Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              282</s>
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              <s id="s.003451">Sextus locus
                <emph type="italics"/>
              (Rurſus
                <expan abbr="quoq;">quoque</expan>
              facilè perſuaderi poteſt ex mota duorurm circulo­
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              rum æqualium, nam quiſquis horum moueatur, oportet per maiorem ſemicirculum
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              moueri, & quæcunque alia huiuſmodi constituta ſunt de lineis, fieri non poſſe, vt
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              talis vllus motus peragatur, quin prius omnibus, & ſingulis interiectis occurrat.
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              </s>
              <s id="s.003452">Atque hæc Mathematicorum ſcita, multò magis ab omnibus conceſſa ſunt, quàm
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              illorum dicta.
                <emph.end type="italics"/>
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              <s id="s.003453">Hæc eſt alia ratio, qua probat totam circuli periphæriam eſſe diuiduam.
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              ſint enim duo circuli æquales primum in eo­
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              dem loco,
                <expan abbr="vocenturq́">vocenturque</expan>
              ; A, & B, deinde circu­
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              lus B, moueatur, & diſcedat à circulo A, ma­
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              nente; ſtatim
                <expan abbr="namq;">namque</expan>
              pars egreſſa E F G, erit
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              maior ſemicirculo, & ſemper fiet maior, ac
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              maior. </s>
              <s id="s.003454">
                <expan abbr="atq;">atque</expan>
              in tali motu omnes partes egre­
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              dientis circuli ſecantur ab omnibus partibus
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              circuli manentis. </s>
              <s id="s.003455">vnde patet nihil eſſe in eo­
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              rum periphærijs, quod non diuidatur. </s>
              <s id="s.003456">nul­
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              lum igitur in eis eſt indiuiduum. </s>
              <s id="s.003457">falluntur igitur aduerſarij.</s>
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              283</s>
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              <s id="s.003460">Septimus locus
                <emph type="italics"/>
              (Quamuis autem ex confutatis nuper rationibus appareat, ne­
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              que probabile, neque neceſſarium eſſe lineas vllas indiuiduas extare, tamen ex ijs
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              etiam, quæ deinceps ſubiungam, multò magis perſpicuum euadet. </s>
              <s id="s.003461">& primò quidem
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              per ea, quæ Mathematici demonſtrant, at que addiſcenda proponunt, quæ mutare
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              non decet, niſt probabiliores rationes habeamus. </s>
              <s id="s.003462">Nam neque lineæ, neque rectæ li­
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              neæ definitio cum inſecabili linea conſentit, vt quæ nec inter duo puncta extenſa
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              ſit, nec medium vllam habeat.
                <emph.end type="italics"/>
              </s>
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              <s id="s.003463">Idem, ſed paulò mutatis verbis poſtea repetit, quæ fortè ab aliquo per
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              errorem addita ſunt. </s>
              <s id="s.003464">Verumenimuerò maximè conſiderandum eſt, quan­
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              tum hoc loco Ariſt. Mathematicis demonſtrationibus tribuat: quod dixe­
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              rim propter recentiores quoſdam, qui eò audaciæ deuenerunt, vt Euclidis
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              firmiſſimas,
                <expan abbr="atq;">atque</expan>
              Ariſtot. teſtimonio,
                <expan abbr="veterumq́">veterumque</expan>
              ; Philoſophorum omnium
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              comprobatas, negare non verentur Demonſtrationes.</s>
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              <s id="s.003465">Cæterùm Ariſt. iterum opinionem
                <expan abbr="aſſerẽtium">aſſerentium</expan>
              lineas inſecabiles hoc mo­
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              do confutat: nam ſi inquit, lineam illam, quam vocant inſecabilem, eſt non
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              ſolum linea, ſed etiam linea recta, illi conueniret rectæ lineæ definitio, ſed
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              nullo modo poteſt ci conuenire, ergò tollendæ ſunt de rerum natura huiuſ­
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              modi lineæ. </s>
              <s id="s.003466">Porrò definitio lineæ eſt, vt ſit longitudo latitudinis expers, &
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              ſi recta ſit ex æquo ſua interiacet puncta extrema, ergò ipſa linea media erit
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              inter duo indiuidua extrema puncta; at verò linea, quam ipſi volunt eſſe
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              indiuiduum quoddam, qua ratione medium erit inter alia duo indiuidua?
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              </s>
              <s id="s.003467">ipſi enim
                <expan abbr="vidẽtur">videntur</expan>
              velle iſtam lineam non habere medium vllum, ſi enim con­
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              cederent habere medium, iam poſſet in medio ſecari, quod ipſi nequaquam
                <lb/>
              concederent: patet igitur definitionem lineæ minimè illi conuenire, & pro­
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              pterea
                <expan abbr="neq;">neque</expan>
              eſſe inter lineas enumerandam.</s>
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              284</s>
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              <s id="s.003470">Octauus locus
                <emph type="italics"/>
              (Deinde omnes lineæ commenſurabiles erunt: nam omnes ab in­
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              diuiduis lineis dimetientur, quæqué; longitudine, quæqué; potentia ſunt commenſurabi­
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              les. </s>
              <s id="s.003471">indiuiduæ autem lineæ ſibi ipſis commenſurabiles ſunt longitudine, cum inter ſe
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              fiat æquales; quare potentia quoque, quod ſi hoc eſt, diuiduum erit quadratum.
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