Cardano, Geronimo, Opvs novvm de proportionibvs nvmerorvm, motvvm, pondervm, sonorvm, aliarvmqv'e rervm mensurandarum, non solùm geometrico more stabilitum, sed etiam uarijs experimentis & observationibus rerum in natura, solerti demonstratione illustratum, ad multiplices usus accommodatum, & in V libros digestum. Praeterea Artis Magnae, sive de regvlis algebraicis, liber vnvs abstrvsissimvs & inexhaustus planetotius Ariothmeticae thesaurus ... Item De Aliza Regvla Liber, hoc est, algebraicae logisticae suae, numeros recondita numerandi subtilitate, secundum Geometricas quantitates inquirentis ...
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    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="239" xlink:href="015/01/258.jpg"/>
            <p type="head">
              <s id="id004084">LEMMA PRIMVM.</s>
            </p>
            <p type="main">
              <s id="id004085">Omne graue
                <expan abbr="motũ">motum</expan>
              à centro grauitatis, reſtituto ad eundem ſitum
                <lb/>
              pondere mobili aut inmobili, continente ultra centrum grauitatis
                <lb/>
              naturalis uiolenter fertur.</s>
            </p>
            <p type="main">
              <s id="id004086">Seu ſit pondus per ſe non fluctuans in penſili lecto, ſeu humor in </s>
            </p>
            <p type="main">
              <s id="id004087">
                <arrow.to.target n="marg799"/>
                <lb/>
              patera, quum
                <expan abbr="põdus">pondus</expan>
              moueatur ſolum ratione una, ſcilicet lecti pen­
                <lb/>
              ſilis homo uel plumbum, humor autem aqua uel uinum bifariam
                <lb/>
              & ratione pateræ ſi mobilis ſit in a laxa manu, & etiam per humo­
                <lb/>
              rem ipſum redeuntem ad locum
                <expan abbr="ſuũ">ſuum</expan>
              : adeò quòd ſi eſſet & immobi­
                <lb/>
              lis patera, humor ſaltem reflueret propria inundatione ad locum
                <lb/>
              ſuum centri grauitatis, licet in patera eſſet immobilis locus grauita­
                <lb/>
              tis uelocius & maiore cum impetu, adeò ut tranſeat uerſus e,
                <expan abbr="cũ">cum</expan>
              fu
                <lb/>
              erit motus primus ex e in f, et reſtitutio ex fin e: ſeu in immobili pon
                <lb/>
              dere mobilis continenti, ut in lecto penſili: ſeu in immobili conti­
                <lb/>
              nente, ſcilicet poſtquàm ad locum ſuum reſtitutum fuerit per uim
                <lb/>
              retenta patera à manu iuxta ſitum priorem in a, mobili autem con­
                <lb/>
              tento, id eſt, humore, multo autem magis contento, & continente
                <lb/>
              mobilibus. </s>
              <s id="id004088">Vt ſi patera & humor ipſe ſimul
                <expan abbr="moueãtur">moueantur</expan>
              , nam & pate
                <lb/>
              ra tranſgredietur locum ſuum, & humor duplici motu ſuperau­
                <lb/>
                <arrow.to.target n="marg800"/>
                <lb/>
              ctus tranſgredietur motum naturalem. </s>
              <s id="id004089">Cum enim a d eſt remotum
                <lb/>
              a g, & eſt in f, mouetur maiore impetu, quam ſit pro ratione pon­
                <lb/>
              deris, ut demonſtratum eſt, igitur tranſibit ad e, cum ergo redeat
                <lb/>
              ad g motu naturali, neceſſe eſt ut motus uiolentus ſit ualidior ea
                <lb/>
              parte naturalis, qua d reſiſtit, dum eſt in g, ne dimoueatur à g, ſi igi­
                <lb/>
              tur tractum ad c, ſuperauit uim qua manet in g, in eo quod moue­
                <lb/>
              tur ad f, igitur in reditu mouebitur tantum ultra g uerſus e, quan­
                <lb/>
              tum eſt acquiſitum ex ui tranſitus ultra g uerſus f, quanto ergo ma­
                <lb/>
              ior eſt arcus e d, tanto maior eſt d f, & quanto maior eſt arcus d f,
                <lb/>
              tanto maior d h.</s>
            </p>
            <p type="margin">
              <s id="id004090">
                <margin.target id="marg799"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id004091">
                <margin.target id="marg800"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              30.</s>
            </p>
            <p type="main">
              <s id="id004092">Ex quo patet, quod quanto magis remouetur d à g, tanto maio­
                <lb/>
                <arrow.to.target n="marg801"/>
                <lb/>
              re impetu fertur uerſus extremum aliud & ultra medium.</s>
            </p>
            <p type="margin">
              <s id="id004093">
                <margin.target id="marg801"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="head">
              <s id="id004094">LEMMA SECVNDVM.</s>
            </p>
            <p type="main">
              <s id="id004095">Omne pondus appenſum eſt graue comparatione medij graui­
                <lb/>
              tatis, ad hoc ut ab eo remoueatur, quantum eſt pro ratione anguli
                <lb/>
              ex quo appenſum eſt.</s>
            </p>
            <p type="main">
              <s id="id004096">Sit d appenſum in a & in b, & ſit angulus c b d, triplus angu­
                <lb/>
                <arrow.to.target n="marg802"/>
                <lb/>
              lo c a d, dico quod tripla eſt uis quæ transfert d in c ex b, ei quæ
                <lb/>
              transfert ex a, quoniam enim mixtus eſt in b & a, igitur a d æqua­
                <lb/>
                <arrow.to.target n="marg803"/>
                <lb/>
              lia ſpatia æquales uires exigentur: igitur uirium proportio ut
                <lb/>
              angulorum, at quanto maior eſt a d in proportione ab b d tanto
                <lb/>
              maior eſt proportio anguli c b d ad
                <expan abbr="angulũ">angulum</expan>
              c a d, igitur quanto </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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