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<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></translator>
        <lang>la</lang>
        <cvs_file>varro_demot_044_la_1584.xml</cvs_file>
        <cvs_version></cvs_version>
        <locator>044.xml</locator>
        <echodir>/permanent/library/TPQ025WW</echodir>
    </info>
    <text>
        <front>
            <section>
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                <p type="head">
                    <s>TERRA <lb></lb> MACHINIS MOTA <lb></lb> DISSERTATIONES <lb></lb> GEOMETRICAE, MECHANICAE
                        <lb></lb> PHYSICAE, HYDROSTATICAE <lb></lb> In quibus <lb></lb> Machinarum Coniugatarum
                        uires inter ſe comparantur: <lb></lb> Multiplici Noua Methodo Terrae
                        magnitudo et <lb></lb> Grauitas inueſtigatur: ARCHIMEDES <lb></lb> terrae
                        motionem ſpondens ab arrogantia <lb></lb> ſuſpicione
                        uindicatur. <lb></lb></s>
                    <s>AVTHORE <lb></lb> PAVLO CASATO <lb></lb> E SOCIETATE IESV. <lb></lb></s>
                    <s>ROMAE. <lb></lb></s>
                    <s>Ex Typographia Ignatij de Lazaris.</s>
                    <s>M.DC.LVIII.<lb></lb></s>
                    <s>SVPERIORVM PERMISSV.<lb></lb></s>
                </p>
                <pb xlink:href="044/01/002.jpg"></pb>
                <pb xlink:href="044/01/003.jpg" id="p.0001"></pb>
                <p type="head">


                    <s>ILLVSTRI ET IN <lb></lb> PRIMIS GENEROSO DOMINO, <lb></lb> DOMINO CAROLO BARONI <lb></lb>
                        Azerotin, Nameſtij Roſicij <lb></lb> Brandeiſij Domino, <lb></lb>
                        MICH. VARRO. S. P. D.</s>
                </p>
                <p type="main">


                    <s><emph type="italics"></emph>CVM ab Ineunte ætate in Ma­<lb></lb> thematicis
                        me exercuiſſem, ſem­<lb></lb> per animo meo in
                        hæſit hoc deſide­<lb></lb> rium, vt quæ de Archimede
                        Syra­<lb></lb> cuſano referuntur, ea &amp; ratione <lb></lb>
                        demonſtrare &amp; experimento comprobare poſſem. <lb></lb>
                    </s>
                    <s>Cumque multa in eo genere meditatus eſſem, poſt­<lb></lb>
                        quam ad iuris ciuilis ſtudium tranſii, ac tandem <lb></lb> ad
                        Rempub. nunquam mihi tantum otii contigit, <lb></lb> vt ea in
                        ordinem redigere potuerim. </s>
                    <s>At cum pau­<lb></lb> cis retrò annis ſatis longam peregrinationem
                        per <lb></lb> Sarmatiam ſuſcepiſſem,
                        eſſetque vacuus curis a-<emph.end type="italics"></emph.end>
                        <pb xlink:href="044/01/004.jpg"></pb><emph type="italics"></emph>nimus, atque ad earum
                        rerum meditationem me <lb></lb> impelleret genius meus, cœpi aliquid de
                        his ſcribe­<lb></lb> re, quantum ipſe iter faciendo meo marte
                        aſſequi <lb></lb> potui cum libris deſtituerer. </s>
                    <s>Scriptum illud cum <lb></lb> in maximè ardua &amp; difficìli
                        contemplatione ver<lb></lb> ſetur, nec ab eo tempore ex quo
                        adſolitas occupa­<lb></lb> tiones redii ei extremam manum apponere
                        mihi <lb></lb> licuerit, decreueram inter priuatas meas muſas <lb></lb>
                        aſſeruare Verebar enim vulgi <expan abbr="iudiciũ">iudicium</expan>, (cuius <expan abbr="ta-mẽ">ta­<lb></lb>
                            men</expan> rationem viro politico <expan abbr="habendã">habendam</expan> eſſe cenſeo) ne­<lb></lb> que
                        ſolum vulgi, verum etiam <expan abbr="eorũ">eorum</expan> qui
                        doctorum <lb></lb> nomine gaudent, cum inaudita quædam interdum <lb></lb>
                        quæque ab eorum opinione recedere <expan abbr="videãtur">videantur</expan> at­<lb></lb> tingam. </s>
                    <s><expan abbr="Cupiebã">Cupiebam</expan> etiam in eo argumento
                        vlteriùs <lb></lb> progredi, antè quam quidquam ederem, atque ea <lb></lb>
                        quæ in meis aduerſariis ea de re ſparſa habeo, iis
                        <lb></lb> quæ <expan abbr="congeſſerã">congeſſeram</expan> ſubiicere, vt iuſtum <expan abbr="volumẽ">volumen</expan> fieret.<emph.end type="italics"></emph.end></s>
                </p>
                <p type="main">

                    <s><emph type="italics"></emph>Poſtquam verò te diſceſſum
                        ex hac nostra ci­<lb></lb> uitate parare intellexi, in qua dum
                        verſatus es. <lb></lb>
                    </s>
                    <s>non ſolùm ei <expan abbr="ornamẽto">ornamento</expan>
                        fuiſti, ſed etiam optimos <lb></lb> quoſque virtutum tuarum
                        admiratione tibi con­<lb></lb> ciliasti: mihi verò peculiariter
                        innumera beneuo-<emph.end type="italics"></emph.end>
                        <pb xlink:href="044/01/005.jpg"></pb><emph type="italics"></emph>lentiæ
                        ſigna exhibuiſti, non potui tantum virum, <lb></lb> meíque
                            <expan abbr="amãtem">amantem</expan> ſine aliquo munere
                            aut<emph.end type="italics"></emph.end>
                        <foreign lang="grc">μνημοσύνῳ</foreign><lb></lb>
                        <emph type="italics"></emph>dimittere. </s>
                    <s>Itaque libellum hunc tibi dicare, &amp; <lb></lb> ſub tuo nomine in
                        publicum edere ſtatui. </s>
                    <s>Squalli­<lb></lb> dus quidem prodit, &amp; rudis, mole etiam
                        perexi­<lb></lb> guus: ſplendidius aliquid &amp; magis elaboratum
                        <lb></lb> postularet tua dignitas. </s>
                    <s>Atqui ea eſt argumenti <lb></lb> illius magnitudo, vt in eo aliquid
                        voluiſſe ſatis <lb></lb> ſit. </s>
                    <s>Militare ſanè munus eſt, eóque nomine tibi <lb></lb>
                        conueniens: ſi quis enim hac cognitione inſtructus <lb></lb> fuerit,
                        non minùs ea in re bellica vti poterit, <lb></lb> quam Archimedes in
                        Syracuſis defendendis <lb></lb> aduerſus Marcum Marcellum vſus
                        est. </s>
                    <s>Eá­<lb></lb> que mirari deſinet quæ de eo Plutarchus
                        nar­<lb></lb> rat. </s>
                    <s>Id lucidius <expan abbr="demõſtrare">demonſtrare</expan>
                        potuiſſem, ſi mihi hæc <lb></lb> vlterius
                        perſequendi otium fuiſſet: Jeiuna enim <lb></lb> per ſe
                        videntur, niſi quis ſuccum qui ſub corti­<lb></lb> ce
                        latet, eliciat. </s>
                    <s>Malui tamen hoc veluti pro­<lb></lb> gymnaſmate alios quibus plus est
                        otii &amp; in­<lb></lb> genii ad eiuſmodi inquiſitionem hortari
                        &amp; ac­<lb></lb> cendere, quàm præclaram illam
                        cognitio­<lb></lb> nem diutius ſepultam relinquere cum ne-<emph.end type="italics"></emph.end>
                        <pb xlink:href="044/01/006.jpg"></pb>
                        <emph type="italics"></emph>minem hodie animaduertam qui ei inſudet, <lb></lb>
                        neque mihi ſpes vlla affulgeat diuturni otii, cuius <lb></lb> ope in hoc
                        ſtadio pergere poßim: Quòd ſi fortè <lb></lb> mihi
                        aliquando contingat, riuos plurimos ex his <lb></lb> fontibus me educturum;
                            <expan abbr="cõfido">confido</expan>; quibus multum <lb></lb>
                        <expan abbr="cõmoditàtis">commoditàtis</expan> rebus humanis
                        accedat. </s>
                    <s>Quæ enim <lb></lb> hic traduntur, ad motus omnes atque ad omnis ge<lb></lb>
                        neris virium comparationes accommodari poſ­<lb></lb> ſunt ad
                        fines propoſitos aſſequendos. </s>
                    <s>Quod quàm <lb></lb> latè pateat, dici non poteſt. </s>
                    <s>Eſt enim eorum vſus <lb></lb> non ſolùm in mechanicis, in
                        quibus tamen eſt ma <lb></lb> ximus, ſed etiam in politicis &amp;
                        œconomicis: ſunt <lb></lb> enim in illis motus, ſunt vires
                        &amp; reſistentiæ. </s>
                    <s>In <lb></lb> arte medica &amp; reliquis phyſices partibus pra­<lb></lb>
                        cticis, quantus ſit, nemo fando exprimere poßit. <lb></lb>
                    </s>
                    <s>Quia vero ea quæ praxim docent gratiora ſunt <lb></lb> ipſa
                        contemplatione, &amp; cauſæ propter effecta in­<lb></lb>
                            quirantur,<emph.end type="italics"></emph.end>
                        <foreign lang="grc">Ἀλφήστας</foreign>
                        <emph type="italics"></emph>omnes hortor vt quod ego in­<lb></lb> numeris aliis
                        cur is implicitus addere non poſ­<lb></lb> ſum, ipſi
                        addant. </s>
                    <s>Abundat nunc Europa præ­<lb></lb> ſtantibus ingeniis, ſi
                        Mœcenates adeſſent. <lb></lb>
                    </s>
                    <s>Ea autem quæ præter hæc meditatus ſum, ac fer-<emph.end type="italics"></emph.end><pb xlink:href="044/01/007.jpg"></pb>
                        <emph type="italics"></emph>mè parata habeo, hæc ſunt. </s>
                    <s>Tractatus de iactu. <lb></lb>
                    </s>
                    <s>De continuitate eiuſque ſolutione. </s>
                    <s>De <expan abbr="cõdenſa-tione">condenſa­<lb></lb>
                            tione</expan> &amp; rarefactione earumque cauſis &amp;
                        effecti­<lb></lb> bus: <expan abbr="Itẽ">Item</expan> in Mechanicis,
                        tractatus de variis ma­<lb></lb> chinis ad motus <expan abbr="ciẽdos">ciendos</expan>, ac de perfectißimæ
                        cuiuſ­<lb></lb> que ad id quod propoſitum fuerit moliendum
                        in­<lb></lb> ueſtigatione. </s>
                    <s>Nonnulla <expan abbr="etiã">etiam</expan> de <expan abbr="Rerumpublicarũ">Rerumpublicarum</expan>
                        <lb></lb> motu tum interno <expan abbr="tũ">tum</expan> externo notaui,
                        quæ <expan abbr="eodẽ">eodem</expan> or­<lb></lb> dine tradere
                        optarem: quorum omnium principia <lb></lb> hic ſi quis diligenter
                        animaduertat tradita ſunt. <lb></lb>
                    </s>
                    <s>Si quis mihi in his <expan abbr="palmã">palmam</expan> præripuerit,
                        meque an­<lb></lb> teuerterit ei maximas gratias agam. </s>
                    <s>Sunt tamen <lb></lb> inter hæc quædam quæ vulgò pandere
                        nephas est. <lb></lb>
                    </s>
                    <s>Itaque theoriæ magis inſiſtendum puto, in qua ſi <lb></lb>
                        quis exercitatus fuerit, nullo negotio illam in opus <lb></lb> educere poterit,
                        idque ſine periculo fiet, cum vul­<lb></lb> go non pateat. </s>
                    <s>Alioqui <expan abbr="periculũ">periculum</expan> eſt, ne ſi
                        particu­<lb></lb> laria tradantur iis contenti homines, vt fieri
                        ſolet <lb></lb> vniuerſalem cognitionem &amp; cauſarum
                        inquiſi­<lb></lb> tionem negligant, pereatque ſcientia. </s>
                    <s>Eaque de <lb></lb> cauſa nihil quicquam de his quæ fecerat
                            Archi-<emph.end type="italics"></emph.end>
                        <pb xlink:href="044/01/008.jpg"></pb>
                        <emph type="italics"></emph>medes ſcriptum relinquere voluit. </s>
                    <s><expan abbr="Exiſtimãs">Exiſtimans</expan> eos <lb></lb> qui in
                        iis quæ<emph.end type="italics"></emph.end>
                        <foreign lang="grc">θεωρητικῶς</foreign>
                        <emph type="italics"></emph>tradiderat, diligentem ope­<lb></lb> ram ponere
                            <expan abbr="vellẽt">vellent</expan>, multò maiora quoties
                        opus fo­<lb></lb> ret præſtituros. </s>
                    <s>Equidem mihi perſuadeo non de­<lb></lb> futuros qui varia iudicia de
                        hoc noſtro ſcripto fe­<lb></lb> rant &amp; quaſi nouum
                        athletam in arenàm pro­<lb></lb> deuntem mirentur. </s>
                    <s>Quibus vno verbo reſpon­<lb></lb> ſum volo, me nullius vnquam in
                        verba ma­<lb></lb> gistri iuraſſe, ſed liberrimè
                        ſemper philoſo­<lb></lb> phatum eſſe: ita vt etiam
                        in principia ab aliis <lb></lb> ſtatuta animaduertere mihi licere
                        putauerim. <lb></lb>
                    </s>
                    <s>Quod eò liberiùs feci, poſtquam magnam <expan abbr="partẽ">partem</expan>
                        <lb></lb> vulgo receptarum opinionum falſam eſſe re ipſa
                        <lb></lb> deprehendi. </s>
                    <s>Omnibus placuero, ſi tibi placuero. </s>
                    <s>Si <lb></lb> quid in his obſcurius fuerit, habes <expan abbr="clarißimũ">clarißimum</expan> vi­<lb></lb> rum
                        Wenceſlaum lauinium tuum, abſtruſioris <lb></lb>
                        philoſophiæ indagatorem <expan abbr="ſummũ">ſummum</expan>, qui tibi omnia <lb></lb> explicabit. </s>
                    <s>Hoc igitur <expan abbr="munuſculũ">munuſculum</expan> vt
                        ſerena <expan abbr="frõ-te">fron­<lb></lb> te</expan>
                        ſuſcipias rogo. </s>
                    <s>Vale. </s>
                    <s>V I. </s>
                    <s>K al. Jun. Anno <lb></lb> Christi Domini<emph.end type="italics"></emph.end> M. D. LXXXIV. </s>



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

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

                    <s><emph type="italics"></emph>PROBLEMA.<emph.end type="italics"></emph.end></s>
                </p>
                <p type="head">

