Biancani, Giuseppe, Aristotelis loca mathematica, 1615

Table of figures

< >
[Figure 71]
Page: 133
[Figure 72]
Page: 133
[Figure 73]
Page: 135
[Figure 74]
Page: 141
[Figure 75]
Page: 142
[Figure 76]
Page: 142
[Figure 77]
Page: 143
[Figure 78]
Page: 150
[Figure 79]
Page: 151
[Figure 80]
Page: 151
[Figure 81]
Page: 152
[Figure 82]
Page: 154
[Figure 83]
Page: 155
[Figure 84]
Page: 155
[Figure 85]
Page: 155
[Figure 86]
Page: 156
[Figure 87]
Page: 158
[Figure 88]
Page: 159
[Figure 89]
Page: 161
[Figure 90]
Page: 162
[Figure 91]
Page: 163
[Figure 92]
Page: 164
[Figure 93]
Page: 165
[Figure 94]
Page: 166
[Figure 95]
Page: 167
[Figure 96]
Page: 169
[Figure 97]
Page: 170
[Figure 98]
Page: 171
[Figure 99]
Page: 173
[Figure 100]
Page: 176
< >
page |< < of 355 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.001377">
                <pb pagenum="75" xlink:href="009/01/075.jpg"/>
              tum procedatur, numeri ſemper quadrati progignentur. </s>
              <s id="s.001378">Vides igitur, qui
                <lb/>
              ratione Gnomonum, ſiue imparium additione fiat ſemper eadem ſpecies,
                <lb/>
              ſcilicet quadratus numerus, quod ſignum eſt, inquiunt, imparem numerum
                <lb/>
              non infinitatis, ſed finitatis eſſe auctorem. </s>
              <s id="s.001379">Poſt prædictam 26. propoſitio­
                <lb/>
              nem Iordani, ſunt aliquot propoſitiones, quarum ſumma hæc eſt: ſi pares
                <lb/>
              numeri ab vnitate coaceruentur; coaceruati erunt ſemper variæ formæ nu­
                <lb/>
              merorum. </s>
              <s id="s.001380">quæ ſic explicantur: ſint ab vnitate pares diſpoſiti ordinatim
                <lb/>
              hoc modo, 1. 2. 4. 6. &c. </s>
              <s id="s.001381">ſi igitur vnitati binarius coaceruetur, fit numerus
                <lb/>
                <figure id="id.009.01.075.1.jpg" place="text" xlink:href="009/01/075/1.jpg" number="41"/>
                <lb/>
              triangularis, vt in prima figura. </s>
              <s id="s.001382">ſi huic ternario
                <lb/>
              coaceruetur ſequens par, fiet altera ſpecies, ni­
                <lb/>
              mirum hexagonus numerus, vt in ſecunda figu­
                <lb/>
              ra. </s>
              <s id="s.001383">cui ſi ſequens addatur par, ſcilicet ſenarius,
                <lb/>
              fiet iterum noua numeri forma, v. g. </s>
              <s id="s.001384">dodecago­
                <lb/>
              nus, vt in tertia figura. </s>
              <s id="s.001385">& ſic ſemper in infinitum nouæ ac variæ numerorum
                <lb/>
              formæ ex hac additione parium prouenient, quod argumento eſt numerum
                <lb/>
              parem infiniti naturam ſapere. </s>
              <s id="s.001386">Porrò reperiri numeros triangulares, pen­
                <lb/>
              tagonos, & ſimiles, conſtat ex Arithmetica Nicomachi, Boetij, & Iordani,
                <lb/>
              citati in definitionibus 7. ſuæ Arithmeticæ, atque ex tractatu Diophantis
                <lb/>
              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">
                <arrow.to.target n="marg94"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.001389">
                <margin.target id="marg94"/>
              94</s>
            </p>
            <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
                <lb/>
              cunt lineas quantumuis longas, ſeu indefinitæ longitudinis, quas etiam in­
                <lb/>
              finitas appellant: & hoc modo vtuntur infinito, vt infra tex. 71. ipſe Ariſt.
                <lb/>
              exponit. </s>
              <s id="s.001391">alio præterea modo vtuntur infinito, vt quando ſupponunt data
                <lb/>
              quauis quantitate poſſe ſumi maiorem, vel etiam minorem in infinitum, vt
                <lb/>
              patet ex 6. poſtulato primi Elem. editionis Clauianæ. </s>
              <s id="s.001392">numerum
                <expan abbr="quoq;">quoque</expan>
              au­
                <lb/>
              geri poſſe in infinitum, eſt ſecundum poſtulatum libri 7. Elem. vel demum
                <lb/>
              quando probant quamlibet lineam poſſe diuidi bifariam, quia hinc ſequitur
                <lb/>
              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">
                <arrow.to.target n="marg95"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.001394">
                <margin.target id="marg95"/>
              95</s>
            </p>
            <p type="main">
              <s id="s.001395">Tex. 68. & 69. plura de magnitudine, & numero continent; ſed quæ non
                <lb/>
              indigeant opera noſtra.</s>
            </p>
            <p type="main">
              <s id="s.001396">
                <arrow.to.target n="marg96"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.001397">
                <margin.target id="marg96"/>
              96</s>
            </p>
            <p type="main">
              <s id="s.001398">Tex. 71.
                <emph type="italics"/>
              (Non remouet autem ratio Mathematicos à contemplatione auferens
                <lb/>
              ſic eſſe infinitum, vt actu ſit verſus augmentum, vt intranſibile,
                <expan abbr="ncq;">neque</expan>
              enim nunc in­
                <lb/>
              digent infinito,
                <expan abbr="neq;">neque</expan>
              vtuntur, ſed ſolum eſſe
                <expan abbr="quantumcunqu;">quantumcunque</expan>
              velint finitam)
                <emph.end type="italics"/>
              ratio
                <lb/>
              phyſica tollens infinitum actu, non eſt Mathematicis impedimento, quia ipſi
                <lb/>
              non vtuntur infinito actu; quam enim ipſi ducunt lineam infinitam, non eſt
                <lb/>
              verè infinita, ſed indefinita, eam enim quantumlibet magnam producunt, vt
                <lb/>
              poſſit ad demonſtrandum ſufficere.</s>
            </p>
          </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">
                <arrow.to.target n="marg97"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.001401">
                <margin.target id="marg97"/>
              97</s>
            </p>
            <p type="main">
              <s id="s.001402">Tex. 120. ter in hoc textu meminit commenſurabilitatis, & incommen­
                <lb/>
              ſurabilitatis, quæ eſt diametri ad coſtam: cuius explicationem vide
                <lb/>
              primo Priorum, ſecto primo, cap. 23.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum