Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.003390">
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              iſtud diſſerere. </s>
              <s id="s.003391">& quia partim rationibus phyſicis, partim geometricis vti­
                <lb/>
              tur, ideò nec omninò phyſicus nec omninò mathematicus eſt. </s>
              <s id="s.003392">Ego igitur,
                <lb/>
              quæ mathematica ſunt, ex inſtituto exponere aggrediar.</s>
            </p>
            <p type="main">
              <s id="s.003393">Ad intelligentiam igitur huius operis neceſſarium eſt nouiſſe, quæ nam
                <lb/>
              ſint quantitates commenſurabiles, & quæ in commenſurabiles. </s>
              <s id="s.003394">quæ prima,
                <lb/>
              & ſecunda definitione 10. Elem. explicantur;
                <expan abbr="egoq́">egoque</expan>
              ; eas primo Priorum oc­
                <lb/>
              caſione aſymetriæ diametri cum coſta ſatis expoſui: vtrumuis locum vide­
                <lb/>
              ris præſenti neceſſitati conſultum erit.</s>
            </p>
            <p type="main">
              <s id="s.003395">
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            <p type="margin">
              <s id="s.003396">
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              277</s>
            </p>
            <p type="main">
              <s id="s.003397">Primus locus Mathematicus eſt hic
                <emph type="italics"/>
              (Poſtremò ex ijs, quæ tradunt Mathe­
                <lb/>
              maticis imbuti diſciplinis, quiuis lineam aliquam inſecabilem eſſe concedet. </s>
              <s id="s.003398">nam
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              ſi, vt aiunt, illæ commenſurabiles ſunt lineæ, quæ eadem menſura dimetiri queunt,
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              & nihil impedit, quin omnes commenſurabiles re ipſa dimetiantur, extabit profe­
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              ctò longitudo aliqua, qua omnes commenſurabuntur; quæ neceſſario erit indiuidua,
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              nam ſi dicatur eſſe diuidua, huius
                <expan abbr="quoq;">quoque</expan>
              menſuræ partes, menſuram aliquam com­
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              munem habebunt, partes enim toti commenſurabiles ſunt ita, vt portio partis il­
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              lius, quæ dimidium totius fuerat, efficiatur dupla alterius; quoniam autem hoc
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              fieri nequit, atoma debet eſſe menſura hæc communis.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.003399">
                <emph type="italics"/>
              Eodem modo, & quæ ſimul ab ipſa menſura commenſuratæ, tanquam omnes ex
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              ea menſura compoſitæ ſunt lineæ, veluti ex atomis conflantur.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.003400">Affert rationem quandam ex Mathematicis, qua nonnulli probabant ex­
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              tare lineas atomas, ex quibus cæteræ lineæ tanquam partibus conſtarent:
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              ac proinde negabant lineas eſſe in infinitum diuiduas, ſeu quamlibet lineam
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              ſecari poſſe, ſed aſſerebant
                <expan abbr="diuidẽdo">diuidendo</expan>
              , tandem ad indiuiduas
                <expan abbr="deueniendũ">deueniendum</expan>
              eſſe.</s>
            </p>
            <p type="main">
              <s id="s.003401">Præmiſſa igitur, vt monui commenſurabilium, & incommenſurabilium
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              linearum cognitione in hunc modum, & textum Ariſtot. & rationem ipſo­
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              rum exponam.</s>
            </p>
            <p type="main">
              <s id="s.003402">Mathematici oſtendunt extare lineas commenſurabiles, quæ ſcilicet ea­
                <lb/>
              dem communi menſura menſurantur: at nihil impedit quin omnes
                <expan abbr="cõmen-ſurabiles">commen­
                  <lb/>
                ſurabiles</expan>
              re ipſa menſurentur, debet ergò extare vna aliqua longitudo, qua
                <lb/>
              omnes commenſurabiles dimetiamur. </s>
              <s id="s.003403">hanc autem neceſſe eſt eſſe atomam,
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              nam ſi diuidua ſtatuatur, poterit ſemper ſecari, & ſubſecari bifariam, qua­
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              re cum partes huiuſmodi ſint toti commenſurabiles, ſequetur aliam exiſtere
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              menſuram, qua omnes hæ partes, & proinde tota linea commenſurentur.
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              </s>
              <s id="s.003404">Verùm hoc fieri nequit, nam hoc pacto non eſſet vna tantum longitudo om­
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              nium commenſurabilium linearum communis menſura, verùm plures, &
                <lb/>
              plures in infinitum, quod eſt contra Mathematicorum placita. </s>
              <s id="s.003405">dicendum,
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              itaque, communem illam omnium menſuram eſſe omnis diuiſionis exper­
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              tem; & propterea etiam lineas omnes commenſurabiles ex atomis lineis
                <lb/>
              componi, quæ nimirum prædictæ communi menſuræ æquales ſint. </s>
              <s id="s.003406">
                <expan abbr="atq;">atque</expan>
              hæc
                <lb/>
              eſt illarum prima argumentatio.</s>
            </p>
            <p type="main">
              <s id="s.003407">
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              </s>
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            <p type="margin">
              <s id="s.003408">
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              278</s>
            </p>
            <p type="main">
              <s id="s.003409">Secundus locus
                <emph type="italics"/>
              (Idem etiam contingit in figuris planis, quæ à lineis rationa­
                <lb/>
              libus procreantur: nam omnes huiuſmodi figuræ erunt etiam inuicem commenſura­
                <lb/>
              biles, quare
                <expan abbr="ēadem">eadem</expan>
              ratione, qua in lineis proximè vſi ſumus, ſequetur earum com­
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              munem menſuram eſſe pariter indiuiduam.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.003410">Sciendum eſt omnes lineas
                <expan abbr="cõmenſurabiles">commenſurabiles</expan>
              longitudine, eſſe etiam com­
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              menſurabiles (vt aiunt Geometræ) potentia, ideſt ſecundum quadrata </s>
            </p>
          </chap>
        </body>
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    </archimedes>
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