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

                    <s>Hoc problema prima quidem <lb></lb> fronte mirabile videtur, vt ſcilicet
                        <lb></lb> pondus vel maximum viribus ta­<lb></lb> men minimis, vt puta ſi
                        dicas vnius <lb></lb> hominis, vel etiam imbecillioris a­<lb></lb> licuius
                        animalis viribus totum ter­<lb></lb> ræ globum loco moueri
                        poſſe. </s>
                    <s>Quod Archimedem <lb></lb> Syracuſanum iactaſſe referunt hoc
                        dicto, <foreign lang="grc">δὸς ποῦ στῷ <lb></lb> τὰν γὰν κινῷ.
                        </foreign></s>
                    <s>Si quis tamen in Geometrico puluere <lb></lb> verſatus fuerit,
                        preſertim verò in iis quæ ab ipſo in <lb></lb> ſuo
                            <foreign lang="grc">ἰσοροπικῶν</foreign> libello <expan abbr="tradũtur">traduntur</expan>. </s>
                    <s>Illud cæteráque eiuſ­<lb></lb> modi, ludicra Geometriæ,
                        vt &amp; ipſe facere ſolitus di<lb></lb> citur, appellabit. </s>
                    <s>Ex huius autem problematis expli<lb></lb> catione, omnium machinarum quę ad
                        motus cien­<lb></lb> dos excogitari poſſunt, ratio pendet. </s>
                    <s>Etſi verò <expan abbr="totũ">totum</expan>
                        <lb></lb> Geometrica demonſtratione expediri poſſit, quo­
                            <pb xlink:href="044/01/010.jpg" pagenum="2"></pb>niam tamen hęc
                        conſideratio, quæ Græcis <foreign lang="grc">σταθμικὴ</foreign> di<lb></lb> citur Geometriæ tantùm eſt
                            <foreign lang="grc">ὑπάλληλος</foreign> mixta ſcili­<lb></lb>
                        cet ex phyſica &amp; Geometrica eo quòd illius
                        ſubie­<lb></lb> ctum ſit motus. </s>
                    <s>Ideò paulò craſſiori Minerua &amp; <lb></lb> præter
                        Geometricam ſimplicitatem <foreign lang="grc">φυσικῶς</foreign>
                        etiam <lb></lb> tractanda eſt: alioqui Archimedicis
                        demonſtratio­<lb></lb> nibus ſtandum eſſet,
                        quæ in eo mancæ ſunt, quòd il­<lb></lb> læ
                        propoſitiones quæ ex phyſicis peti debent, inde­<lb></lb>
                        monſtratæ manent, nec explicantur, ſed pro
                        confeſ­<lb></lb> ſis principiorum loco poſtulantur. </s>
                    <s>Eas igitur, qua­<lb></lb> tenus ad huius problematis explicationem faciunt,
                        <lb></lb> hic diſcutiemus. </s>
                    <s>Neque enim Euclidis <expan abbr="librũ">librum</expan> de
                        gra­<lb></lb> ui &amp; leui, in quo hoc argumentum perſequi
                        voluiſ­<lb></lb> ſe videtur, integrum habemus. </s>
                    <s>Ariſtoteles verò in <lb></lb> eo quod ab ipſo ſcriptum
                        extat de Mechanicis fra­<lb></lb> gmento pręter ſuum morem,
                        cùm alio qui in omni­<lb></lb> bus exactiſſimus ſit,
                        hanc quæſtionem potiùs nota­<lb></lb> uit quàm
                        explicuit in ſexto &amp; ſeptimo phyſicorum <lb></lb> libro
                        multa prætermiſit. </s>
                    <s>Vt igitur ad rem aggredia­<lb></lb> mur, primùm voces, quibus vtendum
                        eſt, definie­<lb></lb> mus, vt intelligatur quo ſenſu eas
                        accipiamus. </s>
                </p>
                <p type="head">

                    <s>DEFINITIO I.</s>
                </p>
                <p type="main">

                    <s>Vis dicitur agendi aut agenti reſiſtendi <expan abbr="potẽtia">potentia</expan>, <lb></lb> præſertim
                        verò mouendi &amp; mouenti reſiſtendi. </s>
                </p>
                <p type="head">

                    <s>II.</s>
                </p>
                <p type="main">

                    <s>Vis ſubiectum dicitur id quod vis mouet, vel <pb xlink:href="044/01/011.jpg" pagenum="3"></pb>quod à vi mouetur. </s>
                </p>
                <p type="main">

                    <s>Hîc non agimus de vi primaria quæ virium o­<lb></lb> mnium
                        principium eſt, mouétque omnia, nec <expan abbr="tamẽ">tamen</expan>
                        <lb></lb> mouetur, ſed de ea, quę dum mouet, <expan abbr="etiã">etiam</expan> cum ſub­<lb></lb> iecto, cui ineſt, mouetur.
                    </s>
                </p>
                <p type="main">

                    <s>Subiecta verò quæ nullam vim habent, nec mo­<lb></lb> uentur, nec
                        mouenti <expan abbr="reſiſtũt">reſiſtunt</expan>: ſi qua verò vis illis
                        ac­<lb></lb> cedat, tum ab ea ſe moueri patiuntur. </s>
                </p>
                <p type="main">

                    <s>Etſi autem plura ſint virium genera, tot ſcilicet, <lb></lb>
                        quot ſunt in rerum natura contrariorum, actionem <lb></lb> &amp;
                        paſſionem recipientium, vt leue graue, rarum <expan abbr="dẽ-ſum">den­<lb></lb> ſum</expan>, plenum
                        vacuum, durum molle, &amp; cætera eiuſ­<lb></lb> modi, quoniam
                        tamen ea omnia hîc perſequi noſtri <lb></lb> non eſt
                        inſtituti, cùm de ea tantùm qua motus fit a­<lb></lb> gere
                        ſtatuerimus. </s>
                </p>
                <p type="head">

                    <s>III.</s>
                </p>
                <p type="main">

                    <s>Cùm de motu hîc agemus motum ad locum, <lb></lb> quem Græci
                            <foreign lang="grc">φορὰν</foreign> vocant, intelligi volumus. </s>
                </p>
                <p type="head">

                    <s>IIII.</s>
                </p>
                <p type="main">

                    <s>Linea autem recta quæ eſt ab eo loco à quo mo­<lb></lb> tus
                        fieri incipit ad illum ad quem tendit. </s>
                    <s>Illius vis <lb></lb> quæ motum efficit, nutus dicetur. </s>
                </p>
                <p type="main">

                    <s><expan abbr="Eadẽ">Eadem</expan> verò linea <expan abbr="cõſiderata">conſiderata</expan> à loco ad
                            <expan abbr="quẽ">quem</expan>
                        <expan abbr="tẽdit">tendit</expan> vis <lb></lb> ad <expan abbr="illũ">illum</expan> à quo motus fieri incipit, contra
                            <expan abbr="nutũ">nutum</expan> dicitur. </s>
                </p>
                <p type="main">

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

                    <s>Quæ verò lineæ vel rectæ, vel curuæ, nutus <expan abbr="lineã">lineam</expan>
                        <pb xlink:href="044/01/012.jpg" pagenum="4"></pb>ad angulos inæquales
                        ſecant, illæ obliquè nutum <lb></lb> verſus, vel contra
                        nutum ferri <expan abbr="dicũtur">dicuntur</expan>, habita
                        ratio­<lb></lb> ne partium, quas ſpectant. </s>
                </p>
                <p type="main">

                    <s>Plurimùm autem à ſitu corporis humani deno­<lb></lb>
                        minationem accipiunt illæ partes, vt ſurſum,
                        deor­<lb></lb> ſum, dextrorſum, ſiniſtrorſum,
                        antè vel ponè di­<lb></lb> cantur. </s>
                    <s>Quæ verò lineæ, nutus lineam ad angulos <lb></lb> rectos
                        ſecant, neque verſus nutum, neque contra <lb></lb> nutum ferri
                        dicuntur, ſed æquè diſtant à loco natu­<lb></lb>
                        rali. </s>
                </p>
            </chap>
            <chap>
                <p type="head">

                    <s><emph type="italics"></emph>Virium diuiſio.<emph.end type="italics"></emph.end></s>
                </p>
                <p type="main">

                    <s>Vis autem omnis aut naturalis eſt, aut non natu­<lb></lb> ralis, aut
                        mixta. </s>
                    <s>Naturalis vis eſt, qua res quælibet <lb></lb> natura ſua
                        mouetur, aut mouenti reſiſtit habita ra­<lb></lb> tione tum
                        loci ſui naturalis, tum etiam ſitus ſuarum <lb></lb> partium. </s>
                    <s>Non naturalis eſt quæ nec ratione loci ſui <lb></lb> naturalis,
                        nec ſitus partium mouet. </s>
                    <s>Eſt autem hæc <lb></lb> duplex, fortuita ſcilicet &amp;
                        voluntaria: illa vt vis ven­<lb></lb> torum &amp; ſpirituum
                        intellectu carentium, hæc vt a­<lb></lb> nimalium &amp;
                        ſpirituum intelligentium &amp; ſimilium. <lb></lb>
                    </s>
                    <s>Mixta dicitur, quæ partim naturalis eſt, partim non <lb></lb>
                        naturalis. </s>
                </p>
                <p type="main">

                    <s>Locus autem naturalis cuiuſque rei eſt, in quo <lb></lb>
                        exiſtens ipſa quieſcit, &amp; ſi inde remota
                        ſit, vis ei à na<lb></lb> tura inſita eam illuc impellit. </s>
                    <s>Huius verò motus aut <lb></lb> quietis cauſſa nulla alia
                        aſſignari poteſt præter pri- <pb xlink:href="044/01/013.jpg" pagenum="5"></pb>mam illam rerum omnium
                        conditricem, quę, ne o­<lb></lb> mnia in omnibus eſſent
                        ſingulis partibus vniuerſi <lb></lb> ſingula loca attribuit
                        circa quæ conglobantur, &amp; i­<lb></lb> bi hærent. </s>
                    <s>Quicquid enim terreum eſt, in terræ glo­<lb></lb> bum <expan abbr="cõfluxit">confluxit</expan>. </s>
                    <s>Ita quicquid ſoli homogenes in Solis <lb></lb> corpus, lunaria omnia in
                        lunam, &amp; ſic de cæteris cor<lb></lb> poribus vniuerſi. </s>
                    <s>Singulæ autem eorum partes ſuis <lb></lb> totis adhærent, nec
                        inde ſponte <expan abbr="mouẽtur">mouentur</expan>: ſi
                        verò in­<lb></lb> de motæ fuerint, eò redire nituntur. </s>
                    <s>Quod enim in <lb></lb> terra fieri videmus, idem &amp; in reliquis corporibus
                        v­<lb></lb> niuerſi fieri dicere poſſumus, ſcilicet
                        quod vnita cir<lb></lb> ca locum ſuum naturalem maneant: ſi enim
                        partes <lb></lb> eorum ſponte ſepararentur, &amp; vi ab ipſis
                        ſeparatæ <lb></lb> ad locum ſuum non redirent, ſtatim
                        tota diſſolue­<lb></lb> rentur. </s>
                </p>
                <p type="main">

                    <s>Vis igitur illa in loco ſuo quieſcendi grauitas di­<lb></lb>
                        citur, cuius contrarium eſt leuitas. </s>
                    <s>Res autem nulla <lb></lb> per ſe leuis dicitur, ſed <expan abbr="tãtùm">tantùm</expan> habita ratione alterius <lb></lb>
                        loci, quàm ſui naturalis: vt puta ſi pars aliqua Solis
                        <lb></lb> vi quapiam in terram inuecta eſſet, ſuóque
                        arbitrio <lb></lb> committeretur, illa ſtatim Solem peteret: ita ſi
                        ter­<lb></lb> ræ pars in Solem inuecta eſſet,
                        ſuóque arbitrio com<lb></lb> mitteretur, ſtatim à
                        ſole euolaret, &amp; ſe per cælum <lb></lb> terram verſus
                        proriperet. </s>
                    <s>Vt igitur terræ partes in <lb></lb> terra graues ſunt: ſic Solis
                        partes in ſole graues ſunt: <lb></lb> in terra verò leues,
                        terræ verò partes in Sole leues <pb xlink:href="044/01/014.jpg" pagenum="6"></pb>ſunt. </s>
                    <s>Idem de cæteris corporibus vniuerſi dici po­<lb></lb> teſt. </s>
                    <s>Neque enim faciliùs ex globo lunæ particulam <lb></lb> abſtrahas,
                        quàm ex terra glebam. </s>
                </p>
                <p type="main">

                    <s>Aer autem nullum proprium habet locum natu<lb></lb> ralem, ſed vbique
                        eſſe poteſt, cùm rerum omnium <lb></lb> locus
                        vniuerſalis eſſe videatur: de quo dubitari po­<lb></lb>
                        teſt an ſit infinitus, cùm omnia contineat, à nulla re
                        <lb></lb> verò totus comprehendatur, ſed hæc diſputatio
                        non <lb></lb> eſt huius loci. </s>
                </p>
                <p type="main">

                    <s>Etſi autem nullum proprium habet locum natu<lb></lb> ralem, neque leuis aut
                        grauis ſit: leuis tamen eſſe vi­<lb></lb> detur, cùm
                        grauis non ſit, nec ægrè ſe moueri patia­<lb></lb>
                        tur. </s>
                    <s>Itaque ſi quo modo ita conſtitutus ſit, vt rem a­<lb></lb>
                        liquam, quò minùs ad locum ſuum naturalem per­<lb></lb>
                        uenire poſſit, impediat, tum per expreſſionem
                        ſeu <lb></lb>
                        <foreign lang="grc">ἔκθλιψιν</foreign>, ab ea eiicietur, in
                        eiúſque locum ſuccedet, <lb></lb> vt fit in aqua, cùm ei
                        introducitur. </s>
                    <s>Quæ quidem <foreign lang="grc">ἔκ­<lb></lb> θλιψις</foreign> iis
                        etiam accidit quæ loco naturali gaudent, <lb></lb> cùm
                        ſeſe mutuò impediunt, ne ad illum ferantur. <lb></lb>
                    </s>
                    <s>Præſertim verò in liquidis locum habet, quorum <lb></lb> partes
                        facilius mouentur, quàm rerum <expan abbr="cohærentiũ">cohærentium</expan>
                        <lb></lb> &amp; compactarum. </s>
                    <s>Inde accidit vt quicquid liquidis <lb></lb> immergitur, tantò fiat in illis
                        leuius quàm grauius, <lb></lb> eſt moles eiuſdem liquoris
                        ipſorum moli æqualis. <lb></lb>
                    </s>
                    <s>Sed hæc de loco naturali fuſiùs à nobis alibi
                        medita­<lb></lb> ta, obiter hîc attigiſſe ſufficiat,
                        vt intelligatur quid <pb xlink:href="044/01/015.jpg" pagenum="7"></pb>ſit
                        vis naturalis. </s>
                </p>
                <p type="main">

                    <s>Vis autem voluntaria nullum certum nutum <lb></lb> habet, ſed illum
                        tantùm in quo mouentis voluntas <lb></lb> conquieſcit. </s>
                    <s>Cúmque vis naturalis vnum tantùm <lb></lb> nutum habeat, ſcilicet
                        à loco à naturali requie re­<lb></lb> moto, ad ipſam
                        naturalem requiem, illa infinitos nu <lb></lb> tus habet &amp; indeterminatos
                        per ſe ac voluntatis tan <lb></lb> tùm decreto determinabiles. </s>
                </p>
                <p type="main">

                    <s>Fortuita verò ipſo tantùm caſu determinabilem <lb></lb>
                        nutum habet: quò enim ipſa tendit, eo munere dici­<lb></lb> tur
                        ſiue ſurſum, ſiue deorſum, ſiue ad
                        latera. </s>
                    <s>Itaque <lb></lb> &amp; hic &amp; ille nutus <foreign lang="grc">ἀδιόριστος</foreign> dicitur. </s>
                    <s>Quemadmodum <lb></lb> &amp; is quem habent vires illæ, quibus res à
                        ſitu <expan abbr="partiũ">partium</expan>
                        <lb></lb> naturali remotæ ad illum redeunt: prout enim ab <lb></lb> eo
                        motæ ſunt, ita ad illum redeunt, prout etiam huc <lb></lb> aut illuc
                        obuerſæ ſunt, vt vis arcus aut baliſtæ. </s>
                </p>
                <p type="head">

                    <s>DEFIN. V.</s>
                </p>
                <p type="main">

                    <s>Vires autem contrariæ dicuntur, quæ contrarios <lb></lb> motus ciere
                        poſſunt, vt ea <expan abbr="quę">quæ</expan>
                        ſurſum mouet &amp; <expan abbr="quę">quæ</expan><lb></lb>
                        deorſum, &amp; ſic de cæteris. </s>
                </p>
                <p type="main">

                    <s>Conſideratur autem in vi <expan abbr="quãtitas">quantitas</expan>,
                        tum eo quòd <lb></lb> vis partibus ſuis conſtet, in quas in
                        infinitum diuidi <lb></lb> poteſt, &amp; rurſus additione aut
                        multiplicatione au­<lb></lb> geri, tum quòd æqualitatis
                        exceſſus &amp; defectus <expan abbr="cõ-parationem">con­<lb></lb> parationem</expan> recipiat. </s>
                </p>


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

                    <s>Ac quoniam vis eſt mouendi potentia, vis par­<lb></lb> tes erunt
                        quæ motus partes efficient, &amp; quæ erit mo<lb></lb> tus partium,
                        menſura eadem erit &amp; vis partium. </s>
                    <s>Et <lb></lb> motus quidem propria menſura eſt linea ſeu <expan abbr="ſpatiũ">ſpatium</expan>. <lb></lb>
                    </s>
                    <s>Quantum enim res quæpiam mota, ſpatij percur­<lb></lb> rit,
                        tantùm mota eſſe dicitur. </s>
                    <s>Quoniam verò in mo<lb></lb> mento vel inſtanti quod inſtar
                        puncti eſt, &amp; magni­<lb></lb> tudine caret, nullus motus fieri
                        poteſt, ſed motus o­<lb></lb> mnis in tempore fit. </s>
                    <s>Ideò ad motus menſuram tem­<lb></lb> pus etiam adhibere oportet. </s>
                    <s>Illud enim cum ſpatio <lb></lb> vel linea, motus dici facit æquales
                        aut inæquales. </s>
                </p>
                <p type="head">

