Schott, Gaspar, Mechanica hydraulico-pneumatica. Pars I. Mechanicae Hydraulico-pnevmaticae Theoriam continet. , 1657

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="051/01/173.jpg" pagenum="142"/>
              ſeat & aquæ effuſæ quantitas, & vaſis ſeu tubi evacuati ſpatium,
                <lb/>
              & aquæ deſcendentis ac effluentis velocitas eo decremento,
                <lb/>
              quod eſt inter numeros impares, verſus unitatem. </s>
              <s>Explico. </s>
              <s>Sit
                <lb/>
              vas quodcunque aquâ plenum, eius fluxus dividere debeat di­
                <lb/>
              em, aut quam cunque diei partem, in quatuor æquales partes;
                <lb/>
              ſintque in vaſe 16 v.g. menſuræ ſeu libræ aquæ, quæ dato
                <lb/>
              tempore effluant. </s>
              <s>Dico, primo tempore effluere ſeptem men­
                <lb/>
              ſuras, ſecundo quinque, tertiò tres, quarto & ultimo unam. </s>
            </p>
            <p type="main">
              <s>Dico iterum, ſi tota vaſis altitudo ab infima ad ſupremam
                <lb/>
              aquæ ſuperficiem dividatur in 16 æquales partes, aquam in pri­
                <lb/>
              mo tempore deſcendere ad 7 ſpatia, in ſecundo ad
                <expan abbr="quinq;">quinque</expan>
              in ter­
                <lb/>
              tio ad tria, in quarto ad unum. </s>
              <s>Dico tandem, aquam in pri­
                <lb/>
              ma hora deſcendere
                <expan abbr="atq;">atque</expan>
              effluere ut ſeptem, in ſecunda ut quin­
                <lb/>
              que, in tertia ut tria, in quarta ut unum. </s>
              <s>Sequitur ex dictis
                <lb/>
              ſuprà Propoſitione 8, 9, & 10, quas vide. </s>
              <s>Eadem ratio in
                <lb/>
              omnibus alijs eſt. </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              Corollarium.
                <emph.end type="center"/>
                <lb/>
                <arrow.to.target n="marg248"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg248"/>
                <emph type="italics"/>
              Vas parare,
                <lb/>
              cuius flux
                <emph type="sup"/>
              9
                <emph.end type="sup"/>
                <lb/>
              dividat da­
                <lb/>
              tum tempus
                <lb/>
              in partes
                <lb/>
              æquales.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>EX his patet, quomodo parandum ſit vas, cuius fluxus dato
                <lb/>
              tempore durans dividat illud tempus in partes æquales. </s>
              <s>Sit
                <lb/>
              enim vas, cuius fluxus duret per ſpatium duodecim horarum, &
                <lb/>
              hoc ſpatium temporis ſit dividendum, beneficio fluxus aquæ, in
                <lb/>
              12 æquales partes ſeu horas. Duc 12. in ſeipſa, & produces 144.
                <lb/>
              Deinde divide vaſis altitudinem à ſuprema ad infimam aquæ ſu­
                <lb/>
              perficiem, in 144 partes ſeu ſpatia æqualia, & inferiùs prope
                <lb/>
              fundum vaſis incipiendo, deputa ultimæ horæ ex duodecim
                <expan abbr="vnũ">vnum</expan>
                <lb/>
              ſpatiolum, penultimæ tria, ante penultimæ quinque, & ſic ul­
                <lb/>
              teriùs progredere ſecun dùm ſeriem ſeu progreſſionem numero­
                <lb/>
              rum
                <expan abbr="impatiũ">impatium</expan>
              , prout apparet in numeris lateri dextro CD ſequen­
                <lb/>
              tis figuræ appoſitis. </s>
              <s>His pręſtitis, diviſum erit vas in ſpatia inęqua­
                <lb/>
              lia, quę ſingulis æqualibus temporibus, nempe horis, evacuantur,
                <lb/>
              videbiſque aquam in prima hora deſcendere à ſpatio ultimo ſeu
                <lb/>
              144, uſque ad ſpatium 121; in ſecunda hora uſque ad ſpatium
                <lb/>
              100; in tertia uſque ad 81; & ſic porrò uſque ad finem; prout </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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