Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.002448">
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              ſunt, ſi igitur quæ ad latus educeretur, videnti mox eſſet manifeſtum
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              ) per deſcri­
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              ptiones, vel figurationes, vel deſignationes intelligendas eſſe demonſtra­
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              tiones Geometricas ſæpius ſupra dictum eſt, & pariter ex hoc loco com­
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              probatur. </s>
              <s id="s.002449">Dicit igitur, quod demonſtrationes ſuas Geometræ inueniunt,
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              reducendo ad actum ea, quæ erant in potentia, diuidentes enim educunt in
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              actum, figuras, angulos, lineas, & cætera huiuſmodi, quæ prius ſolùm erat
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              in potentia, ex quibus poſtea ſuas demonſtrationes perficiunt (
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              Cur triangu­
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              lus duo recti
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              ) affert exemplum eius, quod proximè dixerat, ſcilicet Geome­
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              tras demonſtrare producendo ad actum entia quædam Mathematica, quod
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              exemplum, vt intelligas ijs opus habes, quæ primo Priorum, ſecto 3. cap. 1.
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              conſcripta ſunt (
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              Cur triangulus duo recti?
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              ) ideſt, cur triangulus habet tres
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              angulos æquales duobus rectis angulis (
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              Quia qui circa vnum punctum anguli
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              duobus rectis angulis æquales ſunt
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              ) niſi hoc dictum ad bonum trahatur ſenſum,
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                <figure id="id.009.01.142.1.jpg" place="text" xlink:href="009/01/142/1.jpg" number="75"/>
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              falſum eſt, nam omnes anguli, qui circa vnum
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              punctum, v. g. A, ſunt conſtituti, æquales ſunt
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              non duobus, vt eſt in textu, ſed quatuor rectis,
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              vt patet ex corollario 2. 15. primi Elem. quot­
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              quot enim anguli conſtituantur ad punctum A,
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              omnes ſimul erunt æquales quatuor rectis, quos
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              faciunt præſentes lineæ B C, D E. vniuerſi enim
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              illi congruent his quatuor rectis: ſed Ariſt. ſen­
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              ſus eſt omnes angulos ad eaſdem partes conſti­
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              tutos, v. g. ad partes ſuperiores lineæ B C, eſſe
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              æquales duobus rectis B A D, D A C, vt oſtenditur in 13. primi, necnon
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              etiam patere poteſt ex corollario 2. 15. eiuſdem. </s>
              <s id="s.002450">tales ſunt quatuor anguli
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              ad ſuperiores partes lineæ B C, & ad punctum A, conſtituti, qui, vt patet,
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                <figure id="id.009.01.142.2.jpg" place="text" xlink:href="009/01/142/2.jpg" number="76"/>
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              ſunt æquales duobus rectis B A D, D A C,
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              tales etiam ſunt in hac ſecunda figura tres
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              anguli B C A, A C D, D C E, qui quidem
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              æquales ſunt duobus rectis angulis. </s>
              <s id="s.002451">hoc
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              ſenſiſſe Ariſt. patet ex demonſtratione 32.
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              primi, quæ demonſtrat
                <expan abbr="memoratã">memoratam</expan>
              ab Ari­
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              ſtot. trianguli affectionem, & ad quam
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              propterea ipſe ſpectabat, cuius figura eſt
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              eadem cum hac ſecunda, in qua Euclides oſtendit prædictos tres angulos
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              æquari duobus rectis. </s>
              <s id="s.002452">ſubdit poſtea, ſi igitur linea C D, quæ ad latus A B,
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              parallela eſt in potentia, educeretur in actum, videnti mox eſſet manifeſtum
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              tres angulos trianguli A B C, eſſe pares duobus rectis. </s>
              <s id="s.002453">ducta enim C D, pa­
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              rallela lateri B A, apparet ſtatim angulus A, æqualis angulo A C D, & an­
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              gulus B, angulo D C E; cum reliquus verò
                <expan abbr="triãguli">trianguli</expan>
              angulus B C A, ſit apud
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              prædictos duos ad idem punctum C, conſtitutus;
                <expan abbr="atq;">atque</expan>
              omnes hi tres duobus
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              rectis æquentur, mox inſpicienti talem figurationem manifeſtum fit tres an­
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              gulos illius trianguli eſſe duobus rectis æquales.</s>
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            <p type="main">
              <s id="s.002454">
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              222</s>
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            <p type="main">
              <s id="s.002456">Ibidem (
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              Cur in ſemicirculo vniuerſaliter rectus? </s>
              <s id="s.002457">quia ſi tres æquales, & quæ
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              baſis eſt duo, & quæ ex medio ſupra stat recta, videnti manifestum erit ei, qui illud
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              ſciat
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              ) In 2. Poſter. tex. 11. inuenies huius loci expoſitionem. </s>
              <s id="s.002458">nunc ſolùm </s>
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          </chap>
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    </archimedes>
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