Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <p type="main">
              <s id="s.001190">
                <pb pagenum="64" xlink:href="009/01/064.jpg"/>
              ex
                <expan abbr="quinq;">quinque</expan>
              prædictis proportionibus, ſi ſimul coaluerint, ita vt ex eis vnus
                <lb/>
              tantum ſonus efficiatur; ſonus ille erit concordans, & auribus gratus. </s>
              <s id="s.001191">
                <expan abbr="atq;">atque</expan>
                <lb/>
              hæc eſt ſententia priſcorum præſertim Pythagoreorum, qui propterea di­
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              cebant non licere Muſico vltra quaternarium pertranſire, eò quod ſolæ pro­
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              portiones, vt diximus, numerorum quaternario contentorum, concordem,
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              ac conſonantem concentum efficere poterant: quod vt adhuc melius per­
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                <figure id="id.009.01.064.1.jpg" place="text" xlink:href="009/01/064/1.jpg" number="31"/>
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              cipiamus, accipe exemplum. </s>
              <s id="s.001192">Sint duæ chordæ
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              A, & B, æqualis craſſitici, & æquè tenſæ. </s>
              <s id="s.001193">qua­
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              rum A, dupla ſit ipſius B, quia igitur corpora
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              ſonantia ſunt in dupla proportione, erunt pa­
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              riter eorum ſoni in ratione dupla (vt patet ex
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              principijs harmonicæ) hoc eſt,
                <expan abbr="eorũ">eorum</expan>
              ſoni erunt,
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              vt 2. ad 1. quia ſcilicet ſonus maioris chordæ A, erit duplus ad ſonum mi­
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              noris chordæ B. hoc eſt, erit, vt 2. ad 1. & propterea, ſi ſimul ambæ chordæ
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              pulſentur, ſonus, quem ex duobus mixtum edent, conſonans,
                <expan abbr="atq;">atque</expan>
              gratiſſi­
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              mus auribus noſtris perueniet. </s>
              <s id="s.001194">huiuſmodi porrò conſonantia, quæ eſt in
                <lb/>
              proportione dupla,
                <expan abbr="quæq́">quæque</expan>
              omnium ſuauiſſima eſt, à græcis dicebatur Dia­
                <lb/>
              paſon. </s>
              <s id="s.001195">
                <expan abbr="atq;">atque</expan>
              hæc in præſentia ſufficiant, cum plura de his ad ſectionem pro­
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              blematum 19. quæ tota eſt de Muſica, dicenda ſint.</s>
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            <p type="main">
              <s id="s.001196">
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            <p type="margin">
              <s id="s.001197">
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              65</s>
            </p>
            <p type="main">
              <s id="s.001198">Tex. 2.
                <emph type="italics"/>
              (Vt quod omnis triangulus duobus rectis æquales habet)
                <emph.end type="italics"/>
              vide anno­
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              tata lib. 1. Priorum ſecto 3. cap. 1.</s>
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            <p type="main">
              <s id="s.001199">
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            <p type="margin">
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              66</s>
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            <p type="main">
              <s id="s.001201">Eodem tex.
                <emph type="italics"/>
              (Definitiones verò apparent omnes ſupponentes, & accipientes
                <lb/>
              ipſum quid eſt, vt Mathematicæ, quid vnitas, quid par, & impar)
                <emph.end type="italics"/>
              alludit ad de­
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              finitiones 7. Elem. vbi agitur de numeris. </s>
              <s id="s.001202">Quæ verò hoc loco de principijs
                <lb/>
              dicuntur, luculentiſſimè patent conſideranti definitiones, & axiomata, quæ
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              Mathematicis demonſtrationibus in omnibus ferè libris præmittuntur; ex
                <lb/>
              quibus ſtatim demonſtrationes deriuantur.</s>
            </p>
            <p type="main">
              <s id="s.001203">
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              </s>
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            <p type="margin">
              <s id="s.001204">
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              67</s>
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            <p type="main">
              <s id="s.001205">Et paulo poſt
                <emph type="italics"/>
              (
                <expan abbr="Neq;">Neque</expan>
                <expan abbr="vtiq;">vtique</expan>
              de plano figura, non enim eſt planum figura,
                <expan abbr="neq;">neque</expan>
              fi­
                <lb/>
              gura planum)
                <emph.end type="italics"/>
              alludit ad definitiones planarum figurarum, qualis eſt circu­
                <lb/>
              lus, cuius definitio eſt inter definitiones primi Elem. 15. & eſt huiuſmodi:
                <lb/>
              circulus eſt figura plana, ſub vnica linea comprehenſa, quæ periphæria ap­
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              pellatur, ad quam ab vno puncto eorum, quæ intra figuram ſunt poſita, ca­
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              dentes omnes rectæ lineæ inter ſe ſunt æquales: in qua quidem definitione
                <lb/>
              non prædicatur planum de figura, nec figura de plano:
                <expan abbr="neq;">neque</expan>
              enim planum,
                <lb/>
              ſeu plana ſuperficies eſt figura ſecundum ſe, niſi terminetur;
                <expan abbr="neq;">neque</expan>
              figura eſt
                <lb/>
              plana ſuperficies, cum plurimæ ſint figuræ curuæ, & præterea ſolidæ quam­
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              plurimæ.</s>
            </p>
            <p type="main">
              <s id="s.001206">
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              </s>
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            <p type="margin">
              <s id="s.001207">
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              68</s>
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            <p type="main">
              <s id="s.001208">Ibidem
                <emph type="italics"/>
              (Quoniam monſtratum eſt Iſoſceles habere tres angulos æquales duo­
                <lb/>
              bus rectis, ſi id de omni triangulo monſtratum ſit)
                <emph.end type="italics"/>
              ex dictis lib. 1. Priorum ſecto
                <lb/>
              3. cap. 1. petatur huius loci declaratio.</s>
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            <p type="main">
              <s id="s.001209">
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              </s>
            </p>
            <p type="margin">
              <s id="s.001210">
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              69</s>
            </p>
            <p type="main">
              <s id="s.001211">Tex. 7.
                <emph type="italics"/>
              (Quid enim ſignificat triangulum, accipit Geometra)
                <emph.end type="italics"/>
              vt manifeſtum
                <lb/>
              eſt in 20. definitione primi Elem.</s>
            </p>
            <p type="main">
              <s id="s.001212">
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              </s>
            </p>
            <p type="margin">
              <s id="s.001213">
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              70</s>
            </p>
            <p type="main">
              <s id="s.001214">Ibidem
                <emph type="italics"/>
              (Quod autem ſit, monstrat)
                <emph.end type="italics"/>
              vt perſpicuum eſt in prima
                <expan abbr="demõſtra-tione">demonſtra­
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                tione</expan>
              primi Elem. vbi triangulum æquilaterum conſtruit, & poſtea probat
                <lb/>
              illud eſſe triangulum æquilaterum. </s>
              <s id="s.001215">Certum tamen eſt, Geometram ſuppo­
                <lb/>
              nere triangulum in communi, cum inter definitiones ipſius </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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