                    <s>DEFIN. VI.</s>
                </p>
                <p type="main">

                    <s>Æquales igitur motus dicuntur, qui æqualibus <lb></lb> temporibus
                        æqualia ſpatia percurrunt. </s>
                </p>
                <p type="main">

                    <s>Qui autem æqualibus temporibus æqualia ſpa­<lb></lb> tia
                        permeant, illi iidem proportionales ſunt: hoc <lb></lb> eſt,
                        quæ eſt ratio temporis, quo alter eorum fit ad <lb></lb> tempus quo
                        fit alter, eadem eſt ſpatij quod percurrit <lb></lb> alter ad
                        ſpatium quod reliquus percurrit. </s>
                    <s>Si enim <lb></lb> duorum quorum ſinguli vna hora miliaris vnius
                        i­<lb></lb> ter conficiunt, alter eodem motu per tria miliaria <lb></lb> ferri
                        pergat, alter verò per duo <expan abbr="tãtùm">tantùm</expan>. </s>
                    <s>Ille tribus ho­<lb></lb> ris ea abſoluet, hic verò duabus, &amp;
                        æquè celeriter <lb></lb> ferri dicentur, licet ſpatia
                        inæqualia <expan abbr="percurrãt">percurrant</expan>,
                        quo­<lb></lb> niam illa ſunt temporibus proportionalia. </s>
                </p>


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

                    <s>VII.</s>
                </p>
                <p type="main">

                    <s>Inæquales autem motus dicuntur, quorum tem­<lb></lb> pora non
                        ſunt ſpatiis proportionalia. </s>
                    <s>Eorum autem <lb></lb> maior ille dicitur, cuius maior erit ratio ſpatij ad
                        ſpa<lb></lb> tium, quàm temporis ad tempus, quibus fiunt illi <lb></lb>
                        motus. </s>
                    <s>Ex quo intelligitur etiam quis minor dica­<lb></lb> tur. </s>
                    <s>Maior igitur dicetur qui celeriùs feretur, minor, <lb></lb> qui
                        tardiùs. </s>
                </p>
                <p type="head">

                    <s>VIII.</s>
                </p>
                <p type="main">

                    <s>Æquales igitur vires dicentur, quæ æqualibus <lb></lb> motibus
                        ſubiecta ſua mouebunt. </s>
                    <s>Maior verò quæ <lb></lb> ſubiectum ſuum magis vel
                        celeriùs mouebit. </s>
                    <s>Mi­<lb></lb> nor, quæ minùs vel tardiùs. </s>
                </p>
            </chap>
            <chap>
                <p type="head">

                    <s><emph type="italics"></emph>Motuum diuiſio.<emph.end type="italics"></emph.end></s>
                </p>
                <p type="main">

                    <s>Comparantur autem motus ſecundum omnes <lb></lb> comparationis gradus, hoc
                        eſt, æqualitatem, exceſ­<lb></lb> ſum &amp;
                        defectum: tum ſibi ipſis, cùm totus ſuis
                        par­<lb></lb> tibus confertur, tum alij aliis. </s>
                </p>
                <p type="main">

                    <s>Quatenus autem ſibi ipſi motus <expan abbr="cõparatur">comparatur</expan>, aut <lb></lb> eſt <foreign lang="grc">ὁμοιομερὴς</foreign> ſeu æquabilis aut <foreign lang="grc">ἀνομοιομερὴς</foreign>, id eſt inæ­<lb></lb>
                        quabilis. </s>
                    <s>Aequabilis, cuius omnes partes tum mini­<lb></lb> mæ tum maiores
                        tempora habent ſpatiis per quæ <lb></lb> cientur proportionalia. </s>
                    <s>Inæquabilis verò, in quo illa <lb></lb> non ſunt proportionalia.
                    </s>
                </p>
                <p type="main">

                    <s>Inæquabilium autem motuum duo ſunt genera, <pb xlink:href="044/01/018.jpg" pagenum="10"></pb>creſcens ſcilicet
                        &amp; decreſcens, ídque vel continuè, <lb></lb> vel per
                        interualla, ordinatim vel <foreign lang="grc">ἀτακτῶς. </foreign></s>
                </p>
                <p type="main">

                    <s>Creſcens dicitur, quando partium poſteriorum <lb></lb> ipſius
                        maior eſt celeritas, quàm priorum: <expan abbr="decreſcẽs">decreſcens</expan>, <lb></lb> quando
                        minor. </s>
                </p>
                <p type="main">

                    <s>Continuè, quando nulla pars illius vel minima <lb></lb> alteri parti
                        eſt æqualis ſeu ſibi ipſi æquabilis. </s>
                </p>
                <p type="main">

                    <s>Per interualla verò, quando partes quidem illius <lb></lb> ſibi
                        ipſis æquabiles ſunt, aliæ verò aliis
                        comparatæ <lb></lb> inæquabiles. </s>
                </p>
                <p type="main">

                    <s>Ordinatim, quando incrementum aut <expan abbr="decremẽ-tum">decremen­<lb></lb> tum</expan> illud certa aliqua proportionis
                        progreſſione <lb></lb> fit, vt ſi in motu continuè
                        creſcente, diuiſo toto mo<lb></lb> tus ſpatio in aliquot
                        partes æquales eadem ſit ratio <lb></lb> celeritatis, finis primi
                        ſpatij ad celeritatem finis ſe­<lb></lb> cundi, quæ finis
                        ſecundi ad finem tertij, &amp; ſic dein­<lb></lb> ceps: vel
                        ſi finis ſecundi ſpatij duplo citiùs feratur, <lb></lb>
                        quàm finis primi &amp; finis tertij, triplo quàm primi: <lb></lb>
                        finis verò quarti quadruplo, &amp; ſic deinceps. </s>
                    <s>Idem ſi <lb></lb> in quauis alia proportionis progreſſione
                        illarum <lb></lb> partium celeritas, aliarum ad alias ſe habeat. </s>
                    <s>In mo­<lb></lb> tu verò per interualla creſcente <expan abbr="augmẽtum">augmentum</expan> illud or­<lb></lb> dinatim
                        fieri dicetur, ſi interuallorum proportio a­<lb></lb> liquem
                        progreſſionis ordinem ſeruet: puta ſi <expan abbr="primũ">primum</expan>
                        <lb></lb> interuallum duplo tardiùs <expan abbr="ſecũdo">ſecundo</expan> moueatur, triplo <lb></lb> verò tardiùs
                        tertio, &amp;c. </s>
                </p>


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

                    <s>Inordinatè autem creſcere vel decreſcere dicetur <lb></lb>
                        motus, ſi incrementum illud aut decrementum nul<lb></lb> la certa &amp;
                        ordinata proportione fiat. </s>
                </p>
                <p type="main">

                    <s>Comparantur autem motus alij aliis, æquabiles <lb></lb> ſcilicet &amp;
                        inæquabiles ordinatim progredientes: de <lb></lb> inordinatorum enim tum
                        inter ſe, tum cum aliis <expan abbr="cõ||">com</expan><lb></lb>
                        paratione nihil certò ſtatui poteſt. </s>
                </p>
                <p type="main">

                    <s>Comparantur igitur æquabiles cum æquabili­<lb></lb> bus aut cum
                        inæquabilibus, ac etiam inæquabiles <lb></lb> cum inæquabilibus.
                    </s>
                </p>
                <p type="main">

                    <s>Æquabiles autem cum æquabilibus compara­<lb></lb> tionibus
                        ſuis partibus correſpondentibus ſunt pro­<lb></lb>
                        portionales. </s>
                    <s>Si enim <expan abbr="proponãtur">proponantur</expan> duo motus
                        æqua­<lb></lb> biles, quorum alter altero maior ſit, quæ
                        erit ratio <lb></lb> dimidiæ partis vnius ad dimidiam partem alterius,
                        <lb></lb> eadem erit tertiæ ad tertiam, &amp; ſic deinceps. </s>
                </p>
                <p type="main">

                    <s>Æquabilium verò motuum cum inæquabilibus, <lb></lb> cum iis
                        ſcilicet qui per interualla creſcunt, compa­<lb></lb> ratio fit
                        tanquam cum pluribus diuerſis motibus æ­<lb></lb> quabilibus,
                        ſunt enim interuallorum <expan abbr="illorũ">illorum</expan>
                        motus <lb></lb> æquabiles. </s>
                    <s>At cum continuè <expan abbr="creſcẽtibus">creſcentibus</expan> aut decre­<lb></lb> ſcentibus
                        difficile eſt comparationis modum defi­<lb></lb> nire, cùm ne
                        momento quidem ſtabilis maneat par<lb></lb> tium illarum quantitas. </s>
                    <s>Eſt tamen motus æquabilis <lb></lb> illorum menſura: tanti enim
                        eſſe dicuntur, quanti <lb></lb> forent, ſi in ea celeritatis
                        menſura ad quam perue­ <pb xlink:href="044/01/020.jpg" pagenum="12"></pb>nerunt, æquabiliter pergerent. </s>
                </p>
                <p type="main">

                    <s>Creſcentes verò cum creſcentibus continuè, <expan abbr="cõ-parati">con­<lb></lb> parati</expan> ſiquidem eadem
                        progreſſionis proportione <lb></lb> creſcant, æqualia
                        ſpatia ab eorum principiis nume­<lb></lb> rata, æqualibus
                        temporibus emenſa habebunt, idem <lb></lb> in decreſcentibus. </s>
                    <s>Sed hęc hactenus inquiſiuiſſe ſuf­<lb></lb>
                        ficiat: ſi quis enim particulatim omnia <expan abbr="expẽdere">expendere</expan> vel­<lb></lb> let, in infinitum ſeſe
                        extenderet hęc partium &amp; pro­<lb></lb> portionum motuum
                        ſupputatio. </s>
                </p>
                <p type="main">

                    <s>Iam videamus quæ vires quos horum motuum <lb></lb> cieant. </s>
                    <s>Et vis quidem ea qua res quælibet ad ſitum <lb></lb> naturalem
                        ſuarum partium redit, motu <expan abbr="cõtinuè">continuè</expan> de­<lb></lb> creſcente mouet: quo enim
                        propiùs ad ſitum natu­<lb></lb> ralem partium accedit, eo
                        tardior &amp; languidior eſt. <lb></lb>
                    </s>
                    <s>Arcus enim cùm primùm laxari incipit, celeriùs <lb></lb> mouetur,
                        quàm cùm motus ſui finis propior eſt. </s>
                </p>
                <p type="main">

                    <s>Vis verò naturalis, qua res quęlibet ad <expan abbr="locũ">locum</expan> ſuum <lb></lb> naturalem tendit, ſubiectum
                        ſuum, motu continuè <lb></lb> &amp; ordinatim creſcente, mouet. </s>
                    <s>Illius autem motus <lb></lb> cauſa eſt quòd faciliùs id
                        moueatur, quod in motu <lb></lb> eſt, quàm quod quieſcit. </s>
                    <s>Vis igitur eadem, <expan abbr="ſubiectũ">ſubiectum</expan>
                        <lb></lb> quod iam in motu eſt premens, illud magis moue­<lb></lb> bit,
                        quàm ſi quieſcat, &amp; magis motum, magis etiam <lb></lb>
                        mouebit: ita vt eadem vis motione maior fiat, quàm <lb></lb> per ſe
                        ſit. </s>
                    <s>Et hæc eſt cauſa cur ictus, quo magis ab al­<lb></lb> tero
                        venit, eo vehementior ſit. </s>
                    <s>Motus autem huius <pb xlink:href="044/01/021.jpg" pagenum="13"></pb>ſpatia
                        hanc celeritatis proportionem ſeruant, vt <expan abbr="quę">quæ</expan>
                        <lb></lb> eſt ratio totius ſpatij, per quod fit ille motus ad
                        par­<lb></lb> tem ipſius (vtriuſque initio inde ſumpto,
                        vbi eſt mo<lb></lb> tus initium) eadem ſit celeritatis ad
                        celeritatem. <lb></lb>
                        <figure id="id.044.01.021.1.jpg" xlink:href="044/01/021/1.jpg"></figure><lb></lb>
                        Exempli gratia, ſi vis aliqua per lineam ABC <lb></lb> mouerit,
                        ſitque AB illius lineæ pars, quæ erit <lb></lb> ratio AC ad AB,
                        eadem erit celeritatis motus <lb></lb> in puncto C ad <expan abbr="celeritatẽ">celeritatem</expan> motus in puncto B. <lb></lb>
                        </s>
                    <s>Cuiuſmodi proportio obſeruatur in paralle­<lb></lb> lis
                        triangulum ſecantibus. </s>
                    <s>Vt enim ſe habet <lb></lb>
                        <figure id="id.044.01.021.2.jpg" xlink:href="044/01/021/2.jpg"></figure><lb></lb> AC ad
                        AB, ſic CG ad BF, &amp; vt AD ad <lb></lb> AC, ſic DH ad CG.
                        </s>
                    <s>Itaque ſi in ſpatia ali­<lb></lb> quot æqualia diuidatur
                        totius motus ſpa<lb></lb> tium, finis ſecundi duplo citiùs
                        feretur, <lb></lb> quàm finis primi: finis verò tertijtriplo <lb></lb>
                        citiùs quàm finis primi, &amp; ſic deinceps. <lb></lb>
                    </s>
                    <s>Hac autem ratione fit, vt ſpatiorum illo­<lb></lb> rum initio maxima
                        ſit celeritatis <expan abbr="differẽ-tia">differen­<lb></lb>
                            tia</expan>: progreſſu verò ſemper minuatur, ac
                        tandem fer­<lb></lb> mè eadem ſit, vt fit in trianguli
                        lateribus, quæ lon­<lb></lb> giſſimè producta
                        æquè diſtare videntur. </s>
                    <s>Eáque eſt <lb></lb> ratio cur Solis &amp; Lunæ radij,
                        etiamſi concurrant (in <lb></lb> ipſorum ſcilicet corporibus,
                        aut vltra res quas <expan abbr="illu-ſtrãt">illu­<lb></lb>
                            ſtrant</expan>) paralleli <expan abbr="tamẽ">tamen</expan>
                        <expan abbr="appareãt">appareant</expan>. </s>
                    <s><expan abbr="Eadẽ">Eadem</expan>
                        <expan abbr="etiã">etiam</expan> cauſa eſt cur <lb></lb>
                        lineę omnes ad <expan abbr="perpẽdiculũ">perpendiculum</expan> in <expan abbr="terrã">terram</expan>
                        cadentes, paral­<lb></lb> lelæ videantur, cùm <expan abbr="tamẽ">tamen</expan> in centro terræ <expan abbr="cõcurrant">concurrant</expan>. </s>
                </p>


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

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

                    <s>Vis autem voluntaria motum omnem ciere apta <lb></lb> eſt. </s>
                    <s>Fortuita verò inordinatum tantùm motum effi­<lb></lb> cit. </s>
                    <s>Et hæc de variis virium motibus, <expan abbr="eorúmq;">eorúmque</expan> pro­<lb></lb> portione &amp; partibus. </s>
                </p>
                <p type="main">

                    <s>Eſt verò etiam virium partitio quædam, quæ ex <lb></lb>
                        eorum quibus <expan abbr="inhærẽt">inhærent</expan>
                        ſubiectorum diuiſione, aut <lb></lb> alterius ad alterum proportione
                        reſultat. </s>
                    <s>In ſubie­<lb></lb> ctis enim, quæ <foreign lang="grc">ὁμοιομερῆ</foreign> ſunt, vis naturalis æqualiter <lb></lb>
                        per omnes partes diffuſa eſt: ita vt quæ eſt ratio
                        mo­<lb></lb> lis ad molem ſub eadem figura, <expan abbr="eadẽ">eadem</expan> ſit vis ad vim: <lb></lb> vt ſi globus alicuius
                        metalli, ad alium globum eiuſ­<lb></lb> dem metalli mole quadruplus
                        ſit, illius quoque <expan abbr="põ-dus">pon­<lb></lb>
                            dus</expan> ad huius pondus quadruplum erit. </s>
                </p>
                <p type="main">

                    <s>Hactenus vim <expan abbr="cõſiderauimus">conſiderauimus</expan> quatenus mouet, <lb></lb> ſupereſt
                        vt eam conſideremus, quatenus mouenti <lb></lb> reſiſtit. </s>
                    <s>Habet autem locum reſiſtentia, vbi duæ vi­<lb></lb> res
                        contrariæ committuntur: ſi enim vtraque <expan abbr="eodẽ">eodem</expan>
                        <lb></lb> motu moueat, nulla erit reſiſtentia, ſed altera
                        alteri <lb></lb> addita maiorem vim conſtituet. </s>
                </p>
                <p type="main">

