlink:href="044/01/015.jpg" pagenum="7"/>&longs;it vis naturalis. </s></p><p type="main">

<s>Vis autem voluntaria nullum certum nutum <lb/>
habet, &longs;ed illum tant&ugrave;m in quo mouentis voluntas <lb/>
conquie&longs;cit. </s><s>C&uacute;mque vis naturalis vnum tant&ugrave;m <lb/>
nutum habeat, &longs;cilicet &agrave; loco &agrave; naturali requie re&shy;<lb/>
moto, ad ip&longs;am naturalem requiem, illa infinitos nu <lb/>
tus habet &amp; indeterminatos per &longs;e ac voluntatis tan <lb/>
t&ugrave;m decreto determinabiles. </s></p><p type="main">

<s>Fortuita ver&ograve; ip&longs;o tant&ugrave;m ca&longs;u determinabilem <lb/>
nutum habet: qu&ograve; enim ip&longs;a tendit, eo munere dici&shy;<lb/>
tur &longs;iue &longs;ur&longs;um, &longs;iue deor&longs;um, &longs;iue ad latera. </s><s>Itaque <lb/>
&amp; hic &amp; ille nutus <foreign lang="greek">a)dio/ristos</foreign> dicitur. </s><s>Quemadmodum <lb/>
&amp; is quem habent vires ill&aelig;, quibus res &agrave; &longs;itu <expan abbr="parti&utilde;">partium</expan> <lb/>
naturali remot&aelig; ad illum redeunt: prout enim ab <lb/>
eo mot&aelig; &longs;unt, ita ad illum redeunt, prout etiam huc <lb/>
aut illuc obuer&longs;&aelig; &longs;unt, vt vis arcus aut bali&longs;t&aelig;. </s></p><p type="head">

<s>DEFIN. V.<!-- KEEP S--></s></p><p type="main">

<s>Vires autem contrari&aelig; dicuntur, qu&aelig; contrarios <lb/>
motus ciere po&longs;&longs;unt, vt ea <expan abbr="qu&ecedil;">qu&aelig;</expan> &longs;ur&longs;um mouet &amp; <expan abbr="qu&ecedil;">qu&aelig;</expan><lb/>
deor&longs;um, &amp; &longs;ic de c&aelig;teris. </s></p><p type="main">

<s>Con&longs;ideratur autem in vi <expan abbr="qu&atilde;titas">quantitas</expan>, tum eo qu&ograve;d <lb/>
vis partibus &longs;uis con&longs;tet, in quas in infinitum diuidi <lb/>
pote&longs;t, &amp; rur&longs;us additione aut multiplicatione au&shy;<lb/>
geri, tum qu&ograve;d &aelig;qualitatis exce&longs;&longs;us &amp; defectus <expan abbr="c&otilde;-parationem">con&shy;<lb/>
parationem</expan> recipiat. </s></p>


<pb xlink:href="044/01/016.jpg" pagenum="8"/><p type="main">

<s>Ac quoniam vis e&longs;t mouendi potentia, vis par&shy;<lb/>
tes erunt qu&aelig; motus partes efficient, &amp; qu&aelig; erit mo<lb/>
tus partium, men&longs;ura eadem erit &amp; vis partium. </s><s>Et <lb/>
motus quidem propria men&longs;ura e&longs;t linea &longs;eu <expan abbr="&longs;pati&utilde;">&longs;patium</expan>. <lb/>
</s><s>Quantum enim res qu&aelig;piam mota, &longs;patij percur&shy;<lb/>
rit, tant&ugrave;m mota e&longs;&longs;e dicitur. </s><s>Quoniam ver&ograve; in mo<lb/>
mento vel in&longs;tanti quod in&longs;tar puncti e&longs;t, &amp; magni&shy;<lb/>
tudine caret, nullus motus fieri pote&longs;t, &longs;ed motus o&shy;<lb/>
mnis in tempore fit. </s><s>Ide&ograve; ad motus men&longs;uram tem&shy;<lb/>
pus etiam adhibere oportet. </s><s>Illud enim cum &longs;patio <lb/>
vel linea, motus dici facit &aelig;quales aut in&aelig;quales. </s></p><p type="head">

<s>DEFIN. VI.<!-- KEEP S--></s></p><p type="main">

<s>&AElig;quales igitur motus dicuntur, qui &aelig;qualibus <lb/>
temporibus &aelig;qualia &longs;patia percurrunt. </s></p><p type="main">

<s>Qui autem &aelig;qualibus temporibus &aelig;qualia &longs;pa&shy;<lb/>
tia permeant, illi iidem proportionales &longs;unt: hoc <lb/>
e&longs;t, qu&aelig; e&longs;t ratio temporis, quo alter eorum fit ad <lb/>
tempus quo fit alter, eadem e&longs;t &longs;patij quod percurrit <lb/>
alter ad &longs;patium quod reliquus percurrit. </s><s>Si enim <lb/>
duorum quorum &longs;inguli vna hora miliaris vnius i&shy;<lb/>
ter conficiunt, alter eodem motu per tria miliaria <lb/>
ferri pergat, alter ver&ograve; per duo <expan abbr="t&atilde;t&ugrave;m">tant&ugrave;m</expan>. </s><s>Ille tribus ho&shy;<lb/>
ris ea ab&longs;oluet, hic ver&ograve; duabus, &amp; &aelig;qu&egrave; celeriter <lb/>
ferri dicentur, licet &longs;patia in&aelig;qualia <expan abbr="percurr&atilde;t">percurrant</expan>, quo&shy;<lb/>
niam illa &longs;unt temporibus proportionalia. </s></p>


<pb xlink:href="044/01/017.jpg" pagenum="9"/><p type="head">

<s>VII.<!-- KEEP S--></s></p><p type="main">

<s>In&aelig;quales autem motus dicuntur, quorum tem&shy;<lb/>
pora non &longs;unt &longs;patiis proportionalia. </s><s>Eorum autem <lb/>
maior ille dicitur, cuius maior erit ratio &longs;patij ad &longs;pa<lb/>
tium, qu&agrave;m temporis ad tempus, quibus fiunt illi <lb/>
motus. </s><s>Ex quo intelligitur etiam quis minor dica&shy;<lb/>
tur. </s><s>Maior igitur dicetur qui celeri&ugrave;s feretur, minor, <lb/>
qui tardi&ugrave;s. </s></p><p type="head">

<s>VIII.<!-- KEEP S--></s></p><p type="main">

<s>&AElig;quales igitur vires dicentur, qu&aelig; &aelig;qualibus <lb/>
motibus &longs;ubiecta &longs;ua mouebunt. </s><s>Maior ver&ograve; qu&aelig; <lb/>
&longs;ubiectum &longs;uum magis vel celeri&ugrave;s mouebit. </s><s>Mi&shy;<lb/>
nor, qu&aelig; min&ugrave;s vel tardi&ugrave;s. </s></p></chap><chap><p type="head">

<s><emph type="italics"/>Motuum diui&longs;io.<emph.end type="italics"/></s></p><p type="main">

<s>Comparantur autem motus &longs;ecundum omnes <lb/>
comparationis gradus, hoc e&longs;t, &aelig;qualitatem, exce&longs;&shy;<lb/>
&longs;um &amp; defectum: tum &longs;ibi ip&longs;is, c&ugrave;m totus &longs;uis par&shy;<lb/>
tibus confertur, tum alij aliis. </s></p><p type="main">

<s>Quatenus autem &longs;ibi ip&longs;i motus <expan abbr="c&otilde;paratur">comparatur</expan>, aut <lb/>
e&longs;t <foreign lang="greek">o(moiomerh\s</foreign> &longs;eu &aelig;quabilis aut <foreign lang="greek">a)nomoiomerh\s</foreign>, id e&longs;t in&aelig;&shy;<lb/>
quabilis. </s><s>Aequabilis, cuius omnes partes tum mini&shy;<lb/>
m&aelig; tum maiores tempora habent &longs;patiis per qu&aelig; <lb/>
cientur proportionalia. </s><s>In&aelig;quabilis ver&ograve;, in quo illa <lb/>
non &longs;unt proportionalia. </s></p><p type="main">

<s>In&aelig;quabilium autem motuum duo &longs;unt genera, 


<pb xlink:href="044/01/018.jpg" pagenum="10"/>cre&longs;cens &longs;cilicet &amp; decre&longs;cens, &iacute;dque vel continu&egrave;, <lb/>
vel per interualla, ordinatim vel <foreign lang="greek">a)taktw=s. </foreign></s></p><p type="main">

<s>Cre&longs;cens dicitur, quando partium po&longs;teriorum <lb/>
ip&longs;ius maior e&longs;t celeritas, qu&agrave;m priorum: <expan abbr="decre&longs;c&etilde;s">decre&longs;cens</expan>, <lb/>
quando minor. </s></p><p type="main">

<s>Continu&egrave;, quando nulla pars illius vel minima <lb/>
alteri parti e&longs;t &aelig;qualis &longs;eu &longs;ibi ip&longs;i &aelig;quabilis. </s></p><p type="main">

<s>Per interualla ver&ograve;, quando partes quidem illius <lb/>
&longs;ibi ip&longs;is &aelig;quabiles &longs;unt, ali&aelig; ver&ograve; aliis comparat&aelig; <lb/>
in&aelig;quabiles. </s></p><p type="main">

<s>Ordinatim, quando incrementum aut <expan abbr="decrem&etilde;-tum">decremen&shy;<lb/>
tum</expan> illud certa aliqua proportionis progre&longs;&longs;ione <lb/>
fit, vt &longs;i in motu continu&egrave; cre&longs;cente, diui&longs;o toto mo<lb/>
tus &longs;patio in aliquot partes &aelig;quales eadem &longs;it ratio <lb/>
celeritatis, finis primi &longs;patij ad celeritatem finis &longs;e&shy;<lb/>
cundi, qu&aelig; finis &longs;ecundi ad finem tertij, &amp; &longs;ic dein&shy;<lb/>
ceps: vel &longs;i finis &longs;ecundi &longs;patij duplo citi&ugrave;s feratur, <lb/>
qu&agrave;m finis primi &amp; finis tertij, triplo qu&agrave;m primi: <lb/>
finis ver&ograve; quarti quadruplo, &amp; &longs;ic deinceps. </s><s>Idem &longs;i <lb/>
in quauis alia proportionis progre&longs;&longs;ione illarum <lb/>
partium celeritas, aliarum ad alias &longs;e habeat. </s><s>In mo&shy;<lb/>
tu ver&ograve; per interualla cre&longs;cente <expan abbr="augm&etilde;tum">augmentum</expan> illud or&shy;<lb/>
dinatim fieri dicetur, &longs;i interuallorum proportio a&shy;<lb/>
liquem progre&longs;&longs;ionis ordinem &longs;eruet: puta &longs;i <expan abbr="prim&utilde;">primum</expan> <lb/>
interuallum duplo tardi&ugrave;s <expan abbr="&longs;ec&utilde;do">&longs;ecundo</expan> moueatur, triplo <lb/>
ver&ograve; tardi&ugrave;s tertio, &amp;c. </s></p>


<pb xlink:href="044/01/019.jpg" pagenum="11"/><p type="main">

<s>Inordinat&egrave; autem cre&longs;cere vel decre&longs;cere dicetur <lb/>
motus, &longs;i incrementum illud aut decrementum nul<lb/>
la certa &amp; ordinata proportione fiat. </s></p><p type="main">

<s>Comparantur autem motus alij aliis, &aelig;quabiles <lb/>
&longs;cilicet &amp; in&aelig;quabiles ordinatim progredientes: de <lb/>
inordinatorum enim tum inter &longs;e, tum cum aliis <expan abbr="c&otilde;||">com</expan><lb/>
paratione nihil cert&ograve; &longs;tatui pote&longs;t. </s></p><p type="main">

<s>Comparantur igitur &aelig;quabiles cum &aelig;quabili&shy;<lb/>
bus aut cum in&aelig;quabilibus, ac etiam in&aelig;quabiles <lb/>
cum in&aelig;quabilibus. </s></p><p type="main">

<s>&AElig;quabiles autem cum &aelig;quabilibus compara&shy;<lb/>
tionibus &longs;uis partibus corre&longs;pondentibus &longs;unt pro&shy;<lb/>
portionales. </s><s>Si enim <expan abbr="propon&atilde;tur">proponantur</expan> duo motus &aelig;qua&shy;<lb/>
biles, quorum alter altero maior &longs;it, qu&aelig; erit ratio <lb/>
dimidi&aelig; partis vnius ad dimidiam partem alterius, <lb/>
eadem erit terti&aelig; ad tertiam, &amp; &longs;ic deinceps. </s></p><p type="main">

<s>&AElig;quabilium ver&ograve; motuum cum in&aelig;quabilibus, <lb/>
cum iis &longs;cilicet qui per interualla cre&longs;cunt, compa&shy;<lb/>
ratio fit tanquam cum pluribus diuer&longs;is motibus &aelig;&shy;<lb/>
quabilibus, &longs;unt enim interuallorum <expan abbr="illor&utilde;">illorum</expan> motus <lb/>
&aelig;quabiles. </s><s>At cum continu&egrave; <expan abbr="cre&longs;c&etilde;tibus">cre&longs;centibus</expan> aut decre&shy;<lb/>
&longs;centibus difficile e&longs;t comparationis modum defi&shy;<lb/>
nire, c&ugrave;m ne momento quidem &longs;tabilis maneat par<lb/>
tium illarum quantitas. </s><s>E&longs;t tamen motus &aelig;quabilis <lb/>
illorum men&longs;ura: tanti enim e&longs;&longs;e dicuntur, quanti <lb/>
forent, &longs;i in ea celeritatis men&longs;ura ad quam perue&shy;


<pb xlink:href="044/01/020.jpg" pagenum="12"/>nerunt, &aelig;quabiliter pergerent. </s></p><p type="main">

<s>Cre&longs;centes ver&ograve; cum cre&longs;centibus continu&egrave;, <expan abbr="c&otilde;-parati">con&shy;<lb/>
parati</expan> &longs;iquidem eadem progre&longs;&longs;ionis proportione <lb/>
cre&longs;cant, &aelig;qualia &longs;patia ab eorum principiis nume&shy;<lb/>
rata, &aelig;qualibus temporibus emen&longs;a habebunt, idem <lb/>
in decre&longs;centibus. </s><s>Sed h&ecedil;c hactenus inqui&longs;iui&longs;&longs;e &longs;uf&shy;<lb/>
ficiat: &longs;i quis enim particulatim omnia <expan abbr="exp&etilde;dere">expendere</expan> vel&shy;<lb/>
let, in infinitum &longs;e&longs;e extenderet h&ecedil;c partium &amp; pro&shy;<lb/>
portionum motuum &longs;upputatio. </s></p><p type="main">

