Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
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0013
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<
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">IO. BAPTISTAE
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BENEDICTI
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PATRITII VENETI
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SERENISS. CAR. EM.
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ALLOBROGVM DVCIS
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PHILOSOPHI.</
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<
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multa veteres mathematici philoſophi de nu
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meris eorumq́ue effectibus excogitata poſteris tradide-
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runt, quorum cum vix vllam rationem reddiderint, aut
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certè per exiguam, occaſione diuerſorum problematum
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mihi à Sereniſſimo Sabaudiæ Duce propoſitorum præbi-
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ta, de ijs quæ ab antiquis propoſita fuerunt contemplanda
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nonnulla occurrerunt, quæ poſteritati comendare non
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inutile arbitratus fum, ne hæ meæ cogitationes intercide-
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rent, & occaſionem præberem quamplurimis abſtruſa hęc
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indagandi, quæ problematibus & thæorematibus inuoluta, vix aliquem qui euol-
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ueret nacta funt.</
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<
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">Inter cætera vero à me queſita, hoc fuit theorema.</
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xml:space
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">THEOREMA PRIMVM.</
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<
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me Sereniſſimus Dux Sabaudiæ, qua ratione cognoſci poſ-
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ſet ſcientificè & ſpeculatiue (vt dicitur) productum ex duobus fractis numeris,
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quolibet producentium minus eſſe. </
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<
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xml:space
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">Cui reſpondi, mente & cogitatione conci-
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piendum eſſe fractos producentes cum fractis productis, non vnius eiuſdemq́ue na-
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turæ eſſe, imò longè diuerfæ.</
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<
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<
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xml:space
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">Exempli gratia, fractis numeris propofitis
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et
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quorum integri ſint
<
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>.a.
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b.</
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et
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>.a.d.</
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qui tanquam lineæ cogitentur, apertum fanè eſſet productum
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>.c.i.</
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>
fu-
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perficiale futurum, quod nomen caperet à producto ſuperficiali
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>.d.b.</
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>
generato ex
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vno in aliud totorum linearium, nam ſi conſtitueretur
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>.a.i.</
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>
octauum ipſius
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>.a.b.</
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et
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>.a.
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c.</
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dimidium
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multiplicato
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cum
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produceretur fextumdecimum ipſius
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d.b</
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. </
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xml:space
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">Quare
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eſſet totum
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ipſius
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>
non aliquod totum producentium.
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<
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xml:space
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">Mirum itaque non eſt ſi productum
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minus videatur fuis producentibus, cum
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toto, diuerſæ naturæ à primis conferatur, fractum fiquidem ab integro eiuſdem
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naturæ, linearis, ſuperficialis, aut corporeæ denominatur.</
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<
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xml:space
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">Quòd ſi amplioris cognitionis gratia ex ſcientiæ præceptis ſpeculari voluerit a@ </
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