Cardano, Girolamo, De subtilitate, 1663

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.003375">
                <pb pagenum="431" xlink:href="016/01/080.jpg"/>
              venit, neutro modo etiam ad perpendicu­
                <lb/>
              lum ad nos venient: igitur æſtas non vbi­
                <lb/>
              que erit.
                <lb/>
                <arrow.to.target n="marg414"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.003376">
                <margin.target id="marg412"/>
              Cur non vbi­
                <lb/>
              que ſemper
                <lb/>
              æſtas.</s>
            </p>
            <p type="margin">
              <s id="s.003377">
                <margin.target id="marg413"/>
              Quomodo
                <lb/>
              plana ſpecu­
                <lb/>
              la vt
                <expan abbr="reddãt">reddant</expan>
                <lb/>
              radium
                <expan abbr="per-pendicularẽ">per­
                  <lb/>
                pendicularem</expan>
              ,
                <lb/>
              debeant col­
                <lb/>
              locari in ſole.</s>
            </p>
            <p type="margin">
              <s id="s.003378">
                <margin.target id="marg414"/>
              Ædificia
                <lb/>
              quæ multum
                <lb/>
              excalefacere
                <lb/>
                <expan abbr="aërẽ">aërem</expan>
              poſſunt.</s>
            </p>
            <p type="main">
              <s id="s.003379">Liquet autem ex his, ædificia poſſe fieri,
                <lb/>
              quæ etiam hyeme non parum aërem exca­
                <lb/>
              lefacient. </s>
              <s id="s.003380">Hæc verò non ad terræ centrum
                <lb/>
              erecta rectè eſſe oportet, ſed vt Solem hye­
                <lb/>
              malem ad perpendiculum excipiant. </s>
              <s id="s.003381">Itaque
                <lb/>
              vt exemplum rei præbeam, ſit habitatio no­
                <lb/>
              ſtra in A, ſuper plano AF, quæ ad perpendi­
                <lb/>
              culum è noſtro vertice ad centrum terræ AB
                <lb/>
              quam conſtat diſtare ab æquinoctij circu­
                <lb/>
              lo partibus 44. & media: ab hyemali igitur
                <lb/>
                <figure id="id.016.01.080.1.jpg" xlink:href="016/01/080/1.jpg" number="53"/>
                <lb/>
              diſtabit partibus 68. fiat igitur circuli pars
                <lb/>
              quarta BCF, & fiat BC partium 22. ex his
                <lb/>
              quibus BF ex nonaginta, diſtabit igitur pun­
                <lb/>
              ctus C partibus nonaginta ab hyemali tro­
                <lb/>
              pico: quare cùm Sol ibi erit, erecta plana
                <lb/>
              aut caua cylindrica ſuperficie A C, in meri­
                <lb/>
              die radios ad perpendiculum excipiet. </s>
              <s id="s.003382">Fiat
                <lb/>
              etiam arcus CE partium 47. & iuxta decli­
                <lb/>
              nationem cuiuſque diei Solis deſcribantur
                <lb/>
              partes, & moles AC retrò agatur: ſicque to­
                <lb/>
              to anno radios ad perpendiculum ſtantes
                <lb/>
              excipiet, vt ante tempus olera & fructus
                <lb/>
              habere poſſis, reddatúrque iucunda manſio. </s>
            </p>
            <p type="main">
              <s id="s.003383">Iam his de cauſis intelligis non ſolùm
                <lb/>
              duplicem eorum, qui ad perpendiculum
                <lb/>
              ſtant radiorum rationem, ſed etiam vmbra­
                <lb/>
              rum diſcrimina, quæ qui­
                <lb/>
              dem in omnibus mutantur
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              corporibus ob ſitum cor­
                <arrow.to.target n="marg415"/>
                <lb/>
              poris, ſola ſphæra exce­
                <lb/>
              pta: nam illa eodem lo­
                <lb/>
              co manens, luce etiam qui­
                <lb/>
              eſcente eandem vmbram
                <lb/>
              facit. </s>
              <s id="s.003384">At non ſic reliqua
                <lb/>
              corpora, ſed virgæ ſi ſe­
                <lb/>
