Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <p type="main">
              <s id="s.000897">
                <pb pagenum="48" xlink:href="009/01/048.jpg"/>
                <emph type="italics"/>
              est declarante, quemadmodum rectum ineſt lineæ, & circulare: & impar, & par
                <lb/>
              numero, & primum, & compoſitum, & æquilaterum, & altera parte longius. &
                <lb/>
                <expan abbr="oĩbus">omnibus</expan>
              bis inſunt in oratione, quid eſt
                <expan abbr="declarãte">declarante</expan>
              , ibi quidem linea, hic vero numerus)
                <emph.end type="italics"/>
                <lb/>
              quia locus hic benè exponitur à Toleto, & melius etiam à Conymbr. </s>
              <s id="s.000898">addam
                <lb/>
              tantummodo quædam, quæ ad perfectam eius intelligentiam deſiderantur.
                <lb/>
              </s>
              <s id="s.000899">Sciendum igitur primò, nuſquam ab Euclide definiri rectum, circulare,
                <lb/>
              impar, par, primum, compoſitum, æquilaterum, nec altera parte longius:
                <lb/>
                <expan abbr="verũ">verum</expan>
              ab ipſo in definitionibus primi definiri lineam rectam, non tamen cir­
                <lb/>
              cularem expreſsè. </s>
              <s id="s.000900">in definitionibus deinde ſeptimi definiri
                <expan abbr="numerũ">numerum</expan>
              parem,
                <lb/>
              & imparem, item numerum primum, & compoſitum, & æquilaterum, & al­
                <lb/>
              tera parte longiorem. </s>
              <s id="s.000901">ex quibus definitionibus poſſunt erui definitiones re­
                <lb/>
              cti, circularis, imparis, & cæterorum, quorum hic Ariſtoteles meminit.
                <lb/>
              </s>
              <s id="s.000902">Cæterum Euclides definitione 11. ſeptimi, ſic definit numerum primum:
                <lb/>
              primus numerus eſt, quem vnitas ſola metitur. </s>
              <s id="s.000903">numerus autem, vel vnitas
                <lb/>
              metiri dicitur alium numerum, quando ſæpius repetita ipſum omnino ad­
                <lb/>
              æquat, vt ternarius metitur nouenarium, quia ter repetitus ipſum ad vn­
                <lb/>
              guem explet. </s>
              <s id="s.000904">illi igitur numeri dicuntur ab Arithmeticis primi, qui à nullo
                <lb/>
              alio, præterquam ab vnitate menſurantur, quales ſunt, 2. 3. 5. 7. &c. </s>
              <s id="s.000905">Defi­
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              nitione verò 13. definit numerum compoſitum ſic; compoſitus numerus eſt,
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              quem numerus quiſpiam metitur, vt ſenarius erit compoſitus, quia ipſum
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              binarius metitur, nam ter repetitus, ipſi perfectè adæquatur.</s>
            </p>
            <p type="main">
              <s id="s.000906">Per æquilaterum, intelligit quadratum, quadratus autem numerus defi­
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              nitione 18. ſeptimi ſic explicatur: Quadratus numerus eſt, qui ſub duobus
                <lb/>
              æqualibus numeris continetur, ideſt, qui fit ex ductu vnius numeri in ſe ip­
                <lb/>
                <figure id="id.009.01.048.1.jpg" place="text" xlink:href="009/01/048/1.jpg" number="16"/>
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              ſum, vt ſi ducantur 3. in 3. fient 9. qui continetur ſub duobus
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              ternarijs; omnes autem ternarij ſunt æquales. </s>
              <s id="s.000907">is autem nu­
                <lb/>
              merus dicetur quadratus, quia, vt apparet in figura, nouem
                <lb/>
              ipſius vnitates poſſunt in plano ita ad inuicem collocari, vt
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              referant quadratum; & ſicuti quadratum geometricum ha­
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              bet latera æqualia, ita etiam quadratum arithmeticum: ſi­
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              ue numerus quadratus, habet ſua latera æqualia, quot enim vnitates ſunt
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              in vno, tot etiam ſunt in reliquis, vt in præſenti ſunt tres vnitates in ſingulis
                <lb/>
              lateribus. </s>
              <s id="s.000908">pręterea quemadmodum quadratum geometricum reſolui poteſt
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              in plura quadrata, ita etiam arithmeticum, vt præſens, qui reſoluitur in
                <lb/>
              quatuor quadrata arithmetica. </s>
              <s id="s.000909">
                <expan abbr="Neq;">Neque</expan>
              enim poteſt quilibet numerus, vt opi­
                <lb/>
              nantur ageometreti, in hunc modum diſponi, ſed ſolum ij, qui producuntur
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              ex multiplicatione numeri alicuius in ſe ipſum.</s>
            </p>
            <p type="main">
              <s id="s.000910">Per altera parte longius, intelligit numerum, qui producitur à duobus
                <lb/>
                <figure id="id.009.01.048.2.jpg" place="text" xlink:href="009/01/048/2.jpg" number="17"/>
                <lb/>
              numeris inæqualibus inuicem multiplicatis, qualis eſt
                <lb/>
              duodenarius, qui ex ductu trium in quatuor produci­
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              tur, & refert figuram altera parte longiorem, ſiue, vt
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              ait Boetius longilateram, cuius vnum latus eſt maius
                <lb/>
              altero, vt in appoſita figura videre licet. </s>
              <s id="s.000911">atque hæc
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              ſunt, quæ ex Mathematicis petenda erant, ad huius
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              loci intelligentiam.</s>
            </p>
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              25</s>
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            <p type="main">
              <s id="s.000914">Tex. 11.
                <emph type="italics"/>
              (Per ſe autem, & ſecundum quod ipſum, idem, vt per ſe lineæ inest
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
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