Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.005526">
                <pb pagenum="29" xlink:href="009/01/313.jpg"/>
              retur. </s>
              <s id="s.005527">mirum eſt, quam breui ex apertiſſimis ad obſcuriſſima trahat, & ex
                <lb/>
              humillimis in altiſſima ſtatim aſſurgat.</s>
            </p>
            <p type="main">
              <s id="s.005528">Sed iam Arithmeticæ etiam fructus inſpiciamus: in qua pręter ea, quæ
                <lb/>
              Euclides, Iordanus, & Maurolicus egregia ſanè adinuenerunt, quàm mira­
                <lb/>
              bile eſt illud veluti ſcientiarum monſtrum, ac portentum, quod Algebram
                <lb/>
              vocant? </s>
              <s id="s.005529">nihil fortaſſe in tota peritiæ Encyclopedia ſubtilius, profundius ni­
                <lb/>
              hil, non humano ingenio par eſt, ſed quid cœlitus reuelatum dixeris: nume­
                <lb/>
              ros illos, quos ſurdos vocant, & qui nullo modo exprimi poſſunt, addit, ſub­
                <lb/>
              trahit, multiplicat, diuidit, perinde ac ſi numeri communes eſſent: illis ve­
                <lb/>
              rò, quos minores, quàm nihil
                <expan abbr="cõfingit">confingit</expan>
              , quid abſtruſius? </s>
              <s id="s.005530">quibus tamen
                <expan abbr="vtriſq́">vtriſque</expan>
              ;
                <lb/>
              admirandas adeò diſſoluit quæſtiones, & enigmata, vt ij, qui hanc callent
                <lb/>
              eruditionem, nihil in numerorum infinita ditione
                <expan abbr="obſcurũ">obſcurum</expan>
              , nihil arduum ti­
                <lb/>
              meant; vt propterea eos non homines, ſed vel intelligentias quaſdam ſepa­
                <lb/>
              ratas, aut præſtigiatores quoſdam eſſe exiſtimes.</s>
            </p>
            <p type="main">
              <s id="s.005531">Hanc tandem Geometriæ, & Arithmeticæ tractationem abſoluentes, ex
                <lb/>
              prędictis breuiter earum prærogatiuas ſic perſtringamus: quarum.</s>
            </p>
            <p type="main">
              <s id="s.005532">Prima ſit, quòd omnes ſcientiæ partes ab inuicem diſtinctas obtinent, vi­
                <lb/>
              delicet primo loco definitiones,
                <expan abbr="easq́">easque</expan>
              ; eſſentiales. </s>
              <s id="s.005533">Secundò, poſtulata. </s>
              <s id="s.005534">Ter­
                <lb/>
              tiò, axiomata, quę ſunt tria principiorum genera; ex quibus ſcientia dedu
                <lb/>
              citur. </s>
              <s id="s.005535">quapropter quarto loco ſuccedunt propoſitiones cum ſuis demon­
                <lb/>
              ſtrationibus: quæ partim problemata, partim Theoremata ſunt. </s>
              <s id="s.005536">hunc por­
                <lb/>
              rò doctrinæ ordinem pulcherrimum ab Ariſt. etiam traditum, præterquam
                <lb/>
              in Mathematicis, & maximè hiſce puris nuſquam eſt reperire.</s>
            </p>
            <p type="main">
              <s id="s.005537">Secunda, ex principiorum autem præmiſſorum certitudine fit, vt proce­
                <lb/>
              dant à notioribus nobis, & natura.</s>
            </p>
            <p type="main">
              <s id="s.005538">Tertia, quod omnes earum comprobationes ſunt
                <expan abbr="demõſtrationes">demonſtrationes</expan>
              , partim
                <lb/>
              à priori, partim à poſteriori, vbi nihil probabile, nulla opinionum diſcordia,
                <lb/>
              ſed totum euidens, concors, & verum cernitur.</s>
            </p>
            <p type="main">
              <s id="s.005539">Quarta, demonſtrationes à priori ſunt tantum à cauſis intrinſecis mate­
                <lb/>
              ria, & forma.</s>
            </p>
            <p type="main">
              <s id="s.005540">Quinta, demonſtrationes earum, vt plurimum, & quod, & propter quid
                <lb/>
              ſimul manifeſtant.</s>
            </p>
            <p type="main">
              <s id="s.005541">Sexta, eſt mirabilis, & perpetua demonſtrationum connexio, & depen­den
                <lb/>
              tia ab inuicem.</s>
            </p>
            <p type="head">
              <s id="s.005542">
                <emph type="italics"/>
              De Mathematicis medijs, Aſtronomia, Perſpectiua,
                <lb/>
              Mathematica, Muſica. </s>
              <s id="s.005543">Cap. 5.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.005544">De materia harum, cùm apud Philoſophos conueniat, nihil eſt,
                <lb/>
              cur de ea dicamus. </s>
              <s id="s.005545">Eas verò habere perfectiſſimas demonſtra­
                <lb/>
              tiones, quibus etiam mirabiles veritates,
                <expan abbr="easq́">easque</expan>
              ; ſcitu iucundiſſi­
                <lb/>
              mas nobis patefaciunt, vna,
                <expan abbr="eademq́">eademque</expan>
              , opera breuiter demonſtra­
                <lb/>
              bimus. </s>
              <s id="s.005546">non deeſt tamen Ariſt. authoritas 1. Poſter. tex. 30. aſſerentis eas
                <lb/>
              habere cauſas demonſtrationum, ſic. </s>
              <s id="s.005547">Hic enim ipſum quidem quòd ſenſi­
                <lb/>
              tiuorum eſt ſcire, ipſum verò propter quid Mathematicorum, hi
                <expan abbr="namq́">namque</expan>
              ; </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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