Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.003714">
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              beat neceſſe eſt. </s>
              <s id="s.003715">& ſi triangulum ſecus, ita etiam, & quadratum commutabitur,
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              ex altera parte enim ei reſpondet. </s>
              <s id="s.003716">& ſi quadratum quatuor angulis rectis æquales,
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              non habuerit angulos ne quidem triangulum duobus rectis habebit æquales)
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              Hanc
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              trianguli affectionem, habere ſcilicet, ſuos tres angulos æquales duobus re­
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              ctis angulis abundè explicaui libro 1. Priorum, ſecto 3. cap. 1. quam Eucli­
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              des propoſit. </s>
              <s id="s.003717">32. primi demonſtrauit, ex qua demonſtratione, tanquam ex
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              Geometrico principio ſequitur omne
                <expan abbr="quoq;">quoque</expan>
              quadrangulum habere quatuor
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              angulos æquales quatuor rectis angulis; omne
                <expan abbr="namq;">namque</expan>
              quadrangulum eſt po­
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              tentia duo triangula, cum diuidatur ducta ipſius diametro in duo
                <expan abbr="trìãgula">trìangula</expan>
              .
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              </s>
              <s id="s.003718">quod ſi triangulus proprietatem illam non haberet,
                <expan abbr="neq;">neque</expan>
              hæc quadrangulo
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              conueniret. </s>
              <s id="s.003719">& ſi quadrangulum non haberet quatuor angulos æquales qua­
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              tuor rectis angulis, neque triangulum habere poſſet tres angulos æqua­
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              les duobus rectis, cum nihil ſit aliud triangulum, quàm dimidiatum qua­
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              drangulum.</s>
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              <s id="s.003720">
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              320</s>
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              <s id="s.003722">Cap. 16.
                <emph type="italics"/>
              (In Geometria ſi quidem cum quis dixerit quadrangulŭm quatuor rectis
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              æquales habere, & percunctatur propter quid, occurrit, quia etiam triangulŭm duo­
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              bus rectis æquales habet. </s>
              <s id="s.003723">in his igitur ex determinato ſibi principio propter quid
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              aſſumpſerunt)
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              Lege, quæ proximè in præcedenti loco expoſui, ea enim om­
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              nia huc etiam pertinent. </s>
              <s id="s.003724">hoc ſolum addendum ad illorum verborum (
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              Ex de­
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              terminato ſibi principio propter quid aſſumpſerunt
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              ) intelligentiam, ideſt ex vna
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              concluſione demonſtrata, tanquam principio alia demonſtrant; quod rectè
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              fieri Ariſt. in primo Poſter. docet.</s>
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              <s id="s.003726">
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              321</s>
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            <p type="main">
              <s id="s.003727">Cap. 31. (
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              A qui proportionale in quatuor nihilominus perficitur: nam quem­
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              admodum A, ad B, ita C, ad D.
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              ) ideſt proportionalitas in quatuor terminis
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              conſiſtit, quemadmodum pluribus ſupra lib. 5. cap. 3. Ethycorum explica­
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              tum eſt: quò nunc Lectorem ablego.</s>
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          <chap>
            <p type="head">
              <s id="s.003728">
                <emph type="italics"/>
              Ex primo Libro Moralium Eudemiorum.
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            </p>
            <p type="main">
              <s id="s.003729">
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              <s id="s.003730">
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              322</s>
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            <p type="main">
              <s id="s.003731">Cap. 5 (
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              Vt ſi duplum multiplicium primum est, non licet multiplex com­
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              muniter prædicatum ſeparari, quippe, quod duplo prius eſt
                <emph.end type="italics"/>
              ) Inter pro­
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              portionum genera vnum eſt, quod dicitur multiplex, quod ſub ſe
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              infinitas ſpecies continet, vt Duplum, Triplum, Quadruplum, & c.
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              in infinitum. </s>
              <s id="s.003732">vbi vides, cur Ariſt. dixerit duplum eſſe primum inter multi­
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              plicia, cum verè naturali ordine numerorum ipſi primus debeatur locus.
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              </s>
              <s id="s.003733">Vides etiam cur non liceat, Multiplex ipſum genus commune prædicatum
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              omnibus ſpeciebus veluti Idæam ſeparari; tunc enim ait, ipſum mul­
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              tiplex abſtractum eſſet prius ordine ipſo primo multiplici, ſci­
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              licet duplo; & Duplum non eſſet primum inter mul­
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              tiplicia, quæ
                <expan abbr="vtraq;">vtraque</expan>
              ſunt abſurda; non igitur
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              illud tanquam Idæam licet ſepa­
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              ratum ponere.</s>
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