Cardano, Girolamo, De subtilitate, 1663

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.003149">
                <pb pagenum="427" xlink:href="016/01/076.jpg"/>
              ſed exquiſitiſſima cylyndrica connexa. </s>
              <s id="s.003150">Con­
                <lb/>
              ſeruatur rima feneſtræ è directo alicuius ta­
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              bulæ pictæ, ſic vt è loco quopiam cubiculi
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              per rimam poſſit inſpici, eo verò in loco cy­
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              lindricum ſpeculum conuexum ſtatuatur ſu­
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              per tripodem ad planum perpendiculare: in­
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              de oculum ſic colloca, vt è ſpeculo videre
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              poſſis tabulam quam extrà poſuiſti: eam
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              igitur imaginem vt in aere pendentem
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              videbis inter ſpeculum atque feneſtræ ri­
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              mam. </s>
            </p>
            <p type="main">
              <s id="s.003151">Quod ad formam autem attinet: caua ma­
                <lb/>
              iores oſtendunt rerum imagines, rotunda
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              multò minore, plana æqualia paulò, iuxta
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              verò magnitudinem & ſitum magna maio­
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              res, & prope parua autem procul. </s>
              <s id="s.003152">Ergo ro­
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              tunda prope ſimilia ſunt paruis planis, quo­
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              niam reflexio exigua ex portione in eis fit.
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              </s>
              <s id="s.003153">Concurſus etiam radiorum cum ea, quæ ad
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              centrum tendit propinquior eſt, quapropter
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              baſis minor. </s>
              <s id="s.003154">Procul ergo grandeſcunt, etiam
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              vltra ipſius rei viſæ magnitudinem. </s>
              <s id="s.003155">Simili­
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              ter & ob rei ſitum obliquum ſpeculi com­
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              paratione, vt in ſecundo optices pater meus
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              adnotauit.
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                <arrow.to.target n="marg368"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.003156">
                <margin.target id="marg368"/>
                <expan abbr="ſpeculũ">ſpeculum</expan>
              quod
                <lb/>
              repræſentat
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              homines vo­
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              lantes.</s>
            </p>
            <p type="main">
              <s id="s.003157">Quòd ſi homines volantes videri in ſpe­
                <lb/>
              culo libeat, vt volare videantur, quatuor ſunt
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              neceſſaria, vt moueantur, vt brachia agitent:
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              hæc duo præſtabit homo, quem volantem
                <lb/>
              videre deſideras, ſeu ipſius fueris, ſeu alij
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              ſint, quanquam & motum aſſimilare poſſis
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              ſpeculi motu, ſed non leue eſt hoc incommo­
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              dum. </s>
              <s id="s.003158">Tertium eſt, vt in ſublimi pendeat, ne
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              terræ hærere videantur: quartum, vt pedes
                <lb/>
              velut in volantibus auibus cum capite &
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              brachiis æquidiſtent pauimento: hæc igi­
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              tur duo ſpeculum præſtabit pulcherrimè.
                <lb/>
              </s>
              <s id="s.003159">Duo igitur tigna æqualia ad angulum re­
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              ctum iuncta, vt rectus angulus in ſublimi
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              ſit, ac leuia, modum gnominis compones:
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              iuxta angulum intus duo magna ſpecula pla­
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              na ex aduerſo æquali altitudine conſtitues,
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              quæ pendula eſſe ſatis intelligis. </s>
              <s id="s.003160">Cùm ita­
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              que ab his tantùm abſcedis, vt in altero cal­
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              caneum ad vnguem aſſequaris, ex motu ſe­
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              cundum rectam lineam, & brachiorum ia­
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              ctatione, volantem inſpicere videberis.
                <arrow.to.target n="marg369"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.003161">
                <margin.target id="marg369"/>
              Vt imaginem
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              tuam ſimul
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              accedentem
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              & receden­
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              tem videas.</s>
            </p>
            <p type="main">
              <s id="s.003162">Eiſdem rationibus quas diximus, ſi ſpecu­
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              la duo ſe contangentia, atque in vna ſuper­
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              ficie plana, ita collocaueris, vt altero ad te
                <lb/>
              accedente, reliquam abſcedat: quod fiet ſi ſu­
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              per ttabe rectè, & ad perpendiculum collo­
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              catis, vinculum quod inuolutum ſit ſenſim
                <lb/>
              explicetur: videbis imaginem tuam acceden­
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              tem in altero, in reliquo retrocedentem.
                <arrow.to.target n="marg370"/>
                <lb/>
              Quòd ſi dorſum tuum videre velis, ſpeculis
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              duobus plane id commodè aſſequêris, quæ
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              quantò maiori fuerint, eò erunt etiam me­
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              liora. </s>
              <s id="s.003163">Primùm retrò collocabis medio ſitu
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              inter ſupinum & erectum, alterum, ſublimio­
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              re loco quàm tu ſis, medio ſitu inter pronum
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              & erectum ante oculos tuos, optiméque
                <lb/>
              quæcunque in tergo habes videre poteris.
                <lb/>
              </s>
              <s id="s.003164">Memineris etiam ſi (gratia exempli annu­
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              lum ex aduerſo ſpeculo collocaueris, annu­
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              lus verò & ipſe ſpeculum ſit, velut incluſo
                <lb/>
              ſaphiro, videbis in ſpeculo imaginem annu­
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              li, in cuius gemma imago tua apparebit: hoc
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              autem ex multiplici reflectione continget.
