Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.001535">
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              lectu perceptibilis. </s>
              <s id="s.001536">Hanc eandem ſupponunt eſſe diuiſibilem in infinitum,
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              vt ſupra 3. Phyſ. textu 31. dictum eſt.</s>
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              120</s>
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              <s id="s.001539">Tex. 66.
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              (Omninò autem eniti ſimplicibus corporibus figuras tribuere irratio­
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              nabile eſt. </s>
              <s id="s.001540">primò quidem, quia accidit non repleri totum; nam in planis tres figuræ
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              videntur implere locum, Triangulus, Quadratum, & Sexangulus)
                <emph.end type="italics"/>
              per ſimplicia
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              corpora intelligit quatuor elementa. </s>
              <s id="s.001541">Vult enim probare quatuor elemen­
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              ta non habere figuras illas mathematicas, quas illis Plato tribuebat, vt au­
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              tem Ariſt. rationem probè percipiamus, ſciendum, quod implere totum,
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              ſiue locum, illæ figuræ dicuntur, quæ ſimul ſuis angulis in plano quopiam ad
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              vnum,
                <expan abbr="atq;">atque</expan>
              idem punctum vnitæ locum illum totum, qui circa punctum il­
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              lud conſiſtit,
                <expan abbr="cõtegunt">contegunt</expan>
              , ita vt nihil vacui inter ipſas relinquatur. </s>
              <s id="s.001542">tales ſunt,
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              quibus fieri poſſunt pauimenta, oportet enim, vt ſimul vnitæ nihil vacui in
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              pauimento relinquant. </s>
              <s id="s.001543">huiuſmodi ſunt triangula æquilatera (de his enim
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              intelligendus eſt textus) quadrata, & hexagona, ſiue ſexilatera regularia;
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                <figure id="id.009.01.084.1.jpg" place="text" xlink:href="009/01/084/1.jpg" number="47"/>
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              nam ſex triangula æquilatera ſimul iuncta in plano paui­
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              re poſſunt, vt patet in figura præſenti; ratio huius eſt,
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              quia omnes anguli circa idem punctum (y. </s>
              <s id="s.001544">g. A, in hac
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              figura) in plano, quotquot fuerint conſtituti, ſunt æqua­
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              les quatuor rectis, ex coroll. </s>
              <s id="s.001545">ſecundo 15. primi Elemen­
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              ti: cum igitur ſex anguli, trianguli æquilateri
                <expan abbr="æquiualeãt">æquiualeant</expan>
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              quatuor rectis angulis, conſtituti omnes circa punctum
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              A, totum locum circa illud implere poſſunt. </s>
              <s id="s.001546">Quadratum etiam replere lo­
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              cum manifeſtum eſt, cum enim ipſius anguli ſint recti, ſi
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              quatuor quadrata ad idem punctum A, copulentur, vt in
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              figura apparet, replebunt eadem de cauſa vacuum.</s>
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              <s id="s.001547">Hexagonum quoque regulare, ideſt æquilaterum, &
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              æquiangulum idem præſtare poteſt; cum enim tres angu­
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              li ipſius æquiualeant quatuor rectis, ſi tria hexagona ad
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              idem punctum A, vt in figura adaptentur, neceſſariò ni­
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              hil vacui inter ipſa relinquetur, vt in figura hac oſtenditur. </s>
              <s id="s.001548">præter has tres
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              figuras, nulla alia reperitur, quæ iſtud efficere poſ­
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              ſit. </s>
              <s id="s.001549">cuius demonſtrationem perfectam videre pote­
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              ris in fine commentarij P. Clauij ſuper 4. Elem. nos
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              ea tantum attingimus, quæ percipi poſſint ab homi­
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              ne vix mathematicis tincto: ſed tamen, quæ ſenſum
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              Ariſtotelis patefaciunt. </s>
              <s id="s.001550">Aliæ porrò figuræ replen­
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              tes locum planum, quibus aliquando Architectores
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              vtuntur, vel ſunt irregulares, vel ad prædictas redu­
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              ci poſſunt. </s>
              <s id="s.001551">cum igitur tres tantum ex figuris planis
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              totum repleant, hæ ſolæ poterunt elementis attri­
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              bui, ac propterea non ſufficient, niſi pro tribus elementis. </s>
              <s id="s.001552">quare quartum
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                <expan abbr="abſq;">abſque</expan>
              figura relinquetur; quod eſt abſurdum.</s>
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