Biancani, Giuseppe, Aristotelis loca mathematica, 1615

Page concordance

< >
Scan Original
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
< >
page |< < of 355 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000744">
                <pb pagenum="38" xlink:href="009/01/038.jpg"/>
              propoſitionis, quæ falſa eſt, nimirum ſuppoſito prædictas lineas eſſe comm.
                <lb/>
              deducit ad impoſſibile, ſiue, vt ait hic Ariſt. falſum ratiocinatur, quod ſci­
                <lb/>
              licet idem numerus eſſet par, & impar, quod Ariſt. ſignificat, quando ait,
                <lb/>
              imparia æqualia paribus fiunt. </s>
              <s id="s.000745">ex quo abſurdo deducitur falſam eſſe prædi­
                <lb/>
              ctam ſuppoſitionem, quæ aſtruebat eſſe comm. & proinde altera pars con­
                <lb/>
              tradictionis, quæ eſt, eſſe incomm. vera aſtruitur. </s>
              <s id="s.000746">ex quibus ſatis videtur ex­
                <lb/>
              plicari hic locus. </s>
              <s id="s.000747">videas igitur, quàm leuiter nonnulli noſtræ tempeſtatis
                <lb/>
              ageometreti iſtud exponant, dicentes diametrum eſſe incomm. coſtæ, nihil
                <lb/>
              aliud ſignificare, quam diametrum eſſe longiorem coſta, qua expoſitione
                <lb/>
              nihil ineptius. </s>
              <s id="s.000748">Aduerte tandem figuram vulgatæ editionis eſſe ineptam,
                <lb/>
              cum habeat duo quadrata alterum ſuper diametro alterius, quorum maius
                <lb/>
              ſuperuacaneum eſt.</s>
            </p>
            <p type="main">
              <s id="s.000749">
                <arrow.to.target n="marg6"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.000750">
                <margin.target id="marg6"/>
              6</s>
            </p>
            <p type="main">
              <s id="s.000751">Et cap. 24. ſecti primi libri primi
                <emph type="italics"/>
              (Sed magis efficitur manifeſtum in deſcri­
                <lb/>
              ptionibus, vt quod æquicruris, qui ad baſim æquales ſint, ad centrum ductæ A B,
                <lb/>
              A C, ſi igitur æqualem accipiat A G, angulum ipſi A B D, non omnino exiſtimans
                <lb/>
              æquales, qui ſemicirculorum, & rurſus G, ipſi D, non omnem aſſumens eum, qui ſe­
                <lb/>
              cti. </s>
              <s id="s.000752">amplius ab æqualibus existentibus totis angulis, & ablatorum æquales eſſe re­
                <lb/>
              liquos E, F, quod ex principio petet, niſi acceperit ab æqualibus demptis æqualia
                <lb/>
              derelinqui.)
                <emph.end type="italics"/>
              Primum ſcias characteres vulgatæ editionis, vna cum figura ip­
                <lb/>
              ſis reſpondente, eſſe mendoſos; propterea ex textu græco vtrunque corri­
                <lb/>
              gendum putaui in hunc, quem vidiſti modum. </s>
              <s id="s.000753">Secundo, per deſcriptiones
                <lb/>
              Ariſt. intelligere
                <expan abbr="demõſtrationes">demonſtrationes</expan>
              Geometricas ſupra diximus, quod ex hoc
                <lb/>
              loco euidenter confirmatur, vbi manifeſtè loco deſcriptionis ſupponit li­
                <lb/>
              nearem demonſtrationem. </s>
              <s id="s.000754">In hoc
                <expan abbr="itaq;">itaque</expan>
              exemplo vult Ariſt. illud demon­
                <lb/>
              ſtrare, quod Euclides in 5. primi oſtendit, alio tamen modo, ſcilicet Iſoſce­
                <lb/>
              lium triangulorum, qui ad baſim ſunt anguli, inter ſe ſunt æquales. </s>
              <s id="s.000755">eſt au­
                <lb/>
              tem figura in omnibus textibus deprauata, quam ſic puto
                <expan abbr="rèſtītuendam">rèſtituendam</expan>
              eſſe
                <lb/>
              ex quodam græco codice, qui characteres hoc modo appoſuerat. </s>
              <s id="s.000756">ſit Iſoſce­
                <lb/>
                <figure id="id.009.01.038.1.jpg" place="text" xlink:href="009/01/038/1.jpg" number="6"/>
                <lb/>
              les C A B, cuius baſis C B, Dico angulos ſupra baſim,
                <lb/>
              in quibus literæ E F, eſſe inuicem æquales. </s>
              <s id="s.000757">facto centro
                <lb/>
              in A, deſcribatur circulus A B C, tranſiens per puncta
                <lb/>
              C B, iam ſic. </s>
              <s id="s.000758">omnes anguli ſemicirculi ſunt æquales in­
                <lb/>
              ter ſe, ergo anguli A C G, A B D, ſunt æquales. </s>
              <s id="s.000759">Præte­
                <lb/>
              rea cùm anguli eiuſdem ſectionis ſint æquales ad inui­
                <lb/>
              cem, erunt anguli ſectionis C B D G, nimirum anguli,
                <lb/>
              in quibus ſunt G, & D, inter ſe æquales:
                <expan abbr="cumq́">cumque</expan>
              ; hi duo
                <lb/>
              anguli ſectionis ſint partes
                <expan abbr="angulorũ">angulorum</expan>
              ſemicirculi A C G,
                <lb/>
              A B D, ſi illi ab his auferantur, auferuntur æquales anguli ab æqualibus an­
                <lb/>
              gulis, ergo anguli, qui remanent, ſcilicet E, & F, erunt æquales, quod erat
                <lb/>
              demonſtrandum. </s>
              <s id="s.000760">hinc Ariſt. infert manifeſtum eſſe oportere in omni ſyllo­
                <lb/>
              giſmo, reperiri vniuerſales, & affirmatiuas propoſitiones, vt Factum eſt in
                <lb/>
              præcedenti aliter eſſet petitio principij. </s>
              <s id="s.000761">Quænam vero ſit æqualitas, quam
                <lb/>
              Geometræ conſiderant, infra cap. 1. ſecti 3. explicabitur.</s>
            </p>
            <p type="main">
              <s id="s.000762">
                <arrow.to.target n="marg7"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.000763">
                <margin.target id="marg7"/>
              7</s>
            </p>
            <p type="main">
              <s id="s.000764">Ex cap. 2. ſecti 2. lib. 1.
                <emph type="italics"/>
              (Secundum veritatem quidem ex ijs, quæ ſecundum
                <lb/>
              veritatem deſcribuntur ineſſe, ad dialecticos autem ſyllogiſmos ex propoſitionibus
                <lb/>
              ſecundum opinionem)
                <emph.end type="italics"/>
              verba illa; ex ijs, quæ
                <expan abbr="ſecundũ">ſecundum</expan>
              veritatem deſcribuntur </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum