Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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    <archimedes>
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              <s id="s.005277">
                <pb pagenum="16" xlink:href="009/01/300.jpg"/>
              & adæquatam, propter quam res eſt. </s>
              <s id="s.005278">Vbi notandum effectum re vera diſtin­
                <lb/>
              gui à ſua cauſa, eſſe enim quadratum (qui effectus eſt) non eſt habere, qua­
                <lb/>
              tuor angulos rectos ſolum:
                <expan abbr="neq;">neque</expan>
              habere quatuor latera æqualia ſolum, ſed
                <lb/>
                <expan abbr="vtrunq;">vtrunque</expan>
              ſimul in eodem; vnde reſultat totum, ſeu
                <expan abbr="compoſitũ">compoſitum</expan>
              , quod eſt quid
                <lb/>
              diuerſum à partibus ſeorſum ſumptis. </s>
              <s id="s.005279">in demonſtratione autem hac, cauſa
                <lb/>
              ſunt partes ſeorſim ſumptæ; effectus verò eſt compoſitum, ex earum vnione
                <lb/>
              reſultans. </s>
              <s id="s.005280">Notandum præterea eandem demonſtrationem procedere à de­
                <lb/>
              finitione ſubiecti, nam illa duo quadrati eſſentialia, ex definitione eorum,
                <lb/>
              quæ ſunt in conſtitutione petuntur, quæ conſtitutio eſt inſtar ſubiecti, vt ſu­
                <lb/>
              pra monui: ex hac autem definitione partium ſubiecti in demonſtratione
                <lb/>
              contenta, eruitur definitio cauſalis ipſius paſsionis, quæ eſt, quadratum eſt
                <lb/>
              figura habens quatuor angulos rectos, & quatuor latera æqualia, ex tali
                <expan abbr="cõ-ſtructione">con­
                  <lb/>
                ſtructione</expan>
              producta. </s>
              <s id="s.005281">Notandum tandem quouis modo ſiue à cauſa, ſiue ab
                <lb/>
              effectu oſtendantur illa duo eſſentialia quadrati, ineſſe ipſi, nihil referre ad
                <lb/>
              demonſtrationis perfectionem. </s>
              <s id="s.005282">Satis. </s>
              <s id="s.005283">n. </s>
              <s id="s.005284">eſt, ſi habeamus rei cauſam
                <expan abbr="propriã">propriam</expan>
              ,
                <lb/>
              ita vt aliter ſe habere nequeat. </s>
              <s id="s.005285">ſexcentæ huiuſmodi per formalem cauſam,
                <lb/>
              apud Euclid. Archim Appoll. </s>
              <s id="s.005286">& alios Geometras reperies. </s>
              <s id="s.005287">vide Appendi­
                <lb/>
              cem, ad finem operis, in qua omnes primi elem. </s>
              <s id="s.005288">demonſtrationes reſolutas
                <lb/>
              inuenies,
                <expan abbr="plurimasq́">plurimasque</expan>
              ; à cuſa formali.</s>
            </p>
            <p type="main">
              <s id="s.005289">Sed iam materialem cauſam indagemus,
                <expan abbr="idq́">idque</expan>
              ; duce Ariſt. accipiamus igi
                <lb/>
              tur celeberrimam illam 32. primi elem. </s>
              <s id="s.005290">quam Mathematicis
                <expan abbr="ſoiẽt">ſolent</expan>
              aduerſa­
                <lb/>
              rij opponere. </s>
              <s id="s.005291">& quoniam ſupra tex. 23. 1. Poſter. nos eam per cauſam ma­
                <lb/>
              terialem procedere oſtendimus, ideò ne actum agamus,
                <expan abbr="explicationẽ">explicationem</expan>
              illam
                <lb/>
              nunc opus eſt relegere. </s>
              <s id="s.005292">Hoc tamen loco partem ipſius primam, angulum,
                <lb/>
              videlicet externum cuiuſuis trianguli, æqualem eſſe duobus internis, & op­
                <lb/>
              poſitis, examinabo; cuius medium, ſi ad rigorem demonſtrationis rediga­
                <lb/>
              tur, eſt hoc; externus angulus eſt diuiſibilis in duos angulos, quorum ſingu­
                <lb/>
              li ſingulis internis ſunt æ quales, ergo
                <expan abbr="etiã">etiam</expan>
              totalis anguius erit æqualis am­
                <lb/>
              bobus internis ſimul ſumptis. </s>
              <s id="s.005293">Quod autem externus angulus ſit diuiſibilis
                <lb/>
              in duas partes æquales internis angulis probat diuidendo illum per lineam
                <lb/>
              illam oppoſito trianguli lateri parallelam, vnde ſtatim ex parallelarum na
                <lb/>
              tura apparet partiales angulos anguli externi æquales eſſe internis triangu
                <lb/>
              li; ex quo ſequitur totum externum angulum eſſe æqualem duobus internis
                <lb/>
              ſimul ſumptis. </s>
              <s id="s.005294">Hic autem modus argumentandus, à partibus poſsibilibus ad
                <lb/>
              totum, eſſe à cauſa materiali, apud omnes Philoſophos in
                <expan abbr="cõfeſſo">confeſſo</expan>
              eſt, & Ari­
                <lb/>
              ſtot. ipſe tex. 3. 5. Metaph. id aſſerit. </s>
              <s id="s.005295">& tex. 11. 2. Poſter. vtitur ſimili
                <expan abbr="exẽ-plo">exem­
                  <lb/>
                plo</expan>
              ad
                <expan abbr="materialẽ">materialem</expan>
              cauſam explicandam. </s>
              <s id="s.005296">quamuis autem Geometræ non di­
                <lb/>
              cant talem angulum, vel talem figuram eſſe
                <expan abbr="diuiſibilẽ">diuiſibilem</expan>
              in partes æquales alijs
                <lb/>
              quibuſdam, ſed ſtatim diuidant, id faciunt breuitatis cauſa; vtuntur enim
                <lb/>
              actu pro potentia, quia actus potentiam ſupponit, quòd optimè Ariſtot. 9.
                <lb/>
              Metaphyſ. tex. 20. annotauit, ſic; Deſcriptiones quoque actu inueniuntur,
                <lb/>
              diuidentes namque inueniunt, quòd ſi diuiſæ eſſent, manifeſtæ eſſent, nunc
                <lb/>
              autem inſunt potentia, &c. </s>
              <s id="s.005297">Cuius loci noſtram ſuperius allatam explicatio­
                <lb/>
              nem habes. </s>
              <s id="s.005298">per deſcriptiones autem intelligit Geometricas demonſtratio­
                <lb/>
              nes, vt ſæpius ſupra in opere oſtenſum eſt. </s>
              <s id="s.005299">Innumeræ ſunt apud Geometras,
                <lb/>
              quę per hanc poſsibilem diuiſionem procedunt,
                <expan abbr="quęq;">quęque</expan>
              ideò ſunt à cauſa </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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