Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <p type="main">
              <s id="s.001572">
                <pb pagenum="86" xlink:href="009/01/086.jpg"/>
              fortè fuit Ariſt. eò quod videret Icoſaedrum conſtare ex viginti pyramidi­
                <lb/>
              bus, verùm illæ non ſunt regulares, ideſt
                <expan abbr="nõ">non</expan>
              ſunt Tetraedra, vt poſtea oſten­
                <lb/>
              dam. </s>
              <s id="s.001573">Verum quidem eſt octo cubos ſimul adactos ſoliditatem conficere,
                <lb/>
              quia ad id neceſſarij ſunt octo anguli ſolidi, quos octo cubi præbere poſſunt,
                <lb/>
              cum anguli ipſorum ſint recti, & ſolidi. </s>
              <s id="s.001574">Verum enim verò plures pyramides
                <lb/>
              regulares, ſiue plura Tetraedra non poſſe replere vacuum,
                <expan abbr="ſolidumq́">ſolidumque</expan>
              ; con­
                <lb/>
              ſtituere, ex eo patet, quia ſi id præſtarent, conflarent neceſſariò, vel vnum
                <lb/>
              ex
                <expan abbr="quinq;">quinque</expan>
              corporibus regularibus, de quibus in 13. Elemen. vel aliud quod­
                <lb/>
              piam; non aliud, nam, vt patet ex ſcholio 13. Elem. non dantur, niſi illa.
                <lb/>
              </s>
              <s id="s.001575">quinque;
                <expan abbr="neq;">neque</expan>
              vllum ex illis, quia diameter huiuſmodi corporis, quod com­
                <lb/>
              poneretur ex illis pyramidibus, eſſet dupla lateris eiuſdem, vt patet, quia
                <lb/>
              pyramides illæ omnes concurrerent ad centrum ſphæræ illas omnes com­
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              plectentis, quare latus vnius pyramidis à ſuperficie ſphæræ incipiens deſi­
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              neret in centrum, ergo latus iſtud eſſet ſemidiameter, quapropter tota dia­
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              meter illius ſphęræ, & conſequenter huius corporis in illa inſcripti, eſſet du­
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              pla lateris eiuſdem figuræ ſolidæ inſcriptæ, ſed nullo talis proportio diame­
                <lb/>
              tri alicuius ex illis
                <expan abbr="quinq;">quinque</expan>
              ſolidis regularibus ad latus eiuſdem reperitur,
                <lb/>
              quæ ſit nimirum dupla, vt patet ex vltimis demonſtrationibus 13. Elem. ini­
                <lb/>
              tio facto à 13. demonſtratione, in quibus nulla reperitur proportio dupla
                <lb/>
              inter diametrum, & latus eiuſdem alicuius ex illis ſolidis; ex quibus mani­
                <lb/>
              feſtum eſt, plures regulares pyramides quouis pacto ſimul vnitas nullo mo­
                <lb/>
              do replere locum ſolidum. </s>
              <s id="s.001576">cum igitur animaduerterem, ſenſum Ariſt. nullo
                <lb/>
              modo poſſe verificari de repletione ſolidi per plura Tetraedra, & omnes
                <lb/>
              tamen commentatores auctoritate Ariſt. decepti pro ipſo ſtarent, dubius,
                <lb/>
                <expan abbr="ancepsq́">ancepsque</expan>
              ; diu hæſi, neque quid quam mea Minerua aſſerere auſus ſum, ſed P.
                <lb/>
              Clauium præceptorem meum per literas conſului, qui in hunc modum hu­
                <lb/>
              maniſſimè reſpondit; cubus implet locum quater ſumptus, ad idem enim
                <lb/>
              punctum quatuor cubi coaptantur: ſic etiam pyramis ſexies ſumpta, ſeu ſex
                <lb/>
              pyramides ad idem punctum iunctæ ratione ſubſtantium
                <expan abbr="triangulorũ">triangulorum</expan>
              æqui­
                <lb/>
              laterorum. </s>
              <s id="s.001577">Verum hac ratione non videntur implere locum ſolidum, fa­
                <lb/>
              teor; ſed tamen Ariſt. in eo tex. non loquitur de repletione loci ſolidi. </s>
              <s id="s.001578">hæc
                <lb/>
              ipſe. </s>
              <s id="s.001579">ſi igitur libeat Ariſtotelem, quod fortè Clauius intendebat defendere,
                <lb/>
              dicendum eſt cum eo Ariſt non loqui de repletione loci ſolidi:
                <expan abbr="neq;">neque</expan>
              loqui
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              de cubo, & Tetraedro, quatenus ſunt corpora, ſed quatenus habent ſuper­
                <lb/>
              ficies, cubus quidem ſex quadratas, Tetraedrum autem quatuor æquilate­
                <lb/>
              ras ſuperficies, quæ duæ figuræ, vt ſupra in hoc textu vidimus, replent lo­
                <lb/>
              cum:
                <expan abbr="atq;">atque</expan>
              hoc modo facimus Ariſtotelem non formaliter loquentem. </s>
              <s id="s.001580">ex­
                <lb/>
              aduersò ne videamur magis Ariſt. quam veritatem ſequi, videtur dicen­
                <lb/>
              dum, Ariſtotilem formaliter locutum eſſe, & vt patet ex rationibus ſupra
                <lb/>
              allatis de repletione ſolidi eſſe intelligendum, vt etiam intellexerunt omnes
                <lb/>
              huius loci expoſitores; Verumtamen ipſum erraſſe, dum plures pyramides
                <lb/>
              replere ſolidum exiſtimauit. </s>
              <s id="s.001581">Vtrumuis dixerimus, non tamen Ariſt. ab om­
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              ni errore vindicabimus. </s>
              <s id="s.001582">Hoc tamen certum eſt, ex prædictis, Græcos om­
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              nes pariter, ac Latinos, illos ſequentes, lapos eſſe, aſſerentes duodecim py­
                <lb/>
              ramides complere ſolidum locum,
                <expan abbr="atq;">atque</expan>
              Dodecaedrum conſtituere; nam py­
                <lb/>
              ramides Dodecaedron conſtituentes non ſunt regulares, ideſt, non ſunt </s>
            </p>
          </chap>
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    </archimedes>
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