                    <s>Committi autem dicuntur vires, quando ita ap­<lb></lb> plicantur &amp;
                            <expan abbr="connectũtur">connectuntur</expan>, vt altera nutu
                        ſuo moueri <lb></lb> non poſſit, quin altera contra nutum
                        ſuum mouea­<lb></lb> tur. </s>
                    <s>Viribus autem ita connexis, accidit vt altera in <lb></lb> alterius
                        ſubiectum agat, &amp; altera in ſubiecto ſuo exi- <pb xlink:href="044/01/023.jpg" pagenum="15"></pb>ſtens, alteri in altero
                        ſubiecto exiſtenti reſiſtat, ita vt <lb></lb> eorum
                        ſubiecta quodammodo reciproca fiant. </s>
                </p>
                <p type="head">

                    <s>CONCLVSIO I.</s>
                </p>
                <p type="main">

                    <s>Illam autem reſiſtentiam vi momenti in eodem <lb></lb> ſubiecto
                        æqualem, aut eandem cum ea eſſe, ex ipſius <lb></lb>
                        definitione conſtat. </s>
                    <s>Eſt enim reſiſtere <expan abbr="nõ">non</expan> pati
                        ſe mo­<lb></lb> ueri. </s>
                    <s>Quantum autem vis quælibet <expan abbr="ſubiectũ">ſubiectum</expan> ſuum <lb></lb> nutu ſuo mouet, tantum
                        illud contra nutum ſuum <lb></lb> moueri non patitur. </s>
                    <s>Mouendi igitur &amp; <expan abbr="mouẽti">mouenti</expan>
                        re­<lb></lb> ſiſtendi potentia in eodem ſubiecto
                        æquales ſunt. </s>
                </p>
                <p type="head">

                    <s>II.</s>
                </p>
                <p type="main">

                    <s>Quemadmodum autem in eodem ſubiecto ma­<lb></lb> ior vis
                        ineſſe dicitur, in quo eſt maioris motus po­<lb></lb>
                        tentia, ſic maior reſiſtentia erit maioris motus
                        con­<lb></lb> trarij impatientia. </s>
                    <s>Eadem igitur vis magis mouere <lb></lb> nitenti <expan abbr="cõtra">contra</expan> ipſius nutum magis reſiſtet, minus
                        ve­<lb></lb> rò nitenti minùs reſiſtet. </s>
                </p>
                <p type="head">

                    <s>III.</s>
                </p>
                <p type="main">

                    <s>Et quo maior erit motus contrarius, eo magis re­<lb></lb>
                        ſiſtet: id eſt, quo celerius vis quælibet à nutu
                        ſuo re­<lb></lb> uelletur, eo magis reſiſtet. </s>
                    <s>Duplo igitur citiùs re­<lb></lb> uellenti duplo reſiſtet,
                        triplo citius triplo reſiſtet, &amp; <lb></lb> ſic <foreign lang="grc">ἀναλόγως</foreign> in omni proportione. </s>
                    <s>Quæ igitur erit <lb></lb> ratio motus ad motum, contra nutum eadem erit
                        <lb></lb> in vna &amp; eadem vi ratio reſiſtentiæ ad
                        reſiſtentiam. </s>
                </p>
                <p type="main">

                    <s>Si verò plures vires comparentur. </s>
                </p>


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

                    <s>IIII.</s>
                </p>
                <p type="main">

                    <s>Æqualium quidem virium æqualibus motibus <lb></lb> æquales erunt
                        reſiſtentiæ. </s>
                    <s>Si enim æquales vires æ­<lb></lb> qualiter à ſuis
                        nutibus reuellantur, æqualiter reſi­<lb></lb> ſtent. </s>
                </p>
                <p type="head">

                    <s>V.</s>
                </p>
                <p type="main">

                    <s>Inæqualibus verò motibus, earum reſiſtentię
                        in­<lb></lb> æquales erunt, &amp; motuum proportionem
                        ſequen­<lb></lb> tur. </s>
                    <s>Exempli gratia, ſint duæ vires A &amp; B, quarum v­<lb></lb>
                        traque vna hora miliare vnum percurrat, illæ æqua­<lb></lb> les
                        erunt. </s>
                    <s>Si igitur vtraque quarta parte vnius milia­<lb></lb> ris, vel dimidio
                        miliari à ſuo nutu eodem tempore <lb></lb> reuellatur, eadem erit
                        vtriuſque illi motui reſiſten­<lb></lb> tia. </s>
                    <s>Sin verò altera quidem quarta parte vnius milia­<lb></lb> ris à
                        nutu ſuo reuellatur, altera verò eodem tempo­<lb></lb> re
                        integro miliari reuellatur: hæc reſiſtentia ad
                        il­<lb></lb> lam quadrupla erit, &amp; ſic de cæteris motuum
                        pro­<lb></lb> portionibus. </s>
                </p>
                <p type="head">

                    <s>VI.</s>
                </p>
                <p type="main">

                    <s>Inæqualium verò virium reſiſtentiæ æqualibus
                        <lb></lb> motibus ipſarum virium proportionem ſequentur. <lb></lb>
                    </s>
                    <s>Quo maior enim eſt vis, eo magis eodem tempore <lb></lb> eodémque
                        ſpatio contra nutum mouenti reſiſtit. <lb></lb>
                    </s>
                    <s><expan abbr="Exẽpli">Exempli</expan> gratia, ſit vis A quadrupla
                        ad vim B, vis A mo­<lb></lb> uenti ſe vno miliari quadruplo
                        reſiſtet, quàm B mo­<lb></lb> uenti ſe vno miliari
                        eodem tempore. </s>
                </p>


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

                    <s>Inæqualium verò virium inæqualibus motibus <lb></lb>
                        reſiſtentiæ, quando motus eam inter ſe
                        proportio­<lb></lb> nem ſeruabunt, quæ eſt inter eas
                            <foreign lang="grc">ἀντιπεπονθῶς</foreign>, ſeu <lb></lb>
                        reciprocè, æquales erunt. </s>
                    <s>Sit enim vis A quæ ad vim <lb></lb> B eandem habeat <expan abbr="rationẽ">rationem</expan> quam C ad D, puta quam <lb></lb> 3 ad
                        1, aut 4 ad 1, aut quæcunque alia ſit, <expan abbr="moueatúrq;">moueatúrque</expan>
                        <lb></lb> vtraque ſpatio E contra nutum ſuum eodem tem­<lb></lb>
                        pore, reſiſtentia A ad reſiſtentiam B ſe
                        habebit, vt C <lb></lb> ad D per proximam concluſionem. </s>
                    <s>Si verò B moue­<lb></lb> atur eodem tempore ſpatio aliquo quod
                        ſe habeat <lb></lb> ad ſpatium E vt C ad D, reſiſtentia
                        B huic motui ſe <lb></lb> habebit ad reſiſtentiam priori
                        motui, vt C ad D per <lb></lb> quartam <expan abbr="concluſionẽ">concluſionem</expan>. </s>
                    <s>Duæ ergo reſiſtentiæ ad ean­<lb></lb> dem, eandem
                        habebunt rationem, ergo æquales e­<lb></lb> runt per <emph type="italics"></emph>9<emph.end type="italics"></emph.end> prop. <emph type="italics"></emph>5.<emph.end type="italics"></emph.end> Elem. Eucl.
                        </s>
                </p>
                <p type="head">

                    <s>VIII.</s>
                </p>
                <p type="main">

                    <s>Si verò motuum virium inæqualium proportio <lb></lb> non ſit
                        eadem quæ eſt ipſarum virium reciprocè, vis <lb></lb>
                        illius quæ ad alteram maiorem habebit rationem, <lb></lb> quàm motus
                        alterius ad motum ipſius, reſiſtentia <lb></lb> maior erit,
                        altera verò minor. </s>
                    <s>Exempli gratia, ſi vis <lb></lb> A ſit tripla ad vim B, &amp; motus
                        quo B à nutu ſuo reuel<lb></lb> letur, ſit minor quàm
                        triplus ad motum A, reſiſten­<lb></lb> tia A erit maior
                        quàm reſiſtentia B. </s>
                    <s>Idem erit, ſi ma­<lb></lb> ior ſit ratio A ad B, quàm 3
                        ado, motus verò B ad mo­ <pb xlink:href="044/01/026.jpg" pagenum="18"></pb>tum A ſit triplus. </s>
                    <s>Contrà verò ſi A ad B ſit tripla: mo­<lb></lb> tus
                        verò B ad motum A ſit maior quàm triplus, ma­<lb></lb> ior
                        erit reſiſtentia B quàm A. </s>
                    <s>Idem accidet, ſi A ad B <lb></lb> ratio minor ſit quàm 3 ad 1,
                        motus verò B ad motum <lb></lb> A ſit triplus. </s>
                    <s>Hunc autem exceſſum &amp; defectum <expan abbr="nõ">non</expan>
                        <lb></lb> vlteriùs ſcrutabimur, vt ipſius quantitatis <expan abbr="menſurã">menſuram</expan>
                        <lb></lb> aſſequamur: alioqui in infinitum fieret
                        progreſſus. </s>
                </p>
                <p type="main">

                    <s>Ex his colligimus <expan abbr="reſiſtẽtias">reſiſtentias</expan> tribus modis æqua­<lb></lb> les
                        aut inæquales dici, per ſe ſcilicet aut motione, aut <lb></lb>
                        vtroque modo. </s>
                    <s>Per ſe quidem cùm ſubiectorum <lb></lb> vires ſunt
                        æquales (id eſt æqualiter ſua ſubiecta
                        mo­<lb></lb> uent) aut inæquales. </s>
                    <s>Motione verò quando per ſe <lb></lb> quidem in æquales
                        ſunt, motione verò æquales <expan abbr="fiũt">fiunt</expan>: <lb></lb> aut quando per ſe æquales ſunt,
                        motione verò inæ­<lb></lb> quales <expan abbr="fiũt">fiunt</expan> eo, quo dictum eſt, modo. </s>
                    <s>Vtroque mo <lb></lb> do æquales aut inæquales <expan abbr="dicũtur">dicuntur</expan>, quando tum per <lb></lb> ſe,
                        tum motione tales fiunt. </s>
                    <s>His explicatis videamus <lb></lb> quis eorum ſit effectus, vbi vires
                        committentur. </s>
                </p>
                <p type="head">

                    <s>IX.</s>
                </p>
                <p type="main">

                    <s>Primùm ex prima concluſione ſequitur quę erit <lb></lb>
                        ratio reſiſtentiæ ad reſiſtentiam, eandem fore
                        reſi­<lb></lb> ſtentiæ ad vim cuius eſt altera
                        reſiſtentia: ſunt enim <lb></lb> vis &amp; <expan abbr="reſiſtẽtia">reſiſtentia</expan> in
                            <expan abbr="eodẽ">eodem</expan> ſubiecto æquales. </s>
                    <s>Ergo mul­<lb></lb> to magis ſequitur, ſi <expan abbr="reſiſtẽtia">reſiſtentia</expan>
                        altera maior, altera mi <lb></lb> nor fuerit, illam huius vi <expan abbr="maiorẽ">maiorem</expan> fore, vel illius vim <lb></lb> hac
                        reſiſtentia maiorem, ſi æqualis æqualem. </s>
                </p>


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

                    <s>X</s>
                </p>
                <p type="main">

                    <s>Reſiſtentia autem vi contrariæ commiſſa <expan abbr="tãtum">tantum</expan>
                        <lb></lb> de ea tollit quanta eſt ipſa reſiſtentia. </s>
                    <s>Sublata autem <lb></lb> vi tollitur motus: ſublata verò
                        reſiſtentia, ſi vis adſit, <lb></lb> ſequitur
                        motus. </s>
                    <s>Vbi igitur vis &amp; reſiſtentia inęqua­<lb></lb> les
                        committentur, ſi vis maior ſit quàm
                        reſiſtentia, <lb></lb> fiet motus ſecundum vis illius nutum,
                        &amp; contra nu­<lb></lb> tum vis illius quæ reſiſtit. </s>
                    <s>Si verò reſiſtentia maior <lb></lb> fuerit, tum ipſa fiet
                        vis mouens, &amp; vim contrariam <lb></lb> contra nutum ipſius mouebit,
                        dum ipſa nutu ſuo <lb></lb> mouebitur. </s>
                    <s>Hinc ſequuntur duo theoremata, circa <lb></lb> quæ totius huius
                        conſiderationis cardo vertitur. </s>
                </p>
                <p type="head">

                    <s>THEOREMA I.</s>
                </p>
                <p type="main">

                    <s>Duarum virium connexarum, quarum (ſi mo­<lb></lb> ueantur) motus erunt
                        ipſis <foreign lang="grc">ἀντιπεπονθῶς</foreign>
                        proportiona­<lb></lb> les neutra alteram mouebit, ſed
                        æquilibrium <expan abbr="faciẽt">facient</expan>. </s>
                </p>
                <p type="main">

                    <s>Sit vis A commiſſa cum vi B, ſitque vis A ad vim <lb></lb> B
                        ratio per ſe, vt C ad D <expan abbr="quæcũque">quæcunque</expan> illa ſit, ſiue dupla, <lb></lb>
                        ſiue tripla, ſiue alia. </s>
                    <s>Sit etiam <expan abbr="eadẽ">eadem</expan> ratio motus quo <lb></lb> B
                        mouebitur, ſi ita, vt connexa ſunt, moueantur) ad <lb></lb> motum
                        quo A mouebitur, quæ eſt C ad D, dico mo­<lb></lb> tum non
                        ſequuturum, ſed factum iri æquilibrium. <lb></lb>
                    </s>
                    <s>Aut enim A &amp; B vires per ſe erunt æquales aut
                        inæ­<lb></lb> quales: ſi æquales, ergo &amp; ipſarum
                        motus æquales e­<lb></lb> runt: ſunt enim ex hypotheſi
                        ipſis proportionales: <pb xlink:href="044/01/028.jpg" pagenum="20"></pb>ergo per quartam concluſionem earum reſiſtentiæ
                        <lb></lb> æquales erunt, ergo per decimam concluſionem <expan abbr="nõ">non</expan>
                        <lb></lb> fiet motus. </s>
                    <s>Si verò ſunt inæquales, cùm earum mo­<lb></lb> tus ex
                        hypotheſi ſint <foreign lang="grc">ἀντιπεπονθῶς</foreign>
                        proportionales per <lb></lb> ſeptimam concluſionem æquales
                        erunt etiam reſi­<lb></lb> ſtentiæ. </s>
                    <s>Ergo nec motus fiet: nullo igitur modo fiet <lb></lb> earum motus. </s>
                    <s>Quod demonſtrandum erat. </s>
                </p>
                <p type="head">

                    <s>THEOREMA II.</s>
                </p>
                <p type="main">

                    <s>Quarum verò ita connexarum (ſi <expan abbr="moueãtur">moueantur</expan>) mo<lb></lb> tus, ipſis proportionales non erunt:
                        illa alteram mo­<lb></lb> uebit, cuius ad alteram ratio maior erit,
                        quàm huius <lb></lb> motus ad illius motum. </s>
                </p>
                <p type="main">

                    <s>Sit vis A cum vi B commiſſa, ſitque A ad B ratio <lb></lb> per
                        ſe, vt C ad D: ita verò connexæ ſint, vt ſi
                        mouean­<lb></lb> tur, minor ſit ratio motus quo B mouebitur ad
                        mo­<lb></lb> tum, quo A mouebitur, quum C ad D dico A motu­<lb></lb> ram
                        B: erit enim per octauam concluſionem reſi­<lb></lb>
                        ſtentia B minor reſiſtentia A: ergo per nonam
                        con­<lb></lb> cluſionem reſiſtentia B minor vi A: vis
                        igitur A vim <lb></lb> B mouebit per vndecimam concluſionem. </s>
                    <s>Quod <lb></lb> demonſtrandum erat. </s>
                </p>
                <p type="main">

                    <s>Hinc poſſemus ad problematis noſtri demon­<lb></lb>
                        ſtrationem rectà pergere: ante tamen craſſiùs
                        ali­<lb></lb> quanto hæc explicanda ſunt, vt à quouis
                        faciliùs in­<lb></lb> telligantur. </s>
                    <s>Duæ ſunt motus menſuræ, locus ſcilicet <lb></lb>
                        &amp; tempus: vtroque igitur, tempore videlicet &amp; loco <pb xlink:href="044/01/029.jpg" pagenum="21"></pb>maior, minor aut æqualis
                        dicitur: &amp; quo minori <expan abbr="tẽ-pore">tem­<lb></lb>
                            pore</expan> idem ſpatium abſoluitur, eo maior eſt,
                        vel quo <lb></lb> maius ſpatium eodem tempore. </s>
                </p>
                <p type="main">

                    <s>Vt igitur motus magnus dicatur, perinde eſt ſi <lb></lb> paruo
                        tempore fiat, aut magno ſpatio. </s>
                </p>
                <p type="main">

