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="id001889">
                <pb pagenum="104" xlink:href="015/01/123.jpg"/>
              per eſt in
                <expan abbr="eadẽ">eadem</expan>
              . </s>
              <s id="id001890">Ergo ſola inclinatio ad hoc ut
                <expan abbr="mediũ">medium</expan>
              grauis ſit in li­
                <lb/>
              nea
                <expan abbr="centrorũ">centrorum</expan>
              grauitatis & terræ, ſufficit. </s>
              <s id="id001891">Eſt ergo principium in ſe i­
                <lb/>
              pſo. </s>
              <s id="id001892">In appenſis ſimiliter. </s>
              <s id="id001893">Trutina enim, & finis iugi, & grauis
                <expan abbr="cen­trũ">cen­
                  <lb/>
                trum</expan>
              mundi
                <expan abbr="centrũ">centrum</expan>
              ſunt in
                <expan abbr="eadẽ">eadem</expan>
              linea, ut eſſe poſſunt, cum exigua illa
                <lb/>
              & ſola diſtantia intercedat. </s>
              <s id="id001894">& hoc eſt primum. </s>
              <s id="id001895">Quia ergo
                <expan abbr="iugũ">iugum</expan>
              eſt
                <lb/>
              ex materia ſolida, mouetur ratione, quæ dicta eſt, lances autem
                <lb/>
              oportet cum filis appenſi ſint, ut puncta f & h, uel l, & g k, uel g m
                <lb/>
              ſint in una linea cum centro terræ. </s>
              <s id="id001896">Et quia l magis diſtat a b f quam
                <lb/>
              h, & m a g magis, quam k, & oportet faciant eandem inclinatio­
                <lb/>
              nem, quia anguli trutinæ cum iugó ſunt ijdem, & linea cl eſt ma­
                <lb/>
              ior c h, & c m, quàm c k in quouis ſitu, ergo ſpatium, quod ambitur,
                <lb/>
              eſt maius ergo per d e monſtrata ſuperius l eſt grauius h etiam
                <lb/>
              præter uinculorum additionem, & m grauius k. </s>
              <s id="id001897">Quanto igi­
                <lb/>
              tur longiores ſunt funiculi à libræ extremitate ſeu iugi, tanto gra­
                <lb/>
              uius redditur pondus, quod tamen multi putant eſſe falſum: nec
                <lb/>
              aliquid referre, quòd ſit longum, aut breue ſuſtentaculum.</s>
            </p>
            <p type="main">
              <s id="id001898">Propoſitio centeſima decima.</s>
            </p>
            <p type="main">
              <s id="id001899">Si duæ ſphæræ ex eadem materia deſcendant in
                <expan abbr="aẽ">ae</expan>
                <lb/>
              re eodem temporis momento ad planum ueniunt.
                <lb/>
                <figure id="id.015.01.123.1.jpg" xlink:href="015/01/123/1.jpg" number="118"/>
                <lb/>
                <arrow.to.target n="marg391"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001900">
                <margin.target id="marg391"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001901">Supponitur quod ex eodem loco. </s>
              <s id="id001902">Sermo enim
                <lb/>
              abſurda ſub interpretatione nunquam niſi ab inui­
                <lb/>
              dioſo, uel imperito intelligi debet. </s>
              <s id="id001903">Sit ergo a tripla
                <lb/>
              ad b, ſphærula ad ſphærulam ex plumbo ambæ fer­
                <lb/>
              ro uel lapide eiuſdem generis, dico, quòd inæquali
                <lb/>
              tempore peruenient ad planum c d. </s>
              <s id="id001904">Nam a propor­
                <lb/>
              tionem habet ad b, ut uiginti ſeptem ad unum. </s>
              <s id="id001905">pro­
                <lb/>
              portio autem ſpatij a ad ſpatium b nonupla eſt, &
                <lb/>
              proportio denſitatis aëris ad aërem eſt tripla, propterea quod den­
                <lb/>
              ſitas illa multiplicatur propter impetus magnitudinem. </s>
              <s id="id001906">nam ſi ro­
                <lb/>
              bur, ut decem percutiat baculo lato, ut quatuor ictus erit maior du­
                <lb/>
              plo, quàm ſit robur, ut quinque percutiat baculo, ut duo: propter
                <lb/>
              denſitatem ergo maiorem aëris in a, quam in b: & quoniam ſi ſub
                <lb/>
              maiore impetu mouetur
                <expan abbr="aẽr">aer</expan>
              ſub a, quam ſub b, igitur proportio
                <lb/>
              erit comparanda longitudini à centro a ad longitudinem a centro
                <lb/>
              b, quæ eſt tripla. </s>
              <s id="id001907">Si ergo ſubtripla eſt ratio motus b ad a, quod
                <lb/>
              ad medium attinet, tripla autem propter uelocitatem diſceſſus aë­
                <lb/>
              ris à medio grauitatis, quod eſt in ſuperficie e regione centri graui­
                <lb/>
              tatis in linea ad centrum mundi, ut dictum eſt in præcedenti: mani­
                <lb/>
              feſtum eſt, quod a, & b inæquali tempore peruenient ad ſubie­
                <lb/>
              ctum planum, & æquidiſtans centris eorum. </s>
              <s id="id001908">Similiter & in aqua: </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>