Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <pb pagenum="73" xlink:href="009/01/073.jpg"/>
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              <s id="s.001353">
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              91</s>
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              <s id="s.001355">Tex. 68. (
                <emph type="italics"/>
              Aut enim ad ipſum quid eſt, reducitur ipſum propter quid in immo­
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              bilibus, vt in Mathematicis, ad definitionem enim recti, aut commenſurabilis, aut
                <lb/>
              alius cuiuſpiam reducitur vltimum
                <emph.end type="italics"/>
              ) ex his manifeſtè videas Mathematicas
                <expan abbr="de-mõſtrare">de­
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                monſtrare</expan>
              per cauſam formalem, cum cauſam ipſam ad ipſum quid eſt, ideſt,
                <lb/>
              ad definitionem reducant. </s>
              <s id="s.001356">quorum exempla in logicis ex Mathematicis at­
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              tuli: ſed etiam ſequentis loci exemplum de triangulo idem apertè manife­
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              ſtat; in quo probat duos angulos A C B, A C D, eſſe rectos, ex definitione
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              ipſorum, ſiue ex definitione lineæ perpendicularis A C, quod idem eſt.</s>
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            <p type="main">
              <s id="s.001357">
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            <p type="margin">
              <s id="s.001358">
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              92</s>
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            <p type="main">
              <s id="s.001359">Tex 89. (
                <emph type="italics"/>
              Eſt autem neceſſarium in Mathematicis, & in his, quæ ſecundum
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              naturam fiunt quaſi eodem modo; quoniam enim hoc rectum eſt, neceſſe eſt, trian­
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              gulum tres angulos habere æquales duobus rectis; ſed non, ſi hoc, illud; ſed ſi hoc
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              non eſt,
                <expan abbr="neq;">neque</expan>
              rectum eſt.
                <emph.end type="italics"/>
              ) cum animaduerterim non parum eſſe diſſenſionis, &
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              difficultatis in exemplo hoc mathematico explicando, ita vt recentiores
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              quidam textum
                <expan abbr="hũc">hunc</expan>
              pro arbitratu ſuo perperam latinè verterint: ideò pri­
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              mum ex græcis codicibus interpretationem hanc veram attuli. </s>
              <s id="s.001360">deinde, quia
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              etiam græci in exemplo mathematico enodando, vel malè, vt Simplicius;
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              vel obſcurè nimis, vt reliqui; Latini verò vel nihil, vel peius multò loquun­
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              tur, ideò ſic ego exponendum cenſui. </s>
              <s id="s.001361">cum velit Ariſt. oſtendere neceſſita­
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              tem, quæ in ſcientijs inter præmiſſas, ſeu medium, & concluſionem reperi­
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              tur, affert exemplum illud mathematicum ſibi familiare, demonſtrationem
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              ſcilicet illam, qua oſtenditur, omne triangulum habere tres angulos æqua­
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              les duobus rectis angulis, cuius fuſiſſimam explicationem inuenies ſupra in
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              primo Priorum, ſecto 3. cap. 1. quam neceſſe eſt, conſulas. </s>
              <s id="s.001362">pro medio autem
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              huius paſſionis accipit lineam perpendicularem, quam innuit verbis illis
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                <emph type="italics"/>
              (quoniam enim hoc rectum eſt
                <emph.end type="italics"/>
              ) vt in figura ſit triangulum A B C,
                <expan abbr="ſitq́">ſitque</expan>
              ; vt latus
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                <figure id="id.009.01.073.1.jpg" place="text" xlink:href="009/01/073/1.jpg" number="36"/>
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              A C, ſit perpendiculare
                <expan abbr="cũ">cum</expan>
              latere B C, & pro­
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              ducatur B C, in D; tunc triangulum A B C,
                <lb/>
              habere tres angulos, A, B, & A C B, æquales
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              duobus rectis planum erit: nam
                <expan abbr="cũ">cum</expan>
              latus A C,
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              ſit perpendiculare (quod Ariſt. dicit, cum
                <expan abbr="re-ctũ">re­
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                ctum</expan>
              hoc ſit) erunt duo anguli deinceps A C B,
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              A C D, recti, ex definitione lineæ perpendicu­
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              laris, cum ergo duo anguli A, & B, externo,
                <expan abbr="rectoq́">rectoque</expan>
              ; A C D, ſint æquales per
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              32. primi, & reliquus angulus A C B, communis, ideſt, ſit angulus triangu­
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              li, & angulus vnus lineæ perpendicularis, & ideò rectus; manifeſtè apparet,
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              tres angulos A, B, A C B, eſſe æquales neceſſariò duobus rectis, ex poſitio­
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              ne illius recti, ſiue lateris perpendicularis, quia ex verò, verum neceſſariò
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              ſequitur; non tamen poſita hac paſſione, ſiue concluſione, habere ſcilicet
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              tres angulos æquales duobus rectis, neceſſariò ſequitur illud eſſe rectum,
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              ideſt latus illud A C, eſſe perpendiculare ad latus B C, quia verum
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              ſequi poteſt ex verò, & falsò. </s>
              <s id="s.001363">valebit tamen hæc conſequen­
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              tia, ſi triangulum non habet hanc proprietatem, ne­
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              que illud rectum eſt, ideſt,
                <expan abbr="neq;">neque</expan>
              latus prædi­
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              ctum erit
                <expan abbr="perpẽdiculare">perpendiculare</expan>
              , quia falſum
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              non, niſi ex falſo ſequitur.</s>
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          </chap>
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    </archimedes>
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