<s>Iam videamus qu&aelig; vires quos horum motuum <lb/>
cieant. </s><s>Et vis quidem ea qua res qu&aelig;libet ad &longs;itum <lb/>
naturalem &longs;uarum partium redit, motu <expan abbr="c&otilde;tinu&egrave;">continu&egrave;</expan> de&shy;<lb/>
cre&longs;cente mouet: quo enim propi&ugrave;s ad &longs;itum natu&shy;<lb/>
ralem partium accedit, eo tardior &amp; languidior e&longs;t. <lb/>
</s><s>Arcus enim c&ugrave;m prim&ugrave;m laxari incipit, celeri&ugrave;s <lb/>
mouetur, qu&agrave;m c&ugrave;m motus &longs;ui finis propior e&longs;t. </s></p><p type="main">

<s>Vis ver&ograve; naturalis, qua res qu&ecedil;libet ad <expan abbr="loc&utilde;">locum</expan> &longs;uum <lb/>
naturalem tendit, &longs;ubiectum &longs;uum, motu continu&egrave; <lb/>
&amp; ordinatim cre&longs;cente, mouet. </s><s>Illius autem motus <lb/>
cau&longs;a e&longs;t qu&ograve;d facili&ugrave;s id moueatur, quod in motu <lb/>
e&longs;t, qu&agrave;m quod quie&longs;cit. </s><s>Vis igitur eadem, <expan abbr="&longs;ubiect&utilde;">&longs;ubiectum</expan> <lb/>
quod iam in motu e&longs;t premens, illud magis moue&shy;<lb/>
bit, qu&agrave;m &longs;i quie&longs;cat, &amp; magis motum, magis etiam <lb/>
mouebit: ita vt eadem vis motione maior fiat, qu&agrave;m <lb/>
per &longs;e &longs;it. </s><s>Et h&aelig;c e&longs;t cau&longs;a cur ictus, quo magis ab al&shy;<lb/>
tero venit, eo vehementior &longs;it. </s><s>Motus autem huius 


<pb xlink:href="044/01/021.jpg" pagenum="13"/>&longs;patia hanc celeritatis proportionem &longs;eruant, vt <expan abbr="qu&ecedil;">qu&aelig;</expan> <lb/>
e&longs;t ratio totius &longs;patij, per quod fit ille motus ad par&shy;<lb/>
tem ip&longs;ius (vtriu&longs;que initio inde &longs;umpto, vbi e&longs;t mo<lb/>
tus initium) eadem &longs;it celeritatis ad celeritatem. <lb/>
<figure id="id.044.01.021.1.jpg" xlink:href="044/01/021/1.jpg"/><lb/>
Exempli gratia, &longs;i vis aliqua per lineam ABC <lb/>
mouerit, &longs;itque AB illius line&aelig; pars, qu&aelig; erit <lb/>
ratio AC ad AB, eadem erit celeritatis motus <lb/>
in puncto C ad <expan abbr="celeritat&etilde;">celeritatem</expan> motus in puncto B. <lb/>
<!-- KEEP S--></s><s>Cuiu&longs;modi proportio ob&longs;eruatur in paralle&shy;<lb/>
lis triangulum &longs;ecantibus. </s><s>Vt enim &longs;e habet <lb/>
<figure id="id.044.01.021.2.jpg" xlink:href="044/01/021/2.jpg"/><lb/>
AC ad AB, &longs;ic CG ad BF, &amp; vt AD ad <lb/>
AC, &longs;ic DH ad CG. <!-- KEEP S--></s><s>Itaque &longs;i in &longs;patia ali&shy;<lb/>
quot &aelig;qualia diuidatur totius motus &longs;pa<lb/>
tium, finis &longs;ecundi duplo citi&ugrave;s feretur, <lb/>
qu&agrave;m finis primi: finis ver&ograve; tertijtriplo <lb/>
citi&ugrave;s qu&agrave;m finis primi, &amp; &longs;ic deinceps. <lb/>
</s><s>Hac autem ratione fit, vt &longs;patiorum illo&shy;<lb/>
rum initio maxima &longs;it celeritatis <expan abbr="differ&etilde;-tia">differen&shy;<lb/>
tia</expan>: progre&longs;&longs;u ver&ograve; &longs;emper minuatur, ac tandem fer&shy;<lb/>
m&egrave; eadem &longs;it, vt fit in trianguli lateribus, qu&aelig; lon&shy;<lb/>
gi&longs;&longs;im&egrave; producta &aelig;qu&egrave; di&longs;tare videntur. </s><s>E&aacute;que e&longs;t <lb/>
ratio cur Solis &amp; Lun&aelig; radij, etiam&longs;i concurrant (in <lb/>
ip&longs;orum &longs;cilicet corporibus, aut vltra res quas <expan abbr="illu-&longs;tr&atilde;t">illu&shy;<lb/>
&longs;trant</expan>) paralleli <expan abbr="tam&etilde;">tamen</expan> <expan abbr="appare&atilde;t">appareant</expan>. </s><s><expan abbr="Ead&etilde;">Eadem</expan> <expan abbr="eti&atilde;">etiam</expan> cau&longs;a e&longs;t cur <lb/>
line&ecedil; omnes ad <expan abbr="perp&etilde;dicul&utilde;">perpendiculum</expan> in <expan abbr="terr&atilde;">terram</expan> cadentes, paral&shy;<lb/>
lel&aelig; videantur, c&ugrave;m <expan abbr="tam&etilde;">tamen</expan> in centro terr&aelig; <expan abbr="c&otilde;currant">concurrant</expan>. </s></p>


<pb xlink:href="044/01/022.jpg" pagenum="14"/><p type="main">

<s>Hunc igitur motum vis naturalis efficit, mod&ograve; <lb/>
nulla quies intercedat. </s></p><p type="main">

<s>Vis autem voluntaria motum omnem ciere apta <lb/>
e&longs;t. </s><s>Fortuita ver&ograve; inordinatum tant&ugrave;m motum effi&shy;<lb/>
cit. </s><s>Et h&aelig;c de variis virium motibus, <expan abbr="eor&uacute;mq;">eor&uacute;mque</expan> pro&shy;<lb/>
portione &amp; partibus. </s></p><p type="main">

<s>E&longs;t ver&ograve; etiam virium partitio qu&aelig;dam, qu&aelig; ex <lb/>
eorum quibus <expan abbr="inh&aelig;r&etilde;t">inh&aelig;rent</expan> &longs;ubiectorum diui&longs;ione, aut <lb/>
alterius ad alterum proportione re&longs;ultat. </s><s>In &longs;ubie&shy;<lb/>
ctis enim, qu&aelig; <foreign lang="greek">o(moiomerh=</foreign> &longs;unt, vis naturalis &aelig;qualiter <lb/>
per omnes partes diffu&longs;a e&longs;t: ita vt qu&aelig; e&longs;t ratio mo&shy;<lb/>
lis ad molem &longs;ub eadem figura, <expan abbr="ead&etilde;">eadem</expan> &longs;it vis ad vim: <lb/>
vt &longs;i globus alicuius metalli, ad alium globum eiu&longs;&shy;<lb/>
dem metalli mole quadruplus &longs;it, illius quoque <expan abbr="p&otilde;-dus">pon&shy;<lb/>
dus</expan> ad huius pondus quadruplum erit. </s></p><p type="main">

<s>Hactenus vim <expan abbr="c&otilde;&longs;iderauimus">con&longs;iderauimus</expan> quatenus mouet, <lb/>
&longs;upere&longs;t vt eam con&longs;ideremus, quatenus mouenti <lb/>
re&longs;i&longs;tit. </s><s>Habet autem locum re&longs;i&longs;tentia, vbi du&aelig; vi&shy;<lb/>
res contrari&aelig; committuntur: &longs;i enim vtraque <expan abbr="eod&etilde;">eodem</expan> <lb/>
motu moueat, nulla erit re&longs;i&longs;tentia, &longs;ed altera alteri <lb/>
addita maiorem vim con&longs;tituet. </s></p><p type="main">

<s>Committi autem dicuntur vires, quando ita ap&shy;<lb/>
plicantur &amp; <expan abbr="connect&utilde;tur">connectuntur</expan>, vt altera nutu &longs;uo moueri <lb/>
non po&longs;&longs;it, quin altera contra nutum &longs;uum mouea&shy;<lb/>
tur. </s><s>Viribus autem ita connexis, accidit vt altera in <lb/>
alterius &longs;ubiectum agat, &amp; altera in &longs;ubiecto &longs;uo exi-


<pb xlink:href="044/01/023.jpg" pagenum="15"/>&longs;tens, alteri in altero &longs;ubiecto exi&longs;tenti re&longs;i&longs;tat, ita vt <lb/>
eorum &longs;ubiecta quodammodo reciproca fiant. </s></p><p type="head">

<s>CONCLVSIO I.<!-- KEEP S--></s></p><p type="main">

<s>Illam autem re&longs;i&longs;tentiam vi momenti in eodem <lb/>
&longs;ubiecto &aelig;qualem, aut eandem cum ea e&longs;&longs;e, ex ip&longs;ius <lb/>
definitione con&longs;tat. </s><s>E&longs;t enim re&longs;i&longs;tere <expan abbr="n&otilde;">non</expan> pati &longs;e mo&shy;<lb/>
ueri. </s><s>Quantum autem vis qu&aelig;libet <expan abbr="&longs;ubiect&utilde;">&longs;ubiectum</expan> &longs;uum <lb/>
nutu &longs;uo mouet, tantum illud contra nutum &longs;uum <lb/>
moueri non patitur. </s><s>Mouendi igitur &amp; <expan abbr="mou&etilde;ti">mouenti</expan> re&shy;<lb/>
&longs;i&longs;tendi potentia in eodem &longs;ubiecto &aelig;quales &longs;unt. </s></p><p type="head">

<s>II.<!-- KEEP S--></s></p><p type="main">

<s>Quemadmodum autem in eodem &longs;ubiecto ma&shy;<lb/>
ior vis ine&longs;&longs;e dicitur, in quo e&longs;t maioris motus po&shy;<lb/>
tentia, &longs;ic maior re&longs;i&longs;tentia erit maioris motus con&shy;<lb/>
trarij impatientia. </s><s>Eadem igitur vis magis mouere <lb/>
nitenti <expan abbr="c&otilde;tra">contra</expan> ip&longs;ius nutum magis re&longs;i&longs;tet, minus ve&shy;<lb/>
r&ograve; nitenti min&ugrave;s re&longs;i&longs;tet. </s></p><p type="head">

<s>III.<!-- KEEP S--></s></p><p type="main">

<s>Et quo maior erit motus contrarius, eo magis re&shy;<lb/>
&longs;i&longs;tet: id e&longs;t, quo celerius vis qu&aelig;libet &agrave; nutu &longs;uo re&shy;<lb/>
uelletur, eo magis re&longs;i&longs;tet. </s><s>Duplo igitur citi&ugrave;s re&shy;<lb/>
uellenti duplo re&longs;i&longs;tet, triplo citius triplo re&longs;i&longs;tet, &amp; <lb/>
&longs;ic <foreign lang="greek">a)nalo/gws</foreign> in omni proportione. </s><s>Qu&aelig; igitur erit <lb/>
ratio motus ad motum, contra nutum eadem erit <lb/>
in vna &amp; eadem vi ratio re&longs;i&longs;tenti&aelig; ad re&longs;i&longs;tentiam. </s></p><p type="main">

<s>Si ver&ograve; plures vires comparentur. </s></p>


<pb xlink:href="044/01/024.jpg" pagenum="16"/><p type="head">

<s>IIII.<!-- KEEP S--></s></p><p type="main">

<s>&AElig;qualium quidem virium &aelig;qualibus motibus <lb/>
&aelig;quales erunt re&longs;i&longs;tenti&aelig;. </s><s>Si enim &aelig;quales vires &aelig;&shy;<lb/>
qualiter &agrave; &longs;uis nutibus reuellantur, &aelig;qualiter re&longs;i&shy;<lb/>
&longs;tent. </s></p><p type="head">

<s>V.<!-- KEEP S--></s></p><p type="main">

<s>In&aelig;qualibus ver&ograve; motibus, earum re&longs;i&longs;tenti&ecedil; in&shy;<lb/>
&aelig;quales erunt, &amp; motuum proportionem &longs;equen&shy;<lb/>
tur. </s><s>Exempli gratia, &longs;int du&aelig; vires A &amp; B, quarum v&shy;<lb/>
traque vna hora miliare vnum percurrat, ill&aelig; &aelig;qua&shy;<lb/>
les erunt. </s><s>Si igitur vtraque quarta parte vnius milia&shy;<lb/>
ris, vel dimidio miliari &agrave; &longs;uo nutu eodem tempore <lb/>
reuellatur, eadem erit vtriu&longs;que illi motui re&longs;i&longs;ten&shy;<lb/>
tia. </s><s>Sin ver&ograve; altera quidem quarta parte vnius milia&shy;<lb/>
ris &agrave; nutu &longs;uo reuellatur, altera ver&ograve; eodem tempo&shy;<lb/>
re integro miliari reuellatur: h&aelig;c re&longs;i&longs;tentia ad il&shy;<lb/>
lam quadrupla erit, &amp; &longs;ic de c&aelig;teris motuum pro&shy;<lb/>
portionibus. </s></p><p type="head">

<s>VI.<!-- KEEP S--></s></p><p type="main">

<s>In&aelig;qualium ver&ograve; virium re&longs;i&longs;tenti&aelig; &aelig;qualibus <lb/>
motibus ip&longs;arum virium proportionem &longs;equentur. <lb/>
</s><s>Quo maior enim e&longs;t vis, eo magis eodem tempore <lb/>
eod&eacute;mque &longs;patio contra nutum mouenti re&longs;i&longs;tit. <lb/>
</s><s><expan abbr="Ex&etilde;pli">Exempli</expan> gratia, &longs;it vis A quadrupla ad vim B, vis A mo&shy;<lb/>
uenti &longs;e vno miliari quadruplo re&longs;i&longs;tet, qu&agrave;m B mo&shy;<lb/>
uenti &longs;e vno miliari eodem tempore. </s></p>


