Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000785">
                <pb pagenum="41" xlink:href="009/01/041.jpg"/>
              æqualitas nullum diſcrimen, quantumuis minimum admittat, quod ſenſui
                <lb/>
              vitare ob ſui imperfectionem non licet: vnde inter eæ, quæ mathematicè
                <lb/>
              ſunt æqualia, nullus intellectus aliquam valeat reperire differentiam) ſumat
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              inquam triangulum quodpiam materiale, vt ex charta, quantum fieri po­
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              teſt perfectum, deinde ducat lineam vnam perpendicularem ſuper aliam,
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              quæ ſcilicet faciat, cum illa duos angulos rectos. </s>
              <s id="s.000786">poſtea abſcindat tres an­
                <lb/>
              gulos trianguli materialis,
                <expan abbr="eosq́">eosque</expan>
              ; ita ſimul componat, vt mucrones illorum
                <lb/>
              ſint vniti, & contigui ad punctum lineæ perpendicularis cum altera, vti eſt
                <lb/>
              in ſuperiori figura punctum E; & illicò apparebit tres illos angulos mate­
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              riales obtegere adæquatè totum illud ſpatium duorum rectorum, quos per­
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              pendicularis conſtituit. </s>
              <s id="s.000787">Hoc autem experiri poteris in diuerſis admodum
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              triangulis Scalenis, Rectangulis, Iſoſcelibus, Aequilateris, &c. </s>
              <s id="s.000788">non ſine de­
                <lb/>
              lectatione, atque hic eſt ſenſus illorum verborum, omnis triangulus habet
                <lb/>
              tres ęquales duobus rectis. </s>
              <s id="s.000789">Abſtineo à demonſtrationibus geometricis, quo­
                <lb/>
              niam ij, qui Mathematicis ſunt imbuti, noſtra hac opera parum indigent.
                <lb/>
              </s>
              <s id="s.000790">ſi quis tamen volet, conſulat 32. primi Elem. </s>
              <s id="s.000791">Ex hac igitur declaratione
                <lb/>
              licet cognoſcere nonnullos ageometretos locum hunc, & ſimiles ſubſequen­
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              tes non ſatis intelligere, dicentes, nihil aliud verba illa Ariſt. velle ſignifi­
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              care, quàm omnem triangulum habere tres angulos, quod inquiunt, notiſ­
                <lb/>
              ſimum eſt. </s>
              <s id="s.000792">Sed ſi incidant in ſequentia; æquales duobus rectis, tunc, cum
                <lb/>
              hæc non intelligant, abſtinent etiam à priorum declaratione, quibus præ­
                <lb/>
              miſſis facile eſt Ariſt. textum percipere. </s>
              <s id="s.000793">ſit A, duo recti, ideſt, duo anguli
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              recti ſint paſſio demonſtranda, in quo B, triangulus, in quo C, æquicrus. </s>
              <s id="s.000794">ipſi
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              itaque C, ideſt triangulo æquicruſi, ineſt A, ſcilicet duo recti, hoc eſt, ineſt
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              æquicruſi hæc, paſſio habere tres angulos æquales duobus rectis per B, ideſt
                <lb/>
              per
                <expan abbr="triangulũ">triangulum</expan>
              vniuerſale, quia hæc proprietas eſt trianguli propria, &
                <expan abbr="cõpe-tit">compe­
                  <lb/>
                tit</expan>
              æquicruſi, non vt æquicrus eſt, ſed, vt triangulum eſt; quare B, non erit
                <lb/>
              medium ipſius A, quia prædicta paſſio. </s>
              <s id="s.000795">A, non competit triangulo B, per
                <lb/>
              aliud, ſed per ſe, de eo enim primo, & per ſe demonſtratur in 32. primi Elem.
                <lb/>
              optimè Aegydius, & Niphus in hunc locum.</s>
            </p>
            <p type="main">
              <s id="s.000796">
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              </s>
            </p>
            <p type="margin">
              <s id="s.000797">
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              11</s>
            </p>
            <p type="main">
              <s id="s.000798">Ex eodem cap.
                <emph type="italics"/>
              (Non oportet autem exiſtimare penes id, quod exponimus, ali­
                <lb/>
              quid accidere abſurdum, nihil enim vtimur eo, quod eſt hoc aliquid eſſe. </s>
              <s id="s.000799">ſed ſicut
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              Geometra pedalem, & rectam hanc, & ſine latitudine dicit, quæ non ſunt. </s>
              <s id="s.000800">verum
                <lb/>
              non ſic vtitur, tanquam ex his ratiocinans)
                <emph.end type="italics"/>
              Quoniam Ariſt. in exemplis affert
                <lb/>
              pro rebus characteres, A, B, C, poſſet quiſpiam ſuſpicari aliquod propterea
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              abſurdum accidere: cui ſuſpicioni Ariſt. reſpondet, dicens, nihil inde abſur­
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              di accidere poſſe, quoniam ipſe vtitur hiſce literis,
                <expan abbr="nõ">non</expan>
              quatenus literæ ſunt,
                <lb/>
              ſed quatenus rerum vicem, pro quibus exponuntur, gerunt: quemadmodum
                <lb/>
              etiam Geometræ faciunt, qui lineam, quæ pedalis non eſt, pedalem, & quæ
                <lb/>
              non eſt recta, rectam; & quæ lata eſt, non latam, ſupponunt, & tamen nihil
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              inde abſurdi contingit. </s>
              <s id="s.000801">Ex quibus intelligimus per lineas illas ſenſibiles, &
                <lb/>
              phyſicas, quas Geometræ in ſuis figuris ducunt, intelligendas eſſe lineas ve­
                <lb/>
              rè Mathematicas omni latitudine carentes; vtitur enim inquit Ariſt. Geo­
                <lb/>
              metra lineis phyſicis, non tanquam phyſicis, nec de eis tanquam de phyſicis
                <lb/>
              lineis ratiocinatur, ſed ijs vtitur tanquam verè mathematicis. </s>
              <s id="s.000802">idem dicen­
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              dum eſt de ſuperficiebus, necnon de corporibus, quæ ijdem Geometræ de­
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              ſcribunt, vt per ea, de verè mathematicis diſcurrant.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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