Cardano, Girolamo, De subtilitate, 1663

Table of figures

< >
[Figure 11]
Page: 14
[Figure 12]
Page: 15
[Figure 13]
Page: 16
[Figure 14]
Page: 16
[Figure 15]
Page: 18
[Figure 16]
Page: 18
[Figure 17]
Page: 19
[Figure 18]
Page: 19
[Figure 19]
Page: 20
[Figure 20]
Page: 21
[Figure 21]
Page: 24
[Figure 22]
Page: 29
[Figure 23]
Page: 42
[Figure 24]
Page: 42
[Figure 25]
Page: 42
[Figure 26]
Page: 43
[Figure 27]
Page: 43
[Figure 28]
Page: 44
[Figure 29]
Page: 50
[Figure 30]
Page: 50
[Figure 31]
Page: 60
[Figure 32]
Page: 61
[Figure 33]
Page: 61
[Figure 34]
Page: 62
[Figure 35]
Page: 62
[Figure 36]
Page: 62
[Figure 37]
Page: 63
[Figure 38]
Page: 63
[Figure 39]
Page: 64
[Figure 40]
Page: 64
< >
page |< < of 403 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="414" xlink:href="016/01/063.jpg"/>
            <p type="margin">
              <s id="s.002661">
                <margin.target id="marg297"/>
              Tria quæ ne­
                <lb/>
              ceſſaria ſunt
                <lb/>
              ad viſus ra­
                <lb/>
              tionem aſſe­
                <lb/>
              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
                <lb/>
              puncto D ad A oculum dirigitur, non eſt
                <lb/>
              minor linea BA, nec CA, niſi in vna linea,
                <lb/>
              quæ minor eſt DE: eò fit vt cùm linea DE,
                <lb/>
              nullam habeat comparationem ad DA,
                <lb/>
              propter nimiam aſtrorum altitudinem, igi­
                <lb/>
              tur non percipitur differentia vlla inter
                <lb/>
              AB, & AC, & AD, quare omnes vi­
                <lb/>
              debuntur ab eodem plano erigi, igitur B
                <lb/>
              DC videbitur plana, omnia igitur rotunda
                <lb/>
              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
                <lb/>
              nunc oſtendatur, & quòd maximè diſtent
                <lb/>
                <arrow.to.target n="marg298"/>
                <lb/>
              primò, inde quòd ſint maxima. </s>
              <s id="s.002664">Cùm igi­
                <lb/>
              tur duæ lineæ AB, & AC, producuntur ab
                <lb/>
              eodem puncto A, & ipſæ ſunt æquales, &
                <lb/>
              ſecantur duæ æquales FB, & FD, & duæ il­
                <lb/>
              lis etiam æquales GE, & GC, & ductæ
                <lb/>
              fuerint BC & FG, & perpendiculares DH,
                <lb/>
              EK, FL, & GM, erunt anguli L & H
                <lb/>
              æquales, quia recti, item BFL, & FDH, eò
                <lb/>
              quòd D H & FL, æquidiſtant, & linea DF,
                <lb/>
              recto oppoſita æqualis FB, oppoſitæ recto,
                <lb/>
              quare BL, æqualis FH, & MC, æqualis
                <lb/>
              KG eadem ratione. </s>
              <s id="s.002665">Sic igitur cùm BD ſit
                <lb/>
              maior FG, vt palam eſt ex quarta ſexti ele­
                <lb/>
              mentorum Euclidis, erit vt BC poſſit augeri
                <lb/>
              tantùm, vt BL, & MC, quæ ſemper æqua­
                <lb/>
              les manent, ſint minores in comparatione
                <lb/>
              diſtantiæ, data minima quantitate: igitur
                <lb/>
              tunc ex tertio ſuppoſito latente differentia
                <lb/>
              FB, & GC, vt æquidiſtantes habebuntur.
                <lb/>
              </s>
              <s id="s.002666">Hanc conatus eſt Vitellio oſtendere, quàm
                <lb/>
              non declarauit, multiſque tandem erroribus
                <lb/>
              admiſſis, quòd falſum oſtendere conatus eſt,
                <lb/>
              ſcilicet quòd BL eſſet minor FH: hoc au­
                <lb/>
              tem falſum eſt: eſt enim, vt demonſtraui, æ­
                <lb/>
              qualis, & ex hac æqualitate minorem ha­
                <lb/>
              bet rationem ad BC ipſa BL, quàm FH ad
                <lb/>
              FG. </s>
              <s id="s.002667">Et hoc ſufficit ad propoſitum demon­
                <lb/>
              ſtrandum. </s>
              <s id="s.002668">Cùm igitur Sol aut Luna, aut
                <lb/>
              aſtrum aliud vmbram faciat fermè æqua­
                <lb/>
              lem in terra rei quæ videtur, aut ligno
                <lb/>
              quod radiis illius opponitur, ſeu ex vno
                <lb/>
              puncto radij procedant, ſeu ex toto corpo­
                <lb/>
              re, permutata hac demonſtratione, conſtat
                <lb/>
              altitudinis ad FG proportionem eſſe in­
                <lb/>
              comparabilem. </s>
              <s id="s.002669">Cùm hoc igitur contingat
                <lb/>
              etiam in turribus & montibus maximis, ne­
                <lb/>
              ceſſe eſt, vt lineæ FB & GC ſint æquidi­
                <lb/>
              ſtantes: quare altitudo A aſtri maxima,
                <lb/>
                <arrow.to.target n="marg299"/>
                <lb/>
              maximum igitur etiam aſtrum quod tam
                <lb/>
              procul ſub illa magnitudine, quam videmus,
                <lb/>
              cernitur. </s>
              <s id="s.002670">Eſt autem deducta ratione ex vm­
                <lb/>
              bra terræ in deliquiis Solis, dimetiens ex
                <lb/>
              his partibus, quibus rerræ dimetiens eſt duo,
                <lb/>
              vndecim: quare cùm terræ dimetiens ſit bis
                <lb/>
              quinque millia paſſuum, erit Solis dime­
                <lb/>
              tiens vndecies quinque millia paſſuum, id
                <lb/>
              eſt, paſſus millies quinquagintaquinque
                <lb/>
              millia. </s>
              <s id="s.002671">Solis autem corpus ad terram pro­
                <lb/>
              portionem habet, quam quæ 166. & tres ex
                <lb/>
              octo partibus ad vnum, ambitus maioris
                <lb/>
              circuli M. paſſuum 173000. inſuperque 250.
