Cardano, Girolamo, De subtilitate, 1663

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