Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.000914">
                <pb pagenum="49" xlink:href="009/01/049.jpg"/>
                <emph type="italics"/>
              punctum, & rectum; etenim ſecundum quod linea, & triangulo, ſecundum quod
                <lb/>
              triangulum duo recti: etenim per ſe triangulum duobus rectis æquale. </s>
              <s id="s.000915">Vniuerſale
                <lb/>
              autem eſt tunc, quando in quolibet, & primo monſtratur, vt duos rectos habere,
                <lb/>
                <expan abbr="neq;">neque</expan>
              figuræ eſt vniuerſale, quamuis eſt monſtrare de figura, quod duos rectos habet,
                <lb/>
              ſed non de qualibet figura,
                <expan abbr="neq;">neque</expan>
              vtitur qualibet figura monstrans, quadrangulum
                <lb/>
              enim figura a quidem est, non habet autem duobus rectis æquales. </s>
              <s id="s.000916">Aequicrus verò
                <lb/>
              habet quidem
                <expan abbr="quodcunq;">quodcunque</expan>
              duobus rectis æquales, ſed non primò, ſed triangulum
                <lb/>
              prius. </s>
              <s id="s.000917">quod igitur quoduis primum monſtratur duos rectos habens, aut
                <expan abbr="quodcunq;">quodcunque</expan>
                <lb/>
              aliud, huic primo ineſt vniuerſale, & demonstratio de hoc vniuerſaliter eſt, de alijs
                <lb/>
              verò quodammodo, non per ſe,
                <expan abbr="neq;">neque</expan>
              de æquicrure eſt vniuerſaliter, ſed in plus)
                <emph.end type="italics"/>
              pro
                <lb/>
              quorum intelligentia neceſſaria ſunt ea, quæ primo Priorum ſecto 3. cap. 1.
                <lb/>
              ſcripſimus. </s>
              <s id="s.000918">deinde memineris figuram vniuerſaliorem eſſe triangulo, & tri­
                <lb/>
              angulum vniuerſalius æquicrure. </s>
              <s id="s.000919">quando ait (vt duos rectos habere) vult
                <lb/>
              dicere, habere duos angulos rectos non actu, ſed potentia; quæ affectio eſt
                <lb/>
              trianguli, quia, vt ſuperius diximus, habet tres angulos æquales duobus
                <lb/>
              rectis angulis: quæ proprietas vniuerſaliter, & primò competit triangulo.
                <lb/>
              </s>
              <s id="s.000920">non autem figuræ, quia figura eſt vniuerſalior. </s>
              <s id="s.000921">
                <expan abbr="neq;">neque</expan>
              iſoſceli, quia iſoſceles eſt
                <lb/>
              reſtrictius triangulo. </s>
              <s id="s.000922">omittimus reliqua ſingillatim exponere, tum quia ſa­
                <lb/>
              tis clara ſunt, tum quia ab interpretibus benè explicantur.</s>
            </p>
            <p type="main">
              <s id="s.000923">
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              <s id="s.000924">
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              26</s>
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            <p type="main">
              <s id="s.000925">Tex. 13.
                <emph type="italics"/>
              (Si quis igitur monſtrauerit, quod rectæ
                <expan abbr="nõ">non</expan>
              coincidunt, videbitur
                <expan abbr="vtiq;">vtique</expan>
                <lb/>
              huius eſſe demonstratio, eo quod in omnibus eſt rectis; non eſt autem: ſi quidem
                <lb/>
              non quoniam ſic æquales, fit hoc, ſed ſecundum quod
                <expan abbr="quomodocunq;">quomodocunque</expan>
              æquales)
                <emph.end type="italics"/>
              pro­
                <lb/>
              ponit tres errores, qui circa demonſtrationem de vniuerſali contingunt,
                <lb/>
              quos omnes Geometricis exemplis illuſtrat; affert autem primo pro tertio
                <lb/>
              errore duo exempla, quorum primum in præmiſſis verbis continetur,
                <expan abbr="atq;">atque</expan>
                <lb/>
              ex 28. primi Elem. deſumitur, quam propterea primo loco exponendam
                <lb/>
                <figure id="id.009.01.049.1.jpg" place="text" xlink:href="009/01/049/1.jpg" number="18"/>
                <lb/>
              cenſui. </s>
              <s id="s.000926">Quando igitur duæ rectæ conſtitu­
                <lb/>
              tæ fuerint, vt A B, C D, in quas alia recta,
                <lb/>
              vt G F, incidens, faciat duos angulos in­
                <lb/>
              ternos, reſpectu rectarum A B, C D, & ad
                <lb/>
              eaſdem partes rectæ E F, vt ſunt ex parte
                <lb/>
              ſiniſtra anguli A G H, C H G; exparte ve­
                <lb/>
              rò dextra B G H, D H G; ſi
                <expan abbr="inquã">inquam</expan>
              linea E F,
                <lb/>
              fecerit duos illos angulos ex parte ſiniſtra ſimul ſumptos, æquales duobus
                <lb/>
              rectis angulis, vel duos ex parte dextra pariter æquales duobus rectis, pro­
                <lb/>
              bat Euclides rectas A B, C D, non concurrere, ſiue parallelas eſſe. </s>
              <s id="s.000927">Verum,
                <lb/>
              quia linea E F, poteſt facere aliquando prædictos angulos non
                <expan abbr="tantũ">tantum</expan>
              æqua­
                <lb/>
              les duobus rectis, verum etiam rectos, quo etiam modo
                <expan abbr="probarẽtur">probarentur</expan>
              cædem
                <lb/>
              lineæ eſſe parallelæ, vt in ſequenti figura, cum ſint anguli A G I, C I G, re­
                <lb/>
                <figure id="id.009.01.049.2.jpg" place="text" xlink:href="009/01/049/2.jpg" number="19"/>
                <lb/>
              cti, probabitur de rectis A B, C D, æquidiſtan­
                <lb/>
              tia. </s>
              <s id="s.000928">Ex his facile textum in hunc modum expo­
                <lb/>
              nemus; ſi quis igitur monſtrauerit, quod rectæ
                <lb/>
              A B, C D, nunquam coincidunt, etiamſi in infi­
                <lb/>
              nitum producantur, ſeu quod ſunt æquidiſtantes,
                <lb/>
              quando anguli prædicti interni ſunt duo recti,
                <lb/>
              videbitur
                <expan abbr="vtiq;">vtique</expan>
              huius eſſe demonſtratio de vniuerſali per ſe, & de primo </s>
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