<pb xlink:href="044/01/025.jpg" pagenum="17"/><p type="main">

<s>In&aelig;qualium ver&ograve; virium in&aelig;qualibus motibus <lb/>
re&longs;i&longs;tenti&aelig;, quando motus eam inter &longs;e proportio&shy;<lb/>
nem &longs;eruabunt, qu&aelig; e&longs;t inter eas <foreign lang="greek">a)ntipeponqw=s</foreign>, &longs;eu <lb/>
reciproc&egrave;, &aelig;quales erunt. </s><s>Sit enim vis A qu&aelig; ad vim <lb/>
B eandem habeat <expan abbr="ration&etilde;">rationem</expan> quam C ad D, puta quam <lb/>
3 ad 1, aut 4 ad 1, aut qu&aelig;cunque alia &longs;it, <expan abbr="moueat&uacute;rq;">moueat&uacute;rque</expan> <lb/>
vtraque &longs;patio E contra nutum &longs;uum eodem tem&shy;<lb/>
pore, re&longs;i&longs;tentia A ad re&longs;i&longs;tentiam B &longs;e habebit, vt C <lb/>
ad D per proximam conclu&longs;ionem. </s><s>Si ver&ograve; B moue&shy;<lb/>
atur eodem tempore &longs;patio aliquo quod &longs;e habeat <lb/>
ad &longs;patium E vt C ad D, re&longs;i&longs;tentia B huic motui &longs;e <lb/>
habebit ad re&longs;i&longs;tentiam priori motui, vt C ad D per <lb/>
quartam <expan abbr="conclu&longs;ion&etilde;">conclu&longs;ionem</expan>. </s><s>Du&aelig; ergo re&longs;i&longs;tenti&aelig; ad ean&shy;<lb/>
dem, eandem habebunt rationem, ergo &aelig;quales e&shy;<lb/>
runt per <emph type="italics"/>9<emph.end type="italics"/> prop. <emph type="italics"/>5.<emph.end type="italics"/><!-- REMOVE S--> Elem. Eucl. <!-- KEEP S--></s></p><p type="head">

<s>VIII.<!-- KEEP S--></s></p><p type="main">

<s>Si ver&ograve; motuum virium in&aelig;qualium proportio <lb/>
non &longs;it eadem qu&aelig; e&longs;t ip&longs;arum virium reciproc&egrave;, vis <lb/>
illius qu&aelig; ad alteram maiorem habebit rationem, <lb/>
qu&agrave;m motus alterius ad motum ip&longs;ius, re&longs;i&longs;tentia <lb/>
maior erit, altera ver&ograve; minor. </s><s>Exempli gratia, &longs;i vis <lb/>
A &longs;it tripla ad vim B, &amp; motus quo B &agrave; nutu &longs;uo reuel<lb/>
letur, &longs;it minor qu&agrave;m triplus ad motum A, re&longs;i&longs;ten&shy;<lb/>
tia A erit maior qu&agrave;m re&longs;i&longs;tentia B. <!-- KEEP S--></s><s>Idem erit, &longs;i ma&shy;<lb/>
ior &longs;it ratio A ad B, qu&agrave;m 3 ado, motus ver&ograve; B ad mo&shy;


<pb xlink:href="044/01/026.jpg" pagenum="18"/>tum A &longs;it triplus. </s><s>Contr&agrave; ver&ograve; &longs;i A ad B &longs;it tripla: mo&shy;<lb/>
tus ver&ograve; B ad motum A &longs;it maior qu&agrave;m triplus, ma&shy;<lb/>
ior erit re&longs;i&longs;tentia B qu&agrave;m A. <!-- KEEP S--></s><s>Idem accidet, &longs;i A ad B <lb/>
ratio minor &longs;it qu&agrave;m 3 ad 1, motus ver&ograve; B ad motum <lb/>
A &longs;it triplus. </s><s>Hunc autem exce&longs;&longs;um &amp; defectum <expan abbr="n&otilde;">non</expan> <lb/>
vlteri&ugrave;s &longs;crutabimur, vt ip&longs;ius quantitatis <expan abbr="men&longs;ur&atilde;">men&longs;uram</expan> <lb/>
a&longs;&longs;equamur: alioqui in infinitum fieret progre&longs;&longs;us. </s></p><p type="main">

<s>Ex his colligimus <expan abbr="re&longs;i&longs;t&etilde;tias">re&longs;i&longs;tentias</expan> tribus modis &aelig;qua&shy;<lb/>
les aut in&aelig;quales dici, per &longs;e &longs;cilicet aut motione, aut <lb/>
vtroque modo. </s><s>Per &longs;e quidem c&ugrave;m &longs;ubiectorum <lb/>
vires &longs;unt &aelig;quales (id e&longs;t &aelig;qualiter &longs;ua &longs;ubiecta mo&shy;<lb/>
uent) aut in&aelig;quales. </s><s>Motione ver&ograve; quando per &longs;e <lb/>
quidem in &aelig;quales &longs;unt, motione ver&ograve; &aelig;quales <expan abbr="fi&utilde;t">fiunt</expan>: <lb/>
aut quando per &longs;e &aelig;quales &longs;unt, motione ver&ograve; in&aelig;&shy;<lb/>
quales <expan abbr="fi&utilde;t">fiunt</expan> eo, quo dictum e&longs;t, modo. </s><s>Vtroque mo <lb/>
do &aelig;quales aut in&aelig;quales <expan abbr="dic&utilde;tur">dicuntur</expan>, quando tum per <lb/>
&longs;e, tum motione tales fiunt. </s><s>His explicatis videamus <lb/>
quis eorum &longs;it effectus, vbi vires committentur. </s></p><p type="head">

<s>IX.<!-- KEEP S--></s></p><p type="main">

<s>Prim&ugrave;m ex prima conclu&longs;ione &longs;equitur qu&ecedil; erit <lb/>
ratio re&longs;i&longs;tenti&aelig; ad re&longs;i&longs;tentiam, eandem fore re&longs;i&shy;<lb/>
&longs;tenti&aelig; ad vim cuius e&longs;t altera re&longs;i&longs;tentia: &longs;unt enim <lb/>
vis &amp; <expan abbr="re&longs;i&longs;t&etilde;tia">re&longs;i&longs;tentia</expan> in <expan abbr="eod&etilde;">eodem</expan> &longs;ubiecto &aelig;quales. </s><s>Ergo mul&shy;<lb/>
to magis &longs;equitur, &longs;i <expan abbr="re&longs;i&longs;t&etilde;tia">re&longs;i&longs;tentia</expan> altera maior, altera mi <lb/>
nor fuerit, illam huius vi <expan abbr="maior&etilde;">maiorem</expan> fore, vel illius vim <lb/>
hac re&longs;i&longs;tentia maiorem, &longs;i &aelig;qualis &aelig;qualem. </s></p>


<pb xlink:href="044/01/027.jpg" pagenum="19"/><p type="head">

<s>X<!-- KEEP S--></s></p><p type="main">

<s>Re&longs;i&longs;tentia autem vi contrari&aelig; commi&longs;&longs;a <expan abbr="t&atilde;tum">tantum</expan> <lb/>
de ea tollit quanta e&longs;t ip&longs;a re&longs;i&longs;tentia. </s><s>Sublata autem <lb/>
vi tollitur motus: &longs;ublata ver&ograve; re&longs;i&longs;tentia, &longs;i vis ad&longs;it, <lb/>
&longs;equitur motus. </s><s>Vbi igitur vis &amp; re&longs;i&longs;tentia in&ecedil;qua&shy;<lb/>
les committentur, &longs;i vis maior &longs;it qu&agrave;m re&longs;i&longs;tentia, <lb/>
fiet motus &longs;ecundum vis illius nutum, &amp; contra nu&shy;<lb/>
tum vis illius qu&aelig; re&longs;i&longs;tit. </s><s>Si ver&ograve; re&longs;i&longs;tentia maior <lb/>
fuerit, tum ip&longs;a fiet vis mouens, &amp; vim contrariam <lb/>
contra nutum ip&longs;ius mouebit, dum ip&longs;a nutu &longs;uo <lb/>
mouebitur. </s><s>Hinc &longs;equuntur duo theoremata, circa <lb/>
qu&aelig; totius huius con&longs;iderationis cardo vertitur. </s></p><p type="head">

<s>THEOREMA I.<!-- KEEP S--></s></p><p type="main">

<s>Duarum virium connexarum, quarum (&longs;i mo&shy;<lb/>
ueantur) motus erunt ip&longs;is <foreign lang="greek">a)ntipeponqw=s</foreign> proportiona&shy;<lb/>
les neutra alteram mouebit, &longs;ed &aelig;quilibrium <expan abbr="faci&etilde;t">facient</expan>. </s></p><p type="main">

<s>Sit vis A commi&longs;&longs;a cum vi B, &longs;itque vis A ad vim <lb/>
B ratio per &longs;e, vt C ad D <expan abbr="qu&aelig;c&utilde;que">qu&aelig;cunque</expan> illa &longs;it, &longs;iue dupla, <lb/>
&longs;iue tripla, &longs;iue alia. </s><s>Sit etiam <expan abbr="ead&etilde;">eadem</expan> ratio motus quo <lb/>
B mouebitur, &longs;i ita, vt connexa &longs;unt, moueantur) ad <lb/>
motum quo A mouebitur, qu&aelig; e&longs;t C ad D, dico mo&shy;<lb/>
tum non &longs;equuturum, &longs;ed factum iri &aelig;quilibrium. <lb/>
</s><s>Aut enim A &amp; B vires per &longs;e erunt &aelig;quales aut in&aelig;&shy;<lb/>
quales: &longs;i &aelig;quales, ergo &amp; ip&longs;arum motus &aelig;quales e&shy;<lb/>
runt: &longs;unt enim ex hypothe&longs;i ip&longs;is proportionales: 


<pb xlink:href="044/01/028.jpg" pagenum="20"/>ergo per quartam conclu&longs;ionem earum re&longs;i&longs;tenti&aelig; <lb/>
&aelig;quales erunt, ergo per decimam conclu&longs;ionem <expan abbr="n&otilde;">non</expan> <lb/>
fiet motus. </s><s>Si ver&ograve; &longs;unt in&aelig;quales, c&ugrave;m earum mo&shy;<lb/>
tus ex hypothe&longs;i &longs;int <foreign lang="greek">a)ntipeponqw=s</foreign> proportionales per <lb/>
&longs;eptimam conclu&longs;ionem &aelig;quales erunt etiam re&longs;i&shy;<lb/>
&longs;tenti&aelig;. </s><s>Ergo nec motus fiet: nullo igitur modo fiet <lb/>
earum motus. </s><s>Quod demon&longs;trandum erat. </s></p><p type="head">

<s>THEOREMA II.<!-- KEEP S--></s></p><p type="main">

<s>Quarum ver&ograve; ita connexarum (&longs;i <expan abbr="moue&atilde;tur">moueantur</expan>) mo<lb/>
tus, ip&longs;is proportionales non erunt: illa alteram mo&shy;<lb/>
uebit, cuius ad alteram ratio maior erit, qu&agrave;m huius <lb/>
motus ad illius motum. </s></p><p type="main">

<s>Sit vis A cum vi B commi&longs;&longs;a, &longs;itque A ad B ratio <lb/>
per &longs;e, vt C ad D: ita ver&ograve; connex&aelig; &longs;int, vt &longs;i mouean&shy;<lb/>
tur, minor &longs;it ratio motus quo B mouebitur ad mo&shy;<lb/>
tum, quo A mouebitur, quum C ad D dico A motu&shy;<lb/>
ram B: erit enim per octauam conclu&longs;ionem re&longs;i&shy;<lb/>
&longs;tentia B minor re&longs;i&longs;tentia A: ergo per nonam con&shy;<lb/>
clu&longs;ionem re&longs;i&longs;tentia B minor vi A: vis igitur A vim <lb/>
B mouebit per vndecimam conclu&longs;ionem. </s><s>Quod <lb/>
demon&longs;trandum erat. </s></p><p type="main">

<s>Hinc po&longs;&longs;emus ad problematis no&longs;tri demon&shy;<lb/>
&longs;trationem rect&agrave; pergere: ante tamen cra&longs;&longs;i&ugrave;s ali&shy;<lb/>
quanto h&aelig;c explicanda &longs;unt, vt &agrave; quouis facili&ugrave;s in&shy;<lb/>
telligantur. </s><s>Du&aelig; &longs;unt motus men&longs;ur&aelig;, locus &longs;cilicet <lb/>
&amp; tempus: vtroque igitur, tempore videlicet &amp; loco 


<pb xlink:href="044/01/029.jpg" pagenum="21"/>maior, minor aut &aelig;qualis dicitur: &amp; quo minori <expan abbr="t&etilde;-pore">tem&shy;<lb/>
pore</expan> idem &longs;patium ab&longs;oluitur, eo maior e&longs;t, vel quo <lb/>
maius &longs;patium eodem tempore. </s></p><p type="main">

<s>Vt igitur motus magnus dicatur, perinde e&longs;t &longs;i <lb/>
paruo tempore fiat, aut magno &longs;patio. </s></p><p type="main">

<s>Quod autem maiorem <expan abbr="mot&utilde;">motum</expan> ciere pote&longs;t illud, <lb/>
vis maior dicitur, qu&ograve;d minorem minor. </s></p><p type="main">

<s>Vis autem &longs;eu mouendi potentia in eodem &longs;ub&shy;<lb/>
iecto certa &amp; finita e&longs;t. </s><s>Qu&ecedil;libet enim res vi natura&shy;<lb/>
li pr&ecedil;dita, &longs;i &agrave; loco naturali ab&longs;it, &longs;u&oacute;que arbitrio <expan abbr="c&otilde;-mittatur">con&shy;<lb/>
mittatur</expan>, certo tempore e&ograve; redit. </s><s>E&longs;t enim certum <lb/>
in rerum natura quanto tempore libr&aelig; vnius <expan abbr="p&otilde;dus">pondus</expan> <lb/>
deor&longs;um &longs;ponte &longs;ua delatum, miliare vnum aut duo <lb/>
conficiat pro ratione materi&ecedil;, vel quantum &longs;patij v&shy;<lb/>
na vel duabus horis percurrat. </s><s>Id ver&ograve; quantum &longs;it, <lb/>
hominum indu&longs;tria nondum quod &longs;ciam explora&shy;<lb/>
tum e&longs;t: ali&acirc;s autem id demon&longs;trare conabimur. </s></p><p type="main">

<s>Mouendi ver&ograve; potentia in alieno &longs;ubiecto infi&shy;<lb/>
nita e&longs;t, hoc e&longs;t, in <expan abbr="infinit&utilde;">infinitum</expan> augeri vel minui pote&longs;t, <lb/>
quoniam in finita auctione &amp; diminutione e&longs;t re&longs;i&shy;<lb/>
&longs;tentia: tanta enim e&longs;t, quanta e&longs;t in eodem &longs;ubiecto <lb/>
vis: <expan abbr="quant&uacute;&longs;q;">quant&uacute;&longs;que</expan> motus illius e&longs;t vis alterius re&longs;pectu. <lb/>
</s><s>Quo igitur vis qu&aelig; alienum &longs;ubiectum mouere ni&shy;<lb/>
titur, illud magis mouere nitetur, eo min&ugrave;s illud <lb/>
mouere poterit, maior enim erit illius re&longs;i&longs;tentia. <lb/>
</s><s>Quemadmodum enim quod magis nutu &longs;uo mo&shy;


