Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.000974">
                <pb pagenum="53" xlink:href="009/01/053.jpg"/>
              & altitudo, eſt 2. Similiter cubus numerus eſt 27. quia ſit ex tribus terna­
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              rijs inuicem modo prædicto multiplicatis, 3. 3. 3. nam 3. in 3. ductis ſit 9.
                <lb/>
                <figure id="id.009.01.053.1.jpg" place="text" xlink:href="009/01/053/1.jpg" number="23"/>
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              qui eſt quadratus. </s>
              <s id="s.000975">quo deinde ducto in tertium ter­
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              narium, producitur 27. qui eſt cubus, & refert figu­
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              ram cubicam hanc. </s>
              <s id="s.000976">Iam verò ſi cubus 8. multipli­
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              cet cubum 27. procreabitur 216. qui pariter cubus
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              eſt. </s>
              <s id="s.000977">
                <expan abbr="atq;">atque</expan>
              hoc ſibi volunt verba illa, ſi duo cubi cubus,
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              ideſt, ſi duo numeri cubi multiplicentur mutuò, cu­
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              bus alter producetur; ex quibus videas, quam in­
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              eptè illi
                <expan abbr="interpretẽtur">interpretentur</expan>
              hunc locum, qui dicunt, Ari­
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              ſtotilem velle dicere non pertinere ad Geometram
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              probare duos cubos geometricos ſibi additos face­
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              re alium cubum, quod erat problema Delphicum de
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              duplatione cubi, nondum inuentum; bis enim iſti peccant, primo in Logi­
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              cam, quia ſic non tranſiret Geometra de genere in genus, ipſius enim eſt
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              agere de duplatione cubi; ſecundò in Mathematicas, cum nondum noue­
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              rint arithmeticos cubos; & præterea ignorent duos cubos ſibi additos, non
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              facere alium cubum. </s>
              <s id="s.000978">Quod præterea hoc loco intelligendi ſint cubi arith­
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              metici certò certius conſtat, ex ſequenti 24. textu, vbi ſic dicitur
                <emph type="italics"/>
              (Veluti
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              Arithmetica quidem, quid impar, aut par, aut quadrangulum, aut cubus.)
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.000979">
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              <s id="s.000980">
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              34</s>
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            <p type="main">
              <s id="s.000981">Ibidem
                <emph type="italics"/>
              (
                <expan abbr="Neq;">Neque</expan>
              alij ſcientiæ quod alterius, niſi
                <expan abbr="quæcunq;">quæcunque</expan>
              ita ſe habent inter ſe,
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              vt ſit alterum ſub altero, vt perſpectiua ad Geometriam, & harmonica ad Arith­
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              meticam)
                <emph.end type="italics"/>
              excipit ab illa regula (qua prohibetur, quamuis ſcientiam in alie­
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              nam falcem immittere) ſcientias ſubalternatas, quæ propriè in Mathemati­
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              cis reperiuntur, Perſpectiua enim propriè ſubalternatur Geometriæ, quia
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              vtitur Demonſtrationibus linearibus, quas applicat lineis viſualibus, & Mu­
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              ſica ſubalternatur Arithmeticæ, quia ab ipſa mutuatur
                <expan abbr="demõſtrationes">demonſtrationes</expan>
              nu­
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              merorum, quas applicat numeris ſonoris. </s>
              <s id="s.000982">v.g. Perſpectiua dicit, ea, quæ vi­
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              dentur eminus videri minora, quam quæ videntur cominus, quia illa viden­
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              tur ſub angulo minori, hæc verò ſub angulo maiori, quod verò remotiora
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              videantur ſub angulo minori, quam propinquiora cæteris paribus probat
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                <figure id="id.009.01.053.2.jpg" place="text" xlink:href="009/01/053/2.jpg" number="24"/>
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              per 21. primi Elem. ſit enim ma­
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              gnitudo viſa A B, remotior ab o­
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              culo in C, poſito, & viſa propin­
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              quior ab oculo in D. ductis lineis
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              viſualibus C A, C B: D A, D B; ab
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              oculis C, & D, ad extremitates
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              ſpectatæ magnitudinis, erit remo­
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              tioris viſionis angulus C, minor
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              angulo D, propinquioris, vt ex præallegata Demonſtratione pater. </s>
              <s id="s.000983">Hine
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              perſpicuè vides, qua ratione Perſpectiua Geometriæ ſubalternetur, ſiue
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              quid ſit ipſa ſubalternatio, vbi medium eſt Geometricum, concluſio autem
                <lb/>
              optica. </s>
              <s id="s.000984">Exemplum ſubalternationis Muſicæ ſit,
                <expan abbr="conſonãtia">conſonantia</expan>
              Diapaſon, quam
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              vulgò octauam appellant in data chorda collocare, hoc eſt, vocem grauio­
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              rem facere duplam vocis acutioris ſumatur chorda A B, & diuidatur bifa­
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              riam, ſine in æqualia in C; tota igitur chorda A B, ad dimidium A C, habet </s>
            </p>
          </chap>
        </body>
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