              cundum radiorum Solis
                <lb/>
              longitudinem extendantur,
                <lb/>
                <expan abbr="nullã">nullam</expan>
              propemodum faciunt
                <lb/>
              vmbram, niſi quantam
                <lb/>
                <figure id="id.016.01.080.2.jpg" xlink:href="016/01/080/2.jpg" number="54"/>
                <lb/>
              ipſa virga habuerit craſſitudinis. </s>
              <s id="s.003385">Si verò
                <lb/>
              virga ſic ſtatuatur, vt vmbra eius ad per­
                <lb/>
              pendiculum ſit ſuper vmbram erectæ al­
                <lb/>
              terius virgæ in plano, tunc erit hæc vm­
                <lb/>
              bra media, æqualíſque ad vnguem ipſi vir­
                <lb/>
              gæ, niſi quantum ex elongatione à plano
                <lb/>
                <arrow.to.target n="marg416"/>
                <lb/>
              terræ propter Solis magnitudinem illi de­
                <lb/>
              ceſſerit: quod perexiguum tamen eſt: ita
                <lb/>
              tamen perexiguum, quod omne corpus So­
                <lb/>
              li expoſitum hac ratione vmbram finit in
                <lb/>
                <arrow.to.target n="marg417"/>
                <lb/>
              tanta diſtantia, quanta eſt magnitudo di­
                <lb/>
              metientis illius corporis centies ac nouies
                <lb/>
              ſumpta: talis enim proportio diſtantiæ So­
                <lb/>
              lis à terra ad ſuam, ſcilicet Solis diametrum
                <lb/>
              fermè. </s>
              <s id="s.003386">Ex quo patet, non obſcura ratio co­
                <lb/>
              gnoſcendi proportionem altitudinis, cuiuſ­
                <lb/>
              cunque ſyderis ad ſuam magnitudinem. </s>
              <s id="s.003387">Nam
                <lb/>
              collocata ſphæra notæ diametri in ſummo
                <lb/>
              montis, videbis qua in diſtantia finiatur vm­
                <lb/>
              bra, inde colliges eam eſſe proportionem al­
                <lb/>
              titudinis ad diametrum ſy­
                <lb/>
                <figure id="id.016.01.080.3.jpg" xlink:href="016/01/080/3.jpg" number="55"/>
                <lb/>
              deris, quæ eſt rectæ diſtantiæ
                <lb/>
              inter locum finis vmbræ, &
                <lb/>
              diametrum ſphæræ. </s>
              <s id="s.003388">Cum
                <lb/>
              igitur ſuper virgam plano
                <lb/>
              æquidiſtantem, quæ vmbram
                <lb/>
              ſibi æqualem faciat, virgam
                <lb/>
              aliam ſuper, ad perpendicu­
                <lb/>
              lum conſtitues, ita quòd So­
                <lb/>
              lis radius ſuper eam rectè
                <lb/>
              cadat, tunc maxima vmbra
                <lb/>
              fiet, quæ à tali magnitudi­
                <lb/>
              ne, & Solis tali ſitu poſſit
                <lb/>
              prouenire. </s>
              <s id="s.003389">Hæc autem non
                <lb/>
              paulò maior erit ipſa virgæ
                <lb/>
              longitudine. </s>
              <s id="s.003390">Contingítque
                <lb/>
              hoc ob plani terræ inclina­
                <lb/>
              tionem à ſitu ſuperficiei, in quam ex cen­
                <lb/>
              tro Solis ad perpendiculum ductus radius
                <lb/>
              cadit: reliquæ omnes intra hos terminos
                <lb/>
              conſtituuntur, permiſcentúrque magnitudi­
                <lb/>
              nis & paruitatis cauſæ, vt ad hos ſimpli­
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              ces ſitus magis aut minus acceſſerint. </s>
              <s id="s.003391">Cæ­
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                <arrow.to.target n="marg418"/>
                <lb/>
              terum ſeu ex centro ſolo Solis, ſeu ex toto
                <lb/>
              ambitu radij dirigantur quodlibet opacum
                <lb/>
              quantumcunque magnum, æqualem facit
                <lb/>
              vmbram, ſi iuxta ſitum ad perpendiculum
                <lb/>
              ſteterit ſuper ſuperficiem,
                <lb/>
                <figure id="id.016.01.080.4.jpg" xlink:href="016/01/080/4.jpg" number="56"/>
