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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      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id002264">
                <pb pagenum="126" xlink:href="015/01/145.jpg"/>
                <arrow.to.target n="marg448"/>
                <lb/>
              notus, & ita extendemus per totum annum. </s>
              <s id="id002265">Cum uerò fuerit g ele­
                <lb/>
              uatus erit, ut
                <expan abbr="demõſtratum">demonſtratum</expan>
              eſt, in circulo magno uerticali, ergo an­
                <lb/>
              gulus fiet in eodem circulo, quia gnomo eſt etiam in illius ſuperfi­
                <lb/>
              cie. </s>
              <s id="id002266">Ergo angulus erit æqualis angulo, quem faceret ſol, ſi oriretur
                <lb/>
                <arrow.to.target n="marg449"/>
                <lb/>
                <figure id="id.015.01.145.1.jpg" xlink:href="015/01/145/1.jpg" number="136"/>
                <lb/>
              in puncto horizontis, quem ſecat circulus
                <lb/>
              uerticalis ſub ea altitudine: ſed his eſt no­
                <lb/>
              tus: nam in priore figura g h f eſt notus ea­
                <lb/>
                <arrow.to.target n="marg450"/>
                <lb/>
                <expan abbr="dẽ">dem</expan>
              ratione, qua f, & ideò ei oppoſitus k h n,
                <lb/>
              & k rectus, eſt enim f polus b d, & h k decli
                <lb/>
              natio nota ergo k n, & h n notæ. </s>
              <s id="id002267">At e k, &
                <lb/>
              g h fuere notæ. </s>
              <s id="id002268">Ergo e n, & g n, quare reſi­
                <lb/>
              duæ n l & n b notæ. </s>
              <s id="id002269">Eſt autem angulus l
                <lb/>
              rectus. </s>
              <s id="id002270">ergo ortus amplitudo puncti l nota
                <lb/>
              ſcilicet arcus l b, ergo in præſenti figura angulus m h b, ergo k h l.
                <lb/>
              </s>
              <s id="id002271">igitur poterimus ſtatuere angulos umbrarum, & iam poſſumus
                <lb/>
              determinare magnitudinem: ergo punctum ad
                <expan abbr="unguẽ">unguem</expan>
              umbrę qua­
                <lb/>
              libet hora, & parte horæ ſingulis diebus in quacunque regione datæ
                <lb/>
              altitudinis poli uerſa, & rects. </s>
              <s id="id002272">In cylindrica autem eodem modo ſi­
                <lb/>
              cut in uerſa, eſt enim ſpecies umbrę uerſę, niſi quod analema ob ob­
                <lb/>
              liquitatem cylindri melius aptatur, rotundum ſcilicet cum
                <expan abbr="rotũdo">rotundo</expan>
              .</s>
            </p>
            <p type="margin">
              <s id="id002273">
                <margin.target id="marg445"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id002274">
                <margin.target id="marg446"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              28.
                <emph type="italics"/>
              li.
                <emph.end type="italics"/>
              4.
                <lb/>
                <emph type="italics"/>
              loan. </s>
              <s id="id002275">de
                <emph.end type="italics"/>
              M
                <emph type="italics"/>
              on
                <lb/>
              teregij de
                <emph.end type="italics"/>
                <lb/>
              T
                <emph type="italics"/>
              riang.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002276">
                <margin.target id="marg447"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              123.
                <lb/>
                <emph type="italics"/>
              uel
                <emph.end type="italics"/>
              124.
                <lb/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002277">
                <margin.target id="marg448"/>
              P
                <emph type="italics"/>
              rop.
                <emph.end type="italics"/>
              123.
                <lb/>
              C
                <emph type="italics"/>
              orol.
                <emph.end type="italics"/>
              1.</s>
            </p>
            <p type="margin">
              <s id="id002278">
                <margin.target id="marg449"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              127.
                <lb/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002279">
                <margin.target id="marg450"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              15.
                <emph type="italics"/>
              pri
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id002280">Propoſitio centeſima trigeſima prima.</s>
            </p>
            <p type="main">
              <s id="id002281">Si lineæ alicui dupla alterius
                <expan abbr="adiungat̃">adiungatur</expan>
              , erit proportio duarum ad
                <lb/>
                <expan abbr="primã">primam</expan>
              maior, quam dupli, cum prima ad primam cum una adiecta.</s>
            </p>
            <p type="main">
              <s id="id002282">Sit a b linea, cui adiecta ſit b c, & rurſus ad b c c d
                <expan abbr="æq́ualis">æqualis</expan>
              b c
                <lb/>
              dico, quod proportio a c ad a b eſt maior, quàm a d ad a c. </s>
              <s id="id002283">Propor
                <lb/>
                <arrow.to.target n="marg451"/>
                <lb/>
              tio enim c d ad c a minor eſt, quàm ad a b per octauam quinti E­
                <lb/>
              lementorum. </s>
              <s id="id002284">Ergo minor d c ad c a quàm c b ad a b, quia b c & c d
                <lb/>
              ſunt æquales, ideò
                <expan abbr="æqualẽ">æqualem</expan>
              habent
                <expan abbr="proportionẽ">proportionem</expan>
                <lb/>
              ad a b:
                <expan abbr="igit̃">igitur</expan>
              coniungendo per 28. Quinti propor
                <lb/>
                <figure id="id.015.01.145.2.jpg" xlink:href="015/01/145/2.jpg" number="137"/>
                <lb/>
              tio d a ad a c minor, quam c a ad a b, quod erat demonſtrandum.
                <lb/>
                <arrow.to.target n="marg452"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002285">
                <margin.target id="marg451"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="margin">
              <s id="id002286">
                <margin.target id="marg452"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              7.
                <emph type="italics"/>
              quin­
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id002287">Propoſitio centeſima trigeſima ſecunda.</s>
            </p>
            <p type="main">
              <s id="id002288">Si ad duas lineas, quarum una alteri dupla ſit eadem linea adda­
                <lb/>
              tur erit aggregati ex minore, & a d adiecta ad ipſam
                <expan abbr="minorẽ">minorem</expan>
              minor
                <lb/>
              proportio quam aggregati ex maiore, & adiecta ad ipſam maio­
                <lb/>
              rem duplicata.</s>
            </p>
            <p type="main">
              <s id="id002289">
                <arrow.to.target n="marg453"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002290">
                <margin.target id="marg453"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="main">
              <s id="id002291">Sint duæ lineę a b, & c d. </s>
              <s id="id002292">& ſit c d dupla ad a b, ad datur
                <expan abbr="cõmunis">communis</expan>
                <lb/>
                <figure id="id.015.01.145.3.jpg" xlink:href="015/01/145/3.jpg" number="138"/>
                <lb/>
              b e, & uocetur iuncta c d, d f dico,
                <lb/>
              quod proportio e a ad a b, eſt mi­
                <lb/>
              nor duplicata f c ad c d, adijcia­
                <lb/>
              tur d f æqualis g f, quia ergo g d
                <lb/>
              eſt dupla ad f d, ideo ad e b c d autem eſt dupla ad a b, tota igitur </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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