Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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& 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.
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qui eſt quadratus. </
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<
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">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. </
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<
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id
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">Iam verò ſi cubus 8. multipli
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cet cubum 27. procreabitur 216. qui pariter cubus
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eſt. </
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atq;
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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
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interpretẽtur
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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. </
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<
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">Quod præterea hoc loco intelligendi ſint cubi arith
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metici certò certius conſtat, ex ſequenti 24. textu, vbi ſic dicitur
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(Veluti
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Arithmetica quidem, quid impar, aut par, aut quadrangulum, aut cubus.)
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34</
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<
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(
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Neq;
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alij ſcientiæ quod alterius, niſi
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quæcunq;
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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)
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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
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demõſtrationes
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nu
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merorum, quas applicat numeris ſonoris. </
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<
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">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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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. </
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<
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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
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optica. </
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<
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">Exemplum ſubalternationis Muſicæ ſit,
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conſonãtia
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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 </
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