                    <s>Quod autem maiorem <expan abbr="motũ">motum</expan> ciere poteſt
                        illud, <lb></lb> vis maior dicitur, quòd minorem minor. </s>
                </p>
                <p type="main">

                    <s>Vis autem ſeu mouendi potentia in eodem ſub­<lb></lb> iecto
                        certa &amp; finita eſt. </s>
                    <s>Quęlibet enim res vi natura­<lb></lb> li prędita, ſi
                        à loco naturali abſit, ſuóque arbitrio <expan abbr="cõ-mittatur">con­<lb></lb> mittatur</expan>, certo tempore
                        eò redit. </s>
                    <s>Eſt enim certum <lb></lb> in rerum natura quanto tempore libræ vnius
                            <expan abbr="põdus">pondus</expan>
                        <lb></lb> deorſum ſponte ſua delatum, miliare vnum aut duo
                        <lb></lb> conficiat pro ratione materię, vel quantum ſpatij
                        v­<lb></lb> na vel duabus horis percurrat. </s>
                    <s>Id verò quantum ſit, <lb></lb> hominum induſtria nondum quod
                        ſciam explora­<lb></lb> tum eſt: aliâs autem id
                        demonſtrare conabimur. </s>
                </p>
                <p type="main">

                    <s>Mouendi verò potentia in alieno ſubiecto infi­<lb></lb> nita
                        eſt, hoc eſt, in <expan abbr="infinitũ">infinitum</expan>
                        augeri vel minui poteſt, <lb></lb> quoniam in finita auctione &amp;
                        diminutione eſt reſi­<lb></lb> ſtentia: tanta enim
                        eſt, quanta eſt in eodem ſubiecto <lb></lb> vis: <expan abbr="quantúſq;">quantúſque</expan> motus illius
                        eſt vis alterius reſpectu. <lb></lb>
                    </s>
                    <s>Quo igitur vis quæ alienum ſubiectum mouere ni­<lb></lb> titur,
                        illud magis mouere nitetur, eo minùs illud <lb></lb> mouere poterit, maior
                        enim erit illius reſiſtentia. <lb></lb>
                    </s>
                    <s>Quemadmodum enim quod magis nutu ſuo mo­ <pb xlink:href="044/01/030.jpg" pagenum="22"></pb>uetur, maiorem vim mouendi
                        habet. </s>
                    <s>Ita illud idem <lb></lb> quod magis contra nutum ſuum mouetur, <expan abbr="maiorẽ">maiorem</expan>
                        <lb></lb> vim reſiſtendi habet. </s>
                    <s>E contrario verò quo vis quæ­<lb></lb> libet minorem motum in
                        alieno ſubiecto ciere ni­<lb></lb> tetur, eo faciliùs illud
                        mouebit. </s>
                </p>
                <p type="main">

                    <s>Tarditate igitur motus, reſiſtentia in infinitum <lb></lb> minui
                        poteſt: minuta verò reſiſtentia vis contrariæ
                        <lb></lb> effectus augetur, ita vt vis quæ per ſe minima eſt,
                        in <lb></lb> contrariam cui plurimum diminuta ſit, reſiſtentia
                        <lb></lb> maximè agat. </s>
                    <s>Perinde igitur eſt, ſi vis mouens ma­<lb></lb> gna ſit,
                        mouenda verò parua, ac ſi illa celeriter fera­<lb></lb> tur,
                        hæc verò tardè: <expan abbr="quãtum">quantum</expan>
                        enim vis mouens ſi ma­<lb></lb> gna fuerit in mouendam minorem
                        poterit, tantum <lb></lb> vis parua celeriter mota in magnam tardè motam
                        <lb></lb> poterit. </s>
                    <s>Si igitur velimus vt vis parua magnam mo­<lb></lb> ueat, eas ita collocare
                        oportet, vt quantum magna <lb></lb> paruam ſuperat, tantum illi de motus
                        celeritate de­<lb></lb> trahatur, &amp; aliquid ampliùs. </s>
                    <s>Si enim tanta ſit tardi­<lb></lb> tas motus vis vnius, reſpectu
                        motus vis alterius, <expan abbr="quã-ta">quan­<lb></lb> ta</expan>
                        eſt proportio vis illius, ad hanc non fiet motus: vt <lb></lb> ſi
                        pondus A quatuor librarum cum pondere B libræ <lb></lb> vnius committatur:
                        ſintque ita connexa, vt dum <lb></lb> A vno ſpatio mouebitur, B
                        quatuor ſpatiis mouea­<lb></lb> tur, ita vt motus A quadruplo tardior
                        ſit motu B <expan abbr="nõ">non</expan>
                        <lb></lb> fiet motus, quia quantum A excedit B pondere tan­<lb></lb> tùm
                        deficit motus tarditate. </s>
                </p>


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

                    <s>Tantum enim eſt libram vnam quatuor ſpatiis <lb></lb> moueri, quantum
                        libras quatuor vno ſpatio eodem <lb></lb> tempore: ſi igitur
                        alterutri eorum ita <expan abbr="conſtitutorũ">conſtitutorum</expan>, <lb></lb> vel momentum vis addatur, id cui
                        additum fuerit, <lb></lb> alterum mouebit. </s>
                    <s>Idem fiet ſi A ita connectatur vt <lb></lb> vel momento citiùs
                        quàm moueri poſitum eſt, mo<lb></lb> ueatur vel B tardiùs.
                    </s>
                </p>
                <p type="main">

                    <s>Id etiam alia ratione oſtendi poteſt, ſi vis A
                        qua­<lb></lb> drupla ſit ad vim B, erunt in A quatuor partes,
                        ipſi B <lb></lb> æquales. </s>
                    <s>Si igitur B cum ſingulis illis committatur, <lb></lb> ita vt æqualiter
                        moueantur, non fiet motus: ſi verò <lb></lb> alterutri aut ipſi
                        B, aut ſingulis illis partibus vis vel <lb></lb> motus momentum adiiciatur
                        vel detrahatur, illa cui <lb></lb> adiectum fuerit, aut cui non detractum
                        fuerit, nutu <lb></lb> ſuo mouebitur, &amp; aliam contra nutum eius
                        moue­<lb></lb> bit. </s>
                    <s>Addito igitur ipſi B momento, dum vno ſpatio <lb></lb> mouebitur,
                        ſingulas illas partes vno ſpatio moue­<lb></lb> bit. </s>
                    <s>Vbi igitur ſingulas ſemel mouerit, ipſa quater <lb></lb> mota
                        erit. </s>
                    <s>Dum verò ſingulæ ſemel motæ erunt, to­<lb></lb>
                        tum ex illis conſtans ſemel motum intelligetur: po­<lb></lb>
                        terit igitur B addito ipſi momento, dum quater mo<lb></lb> uebitur,
                        ſemel totum A mouere. </s>
                </p>
                <p type="main">

                    <s>Tertio modo id ipſum concludere poſſumus. </s>
                    <s>Si <lb></lb> duæ vires æquales connectantur, ita vt motæ,
                        æqua­<lb></lb> liter moueantur, altera in <expan abbr="alterã">alteram</expan> non aget. </s>
                    <s>Si verò ita <lb></lb> connectantur vt motæ inæqualiter moueantur,
                            <pb xlink:href="044/01/032.jpg" pagenum="24"></pb>quantum altera alteram
                        celeritate ſuperabit, <expan abbr="tãtum">tantum</expan>
                        <lb></lb> &amp; vi ſuperabit. </s>
                    <s>Vt ſi vis A vi B æqualis ſit, ac ita <expan abbr="con-nectãtur">con­<lb></lb> nectantur</expan>, vt B quatuor
                        ſpatiis moueatur, dum A vno <lb></lb> ſpatio mouebitur, B quadruplam
                        vim habebit ad A, <lb></lb> quia eam in motibus ſuis proportionem
                        ſeruant, <lb></lb> quam ſi <expan abbr="ſeruarẽt">ſeruarent</expan> arbitrio ſuo commiſſæ, B
                        ad A qua­<lb></lb> drupla eſſet. </s>
                    <s>Si igitur illis ita connexis, ipſi A adda­<lb></lb> tur vis triplo
                        maior quàm ipſa ſit, B illis quatuor re­<lb></lb>
                        ſiſtet, nec fiet motus. </s>
                </p>
                <p type="main">

                    <s>Duarum igitur virium comparatarum, quanto <lb></lb> altera ſubiectum
                        ſuum celeriùs mouebit, quàm al­<lb></lb> tera: tanto illa
                        hanc celeriùs mouere poterit, quàm <lb></lb> ipſa moueatur,
                        ſi illi vis <expan abbr="momẽtum">momentum</expan> additum
                        fuerit. <lb></lb>
                    </s>
                    <s>Ita vt quæ erit proportio vis ad vim, eadem ſit mo­<lb></lb> tus,
                        quem illa in hac ciere poteſt ad motum quo ipſa <lb></lb> mouebitur. </s>
                    <s>Et è conuerſo quæ erit ratio motus ad <lb></lb> motum, eadem erit
                        vis cui additum fuerit momen­<lb></lb> tum ad eam quam ipſa mouere
                        poterit ratio reci­<lb></lb> procè. </s>
                    <s>Iam ad problematis noſtri demonſtratio­<lb></lb> nem veniamus.
                    </s>
                </p>
            </chap>
            <chap>
                <p type="head">

                    <s><emph type="italics"></emph>Propoſiti problematis
                            demonſtratio.<emph.end type="italics"></emph.end></s>
                </p>
                <p type="main">

                    <s>Sit data vis A quantacunque illa ſit magna vel <lb></lb> parua: datum
                        verò pondus B quantumquantum il­<lb></lb> lud ſit, dico me vi A
                        pondus B tollere poſſe. </s>
                    <s>Id ſic de­<lb></lb> monſtro. </s>
                </p>


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

                    <s>Primùm enim ex doctrina ſecundi <expan abbr="lẽmatis">lemmatis</expan>, quod <lb></lb> inferiùs demonſtrabitur,
                        ſciam proportionem pro­<lb></lb> ximè maiorem, quàm
                        ſit A ad B proportio. </s>
                    <s>Deinde <lb></lb> ex doctrina primi lemmatis ita connectam A &amp; B, <lb></lb> vt
                        quando ambo mouebuntur, nunc ſit ratio motus <lb></lb> quo B mouebitur ad
                            <expan abbr="motũ">motum</expan> quo A mouebitur, quàm <lb></lb>
                        ſit A ad B. </s>
                    <s>His peractis ſequitur vim A pondus B mo­<lb></lb> turam ex
                        ſecundo ſuperiùs demonſtrato theorema­<lb></lb> te. </s>
                    <s>Quod erat propoſitum. </s>
                </p>
                <p type="head">

                    <s>LEMMA I.</s>
                </p>
                <p type="main">

                    <s>Duas vires ita connectere, vt ſi moueantur, <expan abbr="earũ">earum</expan>
                        <lb></lb> motus, in data ratione alter ad alterum ſe habeant <lb></lb> vires
                        contrariæ, aut medio aliquo, aut per ſe abſque <lb></lb> vllo
                        medio committuntur. </s>
                    <s>Si abſque medio com­<lb></lb> mittant, eodem motu mouebuntur, maior
                        enim mi<lb></lb> norem eodem motu, quo ipſa moueri poterit, mo­<lb></lb>
                        uebit: aut æquilibrium <expan abbr="faciẽt">facient</expan>,
                        ſi æquales ſint: vt ſi le­<lb></lb> ue graui
                        committatur, ſiquidem leuitas grauitate <lb></lb> maior ſit,
                        attolletur graue: ſin verò grauitas maior <lb></lb> ſit, leue
                        deprimetur: ſi æqualia ſint, non mouebun­<lb></lb> tur.
                    </s>
                </p>
                <p type="main">

                    <s>Si verò medio aliquo connectantur mediorum <lb></lb> varia ſunt
                        genera. </s>
                    <s>Aut enim medium eſt flexibile &amp; <lb></lb>
                        <foreign lang="grc">ὁμοιομερὲς</foreign>, vt funis, catena, &amp;c. </s>
                    <s>aut eſt inflexibile, il­<lb></lb> lúdque aut rectum, aut curuum,
                        vt recta linea vel <lb></lb> curua vel angulus. </s>
                    <s>Atque hæc omnia aut continua <pb xlink:href="044/01/034.jpg" pagenum="26"></pb>ſunt aut diuiſa, ſimplicia aut
                        compoſita. </s>
                </p>
                <p type="main">

                    <s>Horum autem mediorum opera fit vt vires illis <lb></lb> applicatæ, quarum
                        iidem ſunt nutus, contrariis mo­<lb></lb> tibus moueantur. </s>
                    <s>Id <expan abbr="autẽ">autem</expan> fit cùm in mediis illis inter <lb></lb>
                        <expan abbr="eorũ">eorum</expan> extrema interiacet quies vna vel
                        plures. </s>
                    <s><expan abbr="Exẽpli">Exempli</expan>
                        <lb></lb> gratia, ſi duo pondera funis extremitatibus alligata <lb></lb>
                        ſint, &amp; funis clauo fixo &amp; immobili incumbat pro­<lb></lb>
                        pter illam quietem inter <expan abbr="vtrumq;">vtrumque</expan> pondus
                            <expan abbr="poſitã">poſitam</expan>
                        <expan abbr="nõ">non</expan>
                        <lb></lb> poterit <expan abbr="alterũ">alterum</expan> deorſum
                        moueri, quin <expan abbr="alterũ">alterum</expan> ſurſum
                        <lb></lb> moueatur. </s>
                    <s><expan abbr="Idẽ">Idem</expan> fiet in linea recta, ſi enim
                        illius extre­<lb></lb> mitatibus pondera duo annexa ſint, &amp; inter
                        ea ſit in <lb></lb> illa <expan abbr="punctũ">punctum</expan>
                        aliquod quieſcens, dum alterum ex illis <lb></lb> ponderibus deorſum
                        feretur, alterum aſcendet. </s>
                    <s><expan abbr="Pũ-ctum">Pun­<lb></lb> ctum</expan> autem illud
                        quieſcens in linea illa recta, Gręcis <lb></lb> hypomochlium
                        dicitur, eò quòd vecti, quem <foreign lang="grc">μόχλον</foreign><lb></lb> vocant, ſubiiciatur. </s>
                    <s>Huius autem hypomochlij, in <lb></lb> recta linea ſe vecte collocatio
                        faciet, vt lineæ extre­<lb></lb> ma ſecundum datam rationem
                        moueantur. </s>
                    <s>Si enim <lb></lb> recta linea in datam rationem diuiſa fuerit, hoc
                        eſt, <lb></lb> vt pars altera ad <expan abbr="alterã">alteram</expan>
                        eam habeat <expan abbr="rationẽ">rationem</expan>, <expan abbr="quã">quam</expan> quis <lb></lb> voluerit. (Quod <expan abbr="quidẽ">quidem</expan> quo modo fiat docet Euc.) &amp; <lb></lb>
                        in puncto diuiſionis collocetur <expan abbr="hypomochliũ">hypomochlium</expan>, illius <lb></lb> lineæ extrema ſecundum
                            <expan abbr="illã">illam</expan>
                        <expan abbr="rationẽ">rationem</expan> mouebuntur: <lb></lb> ſiue
                        enim conſideretur <expan abbr="circulorũ">circulorum</expan>,
                        quos illa extrema <lb></lb> deſcribent, proportio ſiue ſpatium
                        quod illa in linea <lb></lb> perpendiculari notabunt vtroque modo illi motus,
                            <pb xlink:href="044/01/035.jpg" pagenum="27"></pb><expan abbr="partiũ">partium</expan>
                        <expan abbr="illarũ">illarum</expan>
                        <expan abbr="proportionẽ">proportionem</expan>
                        <expan abbr="ſeruabũt">ſeruabunt</expan>. </s>
                    <s>Sit <expan abbr="exẽpli">exempli</expan> gratia <lb></lb> linea AB,
                        quæ in puncto C in datam rationem ſecta <lb></lb> ſit, puta vt
                        pars AC quadrupla ſit ad partem CB, mo­<lb></lb> ueatúrque circa
                        centrum C, punctum A deſcribet cir<lb></lb> culum <expan abbr="quadruplũ">quadruplum</expan> ad illum quem B <lb></lb>
                        deſcribet. </s>
                    <s>Eſt enim <expan abbr="eadẽ">eadem</expan> ratio in
                        cir­<lb></lb> culo diametri ad <expan abbr="diametrũ">diametrum</expan>, quæ eſt <lb></lb> circunferentiæ ad
                            <expan abbr="circunferentiã">circunferentiam</expan> (vt <lb></lb>
                        alibi demonſtrauimus.) Hac igitur <lb></lb> ratione A puncti motus
                        quadruplus <lb></lb>
                        <figure id="id.044.01.035.1.jpg" xlink:href="044/01/035/1.jpg"></figure><lb></lb> erit
                        ad puncti B <expan abbr="motũ">motum</expan>. </s>
                    <s>Si verò ponamus AD <expan abbr="perpen-dicularẽ">perpen­<lb></lb> dicularem</expan> eſſe, &amp; linea AB
                        illi primùm <expan abbr="coincidẽs">coincidens</expan> circa
                        <lb></lb> punctum C, moueatur donec A ad D perueniat: tum <lb></lb>
                        <expan abbr="eodẽ">eodem</expan> momento B perueniet ad E: motum
                        igitur erit <lb></lb> A in linea <expan abbr="perpẽdiculari">perpendiculari</expan> tota circuli maioris diame­<lb></lb> tro,
                        quæ eſt AD:B verò in <expan abbr="eadẽ">eadem</expan>
                        linea, minoris <expan abbr="tãtùm">tantùm</expan>
                        <lb></lb> circuli diametro <expan abbr="motũ">motum</expan> erit,
                        quę eſt BE. </s>
                    <s>Atqui diame<lb></lb> ter AD quadrupla eſt ad BE, quia ex hypotheſi
                            <expan abbr="ſemi-diametrorũ">ſemi­<lb></lb>
                            diametrorum</expan>
                        <expan abbr="illorũ">illorum</expan>
                        <expan abbr="circulorũ">circulorum</expan> proportio eſt, vt 4
                        ad 1. <lb></lb> Motus igitur <expan abbr="pũcti">puncti</expan> in linea A
                            <expan abbr="perpẽdiculari">perpendiculari</expan> ad <expan abbr="motũ">motum</expan>
                        <lb></lb>
                        <expan abbr="pũcti">puncti</expan> B quadruplus erit: <expan abbr="Idẽ">Idem</expan> dicetur ſi in data aliqua <lb></lb>
                        alia ratione ſecta ſit linea AB. <expan abbr="Demõſtratũ">Demonſtratum</expan> igitur
                        eſt <lb></lb> quomodo fieri poſſit vt rectæ lineę
                        extrema <expan abbr="ſecũdũ">ſecundum</expan>
                        <lb></lb>
                        <expan abbr="datã">datam</expan>
                        <expan abbr="rationẽ">rationem</expan> moueantur. </s>
                    <s>Si igitur illis extremis duæ <lb></lb> vires applicentur, <expan abbr="mouebũtur">mouebuntur</expan>
                        <expan abbr="eodẽ">eodem</expan> ipſo motu: ergo <lb></lb>
                        ſecundum datam vel propoſitam rationem. </s>
                    <s>Quod <lb></lb> aſſumptum erat. </s>
                </p>


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

                    <s>Quod autem in vecte demonſtratum eſt, illud e­<lb></lb> tiam in
                        reliquis mediis demonſtrandum erit, etſi <lb></lb> lemmati
                        ſatisfactum eſt, dum in vno exemplo id <lb></lb> probatum eſt. </s>
                    <s>Ante igitur ſecundum lemma de­<lb></lb> monſtrabimus. </s>
                </p>
                <p type="head">

                    <s>LEMMA II.</s>
                </p>
                <p type="main">

                    <s>Proportionem proximè maiorem vel minorem, <lb></lb> quàm ſit
                        datæ vis ad datum pondus proportio, de­<lb></lb> terminare vis
                        cuiuslibet quantitas ex motu ciere po|| <lb></lb> teſt, metienda
                        eſt. </s>
                    <s>Motum autem ciere poteſt vel in <lb></lb> ſubiecto ſuo, vel in
                        alieno. </s>
                    <s>Vis autem menſura non <lb></lb> ſumitur ex eo motu quem in
                        ſubiecto ſuo ciere po­<lb></lb> teſt, eo quòd licet
                        vis quælibet certum motum ha­<lb></lb> beat &amp; <expan abbr="determinatũ">determinatum</expan> quo ſubiectum
                        ſuum mouet, <lb></lb> illius tamen quantitas, vt ſuprà diximus,
                        nondum <lb></lb> demonſtrata eſt. </s>
                    <s>Supereſt igitur vt vires motu illo <lb></lb> metiamur, quem in alieno
                        ſubiecto ciere poſſunt, vt <lb></lb> id fiat, quærenda
                        nobis ſunt ſubiecta quæ in homi­<lb></lb> num
                        poteſtate ſint, &amp; cum vi qualibet committi <lb></lb>
                        poſſint. </s>
                    <s>Omnium autem mobilium ſubiectorum, <lb></lb> maximè in hominum
                        poteſtate ſunt grauia: leuia e­<lb></lb> nim coercere vix
                        poſſumus. </s>
                    <s>Ideo vires illis metiri <lb></lb> ſolemus, ſed grauibus quæ vel
                        vel figuris ſuis &amp; com<lb></lb> page vel vaſe aliquo coercentur. </s>
                    <s>Itaque vſus homi­<lb></lb> num certas quaſdam ponderum
                        menſuras ſibi ſta <lb></lb> tui, ponderibus ſcilicet
                        quibuſdam certa <expan abbr="quãtitate">quantitate</expan>
                        <pb xlink:href="044/01/037.jpg" pagenum="29"></pb>conſtantibus inditis
                        nominibus, vt eſſent <expan abbr="ponderũ">ponderum</expan>
                        <lb></lb> omnium communes menſuræ, vt ſunt libræ, vncia, <lb></lb>
                        <expan abbr="drachmę">drachmæ</expan>, &amp;c. </s>
                    <s>quas famoſas menſuras <expan abbr="vocãt">vocant</expan>. </s>
                    <s>Quem­<lb></lb> admodum igitur numeros numeris, ſic pondera <expan abbr="põ-deribus">pon­<lb></lb> deribus</expan> metimur. </s>
                    <s><expan abbr="Tãtum">Tantum</expan> enim pondus eſſe dicitur,
                        <lb></lb> quot libras vncias drachmas æqualiter mouere po­<lb></lb>
                        teſt dempto momento. </s>
                    <s>Nec tantum pondera hoc <lb></lb> modo metimur, ſed etiam alias omnes vires
                        motum <lb></lb> ad locum cientes. </s>
                    <s>Quot enim libras vir aut aliud a­<lb></lb> nimal vel <expan abbr="vẽtus">ventus</expan> aut ignis, aut aliqua alia vis dempto
                        <lb></lb> momento mouere poterit, tot libris illam æqualem <lb></lb>
                        eſſe dicemus. </s>
                    <s>Si igitur data vel propoſita vis metien­<lb></lb> da ſit,
                        ſiquidem naturalis ſit, quoniam docuimus <lb></lb> vim naturalem per
                        totum ſubiectum diffuſam eſſe <lb></lb> in rebus
                        homogeneis: id eſt, vt quæ eſt proportio <lb></lb> molis ad
                        molem, eadem ſit ponderis ad pondus: ſu­<lb></lb> memus partem
                        aliquam illi homogeneam, aut ex i­<lb></lb> pſo ſubiecto, aut
                        ex alio ipſi homogeneo, eámque <lb></lb> famoſa aliqua
                        menſura metiemur, vtramque ſcili­<lb></lb> cet committendo
                        &amp; obſeruando, quem motum al­<lb></lb> tera in altera ciere
                        poſſit, vbi enim æquilibrium fa­<lb></lb> cient motibus
                        extremorum, quibus affixæ fuerint, <lb></lb> proportionales erunt per 1
                        theorema: motus autem <lb></lb> illi linearum dimenſione quam Geometria
                        docet, <lb></lb> noti erunt, &amp; eorum proportio, nota igitur erit &amp; <lb></lb>
                        virium proportio. </s>
                    <s>Atqui menſuræ famoſæ nota, per <pb xlink:href="044/01/038.jpg" pagenum="30"></pb>ſe eſt quantitas:
                        duorum autem proportione cogni­<lb></lb> ta &amp; alterius quantitate,
                        ſtatim &amp; reliqui quantitas <lb></lb> innoteſcit per
                        ſecundam da. Eu. nota igitur vis
                            <expan abbr="quã-titate">quan­<lb></lb> titate</expan> quæ
                        parti illi ineſt, noſcetur &amp; vis <expan abbr="quãtitas">quantitas</expan>
                        <expan abbr="quę">quæ</expan><lb></lb> toti inerit: quæ enim
                        erit ratio molis ſubiecti vis da­<lb></lb> tæ ad molem
                        particulę ſumptę, eadem erit vis totius <lb></lb> ad vim
                        partis. </s>





                    <s>Hîc igitur erunt quatuor proportio­<lb></lb> nalia, ſcilicet vt
                        moles ad molem: ſic vis ad vim ex <lb></lb> quibus tria nota erunt: moles
                        enim metiri Geome­<lb></lb> tria nos docuit, præterea vis partis, vt
                        demonſtraui­<lb></lb> mus, nota eſt, ergo &amp; vis totius
                        quantitas per deci­<lb></lb> mam ſeptimam ſeptimi Elem. Eucl.
                        </s>
                </p>
                <p type="main">

                    <s>Si verò ſubiectum non ſit homogeneum, vi ta­<lb></lb> men
                        naturali ſit præditum, ſi quidem data vis quam <lb></lb> metiri
                        volumus, ea ſitque motum ciere volumus, <lb></lb> tum conſiderabimus
                        quæ pars in illa, vis minimum <lb></lb> habeat: &amp; ex ea totam
                        ipſius molem æſtimabimus: <lb></lb> ſi verò
                        ſit vis mouenda, ſtatuemus quaſi tota ſit
                        ho­<lb></lb> mogenea ipſius parti, quæ vis plurimum in ſe
                        habe­<lb></lb> bit, &amp; ex ea totam ipſius molem
                        æſtimabimus. </s>
                    <s>Ita­<lb></lb> que tum illius quanta minima, tum huius quanta <lb></lb> maxima
                        eſſe poteſt, vis quantitas nobis nota erit per <lb></lb>
                        proximè demonſtratam rationem. </s>
                    <s>Notis autem vi­<lb></lb> rium quantitatibus, nota erit &amp; earum
                        proportio: <lb></lb> ergo &amp; proportio ipſa proximè maior vel
                        mi­<lb></lb> nor: addita enim vel detracta ipſius denomi- <pb xlink:href="044/01/039.jpg" pagenum="31"></pb>nationi, vnitate erit
                        proximè maior vel mi­<lb></lb> nor. </s>
                </p>
                <p type="main">

                    <s>Si verò vis data non ſit naturalis, <expan abbr="voluntariã">voluntariam</expan> qui­<lb></lb> dem ita æſtimare
                        poſſumus, qualis vt plurimum <lb></lb> eſt, &amp; ſi
                        quidem ea ſit, qua mouere volumus, eam <lb></lb> ſtatuemus, quanta
                        minima in eiuſdem generis ſub­<lb></lb> iecto eſſe
                        poteſt, vt ſi vim hominis quinquaginta li­<lb></lb> bris
                        æqualem ponamus, vim equi centum: ſi verò <lb></lb> ea ſit
                        quam mouere volumus, ſtatuemus eam <expan abbr="quã-ta">quan­<lb></lb> ta</expan> maxima eſſe poteſt, vt vim
                        hominis 300 libra­<lb></lb> rum, vim equi 500 librarum, &amp; ſic
                        dé cæteris: ita vt <lb></lb> nullum ſit dubium quin illa minor
                        ſit, quam ſtatue­<lb></lb> rimus, hæc verò maior.
                    </s>
                </p>
                <p type="main">

                    <s>Vis verò fortuitæ quantitatem nulla certa con­<lb></lb> iectura
                        aſſequi poſſumus: ita vt quaſcunque
                        ma­<lb></lb> chinas ei aptemus, modò moueat, modò non
                        mo­<lb></lb> ueat, neque ad noſtrum <expan abbr="inſtitutũ">inſtitutum</expan> magnoperè
                        per­<lb></lb> tinet illa inquiſitio: cum fortuitorum nulla ſit
                        diſci­<lb></lb> plina. </s>
                </p>
                <p type="main">

                    <s>His igitur modis virium duarum datarum pro­<lb></lb> portio proximè
                        maior nota fiet, quod in ſecundo <lb></lb> lemmate demonſtrandum
                        ſumpſeramus. </s>
                </p>
                <p type="main">

                    <s>Iam redeamus ad mediorum, quibus vi­<lb></lb> res annectuntur,
                        conſide­<lb></lb> rationem. </s>
                </p>


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

                    <s>Docuimus quis ſit ſimplicis ve­<lb></lb> ctis effectus,
                        ſimplex autem ve­<lb></lb> ctis ſemicirculi conuerſione
                        ſuam <lb></lb> operationem abſouit, ita vt ſi <lb></lb>
                        vlteriùs F moueatur in in alio ſe­<lb></lb> micirculo motus
                        prioribus contra­<lb></lb> rios cieat: vt exempli gratia, ſit <lb></lb>
                        vectis AB, cuius hypomochium <lb></lb> ſit C, dum A punctum
                        deſcribet ſemicirculum AFD, <lb></lb> motus ille deorſum erit:
                        interea verò B punctum <lb></lb> deſcribet ſemicirculum BGE
                        aſcendendo: ſi verò A <lb></lb> tranſcendat, D incipiet
                        aſcendere: B verò tranſcen­<lb></lb> dens, E <expan abbr="deſcẽdet">deſcendet</expan>: ideo excogitata
                        eſt vectis ratio per­<lb></lb> petua ex plurium vectium
                        ſucceſſione circa idem <lb></lb> hypomochlium: eſt autem
                        illa tum in ergatis aut ſu­<lb></lb> culis, tum in duorum tympanorum
                        homocentrico­<lb></lb> rum, ſeu eadem axe transfixorum in planis
                        parallelis <lb></lb> aptatione, quorum ſemidiametri ſint in eadem
                        pro­<lb></lb> portione quæ in vecte ad propoſitum motum
                        cien­<lb></lb> dum neceſſaria eſt: centrum verò
                        eorum ſeu axis fi­<lb></lb> xa ſit, ac ita vires aptentur, vt
                        maior minorem, mi­<lb></lb> nor verò maiorem tympanum impellat. </s>
                    <s>Quemad­<lb></lb> modum autem horum tympanorum homocentri­<lb></lb> corum
                        opera vectis perpetui ratio <expan abbr="inuẽta">inuenta</expan>
                        eſt, ita eo­<lb></lb> rum multiplicatione motus, &amp; mouentis &amp;
                            <expan abbr="mouẽ-di">mouen­<lb></lb> di</expan>, proportio in
                        infinitum augeri poteſt. </s>
                    <s>Cuius rei <pb xlink:href="044/01/041.jpg" pagenum="33"></pb>maximus eſt
                        vſus: nec enim materia ad vectem, cu­<lb></lb> ius longitudo
                        ſtadij vnius requireretur, idonea in­<lb></lb> ueniri
                        poſſet: plurium autem tympanorum propor­<lb></lb> tionalium
                        aptatione fiet machina tractabilis, cuius <lb></lb> vis maior erit quàm
                        vectis, cuius longitudo ſtadij v­<lb></lb> nius eſſet. </s>
                    <s>Si enim duo tympani homocentrici a­<lb></lb> ptentur, quorum proportio
                        ſit alterius ad alterum, <lb></lb> decupla, vis quæ libram vnam
                        æquabit, vim decem <lb></lb> libris æqualem dempto momento mouebit,
                        ſi con­<lb></lb> gruè illis tympanis aptentur: ſi
                        verò adhuc duo alij <lb></lb> tympani fiant, quorum alterius ad alterum
                        decupla <lb></lb> ſit proportio, ac minor <expan abbr="illorũ">illorum</expan> ita aptetur, vt <expan abbr="maiorẽ">maiorem</expan>
                        <lb></lb> ex prioribus moueat, appendatur deinde minori ex <lb></lb> prioribus
                        tympanis vis centum libris æqualis, maio­<lb></lb> ri verò ex
                        poſterioribus vis vni libræ æqualis, tum <lb></lb> hæc
                        illam mouebit, &amp; ſic in infinitum motus extre­<lb></lb> morum
                        proportio multiplicari poteſt. </s>
                    <s>Flexibili ve­<lb></lb> rò medio quies ita aptari poteſt, vt duo
                        eius extre­<lb></lb> ma diuerſis motibus moueantur, &amp; quidem
                        ſecun­<lb></lb> dum datam rationem. </s>
                    <s>Exemplum habemus in orga <lb></lb> nis polyſpactis, ſeu trochleis, in
                        quibus altero funis <lb></lb> extremo immobili manente, reliquum funis circa
                        <lb></lb> plures trochleas conuoluitur, quarum aliæ centris <lb></lb>
                        immobilibus fixæ ſunt, aliæ verò ipſis
                        contrariæ cen <lb></lb> tris mobilibus. </s>
                    <s>Atque ita circa illas conuoluitur fu­<lb></lb> nis, vt inter eas ſit
                        ſpatium tantum, quanta eſt linea, <pb xlink:href="044/01/042.jpg" pagenum="34"></pb>per quam motum ciere volumus. </s>
                    <s>Quoties igitur fu­<lb></lb> nis extremum quod moueri poteſt, trahitur,
                            <expan abbr="ſingulę">ſingulæ</expan><lb></lb>
                        reuolutiones æqualiter minuuntur, eáque ratione, <lb></lb>
                        <expan abbr="diſtãtia">diſtantia</expan> quæ eſt
                        inter trochleas contrarias minuitur, <lb></lb> ita ſcilicet vt quot
                        ſunt reuolutiones, in tot partes <lb></lb> diſtributum ſit
                        motus ſpatium. </s>
                    <s>Quot igitur reuolu<lb></lb> tiones erunt, totuplex erit motus extremitatis funis
                        <lb></lb> ad motum trochlearum mobilium verſus fixas. </s>
                    <s>Si i­<lb></lb> gitur motus iſtius extrema conſtituantur, alterum <lb></lb>
                        <expan abbr="quidẽ">quidem</expan> funis illa extremitas quæ
                        mouetur, <expan abbr="alterũ">alterum</expan> ve­<lb></lb> rò
                        terminus ſpatij illius, quod eſt à trochleis fixis ad <lb></lb>
                        mobiles contrarias: quæ erit proportio numeri con­<lb></lb> uolutionum
                        funis ad vnitatem, eadem erit motus, <lb></lb> quo funis extremum mouebitur ad
                        motum quo al­<lb></lb> terum extremum mouebitur: poteſt autem in
                        infi­<lb></lb> nitum augeri conuolutionum numerus, ergo &amp; mo<lb></lb> tus
                        illius proportio. </s>
                </p>
                <p type="main">

