Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              ram, cùm enim ad ſummam perfectionem peruenerit, quæ in numero ſoli­
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              do, & cubico ſignificatur, ſi vlterius progreſsura ſit, neceſſariò ſummam
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              perfectionem præteribit, ac derelinquet. </s>
              <s id="s.003824">Quòd autem numerus 1728. ſit
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              numerus ſolidus, & cubus ipſius Duodenarij ſic palàm fiet, ſi tamen prius,
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              ea repetiueris, quæ ſupra in primo Poſter. num. </s>
              <s id="s.003825">33. marginali, de numero
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              Quadrato, & Cubo dicta ſunt: eſt autem cubus numerus is, qui ex gemina­
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              to ductu alicuius numeri in ſe ipſum, producitur. </s>
              <s id="s.003826">multiplica igitur primò
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              12. in 12. & producetur numerus 144. qui quadratus, & planus eſt. </s>
              <s id="s.003827">rurſus
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              duc 12. in hunc 144.
                <expan abbr="produceturq́">produceturque</expan>
              ; numerus 1728. quì cubus, ac proinde
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              ſolidus eſt, vt loco citato explicauimus. </s>
              <s id="s.003828">
                <expan abbr="Atq;">Atque</expan>
              hæc Socratici huius myſterij
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              explicatio ſufficiat.</s>
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          <chap>
            <p type="head">
              <s id="s.003829">
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              Ex Octauo Politicorum.
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            <p type="margin">
              <s id="s.003831">
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              331</s>
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            <p type="main">
              <s id="s.003832">Cap. 5. (
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              Muſicam verò omnes fatemur eſſe ex iucundiſſimis, ſiue nuda ſit,
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              ſiue cum melodia
                <emph.end type="italics"/>
              ) Quamuis latina interpretatio pro melodia, di­
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              cat, modulatione, Gręcus tamen textus habet
                <foreign lang="grc">μετα μελωδιας,</foreign>
              ideſt
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                <expan abbr="cũ">cum</expan>
              melodia. </s>
              <s id="s.003833">per Muſicam nudam, forte Ariſtoteles intelligit eam,
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              quæ ſolis ſonis
                <expan abbr="abſq;">abſque</expan>
              oratione conſtat; per melodiam verò intelligit eam,
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              quam Ioſephus Zarlinus in 2. parte ſuarum Inſtitutionum Muſicalium defi­
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              nit, quæ eſt concentus plurium vocum harmonicus cum rithmo, & oratio­
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              ne, ideſt, qua canitur oratio aliqua ſub aliquo rithmo, aut modo, ſiue vt
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              nunc loquimur, conqualchearia.</s>
            </p>
            <p type="main">
              <s id="s.003834">Ex quibus liquet noſtros contrapuntiſtas toto cœlo aberrare, dum ſuas
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              cantilenas, abſque vlla verborum intelligentia, atque abſque vllo rithmo
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              diſperdunt.</s>
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            <p type="margin">
              <s id="s.003836">
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              332</s>
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            <p type="main">
              <s id="s.003837">Eodem capite propè finem meminit harmoniæ Lydiæ, Mixtæ, Doricæ,
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              Phrygiæ. </s>
              <s id="s.003838">de quibus ſupra 3. lib. Polit. cap. 2. tractaui,
                <expan abbr="earumq́">earumque</expan>
              ; proprieta­
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              tes, quas hic Ariſt. recenſet ibi connumeraui.</s>
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            <p type="main">
              <s id="s.003839">
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              <s id="s.003840">
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              333</s>
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              <s id="s.003841">Ibidem meminit etiam Rithmorum, & Harmonie. </s>
              <s id="s.003842">Quid Rithmus dictum
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              eſt ſuperius lib. 3. Politic. eſſe quem nunc vulgò ariam cantores, ac tibici­
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              nes appellant.</s>
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            <p type="main">
              <s id="s.003843">Harmonia eſt plurium vocum ex acuto, & graui concors modulatio.</s>
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            <p type="main">
              <s id="s.003844">Verùm de his fuſius in Problematibus Muſicis, ſect. </s>
              <s id="s.003845">19.</s>
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              334</s>
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            <p type="main">
              <s id="s.003848">Cap. 7 (
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              Conſiderandum vtrum omnibus vtendum ſit harmonijs, & rithmis
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              )
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              Vide quæ ſupra lib. 3. Politic. cap. 2. annotaui.</s>
            </p>
            <p type="head">
              <s id="s.003849">
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              In Oeconomicis nihil Mathematicum reperi.
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              </s>
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          </chap>
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