Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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      <text>
        <body>
          <chap>
            <pb pagenum="85" xlink:href="009/01/085.jpg"/>
            <p type="head">
              <s id="s.001553">
                <emph type="italics"/>
              Admirabilis quædam Ap̀um industria.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.001554">Cæterum occaſione harum figurarum illud hoc loco apponere vi­
                <lb/>
              ſum eſt, quod Pappus
                <expan abbr="Alexãdrinus">Alexandrinus</expan>
              initio quinti libri collectionum
                <lb/>
              mathematicarum ſcribit, De admirabili Apum induſtria, atque
                <lb/>
              prudentia in conſtruendo ſuas cellulas figura hexagona regulari.
                <lb/>
              </s>
              <s id="s.001555">cum enim vellent omne vacuum excludere, & præterea capaciſſimam
                <expan abbr="om-niũ">om­
                  <lb/>
                nium</expan>
              figuram habere, hexagonam accepere, quæ inter prædictas tres vtrum­
                <lb/>
              que præſtat, nam & inane omne excludit, & illarum trium capaciſſima eſt,
                <lb/>
              cum magis ad circularem figuram accedat: vt patet ex tractatu de figuris
                <lb/>
              Iſoperimetris, qui eſt apud Clauium in ſphæra, necnon in Geometria pra­
                <lb/>
              ctica. </s>
              <s id="s.001556">hoc ideò libentius recenſui, quia animaduerti naturales hiſtoriogra­
                <lb/>
              phos omnes latere, vel ipſum Aldobrandum noſtrum, qui quamuis indu­
                <lb/>
              ſtrioſæ Apis inſtar omnia delibauerit, iſtud tamen de Apibus artificium tan­
                <lb/>
              ta ſapientia plenum, neſcio quo modo prætermiſit.</s>
            </p>
            <p type="main">
              <s id="s.001557">
                <arrow.to.target n="marg121"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.001558">
                <margin.target id="marg121"/>
              121</s>
            </p>
            <p type="main">
              <s id="s.001559">Ibidem
                <emph type="italics"/>
              (In ſolidis verò duæ ſolum pyramis, & cubus)
                <emph.end type="italics"/>
              ideſt replent locum
                <lb/>
              ſolidum. </s>
              <s id="s.001560">nullum reperi, qui in hoc loco explicando non errauerit; nam Græ­
                <lb/>
              ci, qui alioqui ſolent mathematica probè intelligere, hic omnes lapſi ſunt,
                <lb/>
                <expan abbr="ſecumq́">ſecumque</expan>
              ; & Arabes, & Latinos in
                <expan abbr="eãdem">eandem</expan>
              foueam ſupra ſe miſerè traxerunt.
                <lb/>
              </s>
              <s id="s.001561">communis ferè error omnium fuit, pyramides plures ſimul compactas poſ­
                <lb/>
              ſe replere ſolidum locum. </s>
              <s id="s.001562">quod vt melius intelligamus, ſciendum eſt, reple­
                <lb/>
              re locum
                <expan abbr="ſolidũ">ſolidum</expan>
              nihil aliud eſſe, quam ſi plura corpora ſolida ſimul ad idem
                <lb/>
              punctum coaptata, ita conſtipentur, vt totum ſpatium, quod eſt circa pun­
                <lb/>
              ctum illud omninò occupent, hoc eſt, nihil vacui inter ipſa relinquatur: ſi­
                <lb/>
              cut enim prædictæ tres figuræ planæ, de quibus paulò ante, replent locum
                <lb/>
              planum, ideſt ſuperficiem; ita cubi replent ſolidum, ideſt ſoliditatem ſimul
                <lb/>
              vniti conſtituunt, ita vt ſi octo cubi ſimul ad idem punctum
                <expan abbr="coaptẽtur">coaptentur</expan>
              , con­
                <lb/>
              ſtituant corpus ſolidum ex octo illius conſtatum,
                <expan abbr="nihilq́">nihilque</expan>
              ; inane inter ipſos
                <lb/>
              cubos relinquatur. </s>
              <s id="s.001563">& ſicuti planæ illæ figuræ erant conficiendis pauimentis
                <lb/>
              aptæ, ita ſolidæ hæ muris, qui corpora ſunt ſolida,
                <expan abbr="conſtruẽdis">conſtruendis</expan>
              idonea ſunt.
                <lb/>
              </s>
              <s id="s.001564">
                <expan abbr="Notã">Notam</expan>
              dum præterea, quod per pyramidem debemus intelligere pyramidem
                <lb/>
              regularem, quæ dicitur etiam Tetraedrum,
                <expan abbr="eſtq́">eſtque</expan>
              ; ſecunda inter
                <expan abbr="quinq;">quinque</expan>
              cor­
                <lb/>
              pora regularia rectilinea, quæ alias Platonica corpora dicuntur. </s>
              <s id="s.001565">
                <expan abbr="eorumq́">eorumque</expan>
              ;
                <lb/>
              definitiones ſunt in 11. Elem. </s>
              <s id="s.001566">Tetraedrum autem ſic definitur, eſt figura ſo­
                <lb/>
              lida ſub quatuor triangulis æquilateris,
                <expan abbr="atq;">atque</expan>
              inuicem æqualibus contenta:
                <lb/>
              de hac inquam eſt ſermo. </s>
              <s id="s.001567">quia ſi liceret intelligere de irregularibus figuris,
                <lb/>
              infinitæ reperirentur figuræ tam planæ, quam ſolidæ, quæ vtrumque locum
                <lb/>
              complerent. </s>
              <s id="s.001568">Aduertendum tandem Ariſt. videri loqui de repletione loci
                <lb/>
              ſolidi, quia tranſit à planïs figuris ad ſolidas. </s>
              <s id="s.001569">& quia ſi hæ duæ pyramis, &
                <lb/>
              cubus replent locum ſolummodo ſecundum ſuas ſuperficies, quæ ſunt trian­
                <lb/>
              gulum, & quadratum, iam de his cum proximè ante dixiſſet, quid opus fuiſ­
                <lb/>
              ſet idem poſt modum repetere. </s>
              <s id="s.001570">ad hæc ſi in medium ſolida hæc duo profert,
                <lb/>
                <expan abbr="aitq́">aitque</expan>
              ; ipſa replere locum, intelligens, planum, profectò non loquitur forma­
                <lb/>
              liter, ideſt de ipſis, vt ſolida ſunt. </s>
              <s id="s.001571">Quare Ariſt. videretur ſibi non conſtare,
                <lb/>
              vel perperam exiſtimaſſe plura Tetraedra complere ſoliditatem. </s>
              <s id="s.001572">deceptus </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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