                    <s>Angulus autem ad motum ciendum ita ad­<lb></lb> hibetur. </s>
                    <s>Diximus motus menſuram in nutus li­<lb></lb> nea ſumi, quantum
                        igitur vis aliqua per eam verſus <lb></lb> locum naturalem mouetur, tanta
                        eſt, quantum verò <lb></lb> per eam à loco naturali reuellitur,
                        tanta eſt eius reſi­<lb></lb> ſtentia. </s>
                    <s>Quod verò per lineam à loco naturali æquè <lb></lb>
                        diſtantem (id eſt, per eam quæ nutus lineas ſecat ad
                        <lb></lb> angulos rectos) mouetur, illud mouenti non reſi­<lb></lb>
                        ſtit, omnium autem linearum inter illas intercepta- <pb xlink:href="044/01/043.jpg" pagenum="35"></pb>rum, ac cum illis in earum
                        interſectionis puncto <expan abbr="cõ-currentium">con­<lb></lb>
                            currentium</expan>, quæ obliquè nutum verſus, aut contra
                        <lb></lb> nutum ferri dicuntur, quo propiùs quælibet ad nu­<lb></lb>
                        tus lineam accedit, per illam rei motæ vis aut <expan abbr="reſiſtẽ-tia">reſiſten­<lb></lb>
                            tia</expan> maior eſt: quò verò propiùs ad lineam
                        à loco na­<lb></lb> turali æqui diſtantem accedit, eò
                        minor eſt. </s>
                    <s><expan abbr="Omniũ">Omnium</expan>
                        <lb></lb> autem maxima eſt in nutus linea, æquidiſtans
                        verò <lb></lb> à loco naturali motui per lineam nutus omnino op<lb></lb>
                        poſita eſt, obliquæ verò non ita quia ſecundum
                        illas <lb></lb>
                        <expan abbr="eodẽ">eodem</expan> ſpatio delata vis propiùs
                        ad <expan abbr="locũ">locum</expan>
                        <expan abbr="naturalẽ">naturalem</expan> acce­<lb></lb> dit, aut ab
                        eo recedit, quàm eſſet, cùm moueri cœpit. </s>
                </p>
                <figure id="id.044.01.043.1.jpg" xlink:href="044/01/043/1.jpg"></figure>
                <p type="main">
                    <s>Sit exempli gratia AB linea <lb></lb> nutus, vis alicuius, puta ponde­<lb></lb>
                        ris, ſitque A ſurſum &amp; contra nu<lb></lb> tum: B verò
                        deorſum &amp; nutum <lb></lb> verſus, deſcribatúrque
                        circulus, <lb></lb> cuius AB ſit diameter, quàm CD, <lb></lb> alia
                        diameter ſecet ad angulos <lb></lb> rectos in centro E: omnes igitur <lb></lb>
                        lineæ à centro E ad circunferentiam circuli ductæ, <lb></lb>
                        quæ <expan abbr="cadẽt">cadent</expan> intra <expan abbr="ſemicirculũ">ſemicirculum</expan> CAD, contra
                            <expan abbr="nutũ">nutum</expan>
                        <expan abbr="aſcẽ-dere">aſcen­<lb></lb> dere</expan>
                        dicentur, quatenus circunferentiam ſpectant: <lb></lb> quatenus verò
                        centrum ſpectant, deſcendere dicen­<lb></lb> tur: <expan abbr="cõtra">contra</expan> verò omnes in ſemicirculo
                        CBD à centro <lb></lb> ad circunferentiam ductæ deſcendere
                        circunferen­<lb></lb> tiam verſus, &amp; centrum verſus
                        aſcendere dicentur: <pb xlink:href="044/01/044.jpg" pagenum="36"></pb>illæ igitur erunt, quæ obliquè nutum verſus aut
                        con<lb></lb> tra nutum ferri <expan abbr="dicũtur">dicuntur</expan>: linea
                        verò CED, neque <expan abbr="aſcẽ-det">aſcen­<lb></lb> det</expan>, neque deſcendet: lineæ
                        verò in ipſam ad angu­<lb></lb> los rectos incidentes nutus
                        lineæ erunt, quoniam li­<lb></lb> neæ AB parallelæ erunt:
                        ſi igitur à centro E <expan abbr="ducãtur">ducantur</expan>
                        <lb></lb> lineæ ad circunferentiam inter A &amp; D, puta EF, EG, <lb></lb> EH,
                        quarum EF ſit proxima lineæ AB:EH verò pro­<lb></lb> xima
                        lineæ CD, ac per illas moueantur contra <expan abbr="nutũ">nutum</expan>
                        <lb></lb> tres vires æquales eodem tempore, ita vt prima per <lb></lb> lineam
                        EF perueniat ad punctum F: ſecunda verò <lb></lb> per EG perueniat ad
                        G, tertia per EH perueniat ad H, <lb></lb> dico vis motæ per EF maiorem
                        fore reſiſtentiam, <lb></lb> quàm illius quæ per EG aut
                        EH, mouebitur &amp; illius <lb></lb> quæ per EG mouebitur, maiorem
                        quàm eius quæ <lb></lb> per EH mouebitur. </s>
                    <s>Ducantur enim à punctis FGH <lb></lb> in lineam ED perpendiculares FK, GL,
                        HM, illæ <expan abbr="erũt">erunt</expan>
                        <lb></lb> nutus lineæ: quanta igitur erit FK, tantum vis prima <lb></lb> mota
                        cenſebitur, quanta verò GH, tantum vis ſecun<lb></lb> da:
                        quanta verò HM, tantum vis tertia mota cenſebi­<lb></lb> tur: at
                        qui quæ eſt ratio motus ad motum in viribus <lb></lb> æqualibus,
                        per quartam <expan abbr="cõcluſionem">concluſionem</expan>
                        huius tracta­<lb></lb> tus, eadem eſt reſiſtentiæ ad
                        reſiſtentiam: quæ igitur <lb></lb> erit ratio linearum illarum
                        perpendicularium, inter <lb></lb> ſe eadem erit &amp; <expan abbr="reſiſtẽtiarum">reſiſtentiarum</expan> virium per lineas ob­<lb></lb>
                        liquas motarum, à quibus illæ perpendiculares du­<lb></lb>
                        ctæ ſunt, atqui quo lineæ illæ perpendiculares pro- <pb xlink:href="044/01/045.jpg" pagenum="37"></pb>piùs ad AB circuli
                        diametrum accedunt, eò ſunt ma<lb></lb> iores per decimam quartam
                        tertij Elem. Eu. ergo &amp; <lb></lb> vires per eas lineas delatę à
                            <expan abbr="quarũ">quarum</expan> extremitatibus du<lb></lb>
                        <expan abbr="cẽtur">centur</expan>, maiores <expan abbr="reſiſtẽtias">reſiſtentias</expan>
                        <expan abbr="habebũt">habebunt</expan>: at qui quò magis <lb></lb> ad
                        AB, accedunt eo magis ab ED recedunt: quò igi­<lb></lb> tur magis ad
                        ED accedent, eò minores erunt <expan abbr="reſiſtẽ-tiæ">reſiſten­<lb></lb> tiæ</expan>, hinc ſequitur
                        tanquam corollarium. </s>
                    <s>Si duæ vi­<lb></lb> res perſe æquales triangulo rectangulo
                        aptentur, cu<lb></lb> ius latus alterum, angulum rectum <expan abbr="conſtituẽtium">conſtituentium</expan>: <lb></lb>
                        ſit earum nutus linea, ac per illud vis altera mouea­<lb></lb> tur,
                        altera verò per latus angulo recto oppoſitum, <lb></lb> quæ erit
                        ratio huius lateris ad illud, eadem erit reſi­<lb></lb> ſtentia
                        vis illius ad vis huius <expan abbr="reſiſtẽtiam">reſiſtentiam</expan>. </s>
                    <s>Atqui duo­<lb></lb> rum illorum laterum proportio in infinitum
                        auge­<lb></lb> ri vel minui poteſt, ergo &amp;
                        reſiſtentia virium illis ap<lb></lb> plicatarum. </s>
                    <s>Hoc igitur modo poſſumus vti angulo <lb></lb> ſeu triangulo ad
                        motus ciendos, nempe eo immoto <lb></lb> vires per eius latera mouendo. </s>
                </p>
                <p type="main">

                    <s>Sed &amp; alia ratione eo vti poſſumus, ipſum
                        ſcilicet <lb></lb> triangulum mouendo, qui tunc cuneus dicitur. </s>
                    <s>Vt <lb></lb> autem eo hac ratione vtamur, vires ita diſponere o­<lb></lb>
                        portet, vt altera illarum vni ex lateribus angulum <lb></lb> rectum
                        conſtituentibus incumbat, altera verò lateri <lb></lb> ipſum
                        ſubtendenti. </s>
                    <s>Illa enim tantùm mouebitur, <lb></lb> quantum latus cui altera incumbit. </s>
                    <s>Sit exempli gra­ <pb xlink:href="044/01/046.jpg" pagenum="38"></pb><figure id="id.044.01.046.1.jpg" xlink:href="044/01/046/1.jpg"></figure><lb></lb> tia
                        triangulus ABC, cuius angulus B <lb></lb> rectus ſit, latus verò
                        illum ſubtendens <lb></lb> ſit AC, incumbátque vis D lateri AB,
                        <lb></lb> vis verò E lateri AC, ſitque vis D nutus <lb></lb> linea BC,
                        vis verò E nutus ſit linea AB, erigatúrque à <lb></lb>
                        puncto C linea CF <expan abbr="perpẽdicularis">perpendicularis</expan> ad BC æqualis AB, <lb></lb> à qua vis E
                            <expan abbr="nõ">non</expan> diſcedat. </s>
                    <s>Si triangulum illud in plano <lb></lb> fixo moueatur, donec AB perueniat ad CF,
                        mota e­<lb></lb> rit vis D nutu ſuo tantùm, quanta eſt
                        linea BC, vis ve­<lb></lb> rò E tantum, quanta eſt linea AB.
                        </s>
                    <s>Cùm autem poſſit <lb></lb> in infinitum augeri &amp; minui,
                        laterum illorum pro­<lb></lb> portio, poſſunt etiam duorum
                        illorum <expan abbr="extremorũ">extremorum</expan>
                        <lb></lb> motus in data ratione conſtitui. </s>
                    <s>Quanta enim erit <lb></lb> BC ad AB, tantus erit motus vis D ad motum vis E:
                        <lb></lb> ergo &amp; in hoc medio primum lemma noſtrum de­<lb></lb>
                        monſtratum eſt. </s>
                </p>
                <p type="main">

                    <s>In hoc autem medij genere hoc diuerſum ab <lb></lb> aliis mediis accidit,
                        quòd non tam facilè vtrin­<lb></lb> que motus eo cietur, ac in
                        illis, in quibus ſi virium <lb></lb> proportio momento vel ſuperet,
                        vel minor ſit pro­<lb></lb> portione motus <expan abbr="extremorũ">extremorum</expan> medij, tum motus hinc <lb></lb>
                        vel inde cietur. </s>
                    <s>Atqui in hoc propter ſuperficie­<lb></lb> rum contactum, quarum pori
                        vel aſperitates ſe­<lb></lb> ſe mutuò
                        ſubingrediuntur, &amp; ita inuicem adhæ­<lb></lb> rent, fit vt
                        ægriùs cieatur motus, faciliùs ve- <pb xlink:href="044/01/047.jpg" pagenum="39"></pb>rò mouebuntur, ſi
                        illæ ſuperficies leues fue­<lb></lb> rint, vt ſi pinguibus
                        inungantur, vel ex materia <lb></lb> leui conſtent. </s>
                    <s>Ideò enim reliqua faciliùs mo­<lb></lb> uentur, quòd circa
                        puncta veluti quædam mo­<lb></lb> ueantur. </s>
                </p>
                <p type="main">

                    <s>Simplicis autem trianguli rectilinei aut cu­<lb></lb> nei in diuturnis
                        motibus ciendis rarus eſt vſus, <lb></lb> tum ob illud quod
                        notauimus incommodum ex <lb></lb> vitio materiæ, quo fit vt in eo
                        quaſſatione opus <lb></lb> ſit, tum etiam quòd breui eius
                        operatio termine­<lb></lb> tur. </s>
                    <s>Ideo illo vtimur aut cùm ſolutionem con­<lb></lb> tinui molimur,
                        quæ breui tempore fit, vel <lb></lb> cùm aliquid diſtendere aut
                        aliquid figere volu­<lb></lb> mus. </s>
                </p>
                <p type="main">

                    <s>Anguli verò curui linei magnus eſt vſus, præ­<lb></lb>
                        ſertim helicis cylindricæ. </s>
                    <s>Nihil enim aliud eſt he­<lb></lb> lix quàm triangulus curuus:
                        ſi enim alteram ex <lb></lb> lineis rectis angulum conſtituentibus,
                        cylindri <lb></lb> baſi ipſi lineæ æquali obuolueris,
                        reliquam ve­<lb></lb> rò ſeruato eodem quem conſtituunt
                        angulo, ſu­<lb></lb> per cylindri ſuperficiem curuaueris,
                        habebis he­<lb></lb> licem cylindricam, quam ſi iterum ſeruato
                        eo­<lb></lb> dem angulo in rectum extendas, habebis trian­<lb></lb> gulum
                        rectilineum. </s>
                    <s>Hæc autem helix commo­<lb></lb> diſſima eſt, tum
                        quòd in parua mole triangulum <pb xlink:href="044/01/048.jpg" pagenum="40"></pb>longiſſimum obuolutum contineat tum quod
                        par­<lb></lb> tes eius omnes ſibi inuicem <expan abbr="cõgruant">congruant</expan>: omnes enim <lb></lb> partes helicis cylindricæ, aut
                        circa eundem, aut circa <lb></lb> æquales cylindros deſcriptæ,
                        ſeruato eodem angulo <lb></lb> ſibi inuicem
                        ſuppoſitæ congruunt. </s>
                    <s>Quo fit, vt ſi ca­<lb></lb> ui cylindri interiori ſuperficiei
                        impreſſa ſit helix, a­<lb></lb> lia verò cylindri
                        ſuperficiei connexę ipſi cauę æqua­<lb></lb>
                        li, ſeruato eodem qui in illo eſt, angulo, ſibi
                        inui­<lb></lb> cem &amp; omnes vnius omnibus alterius partibus con<lb></lb>
                        gruant. </s>
                </p>
                <p type="main">

