Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <p type="main">
              <s id="s.003440">
                <pb pagenum="205" xlink:href="009/01/205.jpg"/>
                <emph type="italics"/>
              cem diuertere argumentationem, præſertim tam inualidam. </s>
              <s id="s.003441">nam multis modis im­
                <lb/>
              becillis eſt eiuſmodi ratio, & quouis modo licet euitare, ne aut inuſitata dicere, aut
                <lb/>
              argui videamur.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.003442">Refellit hoc loco ſuperiores rationes in tribus locis præmiſſis allatas,
                <lb/>
              quibus nonnulli probabant quantitatem ex indiuiduis conſtare, & proinde
                <lb/>
              concedenda eſſe quædam Quanta, omninò atoma; ſic igitur inquit. </s>
              <s id="s.003443">Quod
                <lb/>
              verò de commenſurabilibus lineis dicunt, omnes videlicet vnica quadam,
                <lb/>
                <expan abbr="eademq́">eademque</expan>
              ; determinata menſura menſurari oportere, falſum omninò eſt, &
                <lb/>
              contra mathematicorum dogmata, non enim Geometræ hoc aſſerunt, cùm
                <lb/>
              ipſorum demonſtrationibus aduerſetur; ſed
                <expan abbr="tantũ">tantum</expan>
              dicunt omnes lineas, quæ
                <lb/>
              ad inuicem ſunt commenſurabiles, commenſurari, vna
                <expan abbr="eademq́">eademque</expan>
              ; menſura,
                <lb/>
                <figure id="id.009.01.205.1.jpg" place="text" xlink:href="009/01/205/1.jpg" number="126"/>
                <lb/>
              ſed non tamen vnica, ideſt non vnica, ac determi­
                <lb/>
              nata. </s>
              <s id="s.003444">poſſunt enim eſſe plures
                <expan abbr="eædemq́">eædemque</expan>
              ; menſuræ
                <lb/>
              communes plurium quantitatum commenſura­
                <lb/>
              bilium, vt præſentium trium linearum 4. 6. 8.
                <lb/>
              communis
                <expan abbr="mẽſura">menſura</expan>
              eſt linea 2. binarius enim tres
                <lb/>
              numeros 4.6. & 8. menſurat. </s>
              <s id="s.003445">& ſi linea 2. bifariam
                <lb/>
              ſecetur, erit dimidium eius linea 1. quæ pariter
                <lb/>
              erit communis menſura trium prædictarum li­
                <lb/>
              nearum, cûm vnitas ſit omnium numerorum communis menſura. benè ve­
                <lb/>
              rum eſt, quod Geometræ, quando ſimpliciter loquuntur de huiuſmodi com­
                <lb/>
              muni menſura, intelligunt de ea, quæ inter omnes eſt maxima: vt in prædi­
                <lb/>
              ctis tribus lineis maxima earum communis menſura eſt linea 2.
                <expan abbr="Atq;">Atque</expan>
              hoc ſi­
                <lb/>
              bi volunt Geometræ, ex quibus totus hic textus intelligi poteſt.</s>
            </p>
            <p type="main">
              <s id="s.003446">
                <arrow.to.target n="marg271"/>
              </s>
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            <p type="margin">
              <s id="s.003447">
                <margin.target id="marg271"/>
              281</s>
            </p>
            <p type="main">
              <s id="s.003448">Quintus locus
                <emph type="italics"/>
              (Ob rectæ verò lineæ motum in ſemicirculum, quam neceſſe eſt
                <lb/>
              in rectum ita diuidere, vt infinitæ circunferentiæ, & interualla totidem inuenian­
                <lb/>
              tur)
                <emph.end type="italics"/>
              Interpres latinus ſic vertit
                <emph type="italics"/>
              (Ob rectæ verò lineæ motum in ſemicirculum
                <lb/>
              diuiduas non credere, &c.)
                <emph.end type="italics"/>
              vbi verba illa
                <emph type="italics"/>
              (Diuiduas non credere)
                <emph.end type="italics"/>
              pro arbitrio,
                <lb/>
              ac ſine ratione, imò contra rationem addidit: tum quia in Græco textu non
                <lb/>
              extant, tum quia ſenſus totius ſententiæ is eſt, vt potius debuiſſet affirmati­
                <lb/>
              uè dicere
                <emph type="italics"/>
              (Diuiduas credere)
                <emph.end type="italics"/>
              nam Ariſtoteles videtur ſic
                <expan abbr="argumẽtari">argumentari</expan>
              , quan­
                <lb/>
                <figure id="id.009.01.205.2.jpg" place="text" xlink:href="009/01/205/2.jpg" number="127"/>
                <lb/>
              do recta linea A B, vt in appoſita figura mo­
                <lb/>
              uetur intrando in ſemicirculum C A D B, ita
                <lb/>
              vt primò ſit in ſitu A B, ſecundò in E F, tertiò
                <lb/>
              in G H, & ſimiliter in alijs omnibus ſemicir­
                <lb/>
              culi locis, neceſſariò accidit, vt infinitæ peri­
                <lb/>
              phęriæ, quales
                <expan abbr="sũt">sunt</expan>
              A B, E A B F, G E A B F H,
                <lb/>
              cadant inter infinitas partes lineæ ingredien­
                <lb/>
              tis, vt ſunt A B, E F, G H,
                <expan abbr="atq;">atque</expan>
              tam tota recta
                <lb/>
              ingrediens, quàm totus ſemicirculus, diuidatur in partes infinitas, ita vt
                <lb/>
              nulla pars lineæ rectæ,
                <expan abbr="neq;">neque</expan>
              vlla ſemicirculi ſuperſit, quæ ſe ſe mutuò non
                <lb/>
              diuidantur, ergò nihil tam in linea, quàm in ſemicirculo remanet, quod non
                <lb/>
              ſecetur: tota igitur linea recta, & periphæria illa diuidua eſt, quam ob rem
                <lb/>
              nullo modo conſtare poteſt ex indiuiduis, ex quibus manifeſtum eſt perpe­
                <lb/>
              ram additamentum illud factum eſſe, & ſimul ratio, & textus Ariſt. eadem
                <lb/>
              opera patefacta ſunt.</s>
            </p>
          </chap>
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