<pb xlink:href="044/01/030.jpg" pagenum="22"/>uetur, maiorem vim mouendi habet. </s><s>Ita illud idem <lb/>
quod magis contra nutum &longs;uum mouetur, <expan abbr="maior&etilde;">maiorem</expan> <lb/>
vim re&longs;i&longs;tendi habet. </s><s>E contrario ver&ograve; quo vis qu&aelig;&shy;<lb/>
libet minorem motum in alieno &longs;ubiecto ciere ni&shy;<lb/>
tetur, eo facili&ugrave;s illud mouebit. </s></p><p type="main">

<s>Tarditate igitur motus, re&longs;i&longs;tentia in infinitum <lb/>
minui pote&longs;t: minuta ver&ograve; re&longs;i&longs;tentia vis contrari&aelig; <lb/>
effectus augetur, ita vt vis qu&aelig; per &longs;e minima e&longs;t, in <lb/>
contrariam cui plurimum diminuta &longs;it, re&longs;i&longs;tentia <lb/>
maxim&egrave; agat. </s><s>Perinde igitur e&longs;t, &longs;i vis mouens ma&shy;<lb/>
gna &longs;it, mouenda ver&ograve; parua, ac &longs;i illa celeriter fera&shy;<lb/>
tur, h&aelig;c ver&ograve; tard&egrave;: <expan abbr="qu&atilde;tum">quantum</expan> enim vis mouens &longs;i ma&shy;<lb/>
gna fuerit in mouendam minorem poterit, tantum <lb/>
vis parua celeriter mota in magnam tard&egrave; motam <lb/>
poterit. </s><s>Si igitur velimus vt vis parua magnam mo&shy;<lb/>
ueat, eas ita collocare oportet, vt quantum magna <lb/>
paruam &longs;uperat, tantum illi de motus celeritate de&shy;<lb/>
trahatur, &amp; aliquid ampli&ugrave;s. </s><s>Si enim tanta &longs;it tardi&shy;<lb/>
tas motus vis vnius, re&longs;pectu motus vis alterius, <expan abbr="qu&atilde;-ta">quan&shy;<lb/>
ta</expan> e&longs;t proportio vis illius, ad hanc non fiet motus: vt <lb/>
&longs;i pondus A quatuor librarum cum pondere B libr&aelig; <lb/>
vnius committatur: &longs;intque ita connexa, vt dum <lb/>
A vno &longs;patio mouebitur, B quatuor &longs;patiis mouea&shy;<lb/>
tur, ita vt motus A quadruplo tardior &longs;it motu B <expan abbr="n&otilde;">non</expan> <lb/>
fiet motus, quia quantum A excedit B pondere tan&shy;<lb/>
t&ugrave;m deficit motus tarditate. </s></p>


<pb xlink:href="044/01/031.jpg" pagenum="23"/><p type="main">

<s>Tantum enim e&longs;t libram vnam quatuor &longs;patiis <lb/>
moueri, quantum libras quatuor vno &longs;patio eodem <lb/>
tempore: &longs;i igitur alterutri eorum ita <expan abbr="con&longs;titutor&utilde;">con&longs;titutorum</expan>, <lb/>
vel momentum vis addatur, id cui additum fuerit, <lb/>
alterum mouebit. </s><s>Idem fiet &longs;i A ita connectatur vt <lb/>
vel momento citi&ugrave;s qu&agrave;m moueri po&longs;itum e&longs;t, mo<lb/>
ueatur vel B tardi&ugrave;s. </s></p><p type="main">

<s>Id etiam alia ratione o&longs;tendi pote&longs;t, &longs;i vis A qua&shy;<lb/>
drupla &longs;it ad vim B, erunt in A quatuor partes, ip&longs;i B <lb/>
&aelig;quales. </s><s>Si igitur B cum &longs;ingulis illis committatur, <lb/>
ita vt &aelig;qualiter moueantur, non fiet motus: &longs;i ver&ograve; <lb/>
alterutri aut ip&longs;i B, aut &longs;ingulis illis partibus vis vel <lb/>
motus momentum adiiciatur vel detrahatur, illa cui <lb/>
adiectum fuerit, aut cui non detractum fuerit, nutu <lb/>
&longs;uo mouebitur, &amp; aliam contra nutum eius moue&shy;<lb/>
bit. </s><s>Addito igitur ip&longs;i B momento, dum vno &longs;patio <lb/>
mouebitur, &longs;ingulas illas partes vno &longs;patio moue&shy;<lb/>
bit. </s><s>Vbi igitur &longs;ingulas &longs;emel mouerit, ip&longs;a quater <lb/>
mota erit. </s><s>Dum ver&ograve; &longs;ingul&aelig; &longs;emel mot&aelig; erunt, to&shy;<lb/>
tum ex illis con&longs;tans &longs;emel motum intelligetur: po&shy;<lb/>
terit igitur B addito ip&longs;i momento, dum quater mo<lb/>
uebitur, &longs;emel totum A mouere. </s></p><p type="main">

<s>Tertio modo id ip&longs;um concludere po&longs;&longs;umus. </s><s>Si <lb/>
du&aelig; vires &aelig;quales connectantur, ita vt mot&aelig;, &aelig;qua&shy;<lb/>
liter moueantur, altera in <expan abbr="alter&atilde;">alteram</expan> non aget. </s><s>Si ver&ograve; ita <lb/>
connectantur vt mot&aelig; in&aelig;qualiter moueantur, 


<pb xlink:href="044/01/032.jpg" pagenum="24"/>quantum altera alteram celeritate &longs;uperabit, <expan abbr="t&atilde;tum">tantum</expan> <lb/>
&amp; vi &longs;uperabit. </s><s>Vt &longs;i vis A vi B &aelig;qualis &longs;it, ac ita <expan abbr="con-nect&atilde;tur">con&shy;<lb/>
nectantur</expan>, vt B quatuor &longs;patiis moueatur, dum A vno <lb/>
&longs;patio mouebitur, B quadruplam vim habebit ad A, <lb/>
quia eam in motibus &longs;uis proportionem &longs;eruant, <lb/>
quam &longs;i <expan abbr="&longs;eruar&etilde;t">&longs;eruarent</expan> arbitrio &longs;uo commi&longs;&longs;&aelig;, B ad A qua&shy;<lb/>
drupla e&longs;&longs;et. </s><s>Si igitur illis ita connexis, ip&longs;i A adda&shy;<lb/>
tur vis triplo maior qu&agrave;m ip&longs;a &longs;it, B illis quatuor re&shy;<lb/>
&longs;i&longs;tet, nec fiet motus. </s></p><p type="main">

<s>Duarum igitur virium comparatarum, quanto <lb/>
altera &longs;ubiectum &longs;uum celeri&ugrave;s mouebit, qu&agrave;m al&shy;<lb/>
tera: tanto illa hanc celeri&ugrave;s mouere poterit, qu&agrave;m <lb/>
ip&longs;a moueatur, &longs;i illi vis <expan abbr="mom&etilde;tum">momentum</expan> additum fuerit. <lb/>
</s><s>Ita vt qu&aelig; erit proportio vis ad vim, eadem &longs;it mo&shy;<lb/>
tus, quem illa in hac ciere pote&longs;t ad motum quo ip&longs;a <lb/>
mouebitur. </s><s>Et &egrave; conuer&longs;o qu&aelig; erit ratio motus ad <lb/>
motum, eadem erit vis cui additum fuerit momen&shy;<lb/>
tum ad eam quam ip&longs;a mouere poterit ratio reci&shy;<lb/>
proc&egrave;. </s><s>Iam ad problematis no&longs;tri demon&longs;tratio&shy;<lb/>
nem veniamus. </s></p></chap><chap><p type="head">

<s><emph type="italics"/>Propo&longs;iti problematis demon&longs;tratio.<emph.end type="italics"/></s></p><p type="main">

<s>Sit data vis A quantacunque illa &longs;it magna vel <lb/>
parua: datum ver&ograve; pondus B quantumquantum il&shy;<lb/>
lud &longs;it, dico me vi A pondus B tollere po&longs;&longs;e. </s><s>Id &longs;ic de&shy;<lb/>
mon&longs;tro. </s></p>


<pb xlink:href="044/01/033.jpg" pagenum="25"/><p type="main">

<s>Prim&ugrave;m enim ex doctrina &longs;ecundi <expan abbr="l&etilde;matis">lemmatis</expan>, quod <lb/>
inferi&ugrave;s demon&longs;trabitur, &longs;ciam proportionem pro&shy;<lb/>
xim&egrave; maiorem, qu&agrave;m &longs;it A ad B proportio. </s><s>Deinde <lb/>
ex doctrina primi lemmatis ita connectam A &amp; B, <lb/>
vt quando ambo mouebuntur, nunc &longs;it ratio motus <lb/>
quo B mouebitur ad <expan abbr="mot&utilde;">motum</expan> quo A mouebitur, qu&agrave;m <lb/>
&longs;it A ad B. <!-- KEEP S--></s><s>His peractis &longs;equitur vim A pondus B mo&shy;<lb/>
turam ex &longs;ecundo &longs;uperi&ugrave;s demon&longs;trato theorema&shy;<lb/>
te. </s><s>Quod erat propo&longs;itum. </s></p><p type="head">

<s>LEMMA I.<!-- KEEP S--></s></p><p type="main">

<s>Duas vires ita connectere, vt &longs;i moueantur, <expan abbr="ear&utilde;">earum</expan> <lb/>
motus, in data ratione alter ad alterum &longs;e habeant <lb/>
vires contrari&aelig;, aut medio aliquo, aut per &longs;e ab&longs;que <lb/>
vllo medio committuntur. </s><s>Si ab&longs;que medio com&shy;<lb/>
mittant, eodem motu mouebuntur, maior enim mi<lb/>
norem eodem motu, quo ip&longs;a moueri poterit, mo&shy;<lb/>
uebit: aut &aelig;quilibrium <expan abbr="faci&etilde;t">facient</expan>, &longs;i &aelig;quales &longs;int: vt &longs;i le&shy;<lb/>
ue graui committatur, &longs;iquidem leuitas grauitate <lb/>
maior &longs;it, attolletur graue: &longs;in ver&ograve; grauitas maior <lb/>
&longs;it, leue deprimetur: &longs;i &aelig;qualia &longs;int, non mouebun&shy;<lb/>
tur. </s></p><p type="main">

<s>Si ver&ograve; medio aliquo connectantur mediorum <lb/>
varia &longs;unt genera. </s><s>Aut enim medium e&longs;t flexibile &amp; <lb/>
<foreign lang="greek">o(moiomere\s</foreign>, vt funis, catena, &amp;c. </s><s>aut e&longs;t inflexibile, il&shy;<lb/>
l&uacute;dque aut rectum, aut curuum, vt recta linea vel <lb/>
curua vel angulus. </s><s>Atque h&aelig;c omnia aut continua 


<pb xlink:href="044/01/034.jpg" pagenum="26"/>&longs;unt aut diui&longs;a, &longs;implicia aut compo&longs;ita. </s></p><p type="main">

<s>Horum autem mediorum opera fit vt vires illis <lb/>
applicat&aelig;, quarum iidem &longs;unt nutus, contrariis mo&shy;<lb/>
tibus moueantur. </s><s>Id <expan abbr="aut&etilde;">autem</expan> fit c&ugrave;m in mediis illis inter <lb/>
<expan abbr="eor&utilde;">eorum</expan> extrema interiacet quies vna vel plures. </s><s><expan abbr="Ex&etilde;pli">Exempli</expan> <lb/>
gratia, &longs;i duo pondera funis extremitatibus alligata <lb/>
&longs;int, &amp; funis clauo fixo &amp; immobili incumbat pro&shy;<lb/>
pter illam quietem inter <expan abbr="vtrumq;">vtrumque</expan> pondus <expan abbr="po&longs;it&atilde;">po&longs;itam</expan> <expan abbr="n&otilde;">non</expan> <lb/>
poterit <expan abbr="alter&utilde;">alterum</expan> deor&longs;um moueri, quin <expan abbr="alter&utilde;">alterum</expan> &longs;ur&longs;um <lb/>
moueatur. </s><s><expan abbr="Id&etilde;">Idem</expan> fiet in linea recta, &longs;i enim illius extre&shy;<lb/>
mitatibus pondera duo annexa &longs;int, &amp; inter ea &longs;it in <lb/>
illa <expan abbr="punct&utilde;">punctum</expan> aliquod quie&longs;cens, dum alterum ex illis <lb/>
ponderibus deor&longs;um feretur, alterum a&longs;cendet. </s><s><expan abbr="P&utilde;-ctum">Pun&shy;<lb/>
ctum</expan> autem illud quie&longs;cens in linea illa recta, Gr&ecedil;cis <lb/>
hypomochlium dicitur, e&ograve; qu&ograve;d vecti, quem <foreign lang="greek">mo/xlon</foreign><lb/>
vocant, &longs;ubiiciatur. </s><s>Huius autem hypomochlij, in <lb/>
recta linea &longs;e vecte collocatio faciet, vt line&aelig; extre&shy;<lb/>
ma &longs;ecundum datam rationem moueantur. </s><s>Si enim <lb/>
recta linea in datam rationem diui&longs;a fuerit, hoc e&longs;t, <lb/>
vt pars altera ad <expan abbr="alter&atilde;">alteram</expan> eam habeat <expan abbr="ration&etilde;">rationem</expan>, <expan abbr="qu&atilde;">quam</expan> quis <lb/>
voluerit. (Quod <expan abbr="quid&etilde;">quidem</expan> quo modo fiat docet Euc.) &amp; <lb/>
in puncto diui&longs;ionis collocetur <expan abbr="hypomochli&utilde;">hypomochlium</expan>, illius <lb/>
line&aelig; extrema &longs;ecundum <expan abbr="ill&atilde;">illam</expan> <expan abbr="ration&etilde;">rationem</expan> mouebuntur: <lb/>
&longs;iue enim con&longs;ideretur <expan abbr="circulor&utilde;">circulorum</expan>, quos illa extrema <lb/>
de&longs;cribent, proportio &longs;iue &longs;patium quod illa in linea <lb/>
perpendiculari notabunt vtroque modo illi motus, 


