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="id001310">
                <pb pagenum="69" xlink:href="015/01/088.jpg"/>
              habent proportionem iuxta exceſſum ad unam, exceſſus igitur
                <lb/>
              duplum purgabunt, & duplo magis, id eſt præter feces libras
                <lb/>
              duas bilis in ſex uicibus.</s>
            </p>
            <p type="margin">
              <s id="id001311">
                <margin.target id="marg277"/>
              E
                <emph type="italics"/>
              x conuerſa
                <emph.end type="italics"/>
              18.
                <emph type="italics"/>
              quint.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001312">
                <margin.target id="marg278"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              37.</s>
            </p>
            <p type="margin">
              <s id="id001313">
                <margin.target id="marg279"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              42.</s>
            </p>
            <p type="main">
              <s id="id001314">Propoſitio octuageſima.</s>
            </p>
            <p type="main">
              <s id="id001315">Proportionem motus ſecundum obliquum ad rectum in ſpa­
                <lb/>
              tio declarare.</s>
            </p>
            <p type="main">
              <s id="id001316">Hæc uídetur ſimilis ſuperiori cuidam propoſitioni, ſed tamen in
                <lb/>
                <arrow.to.target n="marg280"/>
                <lb/>
              hoc differt, quoniam in c a ſupponimus nauim moueri, ut concu­
                <lb/>
              tiat, hic autem iuxta motum ſolum: ut proponamus b nauim ferri
                <lb/>
                <figure id="id.015.01.088.1.jpg" xlink:href="015/01/088/1.jpg" number="84"/>
                <lb/>
              uerſus a uento recto ex b in a: ſit autem uentus ex
                <lb/>
              cin a mouens nauim ex b in a: nòn enim moue­
                <lb/>
              bit ut quidam putant in ratione c a ad b a: ut ſi ca
                <lb/>
              ſit ſexquiquarta ad b a, ut æquali impetu ex b &
                <lb/>
              c flante uento moueretur tardius per c a, quam
                <lb/>
              per b a, quia æqualiter ex ſuppoſito: ergo tanto
                <lb/>
              tardius c fertur in a, quam b in idem quanto lon­
                <lb/>
              gior eſt c a, b a igitur ſi b perueniet in a in qua­
                <lb/>
              tuor diebus c perueniet in idem a in quinque
                <lb/>
              diebus. </s>
              <s id="id001317">Hoc enim eſt per ſe manifeſtum: ſed non quærimus id, ſed
                <lb/>
              ut uento c a æquali per c a ei, qui eſt b a per b a, ubi b moueatur uen
                <lb/>
              to c a per b a, quanto tardius mouebitur. </s>
              <s id="id001318">Mouebitur. </s>
              <s id="id001319">n. </s>
              <s id="id001320">tardius ad
                <lb/>
              a per b a, quam per c a, at per c a tardius, quam ex b in a per æqua­
                <lb/>
              lem uim, ergo multo tardius ex b in a per c a uentum, quam per uen
                <lb/>
              tum ex b in a. </s>
              <s id="id001321">Quærimus ergo compoſitionem horum, ut ſit c
                <lb/>
              nauis, quæ debeat transferri ad a per uentum ex b, & ſequitur,
                <lb/>
              quod tardius, quam ex c per uentum ex c in a, & tardius ex b per
                <lb/>
              uentum ex cin a. </s>
              <s id="id001322">Ergo malus, qui in prora eſt conuoluto eo, qui
                <lb/>
              eſt in puppi, ut etiam Ariſtoteles docet tantundem nititur ad re­
                <lb/>
                <arrow.to.target n="marg281"/>
                <lb/>
              ctum ex cin æquidiſtantem locum ab a quantum c diſtat ab con­
                <lb/>
              tra temo, qui in puppi eſt dirigitur ad h, & ſi ualidius ſit uentus e­
                <lb/>
              tiam adiuuante temonem, ſeu contra nitente, quantum licet mo­
                <lb/>
              bili pondere nauis ad id latus, premitur enim nauis, quaſi ſubmer­
                <lb/>
              gi debeat, uento in aduerſum premente, ut ſi uentus repente huic
                <lb/>
              contrarius exoriatur,
                <expan abbr="periculũ">periculum</expan>
              ſubeat, ne obruatur. </s>
              <s id="id001323">Cum ergo uen­
                <lb/>
              tus ex b feratur, æquidiſtans c h, & c feratur per temonem in k, & ab
                <lb/>
              oppoſitis æqualis actio ſequatur, imò tota impeditur, ex c in h fere­
                <lb/>
              tur iuxta proportionem anguli, quem conſtituit h c cum a c ad to­
                <lb/>
              um rectum, Si igitur ex c in a debuit ferri in duodecim horis ob </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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