Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.005232">
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              tioribus nobis, & natura procedere, tales ſunt Geometricæ vt paulo ſupra
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              patuit, ergò ipſæ potiſſimæ erunt demonſtrationes.</s>
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            <p type="main">
              <s id="s.005233">2. Ex Themiſtio cap, 2. ſuæ paraphr. </s>
              <s id="s.005234">2. Poſter. Demonſtratio potiſſima
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              debet oſtendere, & quod, & Propter quid. </s>
              <s id="s.005235">quod profectò cæteris demon­
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              ſtrationibus melius præſtant Geometricæ, & Arithmeticæ. </s>
              <s id="s.005236">v. g. demonſtra­
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              tio 32. 3. oſtendit angulum in ſemicirculo eſſe rectum, quod omninò igno­
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              tum erat; & affert cauſam, quæ pariter ignorabatur. </s>
              <s id="s.005237">Idem ferè faciunt aliæ
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              omnes. </s>
              <s id="s.005238">in Mathematicis verò medijs, in Phyſica, & Metaphyſica effectus
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                <expan abbr="plerumq;">plerumque</expan>
              noti ſunt, ſed cauſæ latent; dicendum igitur Geometricas demon­
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              ſtrationes ex Auerroe, & Themiſtio præſtantiſſimas eſſe.</s>
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              <s id="s.005239">Tertia, quæ eſt euidentiſſima, ſumatur ex reſolutione aliquot demonſtra­
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              tionum. </s>
              <s id="s.005240">Quid enim opus eſt diſputationem hanc per extraneas ambages
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              agitare? </s>
              <s id="s.005241">cum licear quaſi in rem præſentem ire, & veluti demonſtrationum
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              anatome facta oculis ipſis earum media contueri. </s>
              <s id="s.005242">ſed prius in memoriam
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              redigendum eſt, illam eſſe perfectiſſimam demonſtrationem, quæ non ſolùm
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              rei demonſtrandæ cauſam propriam, & adæquatam affert, verùm etiam
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              euidentiſſimè oſtendit talem paſſionem ab illa cauſa procedere, ita vt non
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              poſsit, vt ait Ariſt. aliter res ſe habere, in quo profectò Mathematicæ ex­
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              cellunt. </s>
              <s id="s.005243">Cauſa verò hæc in Geometria, & Arithmetica aliquando eſt mate­
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              rialis, quando ſcilicet vtuntur pro Medio partibus, reſpectu totius; vel eſt
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              formalis, quando nimirum Medium eſt definitio ſubiecti, aut paſsionis. </s>
              <s id="s.005244">non
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              me tamen latet omnem perfectam demonſtrationem alio ſenſu dici à qui­
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              buſdam procedere per cauſam formalem, quia in ea continetur cauſalis de­
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              finitio paſsionis, quæ definitio cauſam ipſius exhibet, & proinde tanquam
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              forma ipſius eſt, quæ rem in eſſe conſtituat.</s>
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            <p type="main">
              <s id="s.005245">Secundò notandum eſt: Omnem demonſtrationis diſcurſum reſolui tan­
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              dem in aliquid, aut per ſe notum, aut à poſteriori comprobatum. </s>
              <s id="s.005246">Satis. </s>
              <s id="s.005247">n.
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              </s>
              <s id="s.005248">eſt, vt cauſa euidentur appareat,
                <expan abbr="quocunq;">quocunque</expan>
              id modo fiat. </s>
              <s id="s.005249">hoc dixi propter
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              nonnullos, qui cùm in Geometricę demonſtrationibus lineam, aut diuiſionem
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              aliquam, rei, quæ oſtenditur, non intrinſecam animaduertunt, ſtatim exi­
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              ſtimant eas per extrinſeca
                <expan abbr="demõſtrare">demonſtrare</expan>
              : ſed decipiuntur; quia non animad­
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              uertunt lineas illas, aut partitiones, non eſſe medium demonſtrationis, ſed
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              adhiberi ad medij inuentionem, & connexionem cum paſſione. </s>
              <s id="s.005250">Quod au­
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              tem eorum dubitatio omninò vana ſit ex eo patet, quod plurimæ ſunt de­
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              monſtrationes, quæ ſine vlla linearum conſtructione, aut diuiſione compro­
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              bentur, vti ſunt 15.33 34.42. 36. in ſolo primo elementorum. </s>
              <s id="s.005251">atque hæc
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              erroris eorum præcipua cauſa eſt.</s>
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            <p type="main">
              <s id="s.005252">His præmiſſis, primò oſtendemus cauſam formalem in Geometricæ de­
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              monſtrationibus reperiri deinde materialem. </s>
              <s id="s.005253">
                <expan abbr="idq́">idque</expan>
              ; primò per reſolutionem
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              primę Euclidis, quæ à cauſa formali procedit. </s>
              <s id="s.005254">& quia hæc demonſtratio
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              non theorema, ſed problema eſt, ideò ſciendum, quòd minimè aduerſarij
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              animaduerterunt, in omni problemate per
                <expan abbr="quandã">quandam</expan>
                <expan abbr="linearũ">linearum</expan>
              conſtructionem
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              doceri aliquid effici. </s>
              <s id="s.005255">v. g. in præſenti docet Euclides, qua ratione deſcrip­
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              tis
                <expan abbr="quibuſdã">quibuſdam</expan>
              circulis circa datam lineam,
                <expan abbr="ductisq́">ductisque</expan>
              ; aliquot lineis modo prę­
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              ſcripto, gignatur
                <expan abbr="triangulũ">triangulum</expan>
              æquilaterum, vt rem conſideranti manifeſtum
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              eſt. </s>
              <s id="s.005256">quare nullo modo lineamenta illa, vt illę circulorum ſemidiametri ſunt </s>
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          </chap>
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