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 ...
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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id002229">
                <pb pagenum="124" xlink:href="015/01/143.jpg"/>
              Et principalis eſt meridianus, ideò ab illo Aſtrologi horas utrinque
                <lb/>
              ante, & poſt numerant. </s>
              <s id="id002230">Ideò
                <expan abbr="clarũ">clarum</expan>
              eſt, quòd horæ à meridie com­
                <lb/>
              putatæ ſunt
                <expan abbr="cõmunes">communes</expan>
              , habitantibus ſub quauis altitudine poli, &
                <lb/>
              ubiuis ſit, ſol modò regiones æqualiter diſtent à fortunatis, ſeu ſint
                <lb/>
              in eadem longitudine.</s>
            </p>
            <p type="main">
              <s id="id002231">Propoſitio centeſima uigeſima ſeptima.</s>
            </p>
            <p type="main">
              <s id="id002232">Data Poli altitudine ortus amplitudinem demonſtrare.
                <lb/>
                <arrow.to.target n="marg438"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002233">
                <margin.target id="marg438"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002234">Sit horizon a d b æquinoctij circulus
                <lb/>
                <figure id="id.015.01.143.1.jpg" xlink:href="015/01/143/1.jpg" number="134"/>
                <lb/>
              a k f eclyptica c g, & punctus ortus in ea g.
                <lb/>
              </s>
              <s id="id002235">& c initium arietis, & g b amplitudo ortiua
                <lb/>
              & c e, c f quartæ circulorum, ut ſit e f maxi­
                <lb/>
              ma ſolis declinatio, & polus mundi borea­
                <lb/>
              lis l, quia igitur l d nota eſt ex ſuppoſito, &
                <lb/>
              l k quadrans erit k h
                <expan abbr="reſiduũ">reſiduum</expan>
              ad dimidium
                <lb/>
              circuli notum. </s>
              <s id="id002236">Quia uerò æquinoctium, &
                <lb/>
              Meridianus ſecant ſe ad angulos rectos, &
                <lb/>
              b a æquidiſtat ab utro que polo, erit b polus
                <lb/>
              h d, quare b k, quarta circuli, & angulus k
                <lb/>
              rectus. </s>
              <s id="id002237">Igitur ſumus in diſpoſitione tabula­
                <lb/>
              rum primi mobilis, ergo etiam oppoſitus
                <lb/>
              triangulus, qui ei eſt æqualis, & ęquiangu­
                <lb/>
              lus in eadem diſpoſitione b m d, quare cum
                <lb/>
              data ſit g n declinatio
                <expan abbr="pũcti">puncti</expan>
              g dati, datus erit, & arcus g b quæſitus.</s>
            </p>
            <p type="main">
              <s id="id002238">Propoſitio centeſima uigeſima octaua.</s>
            </p>
            <p type="main">
              <s id="id002239">Nota amplitudine ortus cuiuſque
                <expan abbr="pũcti">puncti</expan>
                <expan abbr="arcũ">arcum</expan>
                <expan abbr="ſemidiurnũ">ſemidiurnum</expan>
              inuenire.</s>
            </p>
            <p type="main">
              <s id="id002240">
                <arrow.to.target n="marg439"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002241">
                <margin.target id="marg439"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002242">Sit in eadem figura nota g b, uolo illius
                <expan abbr="arcũ">arcum</expan>
              ſemidiurnum. </s>
              <s id="id002243">Cum
                <lb/>
              ergo g n ſit declinatio, erit pars arcus Meridiani horarij per polos
                <lb/>
              tranſeuntis, compleatur ergo l g n o, & quia g n nota eſt, quia de­
                <lb/>
              clinatio puncti dati, & g b nota ex ſuppoſito, & f angulus rectus,
                <lb/>
              quia e f eſt portio meridiani, erit b n nota differentia aſcenſionis a
                <lb/>
              quarta circuli k b,
                <expan abbr="igit̃">igitur</expan>
              tota k n arcus ſemidiurnus. </s>
              <s id="id002244">
                <expan abbr="Quoniã">Quoniam</expan>
              g p paral
                <lb/>
              lelus ſimilis eſt k n, & in eo
                <expan abbr="reuoluit̃">reuoluitur</expan>
              Sol: ergo quando enim perue­
                <lb/>
              niet ad p. </s>
              <s id="id002245">Poſſumus etiam ſine inuentione arcus ortus amplitudi­
                <lb/>
              nis per triangulum k m d ex notitia g n cognoſcere eandem n b.</s>
            </p>
            <p type="main">
              <s id="id002246">
                <arrow.to.target n="marg440"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002247">
                <margin.target id="marg440"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002248">Ex his duabus ſequitur
                <expan abbr="cõuerſa">conuerſa</expan>
              ſcilicet, quae data magnitudine diei
                <lb/>
                <expan abbr="cuiuſcũque">cuiuſcunque</expan>
              in quauis regione nota erit poli altitudo
                <expan abbr="eiuſdẽ">eiuſdem</expan>
              regionis.</s>
            </p>
            <p type="main">
              <s id="id002249">Propoſitio centeſima uigeſima nona.</s>
            </p>
            <p type="main">
              <s id="id002250">Data altitudine ſolis in quacunque regione quacunque die diſtan­
                <lb/>
              tiam ſolis à Meridiano cognoſcere.</s>
            </p>
            <p type="main">
              <s id="id002251">
                <arrow.to.target n="marg441"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002252">
                <margin.target id="marg441"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002253">Sit Horizon a b c d æquinoctij circulus b e d. </s>
              <s id="id002254">Meridianus a e c
                <lb/>
              Polus mundi Borealis f uertex, g,
                <expan abbr="pũctus">punctus</expan>
              in eclyptica h ducatur ex </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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