<pb xlink:href="044/01/035.jpg" pagenum="27"/><expan abbr="parti&utilde;">partium</expan> <expan abbr="illar&utilde;">illarum</expan> <expan abbr="proportion&etilde;">proportionem</expan> <expan abbr="&longs;eruab&utilde;t">&longs;eruabunt</expan>. </s><s>Sit <expan abbr="ex&etilde;pli">exempli</expan> gratia <lb/>
linea AB, qu&aelig; in puncto C in datam rationem &longs;ecta <lb/>
&longs;it, puta vt pars AC quadrupla &longs;it ad partem CB, mo&shy;<lb/>
ueat&uacute;rque circa centrum C, punctum A de&longs;cribet cir<lb/>
culum <expan abbr="quadrupl&utilde;">quadruplum</expan> ad illum quem B <lb/>
de&longs;cribet. </s><s>E&longs;t enim <expan abbr="ead&etilde;">eadem</expan> ratio in cir&shy;<lb/>
culo diametri ad <expan abbr="diametr&utilde;">diametrum</expan>, qu&aelig; e&longs;t <lb/>
circunferenti&aelig; ad <expan abbr="circunferenti&atilde;">circunferentiam</expan> (vt <lb/>
alibi demon&longs;trauimus.) Hac igitur <lb/>
ratione A puncti motus quadruplus <lb/>
<figure id="id.044.01.035.1.jpg" xlink:href="044/01/035/1.jpg"/><lb/>
erit ad puncti B <expan abbr="mot&utilde;">motum</expan>. </s><s>Si ver&ograve; ponamus AD <expan abbr="perpen-dicular&etilde;">perpen&shy;<lb/>
dicularem</expan> e&longs;&longs;e, &amp; linea AB illi prim&ugrave;m <expan abbr="coincid&etilde;s">coincidens</expan> circa <lb/>
punctum C, moueatur donec A ad D perueniat: tum <lb/>
<expan abbr="eod&etilde;">eodem</expan> momento B perueniet ad E: motum igitur erit <lb/>
A in linea <expan abbr="perp&etilde;diculari">perpendiculari</expan> tota circuli maioris diame&shy;<lb/>
tro, qu&aelig; e&longs;t AD:B ver&ograve; in <expan abbr="ead&etilde;">eadem</expan> linea, minoris <expan abbr="t&atilde;t&ugrave;m">tant&ugrave;m</expan> <lb/>
circuli diametro <expan abbr="mot&utilde;">motum</expan> erit, qu&ecedil; e&longs;t BE. <!-- KEEP S--></s><s>Atqui diame<lb/>
ter AD quadrupla e&longs;t ad BE, quia ex hypothe&longs;i <expan abbr="&longs;emi-diametror&utilde;">&longs;emi&shy;<lb/>
diametrorum</expan> <expan abbr="illor&utilde;">illorum</expan> <expan abbr="circulor&utilde;">circulorum</expan> proportio e&longs;t, vt 4 ad 1. <lb/>
Motus igitur <expan abbr="p&utilde;cti">puncti</expan> in linea A <expan abbr="perp&etilde;diculari">perpendiculari</expan> ad <expan abbr="mot&utilde;">motum</expan> <lb/>
<expan abbr="p&utilde;cti">puncti</expan> B quadruplus erit: <expan abbr="Id&etilde;">Idem</expan> dicetur &longs;i in data aliqua <lb/>
alia ratione &longs;ecta &longs;it linea AB. <expan abbr="Dem&otilde;&longs;trat&utilde;">Demon&longs;tratum</expan> igitur e&longs;t <lb/>
quomodo fieri po&longs;&longs;it vt rect&aelig; line&ecedil; extrema <expan abbr="&longs;ec&utilde;d&utilde;">&longs;ecundum</expan> <lb/>
<expan abbr="dat&atilde;">datam</expan> <expan abbr="ration&etilde;">rationem</expan> moueantur. </s><s>Si igitur illis extremis du&aelig; <lb/>
vires applicentur, <expan abbr="moueb&utilde;tur">mouebuntur</expan> <expan abbr="eod&etilde;">eodem</expan> ip&longs;o motu: ergo <lb/>
&longs;ecundum datam vel propo&longs;itam rationem. </s><s>Quod <lb/>
a&longs;&longs;umptum erat. </s></p>


<pb xlink:href="044/01/036.jpg" pagenum="28"/><p type="main">

<s>Quod autem in vecte demon&longs;tratum e&longs;t, illud e&shy;<lb/>
tiam in reliquis mediis demon&longs;trandum erit, et&longs;i <lb/>
lemmati &longs;atisfactum e&longs;t, dum in vno exemplo id <lb/>
probatum e&longs;t. </s><s>Ante igitur &longs;ecundum lemma de&shy;<lb/>
mon&longs;trabimus. </s></p><p type="head">

<s>LEMMA II.<!-- KEEP S--></s></p><p type="main">

<s>Proportionem proxim&egrave; maiorem vel minorem, <lb/>
qu&agrave;m &longs;it dat&aelig; vis ad datum pondus proportio, de&shy;<lb/>
terminare vis cuiuslibet quantitas ex motu ciere po|| <lb/>
te&longs;t, metienda e&longs;t. </s><s>Motum autem ciere pote&longs;t vel in <lb/>
&longs;ubiecto &longs;uo, vel in alieno. </s><s>Vis autem men&longs;ura non <lb/>
&longs;umitur ex eo motu quem in &longs;ubiecto &longs;uo ciere po&shy;<lb/>
te&longs;t, eo qu&ograve;d licet vis qu&aelig;libet certum motum ha&shy;<lb/>
beat &amp; <expan abbr="determinat&utilde;">determinatum</expan> quo &longs;ubiectum &longs;uum mouet, <lb/>
illius tamen quantitas, vt &longs;upr&agrave; diximus, nondum <lb/>
demon&longs;trata e&longs;t. </s><s>Supere&longs;t igitur vt vires motu illo <lb/>
metiamur, quem in alieno &longs;ubiecto ciere po&longs;&longs;unt, vt <lb/>
id fiat, qu&aelig;renda nobis &longs;unt &longs;ubiecta qu&aelig; in homi&shy;<lb/>
num pote&longs;tate &longs;int, &amp; cum vi qualibet committi <lb/>
po&longs;&longs;int. </s><s>Omnium autem mobilium &longs;ubiectorum, <lb/>
maxim&egrave; in hominum pote&longs;tate &longs;unt grauia: leuia e&shy;<lb/>
nim coercere vix po&longs;&longs;umus. </s><s>Ideo vires illis metiri <lb/>
&longs;olemus, &longs;ed grauibus qu&aelig; vel vel figuris &longs;uis &amp; com<lb/>
page vel va&longs;e aliquo coercentur. </s><s>Itaque v&longs;us homi&shy;<lb/>
num certas qua&longs;dam ponderum men&longs;uras &longs;ibi &longs;ta <lb/>
tui, ponderibus &longs;cilicet quibu&longs;dam certa <expan abbr="qu&atilde;titate">quantitate</expan> 


<pb xlink:href="044/01/037.jpg" pagenum="29"/>con&longs;tantibus inditis nominibus, vt e&longs;&longs;ent <expan abbr="ponder&utilde;">ponderum</expan> <lb/>
omnium communes men&longs;ur&aelig;, vt &longs;unt libr&aelig;, vncia, <lb/>
<expan abbr="drachm&ecedil;">drachm&aelig;</expan>, &amp;c. </s><s>quas famo&longs;as men&longs;uras <expan abbr="voc&atilde;t">vocant</expan>. </s><s>Quem&shy;<lb/>
admodum igitur numeros numeris, &longs;ic pondera <expan abbr="p&otilde;-deribus">pon&shy;<lb/>
deribus</expan> metimur. </s><s><expan abbr="T&atilde;tum">Tantum</expan> enim pondus e&longs;&longs;e dicitur, <lb/>
quot libras vncias drachmas &aelig;qualiter mouere po&shy;<lb/>
te&longs;t dempto momento. </s><s>Nec tantum pondera hoc <lb/>
modo metimur, &longs;ed etiam alias omnes vires motum <lb/>
ad locum cientes. </s><s>Quot enim libras vir aut aliud a&shy;<lb/>
nimal vel <expan abbr="v&etilde;tus">ventus</expan> aut ignis, aut aliqua alia vis dempto <lb/>
momento mouere poterit, tot libris illam &aelig;qualem <lb/>
e&longs;&longs;e dicemus. </s><s>Si igitur data vel propo&longs;ita vis metien&shy;<lb/>
da &longs;it, &longs;iquidem naturalis &longs;it, quoniam docuimus <lb/>
vim naturalem per totum &longs;ubiectum diffu&longs;am e&longs;&longs;e <lb/>
in rebus homogeneis: id e&longs;t, vt qu&aelig; e&longs;t proportio <lb/>
molis ad molem, eadem &longs;it ponderis ad pondus: &longs;u&shy;<lb/>
memus partem aliquam illi homogeneam, aut ex i&shy;<lb/>
p&longs;o &longs;ubiecto, aut ex alio ip&longs;i homogeneo, e&aacute;mque <lb/>
famo&longs;a aliqua men&longs;ura metiemur, vtramque &longs;cili&shy;<lb/>
cet committendo &amp; ob&longs;eruando, quem motum al&shy;<lb/>
tera in altera ciere po&longs;&longs;it, vbi enim &aelig;quilibrium fa&shy;<lb/>
cient motibus extremorum, quibus affix&aelig; fuerint, <lb/>
proportionales erunt per 1 theorema: motus autem <lb/>
illi linearum dimen&longs;ione quam Geometria docet, <lb/>
noti erunt, &amp; eorum proportio, nota igitur erit &amp; <lb/>
virium proportio. </s><s>Atqui men&longs;ur&aelig; famo&longs;&aelig; nota, per 


<pb xlink:href="044/01/038.jpg" pagenum="30"/>&longs;e e&longs;t quantitas: duorum autem proportione cogni&shy;<lb/>
ta &amp; alterius quantitate, &longs;tatim &amp; reliqui quantitas <lb/>
innote&longs;cit per &longs;ecundam da. <!-- REMOVE S-->Eu. <!-- REMOVE S-->nota igitur vis <expan abbr="qu&atilde;-titate">quan&shy;<lb/>
titate</expan> qu&aelig; parti illi ine&longs;t, no&longs;cetur &amp; vis <expan abbr="qu&atilde;titas">quantitas</expan> <expan abbr="qu&ecedil;">qu&aelig;</expan><lb/>
toti inerit: qu&aelig; enim erit ratio molis &longs;ubiecti vis da&shy;<lb/>
t&aelig; ad molem particul&ecedil; &longs;umpt&ecedil;, eadem erit vis totius <lb/>
ad vim partis. </s>





<s>H&icirc;c igitur erunt quatuor proportio&shy;<lb/>
nalia, &longs;cilicet vt moles ad molem: &longs;ic vis ad vim ex <lb/>
quibus tria nota erunt: moles enim metiri Geome&shy;<lb/>
tria nos docuit, pr&aelig;terea vis partis, vt demon&longs;traui&shy;<lb/>
mus, nota e&longs;t, ergo &amp; vis totius quantitas per deci&shy;<lb/>
mam &longs;eptimam &longs;eptimi Elem. Eucl. <!-- KEEP S--></s></p><p type="main">

<s>Si ver&ograve; &longs;ubiectum non &longs;it homogeneum, vi ta&shy;<lb/>
men naturali &longs;it pr&aelig;ditum, &longs;i quidem data vis quam <lb/>
metiri volumus, ea &longs;itque motum ciere volumus, <lb/>
tum con&longs;iderabimus qu&aelig; pars in illa, vis minimum <lb/>
habeat: &amp; ex ea totam ip&longs;ius molem &aelig;&longs;timabimus: <lb/>
&longs;i ver&ograve; &longs;it vis mouenda, &longs;tatuemus qua&longs;i tota &longs;it ho&shy;<lb/>
mogenea ip&longs;ius parti, qu&aelig; vis plurimum in &longs;e habe&shy;<lb/>
bit, &amp; ex ea totam ip&longs;ius molem &aelig;&longs;timabimus. </s><s>Ita&shy;<lb/>
que tum illius quanta minima, tum huius quanta <lb/>
maxima e&longs;&longs;e pote&longs;t, vis quantitas nobis nota erit per <lb/>
proxim&egrave; demon&longs;tratam rationem. </s><s>Notis autem vi&shy;<lb/>
rium quantitatibus, nota erit &amp; earum proportio: <lb/>
ergo &amp; proportio ip&longs;a proxim&egrave; maior vel mi&shy;<lb/>
nor: addita enim vel detracta ip&longs;ius denomi-


<pb xlink:href="044/01/039.jpg" pagenum="31"/>nationi, vnitate erit proxim&egrave; maior vel mi&shy;<lb/>
nor. </s></p><p type="main">

<s>Si ver&ograve; vis data non &longs;it naturalis, <expan abbr="voluntari&atilde;">voluntariam</expan> qui&shy;<lb/>
dem ita &aelig;&longs;timare po&longs;&longs;umus, qualis vt plurimum <lb/>
e&longs;t, &amp; &longs;i quidem ea &longs;it, qua mouere volumus, eam <lb/>
&longs;tatuemus, quanta minima in eiu&longs;dem generis &longs;ub&shy;<lb/>
iecto e&longs;&longs;e pote&longs;t, vt &longs;i vim hominis quinquaginta li&shy;<lb/>
bris &aelig;qualem ponamus, vim equi centum: &longs;i ver&ograve; <lb/>
ea &longs;it quam mouere volumus, &longs;tatuemus eam <expan abbr="qu&atilde;-ta">quan&shy;<lb/>
ta</expan> maxima e&longs;&longs;e pote&longs;t, vt vim hominis 300 libra&shy;<lb/>
rum, vim equi 500 librarum, &amp; &longs;ic d&eacute; c&aelig;teris: ita vt <lb/>
nullum &longs;it dubium quin illa minor &longs;it, quam &longs;tatue&shy;<lb/>
rimus, h&aelig;c ver&ograve; maior. </s></p><p type="main">

<s>Vis ver&ograve; fortuit&aelig; quantitatem nulla certa con&shy;<lb/>
iectura a&longs;&longs;equi po&longs;&longs;umus: ita vt qua&longs;cunque ma&shy;<lb/>
chinas ei aptemus, mod&ograve; moueat, mod&ograve; non mo&shy;<lb/>
ueat, neque ad no&longs;trum <expan abbr="in&longs;titut&utilde;">in&longs;titutum</expan> magnoper&egrave; per&shy;<lb/>
tinet illa inqui&longs;itio: cum fortuitorum nulla &longs;it di&longs;ci&shy;<lb/>
plina. </s></p><p type="main">

<s>His igitur modis virium duarum datarum pro&shy;<lb/>
portio proxim&egrave; maior nota fiet, quod in &longs;ecundo <lb/>
lemmate demon&longs;trandum &longs;ump&longs;eramus. </s></p><p type="main">

