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="78" xlink:href="015/01/097.jpg"/>
            <p type="margin">
              <s id="id001448">
                <margin.target id="marg301"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id001449">
                <margin.target id="marg302"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              13.
                <emph type="italics"/>
              terd
                <lb/>
              tij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001450">Propoſitio octuageſima ſeptima.</s>
            </p>
            <p type="main">
              <s id="id001451">Proportionem craſsitiei aquæ ad aërem in comparatione ad ra­
                <lb/>
              dios demonſtrare.
                <lb/>
                <arrow.to.target n="marg303"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001452">
                <margin.target id="marg303"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001453">Sit in aheno a b c d in imo e dena
                <lb/>
                <figure id="id.015.01.097.1.jpg" xlink:href="015/01/097/1.jpg" number="93"/>
                <lb/>
              rius argenteus cera affixus uel cla­
                <lb/>
              uo, quem uideat ex h impoſita aqua
                <lb/>
              clara uſque ad f, uideat ex k, igitur per
                <lb/>
              aquam deflectitur à perpendiculo
                <lb/>
              per angulum k f n, & in l, per angu­
                <lb/>
              lum l g o creſcente aqua demum in
                <lb/>
              labro m a p, & ſit e annexus, & tabu
                <lb/>
              la h k l m ſit affixa ſolo uel pondere
                <lb/>
              firma foraminibus obliquis infrà
                <lb/>
              ſpectantibus, & per a aſpicientibus extremitatem e. </s>
              <s id="id001454">Poſſumus ergo
                <lb/>
              imaginari primum, quòd omnes inclinationes ſint à perpendicu­
                <lb/>
              lari, dum exit aqua, & ita denarius uideretur, uel in ſuperficie aquæ
                <lb/>
              in directo e, uel in recta ex oculo in imo, quorum neutrum uerum
                <lb/>
              eſt. </s>
              <s id="id001455">Secundus modus eſt, ut radius delatus e a flectatur ad k uel l, &
                <lb/>
              hoc non quia in a non eſt mutatio medij. </s>
              <s id="id001456">Tertius eſt, ut linea ex ocu
                <lb/>
              lo ducta perueniat per punctum a ad ſuperficiem aquæ, & ex ea
                <lb/>
              per directum ad denarium, & tunc quia oculus iudicat ſe uidere
                <lb/>
              per rectam, ideo iudicabit ſe uidere per l a g in q, eo quod ſemper in
                <lb/>
              directo loci in quo eſt e. </s>
              <s id="id001457">At quoniam non ex qua cunque diſtantia ui­
                <lb/>
              detur e, ſed ex longinquiore loco, ubi uas fuerit humilius quod li­
                <lb/>
              neæ ad a ex oculo, quanto a fuerit humilius, tanto propius ipſi e
                <lb/>
              procedunt. </s>
              <s id="id001458">Et uerſa uice lineæ ex e ad a, quanto e eſt humilius ad
                <lb/>
              quencunque locum inflectuntur, tanto inferius
                <expan abbr="cadũt">cadunt</expan>
              . </s>
              <s id="id001459">Ergo cum fue
                <lb/>
              rint ad æquilibrium h, magis diſtabunt ab e, & ita e magis procul
                <lb/>
              uidebitur. </s>
              <s id="id001460">Cauſa ergo triplex eſt humilitas, uel altitudo uaſis: humi
                <lb/>
              litas uel altitudo aquæ: & labri uaſis altitudo. </s>
              <s id="id001461">Sed hanc relinquere
                <lb/>
              poſſumus. </s>
              <s id="id001462">Difficultas ergo experimenti etiam rectè facti eſt, quo­
                <lb/>
              niam poſito uaſe n c d ſolum, ut altitudo ſit tantum n e, procul ma­
                <lb/>
              gis uidebitur e, quàm ſi uas ſit a b c d, & totum plenum. </s>
              <s id="id001463">Vbi autem
                <lb/>
              uas fit a b c d, magis procul uidebitur e cum ſuerit totum plenum,
                <lb/>
              quam cum fuerit plena ſola pars n c d. </s>
              <s id="id001464">Sic difficile eſt conſiderare
                <lb/>
              an altitudo aquæ faciat ad uiſionem procul, cum in humiliore, ſed
                <lb/>
              diſsipari uaſe longius uideatur in pauca, quia labrum non obſtat:
                <lb/>
              in eodem autem longius in pluri aqua, quia labrum etiam non ob­
                <lb/>
              ſtat, ſed alia ratione. </s>
              <s id="id001465">Vt ergo uideamus hoc experimentum, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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