Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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          <pb pagenum="74" xlink:href="009/01/074.jpg"/>
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            <p type="head">
              <s id="s.001364">
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              Ex Tertio Phyſicorum.
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            <p type="main">
              <s id="s.001365">
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              <s id="s.001366">
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              93</s>
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              <s id="s.001367">Tex. 26.
                <emph type="italics"/>
              (Et hi quidem infinitum eſſe par; hoc enim compræhenſura, &
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              ab impari terminatum tribuit ijs, quæ ſunt, infinitatem. </s>
              <s id="s.001368">ſignum autem
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              huius id eſſe, quod contingit in numeris, circumpoſitis enim Gnomoni­
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              bus circa vnum, & ſeorſum, aliquando quidem ſemper aliam fieri ſpe­
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              ciem, aliquando autem vnam)
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              vt melius percipiantur ea, quæ ſequuntur, lege
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              prius, quæ in cap. de Motu in poſt prædicamentis ſcripſi de Gnomone, ad
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              ſimilitudinem enim Gnomonis illius Geometrici, inueniuntur etiam in nu­
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              meris Gnomones Arithmetici. </s>
              <s id="s.001369">Pythagorici enim (à quibus iſta mutuatus
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              eſt Ariſt. numeros impares ſolos appellabant Gnomones, eò quod in for­
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              mam normæ æquilateræ, ſiue Gnomonis conſtitui poſſint, vt patet in his
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                <figure id="id.009.01.074.1.jpg" place="text" xlink:href="009/01/074/1.jpg" number="37"/>
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              nimirum in ternario, quinario, ſeptenario, & ſic de
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              reliquis imparibus. </s>
              <s id="s.001370">pares autem numeri, quia ne­
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              queunt in figuram normæ æquilateræ diſponi, cum
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              non habeant vnitatem pro angulo, & paria poſtea la­
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              tera, vt oportet, non merentur appellari Gnomones, vt quaternarius, ſi di­
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              ſponatur ſic
                <figure id="id.009.01.074.2.jpg" place="text" xlink:href="009/01/074/2.jpg" number="38"/>
              non refert Gnomonem, quia lateribus inęqualibus con­
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              ſtat;
                <expan abbr="neq;">neque</expan>
              ſi hoc modo
                <figure id="id.009.01.074.3.jpg" place="text" xlink:href="009/01/074/3.jpg" number="39"/>
              quia deeſt huic figuræ angularis vnitas, quæ
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              illi neceſſaria eſt. </s>
              <s id="s.001371">Pythagorici igitur dicebant, numerum parem ideò eſſe
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              infinitum ipſum, quia videbant ipſum eſſe cauſam perpetuæ diuiſionis, cum
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              quælibet res quanta ſit diuiſibilis bifariam, ideſt in duo ſecundum numerum
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              parem, & ſubdiuiſibilis poſtea bifariam, & ſic in infinitum, vt de linea pro­
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              blematicè probatur in 10. primi Elem. quamuis theorematicè ſit axioma.
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              </s>
              <s id="s.001372">hunc porrò numerum parem dicebant terminatum eſſe ab impari, quia ori­
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              tur ex diuiſione cuiuſuis rei, quæ vna ſit, ſumentes vnitatem pro impari.
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              </s>
              <s id="s.001373">ſignum præterea huius finitatis ab impari, & infinitatis à pari numero pro­
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              cedentis, aiunt eſſe Gnomones, numeros ſcilicet impares: Gnomones enim,
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              ideſt impares numeri vnitati additi, producunt eandem perpetuò numero­
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              rum formam, videlicet quadratum: at verò è contrariò numeri pares vni­
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              tati additi, conflant perpetuò varias numerorum formas: quapropter vi­
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              dentur numeri impares eſſe finitatis cauſa; ſicut pares ex aduersò infinitatis
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              principium. </s>
              <s id="s.001374">quæ vt melius intelligas, declaranda eſt 26. propoſ. </s>
              <s id="s.001375">7. Arith­
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              metices lordani, vbi iſtud idem demonſtrat, quæ eſt hæc. </s>
              <s id="s.001376">ſit vnitas, & ſuo or­
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              dine ſequantur impares, vt in ſequenti hac ſerie apparet 1. 3. 5. 7. 9. & c.
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                <figure id="id.009.01.074.4.jpg" place="text" xlink:href="009/01/074/4.jpg" number="40"/>
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              ſi igitur vnitati addatur ternarius in Gnomo­
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              nis modum, vt vides in prima figura, produ­
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              cetur quaternarius numerus, qui eſt numerus
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              quadratus (quid ſit quadratus numerus expli­
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              caui in Logicis tex. 9. primi Poſter.) etſi huic
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              quaternario addatur ſequens impar, qui eſt
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              quinarius in modum Gnomonis, vt in ſecunda
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              figura, ſit numerus nouenarius, qui pariter eſt quadratus. </s>
              <s id="s.001377">etſi huic ſimiliter
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              addatur ſequens impar, nimirum ſeptenarius, conflabitur ſedenarius, qui
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              numerus pariter quadratus eſt, vt in tertia figura, & hoc modo, ſi in </s>
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