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>
            <pb pagenum="82" xlink:href="015/01/101.jpg"/>
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              <s id="id001502">
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            <p type="margin">
              <s id="id001503">
                <margin.target id="marg308"/>
              C
                <emph type="italics"/>
              or
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              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001504">Ex hoc ſequitur, quod homo ſi moueretur uelo citate motus ro­
                <lb/>
              tæ moletrinæ in ſex ebdomadibus perueniret ad ſydus Lunæ, nam
                <lb/>
              rotarum earum, quibus ferrum acuitur ſemidimetiens communi­
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              ter eſt bes unius paſſus, ideò dimetiens paſſus cum triente: ambi­
                <lb/>
              tus ergo quatuor paſſus, & xxi pars, colligamus nunc integra, in
                <lb/>
              uno ictu pulſus circumagitur decies, id eſt paſſus xl, in hora ſunt
                <lb/>
              <23> pulſationes: in hora igitur ſpatium pertranſitum eſt cxl paſſuum
                <lb/>
              in M. horis, ergo erunt clx M. paſſuum addita parte xxi, erunt clxviij
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              M. paſſuum, & tantum diſtat luna à terra: & M. horæ ſunt dies penè
                <lb/>
              xlij, ebdomadæ ſcilicet ſex.</s>
            </p>
            <p type="main">
              <s id="id001505">Propoſitio octuageſima nona.</s>
            </p>
            <p type="main">
              <s id="id001506">Proportionem denſitatis aquæ ad aërem per pondera inuenire.</s>
            </p>
            <p type="main">
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              </s>
            </p>
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              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001509">Contingit hoc multis modis: primum acceptis duabus ſphæru­
                <lb/>
              lis æqualibus ex cryſtali ſubſtantia unaque demiſſa ab altiſsima turri,
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              & menſurato ictu per inſtrumentum præcedens, & ſub totidem
                <lb/>
              momentis alia demiſſa in aquam, in de ſub eodem tempore dimen­
                <lb/>
              ſa altitudine, erit proportio ſpatij ad ſpatium, ut denſitatis aquæ, ad
                <lb/>
              denſitatem aëris. </s>
              <s id="id001510">Item emiſſa ſphærula per inſtrumentum in aërem,
                <lb/>
              in de in aquam: & ſumpta proportione. </s>
              <s id="id001511">Et uidimus ſcorpionem,
                <lb/>
              qui
                <expan abbr="ſphærulã">ſphærulam</expan>
              creteam emittebat pedibus lxx, & in aqua per unum
                <lb/>
              & dimidium adeò, ut proportio fuerit, ut quinquaginta ad unum:
                <lb/>
              ideò eſt fallax experimentum in uiolento motu: nam cum emitte­
                <lb/>
              batur in aquam erat propè, & ob id in ſummo robore: cùm in aë­
                <lb/>
              rem, emittitur ſenſim uis. </s>
              <s id="id001512">De hoc ergo loquar.</s>
            </p>
            <p type="main">
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              </s>
            </p>
            <p type="margin">
              <s id="id001514">
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              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001515">Et erumpentia ob id magis quàm è terra, et minus quàm ex aëre:
                <lb/>
              diuiditur enim aqua cum graue petit fundum, & aqua feruet: & eſt
                <lb/>
              mirabilius, quàm utile.</s>
            </p>
            <p type="main">
              <s id="id001516">Propoſitio nonageſima.</s>
            </p>
            <p type="main">
              <s id="id001517">Rationem impetus uiolenti extra miſsi ponderis ad æqualita­
                <lb/>
              tem reducere.</s>
            </p>
            <p type="main">
              <s id="id001518">
                <arrow.to.target n="marg311"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001519">
                <margin.target id="marg311"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001520">Sit uiolentum a quod moueatur per b c d e, e ſpatium, & quia
                <lb/>
              uiolentum contrà nititur naturali, cadat ergo in planum in e: ſunt
                <lb/>
              ergo tria conſideran da, primum quod, ut dixi aliâs, motus uiolen­
                <lb/>
              tus pro certa diſtantia augetur, & cauſam ibi reddidi, ut potè uſque
                <lb/>
              ad c, ſed hoc eſſet difficile cognitu. </s>
              <s id="id001521">Secundum, quod ubi incipit de­
                <lb/>
              creſcere, ſemper magis ac magis decreſcit propter naturalem ni­
                <lb/>
              xum contra operantem. </s>
              <s id="id001522">Tertium quod ubi deſcendere incipit, ibi
                <lb/>
              eſt æqualis uis uiolentum motum agens cum naturali. </s>
              <s id="id001523">Certum eſt
                <lb/>
              etiam quod motus æqualis intelligitur erecta ad perpendiculum
                <lb/>
              e f, donec occurrat a d: & diuiſa tota b f per tempus, locus ergo, in
                <lb/>
              quo mouetur per tantum ſpatium, dicitur locus motus æqualis: </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>