Cardano, Girolamo, De subtilitate, 1663

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        <body>
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            <pb pagenum="414" xlink:href="016/01/063.jpg"/>
            <p type="margin">
              <s id="s.002661">
                <margin.target id="marg297"/>
              Tria quæ ne­
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              ceſſaria ſunt
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              ad viſus ra­
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              tionem aſſe­
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              quendam.</s>
            </p>
            <p type="main">
              <s id="s.002662">Hoc enim modo haud difficile eſt cau­
                <lb/>
              ſam cognoſcere, cur aſtra, cùm plana
                <expan abbr="videã-tur">videan­
                  <lb/>
                tur</expan>
              , ſint tamen rotunda: nam linea quæ à
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              puncto D ad A oculum dirigitur, non eſt
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              minor linea BA, nec CA, niſi in vna linea,
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              quæ minor eſt DE: eò fit vt cùm linea DE,
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              nullam habeat comparationem ad DA,
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              propter nimiam aſtrorum altitudinem, igi­
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              tur non percipitur differentia vlla inter
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              AB, & AC, & AD, quare omnes vi­
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              debuntur ab eodem plano erigi, igitur B
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              DC videbitur plana, omnia igitur rotunda
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              procul plana videbuntur. </s>
            </p>
            <figure id="id.016.01.063.1.jpg" xlink:href="016/01/063/1.jpg" number="37"/>
            <figure id="id.016.01.063.2.jpg" xlink:href="016/01/063/2.jpg" number="38"/>
            <p type="main">
              <s id="s.002663">Eſſe autem aſtara maxima, generaliter
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              nunc oſtendatur, & quòd maximè diſtent
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                <arrow.to.target n="marg298"/>
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              primò, inde quòd ſint maxima. </s>
              <s id="s.002664">Cùm igi­
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              tur duæ lineæ AB, & AC, producuntur ab
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              eodem puncto A, & ipſæ ſunt æquales, &
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              ſecantur duæ æquales FB, & FD, & duæ il­
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              lis etiam æquales GE, & GC, & ductæ
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              fuerint BC & FG, & perpendiculares DH,
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              EK, FL, & GM, erunt anguli L & H
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              æquales, quia recti, item BFL, & FDH, eò
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              quòd D H & FL, æquidiſtant, & linea DF,
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              recto oppoſita æqualis FB, oppoſitæ recto,
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              quare BL, æqualis FH, & MC, æqualis
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              KG eadem ratione. </s>
              <s id="s.002665">Sic igitur cùm BD ſit
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              maior FG, vt palam eſt ex quarta ſexti ele­
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              mentorum Euclidis, erit vt BC poſſit augeri
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              tantùm, vt BL, & MC, quæ ſemper æqua­
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              les manent, ſint minores in comparatione
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              diſtantiæ, data minima quantitate: igitur
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              tunc ex tertio ſuppoſito latente differentia
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              FB, & GC, vt æquidiſtantes habebuntur.
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              </s>
              <s id="s.002666">Hanc conatus eſt Vitellio oſtendere, quàm
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              non declarauit, multiſque tandem erroribus
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              admiſſis, quòd falſum oſtendere conatus eſt,
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              ſcilicet quòd BL eſſet minor FH: hoc au­
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              tem falſum eſt: eſt enim, vt demonſtraui, æ­
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              qualis, & ex hac æqualitate minorem ha­
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              bet rationem ad BC ipſa BL, quàm FH ad
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              FG. </s>
              <s id="s.002667">Et hoc ſufficit ad propoſitum demon­
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              ſtrandum. </s>
              <s id="s.002668">Cùm igitur Sol aut Luna, aut
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              aſtrum aliud vmbram faciat fermè æqua­
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              lem in terra rei quæ videtur, aut ligno
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              quod radiis illius opponitur, ſeu ex vno
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              puncto radij procedant, ſeu ex toto corpo­
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              re, permutata hac demonſtratione, conſtat
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              altitudinis ad FG proportionem eſſe in­
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              comparabilem. </s>
              <s id="s.002669">Cùm hoc igitur contingat
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              etiam in turribus & montibus maximis, ne­
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              ceſſe eſt, vt lineæ FB & GC ſint æquidi­
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              ſtantes: quare altitudo A aſtri maxima,
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                <arrow.to.target n="marg299"/>
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              maximum igitur etiam aſtrum quod tam
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              procul ſub illa magnitudine, quam videmus,
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              cernitur. </s>
              <s id="s.002670">Eſt autem deducta ratione ex vm­
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              bra terræ in deliquiis Solis, dimetiens ex
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              his partibus, quibus rerræ dimetiens eſt duo,
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              vndecim: quare cùm terræ dimetiens ſit bis
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              quinque millia paſſuum, erit Solis dime­
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              tiens vndecies quinque millia paſſuum, id
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              eſt, paſſus millies quinquagintaquinque
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              millia. </s>
              <s id="s.002671">Solis autem corpus ad terram pro­
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              portionem habet, quam quæ 166. & tres ex
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              octo partibus ad vnum, ambitus maioris
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              circuli M. paſſuum 173000. inſuperque 250.
                <lb/>
              Terræ dimetiens ad Lunæ dimetientem, quę
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              eſt 17. ad 5. ratio: itaque terræ corpus Lu­
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              næ corpus continet fermè trigeſies nouies,
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              ac inſuper duas tertias. </s>
              <s id="s.002672">Lunæ dimetiens paſ­
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              ſuum millia 2941. ambitus maioris circuli
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                <expan abbr="paſſuũ">paſſuum</expan>
              milia, 9000. & inſuper 264. Altitudo
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                <arrow.to.target n="marg300"/>
                <lb/>
              etiam horum ex Ptolemæi demonſtratione
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              habita talis eſt. </s>
              <s id="s.002673">Solis quidem à terræ cen­
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              tro M. paſſuum ſexies mille M. & inſuper
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              quingenta. </s>
              <s id="s.002674">Lunæ verò ab eodem centro
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              M. paſſuum trecenta viginti M. & inſuper
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              833. Coni autem vmbræ ab eodem M. paſ­
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              ſuum millies trecenties quadraginta M. </s>
              <s id="s.002675">Vn­
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              de deductis M. paſſuum quinquies mille pro
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              ſemidiametro terræ à ſingulis harum di­
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              ſtantiarum, relinquentur diſtantiæ Solis ac
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              Lunæ, necnon coni vmbræ à ſuperficie ter­
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              ræ, ſeu ab oculis noſtris. </s>
              <s id="s.002676">Diſtantia etiam
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              Solis à Luna, quando Sol deliquium pati­
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              tur, ſeu meliùs orbis ſolaris à Lunari orbe,
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              erit mille paſſuum Italicorum
                <emph type="italics"/>
              (
                <emph.end type="italics"/>
              nam de his
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              ſermo eſt) quinquies mille ſexcenties octua­
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              ginta quatuor millia atque inſuper 167. Il­
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              lud verò mirum quod Philippus Melanthon
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              animaduertiſſe videtur: quòd cùm eccentri
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              Solis centrum Ptolemæi atque Hipparchi
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              ætate diſtaret à terræ centro diametris terræ
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              24. cùm quinta parte, ſeu M. paſſuum
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              242000. nunc ſolùm diſtet diametris terræ
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                <arrow.to.target n="marg301"/>
                <lb/>
              decem & octo, duabuſque partibus ex quin­
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              que ſeu mille paſſuum centum octuaginta
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              quatuor millia ab eodem terræ centro. </s>
              <s id="s.002677">Ar­
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              gumentum quaſi ſeneſcentis mundi. </s>
              <s id="s.002678">Sed
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              ratio deduci poteſt, vel ab inſtrumento­
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              rum varietate, vel cœli ſolaris diſpoſitio­
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              ne, vel æquinoctiorum obſeruatione, quæ
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              varietatem ſuſcipit & à locis, & à Solis
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              magnitudine, propter quam æquino­
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              ctium aliquanto clariùs fit, quàm exiſti­
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              metur. </s>
              <s id="s.002679">Hoc autem cùm obſeruatum eſſet
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              à multis, in Solis magnitudinem rela­
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              tum eſt. </s>
              <s id="s.002680">Sol igitur A B, centrum eius
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                <arrow.to.target n="marg302"/>
                <lb/>
              C, terra DE, centrum eius F, linea
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              CHM, contingens Solem & terram, co­
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              nus M. </s>
              <s id="s.002681">Quoniam igitur GH contingit So­
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              lem & terram, erunt anguli G & H recti,
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              quare GC, æquidiſtans FH, & ideò portio
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              GB, ſimilis portioni HE. </s>
              <s id="s.002682">Si igitur CG, ad
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              FH, proportio cognita eſt: erit & GM, ad
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              MH, qualis CM, ad MF. </s>
              <s id="s.002683">Et quia CM, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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