Cardano, Girolamo, De subtilitate, 1663

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.003024">
                <pb pagenum="423" xlink:href="016/01/072.jpg"/>
              diſtantiam cognitus: quare angulus DCF,
                <lb/>
              & F rectus eſt: igitur trigonus C F D co­
                <lb/>
              gnitus ex tabula de chorda, & arcu. </s>
              <s id="s.003025">Du­
                <lb/>
              cemus igitur C E H, & erit arcus B H ex
                <lb/>
              planiſphærio illicò notus: nam hæc eſt pri­
                <lb/>
              ma operatio, & facillima illius inſtrumen­
                <lb/>
              ti, quæ illicò nobis occurrit. </s>
              <s id="s.003026">Igitur an­
                <lb/>
              gulus BCH notus: & eodem modo CFE re­
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              ctus: igitur trigonus CFE, & proportio quin­
                <lb/>
              que linearum CD, CE, CF, DE, EF, & quan­
                <lb/>
              ta ſit portio ſemicirculi EG ex tabula de chor­
                <lb/>
              da, & arcu: nam poſita DE, 60. duplicabi FG,
                <lb/>
              quam infrà docebo, & arcus illi chordæ è
                <lb/>
              directo ſcriptus, eſt totius iridis, quæ ap­
                <lb/>
              paret, id eſt, dupli G E. </s>
              <s id="s.003027">Et ita habes iam
                <lb/>
              quantitatem iridis, quamuis non videas
                <lb/>
              imum illius, id eſt, punctum G, nam vix
                <lb/>
              vnquam poteſt eſſe certus de puncto G, an
                <lb/>
              ſit ima pars iridis, propter locorum inæ­
                <lb/>
              qualitatem. </s>
              <s id="s.003028">Pòſt procedo ad L, & video
                <lb/>
              altitudinem B M per E punctum, igitur
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              angulus M E H eſt cognitus: quia ( vt de­
                <lb/>
              claratum eſt
                <emph type="italics"/>
              )
                <emph.end type="italics"/>
              vapores parum aſcendunt, ſed
                <lb/>
              longè minus nubes: vt Albertus Magnus
                <lb/>
              exiſtimat, non plus 15. ſtadiis: eſt igitur
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              ac ſi angulus HCM eſſet in centro terræ,
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              & ideò CEL cognitus, & F C E fuit co­
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              gnitus igitur C L E & totus trigonus
                <lb/>
              C E L per eandem tabulam: & quia an­
                <lb/>
              gulus F E C cognitus fuit, & LEC, erit
                <lb/>
              angulus FEL cognitus, quare cum F rectus
                <lb/>
              ſit, erit trigonus FCL cognitus: quare pro­
                <lb/>
              portio FL ad LE cognita, & iam L E ad
                <lb/>
              LC cognita fuit ex trigono ELC, igitur
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              ratio FL ad L C cognita: ſed L C eſt co­
                <lb/>
              gnita menſura, eſt enim proceſſus tuus, igi­
                <lb/>
              tur FL cognita, & etiam FC ex ipſis com­
                <lb/>
              poſita: F G autem cognita fuit & ED: ideò
                <lb/>
              cum duxeris EF in aggregatum ex E D &
                <lb/>
              D E & producti latus quadratum acce­
                <lb/>
                <arrow.to.target n="marg353"/>
                <lb/>
              peris, habebis G F ex S. ſexti, & 31.
                <lb/>
              tertij elementorum Euclidis. </s>
              <s id="s.003029">Ducta igi­
                <lb/>
              tur C F in ſe, & F G in ſe, latus ag­
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              gregati, eſt linea C G diſtantia à loco
                <lb/>
              iridis, vbi terram tangit. </s>
              <s id="s.003030">Conſpicuum
                <lb/>
              autem eſt, quòd ſi quis ſuper montem
                <lb/>
              aſcendat altiſſimum, iridem maiorem ſe­
                <lb/>
              micirculo videbit, & eò maiorem, quò
                <lb/>
              mons altior extiterit: quod enim ha­
                <lb/>
              bet ante oculos ſpatium, vacui habet
                <lb/>
              rationem Neque ignorare decet, maxi­
                <lb/>
              mam iridem non vltra quadraginta duas
                <lb/>
              partes in noſtris regionibus ſupra finito­
                <lb/>
                <arrow.to.target n="marg354"/>
                <lb/>
              rem eleuari. </s>
              <s id="s.003031">Maxima autem fit iris,
                <lb/>
              quum Sol in occaſu, vel ortu extite­
                <lb/>
              rit, & linea C F fuerit longiſſima. </s>
              <s id="s.003032">Con­
                <lb/>
              ſtat igitur etiam ſciri poſſe, quanta ſit
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              maxima iridis à nobis diſtantia, illius
                <lb/>
              ſuppoſita magnitudine, tum verò ex di­
                <lb/>
              ſtantia ipſa magnitudinem, provt defi­
                <lb/>
              nitum eſt, comparata F G linea ad C G
                <lb/>
                <arrow.to.target n="marg355"/>
                <lb/>
              iam cognitam. </s>
              <s id="s.003033">Iam verò ex reflexione
                <lb/>
              conſtat, quòd ſi ſpeculum ponatur ſub
                <lb/>
              aqua, imago Solis ab aqua reflectetur,
                <lb/>
              quæ Solem referet alia verò quæ ex a­
                <lb/>
              quæ ſuperficie coanguſtatur ob medij den­
                <lb/>
              ſitatem, à ſpeculo reflectetur, & ſy­
                <lb/>
              deris exigui imaginem refert, putant­
                <lb/>
              que homines ſydus aliquod eſſe Soli pro­
                <lb/>
              pinquum, quod eo artificio detegatur,
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              cùm ſatis conſtet imaginem eſſe Solis,
                <lb/>
              ſed ab aqua in ſpeculum refractam, quam
                <lb/>
              plerumque in deliquiis Solis homines, dum
                <lb/>
              deliquium ſpectare ſtudent, in ſpeculo vide­
                <lb/>
              re ſolent.
                <lb/>
                <arrow.to.target n="marg356"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.003034">
                <margin.target id="marg352"/>
              Quomodo di­
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              ſtantiam iri­
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              dis à noſtris
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              pedibus de­
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              præhenda
                <lb/>
              mus, & illius
                <lb/>
                <expan abbr="quãtitatem">quantitatem</expan>
              .</s>
            </p>
            <p type="margin">
              <s id="s.003035">
                <margin.target id="marg353"/>
              Quomodo iris
                <lb/>
              maxima poſ­
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              ſit videri.
                <lb/>
              </s>
              <s id="s.003036">
                <expan abbr="Quãtum">Quantum</expan>
              ſu­
                <lb/>
              pra
                <expan abbr="finitorẽ">finitorem</expan>
                <lb/>
              eleuari poſſit
                <lb/>
              iris.</s>
            </p>
            <p type="margin">
              <s id="s.003037">
                <margin.target id="marg354"/>
              in
                <lb/>
              aqua ob ſpe­
                <lb/>
              culum.</s>
            </p>
            <p type="margin">
              <s id="s.003038">
                <margin.target id="marg355"/>
              Cur dum Sol
                <lb/>
              deliquum pa­
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              titur, figura
                <lb/>
              per angulare
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              foramen ra­
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              diorum
                <expan abbr="trã-ſeuntium">tran­
                  <lb/>
                ſeuntium</expan>
              na­
                <lb/>
              uis formam
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              referat.</s>
            </p>
            <p type="margin">
              <s id="s.003039">
                <margin.target id="marg356"/>
              Cur radij
                <lb/>
              per
                <expan abbr="inciſurã">inciſuram</expan>
                <lb/>
              angularem
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              tranſeuntes,
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              in ſubiectum
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              planum ro­
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              tundam fi­
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              guram effin­
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              gant.</s>
            </p>
            <p type="main">
              <s id="s.003040">Sed cur dum Sol deliquium pati­
                <lb/>
              tur, illius imago per angulare foramen
                <lb/>
              delata, nauis formam refert? </s>
              <s id="s.003041">Mira nunc
                <lb/>
              à me ratio radiorum eſt explicanda, ſed
                <lb/>
              ſenſim ob difficultatem: nam cur pri­
                <lb/>
              mò radij per inciſuram angularem tran­
                <lb/>
              ſeuntes, in ſubiectum planum rotundam
                <lb/>
              figuram, non rectam oſtendant, & eò
                <lb/>
              rotundiorem, quò magis procul eſt pla­
                <lb/>
              num ab inciſura, demonſtrandum eſt.
