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="id002026">
                <pb pagenum="112" xlink:href="015/01/131.jpg"/>
              tur una, eadem que eſſe ratio in utriſque. </s>
              <s id="id002027">Conſtituatur can alis a b
                <lb/>
              lońgior, & c d breuior, ut ſit ſexquialter a b ad c d, & ſit rurſus
                <lb/>
                <figure id="id.015.01.131.1.jpg" xlink:href="015/01/131/1.jpg" number="123"/>
                <lb/>
              ſphærulæ locus e in longiore,
                <lb/>
              ſexquialter in diſtantia a b, qua
                <lb/>
              lis eſt in f a d, & erit per dicta
                <lb/>
              ab Euclide in quinto, ac ſexqui
                <lb/>
              altera c f. </s>
              <s id="id002028">Poſſemus igitur di­
                <lb/>
              cere, quod uelut ab hypomo­
                <lb/>
              chlio longiore ſpatio circuma­
                <lb/>
              gitur pondus: ita & a b c, & f.
                <lb/>
              </s>
              <s id="id002029">Sed rurſus incidimus in id, ut
                <lb/>
              maiore impetu feratur e quàm f. </s>
              <s id="id002030">Ideo ſi concedatur maiore ferri ex
                <lb/>
              e, quam ex f non ſequitur, ut celerius, aut maiore impetu. </s>
              <s id="id002031">Percutit
                <lb/>
              puer pugno quanta ui poteſt ac celerrimè, uir robuſtus lentè, & mi­
                <lb/>
              nore impetu, ſed tamen ictus longè maior eſt. </s>
              <s id="id002032">Eſt enim ictus robur
                <lb/>
              non à uelo citate ſolum, ſed maiore ex ponderis grauitate, quæ ſola
                <lb/>
              premit, urget, & frangit etiam ſine motu. </s>
              <s id="id002033">Solum ergo id reſtat du­
                <lb/>
              bium, cur ſi grauius eſt, moueatur eodem fermé impetu: nam quo
                <lb/>
              maiore impetu fertur, eo longius fertur, non tamen magis ferit, con
                <lb/>
              cutit, aut quaſſat, ſed grauitas ad hoc plus facit impetu. </s>
              <s id="id002034">Palea maxi­
                <lb/>
              mo impetu demiſſa non ferit, non ledit, & celerius deſcendit, fer­
                <lb/>
              rum ſola grauitate actum, imò etiam temperato ictu lædit graui­
                <lb/>
              ter, quaſſat, & frangit: itaque f maiore indiget quantitate pyrij pulue­
                <lb/>
              ris, quàm e: ſiquidem tertia parte ponderis ſuæ ſphæræ: at maius
                <lb/>
              eſt pondus f quam e, ergo maius pondus pulueris f quàm e, ergo
                <lb/>
              maior uehementia ictus, ſiquidem ea ſequitur, robur cauſæ mouen
                <lb/>
              tis ſimpliciter: ut concludamus longitudinem ictus ſequi propor­
                <lb/>
              tionem motoris ad motum, ſed uehementia robur motoris: nam ſi
                <lb/>
              ex portione mouet æquale pondus maiore cum impetu mouet,
                <lb/>
              quoniam maior eſt proportio: ſi minore igitur pondus maius eſt,
                <lb/>
              &, ut dixi plus facit magnitudo ponderis cum leui ictu, quàm ma­
                <lb/>
              gnitudo ictus cum leui pondere. </s>
              <s id="id002035">Quæ ergo feruntur per longio­
                <lb/>
              res canales maiore impetu feruntur, & ſocietatem
                <expan abbr="habẽt">habent</expan>
              aëris moti
                <lb/>
              per longius
                <expan abbr="ſpatiũ">ſpatium</expan>
              , ut tardius remittatur, quia longiore tempore
                <expan abbr="uĩs">uis</expan>
                <lb/>
              motus confirmata eſt, & proportio eius, quòd mouet, maior eſt ad id,
                <lb/>
              quod
                <expan abbr="mouet̃">mouetur</expan>
              , quia minus extenditur, at uerò f
                <expan abbr="motũ">motum</expan>
              minore propor­
                <lb/>
              tione
                <expan abbr="ictũ">ictum</expan>
              facit
                <expan abbr="maiorẽ">maiorem</expan>
              , quia, ut dixi,
                <expan abbr="tãto">tanto</expan>
              grauius, eſt quod ferit. </s>
              <s id="id002036">Quod
                <lb/>
                <expan abbr="autẽ">autem</expan>
              minus
                <expan abbr="extẽdatur">extendatur</expan>
              machina a b quam c d,
                <expan abbr="nũc">nunc</expan>
                <expan abbr="oſtẽdere">oſtendere</expan>
              oportet.</s>
            </p>
            <p type="margin">
              <s id="id002037">
                <margin.target id="marg408"/>
              P
                <emph type="italics"/>
              rop.
                <emph.end type="italics"/>
              103.</s>
            </p>
            <p type="main">
              <s id="id002038">Propoſitio centeſima decima ſeptima.</s>
            </p>
            <p type="main">
              <s id="id002039">In cuniculis maior eſt uis pulueris copioſioris ampliore in ſpa­
                <lb/>
              tio, quàm paucioris in minore iuxta proportionem eandem.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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