Cardano, Girolamo, De subtilitate, 1663

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            <p type="main">
              <s id="s.003420">
                <pb pagenum="433" xlink:href="016/01/082.jpg"/>
              niam DBC, eſt rectus, & CBE, obtuſus. </s>
              <s id="s.003421">Ve­
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              rùm de radiis alia eſt ratio: etenim illi motu
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                <arrow.to.target n="marg422"/>
                <lb/>
              ſuo, angulum ſenſilem efficiunt in oculo,
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              ideóque moueri deberent videri. </s>
              <s id="s.003422">Cur autem
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              non videantur, cauſa hæc eſt, quia poſita ter­
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              ra, cuius centrum A, & plano eius
                <emph type="italics"/>
              (
                <emph.end type="italics"/>
              vt dixi)
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              quod refert punctum D, ſed nobis ob ma­
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                <figure id="id.016.01.082.1.jpg" xlink:href="016/01/082/1.jpg" number="61"/>
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              gnitudinem eſt BC, & turris quæ ad perpen­
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              diculum eſt ſuper planum DE, & Sole in F,
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              qui producens radium FEC, producit CD,
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              cum autem Sol proceſſerit in G, producto
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              radio GEK, relinquit vmbram KD, igitur
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              cùm motus indicetur ex vmbra, Sol videbi­
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              tur ſolum pertranſiſſe ex C, in K, dum moue­
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              tur ex F, in G: ſed ſpatium CK, eſt paruum,
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              cùm ſit comparatum ad altitudinem D E,
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              quæ eſt parua: igitur cum ſenſim moueatur,
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              & tranſeat ſolùm ſpatium CK, puta in quar­
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              ta horæ ſingulo momento, nullum ſpatium
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              tranſibit quod angulum ſenſilem efficiat. </s>
              <s id="s.003423">Igi­
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              tur videbitur ex illo ſuppoſito ſæpius repe­
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              tito, radius FC,
                <expan abbr="dũ">dum</expan>
              mouebitur ſemper quieſ­
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              cere. </s>
              <s id="s.003424">Ponamus exemplum, cum Sol eſt in 7.
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              parte Tauri hora circiter 19. cum quarta,
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              vmbra æquatur gnomoni, 21. detracta quar­
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              ta, dupla eſt: conduplicatur ergo vnius & di­
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              midiæ horæ ſpatio. </s>
              <s id="s.003425">Ergo motus eſt iuxta gno­
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              monis longitudinem, non Solis velocitatem.
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              </s>
              <s id="s.003426">Verum dices, cur non videtur moueri radius?
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              </s>
              <s id="s.003427">cauſam intelligo: quomodò verò tantum ſpa­
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              tij ſuperet, nec moueri videatur, cauſam non
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              intelligo. </s>
              <s id="s.003428">Conſtat enim ſub ortu occaſu vm­
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              bras velociſſimè maximiſque incrementis,
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              aut decrementis variati. </s>
              <s id="s.003429">Sit igitur Sol occi­
                <lb/>
                <figure id="id.016.01.082.2.jpg" xlink:href="016/01/082/2.jpg" number="62"/>
                <lb/>
              dens C, planum GE, corpus erectum AB, fi­
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              nis vmbræ
                <emph type="italics"/>
              (
                <emph.end type="italics"/>
              qui idem eſt cum initio radio­
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              rum) E, corpus aliud erectum EF: in quo mo­
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              tus vmbræ inſenſilis ſit, quoniam ſolùm dum
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              Sol occidit radij deſinunt illuſtrare. </s>
              <s id="s.003430">Ipſi verò
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              clariſſimi erunt, quando angulus CEF, rectus
                <lb/>
              eſt. </s>
              <s id="s.003431">At ex puncto E, nulli dubium eſſe poteſt,
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              quin in plano GAE, tum radij, tum vmbra
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              prope Solis occaſum incredibili velocitate
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              ferantur,
                <expan abbr="quãtum">quantum</expan>
              enim punctus in ſuperficie
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              terræ è regione centri Solis mouetur, tanto
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              magis neceſſe eſt vmbras promoueri. </s>
              <s id="s.003432">Sed
                <lb/>
              quoniam in priore figura, ſi F, ponatur in oc­
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              caſu anguli FAE, FEA, erunt quaſi recti ob
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              paruitatem AE, & rationem trigonorum cir­
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              culis inſcriptorum iuxta arcum & chordam,
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              vt vocant, erunt ergo anguli FC, lineæ, cum
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              duabus è centro A, exeuntibus ad illam al­
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              teram, quarum eſt AD, altera velut AK, fer­
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              mè recti: ergo vmbra quæ ſubtenditur quæ­
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              que maxima eſt, minima eſt. </s>
              <s id="s.003433">Igitur non fiet
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              ille progreſſus maximus, niſi DE, fuerit lon­
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              giſſima, quod eſſe non poteſt in comparatio­
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              ne ad AD. </s>
              <s id="s.003434">Alia cauſa eſt, quoniam quantò
