Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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          <chap>
            <p type="main">
              <s id="s.005085">
                <pb pagenum="6" xlink:href="009/01/290.jpg"/>
              quos ſolùm terminatos Arithmeticus accipit. </s>
              <s id="s.005086">eſſe autem genera hæc termi­
                <lb/>
              natæ Quantitatis Geometriæ, aut Arithmeticæ ſubiectum, ex eo patet, quod
                <lb/>
              eas ſolas quantitates ipſi definiunt,
                <expan abbr="deq́">deque</expan>
              ; ipſis varias paſſiones
                <expan abbr="demonſtrãt">demonſtrant</expan>
              ,
                <lb/>
                <expan abbr="easq́">easque</expan>
              ; omninò ab eis diuerſas, quas Phyſicus, & Metaphyſicus in ea abſolu­
                <lb/>
              tè ſpectata conſiderant. </s>
              <s id="s.005087">Vnde manifeſtum eſt, has affectiones, quas Ma­
                <lb/>
              thematicus contemplatur ab ipſa Quantitate, quatenus terminata eſt ema­
                <lb/>
              nare; ſunt autem æqualitas, inæqualitas, talis diuiſio, transfiguratio, pro­
                <lb/>
              portiones variæ, commenſuratio, incommenſuratio, figurarum
                <expan abbr="cõſtructio-nes">conſtructio­
                  <lb/>
                nes</expan>
              , &c. </s>
              <s id="s.005088">Quæ ſanè affectiones ab intrinſeca Quantitatis natura minimè
                <lb/>
              fluunt, poſita enim ea interminata, prædictæ paſſiones non conſequuntur,
                <lb/>
              nihil enim, ea ſic poſita, eſt æquale, aut inæquale, &c. </s>
              <s id="s.005089">ſed addita Quantita­
                <lb/>
              ti terminatione, eæ ab ea per emanationem profluunt. </s>
              <s id="s.005090">Quapropter inrè di­
                <lb/>
              xeris formalem rationem Mathematicæ conſiderationis eſſe Terminatio­
                <lb/>
              nem; & obiectum totale adæquatum eſſe Quantitatem terminatam, qua­
                <lb/>
              tenus terminata eſt. </s>
              <s id="s.005091">Ex hac enim terminatione variæ oriuntur figuræ, &
                <lb/>
              numeri, quas Mathematicus definit,
                <expan abbr="deq́">deque</expan>
              ; ipſis varia demonſtrat. </s>
              <s id="s.005092">
                <expan abbr="Atq;">Atque</expan>
              hæc
                <lb/>
              eſt illa Quantitas, quæ dici ſolet materia intelligibilis, ad differentiam ma­
                <lb/>
              teriæ ſenſibilis, quæ ad Phyſicum ſpectat; illa enim ab hac per intellectum
                <lb/>
              ſeparatur, ac ſolo intellectu percipitur. </s>
              <s id="s.005093">Continuum igitur, & diſcretum,
                <lb/>
                <expan abbr="vtrumq;">vtrumque</expan>
                <expan abbr="terminatũ">terminatum</expan>
              , eſt materia intelligibilis, illud Geometriæ, iſtud Arith­
                <lb/>
              meticæ. </s>
              <s id="s.005094">Hinc etiam patet, cur dicatur Mathematicus conſiderare Quan­
                <lb/>
              titatem finitam, quia accipit terminatam, quæ finita eſt: quod enim habet
                <lb/>
              terminus, ſeu fines, finitum eſt. </s>
              <s id="s.005095">quod ſi dari poſſet quantitas aliqua termi­
                <lb/>
              nata, & ſimul infinita, de ea etiam Demonſtrationes Euclidis fieri poſſent;
                <lb/>
              ſi enim daretur triangulum infinitum, eodem modo de eo oſtendi poſſet ha­
                <lb/>
              bere tres angulos æquales duobus rectis. </s>
              <s id="s.005096">Porrò hanc terminatam Quanti­
                <lb/>
              tatem eſſe Geometriæ, & Arithmeticæ ſubiectum minimè cognouerunt ij,
                <lb/>
              qui Geometricas demonſtrationes impugnarunt, vt in eorum ſcriptis vide­
                <lb/>
              re eſt, quæ prima eis fuit errandi occaſio.</s>
            </p>
            <p type="main">
              <s id="s.005097">Porrò ex hac mathematica abſtractione à materia ſenſibili, fit vt materia
                <lb/>
              hæc abſtracta perfectionem quandam acquirat, quam perfectionem mathe­
                <lb/>
              maticam appellant. </s>
              <s id="s.005098">v. g. triangulum abſtractum eſt omninò planum ex tri­
                <lb/>
              bus lineis omninò rectis,
                <expan abbr="tribusq́">tribusque</expan>
              ; angulis punctis omninò indiuiduis con­
                <lb/>
              ſtitutum, quale in rerum natura (exceptis fortè cœleſtibus) vix puto repe­
                <lb/>
              riri poſſe. </s>
              <s id="s.005099">vnde nonnulli ſolent Mathematicis illud obijcere; entia ſcilicet
                <lb/>
              mathematica non extare, niſi per ſolum intellectum. </s>
              <s id="s.005100">Verumenimuerò ſcien­
                <lb/>
              dum eſt entia hæc mathematica, quamuis in ea perfectione non extent, id
                <lb/>
              tamen eſſe per accidens, conſtat enim naturam, & artem figuras mathema­
                <lb/>
              ticas præcipuè intendere, quamuis propter materiæ ſenſibilis ruditatem, &
                <lb/>
              imperfectionem, quæ perfectas omninò figuras ſuſcipere nequit, ſuo ſine
                <lb/>
              fruſtrentur; natura enim in truncis arborum cylindri figuram affectat, in
                <lb/>
              pomis, & vuarum acinis aut ſphæricam, aut ſphæroidem, in cornea oculi
                <lb/>
              circulum; imò oculus ipſæ maximè ſphæricus eſt. </s>
              <s id="s.005101">Sol,
                <expan abbr="reliquaq́">reliquaque</expan>
              ; aſtra com­
                <lb/>
              muni omnium conſenſu omninò ſphærica ſunt. </s>
              <s id="s.005102">ipſa aquæ ſuperficies globo­
                <lb/>
              ſa eſt. </s>
              <s id="s.005103">
                <expan abbr="terraq́">terraque</expan>
              ; ipſa niſi obſtaret materiæ craſſities, & diuerſitas, rotunda pla­
                <lb/>
              nè euaderet. </s>
              <s id="s.005104">lineæ ſpirales conicæ nonne manifeſtè in marinis cochlæis de­</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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