                <lb/>
              quæ ex centro Solis ad per­
                <lb/>
              pendiculum ſtat ſuper pla­
                <lb/>
              num, illud diuidens iuxta
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              totam inclinationem, nam
                <lb/>
              radij ob diſtantiam opacum
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              amplectentes æquidiſtantes,
                <lb/>
              vtroque modo procedunt ex­
                <lb/>
              quiſitè, ſi ex centro ob in­
                <lb/>
              finitam proportionem A D
                <lb/>
              & A E ad D E, vel ſi ex to­
                <lb/>
              to ſole ob maximam pro­
                <lb/>
              portionem C E & B D ad
                <lb/>
              BC, aliquanto breuior fit in
                <lb/>
              longa diſtantia vmbra opa­
                <lb/>
              co: quoniam radij C E H
                <lb/>
              & BDK minimùm ab æqui­
                <lb/>
              diſtantibus differunt. </s>
              <s id="s.003392">Ita ſeu
                <lb/>
              ſtatuas hoc ſeu illud in illo
                <lb/>
              ſitu, vmbra ſemper opaco
                <lb/>
              æqualis eſſe videtur. </s>
            </p>
            <p type="margin">
              <s id="s.003393">
                <margin.target id="marg415"/>
              Sola ſphæra
                <lb/>
              ſita
                <expan abbr="vmbrã">vmbram</expan>
                <lb/>
              non mutat.</s>
            </p>
            <p type="margin">
              <s id="s.003394">
                <margin.target id="marg416"/>
              Omnis cor­
                <lb/>
              poris vmbra
                <lb/>
              finitur.</s>
            </p>
            <p type="margin">
              <s id="s.003395">
                <margin.target id="marg417"/>
              Ratio cogno­
                <lb/>
              ſcendi pro­
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              portionem
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              cuiuſcunque
                <lb/>
              ſyderis ad
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              ſuam altitu­
                <lb/>
              dinem.</s>
            </p>
            <p type="margin">
              <s id="s.003396">
                <margin.target id="marg418"/>
              Seu radij ex
                <lb/>
              centro ſolis,
                <lb/>
              ſeu terminis
                <lb/>
              eius etiam
                <lb/>
              prodeant,
                <lb/>
              vmbræ erunt
                <lb/>
              eædem.</s>
            </p>
            <p type="main">
              <s id="s.003397">Verùm, vt ad Solis altitu­
                <lb/>
                <arrow.to.target n="marg419"/>
                <lb/>
              dinem, cæterorumque aſtro­
                <lb/>
              rum reuertar, illud demirari
                <lb/>
              contingit, cur aſtra omnia
                <lb/>
              nos iter agentes ſequi videantur, ripæ au­
                <lb/>
              tem recedere à nobis ac retrò agi dum præ­
                <lb/>
              teruehimur naui? </s>
              <s id="s.003398">Cauſa non obſcura eſt,
                <lb/>
              quoniam cùm aſtrorum diſtantia ad to­
                <lb/>
              tam terræ magnitudinem maximam ha­
                <lb/>
              beat proportionem, locum ſyderis progreſ­
                <lb/>
              ſus noſter mutare non poteſt: quod enim
                <lb/>
              oculus non percipit eſſe, ac ſi non foret,
                <lb/>
              iam docuimus. </s>
              <s id="s.003399">Cum igitur ſydus, gratia
                <lb/>
              exempli, nos præcedit cubiti magnitudine,
                <lb/>
              cum per terna millia paſſ. </s>
              <s id="s.003400">proceſſerimus,
                <lb/>
              cubiti magnitudine ſydus etiam præcede­
                <lb/>
              re nos oportet videri: quoniam terna
                <lb/>
              millia paſſ. </s>
              <s id="s.003401">cum ſyderis altitudine an-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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