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 ...

Page concordance

< >
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id001710">
                <pb pagenum="94" xlink:href="015/01/113.jpg"/>
              cta, ſemperque prior hypomochlij locum habet, ueruntamen minus
                <lb/>
              aſſumit laboris, poſterior uerò uectis maiorem partem ſibi ponde­
                <lb/>
              ris ſeruat, uelut in ſuccula etiam iugum traiectum per plures colo­
                <lb/>
              pes facilius uertitur. </s>
              <s id="id001711">Et ſi quis dicat nónne totum pondus inſidet
                <lb/>
              primę trochleæ per trochleam, intelligo nunc ſolùm rotulam cum
                <lb/>
              ipſo axe, ſeu axiculo (ut dicunt) non autem in proprio ſignificato,
                <lb/>
              in quo etiam funis traiectus, & inſidens rotulæ, ſeu rotulis, nam
                <lb/>
              una trochlea plures continere'poteſt orbiculos, & axes. </s>
              <s id="id001712">Licet ergo
                <lb/>
              pondus inſideat primæ trochleæ, ſeu rotulæ, in eo tamen, quod tra
                <lb/>
              hitur, diuiditur', licet non æqualiter dico, præter id funis motum
                <lb/>
              intendi. </s>
              <s id="id001713">nam motus actionem auget, & ideò quanto longior, eo fa­
                <lb/>
              cilius mouet ob concuſsionem, demum quia leuis eſt rotula circa
                <lb/>
              axem, ut plus uecte poſsit.</s>
            </p>
            <p type="margin">
              <s id="id001714">
                <margin.target id="marg349"/>
              I
                <emph type="italics"/>
              n
                <emph.end type="italics"/>
              M
                <emph type="italics"/>
              echan.
                <emph.end type="italics"/>
                <lb/>
              Q
                <emph type="italics"/>
              uæſt.
                <emph.end type="italics"/>
              18.</s>
            </p>
            <p type="main">
              <s id="id001715">Propoſitio centeſima prima.</s>
            </p>
            <p type="main">
              <s id="id001716">Proportionem precij gemmarum ex tribus in eodem genere co
                <lb/>
              gnitis inuenire.
                <lb/>
                <arrow.to.target n="marg350"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001717">
                <margin.target id="marg350"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001718">Solent gemmarij uendere adamantem ponderis unius grani
                <lb/>
              uno coronato, duorum autem granorum tribus coronatis, qua­
                <lb/>
              tuor autem, gratia exempli, quadraginta coronatis, quęritur quan­
                <lb/>
              tum ualebit adamas octo granorum, quoniam ergo proportio
                <lb/>
              non ſeruatur. </s>
              <s id="id001719">Eſt enim in pondere utraque dupla, in precio autem
                <lb/>
              ex prima habetur tripla, ex ſecunda habetur proportio maior,
                <lb/>
              quàm tredecim ad unum, propterea utendum eſt proportione
                <lb/>
              propinquiori, ſi ſatis faceret. </s>
              <s id="id001720">gratia exempli, in prima ad ditione fuit
                <lb/>
              unum granum, & acquiſiuit proportionem triplam, in ſecunda fue
                <lb/>
              runt duo grana, ſi ergo acquiſiſſet ſolum ſexcuplam proportio­
                <lb/>
              nem, haberemus intentum. </s>
              <s id="id001721">Propterea in iſto caſu oportet demon­
                <lb/>
              ſtrare forma Geometrica, ſuppoſito, quòd ſit figura recta ex uno la
                <lb/>
                <figure id="id.015.01.113.1.jpg" xlink:href="015/01/113/1.jpg" number="107"/>
                <lb/>
              tere a b, ita ut angulus, uel minimus capiat b c æqualem a b, & ex
                <lb/>
              æquali b a c addito fiat b d tripla b c, & ex angulo b a e duplo b a d,
                <lb/>
              fiat b c d e quadragintupla a b, & iuxta rationem erit in infinitum.
                <lb/>
              </s>
              <s id="id001722">Siue ſit parabole, ſiue hyperbole, ſeu ſit alia coincidentium.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>