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              </s>
              <s id="s.003165">Idem in duobus continget ſpeculis, & mul­
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              tò maiore miraculo in tribus. </s>
              <s id="s.003166">At ſi profun­
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              da obſcuráque, vt vterum, gulam, cubiculum
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              tenebroſum videre propoſitum ſit, ampho­
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              ram magnam aqua plenam vitream colloca
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              è directo loci, & lumen poſt amphoram, vt
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                <arrow.to.target n="marg371"/>
                <lb/>
              amphora media ſit in recta linea inter lu­
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              men ac locum quem videre deſideras: inde
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              omni alio ſublato lumine, oculum tuum col­
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              loca vbi amphoræ lumen non impedias, lo­
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              cum tamen inſpicere poſſis, videbíſque cun­
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              cta vt in luce clara. </s>
              <s id="s.003167">Quòd ſi ſub faſtigio do­
                <lb/>
              mus loca tuto illuminare velis, nec à parie­
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              tibus excipere lumen ipſum liceat, implu­
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                <figure id="id.016.01.076.1.jpg" xlink:href="016/01/076/1.jpg" number="51"/>
                <lb/>
              uium in tecto è regione oculi conſtitue, &
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              locum clatrata obducito, tectúmque ipſum
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              accliue vſque ad medium tegminis impluuij
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              deducito: ita neque fur, neque imber ingre­
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              di poterit. </s>
            </p>
            <p type="margin">
              <s id="s.003168">
                <margin.target id="marg370"/>
              Quomodo
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              dorſum tuum
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              ſpectare poſ­
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              ſis.</s>
            </p>
            <p type="margin">
              <s id="s.003169">
                <margin.target id="marg371"/>
              Quæ contin­
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              gant ex duo­
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              bus ſpeculis.
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              </s>
              <s id="s.003170">Quomodo
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                <expan abbr="verũ">verum</expan>
              & gu­
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              lam vide­
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              mus.</s>
            </p>
            <p type="main">
              <s id="s.003171">Sunt & qui ſpecula finxerunt tot facies
                <lb/>
                <arrow.to.target n="marg372"/>
                <lb/>
              quot horæ diei ſunt oſtendentia, cuius rei
                <lb/>
              teſtis eſt Ptolemæus. </s>
              <s id="s.003172">Sed & pars imaginis
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              partem cuiuſque horæ declarabat. </s>
              <s id="s.003173">Sit igitur
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              quadrilaterum, rectangulum, tertia parte
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              longius quàm latum, diuiſum autem in duo­
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              decim quadrata æqualia ABCDEFGHK
                <lb/>
              LM & N: conſtituatur
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              ſpeculum iuxta eandem
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              rationem diuiſum toti­
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              dem interuallis, atque
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              ſuper eo velamen altius
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              in A quàm B, & in B
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              quàm C, & in C quam
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              D, ita vt D ſpeculum
                <lb/>
              tangat. </s>
              <s id="s.003174">Eadem ſit pro­
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              portio E ad F, & K ad L,
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                <figure id="id.016.01.076.2.jpg" xlink:href="016/01/076/2.jpg" number="52"/>
                <lb/>
              quæ A ad B, & F ad G, & L ad M, quæ B ad
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              C, atque G ad H, & M ad N, quæ eſt C ad
                <lb/>
              D. </s>
              <s id="s.003175">Sint verò velaminis partes ita diſtinctæ,
                <lb/>
              vt altiores poſſint ſenſim transferri ſuper
                <lb/>
              humiliores, ita vt primò ex A in B, inde
                <lb/>
              vtraque velaminis pars ex B in C, inde par­
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              tes omnes in D: quò fit vt cùm grauius fiat
                <lb/>
              pondus, eò breuiore rota circumferatur, vt
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              tempora tranſlationum fiant æqualia. </s>
              <s id="s.003176">Ad­
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              dantur igitur horologiorum rotæ ſingulis
                <lb/>
              tetramorphis, vt ſint tres rotæ, atque in ſin­
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              gulis diſcrimina æquationum, velut in Pla­
                <lb/>
              netis, vt motus ſit eò velocior propter ro­
                <lb/>
              tam breuiorem, quò pondus magis augetur:
                <lb/>
              ita fiet vt cùm poſt primam tetramorphim
                <lb/>
              ſecunda, inde tertia detegatur, atque in ſin­
                <lb/>
              gulis facies ſingulæ, vt pro horarum nume­
                <lb/>
              ro ac partium, facies ac partes facierum in
                <lb/>
              ſpeculo videantur. </s>
              <s id="s.003177">Hæc autem omnia facilè
                <lb/>
              in horologiis horarum inæqualium, quibus
                <lb/>
              Romani vtebantur, perſpiciuntur. </s>
              <s id="s.003178">Cùm
                <lb/>
              enim rota quæ voluitur, axem habuerit ſu­
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              per quo mouetur extra centrum eius, tanto
                <lb/>
              celerius mouebitur in parte propinqua axi,
                <lb/>
              quò axis ab eadem parte à centro rotæ ma­
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              gis remouebitur. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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