<s>Iam redeamus ad mediorum, quibus vi&shy;<lb/>
res annectuntur, con&longs;ide&shy;<lb/>
rationem. </s></p>


<pb xlink:href="044/01/040.jpg" pagenum="32"/><figure id="id.044.01.040.1.jpg" xlink:href="044/01/040/1.jpg"/><p type="main">

<s>Docuimus quis &longs;it &longs;implicis ve&shy;<lb/>
ctis effectus, &longs;implex autem ve&shy;<lb/>
ctis &longs;emicirculi conuer&longs;ione &longs;uam <lb/>
operationem ab&longs;ouit, ita vt &longs;i <lb/>
vlteri&ugrave;s F moueatur in in alio &longs;e&shy;<lb/>
micirculo motus prioribus contra&shy;<lb/>
rios cieat: vt exempli gratia, &longs;it <lb/>
vectis AB, cuius hypomochium <lb/>
&longs;it C, dum A punctum de&longs;cribet &longs;emicirculum AFD, <lb/>
motus ille deor&longs;um erit: interea ver&ograve; B punctum <lb/>
de&longs;cribet &longs;emicirculum BGE a&longs;cendendo: &longs;i ver&ograve; A <lb/>
tran&longs;cendat, D incipiet a&longs;cendere: B ver&ograve; tran&longs;cen&shy;<lb/>
dens, E <expan abbr="de&longs;c&etilde;det">de&longs;cendet</expan>: ideo excogitata e&longs;t vectis ratio per&shy;<lb/>
petua ex plurium vectium &longs;ucce&longs;&longs;ione circa idem <lb/>
hypomochlium: e&longs;t autem illa tum in ergatis aut &longs;u&shy;<lb/>
culis, tum in duorum tympanorum homocentrico&shy;<lb/>
rum, &longs;eu eadem axe transfixorum in planis parallelis <lb/>
aptatione, quorum &longs;emidiametri &longs;int in eadem pro&shy;<lb/>
portione qu&aelig; in vecte ad propo&longs;itum motum cien&shy;<lb/>
dum nece&longs;&longs;aria e&longs;t: centrum ver&ograve; eorum &longs;eu axis fi&shy;<lb/>
xa &longs;it, ac ita vires aptentur, vt maior minorem, mi&shy;<lb/>
nor ver&ograve; maiorem tympanum impellat. </s><s>Quemad&shy;<lb/>
modum autem horum tympanorum homocentri&shy;<lb/>
corum opera vectis perpetui ratio <expan abbr="inu&etilde;ta">inuenta</expan> e&longs;t, ita eo&shy;<lb/>
rum multiplicatione motus, &amp; mouentis &amp; <expan abbr="mou&etilde;-di">mouen&shy;<lb/>
di</expan>, proportio in infinitum augeri pote&longs;t. </s><s>Cuius rei 


<pb xlink:href="044/01/041.jpg" pagenum="33"/>maximus e&longs;t v&longs;us: nec enim materia ad vectem, cu&shy;<lb/>
ius longitudo &longs;tadij vnius requireretur, idonea in&shy;<lb/>
ueniri po&longs;&longs;et: plurium autem tympanorum propor&shy;<lb/>
tionalium aptatione fiet machina tractabilis, cuius <lb/>
vis maior erit qu&agrave;m vectis, cuius longitudo &longs;tadij v&shy;<lb/>
nius e&longs;&longs;et. </s><s>Si enim duo tympani homocentrici a&shy;<lb/>
ptentur, quorum proportio &longs;it alterius ad alterum, <lb/>
decupla, vis qu&aelig; libram vnam &aelig;quabit, vim decem <lb/>
libris &aelig;qualem dempto momento mouebit, &longs;i con&shy;<lb/>
gru&egrave; illis tympanis aptentur: &longs;i ver&ograve; adhuc duo alij <lb/>
tympani fiant, quorum alterius ad alterum decupla <lb/>
&longs;it proportio, ac minor <expan abbr="illor&utilde;">illorum</expan> ita aptetur, vt <expan abbr="maior&etilde;">maiorem</expan> <lb/>
ex prioribus moueat, appendatur deinde minori ex <lb/>
prioribus tympanis vis centum libris &aelig;qualis, maio&shy;<lb/>
ri ver&ograve; ex po&longs;terioribus vis vni libr&aelig; &aelig;qualis, tum <lb/>
h&aelig;c illam mouebit, &amp; &longs;ic in infinitum motus extre&shy;<lb/>
morum proportio multiplicari pote&longs;t. </s><s>Flexibili ve&shy;<lb/>
r&ograve; medio quies ita aptari pote&longs;t, vt duo eius extre&shy;<lb/>
ma diuer&longs;is motibus moueantur, &amp; quidem &longs;ecun&shy;<lb/>
dum datam rationem. </s><s>Exemplum habemus in orga <lb/>
nis poly&longs;pactis, &longs;eu trochleis, in quibus altero funis <lb/>
extremo immobili manente, reliquum funis circa <lb/>
plures trochleas conuoluitur, quarum ali&aelig; centris <lb/>
immobilibus fix&aelig; &longs;unt, ali&aelig; ver&ograve; ip&longs;is contrari&aelig; cen <lb/>
tris mobilibus. </s><s>Atque ita circa illas conuoluitur fu&shy;<lb/>
nis, vt inter eas &longs;it &longs;patium tantum, quanta e&longs;t linea, 


<pb xlink:href="044/01/042.jpg" pagenum="34"/>per quam motum ciere volumus. </s><s>Quoties igitur fu&shy;<lb/>
nis extremum quod moueri pote&longs;t, trahitur, <expan abbr="&longs;ingul&ecedil;">&longs;ingul&aelig;</expan><lb/>
reuolutiones &aelig;qualiter minuuntur, e&aacute;que ratione, <lb/>
<expan abbr="di&longs;t&atilde;tia">di&longs;tantia</expan> qu&aelig; e&longs;t inter trochleas contrarias minuitur, <lb/>
ita &longs;cilicet vt quot &longs;unt reuolutiones, in tot partes <lb/>
di&longs;tributum &longs;it motus &longs;patium. </s><s>Quot igitur reuolu<lb/>
tiones erunt, totuplex erit motus extremitatis funis <lb/>
ad motum trochlearum mobilium ver&longs;us fixas. </s><s>Si i&shy;<lb/>
gitur motus i&longs;tius extrema con&longs;tituantur, alterum <lb/>
<expan abbr="quid&etilde;">quidem</expan> funis illa extremitas qu&aelig; mouetur, <expan abbr="alter&utilde;">alterum</expan> ve&shy;<lb/>
r&ograve; terminus &longs;patij illius, quod e&longs;t &agrave; trochleis fixis ad <lb/>
mobiles contrarias: qu&aelig; erit proportio numeri con&shy;<lb/>
uolutionum funis ad vnitatem, eadem erit motus, <lb/>
quo funis extremum mouebitur ad motum quo al&shy;<lb/>
terum extremum mouebitur: pote&longs;t autem in infi&shy;<lb/>
nitum augeri conuolutionum numerus, ergo &amp; mo<lb/>
tus illius proportio. </s></p><p type="main">

<s>Angulus autem ad motum ciendum ita ad&shy;<lb/>
hibetur. </s><s>Diximus motus men&longs;uram in nutus li&shy;<lb/>
nea &longs;umi, quantum igitur vis aliqua per eam ver&longs;us <lb/>
locum naturalem mouetur, tanta e&longs;t, quantum ver&ograve; <lb/>
per eam &agrave; loco naturali reuellitur, tanta e&longs;t eius re&longs;i&shy;<lb/>
&longs;tentia. </s><s>Quod ver&ograve; per lineam &agrave; loco naturali &aelig;qu&egrave; <lb/>
di&longs;tantem (id e&longs;t, per eam qu&aelig; nutus lineas &longs;ecat ad <lb/>
angulos rectos) mouetur, illud mouenti non re&longs;i&shy;<lb/>
&longs;tit, omnium autem linearum inter illas intercepta-


<pb xlink:href="044/01/043.jpg" pagenum="35"/>rum, ac cum illis in earum inter&longs;ectionis puncto <expan abbr="c&otilde;-currentium">con&shy;<lb/>
currentium</expan>, qu&aelig; obliqu&egrave; nutum ver&longs;us, aut contra <lb/>
nutum ferri dicuntur, quo propi&ugrave;s qu&aelig;libet ad nu&shy;<lb/>
tus lineam accedit, per illam rei mot&aelig; vis aut <expan abbr="re&longs;i&longs;t&etilde;-tia">re&longs;i&longs;ten&shy;<lb/>
tia</expan> maior e&longs;t: qu&ograve; ver&ograve; propi&ugrave;s ad lineam &agrave; loco na&shy;<lb/>
turali &aelig;qui di&longs;tantem accedit, e&ograve; minor e&longs;t. </s><s><expan abbr="Omni&utilde;">Omnium</expan> <lb/>
autem maxima e&longs;t in nutus linea, &aelig;quidi&longs;tans ver&ograve; <lb/>
&agrave; loco naturali motui per lineam nutus omnino op<lb/>
po&longs;ita e&longs;t, obliqu&aelig; ver&ograve; non ita quia &longs;ecundum illas <lb/>
<expan abbr="eod&etilde;">eodem</expan> &longs;patio delata vis propi&ugrave;s ad <expan abbr="loc&utilde;">locum</expan> <expan abbr="natural&etilde;">naturalem</expan> acce&shy;<lb/>
dit, aut ab eo recedit, qu&agrave;m e&longs;&longs;et, c&ugrave;m moueri c&oelig;pit. </s></p><figure id="id.044.01.043.1.jpg" xlink:href="044/01/043/1.jpg"/><p type="main"><s>Sit exempli gratia AB linea <lb/>
nutus, vis alicuius, puta ponde&shy;<lb/>
ris, &longs;itque A &longs;ur&longs;um &amp; contra nu<lb/>
tum: B ver&ograve; deor&longs;um &amp; nutum <lb/>
ver&longs;us, de&longs;cribat&uacute;rque circulus, <lb/>
cuius AB &longs;it diameter, qu&agrave;m CD, <lb/>
alia diameter &longs;ecet ad angulos <lb/>
rectos in centro E: omnes igitur <lb/>
line&aelig; &agrave; centro E ad circunferentiam circuli duct&aelig;, <lb/>
qu&aelig; <expan abbr="cad&etilde;t">cadent</expan> intra <expan abbr="&longs;emicircul&utilde;">&longs;emicirculum</expan> CAD, contra <expan abbr="nut&utilde;">nutum</expan> <expan abbr="a&longs;c&etilde;-dere">a&longs;cen&shy;<lb/>
dere</expan> dicentur, quatenus circunferentiam &longs;pectant: <lb/>
quatenus ver&ograve; centrum &longs;pectant, de&longs;cendere dicen&shy;<lb/>
tur: <expan abbr="c&otilde;tra">contra</expan> ver&ograve; omnes in &longs;emicirculo CBD &agrave; centro <lb/>
ad circunferentiam duct&aelig; de&longs;cendere circunferen&shy;<lb/>
tiam ver&longs;us, &amp; centrum ver&longs;us a&longs;cendere dicentur: 


<pb xlink:href="044/01/044.jpg" pagenum="36"/>ill&aelig; igitur erunt, qu&aelig; obliqu&egrave; nutum ver&longs;us aut con<lb/>
tra nutum ferri <expan abbr="dic&utilde;tur">dicuntur</expan>: linea ver&ograve; CED, neque <expan abbr="a&longs;c&etilde;-det">a&longs;cen&shy;<lb/>
det</expan>, neque de&longs;cendet: line&aelig; ver&ograve; in ip&longs;am ad angu&shy;<lb/>
los rectos incidentes nutus line&aelig; erunt, quoniam li&shy;<lb/>
ne&aelig; AB parallel&aelig; erunt: &longs;i igitur &agrave; centro E <expan abbr="duc&atilde;tur">ducantur</expan> <lb/>
line&aelig; ad circunferentiam inter A &amp; D, puta EF, EG, <lb/>
EH, quarum EF &longs;it proxima line&aelig; AB:EH ver&ograve; pro&shy;<lb/>
xima line&aelig; CD, ac per illas moueantur contra <expan abbr="nut&utilde;">nutum</expan> <lb/>
tres vires &aelig;quales eodem tempore, ita vt prima per <lb/>
lineam EF perueniat ad punctum F: &longs;ecunda ver&ograve; <lb/>
per EG perueniat ad G, tertia per EH perueniat ad H, <lb/>
dico vis mot&aelig; per EF maiorem fore re&longs;i&longs;tentiam, <lb/>
qu&agrave;m illius qu&aelig; per EG aut EH, mouebitur &amp; illius <lb/>
qu&aelig; per EG mouebitur, maiorem qu&agrave;m eius qu&aelig; <lb/>
per EH mouebitur. </s><s>Ducantur enim &agrave; punctis FGH <lb/>
in lineam ED perpendiculares FK, GL, HM, ill&aelig; <expan abbr="er&utilde;t">erunt</expan> <lb/>
nutus line&aelig;: quanta igitur erit FK, tantum vis prima <lb/>
mota cen&longs;ebitur, quanta ver&ograve; GH, tantum vis &longs;ecun<lb/>
da: quanta ver&ograve; HM, tantum vis tertia mota cen&longs;ebi&shy;<lb/>
tur: at qui qu&aelig; e&longs;t ratio motus ad motum in viribus <lb/>
&aelig;qualibus, per quartam <expan abbr="c&otilde;clu&longs;ionem">conclu&longs;ionem</expan> huius tracta&shy;<lb/>
tus, eadem e&longs;t re&longs;i&longs;tenti&aelig; ad re&longs;i&longs;tentiam: qu&aelig; igitur <lb/>
erit ratio linearum illarum perpendicularium, inter <lb/>
&longs;e eadem erit &amp; <expan abbr="re&longs;i&longs;t&etilde;tiarum">re&longs;i&longs;tentiarum</expan> virium per lineas ob&shy;<lb/>
liquas motarum, &agrave; quibus ill&aelig; perpendiculares du&shy;<lb/>
ct&aelig; &longs;unt, atqui quo line&aelig; ill&aelig; perpendiculares pro-


