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="id001536">
                <pb pagenum="84" xlink:href="015/01/103.jpg"/>
              decliuis, tanto minus deſcendunt, quanto ſunt latiora. </s>
              <s id="id001537">Quia tamen
                <lb/>
              omnia difficiliùs deſcendunt ſphæricis, & facilius quàm in plano,
                <lb/>
              ubi ponderant niſi per dimidium grauitatis, ideò proportio hæc
                <lb/>
              conſtat ex proportione anguli deſcenſus ad totum rectum, & ma­
                <lb/>
              gnitudine ſuperficiei, qua incumbit ad pondus comparata. </s>
              <s id="id001538">Omne
                <lb/>
              enim graue, quanto grauius tam ad quietem, quàm ad motum na­
                <lb/>
              turalem potentius eſt: hoc enim perſpicuum eſt, quia quieti natu­
                <lb/>
              rali motus uiolentus, & motui naturali quies uiolenta opponitur:
                <lb/>
              quia ergo maiore ui opus eſt ad motum præter naturam, ergo ſe­
                <lb/>
              cundum naturam etiam maiore ui quieſcit. </s>
              <s id="id001539">Aſſumpſimus ergo cu­
                <lb/>
              bum, ut magis notum. </s>
              <s id="id001540">Sphæra igitur in omni decliui deſcendit,
                <lb/>
              quia ut dictum eſt, nil habet quod reſiſtat ad motum: & ipſa gra­
                <lb/>
              uior eſt in decliui, quàm in plano, quia c pun­
                <lb/>
              ctus cadit ultra e, ergo punctus contactus, &
                <lb/>
                <figure id="id.015.01.103.1.jpg" xlink:href="015/01/103/1.jpg" number="98"/>
                <lb/>
              centrum grauitatis, & centrum mundi, non ſunt
                <lb/>
              in una linea. </s>
              <s id="id001541">Si enim b c contangeretur, eſſet b c
                <lb/>
              plana. </s>
              <s id="id001542">Si uerò tangit, angulus eſt maior angulo
                <lb/>
              contactus, ergo cum neceſſarium ſit, æquidiſta­
                <lb/>
              re aliter non eſſet ſphæricum, oportet, ut eleue­
                <lb/>
              tur ex parte c, & deſcendat uerſus b, & ideò ut
                <lb/>
              continuetur motus. </s>
              <s id="id001543">Si uerò ſit in linea conta­
                <lb/>
              ctus b c f, & æquidiſtet non erit, ut dixi punctus
                <lb/>
              contactus in linea centrorum, ſed in a c, cum ſuppoſitum ſit lineam
                <lb/>
              a d eſſe lineam centrorum: maior eſt ergo portio g c e, quàm reſi­
                <lb/>
              duum, ergo deſcendet in b. </s>
              <s id="id001544">Cubus uerò non deſcendet, niſi cum di­
                <lb/>
              midium d addito, quod intercipitur inter lineam mediam, & quæ à
                <lb/>
              centro mundi ad punctum medium contactus uſque quò perueniat
                <lb/>
              ad oppoſitam partem, eam habuerit proportionem ad idem me­
                <lb/>
              dium eadem portione detracta, quem iuncta proportioni anguli
                <lb/>
              declinationis ad reſiduum recti dimidiam proportionem efficiat.
                <lb/>
              </s>
              <s id="id001545">Eademque ratio aliorum planorum. </s>
              <s id="id001546">Dico præterea quòd motus
                <lb/>
              ſphæræ, & etiam corporum rectarum ſuperficierum in deſcenſu
                <lb/>
              alius eſt æqualis, & alius inæqualis, & quaſi à latere, uelut ſi angu­
                <lb/>
              lus unus prolabatur, ac fiat circumuolutio: cum ergo facilius fiat
                <lb/>
              hoc, & maximè ſi non retineatur æqualiter, & difficile ſit in medio
                <lb/>
              retinere, propterea prolapſus hi melius
                <expan abbr="retinẽtur">retinentur</expan>
              duobus uinculis,
                <lb/>
              quàm in medio, non ſolum ob hanc æqualitatem, & complexum
                <lb/>
              meliorem, ſed
                <expan abbr="etiã">etiam</expan>
              , quod omnes motus, omnes ponderum nixus fa
                <lb/>
              ciliùs cohibentur, &
                <expan abbr="deducunt̃">deducuntur</expan>
              diuiſi in partes, <08> ſi toti contin
                <expan abbr="eant̃">eantur</expan>
              ,
                <lb/>
              aut ui
                <expan abbr="trahãtur">trahantur</expan>
              . </s>
              <s id="id001547">Et ideo uincula in rami cibus duplicia dextra, & ſini
                <lb/>
              ſtra ſcilicet in
                <expan abbr="eadẽ">eadem</expan>
              parte tamën longe ſunt meliora etiam ferreis, quæ
                <lb/>
              ſolum in medio nectantur.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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