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              magis creſcit AE, eò radiorum vis minuitur
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              propter paruitatem anguli AEB: igitur nec
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              vmbra, nec radius dignoſcitur: quamobrem
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              in dubia luce, neque lux ipſa percipitur, ne­
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              que multo minus vmbra quæ propter lucem
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              dignoſcitur, nec vmbræ magnitudo etiam
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              minus, nec tandem adhúcque minus vmbræ,
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              vel radiorum motus. </s>
              <s id="s.003435">Dices rurſus, quomodo
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              vmbra fiet infinita ſtatim ſi maxima parua
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              eſt? </s>
              <s id="s.003436">coniungitur illa vmbræ rotunditatis terrę
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              quæ maxima eſt, & ſic è parua fit infinita in
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              momento. </s>
              <s id="s.003437">Cùm verò nullum fuerit corpus in
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              plano, velociſſima fit & lucis & vmbrarum
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              diffuſio, ſed quia lux in vtroque crepuſculo
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              (vt ita dicam) dubia eſt, & ſpatium quod ab
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              oculo illuminatum videtur exiguum, ſtatim
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              vtraque facta mutatione latet motus, vt in
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              ſecunda cauſa demonſtratum eſt. </s>
            </p>
            <p type="margin">
              <s id="s.003438">
                <margin.target id="marg421"/>
              Propoſit. 13.</s>
            </p>
            <p type="margin">
              <s id="s.003439">
                <margin.target id="marg422"/>
              Cur ſolis ra­
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              dij cum in
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              23. ſerie ter­
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              ram circum­
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              eant immo­
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              biles vi­
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              deantur.</s>
            </p>
            <p type="main">
              <s id="s.003440">Dubium quoque eſt, cur hæc illuſtratio
                <lb/>
                <arrow.to.target n="marg423"/>
                <lb/>
              in terra ſemper tremere videatur? </s>
              <s id="s.003441">& an ab
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              eorum quæ dicta ſunt aliquid? </s>
              <s id="s.003442">Cauſa igi­
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              tur eſt, quòd mouetur, nec moueri videtur,
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              vt dictum eſt: medium igitur quippiam per­
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              cipitur. </s>
              <s id="s.003443">Idem
                <expan abbr="etiã">etiam</expan>
              & ex ambigua viſione, ter­
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              minus enim vmbræ & luminis, neque vmbra
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              eſt neque lux, tremere autem exiſtimantur
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              quæcunque, an moueantur incertum eſt, hoc
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              autem ob cauſas dictas. </s>
              <s id="s.003444">Sed cur non in horo­
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              logio index? </s>
              <s id="s.003445">Quoniam non eſt is motus ob
                <lb/>
              tarditatem vllo modo ſenſilis: quæ autem
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              tremere videntur, non adeò tardè moueri
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              oportet, vt omninò quieſcere videantur. </s>
            </p>
            <p type="margin">
              <s id="s.003446">
                <margin.target id="marg423"/>
              Cur ſolis il­
                <lb/>
              luſtratio tre­
                <lb/>
              mula videa­
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              tur.</s>
            </p>
            <p type="main">
              <s id="s.003447">His cognitis maius quippiam ſuccedit,
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              quo humana ſubtilitas altitudinem omnium
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              ſyderum tam facilè metiri docuit, vt nemo
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              tam in promptu domus ſuæ partes habeat.
                <lb/>
              </s>
              <s id="s.003448">Cum enim in figura motus Solis altitudo F,
                <lb/>
              nota fuerit, ſeu planiſphærio, ſeu armillis,
                <lb/>
              alióve inſtrumento, aut tabulis, ea detracta
                <lb/>
              ex 90. partibus habebimus angulum FAD,
                <lb/>
              ſed angulus CED, ratione & menſura notus
                <lb/>
              eſt, ſeu C, terminus ſit vmbræ, ſeu oculus: igi­
                <lb/>
                <arrow.to.target n="marg424"/>
                <lb/>
              tur angulus FEA, notus, quare ex traditis ab
                <lb/>
              Euclide in elementis, angulus F, & ratio FE,
                <lb/>
              altitudinis ad AE, dimidium dimetientis ter­
                <lb/>
              ræ, quoſt ſuperius quantum eſſet, demonſtra­
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              uimus. </s>
              <s id="s.003449">Eſt enim quinquies M. paſſ millia.
                <lb/>
              </s>
              <s id="s.003450">Virga autem DE, habere debet circulum in
                <lb/>
              imo chalybèum, cui inſiſtat orthogonia: tum
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              & planum ad vnguem inferna parte
                <expan abbr="circulũ">circulum</expan>
                <lb/>
              eſſe, vt cùm applicetur plano, intelligas an
                <lb/>
              illud verè planum ſit, habeat & ſuperius à
                <lb/>
              quatuor lateribus plumbea perpendicula: &
                <lb/>
              notæ ſit magnitudinis à ſummo verticis
                <expan abbr="vſq;">vſque</expan>
                <lb/>
              ad imam chalybei circuli ſuperficiem. </s>
              <s id="s.003451">Cùm
                <lb/>
              igitur virga fixa circulo tenus illóque hæren.
                <lb/>
              </s>
              <s id="s.003452">te vndequaque plano etiam perpendicula </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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