                    <s>Huius autem medij cùm plures ſint partes, con<lb></lb> ſtat enim
                        duabus ſuperficiebus, pluribus etiam mo<lb></lb> dis variari poteſt. </s>
                    <s>In ſumma autem eius affectus hic <lb></lb> eſt, vt cylindri
                        baſi in ſuperficie immobili circum a­<lb></lb> xem
                        conuerſa, vis mouenda helicem premat: dum <lb></lb> enim cylindrus circum
                        axem conuertetur, vis mo­<lb></lb> uenda qualibet reuolutione tantùm
                        ſecundum cy­<lb></lb> lindri longitudinem mouebitur, quanta eſt
                        diſtan­<lb></lb> tia duarum helicis ſpirarum. </s>
                    <s>Quæ igitur erit propor<lb></lb> tio circunferentiæ circuli baſim
                        cylindri <expan abbr="conſtituẽ-tis">conſtituen­<lb></lb> tis</expan> ad illam <expan abbr="diſtãtiam">diſtantiam</expan>, eadem erit motus
                        orbicularis <lb></lb> cuiuſlibet puncti in cylindri ſuperficie
                        ſignati ad mo<lb></lb> tum rectum vis helicem prementis. </s>
                </p>
                <p type="main">

                    <s>Illud igitur medium ex duobus compoſitum eſt, <lb></lb> recto
                        ſcilicet &amp; curuo: ita igitur vires illi aptandæ <lb></lb>
                        ſunt, vt eius quam mouere volumus, nutus linea ſit <pb xlink:href="044/01/049.jpg" pagenum="41"></pb>cylindri longitudo: illa
                        verò qua mouere volumus, <lb></lb> in orbem moueatur, aut ſi eius
                        nutus linea recta ſit, <lb></lb> circa cylindrum fluens illum moueat
                        contingendo. </s>
                </p>
                <p type="main">

                    <s>Et hæc quidem de mediis in ſuo genere <expan abbr="conſiſtẽ-tibus">conſiſten­<lb></lb> tibus</expan>. </s>
                    <s>Poſſunt autem fieri eorum Syzygiæ vectis
                        ſci­<lb></lb> licet cum trochleis, helicis cum vecte, aut cum
                        tro­<lb></lb> chleis, aut <expan abbr="omniũ">omnium</expan>
                        ſimul. </s>
                    <s>Vectis cum trochleis ſi fu­<lb></lb> nis illud extremum, quod mouetur
                        in trochleis, er­<lb></lb> gatis aut ſuculis inuoluatur: helix cum
                        vecte <expan abbr="coniũ-getur">coniun­<lb></lb> getur</expan>,
                        ſi tympanus circum axem moueatur, ſitque i­<lb></lb> ta
                        denticulatus, vt dentes ipſius helicem in cylindro <lb></lb> excauatam
                        ingrediantur, quam machinam helicem <lb></lb> perpetuam vulgò vocant,
                        eò quòd eius conuerſio <lb></lb> perpetua eſſe
                        poſſit, cum helicis ſimplicis operatio <lb></lb> non excedat
                        ipſius longitudinem. </s>
                    <s>Quorum <expan abbr="omniũ">omnium</expan>
                        <lb></lb> tum inter ſe, tum ad ſubiecta mouenda accommo­<lb></lb>
                        datio adeò varia eſt, vt ſcripto <expan abbr="cõprehẽdi">comprehendi</expan> vix poſſit.
                        <lb></lb>
                    </s>
                    <s>Ex his autem quæ dicta ſunt, mediocris ingenij me­<lb></lb>
                        chanicus poterit ea prout ipſi neceſſe erit aptare. </s>
                    <s>In <lb></lb> machinis autem omnibus hæc cautio <expan abbr="adhibẽda">adhibenda</expan> eſt, <lb></lb> vt earum ſtructura firma
                        ſit, præſertim verò vbi cir­<lb></lb> cum axes
                        aliquas fit motus, deinde vt vincula, qui­<lb></lb> bus illis vires <expan abbr="affingũtur">affinguntur</expan>, valida ſint, illarum
                        enim o­<lb></lb> mnium vis in ſuo ſtatu manendi vtrique vi
                        aptandæ <lb></lb> æqualis eſſe debet: aget enim in illas
                        vis <expan abbr="vtraq;">vtraque</expan>, quòd <lb></lb> ſi medium
                        firmum non ſit, motus in ipſa machina <pb xlink:href="044/01/050.jpg" pagenum="42"></pb>ciebitur. </s>
                    <s>Itaque diſſoluetur, ideò manca videtur pe­<lb></lb> titio
                        illa Archimedis in hoc problemate <foreign lang="grc">δὸς ποῦ στῶ τὰν
                            <lb></lb> γὰν κινῶ</foreign>, quòd locum <expan abbr="tãtùm">tantùm</expan> in quo conſiſtat,
                        ſibi da­<lb></lb> ri poſtulet, cùm pręterea vincula
                        quibus terra à loco <lb></lb> ſuo naturali remota
                        ſuſtineri poſſet, petere debue­<lb></lb> rit: id
                            <expan abbr="autẽ">autem</expan> vt &amp; ea quæ de motu in
                        infinitum augen­<lb></lb> do vel minuendo diximus, ita intelligenda
                        ſunt, vt <lb></lb> ſciamus infinita hominum poteſtati,
                        quacunque ar­<lb></lb> te iuuetur, non ſubeſſe: quamuis
                        enim Geometri­<lb></lb> ca conſideratio in infinitum ſeſe
                            <expan abbr="extẽdat">extendat</expan>, ſunt ta­<lb></lb>
                        men certi fines, vltra quos natura rerum nos pro­<lb></lb> gredi non
                        patitur: ſunt præterea vitia materiæ, <lb></lb> quæ
                        Geometra non conſiderat, illa tamen non <lb></lb> obſtant quò
                        minùs id quod proponitur, <expan abbr="verũ">verum</expan>
                        ſit in <lb></lb> intellectu. </s>
                    <s>An verò id quod proponitur tale ſit, vt in <lb></lb> opus educi
                        poſſit, conſiderabit Geometer habita ra­<lb></lb> tione
                        circunſtantiarum, præſertim verò temporis, <lb></lb> quod
                        ipſi præſcribetur, &amp; ſumptuum quos facere <lb></lb>
                        poterit is qui aliquid faciendum proponet, quæ ſi <lb></lb>
                        abundè ſuppetant, nihil non fieri poterit. </s>
                </p>
                <p type="main">

                    <s>Vt igitur hunc tractatulum concludamus, ac ve­<lb></lb> lut in ſummam
                        contrahamus: In motibus ciendis <lb></lb> tria ſunt conſideranda. </s>
                    <s>Vis qua motum ciere volu­<lb></lb> mus, vis quam mouere volumus, &amp; motum
                        quo <lb></lb> mouere volumus: duo enim quælibet ex illis ter­<lb></lb>
                        tium determinant. </s>
                    <s>Si enim vi parua vim magnam <pb xlink:href="044/01/051.jpg" pagenum="43"></pb>mouere volumus, id nonniſi paruo motu facere <lb></lb>
                        poſſumus: ſi verò vim aliquam magno motu
                        mo­<lb></lb> uere velimus, vi magna mouente ad id opus eſt. </s>
                    <s>Si <lb></lb> vi parua magnum motum ciere volumus, mini­<lb></lb> mam vim
                        mouendam eſſe oportet: vt puta, ſi libra <lb></lb> vna centum
                        libras mouere velimus, oportet motum <lb></lb> illius, motu huius <expan abbr="cẽtuplo">centuplo</expan> maiorem eſſe. </s>
                    <s>Si verò ve­<lb></lb> limus libra vna aliam vim ita mouere, vt ea
                        cen­<lb></lb> tuplo citiùs moueatur, quàm libræ illius
                        pondus, il­<lb></lb> lam centeſimam tantùm libræ vnius
                        partem eſſe ne­<lb></lb> ceſſe eſt: ſi
                        verò libram vnam ita mouere velimus, vt <lb></lb> centuplo citius moueatur,
                        quàm vis quæ illam mo­<lb></lb> uebit, vi centum libris maiore ad
                        id opus erit. </s>
                    <s><expan abbr="Neq;">Neque</expan>
                        <lb></lb> patitur natura ſibi in his vim fieri: ſi enim
                        eiuſmodi <lb></lb> proportio aliquo modo infringi poſſet,
                        ſtatim da­<lb></lb> retur <foreign lang="grc">αὐτώμα
                            ἐνδέλεχες</foreign>, vel vt <expan abbr="vocãt">vocant</expan>,
                        motus perpetuus <lb></lb> in perpetua materia. </s>
                </p>
                <p type="main">

                    <s>Ex his igitur fundamentis inuentæ ſunt machinæ <lb></lb> omnes,
                        quotquot antehac ſunt excogitatę, &amp; quot­<lb></lb> quot
                        poſthac excogitari poterunt, ad ea referentur. </s>
                </p>
                <p type="main">

                    <s>Itaque ſi propoſitæ cuiuſcunque machinæ
                        effe­<lb></lb> ctum ſcire velimus, conſideranda ſunt duo
                        eius <lb></lb> extrema, quibus vires applicantur: quæ enim erit <lb></lb> ratio
                        motus vnius ex illis extremis, ad motum <lb></lb> alterius eadem erit &amp;
                        virium, quæ illis extre­<lb></lb> mis ad motum ciendum applicari
                        poterunt, <pb xlink:href="044/01/052.jpg" pagenum="44"></pb>addito aut dempto
                        momento, vt ſi dum <expan abbr="alterũ">alterum</expan>
                        ma­<lb></lb> chinæ extremum palmo vno mouetur, alterum cen<lb></lb> tum
                        palmis moueatur vis quælibet huic annexa, al­<lb></lb> teram alteri
                        annexam centuplam momento minùs, <lb></lb> mouebit: ſed motu
                        centuplo: mouebit autem &amp; re­<lb></lb> liquas omnes vires, quæ
                        infra centuplam proportio­<lb></lb> nem ad eam habebunt: ſi verò
                        non vim centuplam <lb></lb> mouere, ſed in data vi motum centuplum ciere
                        veli­<lb></lb> mus, eam quidem in extremo quod centuplo citiùs <lb></lb>
                        mouetur, locare oportebit, alteram verò alteri extre<lb></lb> mo centuplo
                        maiorem adhibere neceſſe erit. </s>
                </p>
                <p type="main">

                    <s>Hinc oriuntur tria problemata, videlicet data vi <lb></lb> datum pondus mouere,
                        quod iam <expan abbr="demõſtrauimus">demonſtrauimus</expan>: <lb></lb> item data vi datum motum ciere, quod ex
                            <expan abbr="præcedẽ-tis">præceden­<lb></lb>
                            tis</expan> demonſtratione abſoluitur: tertium, datam vim,
                        <lb></lb> dato motu mouere, quod quidem faciliùs demon­<lb></lb>
                        ſtratur, quàm abſoluitur. </s>
                    <s>Scimus enim, vt id fiat, <lb></lb> vim aliam proportionalem (vt docuimus)
                        requiri, <lb></lb> quo modo autem illam habere poſſimus, explicare
                        <lb></lb> hoc opus, hic labor eſt. </s>
                    <s>Non enim quemadmodum <lb></lb> organa ad motus in data proportione ciendos
                        ha­<lb></lb> bere poſſumus: ita &amp; vires infinitæ
                        magnitudinis po<lb></lb> teſtati noſtræ ſubſunt.
                    </s>
                </p>
                <p type="main">

                    <s>Quod enim ad vires in grauitatis &amp; leuitatis gene<lb></lb> re
                        conſiſtentes attinet, eas vt moueant antè moueri <lb></lb>
                        oportet à loco vel ſitu naturali, vi <expan abbr="autẽ">autem</expan> aliqua id fie- <pb xlink:href="044/01/053.jpg" pagenum="45"></pb>ri oportet, quæ iam in promptu ſit. </s>
                    <s>Quæ ſi tanta eſt, <lb></lb> vt poſſit motum
                        propoſitum ciere, fruſtrà fiat, ſi alij <lb></lb> à
                        loco naturali remouendæ, qua poſtea ad motum <lb></lb> vtendum
                        ſit, adhibeatur. </s>
                </p>
                <p type="main">

                    <s>Nullum igitur ex eiuſmodi viribus commodum <lb></lb> percipi poteſt,
                        niſi quis in futurum ſibi proſpiciens, <lb></lb> multa à
                        loco vel ſitu naturali ex otio remoueat, vt <lb></lb> iis, cùm opus
                        erit ad motus ciendos vtatur. </s>
                    <s>Hac ra­<lb></lb> tione quantas vires in promptuario habebit, tantos <lb></lb>
                        motus ciere poterit. </s>
                    <s>Præcipuum igitur quod ad hu­<lb></lb> ius problematis
                        conſtructionem pertinet, eſt, vt vi­<lb></lb> res quàm
                        maximas poteſtati noſtræ ſubiiciamus, vo<lb></lb>
                        luntariis aut fortuitis viribus naturales præparando, <lb></lb> aut à
                        natura præparatas, quæ poteſtati noſtræ
                        ſub­<lb></lb> ſunt, accipiendo. </s>
                    <s>Qualia multa ſi mortales aduerte­<lb></lb> rent, fieri
                        poſſent, vt aliàs, Deo duce, docebimus. </s>
                </p>
                <p type="main">

                    <s>Earum autem virium quæ in raritatis &amp; denſita­<lb></lb> tis
                        proportione conſiſtunt, ſubiecta plurimùm in <lb></lb>
                        noſtra poteſtate ſunt: multa enim ſunt naturalia
                        ſub <lb></lb> iecta actu, denſa potentia verò rara. </s>
                    <s>Si quod igitur <lb></lb> eorum potentia proxima ſit rariſſimum,
                        ita vt nullo <lb></lb> negotio actus ille raritatis induci poſſit,
                            <expan abbr="concluda-túrq;">concluda­<lb></lb>
                            túrque</expan> loco aliquo anguſto, poſtea inducatur
                        ille a­<lb></lb> ctus, cùm rara <expan abbr="maiorẽ">maiorem</expan> locum occupent, quum den­<lb></lb> ſa, fiet vt
                        locus in omnem partem diſtendatur, illius <lb></lb> autem partes
                        minùs cohærentes, tantum impellen­ <pb xlink:href="044/01/054.jpg" pagenum="46"></pb>tur, quanta eſt
                        proportio molis rei rarefactæ ad mo­<lb></lb> lem illius cùm
                        denſa eſſet: illa autem raritatis po­<lb></lb> tentia
                        proxima eſt in compoſitione ſulphuris <lb></lb> &amp; nitri:
                        ea igitur &amp; ſimilibus ſubiectis, <lb></lb> in data vi datus
                        motus <lb></lb> cieri poteſt. </s>
                </p>
                <p type="head">

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

                    <s>Errata quæ inter imprimendum irrepſerunt, <lb></lb> ſic
                        corrigito.</s>
                </p>
                <p type="main">

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

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

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

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

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

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

                    <s>linea<emph.end type="italics"></emph.end> 13. <emph type="italics"></emph>Vi­<lb></lb> res
                        maiori litera<emph.end type="italics"></emph.end> (<emph type="italics"></emph>eſt
                        enim ſectionis initium. </s>

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

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

                    <s>pag.<emph.end type="italics"></emph.end> 28. <emph type="italics"></emph>lin.<emph.end type="italics"></emph.end> 9. <emph type="italics"></emph>vis, lege Vis, maiori
                            litera<emph.end type="italics"></emph.end> (<emph type="italics"></emph>eſt enim
                        <lb></lb> ſectionis initium. </s>

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

                    <s>lin.<emph.end type="italics"></emph.end> 23. <emph type="italics"></emph>metiri
                        ſolemus, lege non <lb></lb> ſolemus. </s>

                    <s>lin. vlt. ſtatui, lege ſtatuit.</s>

                    <s>pag.<emph.end type="italics"></emph.end> 32. <emph type="italics"></emph>lin.<emph.end type="italics"></emph.end> 4. <emph type="italics"></emph>abſouit, lege
                        abſoluit. </s>

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

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

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

                    <s>pag.<emph.end type="italics"></emph.end> 37. <emph type="italics"></emph>li.<emph.end type="italics"></emph.end><lb></lb> 13. <emph type="italics"></emph>reſiſtentia,
                        lege reſiſtentiæ. </s>

                    <s>pag.<emph.end type="italics"></emph.end> 39. <emph type="italics"></emph>lin.<emph.end type="italics"></emph.end> 3. <emph type="italics"></emph>leui, lege læui. </s>

                    <s>pag.<emph.end type="italics"></emph.end> 40. <emph type="italics"></emph>linea<emph.end type="italics"></emph.end> 5. <emph type="italics"></emph>ſuppoſitæ,
                        lege <lb></lb> ſuperpoſitæ</s>

                    <s>li.<emph.end type="italics"></emph.end> 7. <emph type="italics"></emph>connexæ, lege
                        conuexæ. </s>

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