Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <p type="main">
              <s id="s.003514">
                <pb pagenum="209" xlink:href="009/01/209.jpg"/>
                <emph type="italics"/>
              vnum per aliud diuiditur, at corpus indiuiduum non eſt, cum in ſe latitudinem, &
                <lb/>
              profunditatem contineat: quare nec linea poteſt eſſe atoma. </s>
              <s id="s.003515">corpus ſiquidem in ſu­
                <lb/>
              perficies, ſuperficies verò in lineas ſoluitur)
                <emph.end type="italics"/>
              hoc eſt: præterea, quemadmodum
                <lb/>
              linea per aduerſarium extat indiuidua, ſic & ſuperficies ab eadem linea de­
                <lb/>
              ſcripta erit atoma, & corpus ab hac ſuperficie deſcriptum erit impartibile.
                <lb/>
              </s>
              <s id="s.003516">Sciendum enim, quod ex motu puncti deſcribitur linea: ex motu lineæ de­
                <lb/>
              ſcribitur ſuperficies: ex motu tandem ſuperficiei corpus ortum habet, vt ſo­
                <lb/>
              let in horum definitionibus explicari.</s>
            </p>
            <p type="main">
              <s id="s.003517">Si igitur horum vnum nempè linea ſit atoma, & reliqua, quæ ab ipſa ma­
                <lb/>
              nant erunt indiuiſa, quia corpus diuiditur per ſuperficiem, & ſuperficies
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              per lineam, ideſt ad diuiſionem corporis neceſſe eſt diuidi ſuperficiem, & ad
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              ſuperficiei diuiſionem diuidi lineam, quæ ipſam terminat. </s>
              <s id="s.003518">At cum omne
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              corpus latitudinem, & profunditatem habeat, nullum poterit extare cor­
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              pus, quod diuidi nequeat; quare neque illud, quod ab atoma linea oriretur.
                <lb/>
              </s>
              <s id="s.003519">Quare nec linea illa corporis procreatrix erit indiuidua; corpus ſiquidem
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              in ſuperficies, & ſuperficies in lineas quodammodo reſoluitur: & ex diui­
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              ſione ſolidi ſuperficies ſecari debet, & demum ſuperficiei, ſectionem lineæ
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              ſectio ſubſequitur. </s>
              <s id="s.003520">Tollendæ igitur ſunt de rerum natura lineæ atomæ.</s>
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            <p type="main">
              <s id="s.003521">
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            <p type="margin">
              <s id="s.003522">
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              292</s>
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            <p type="main">
              <s id="s.003523">Decimusſextus locus
                <emph type="italics"/>
              (Quin etiam orbis circunferentia rectam lineam pluri­
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              bus tanget punctis, punctus enim contactus, quiqué eſt in circulo, quiqué eſt in recta,
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              ſe ſe mutuò tangunt. </s>
              <s id="s.003524">quod ſi hoc fieri nequit,
                <expan abbr="neq;">neque</expan>
              punctus punctum tangere valet:
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              quod ſi ſe tangere nequeunt,
                <expan abbr="neq;">neque</expan>
              linea punctis conſtare poteſt, nam neque punctum
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              tangere neceſſarium eſt.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.003525">In 2. 3. & corollario eius demonſtratur circuli peripheriam tangere re­
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              ctam lineam in vnico puncto. </s>
              <s id="s.003526">iam ſi linea conſtaret ex punctis indiuiduis
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              tanquam partibus, poſſet circulus
                <expan abbr="tãgere">tangere</expan>
              rectam lineam in duobus punctis.
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                <figure id="id.009.01.209.1.jpg" place="text" xlink:href="009/01/209/1.jpg" number="133"/>
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              Sit circulus, cuius centrum A, tangens lineam
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              rectam B C, conſtantem ex punctis, quorum vnus
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              ſit in extremo D, lineæ B D, alterum verò in E,
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              principio lineæ E C, circulus A, tangere poterit
                <lb/>
              in F, termino communi vtriuſque lineæ, hocque
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              modo tanget
                <expan abbr="vtrunq;">vtrunque</expan>
              punctum D, & E, quod eſt
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              impoſſibile per 2. 3. ſequitur igitur
                <expan abbr="neq;">neque</expan>
              illa duo puncta D, E, ſe mutuò tan­
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              gere, & eadem ratione nulla alia
                <expan abbr="pũcta">puncta</expan>
              eiuſdem lineæ, ex quibus manifeſtum
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              eſt, impoſſibile eſſe, lineam ex huiuſmodi punctis conſtare poſſe.</s>
            </p>
            <p type="main">
              <s id="s.003527">Reliqua huius opuſculi, quamuis Mathematica alicui videri poſſint,
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              non tamen ſunt, non enim linearibus indigent demonſtrationi­
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              bus,
                <expan abbr="neq;">neque</expan>
              ex Geometriæ principijs procedunt. </s>
              <s id="s.003528">ad Phyſi­
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              cum igitur pertinebunt, cuius eſt diſputare, num
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              indiuidua exiſtant, & quomodo in quanti­
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              tate,
                <expan abbr="idq́">idque</expan>
              ; rationibus aliunde, quàm
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              ex Geometria deductis.</s>
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          </chap>
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