                <lb/>
              Terræ dimetiens ad Lunæ dimetientem, quę
                <lb/>
              eſt 17. ad 5. ratio: itaque terræ corpus Lu­
                <lb/>
              næ corpus continet fermè trigeſies nouies,
                <lb/>
              ac inſuper duas tertias. </s>
              <s id="s.002672">Lunæ dimetiens paſ­
                <lb/>
              ſuum millia 2941. ambitus maioris circuli
                <lb/>
                <expan abbr="paſſuũ">paſſuum</expan>
              milia, 9000. & inſuper 264. Altitudo
                <lb/>
                <arrow.to.target n="marg300"/>
                <lb/>
              etiam horum ex Ptolemæi demonſtratione
                <lb/>
              habita talis eſt. </s>
              <s id="s.002673">Solis quidem à terræ cen­
                <lb/>
              tro M. paſſuum ſexies mille M. & inſuper
                <lb/>
              quingenta. </s>
              <s id="s.002674">Lunæ verò ab eodem centro
                <lb/>
              M. paſſuum trecenta viginti M. & inſuper
                <lb/>
              833. Coni autem vmbræ ab eodem M. paſ­
                <lb/>
              ſuum millies trecenties quadraginta M. </s>
              <s id="s.002675">Vn­
                <lb/>
              de deductis M. paſſuum quinquies mille pro
                <lb/>
              ſemidiametro terræ à ſingulis harum di­
                <lb/>
              ſtantiarum, relinquentur diſtantiæ Solis ac
                <lb/>
              Lunæ, necnon coni vmbræ à ſuperficie ter­
                <lb/>
              ræ, ſeu ab oculis noſtris. </s>
              <s id="s.002676">Diſtantia etiam
                <lb/>
              Solis à Luna, quando Sol deliquium pati­
                <lb/>
              tur, ſeu meliùs orbis ſolaris à Lunari orbe,
                <lb/>
              erit mille paſſuum Italicorum
                <emph type="italics"/>
              (
                <emph.end type="italics"/>
              nam de his
                <lb/>
              ſermo eſt) quinquies mille ſexcenties octua­
                <lb/>
              ginta quatuor millia atque inſuper 167. Il­
                <lb/>
              lud verò mirum quod Philippus Melanthon
                <lb/>
              animaduertiſſe videtur: quòd cùm eccentri
                <lb/>
              Solis centrum Ptolemæi atque Hipparchi
                <lb/>
              ætate diſtaret à terræ centro diametris terræ
                <lb/>
              24. cùm quinta parte, ſeu M. paſſuum
                <lb/>
              242000. nunc ſolùm diſtet diametris terræ
                <lb/>
                <arrow.to.target n="marg301"/>
                <lb/>
              decem & octo, duabuſque partibus ex quin­
                <lb/>
              que ſeu mille paſſuum centum octuaginta
                <lb/>
              quatuor millia ab eodem terræ centro. </s>
              <s id="s.002677">Ar­
                <lb/>
              gumentum quaſi ſeneſcentis mundi. </s>
              <s id="s.002678">Sed
                <lb/>
              ratio deduci poteſt, vel ab inſtrumento­
                <lb/>
              rum varietate, vel cœli ſolaris diſpoſitio­
                <lb/>
              ne, vel æquinoctiorum obſeruatione, quæ
                <lb/>
              varietatem ſuſcipit & à locis, & à Solis
                <lb/>
              magnitudine, propter quam æquino­
                <lb/>
              ctium aliquanto clariùs fit, quàm exiſti­
                <lb/>
              metur. </s>
              <s id="s.002679">Hoc autem cùm obſeruatum eſſet
                <lb/>
              à multis, in Solis magnitudinem rela­
                <lb/>
              tum eſt. </s>
              <s id="s.002680">Sol igitur A B, centrum eius
                <lb/>
                <arrow.to.target n="marg302"/>
                <lb/>
              C, terra DE, centrum eius F, linea
                <lb/>
              CHM, contingens Solem & terram, co­
                <lb/>
              nus M. </s>
              <s id="s.002681">Quoniam igitur GH contingit So­
                <lb/>
              lem & terram, erunt anguli G & H recti,
                <lb/>
              quare GC, æquidiſtans FH, & ideò portio
                <lb/>
              GB, ſimilis portioni HE. </s>
              <s id="s.002682">Si igitur CG, ad
                <lb/>
              FH, proportio cognita eſt: erit & GM, ad
                <lb/>
              MH, qualis CM, ad MF. </s>
              <s id="s.002683">Et quia CM, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum