Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.005656">
                <pb pagenum="34" xlink:href="009/01/318.jpg"/>
              diſtantiæ linearum. </s>
              <s id="s.005657">ſimile dicendum eſt de ſecunda parte demonſtrationis.</s>
            </p>
            <p type="main">
              <s id="s.005658">29 Prima pars probatur ab impoſſibili. </s>
              <s id="s.005659">ſecunda à ſigno, quæ ſuat æqua­
                <lb/>
              lia vni tertio &c. </s>
              <s id="s.005660">Idem dicendum de tertia parte.</s>
            </p>
            <p type="main">
              <s id="s.005661">30 Probat eſſe parallelas ex 27. primi, quare est
                <expan abbr="eiuſdẽ">eiuſdem</expan>
              naturæ cum illa.</s>
            </p>
            <p type="main">
              <s id="s.005662">31
                <expan abbr="Eandẽ">Eandem</expan>
              habet
                <expan abbr="rationẽ">rationem</expan>
              , quam 27. primi. </s>
              <s id="s.005663">per cauſam igitur formalem.</s>
            </p>
            <p type="main">
              <s id="s.005664">32 Primò, probat
                <expan abbr="anguiũ">anguium</expan>
              externum eſſe æqualem duabus internis, & ap­
                <lb/>
              poſitis ex eo, quòd partes anguli externi, ſint æquales partibus illorum: ex
                <lb/>
              æqualitate.ſ partium infert
                <expan abbr="æqualitatẽ">æqualitatem</expan>
              totorum: quæ demonſtratio eſt per
                <lb/>
              cauſam materialem. </s>
              <s id="s.005665">Secundò, probat illam adeò celeberrimam, omnis
                <lb/>
              triangulus habet tres, &c. </s>
              <s id="s.005666">quàm fuſiſſimè explicaui ſupra ad tex. 23. primi
                <lb/>
              Poſter. vbi Ariſt. eam in exemplum perfectiſſimæ demonſtrationis adducit.</s>
            </p>
            <p type="main">
              <s id="s.005667">33 Partim per 4. primi, partim per 27. primi
                <expan abbr="demõſtrat">demonſtrat</expan>
              : quapropter ad
                <lb/>
              earum naturam ſunt referendæ.</s>
            </p>
            <p type="main">
              <s id="s.005668">34 Tria probat. </s>
              <s id="s.005669">
                <expan abbr="primũ">primum</expan>
              , per 26. primi,
                <expan abbr="ſecundũ">ſecundum</expan>
              per illud axioma, ſi æqua­
                <lb/>
              libus æqualia adijcias, tota ſunt æqualia, quod duobus angulis applicat.
                <lb/>
              </s>
              <s id="s.005670">quæ demonſtratio eſt à partibus ad tota: à cauſa nimirum materiali. </s>
              <s id="s.005671">ter­
                <lb/>
              tium per 4. primi concludit.</s>
            </p>
            <p type="main">
              <s id="s.005672">35 Procedit per cauſam materialem: in omni enim caſu probat illa duo
                <lb/>
              parallelogramma eſſe æqualia, quia ſi æqualibus æqualia adijciantur, tota
                <lb/>
              erunt æqualia: vt in præcedenti dictum eſt.</s>
            </p>
            <p type="main">
              <s id="s.005673">36 Probat duo eſſe æqualia, quia ſunt vni tertio æqualia: videlicet à ſi­
                <lb/>
              gno, à poſteriori.</s>
            </p>
            <p type="main">
              <s id="s.005674">37 Probat duo triangula eſſe æqualia, quòd ſint dimidia duorum paral­
                <lb/>
              lelogrammorum æqualium: eſt
                <expan abbr="itaq;">itaque</expan>
              à cauſa materiali.</s>
            </p>
            <p type="main">
              <s id="s.005675">38 Eadem ratione demonſtrat in hac,
                <expan abbr="atq;">atque</expan>
              in præcedenti.</s>
            </p>
            <p type="main">
              <s id="s.005676">39 Propoſitum probat, ad abſurdum deducendo aduerſarium.</s>
            </p>
            <p type="main">
              <s id="s.005677">40 Similiter demonſtrat ac in præcedenti 39.</s>
            </p>
            <p type="main">
              <s id="s.005678">41 Probat vnum eſſe duplum alterius, quòd ſit duplum alterius, quod il­
                <lb/>
              li æquale eſt. </s>
              <s id="s.005679">videtur à ſigno.</s>
            </p>
            <p type="main">
              <s id="s.005680">42 Probat parallelogrammum, &
                <expan abbr="triangulũ">triangulum</expan>
              eſſe æqualia, quoniam
                <expan abbr="vtrũ-que">vtrun­
                  <lb/>
                que</expan>
              duplum ſit eiuſdem trianguli: videlicet per cauſam materialem.</s>
            </p>
            <p type="main">
              <s id="s.005681">43 Probat duo parallelogramma eſſe ęqualia, quoniam ablatis æquali­
                <lb/>
              bus ab æqualibus ſint reſidua. </s>
              <s id="s.005682">cauſa eſt materialis.</s>
            </p>
            <p type="main">
              <s id="s.005683">44 Probat parallelogrammum æquari triangulo, quia
                <expan abbr="vtrunq;">vtrunque</expan>
              cuidam
                <lb/>
              tertio æquatur. </s>
              <s id="s.005684">à ſigno videlicet.</s>
            </p>
            <p type="main">
              <s id="s.005685">45 Probat totum parallelogrammum æquari toti rectilineo; eo, quòd
                <lb/>
              partes amborum totorum ſint æquales: eſt perſpicua cauſa materialis.</s>
            </p>
            <p type="main">
              <s id="s.005686">46 Probat quadrilaterum quoddam eſſe quadratum ex definitione qua­
                <lb/>
              drati, quia ſ habet quatuor angulos rectos, & quatuor latera æqualia. </s>
              <s id="s.005687">eſt
                <lb/>
              igitur à cauſa formali.</s>
            </p>
            <p type="main">
              <s id="s.005688">47 Probat quadratum lateris angulo recto ſubſenſi, eſſe æquale duobus
                <lb/>
              quadratis reliquorum
                <expan abbr="laterũ">laterum</expan>
              trianguli illius: & ratio deſumpta eſt à parti­
                <lb/>
              bus, quia. </s>
              <s id="s.005689">ſ. </s>
              <s id="s.005690">partes prædicti quadrati æquales ſunt ſingillatim prędictis qua­
                <lb/>
              dratis; ergo totum quadratum totis illis quadratis æquale eſt. </s>
              <s id="s.005691">manifeſta eſt
                <lb/>
              cauſa materialis.</s>
            </p>
            <p type="main">
              <s id="s.005692">48 Probat angulum quendam eſſe rectum, eo, quòd æqualis ſit cuidam
                <lb/>
              angulo recto. </s>
              <s id="s.005693">eſt à ſigno.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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