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="id004143">
                <pb pagenum="243" xlink:href="015/01/262.jpg"/>
              dum à plano reſilit (licet refragante Plutarcho) ita ut anguli c b e, &
                <lb/>
              d b f ſint æquales, dico angulos ibidem d b a, & c b a æquales eſſe:
                <lb/>
                <figure id="id.015.01.262.1.jpg" xlink:href="015/01/262/1.jpg" number="263"/>
                <lb/>
              & quod ſi trahatur latus a b uſque ad g, quod anguli d b
                <lb/>
              g & c b g etiam erunt ęquales. </s>
              <s id="id004144">Primum patet, quia an­
                <lb/>
              guli a b e & a b c & a b f æquales ſunt, ſunt enim reſi­
                <lb/>
              dui ad angulos contactus eiuſdem circuli & rectæ, igi
                <lb/>
              tur additis æqualibus ex ſuppoſito c b e, d b f erunt </s>
            </p>
            <p type="main">
              <s id="id004145">
                <arrow.to.target n="marg818"/>
                <lb/>
              per communem animi ſententiam a b c & a b d æqua­
                <lb/>
              les. </s>
              <s id="id004146">Secundum, cum ſint a b c & a b d æquales, & duo
                <lb/>
              anguli a b c, c b g æquales duobus rectis: itemque a b d,
                <lb/>
              d b g duobus rectis æquales: Et omnes recti inuicem æquales ex
                <lb/>
                <arrow.to.target n="marg819"/>
                <lb/>
              petitione Euclidis erunt per communem animi ſententiam, æqua­
                <lb/>
              les reſidui quoque c b g & d b g.</s>
            </p>
            <p type="margin">
              <s id="id004147">
                <margin.target id="marg818"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              16.
                <emph type="italics"/>
              ter
                <lb/>
              tij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004148">
                <margin.target id="marg819"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              13.
                <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="id004149">Ex hoc patet, eam quæ reſilit lineam ſemper ultra lineam à cen­
                <lb/>
                <arrow.to.target n="marg820"/>
                <lb/>
              tro ad punctum, ex quo reſilit ductam ferri.</s>
            </p>
            <p type="margin">
              <s id="id004150">
                <margin.target id="marg820"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id004151">Conſtat quia linea ex centro diuidit angulum per æqualia, ergo
                <lb/>
                <arrow.to.target n="marg821"/>
                <lb/>
              cadit media inter illa quæ incidit, & quæ reſilit.</s>
            </p>
            <p type="margin">
              <s id="id004152">
                <margin.target id="marg821"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id004153">Ex hac etiam patet, quòd conſtituto angulo in cen­
                <lb/>
                <arrow.to.target n="marg822"/>
                <lb/>
              tro a b c, & ducta linea a d à puncto a, ſciemus quo reſi­
                <lb/>
              lit in linea b c: ducta enim c d, faciemus angulum c d e
                <lb/>
                <arrow.to.target n="marg823"/>
                <lb/>
              æqualem a b c, & erit angulus a d g æqualis angulo e d
                <lb/>
              h, igitur d e reſilit ex a b a d linea.</s>
            </p>
            <p type="margin">
              <s id="id004154">
                <margin.target id="marg822"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              m. </s>
              <s id="id004155">2.</s>
            </p>
            <p type="margin">
              <s id="id004156">
                <margin.target id="marg823"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              23.
                <emph type="italics"/>
              pri
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <figure id="id.015.01.262.2.jpg" xlink:href="015/01/262/2.jpg" number="264"/>
            <p type="main">
              <s id="id004157">Propoſitio ducenteſima undecima.</s>
            </p>
            <p type="main">
              <s id="id004158">Si duæ lineæ ex duobus punctis peripheriam contingentes in
                <lb/>
              eandem partem protrahantur, ſemper magis diſtabunt inuicem ea
                <lb/>
              ex parte, & nunquam concurrent.</s>
            </p>
            <figure id="id.015.01.262.3.jpg" xlink:href="015/01/262/3.jpg" number="265"/>
            <p type="main">
              <s id="id004159">Duæ ſemidiametri a b, a c ex terminis earum
                <lb/>
                <arrow.to.target n="marg824"/>
                <lb/>
              duæ contingentes b f, c e, dico quod quanto
                <lb/>
              magis protrahentur in partem e f, tantò magis
                <lb/>
              diſtabunt, nunquàm concurrent: Nam angu­
                <lb/>
              lus a c g rectus eſt: angulus uerò c a d, ſi ſit re­
                <lb/>
                <arrow.to.target n="marg825"/>
                <lb/>
              ctus e g, nun<08> concurret cum a d, æquidiſta­
                <lb/>
              bit enim ei: ſin aut ſit maior recto aut ex altera
                <lb/>
                <arrow.to.target n="marg826"/>
                <lb/>
              parte erit minor, & ita concurret, ergo in alte­
                <lb/>
                <arrow.to.target n="marg827"/>
                <lb/>
              ram partem ductæ nunquàm concurrent, ſed perpetuo magis di­
                <lb/>
              ſtabunt. </s>
              <s id="id004160">Si ergo minor recto ſit angulus c a b, igitur e c ex eadem
                <lb/>
                <arrow.to.target n="marg828"/>
                <lb/>
              parte concurret cum a d: concurrat ergo in g: & quia e g cadit ex­
                <lb/>
                <arrow.to.target n="marg829"/>
                <lb/>
              tra circulum, igitur diuidet b f, quæ tangit circulum. </s>
              <s id="id004161">Sit ergo ut </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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