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="id001875">
                <pb pagenum="103" xlink:href="015/01/122.jpg"/>
              mouebitur in h, quam in d, uelut ſit proportio f g ad a b dupla, ut
                <lb/>
              ergo æqualiter moueantur, ſi ſit dupla ſexquiquarta in d cum lan­
                <lb/>
              ce ad e uacuam, erit in h ſexquialtera, & mouebit æquali tempore.
                <lb/>
              </s>
              <s id="id001876">Ergo iuxta hoc fient libræ, quæ examinabunt decimam, & uigeſi­
                <lb/>
              mam partem grani, quod eſt neceſſarium in pretioſis rebus, & me­
                <lb/>
              dicamentis potentibus, & longè magis in mechanicis experimen­
                <lb/>
              tis, & maximè quæ ad demonſtrationem pertinent magnitudinis
                <lb/>
              ſuperficierum, & conſtat res in tribus, in longitudine, f g iungi, in le
                <lb/>
              uitate materiæ illius, & lancium, nam tanto maior redditur propor
                <lb/>
              tio ponderis exigui, & in firmitate iugi ac rectitudine. </s>
              <s id="id001877">ideò debet
                <lb/>
              fieri ex chalybe purgato, durato ac tenuiſsimo, natura que leui, & ut c
                <lb/>
              ſit in medio, & mobilis f g.</s>
            </p>
            <p type="main">
              <s id="id001878">Conſiderandum eſt demum an f l & g m ſint grauiores f h, &
                <lb/>
              g k. </s>
              <s id="id001879">Vt enim grauiores extiterint minus facilè mouentur. </s>
              <s id="id001880">Viden­
                <lb/>
              tur autem mihi, qui de his conſcripſerunt perperam contempſiſſe
                <lb/>
              hoc, conſtat enim, quòd dum l deſcendit, remouetur a b n c tru­
                <lb/>
              tina, & m, quæ aſcendit contra appropinquat. </s>
              <s id="id001881">Videtur autem hoc
                <lb/>
              bifariam contra naturam: nam ut diximus pondus applicat ſe ad
                <lb/>
              rectam n c, quia uerſus centrum, & etiam quia facit angulum ob­
                <lb/>
              tuſum, cum deberet, ut ab initio ſaltem conſtituere cum iugo re­
                <lb/>
              ctum. </s>
              <s id="id001882">Et de m nihil mirum eſt, cum acutum, ut ſe ad lineam, quæ ad
                <lb/>
              centrum retrahat. </s>
              <s id="id001883">Huiuſmodi præterijſſe Ariſtotelem, demiror,
                <lb/>
              quæ nimis fuerunt in conſpicuo, ut dubitem ne non ſuus ſit ille li­
                <lb/>
              ber, qui eius penè nihil ſapiat præter obſcuritatem. </s>
              <s id="id001884">Tentan­
                <lb/>
              dum eſt igitur horum cauſas aſsignare. </s>
              <s id="id001885">nam quæ huiuſmodi po­
                <lb/>
              teſt eſſe doctrina niſi perfecta fuerit, in omnibus etenim neceſſe eſt
                <lb/>
              aut omnia ſcire, aut ignorare. </s>
              <s id="id001886">In hoc igitur dico, quod h f, ſeu l f,
                <lb/>
              ſemper æquidiſtant n c trutinæ, ergo cum angulus f c n in clina­
                <lb/>
              to iugo fiat obtuſus deſcendente pondere, & n c g aſcendente pon­
                <lb/>
              dere fiat acutus, ergo angulus l f c tantundem fiet obtuſior, & m g c
                <lb/>
              acutior, quanto anguli ad c tales ſunt. </s>
              <s id="id001887">Et cauſa eſt quia n c ratio­
                <lb/>
              ne ponderis eſt directa ad centrum, ergo oportet, ut pondera l, uel
                <lb/>
              h, & m, uel k, ſi debent tendere ad centrum, ut f l, & g m æquidi­
                <lb/>
              ſtent n c, niſi quantum eſt pro diſtantia f, à puncto c, & g a b eodem,
                <lb/>
              quæ comparata ad
                <expan abbr="centrũ">centrum</expan>
              terrę, ſeu mundi, eſt inſenſibilis omnino.
                <lb/>
              </s>
              <s id="id001888">Circa hæc
                <expan abbr="notandũ">notandum</expan>
              iſtud mirabile ſcilicet, quod ratio motus, quan­
                <lb/>
              tumuis exigua ſufficit ad motus
                <expan abbr="modũ">modum</expan>
              , licet uelo citas
                <expan abbr="pẽdeat">pendeat</expan>
              ex gra
                <lb/>
              uitate, & alijs. </s>
              <s id="id001889">Et quae graue, quod expers eſt ſenſus, debeat ſequi ratio
                <lb/>
              nem Geometricam uix ſapientibus
                <expan abbr="cognitã">cognitam</expan>
              , cauſa tamen una eſt, &
                <lb/>
              perſpicua:
                <expan abbr="">nam</expan>
              omne graue eſt in linea à centro
                <expan abbr="mũdi">mundi</expan>
              : ſi
                <expan abbr="aũt">aut</expan>
              medium
                <lb/>
              grauis ſit extra
                <expan abbr="lineã">lineam</expan>
              , uertitur ad illam, quę eſt in eo, nam
                <expan abbr="centrũ">centrum</expan>
              ſem</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>