                <lb/>
              </s>
              <s id="s.003042">Cauſa huius eſt duplex, quæ ſuperiùs
                <lb/>
              eſt enarrata. </s>
              <s id="s.003043">Nam lineæ quæ priùs coi­
                <lb/>
              bant, quantò longiùs procedunt, tan­
                <lb/>
              tò æquidiſtantium magis naturæ appro­
                <lb/>
              pinquant: quò fit, vt ab angulorum na­
                <lb/>
              tura abſcedentes, rotundæ magis acce­
                <lb/>
              dant. </s>
              <s id="s.003044">Hoc igitur iam in ſuperiore figu­
                <lb/>
              ra demonſtrauimus: atque eò magis,
                <lb/>
              quòd radij à toto Sole, non ab vno
                <lb/>
              puncto prodeunt. </s>
              <s id="s.003045">Altera eſt, quòd cùm
                <lb/>
              figura quò magis abſcedit, eò magis au­
                <lb/>
              getur: oculus verò obiecti illam partem
                <lb/>
              relinquit, quæ debilior eſt minima par­
                <lb/>
              te rei, quam videre poteſt, vt iam ſup­
                <lb/>
              poſuimus ab initio. </s>
              <s id="s.003046">Cùm rotundior pars,
                <lb/>
              & ampla, lumine ſuo angulos obum­
                <lb/>
              bret, neceſſe eſt, vt partes tenuiorum
                <lb/>
              virium, id eſt, angulares, priùs mo­
                <lb/>
              uere viſum deſinant mediis, in quas co­
                <lb/>
              pioſus emittitur radius: igitur figuræ il­
                <lb/>
              læ rotundæ apparebunt, & eò rotundio­
                <lb/>
              res, quò magis non ſolum ab inciſura
                <lb/>
              ea, per quam radij tranſeunt illam con­
                <lb/>
              ſtituentes abfuerint, ſed etiam ab ocu­
                <lb/>
              lis intuentium. </s>
              <s id="s.003047">Hæc igitur cum ſint cla­
                <lb/>
              riſſima, & vbi lumen ſub propria qua­
                <lb/>
              ſi quantitate excipitur, ſi quid ſit inter­
                <lb/>
              medium, cum vmbra defertur: imagi­
                <lb/>
              ne igitur Solis quaſi ſub magnitudine
                <lb/>
              redacta, quà ſubiicitur oculis inciſuræ
                <lb/>
              beneficio, cum Luna interpoſita ſit cor­
                <lb/>
              pus denſum atque opacum, neceſſe eſt
                <lb/>
              vmbram etiam Lunæ in figuræ videri.
                <lb/>
              </s>
              <s id="s.003048">Sed Lunæ vmbra rotunda eſt, quia Lu­
                <lb/>
              na ipſa eſt rotunda, & forma à qua ab­
                <lb/>
              ſcinditur rotunda: igitur cum à rotundo
                <lb/>
              rotundum ex vna parte aufertur, relin­
                <lb/>
              quatur nauiculæ ſeu vacuæ Lunæ imago,
                <lb/>
              neceſſe eſt in deliquiis formas, quæ in
                <lb/>
              planis deſcribuntur, à radiis per angula­
                <lb/>
              res inciſuras tranſeuntibus, nec angula­
                <lb/>
              res nec rotundas eſſe, ſed lunares, ſeu
                <lb/>
              ad nauiculæ formam factas. </s>
              <s id="s.003049">Verum opus
                <lb/>
              eſt diligenti conſpectu, quoniam cum
                <lb/>
              Luna ſit peruia, rotunda videbitur eiuſ­
                <lb/>
              modi figura. </s>
              <s id="s.003050">Sed clarior par lunarem for­
                <lb/>
              mam ( vt dixi ) repræſentat. </s>
            </p>
            <p type="main">
              <s id="s.003051">Hæc volui ſubiicere, quoniam hoc in
                <lb/>
              libro, vt præfatus ſum, nihil falſum, aut
                <lb/>
              dubium ſcribere volui. </s>
              <s id="s.003052">Quòd ſi cui ea, quæ
                <lb/>
              proponimus, non ſuccedant, ſeipſum igno­
                <lb/>
              rantiæ, non me accuſet mendacij. </s>
              <s id="s.003053">Sed ad
                <lb/>
              rem regredior. </s>
              <s id="s.003054">Eiuſdem deliquij tempore </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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