Cardano, Geronimo, Opvs novvm de proportionibvs nvmerorvm, motvvm, pondervm, sonorvm, aliarvmqv'e rervm mensurandarum, non solùm geometrico more stabilitum, sed etiam uarijs experimentis & observationibus rerum in natura, solerti demonstratione illustratum, ad multiplices usus accommodatum, & in V libros digestum. Praeterea Artis Magnae, sive de regvlis algebraicis, liber vnvs abstrvsissimvs & inexhaustus planetotius Ariothmeticae thesaurus ... Item De Aliza Regvla Liber, hoc est, algebraicae logisticae suae, numeros recondita numerandi subtilitate, secundum Geometricas quantitates inquirentis ...

Page concordance

< >
Scan Original
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id002896">
                <pb pagenum="165" xlink:href="015/01/184.jpg"/>
              e h ad f g, igitur b c proportio dimetientis ad f g dimetientem nota.
                <lb/>
                <arrow.to.target n="marg571"/>
                <lb/>
              Quare ſphæræ b c ad f g ſphæram. </s>
              <s id="id002897">at nota eſt proportio f g ad e h
                <lb/>
              dimetientium igitur & ſphærarum: igitur nota eſt f g ſphæræ ad or
                <lb/>
              bem e h, igitur cum nota ſit proportio orbis ad a d ſphæram b c, &
                <lb/>
              b c ſphæræ ad f g ſphæram, & f g ſphæræ ad orbem e h, erit propor
                <lb/>
              tio orbis a d ad orbem e h nota, quod eſt propoſitum.</s>
            </p>
            <p type="margin">
              <s id="id002898">
                <margin.target id="marg569"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id002899">
                <margin.target id="marg570"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              18.
                <emph type="italics"/>
              duo
                <lb/>
              decimi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002900">
                <margin.target id="marg571"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              22.
                <lb/>
                <emph type="italics"/>
              quinti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <lb/>
              </s>
              <s id="id002901">&
                <emph.end type="italics"/>
              A
                <emph type="italics"/>
              lizam.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id002902">Propoſitio centeſima ſexageſima tertia.</s>
            </p>
            <p type="main">
              <s id="id002903">Proportionem uirium ſtellarum per motus ſuos indagare.</s>
            </p>
            <p type="main">
              <s id="id002904">Mouentur ſtellæ omnes ab Oriente in Occidentem die una, qui
                <lb/>
                <arrow.to.target n="marg572"/>
                <lb/>
              motus fit à prima mente, quæ mouet: ideò quod ad hoc attinet non
                <lb/>
              eſt diuerſitas: uerùm in motibus ab Occidente in Orientem
                <expan abbr="cũ">cum</expan>
              ſint
                <lb/>
              proprij, oportet conſiderare tempus, in quo
                <expan abbr="circumuertũtur">circumuertuntur</expan>
              , & ma
                <lb/>
              gnitudinem ambitus, & inde magnitudinem orbis, qui circumagi­
                <lb/>
              tur, & horum trium facta comparatione dignoſcitur robur uirium
                <lb/>
              ſtellarum & uitarum quæ mouent eas. </s>
              <s id="id002905">Ponatur ergo, ut uelim pro­
                <lb/>
              portionem uitę Saturni ad uitam Lunæ: erit ergo (ut docet Alphra
                <lb/>
                <arrow.to.target n="marg573"/>
                <lb/>
              ganus) Luna, cum eſt in longitudine propiore, altitudinem habens
                <lb/>
              109000 M.P. & cum eſt in longitudine longiore 208500, tota igitur
                <lb/>
              dimetiens 417000 M.P. mane 218000 M.P. </s>
              <s id="id002906">Igitur proportio ſolida­
                <lb/>
              rum ſphærarum eſt uelut 72511713 ad 10360232, remanebit ergo
                <lb/>
              proportio orbis ad ſphæram elementorum, ut 62151481 ad
                <lb/>
              10360232, & eſt ſexcuplum fermè. </s>
              <s id="id002907">Rurſus proportio dimetientis al­
                <lb/>
              titudinis Saturni ad contentum eſt uelut 2011 ad 1440, & eſt propè
                <lb/>
              201 ad 114, quare 67 ad 38, quare ſphærarum ut 300000 ad 55000
                <lb/>
              ferme. </s>
              <s id="id002908">Igitur ferè ut 60 ad 11. Rurſus proportio dimetientis ſphæ­
                <lb/>
              ræ Saturni ad dimetientem ſphæræ Lunæ eſt propè 313, & ſphæra­
                <lb/>
              rum ſolidarum 306 317 10. Perinde eſt. </s>
              <s id="id002909">Quia ergo proportio ſphæ­
                <lb/>
              ræ Saturni ad ſphæram Lunæ eſt 30631710, & orbis Lunæ eſt 5/6
                <lb/>
              ſolum ſphæræ ſuæ diuidemus 30631710 per 5/6, & exibit proportio
                <lb/>
              ſphæræ Saturni ad orbem Lunæ 36758052, at quia proportio ſo­
                <lb/>
              lidæ ſphæræ Saturni ad contentum eſt ut 60 ad 11, erit ſphæræ ad
                <lb/>
              orbem, ut 60 ad 49 reſiduum, diuidam ergo 36758052 per 60, exe­
                <lb/>
              unt 612634, & ducam per 49, id eſt per 100, fit 61263400, & diuiden
                <lb/>
              do per 2, exit 30631700, detraho 612634, relinquitur proportio or­
                <lb/>
              bis Saturni ad orbem Lunæ 30019066.</s>
            </p>
            <p type="margin">
              <s id="id002910">
                <margin.target id="marg572"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id002911">
                <margin.target id="marg573"/>
              D
                <emph type="italics"/>
              iff.
                <emph.end type="italics"/>
              21.</s>
            </p>
            <p type="main">
              <s id="id002912">Iam uerò circuitus Saturni ad circulum Lunæ, proportio eſt 313,
                <lb/>
              ut uiſum eſt, Lunæ autem tempus per ſex ductum eſt 164 dies, Sa­
                <lb/>
              turni 177 anni propemodum, qui ſunt dies 64649 diuide, duc
                <lb/>
              ergo 313 in 164, fiunt 51332. Idem ergo peragrat Luna in
                <lb/>
              51332 diebus, quod Saturnus in 64649, & eſt quo ad hoc </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum