Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <p type="main">
              <s id="s.005159">
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              conſtructione rectè fieri quadratum, triangulum, lineam perpendicularem,
                <lb/>
              & ſimilia. </s>
              <s id="s.005160">tertiò, in præcedenti dubitatione dictum eſſe ex mente Ariſtot.
                <lb/>
              etiam in Mathematicis eſſe definitiones cauſales,
                <expan abbr="idq́">idque</expan>
              ;
                <expan abbr="exẽplo">exemplo</expan>
              tetragoniſmi
                <lb/>
              confirmatum. </s>
              <s id="s.005161">Ex his, quæ de ſcientiarum definitionibus dicta ſunt, notan­
                <lb/>
              da eſt quædam diſparitas inter alias ſcientias, & Mathematicas in modo
                <lb/>
              procedendi ad ſubiecti proprij cognitionem. </s>
              <s id="s.005162">nam in demonſtrationibus à
                <lb/>
              ſigno, à quibus incipiunt vt plurimum aliæ ſcientiæ, ſola cognitio nominis
                <lb/>
              ſubiecti requiritur, non autem eſſentialis definitio; eius enim eſſentia, quæ
                <lb/>
              occulta eſt, per accidentia, & proprietates à poſteriori indagatur; qua de­
                <lb/>
              tecta ab ea iterum ad demonſtrandas paſſiones diſtinctè, & ſcientificè re­
                <lb/>
              gredimur. </s>
              <s id="s.005163">quod ſi primò perfecta obiecti cognitio obijceretur, vt ſit in Ma­
                <lb/>
              thematicis ob perfectus earum definitiones pulcherrimo naturæ ordine ab
                <lb/>
              eſſentia ipſius ad paſſiones demonſtrandas procederemus, vt fit in demon­
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              ſtrationibus à cauſa, quales ferè ſemper ſunt in Geometria, & Arithmetica
                <lb/>
              exceptis demonſtrationibus ab impoſsibili, vbi nobis primò tota ſubiecti
                <lb/>
              natura ex præmiſsis definitionibus obijcitur, ex qua deinde ſemper à priori
                <lb/>
              ad inueſtigandas illius paſsiones procedimus; in quo proceſſu definitio ſu­
                <lb/>
              biecti pręmitti,
                <expan abbr="eiusq́">eiusque</expan>
              ; quidditas ſupponi debet. </s>
              <s id="s.005164">vnde etiam ſequitur Mathe­
                <lb/>
              maticas haſce à notioribus nobis, & natura, vt vult Auerroes, & cæteri ferè
                <lb/>
              omnes, & ex noſtris maximè Toletus quęſt. </s>
              <s id="s.005165">4. ſecundi Phyſ. procedere. </s>
              <s id="s.005166">no­
                <lb/>
              tioribus nobis, quia primum omnium manifeſta eſt tota figuræ eſſentia ex
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              definitione ipſius allata, ignotis adhuc ipſius affectionibus, notioribus na­
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              tura, quia prius natura eſt ſubiecti eſſentia, quàm paſsiones, quæ ab ea ma­
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              nant,
                <expan abbr="deq́">deque</expan>
              ; ea demonſtrantur:
                <expan abbr="atq;">atque</expan>
              hæc cauſæ eſt, cur ſemper tanti factæ ſine
                <lb/>
              Geometricæ demonſtrationes,
                <expan abbr="primumq́">primumque</expan>
              ; certitudinis gradum obtineant.</s>
            </p>
            <p type="head">
              <s id="s.005167">
                <emph type="italics"/>
              De medio Demonstrationum Geometriæ, & Arith­
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              meticæ, ſeu, An ſint potißimæ Demonſtrationes.
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              </s>
              <s id="s.005168">Cap. 2.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.005169">Coguntur huius tempeſtatis Mathematici ea, quæ antiquiſsimo poſ­
                <lb/>
              ſeſsionis iure tutò hactenus poſsiderunt, à nonnullis recentioribus
                <lb/>
              ea diripere volentibus, omni conatu tutari. </s>
              <s id="s.005170">quis enim vnquam
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              alicuius nominis philoſophus ante Alexandrum Piccolomineum
                <lb/>
              extitit, qui Geometris potiſsimas Demonſtrationes eripere tentauerit?
                <lb/>
              </s>
              <s id="s.005171">profectò nullus fatetur ipſe ſe primum inter recentiores hanc veritatem
                <lb/>
              olfeciſſe, ſed verè omnium etiam antiquorum primus ipſe fuit, nam duos,
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              vel tres, quos ex antiquis in ſuam ſententiam pertrahere conatur, re vera,
                <lb/>
              vt infra patebit, minimè pertrahit.</s>
            </p>
            <p type="main">
              <s id="s.005172">Primo igitur antiquorum auctoritates, præcipuè verò Ariſt. pro parte af­
                <lb/>
              firmatiua afferemus. </s>
              <s id="s.005173">& verò indignum,
                <expan abbr="atq;">atque</expan>
              ſuperuacaneum exiſtimo, cùm
                <lb/>
              eo, qui Ariſt. Analyticos poſteriores legerit, de ipſius ſententia diſputare,
                <lb/>
                <expan abbr="ciusq́">eiusque</expan>
              ; mentem, quaſi in fruſta locis aliquot citandis ſecare, cùm totis duo­
                <lb/>
              bus libris nihil aliud agere videatur, quàm
                <expan abbr="perfectã">perfectam</expan>
              Demonſtrationis idęam </s>
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          </chap>
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