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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          <chap>
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              <s id="id004096">
                <pb pagenum="240" xlink:href="015/01/259.jpg"/>
                <figure id="id.015.01.259.1.jpg" xlink:href="015/01/259/1.jpg" number="258"/>
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              ior eſt a d tanto facilius remouet ęquali ſpa
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                <arrow.to.target n="marg804"/>
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              tio d uerſus e. </s>
              <s id="id004097">Et licet remoueantur ab ipſo
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              d, ſemper eadem proportio manebit, ma­
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                <arrow.to.target n="marg805"/>
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              nente eadem longitudine b d & a d, nam
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                <arrow.to.target n="marg806"/>
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              proportio d f ad d c, eſt uelut f b d ad
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              c b d, & ut d f ad d e, ita f a d ad c a d, quare
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              fb d ad c b d, uelut f a d ad c a d, quare fb d
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              ad f a d, ut c b d ad c a d, quod fuit pro­
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              poſitum.</s>
            </p>
            <p type="margin">
              <s id="id004098">
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              C
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              o
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              _{m}.</s>
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              P
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              er
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              16.
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              pri
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              mi
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              E
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              lem.
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              </s>
            </p>
            <p type="margin">
              <s id="id004100">
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              P
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              er ult. >ſex­
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              ti
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              E
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              lem.
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              </s>
            </p>
            <p type="margin">
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              P
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              er
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              11.
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              quin
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              ti
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              E
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              lem.
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              </s>
            </p>
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              P
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              er
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              16.
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              eiuſ
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              dem.
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              </s>
            </p>
            <p type="head">
              <s id="id004103">LEMMA TERTIVM.</s>
            </p>
            <p type="main">
              <s id="id004104">Grauitatem ponderis appenſi aut fluidi
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              in comparatione ad remotionem à centro
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              grauitatis inuenire.
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                <arrow.to.target n="marg807"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004105">
                <margin.target id="marg807"/>
              C
                <emph type="italics"/>
              o
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              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id004106">Nam cum d trahetur per planum ut ſuſpenſum, & non tractum </s>
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            <p type="main">
              <s id="id004107">
                <arrow.to.target n="marg808"/>
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              a d, erit dimidium ponderis appenſi, igitur ex lemmate ſecundo, pa
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              tebit proportio laboris in remouendo d à loco proprio in quan­
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              cunque partem & diſtantiam, & in quouis loco ſit appenſum.</s>
            </p>
            <p type="margin">
              <s id="id004108">
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              P
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              er
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              16.
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              hu­
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              ius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id004109">Ex hoc ſequitur, quod poterit annulus tam altè appendi, ut iuxta
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                <arrow.to.target n="marg809"/>
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              proportionem angulí & leuitatem propriam cum filo tenuiſsimo,
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              & ut fuerit latus, & poſitus è regione oris, ut ex ſermone circum­
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              agatur quaqua uerſus, & percutiat labra uaſis aqua pleni fermè, ut
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              uideatur plane reſponſa dare.</s>
            </p>
            <p type="margin">
              <s id="id004110">
                <margin.target id="marg809"/>
              C
                <emph type="italics"/>
              or
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              ^{m}. 2.</s>
            </p>
            <p type="head">
              <s id="id004111">LEMMA QVARTVM.</s>
            </p>
            <p type="main">
              <s id="id004112">Quanto magis remotum fuerit pondus ex eodem centro à recta
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              linea, tanto maiore impetu agetur, ut ultra locum medium feratur
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              non æquali, ſed producta proportione.</s>
            </p>
            <p type="main">
              <s id="id004113">Sit a b, & ut dictum eſt, non eſt ei pondus, niſi quatenus remoue­
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                <arrow.to.target n="marg810"/>
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              tur a recta, & in c ſummam habeat grauitatem, & d ſit medium b c,
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                <figure id="id.015.01.259.2.jpg" xlink:href="015/01/259/2.jpg" number="259"/>
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              dico ergo quod multo maiore impetu feretur ex cin
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              b quam ex d, nam cum c ſit ſumma grauitas, erit ſal­
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              tem dupla grauitati d, ſed d grauitas eſt penè infinita,
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              ut demonſtratum eſt in comparatione ad b, ut iuxta
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              ſitum remotionis à linea b, cum ergo proportio ſin­
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                <arrow.to.target n="marg811"/>
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              gularum partium c d ad ſingulas d b medietate b c diſtantes ſit ma­
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                <figure id="id.015.01.259.3.jpg" xlink:href="015/01/259/3.jpg" number="260"/>
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              ior dupla augendo, erit proportio c d ad d b, uelut pro­
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              poſita h k dupla g f, & h e dupla e f, e k h ad e g f quadru­
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              pla, igitur & eo maior quo acquiſitus eſt impetus ex de­
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              monſtratis, quare proportio motus & impetus ex c in
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                <arrow.to.target n="marg812"/>
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              b, eſt multo maior impetu ex d in b quadrupla pro­
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              portione.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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