Biancani, Giuseppe, Aristotelis loca mathematica, 1615

Table of figures

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            <p type="main">
              <s id="s.000778">
                <pb pagenum="40" xlink:href="009/01/040.jpg"/>
                <expan abbr="linearũ">linearum</expan>
              , ſed penes inclinationem, & mucronem, quem faciunt: vnde etiamſi
                <lb/>
              duæ lineæ prædictæ A B, A C, productæ, ſiue etiam decurtatæ fuerint, dum­
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              modo ſitus, ſiue poſitio ipſarum, quam ad inuicem habent, non varietur,
                <lb/>
              erit ſemper eadem quantitas anguli A. </s>
              <s id="s.000779">Aduertendum præterea rationem
                <lb/>
              anguli non poſſe ſaluari in ſolo puncto A, in quo lineæ concurrunt, ſed ne­
                <lb/>
              ceſſariam eſſe aliquam quantitatem, quamuis exiguam, linearum A B, A C.
                <lb/>
              </s>
              <s id="s.000780">Notandum etiam, quod in nominatione angulorum, quæ fit per tres lite­
                <lb/>
              ras, ſemper literam illam eſſe medio loco proferendam, quæ ad acumen ip­
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              ſum poſita eſt, vt in ſuperiori, litera A, debet ſemper media proferri, dicen­
                <lb/>
              do angulum B A C, ſiue C A B,
                <expan abbr="nũquam">nunquam</expan>
              tamen licet dicere angulum A C B,
                <lb/>
              vel C B A. </s>
              <s id="s.000781">Porrò quemadmodum vnus angulus vni angulo æqualis eſt, ita
                <lb/>
                <expan abbr="aliquãdo">aliquando</expan>
              duo anguli ſunt vni angulo æquales, vt patet, ſi vnus angulus, v.g.
                <lb/>
              angulus B A C, diuidatur in duos angulos à linea A D. tunc enim duo angu­
                <lb/>
                <figure id="id.009.01.040.1.jpg" place="text" xlink:href="009/01/040/1.jpg" number="8"/>
                <lb/>
              li partiales B A D, D A C, erunt æquales totali angulo
                <lb/>
              B A C, cum partes omnes ſimul ſumptæ ſint ſuo toti æqua­
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              les. </s>
              <s id="s.000782">pariter tres anguli poſſunt æquari & vni, & duobus
                <lb/>
              alijs angulis, quando nimirum a cumina, ſiue mucrones il­
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              li ſimul ad vnum punctum conſtituti
                <expan abbr="adæquarẽtur">adæquarentur</expan>
              mucro­
                <lb/>
              ni illi, quem conſtituerent alij duo anguli, quibus illi tres
                <lb/>
              ſunt pares, v.g. ſint tres anguli trianguli A B C,
                <expan abbr="ſintq́">ſintque</expan>
              ; alij duo anguli recti,
                <lb/>
                <figure id="id.009.01.040.2.jpg" place="text" xlink:href="009/01/040/2.jpg" number="9"/>
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              quos linea perpendicularis D E, facit cum li­
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              nea F G; ſit
                <expan abbr="inquã">inquam</expan>
              anguli recti D E F, D E G,
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              tunc tres anguli illius
                <expan abbr="triãguli">trianguli</expan>
                <expan abbr="dicẽtur">dicentur</expan>
              æqua­
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              les duobus hiſce rectis, ſi tres illi mucrones
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              trianguli ſimul ſumpti, & vniti ad punctum
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              E, ad quod duo
                <expan abbr="quoq;">quoque</expan>
              mucrones angulorum
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                <figure id="id.009.01.040.3.jpg" place="text" xlink:href="009/01/040/3.jpg" number="10"/>
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              rectorum coeunt, congruent omnino duobus
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              prædictis angulis rectis, ſiue duobus illis mu­
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              cronibus angulorum rectorum, ſiue conſti­
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              tuent lineam rectam F E G, ſicuti faciunt
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              etiam duo illi anguli recti; ſiue etiam dica­
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              mus, occupabunt idem ſpatium omninò, &
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              præcisè, quod occupant duo recti: v.g. ſi mucro B, ibi poneretur, faceret
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              angulum F E H, & ſi ibi iuxta ipſum apponeretur mucro A, faceret angulum
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              H E I. quem ſi deinceps ſubſequetur reliquus angulus C, conſtitueret
                <expan abbr="reli-quũ">reli­
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                quum</expan>
              angulum I E G. iam, vt vides, illi tres anguli ad E, tranſlati, ſunt æqua­
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              les duobus rectis ad E, pariter conſtitutis, cum illi tres fiant partes duorum
                <lb/>
              rectorúm, vel quia occupant idem ſpatium, vel eandem lineam rectam F E G,
                <lb/>
              conſtituant. </s>
              <s id="s.000783">habet igitur omne triangulum ſiue ęquilaterum, ſiue ſcalenum,
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              ſiue Iſoſceles mirabilem hanc proprietatem, vt tres anguli, cuiuſuis trian­
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              guli ſint æquales duobus rectis angulis. </s>
              <s id="s.000784">Quam demonſtrationem primi om­
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              nium Pythagorici perfecerunt, vt refert Proclus ad 32. primi Elem. Eucli­
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              des deinde ibidem aliter, quam Pythagorici idem demonſtrauit. </s>
              <s id="s.000785">Quod ſi
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              quis huius rei
                <expan abbr="experiẽtiam">experientiam</expan>
              aliquam velit; etiamſi non exactam (cum æqua­
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              litas mathematica non cadat ſub ſenſum, ſed ſola intelligentia percipiatur,
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              quippe quæ in materia intelligibili, non autem ſenſibili verſatur, & cuius </s>
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