Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.001377">
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              tum procedatur, numeri ſemper quadrati progignentur. </s>
              <s id="s.001378">Vides igitur, qui
                <lb/>
              ratione Gnomonum, ſiue imparium additione fiat ſemper eadem ſpecies,
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              ſcilicet quadratus numerus, quod ſignum eſt, inquiunt, imparem numerum
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              non infinitatis, ſed finitatis eſſe auctorem. </s>
              <s id="s.001379">Poſt prædictam 26. propoſitio­
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              nem Iordani, ſunt aliquot propoſitiones, quarum ſumma hæc eſt: ſi pares
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              numeri ab vnitate coaceruentur; coaceruati erunt ſemper variæ formæ nu­
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              merorum. </s>
              <s id="s.001380">quæ ſic explicantur: ſint ab vnitate pares diſpoſiti ordinatim
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              hoc modo, 1. 2. 4. 6. &c. </s>
              <s id="s.001381">ſi igitur vnitati binarius coaceruetur, fit numerus
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                <figure id="id.009.01.075.1.jpg" place="text" xlink:href="009/01/075/1.jpg" number="41"/>
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              triangularis, vt in prima figura. </s>
              <s id="s.001382">ſi huic ternario
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              coaceruetur ſequens par, fiet altera ſpecies, ni­
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              mirum hexagonus numerus, vt in ſecunda figu­
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              ra. </s>
              <s id="s.001383">cui ſi ſequens addatur par, ſcilicet ſenarius,
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              fiet iterum noua numeri forma, v. g. </s>
              <s id="s.001384">dodecago­
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              nus, vt in tertia figura. </s>
              <s id="s.001385">& ſic ſemper in infinitum nouæ ac variæ numerorum
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              formæ ex hac additione parium prouenient, quod argumento eſt numerum
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              parem infiniti naturam ſapere. </s>
              <s id="s.001386">Porrò reperiri numeros triangulares, pen­
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              tagonos, & ſimiles, conſtat ex Arithmetica Nicomachi, Boetij, & Iordani,
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              citati in definitionibus 7. ſuæ Arithmeticæ, atque ex tractatu Diophantis
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              Alex. de numeris rectangulis. </s>
              <s id="s.001387">
                <expan abbr="atq;">atque</expan>
              ex his locus hic ſatis clarus redditur.</s>
            </p>
            <p type="main">
              <s id="s.001388">
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              </s>
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            <p type="margin">
              <s id="s.001389">
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              94</s>
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            <p type="main">
              <s id="s.001390">Tex. 31.
                <emph type="italics"/>
              (Vtuntur etiam Mathematici infinito)
                <emph.end type="italics"/>
                <expan abbr="aliquãdo">aliquando</expan>
              Mathematici du­
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              cunt lineas quantumuis longas, ſeu indefinitæ longitudinis, quas etiam in­
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              finitas appellant: & hoc modo vtuntur infinito, vt infra tex. 71. ipſe Ariſt.
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              exponit. </s>
              <s id="s.001391">alio præterea modo vtuntur infinito, vt quando ſupponunt data
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              quauis quantitate poſſe ſumi maiorem, vel etiam minorem in infinitum, vt
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              patet ex 6. poſtulato primi Elem. editionis Clauianæ. </s>
              <s id="s.001392">numerum
                <expan abbr="quoq;">quoque</expan>
              au­
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              geri poſſe in infinitum, eſt ſecundum poſtulatum libri 7. Elem. vel demum
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              quando probant quamlibet lineam poſſe diuidi bifariam, quia hinc ſequitur
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              poſſe ſub diuidi in
                <expan abbr="infinitũ">infinitum</expan>
              ; his igitur modis Mathematicis
                <expan abbr="infinitũ">infinitum</expan>
              in vſu eſt.</s>
            </p>
            <p type="main">
              <s id="s.001393">
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              </s>
            </p>
            <p type="margin">
              <s id="s.001394">
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              95</s>
            </p>
            <p type="main">
              <s id="s.001395">Tex. 68. & 69. plura de magnitudine, & numero continent; ſed quæ non
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              indigeant opera noſtra.</s>
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            <p type="main">
              <s id="s.001396">
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              </s>
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            <p type="margin">
              <s id="s.001397">
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              96</s>
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            <p type="main">
              <s id="s.001398">Tex. 71.
                <emph type="italics"/>
              (Non remouet autem ratio Mathematicos à contemplatione auferens
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              ſic eſſe infinitum, vt actu ſit verſus augmentum, vt intranſibile,
                <expan abbr="ncq;">neque</expan>
              enim nunc in­
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              digent infinito,
                <expan abbr="neq;">neque</expan>
              vtuntur, ſed ſolum eſſe
                <expan abbr="quantumcunqu;">quantumcunque</expan>
              velint finitam)
                <emph.end type="italics"/>
              ratio
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              phyſica tollens infinitum actu, non eſt Mathematicis impedimento, quia ipſi
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              non vtuntur infinito actu; quam enim ipſi ducunt lineam infinitam, non eſt
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              verè infinita, ſed indefinita, eam enim quantumlibet magnam producunt, vt
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              poſſit ad demonſtrandum ſufficere.</s>
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          </chap>
          <chap>
            <p type="head">
              <s id="s.001399">
                <emph type="italics"/>
              Ex Quarto Phyſicorum.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.001400">
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            <p type="margin">
              <s id="s.001401">
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              97</s>
            </p>
            <p type="main">
              <s id="s.001402">Tex. 120. ter in hoc textu meminit commenſurabilitatis, & incommen­
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              ſurabilitatis, quæ eſt diametri ad coſtam: cuius explicationem vide
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              primo Priorum, ſecto primo, cap. 23.</s>
            </p>
          </chap>
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      </text>
    </archimedes>
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