<pb xlink:href="044/01/045.jpg" pagenum="37"/>pi&ugrave;s ad AB circuli diametrum accedunt, e&ograve; &longs;unt ma<lb/>
iores per decimam quartam tertij Elem. Eu. ergo &amp; <lb/>
vires per eas lineas delat&ecedil; &agrave; <expan abbr="quar&utilde;">quarum</expan> extremitatibus du<lb/>
<expan abbr="c&etilde;tur">centur</expan>, maiores <expan abbr="re&longs;i&longs;t&etilde;tias">re&longs;i&longs;tentias</expan> <expan abbr="habeb&utilde;t">habebunt</expan>: at qui qu&ograve; magis <lb/>
ad AB, accedunt eo magis ab ED recedunt: qu&ograve; igi&shy;<lb/>
tur magis ad ED accedent, e&ograve; minores erunt <expan abbr="re&longs;i&longs;t&etilde;-ti&aelig;">re&longs;i&longs;ten&shy;<lb/>
ti&aelig;</expan>, hinc &longs;equitur tanquam corollarium. </s> <s>Si du&aelig; vi&shy;<lb/>
res per&longs;e &aelig;quales triangulo rectangulo aptentur, cu<lb/>
ius latus alterum, angulum rectum <expan abbr="con&longs;titu&etilde;tium">con&longs;tituentium</expan>: <lb/>
&longs;it earum nutus linea, ac per illud vis altera mouea&shy;<lb/>
tur, altera ver&ograve; per latus angulo recto oppo&longs;itum, <lb/>
qu&aelig; erit ratio huius lateris ad illud, eadem erit re&longs;i&shy;<lb/>
&longs;tentia vis illius ad vis huius <expan abbr="re&longs;i&longs;t&etilde;tiam">re&longs;i&longs;tentiam</expan>. </s><s>Atqui duo&shy;<lb/>
rum illorum laterum proportio in infinitum auge&shy;<lb/>
ri vel minui pote&longs;t, ergo &amp; re&longs;i&longs;tentia virium illis ap<lb/>
plicatarum. </s><s>Hoc igitur modo po&longs;&longs;umus vti angulo <lb/>
&longs;eu triangulo ad motus ciendos, nempe eo immoto <lb/>
vires per eius latera mouendo. </s></p><p type="main">

<s>Sed &amp; alia ratione eo vti po&longs;&longs;umus, ip&longs;um &longs;cilicet <lb/>
triangulum mouendo, qui tunc cuneus dicitur. </s><s>Vt <lb/>
autem eo hac ratione vtamur, vires ita di&longs;ponere o&shy;<lb/>
portet, vt altera illarum vni ex lateribus angulum <lb/>
rectum con&longs;tituentibus incumbat, altera ver&ograve; lateri <lb/>
ip&longs;um &longs;ubtendenti. </s><s>Illa enim tant&ugrave;m mouebitur, <lb/>
quantum latus cui altera incumbit. </s><s>Sit exempli gra&shy;


<pb xlink:href="044/01/046.jpg" pagenum="38"/><figure id="id.044.01.046.1.jpg" xlink:href="044/01/046/1.jpg"/><lb/>
tia triangulus ABC, cuius angulus B <lb/>
rectus &longs;it, latus ver&ograve; illum &longs;ubtendens <lb/>
&longs;it AC, incumb&aacute;tque vis D lateri AB, <lb/>
vis ver&ograve; E lateri AC, &longs;itque vis D nutus <lb/>
linea BC, vis ver&ograve; E nutus &longs;it linea AB, erigat&uacute;rque &agrave; <lb/>
puncto C linea CF <expan abbr="perp&etilde;dicularis">perpendicularis</expan> ad BC &aelig;qualis AB, <lb/>
&agrave; qua vis E <expan abbr="n&otilde;">non</expan> di&longs;cedat. </s><s>Si triangulum illud in plano <lb/>
fixo moueatur, donec AB perueniat ad CF, mota e&shy;<lb/>
rit vis D nutu &longs;uo tant&ugrave;m, quanta e&longs;t linea BC, vis ve&shy;<lb/>
r&ograve; E tantum, quanta e&longs;t linea AB. <!-- KEEP S--></s><s>C&ugrave;m autem po&longs;&longs;it <lb/>
in infinitum augeri &amp; minui, laterum illorum pro&shy;<lb/>
portio, po&longs;&longs;unt etiam duorum illorum <expan abbr="extremor&utilde;">extremorum</expan> <lb/>
motus in data ratione con&longs;titui. </s><s>Quanta enim erit <lb/>
BC ad AB, tantus erit motus vis D ad motum vis E: <lb/>
ergo &amp; in hoc medio primum lemma no&longs;trum de&shy;<lb/>
mon&longs;tratum e&longs;t. </s></p><p type="main">

<s>In hoc autem medij genere hoc diuer&longs;um ab <lb/>
aliis mediis accidit, qu&ograve;d non tam facil&egrave; vtrin&shy;<lb/>
que motus eo cietur, ac in illis, in quibus &longs;i virium <lb/>
proportio momento vel &longs;uperet, vel minor &longs;it pro&shy;<lb/>
portione motus <expan abbr="extremor&utilde;">extremorum</expan> medij, tum motus hinc <lb/>
vel inde cietur. </s><s>Atqui in hoc propter &longs;uperficie&shy;<lb/>
rum contactum, quarum pori vel a&longs;peritates &longs;e&shy;<lb/>
&longs;e mutu&ograve; &longs;ubingrediuntur, &amp; ita inuicem adh&aelig;&shy;<lb/>
rent, fit vt &aelig;gri&ugrave;s cieatur motus, facili&ugrave;s ve-


<pb xlink:href="044/01/047.jpg" pagenum="39"/>r&ograve; mouebuntur, &longs;i ill&aelig; &longs;uperficies leues fue&shy;<lb/>
rint, vt &longs;i pinguibus inungantur, vel ex materia <lb/>
leui con&longs;tent. </s><s>Ide&ograve; enim reliqua facili&ugrave;s mo&shy;<lb/>
uentur, qu&ograve;d circa puncta veluti qu&aelig;dam mo&shy;<lb/>
ueantur. </s></p><p type="main">

<s>Simplicis autem trianguli rectilinei aut cu&shy;<lb/>
nei in diuturnis motibus ciendis rarus e&longs;t v&longs;us, <lb/>
tum ob illud quod notauimus incommodum ex <lb/>
vitio materi&aelig;, quo fit vt in eo qua&longs;&longs;atione opus <lb/>
&longs;it, tum etiam qu&ograve;d breui eius operatio termine&shy;<lb/>
tur. </s><s>Ideo illo vtimur aut c&ugrave;m &longs;olutionem con&shy;<lb/>
tinui molimur, qu&aelig; breui tempore fit, vel <lb/>
c&ugrave;m aliquid di&longs;tendere aut aliquid figere volu&shy;<lb/>
mus. </s></p><p type="main">

<s>Anguli ver&ograve; curui linei magnus e&longs;t v&longs;us, pr&aelig;&shy;<lb/>
&longs;ertim helicis cylindric&aelig;. </s><s>Nihil enim aliud e&longs;t he&shy;<lb/>
lix qu&agrave;m triangulus curuus: &longs;i enim alteram ex <lb/>
lineis rectis angulum con&longs;tituentibus, cylindri <lb/>
ba&longs;i ip&longs;i line&aelig; &aelig;quali obuolueris, reliquam ve&shy;<lb/>
r&ograve; &longs;eruato eodem quem con&longs;tituunt angulo, &longs;u&shy;<lb/>
per cylindri &longs;uperficiem curuaueris, habebis he&shy;<lb/>
licem cylindricam, quam &longs;i iterum &longs;eruato eo&shy;<lb/>
dem angulo in rectum extendas, habebis trian&shy;<lb/>
gulum rectilineum. </s><s>H&aelig;c autem helix commo&shy;<lb/>
di&longs;&longs;ima e&longs;t, tum qu&ograve;d in parua mole triangulum 


<pb xlink:href="044/01/048.jpg" pagenum="40"/>longi&longs;&longs;imum obuolutum contineat tum quod par&shy;<lb/>
tes eius omnes &longs;ibi inuicem <expan abbr="c&otilde;gruant">congruant</expan>: omnes enim <lb/>
partes helicis cylindric&aelig;, aut circa eundem, aut circa <lb/>
&aelig;quales cylindros de&longs;cript&aelig;, &longs;eruato eodem angulo <lb/>
&longs;ibi inuicem &longs;uppo&longs;it&aelig; congruunt. </s><s>Quo fit, vt &longs;i ca&shy;<lb/>
ui cylindri interiori &longs;uperficiei impre&longs;&longs;a &longs;it helix, a&shy;<lb/>
lia ver&ograve; cylindri &longs;uperficiei connex&ecedil; ip&longs;i cau&ecedil; &aelig;qua&shy;<lb/>
li, &longs;eruato eodem qui in illo e&longs;t, angulo, &longs;ibi inui&shy;<lb/>
cem &amp; omnes vnius omnibus alterius partibus con<lb/>
gruant. </s></p><p type="main">

<s>Huius autem medij c&ugrave;m plures &longs;int partes, con<lb/>
&longs;tat enim duabus &longs;uperficiebus, pluribus etiam mo<lb/>
dis variari pote&longs;t. </s><s>In &longs;umma autem eius affectus hic <lb/>
e&longs;t, vt cylindri ba&longs;i in &longs;uperficie immobili circum a&shy;<lb/>
xem conuer&longs;a, vis mouenda helicem premat: dum <lb/>
enim cylindrus circum axem conuertetur, vis mo&shy;<lb/>
uenda qualibet reuolutione tant&ugrave;m &longs;ecundum cy&shy;<lb/>
lindri longitudinem mouebitur, quanta e&longs;t di&longs;tan&shy;<lb/>
tia duarum helicis &longs;pirarum. </s><s>Qu&aelig; igitur erit propor<lb/>
tio circunferenti&aelig; circuli ba&longs;im cylindri <expan abbr="con&longs;titu&etilde;-tis">con&longs;tituen&shy;<lb/>
tis</expan> ad illam <expan abbr="di&longs;t&atilde;tiam">di&longs;tantiam</expan>, eadem erit motus orbicularis <lb/>
cuiu&longs;libet puncti in cylindri &longs;uperficie &longs;ignati ad mo<lb/>
tum rectum vis helicem prementis. </s></p><p type="main">

<s>Illud igitur medium ex duobus compo&longs;itum e&longs;t, <lb/>
recto &longs;cilicet &amp; curuo: ita igitur vires illi aptand&aelig; <lb/>
&longs;unt, vt eius quam mouere volumus, nutus linea &longs;it 


<pb xlink:href="044/01/049.jpg" pagenum="41"/>cylindri longitudo: illa ver&ograve; qua mouere volumus, <lb/>
in orbem moueatur, aut &longs;i eius nutus linea recta &longs;it, <lb/>
circa cylindrum fluens illum moueat contingendo. </s></p><p type="main">

<s>Et h&aelig;c quidem de mediis in &longs;uo genere <expan abbr="con&longs;i&longs;t&etilde;-tibus">con&longs;i&longs;ten&shy;<lb/>
tibus</expan>. </s><s>Po&longs;&longs;unt autem fieri eorum Syzygi&aelig; vectis &longs;ci&shy;<lb/>
licet cum trochleis, helicis cum vecte, aut cum tro&shy;<lb/>
chleis, aut <expan abbr="omni&utilde;">omnium</expan> &longs;imul. </s><s>Vectis cum trochleis &longs;i fu&shy;<lb/>
nis illud extremum, quod mouetur in trochleis, er&shy;<lb/>
gatis aut &longs;uculis inuoluatur: helix cum vecte <expan abbr="coni&utilde;-getur">coniun&shy;<lb/>
getur</expan>, &longs;i tympanus circum axem moueatur, &longs;itque i&shy;<lb/>
ta denticulatus, vt dentes ip&longs;ius helicem in cylindro <lb/>
excauatam ingrediantur, quam machinam helicem <lb/>
perpetuam vulg&ograve; vocant, e&ograve; qu&ograve;d eius conuer&longs;io <lb/>
perpetua e&longs;&longs;e po&longs;&longs;it, cum helicis &longs;implicis operatio <lb/>
non excedat ip&longs;ius longitudinem. </s><s>Quorum <expan abbr="omni&utilde;">omnium</expan> <lb/>
tum inter &longs;e, tum ad &longs;ubiecta mouenda accommo&shy;<lb/>
datio ade&ograve; varia e&longs;t, vt &longs;cripto <expan abbr="c&otilde;preh&etilde;di">comprehendi</expan> vix po&longs;&longs;it. <lb/>
</s><s>Ex his autem qu&aelig; dicta &longs;unt, mediocris ingenij me&shy;<lb/>
chanicus poterit ea prout ip&longs;i nece&longs;&longs;e erit aptare. </s><s>In <lb/>
machinis autem omnibus h&aelig;c cautio <expan abbr="adhib&etilde;da">adhibenda</expan> e&longs;t, <lb/>
vt earum &longs;tructura firma &longs;it, pr&aelig;&longs;ertim ver&ograve; vbi cir&shy;<lb/>
cum axes aliquas fit motus, deinde vt vincula, qui&shy;<lb/>
bus illis vires <expan abbr="affing&utilde;tur">affinguntur</expan>, valida &longs;int, illarum enim o&shy;<lb/>
mnium vis in &longs;uo &longs;tatu manendi vtrique vi aptand&aelig; <lb/>
&aelig;qualis e&longs;&longs;e debet: aget enim in illas vis <expan abbr="vtraq;">vtraque</expan>, qu&ograve;d <lb/>
&longs;i medium firmum non &longs;it, motus in ip&longs;a machina 


<pb xlink:href="044/01/050.jpg" pagenum="42"/>ciebitur. </s><s>Itaque di&longs;&longs;oluetur, ide&ograve; manca videtur pe&shy;<lb/>
titio illa Archimedis in hoc problemate <foreign lang="greek">do\s pou= stw= ta\n <lb/>
ga\n kinw=</foreign>, qu&ograve;d locum <expan abbr="t&atilde;t&ugrave;m">tant&ugrave;m</expan> in quo con&longs;i&longs;tat, &longs;ibi da&shy;<lb/>
ri po&longs;tulet, c&ugrave;m pr&ecedil;terea vincula quibus terra &agrave; loco <lb/>
&longs;uo naturali remota &longs;u&longs;tineri po&longs;&longs;et, petere debue&shy;<lb/>
rit: id <expan abbr="aut&etilde;">autem</expan> vt &amp; ea qu&aelig; de motu in infinitum augen&shy;<lb/>
do vel minuendo diximus, ita intelligenda &longs;unt, vt <lb/>
&longs;ciamus infinita hominum pote&longs;tati, quacunque ar&shy;<lb/>
te iuuetur, non &longs;ube&longs;&longs;e: quamuis enim Geometri&shy;<lb/>
ca con&longs;ideratio in infinitum &longs;e&longs;e <expan abbr="ext&etilde;dat">extendat</expan>, &longs;unt ta&shy;<lb/>
men certi fines, vltra quos natura rerum nos pro&shy;<lb/>
gredi non patitur: &longs;unt pr&aelig;terea vitia materi&aelig;, <lb/>
qu&aelig; Geometra non con&longs;iderat, illa tamen non <lb/>
ob&longs;tant qu&ograve; min&ugrave;s id quod proponitur, <expan abbr="ver&utilde;">verum</expan> &longs;it in <lb/>
intellectu. </s><s>An ver&ograve; id quod proponitur tale &longs;it, vt in <lb/>
opus educi po&longs;&longs;it, con&longs;iderabit Geometer habita ra&shy;<lb/>
tione circun&longs;tantiarum, pr&aelig;&longs;ertim ver&ograve; temporis, <lb/>
quod ip&longs;i pr&aelig;&longs;cribetur, &amp; &longs;umptuum quos facere <lb/>
poterit is qui aliquid faciendum proponet, qu&aelig; &longs;i <lb/>
abund&egrave; &longs;uppetant, nihil non fieri poterit. </s></p><p type="main">

<s>Vt igitur hunc tractatulum concludamus, ac ve&shy;<lb/>
lut in &longs;ummam contrahamus: In motibus ciendis <lb/>
tria &longs;unt con&longs;ideranda. </s><s>Vis qua motum ciere volu&shy;<lb/>
mus, vis quam mouere volumus, &amp; motum quo <lb/>
mouere volumus: duo enim qu&aelig;libet ex illis ter&shy;<lb/>
tium determinant. </s><s>Si enim vi parua vim magnam 


<pb xlink:href="044/01/051.jpg" pagenum="43"/>mouere volumus, id nonni&longs;i paruo motu facere <lb/>
po&longs;&longs;umus: &longs;i ver&ograve; vim aliquam magno motu mo&shy;<lb/>
uere velimus, vi magna mouente ad id opus e&longs;t. </s><s>Si <lb/>
vi parua magnum motum ciere volumus, mini&shy;<lb/>
mam vim mouendam e&longs;&longs;e oportet: vt puta, &longs;i libra <lb/>
vna centum libras mouere velimus, oportet motum <lb/>
illius, motu huius <expan abbr="c&etilde;tuplo">centuplo</expan> maiorem e&longs;&longs;e. </s><s>Si ver&ograve; ve&shy;<lb/>
limus libra vna aliam vim ita mouere, vt ea cen&shy;<lb/>
tuplo citi&ugrave;s moueatur, qu&agrave;m libr&aelig; illius pondus, il&shy;<lb/>
lam cente&longs;imam tant&ugrave;m libr&aelig; vnius partem e&longs;&longs;e ne&shy;<lb/>
ce&longs;&longs;e e&longs;t: &longs;i ver&ograve; libram vnam ita mouere velimus, vt <lb/>
centuplo citius moueatur, qu&agrave;m vis qu&aelig; illam mo&shy;<lb/>
uebit, vi centum libris maiore ad id opus erit. </s><s><expan abbr="Neq;">Neque</expan> <lb/>
patitur natura &longs;ibi in his vim fieri: &longs;i enim eiu&longs;modi <lb/>
proportio aliquo modo infringi po&longs;&longs;et, &longs;tatim da&shy;<lb/>
retur <foreign lang="greek">au)tw/ma e)nde/lexes</foreign>, vel vt <expan abbr="voc&atilde;t">vocant</expan>, motus perpetuus <lb/>
in perpetua materia. </s></p><p type="main">

<s>Ex his igitur fundamentis inuent&aelig; &longs;unt machin&aelig; <lb/>
omnes, quotquot antehac &longs;unt excogitat&ecedil;, &amp; quot&shy;<lb/>
quot po&longs;thac excogitari poterunt, ad ea referentur. </s></p><p type="main">

<s>Itaque &longs;i propo&longs;it&aelig; cuiu&longs;cunque machin&aelig; effe&shy;<lb/>
ctum &longs;cire velimus, con&longs;ideranda &longs;unt duo eius <lb/>
extrema, quibus vires applicantur: qu&aelig; enim erit <lb/>
ratio motus vnius ex illis extremis, ad motum <lb/>
alterius eadem erit &amp; virium, qu&aelig; illis extre&shy;<lb/>
mis ad motum ciendum applicari poterunt, 


<pb xlink:href="044/01/052.jpg" pagenum="44"/>addito aut dempto momento, vt &longs;i dum <expan abbr="alter&utilde;">alterum</expan> ma&shy;<lb/>
chin&aelig; extremum palmo vno mouetur, alterum cen<lb/>
tum palmis moueatur vis qu&aelig;libet huic annexa, al&shy;<lb/>
teram alteri annexam centuplam momento min&ugrave;s, <lb/>
mouebit: &longs;ed motu centuplo: mouebit autem &amp; re&shy;<lb/>
liquas omnes vires, qu&aelig; infra centuplam proportio&shy;<lb/>
nem ad eam habebunt: &longs;i ver&ograve; non vim centuplam <lb/>
mouere, &longs;ed in data vi motum centuplum ciere veli&shy;<lb/>
mus, eam quidem in extremo quod centuplo citi&ugrave;s <lb/>
mouetur, locare oportebit, alteram ver&ograve; alteri extre<lb/>
mo centuplo maiorem adhibere nece&longs;&longs;e erit. </s></p><p type="main">

<s>Hinc oriuntur tria problemata, videlicet data vi <lb/>
datum pondus mouere, quod iam <expan abbr="dem&otilde;&longs;trauimus">demon&longs;trauimus</expan>: <lb/>
item data vi datum motum ciere, quod ex <expan abbr="pr&aelig;ced&etilde;-tis">pr&aelig;ceden&shy;<lb/>
tis</expan> demon&longs;tratione ab&longs;oluitur: tertium, datam vim, <lb/>
dato motu mouere, quod quidem facili&ugrave;s demon&shy;<lb/>
&longs;tratur, qu&agrave;m ab&longs;oluitur. </s><s>Scimus enim, vt id fiat, <lb/>
vim aliam proportionalem (vt docuimus) requiri, <lb/>
quo modo autem illam habere po&longs;&longs;imus, explicare <lb/>
hoc opus, hic labor e&longs;t. </s><s>Non enim quemadmodum <lb/>
organa ad motus in data proportione ciendos ha&shy;<lb/>
bere po&longs;&longs;umus: ita &amp; vires infinit&aelig; magnitudinis po<lb/>
te&longs;tati no&longs;tr&aelig; &longs;ub&longs;unt. </s></p><p type="main">

<s>Quod enim ad vires in grauitatis &amp; leuitatis gene<lb/>
re con&longs;i&longs;tentes attinet, eas vt moueant ant&egrave; moueri <lb/>
oportet &agrave; loco vel &longs;itu naturali, vi <expan abbr="aut&etilde;">autem</expan> aliqua id fie-


<pb xlink:href="044/01/053.jpg" pagenum="45"/>ri oportet, qu&aelig; iam in promptu &longs;it. </s><s>Qu&aelig; &longs;i tanta e&longs;t, <lb/>
vt po&longs;&longs;it motum propo&longs;itum ciere, fru&longs;tr&agrave; fiat, &longs;i alij <lb/>
&agrave; loco naturali remouend&aelig;, qua po&longs;tea ad motum <lb/>
vtendum &longs;it, adhibeatur. </s></p><p type="main">

<s>Nullum igitur ex eiu&longs;modi viribus commodum <lb/>
percipi pote&longs;t, ni&longs;i quis in futurum &longs;ibi pro&longs;piciens, <lb/>
multa &agrave; loco vel &longs;itu naturali ex otio remoueat, vt <lb/>
iis, c&ugrave;m opus erit ad motus ciendos vtatur. </s><s>Hac ra&shy;<lb/>
tione quantas vires in promptuario habebit, tantos <lb/>
motus ciere poterit. </s><s>Pr&aelig;cipuum igitur quod ad hu&shy;<lb/>
ius problematis con&longs;tructionem pertinet, e&longs;t, vt vi&shy;<lb/>
res qu&agrave;m maximas pote&longs;tati no&longs;tr&aelig; &longs;ubiiciamus, vo<lb/>
luntariis aut fortuitis viribus naturales pr&aelig;parando, <lb/>
aut &agrave; natura pr&aelig;paratas, qu&aelig; pote&longs;tati no&longs;tr&aelig; &longs;ub&shy;<lb/>
&longs;unt, accipiendo. </s><s>Qualia multa &longs;i mortales aduerte&shy;<lb/>
rent, fieri po&longs;&longs;ent, vt ali&agrave;s, Deo duce, docebimus. </s></p><p type="main">

<s>Earum autem virium qu&aelig; in raritatis &amp; den&longs;ita&shy;<lb/>
tis proportione con&longs;i&longs;tunt, &longs;ubiecta plurim&ugrave;m in <lb/>
no&longs;tra pote&longs;tate &longs;unt: multa enim &longs;unt naturalia &longs;ub <lb/>
iecta actu, den&longs;a potentia ver&ograve; rara. </s><s>Si quod igitur <lb/>
eorum potentia proxima &longs;it rari&longs;&longs;imum, ita vt nullo <lb/>
negotio actus ille raritatis induci po&longs;&longs;it, <expan abbr="concluda-t&uacute;rq;">concluda&shy;<lb/>
t&uacute;rque</expan> loco aliquo angu&longs;to, po&longs;tea inducatur ille a&shy;<lb/>
ctus, c&ugrave;m rara <expan abbr="maior&etilde;">maiorem</expan> locum occupent, quum den&shy;<lb/>
&longs;a, fiet vt locus in omnem partem di&longs;tendatur, illius <lb/>
autem partes min&ugrave;s coh&aelig;rentes, tantum impellen&shy;


<pb xlink:href="044/01/054.jpg" pagenum="46"/>tur, quanta e&longs;t proportio molis rei rarefact&aelig; ad mo&shy;<lb/>
lem illius c&ugrave;m den&longs;a e&longs;&longs;et: illa autem raritatis po&shy;<lb/>
tentia proxima e&longs;t in compo&longs;itione &longs;ulphuris <lb/>
&amp; nitri: ea igitur &amp; &longs;imilibus &longs;ubiectis, <lb/>
in data vi datus motus <lb/>
cieri pote&longs;t. </s></p><p type="head">

<s>FINIS.</s></p><p type="head">

<s>Errata qu&aelig; inter imprimendum irrep&longs;erunt, <lb/>
&longs;ic corrigito.</s></p><p type="main">

<s><emph type="italics"/>Pagina<emph.end type="italics"/> 7. <emph type="italics"/>linea<emph.end type="italics"/> 10, <emph type="italics"/>munere, lege nuere. </s>

<s>pag.<emph.end type="italics"/> 11. <emph type="italics"/>lin.<emph.end type="italics"/> 12, <emph type="italics"/>comparationibus, lege comparati, omni&shy;<lb/>
bus. </s>

<s>pag.<emph.end type="italics"/> 12. <emph type="italics"/>lin.<emph.end type="italics"/> 16. <emph type="italics"/>finis, lege fini. </s>

<s>pag. eadem. lin. penult. Altero, lege Alto.</s>

<s>pag.<emph.end type="italics"/> 20. <lb/>
<emph type="italics"/>lin.<emph.end type="italics"/> 16. <emph type="italics"/>quum<emph.end type="italics"/> C <emph type="italics"/>ad<emph.end type="italics"/> L. <emph type="italics"/>lege quam. </s>

<s>pag.<emph.end type="italics"/> 25. <emph type="italics"/>lin.<emph.end type="italics"/> 5. <emph type="italics"/>nunc &longs;it ratio, lege minor &longs;it. </s>

<s>linea<emph.end type="italics"/> 13. <emph type="italics"/>Vi&shy;<lb/>
res maiori litera<emph.end type="italics"/> (<emph type="italics"/>e&longs;t enim &longs;ectionis initium. </s>

<s>lin.<emph.end type="italics"/> 15. <emph type="italics"/>mittant, lege mittantur. </s>

<s>pag.<emph.end type="italics"/> 27. <emph type="italics"/>li.<emph.end type="italics"/> 20. <lb/>
<emph type="italics"/>puncti in linea<emph.end type="italics"/> A, <emph type="italics"/>lege puncti<emph.end type="italics"/> A <emph type="italics"/>in linea. </s>

<s>pag.<emph.end type="italics"/> 28. <emph type="italics"/>lin.<emph.end type="italics"/> 9. <emph type="italics"/>vis, lege Vis, maiori litera<emph.end type="italics"/> (<emph type="italics"/>e&longs;t enim <lb/>
&longs;ectionis initium. </s>

<s>lin. e. motu ciere, leg. motu quem ciere. </s>

<s>lin.<emph.end type="italics"/> 23. <emph type="italics"/>metiri &longs;olemus, lege non <lb/>
&longs;olemus. </s>

<s>lin. vlt. &longs;tatui, lege &longs;tatuit.</s>

<s>pag.<emph.end type="italics"/> 32. <emph type="italics"/>lin.<emph.end type="italics"/> 4. <emph type="italics"/>ab&longs;ouit, lege ab&longs;oluit. </s>

<s>lin.<emph.end type="italics"/> 5. <emph type="italics"/>dele<emph.end type="italics"/> F. </s>

<s><emph type="italics"/>lin.<emph.end type="italics"/><lb/>
12. <emph type="italics"/>&amp;<emph.end type="italics"/> 13, <emph type="italics"/>pone virgulam po&longs;t<emph.end type="italics"/> D <emph type="italics"/>&amp;<emph.end type="italics"/> E.</s>

<s> <emph type="italics"/>lin.<emph.end type="italics"/> 8. <emph type="italics"/>hypomochium, lege hypomochlium. </s>

<s>pag.<emph.end type="italics"/> 37. <emph type="italics"/>li.<emph.end type="italics"/><lb/>
13. <emph type="italics"/>re&longs;i&longs;tentia, lege re&longs;i&longs;tenti&aelig;. </s>

<s>pag.<emph.end type="italics"/> 39. <emph type="italics"/>lin.<emph.end type="italics"/> 3. <emph type="italics"/>leui, lege l&aelig;ui. </s>

<s>pag.<emph.end type="italics"/> 40. <emph type="italics"/>linea<emph.end type="italics"/> 5. <emph type="italics"/>&longs;uppo&longs;it&aelig;, lege <lb/>
&longs;uperpo&longs;it&aelig;</s>

<s>li.<emph.end type="italics"/> 7. <emph type="italics"/>connex&aelig;, lege conuex&aelig;. </s>

<s>lin.<emph.end type="italics"/> 13. <emph type="italics"/>affectus, lege effectus.<emph.end type="italics"/></s></p>			</chap>		</body>		<back/>	</text></archimedes>