Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <p type="main">
              <s id="s.001295">
                <pb pagenum="69" xlink:href="009/01/069.jpg"/>
              definitio illius rei, de qua diſſeritur. </s>
              <s id="s.001296">Porrò exemplum mathematicum hic
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              allatum ſic videtur explicandum: Conetur aliquis demonſtrare hanc pro­
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              poſitionem; ſi linea ducta fuerit æquidiſtans lateri vnius plani trianguli, ſe­
                <lb/>
              cabit & latera, & locum, ideſt ſuperficiem illam triangularem ſimiliter, ideſt
                <lb/>
                <figure id="id.009.01.069.1.jpg" place="text" xlink:href="009/01/069/1.jpg" number="34"/>
                <lb/>
              in eadem proportione, vt in triangulo A B C,
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              linea D E, parallela baſi B C, ſecat latera A B,
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              & A C, in punctis D, & E, in eadem ratione,
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              in qua etiam fecat totum triangulum, ita vt
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              eadem ſit proportio lineæ A D, ad D B, & lineæ
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              A E, ad E C, quæ eſt partium totalis trianguli
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              A B C, ſcilicet quæ eſt partis A D E, ad partem
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              E D C, fiue ad partem D E B. quod conſtat ex
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              ſecunda 6. Elem. </s>
              <s id="s.001297">Inquit ergo Ariſt. </s>
              <s id="s.001298">Si quis
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              vellet hoc demonſtrare nondum præmiſſa defi­
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              nitione eorum, quæ habent eandem rationem, ſiue nondum definitione al­
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              lata quantitatum proportionalium, hic difficile id valeret oſtendere: at ve­
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              rò allata prius definitione quantitatum proportionalium facile demonſtra­
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              bit. </s>
              <s id="s.001299">Subdit verò Ariſt. dictam definitionem, dicens, tunc quantitates eſſe
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              proportionales, quando habent eandem ablationem, ideſt, eandem diuiſio­
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              nem, ideſt, eadem diuiſio ne tantum proportionaliter de vna, quantum de
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              altera magnitudine reſecatur: Quemadmodum etiam Euclides loco cita­
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              to probat, latera illius trianguli, & ſuperficiem eſſe ſimiliter diuiſa, ex quo
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              ſequitur eſſe proportionalia. </s>
              <s id="s.001300">Porrò Euclides definit. </s>
              <s id="s.001301">ſeptima 5. paulo ali­
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              ter definit quantitates proportionales eſſe illas, quæ eandem habent ratio­
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              nem, v. g. ſi ſit, vt prima ad ſecundam, ita tertia ad quartam. </s>
              <s id="s.001302">ex quibus
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              quoad Mathematicas ſpectat, huic loco ſatisfactum ſit.</s>
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              <s id="s.001303">
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              <s id="s.001304">
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              82</s>
            </p>
            <p type="main">
              <s id="s.001305">Cap. 4. loco 86.
                <emph type="italics"/>
              (Tentandum autem, & ea, in quæ ſæpiſſimè incidunt diſputa­
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              tiones, tenere, nam quemadmodum in Geometria ante opus eſt circa elementa exer­
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              citatum eſſe, & in numeris circa capitales promptè ſe habere, & multum refert ad
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              hoc, & alium numerum cognoſcere multiplicatum)
                <emph.end type="italics"/>
              Elementa vocabant antiqui
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              demonſtrationes faciliores, & ſimpliciores, quales propriè ſunt omnes, quæ
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              ſex prioribus libris Euclidianis continentur: ex illis enim tanquam ex ele­
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              mentis abſtruſiores, & difficiliores demonſtrationes deducebant. </s>
              <s id="s.001306">
                <expan abbr="atq;">atque</expan>
              hæc
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              eſt ratio, cur Euclides ſuos libros elementa nuncupauerit. </s>
              <s id="s.001307">ait igitur curan­
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              dum eſſe horum elementorum cognitionem in promptu habere, quia fre­
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              quens de ipſis incidit diſputatio. </s>
              <s id="s.001308">Per capitales numeros intelligo ſimplices
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              ab vnitate,
                <expan abbr="vſq;">vſque</expan>
              ad nouem incluſiuè. </s>
              <s id="s.001309">& quando ait, alium numerum cogno­
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              ſcere multiplicatum, ſignificat vtile valdè eſſe ad quotidianum vſum
                <lb/>
              cognoſcere, quemnam numerum producant numeri capitales,
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              ſi ad inuicem multiplicentur, quamuis huiuſmodi co­
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              gnitio facilis, ac leuis ſit: qua de cauſa vide­
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              mus vſque in hanc diem pueros diu in
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              Abaco memoriter perdiſcen­
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              do detineri.</s>
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          <chap> </chap>
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