Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.003626">
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              vt in figura, vbi linea A B, inſiſtens alteri D C, perpendiculariter, ideſt ita
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              vt faciat angulos hinc inde æqualis A B D, A B C, prædictos inquam duos
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              angulos conſiderat e. </s>
              <s id="s.003627">ſe rectos. </s>
              <s id="s.003628">contemplatur præterea Geometra omnes
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              angulos rectos eſſe inter ſe æquales, vt in 12. axiomate primi Elem. ponitur,
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              & ſimilia plura alia, quorum conſiderationem Faber omninò negligit.</s>
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              302</s>
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              <s id="s.003631">Libro 2. capite 6.
                <emph type="italics"/>
              (Id quod ſecundum Arithmeticam rationem medium eſt)
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              Arithmetica ratio, fiue proportio ea eſt, cuius termini creſcunt per æqua­
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              les exceſſus, vt 2. 6. 10. 14. horum enim terminorum exceſſus æquales ſunt,
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              cum ſint omnes quaternarij. </s>
              <s id="s.003632">ſimiliter inter hos terminos 3. 6. 9. 12. eſt arith­
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              metica analogia, cùm omnes ternario numero ſuperent præcedentes, & à
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              ſequentibus ſuperentur. </s>
              <s id="s.003633">Porrò apud Mathematicos tria ſunt genera pro­
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              portionum, ſiue medietatum, Arithmetica quam modo ſuppoſui; Geome­
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              trica, & Harmonica, quas inferius oblata occaſione opportunius explicabo.</s>
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              303</s>
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              <s id="s.003636">Lib. 2. cap. 9.
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              (Vt circuli medium deprehendere non
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              cuiuſlibet, ſed
                <expan abbr="ſciẽtis">ſcientis</expan>
              ſolummodo eſt)
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              Reperire medium,
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              ſiue centrum dati circuli docet Euclides propoſitio­
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              ne prima 3. hoc modo. </s>
              <s id="s.003637">in dato circulo ducatur vt­
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              cunque recta B C, quæ per 10. primi diuidatur bifa­
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              riam in F, & per F, ducatur
                <expan abbr="perpẽdicularis">perpendicularis</expan>
              A E F D,
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              quæ ſecetur bifariam in E,
                <expan abbr="eritq́">eritque</expan>
              ; punctum E, non ſo­
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              lum ipſius lineæ medium; ſed etiam totius circuli
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              centrum, quemadmodum ibi demonſtrat Euclides.</s>
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            <p type="margin">
              <s id="s.003639">
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              304</s>
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            <p type="main">
              <s id="s.003640">Lib. 3. cap. 3.
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              (De æternis autem nemo conſultat, vt
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              de mundo, aut diametro, & latere, quod nulla inter ſe
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              æquabilitate conueniant)
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              Qua ratione diameter, & latus eiuſdem quadrati
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              nulla æquabilitate, ideſt nulla communi menſura inter ſe conueniant, fusè
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              explicatum eſt libro Priorum, ſecto 1. cap. 23.</s>
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            <p type="main">
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            <p type="margin">
              <s id="s.003642">
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              305</s>
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              <s id="s.003643">Eodem cap.
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              (Qui enim conſultat quærere videtur, & reſoluere prædicto modo,
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              quemadmodum deſignationes)
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              Per deſignationes Ariſt. intelligere geometri­
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              cas demonſtrationes ſæpius dictum eſt in logicis textibus, quod pariter ex
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              hoc loco confirmatur. </s>
              <s id="s.003644">quando autem ait
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              (Reſoluere prædicto modo, quemad­
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              modum deſignationes)
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              innuit reſolutionem geometricam, de qua abundè di­
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              ctum eſt in explicatione tituli librorum Reſolutoriorum; quam expoſui, ni­
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              hil aliud eſſe, quam medij inquiſitionem ad id, quod propoſitum fuerit de­</s>
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            <p type="main">
              <s id="s.003645">
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              monſtrandum. </s>
              <s id="s.003646">veram autem,
                <expan abbr="atq;">atque</expan>
              germanam fuiſſe huiuſmodi explicatio­
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              nem, hoc loco Ariſt. ipſe confirmat, cum hanc reſolutionem dicat eſſe ſimi­
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              lem conſultationi, ſiue inquiſitioni mediorum ad finem in rebus practicis
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              conſequendum; ipſa verò eſt inquiſitio mediorum ad id, quod in rebus ſpe­
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              culatiuis propoſitum eſt, demonſtrandum. </s>
              <s id="s.003647">conſultatio igitur eſt in rebus
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              practicis, quod in ſpeculatiuis eſt reſolutio.
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              </s>
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            <p type="margin">
              <s id="s.003648">
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              306</s>
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            <p type="margin">
              <s id="s.003649">
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              307</s>
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            <p type="main">
              <s id="s.003650">Lib. 5. cap. 3.
                <emph type="italics"/>
              (Quod enim proportione conſtat, id non tam vnitario numero,
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              quàm numero in vniuerſum proprium eſt)
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              Per vnitarium numerum intelligitur
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              numerus ex vnitatibus abſtractis conφlatus, ideſt, cuius vnitates non ſint res
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              phyſicæ, ſed à naturalibus abſtractæ, qualis conſiderat Arithmeticus: omni
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              tamen numero ſiue abſtracto, ſiue non, conuenit proportiones ſuſcipere,
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              id eſt & numero, & rebus numeratis.</s>
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