Cardano, Girolamo, De subtilitate, 1663

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    <archimedes>
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        <body>
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            <p type="main">
              <s id="s.003091">
                <pb pagenum="425" xlink:href="016/01/074.jpg"/>
              tamen ad angulos æquales, vt à plano ſpe­
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              culo non directè Soli expoſito: nam nec
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              hanc oculus ſuſtinet. </s>
              <s id="s.003092">Quarta reddit imagi­
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              nem ſed ſuſtineri poteſt, cùm radij ad æqua­
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              lem angulum reflectuntur, ſed ſparguntur
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              vt in cauis ſpeculis extra pyramidem vtram­
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              que, & quæ à centro ſpeculi ad ſpeculum,
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              & à centro ſpeculi ad rem viſam: vt ex­
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              tra pyramidem FKL, & FAC. </s>
              <s id="s.003093">Quinta eſt,
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              cùm à corpore non polito reflectuntur ra­
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              dij, ad viſum inutiles: non ad calorem:
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              nam & hi perpendiculares ( vt dixi) reflexi
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              ingeminant caliditatem propter coitionem
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              ſed imaginem haud reddunt. </s>
              <s id="s.003094">Cauſæ autem
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              roboris radiorum per accidens dicuntur,
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              magnitudo & propinquitas lucidi, & quòd
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              radius ille ex centro lucidi proficiſcatur: tum
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              ſynceritas medij, & radiorum ipſorum. </s>
              <s id="s.003095">His
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              cauſis accidit, vt lumen aliud alio euadat
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              validius: vnde reflexionem ſolarium radio­
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              rum ex Luna & ſyderibus ob diſtantiam
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              quanquam puriorem toleramus, à cryſtal­
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              lo, & aqua oculis ferre non poſſumus. </s>
            </p>
            <p type="margin">
              <s id="s.003096">
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              Cur ſpecula
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              caua, cum
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              vbique
                <expan abbr="refle-ctãt">refle­
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                ctant</expan>
              radios,
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              non tamen
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              vbique red­
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              dunt imagi­
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              nem.
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              </s>
              <s id="s.003097">Cauſæ robo­
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              ris radio­
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              rum per ſe,
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              & per acci­
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              dens.</s>
            </p>
            <p type="main">
              <s id="s.003098">Verùm cùm duo videantur eſſe modi ac­
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              cendendi ignem ex ſpeculo: primus, vt om­
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              nes radij in centrum ſpeculi incidentes col­
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              ligantur in vno puncto per reflexionem,
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              qui fit ( vt dictum eſt ) cum cauo ſpeculo
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              ſphærico. </s>
              <s id="s.003099">Secundus eſt, vt omnes æquidi­
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              ſtantes colligantur, qui è ſole prodeunt, in
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              punctum vnum, qui etiam fit parabole: ex­
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              tare de hoc libros Archimedis, vbi docet
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              comburentia ſpecula parabole conſtare,
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              Franciſcum Maurolycum Meſſanenſem ſcri­
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              pſiſſe, apud Conradum Geſnerum inuenio.
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              </s>
              <s id="s.003100">Res autem ſic ſe habet. </s>
              <s id="s.003101">Cùm ſuperficies
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              conum rectum ſecat, & ſuperficiei deme­
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              tiens æquidiſtat lateri trigoni inſcripti ſu­
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              perficiei conum per axem ex vertice ſecantis
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              ſuperficies illa parabole dicitur, quæ ſit
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              A B C. </s>
              <s id="s.003102">Cuius rectà à vertice B diuidens
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              AC rectam ſubiectam æquis lateribus, cur­
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              uis BA & BC, vocetur
                <expan abbr="dimetiẽs">dimetiens</expan>
              BD. AC au­
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              tem diameter, baſis coni K, medium B D:
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              dico HKL talem ſemper habere portionem
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                <figure id="id.016.01.074.1.jpg" xlink:href="016/01/074/1.jpg" number="47"/>
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              ad perpendicularem quamcunque ex latere
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              ſuper dimetiens venientem, qualis eſt ip­
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              ſius perpendicularis ad partem dimetientis
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              inter verticem, & perpendicularem inter­
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              ceptam. </s>
              <s id="s.003103">Velut ſit perpendicularis F G, ta­
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              lem habebit igitur H L proportionem ad
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              GF qualis FG ad GF, & vocabitur tunc HL
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              latus rectum, & omnes æquidiſtantes BD,
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              ſeu radij reflectentur in K. </s>
              <s id="s.003104">Eſt verò HL ſem­
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              per quadrupla BK.
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                <arrow.to.target n="marg362"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.003105">
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              De ſpeculo,
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              quod combu­
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              rit naues
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              procul ve­
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              nientes 3.de
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              emperamen
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              tis, cap.3.</s>
            </p>
            <p type="main">
              <s id="s.003106">Sed ſi propoſitum ſit facere ſpeculum,
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              quod procul comburat, qualem feciſſe Ga­
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              lenus narrat Archimedem, qui hoſtium
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              triremes deuſſerit: manifeſtum eſt ſpecula
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              ſeu à parabole ſumpta fuerint, ſeu à circu­
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              lo ac ſphæra, maxima eſſe oportere, id
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              eſt, proportiones maximarum ſphærarum,
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              aut conorum maximorum, parabolis par­
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              tem non tamen maximam. </s>
              <s id="s.003107">Velut ſi ad mil­
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              le paſſus extendere ignem libeat, circulum
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              deſcribemus, cuius dimetiens ſit duo millia
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              paſſuum, huius tantam aſſumemus portio­
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              nem, vt rotunditas non lateat, partem ſci­
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              licet ſexageſimam, cui dimetientem pro al­
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              titudine in termino vno adiiciemus, & di­
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              metiente fixo circumagemus circuli par­
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              tem, quæ nobis portionem ſphæræ deſcri­
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              bet: quam cùm expoliuerimus, ignem Soli
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              expoſita procul & validiſſimum ad paſſus
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              M. accendet, Nunc autem non adeò vtilis, ob
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                <figure id="id.016.01.074.2.jpg" xlink:href="016/01/074/2.jpg" number="48"/>
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                <figure id="id.016.01.074.3.jpg" xlink:href="016/01/074/3.jpg" number="49"/>
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              bellicas machinas: olim verò tutiſſima. </s>
              <s id="s.003108">Quæ
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              verò à parabole procedit, conflagratio
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              potentior eſt. </s>
              <s id="s.003109">Ea autem ſic fit. </s>
              <s id="s.003110">Sit locus
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              qui comburi debet mille paſſibus diſtans.
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              </s>
              <s id="s.003111">Facio B K paſſuum mille, cui rectam co­
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              æqualem adiicio K D, ipſi autem B D
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              æqualem ad perpendiculum facio A B, &
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              ex altera parte B C æqualem B A, & du­
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              ctis D A & D C, facio D centrum ba­
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              ſis coni, & A D axem, nam angulus ADC
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              rectus eſt, & circumuoluo AC, vt fiat co­
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              nus, & deſcribetur circulus à linea D C
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              tanquam ſemidiametro pro coni baſi, hunc
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              diuido duabus diametris ad rectos angu­
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              los ſe ſecantibus C E & F G in centro D.
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              </s>
              <s id="s.003112">Erit etiam vt B punctus circumferentiam
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              circuli deſcribat circa conum quæ ſit H B.
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              </s>
              <s id="s.003113">Duco igitur à vertice coni rectam ad ex­
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              tremitatem vnius diametri baſis, puta ad
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              C, & vbi ſecat circuli peripheriam, vt
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              in B, ex illo puncto duco lineas rectas
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              ad extremitates alterius diametri B F, &
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              B C: ſuperficies igitur in qua eſt tri­
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              gonus B F C, vbi ſecat ſuperficiem co­
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              ni, facit duas obliquas lineas B F & B G,
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              quas ex chalybe optimo, ne flectantur, fieri
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              oportet, aſſumpta tantùm parte, puta BL &
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              BM æqualibus quæ ſunt latera paraboles.
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              </s>
              <s id="s.003114">Inde aſſumes molem ex gypſo N maiorem </s>
            </p>
          </chap>
        </body>
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    </archimedes>
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