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>
            <p type="main">
              <s id="id003871">
                <pb pagenum="228" xlink:href="015/01/247.jpg"/>
              rum nixu, & ita minus laborabunt. </s>
              <s id="id003872">Et
                <lb/>
                <arrow.to.target n="marg747"/>
                <lb/>
              quo minus laborabunt brachia, plus
                <lb/>
              corpus laborabit. </s>
              <s id="id003873">Et ideò, ut declara­
                <lb/>
              tum eſt ſuprà, minor labor erit cum æ­
                <lb/>
              qualiter ambo laborabunt. </s>
              <s id="id003874">Tertium,
                <lb/>
              quo minor erit proportio c b ad b a,
                <lb/>
              eo maius ſpatium pertranſibit remex,
                <lb/>
              qui mouet ex a in d, ſed tanto facilius
                <lb/>
                <arrow.to.target n="marg748"/>
                <lb/>
              mouebit, quia labor motus b c minue­
                <lb/>
                <figure id="id.015.01.247.1.jpg" xlink:href="015/01/247/1.jpg" number="240"/>
                <lb/>
              tur, ut ſuprà uiſum eſt per longitudinem a b & d b, ut ſuprà demon
                <lb/>
              ſtrauimus. </s>
              <s id="id003875">Quartum, cùm remus tranſierit quoddam ſpatium
                <lb/>
              iuxta robur, puta ex c in e, neceſſe eſt ut eleuetur ſuper aquam, tum
                <lb/>
              quia impediret motum pro greſſus nauis, tum ut transferatur ante:
                <lb/>
              aliter ſi transferretur ante ſub aqua difficilius multo, quam per aë­
                <lb/>
              rem transferretur, & retroageret tantundem nauim, quantum an­
                <lb/>
              tea retroactam impulit. </s>
              <s id="id003876">His per ſe notis dico, quòd translato remo
                <lb/>
              ex c in e, neceſſe eſt nauim contrà transferri ex f in g: nam quia impe
                <lb/>
              dimentum ex aqua tranſitur c in e, maius eſt quam nauis ſuper a­
                <lb/>
              quam, & remus debet transferri ex a in d, & non poteſt transferri
                <lb/>
              niſi uel ſtante naui, & translato c in e, uel ſtante a b c remo, & tranſ­
                <lb/>
              lata naui: & tunc neceſſe eſt, ut e progrediatur ad h, ita deſſecabit a­
                <lb/>
              quam ch, ergo difficultas manet eadem fermè, ex his fit motus com
                <lb/>
              poſitus, ut palma non redeat uſque ad e, ſed maneat remus minus in­
                <lb/>
              clinatus, & quaſi ad perpendiculum in h. </s>
              <s id="id003877">Et manifeſtum eſt, q̊d erit
                <lb/>
              motus compoſitus ex retro ceſſu remi & pro ceſſu nauis. </s>
              <s id="id003878">Qui etiam
                <lb/>
              remiges circa medium ſunt minus laborarent, ſi remus æqualiter
                <lb/>
              promineret extra ſcalmum, ſed magis laborant, quia proportio eſt
                <lb/>
              eadem, & a b eſt longior, & craſsior remus, ut minus flectatur ob
                <lb/>
              longitudinem, aliter ſi eſſet æqualis craſsitudinis, & multo longior
                <lb/>
              flecteretur aut frangeretur, ideò robuſtiores remiges ponuntur in
                <lb/>
              medio triremis. </s>
              <s id="id003879">Iuuatur præterea motus nauis prorſum ex percuſ­
                <lb/>
              ſione remi, & impetu iam aquiſito cum nixu remi in aduerſum ſu­
                <lb/>
              perueniente. </s>
              <s id="id003880">Rurſus cum nauis transferatur eodem tempore antè
                <lb/>
              quò a progreditur ad d, manifeſtum eſt quòd magna pars eſt ex
                <lb/>
              motu nauis, non nixu corporis aut uirium: & ita quod celerius mo
                <lb/>
              uetur ex c in h, ab initio dum nauis quieſcit, aut tardius mouetur,
                <lb/>
              tardius autem dum nauis progreditur.</s>
            </p>
            <p type="margin">
              <s id="id003881">
                <margin.target id="marg745"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              15.
                <emph type="italics"/>
              pri­
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003882">
                <margin.target id="marg746"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              4.
                <emph type="italics"/>
              ſexti
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003883">
                <margin.target id="marg747"/>
              P
                <emph type="italics"/>
              rop.
                <emph.end type="italics"/>
              188.</s>
            </p>
            <p type="margin">
              <s id="id003884">
                <margin.target id="marg748"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              71.</s>
            </p>
            <p type="main">
              <s id="id003885">Propoſitio ducenteſima.</s>
            </p>
            <p type="main">
              <s id="id003886">Cur temo
                <expan abbr="cũ">cum</expan>
              paruus ſit magnam nauim agere poteſt: & cur cum
                <lb/>
              uarietas ſit in prora, ipſe conſtituatur in puppi. </s>
              <s id="id003887">Et cum tranſuerſim
                <lb/>
              ab aqua prematur, rectà nauim dirigat?</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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