Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <pb pagenum="122" xlink:href="009/01/122.jpg"/>
            <p type="main">
              <s id="s.002116">
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            <p type="margin">
              <s id="s.002117">
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              168</s>
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            <p type="main">
              <s id="s.002118">Ibidem
                <emph type="italics"/>
              (Si igitur circumducas ſemicirculŭm, in quo A, circa diametrum in qua
                <lb/>
              G K P, que à G, K, reflexæ ad id in quo M; in omnibus planis ſimiliter ſe habebunt,
                <lb/>
              & æqualem facient angulum, qui K M G, & quem etiam facient angulum, quæ
                <lb/>
              K P, & P M, ſuper eam, quæ G P, ſemper æqualis erit. </s>
              <s id="s.002119">Trianguli igitur ſuper eam,
                <lb/>
              quæ G P, æquales ei, qui G M P. conſiſtunt. </s>
              <s id="s.002120">horum autem perpendiculares ad idem
                <lb/>
              ſignum cadent eius, quæ G P, & æquales erunt, cadunt ad
                <foreign lang="grc">ω,</foreign>
              centrum ergò circuli
                <lb/>
                <foreign lang="grc">ω</foreign>
              ſemicirculus autem, qui circa M N, abſectus eſt ab horizonte)
                <emph.end type="italics"/>
              hac vltima
                <lb/>
              textus parte concludit Iridis portionem ſupra horizontem aſtro
                <expan abbr="oriẽte">oriente</expan>
              exi­
                <lb/>
              ſtentem eſſe ſemicirculum, hoc modo; ſi igitur imaginatione circumducas
                <lb/>
              ſemicirculum, in quo A, circa diametrum horizontis G K P, in hac circum­
                <lb/>
              uolutione duæ lineæ G M, M K, in omnibus planis conſtitui poſſibilibus cir­
                <lb/>
              ca prædictam diametrum, quæ ſupra etiam fieri à triangulis infinitis dixi­
                <lb/>
              mus, ſucceſſiuè erunt; ſiue percurrent ſimiliter omnia illa plana, & facient
                <lb/>
              vbique angulum Iridis K M G, eundem: pariter duæ lineæ K P, P M, facient
                <lb/>
              vndique eundem angulum K P M. quare omnia triangula in predictis planis
                <lb/>
              imaginata, &
                <expan abbr="cõſtituta">conſtituta</expan>
              ſuper linea G P, ſimilia ipſi G M P, & æqualia erunt;
                <lb/>
              ſi igitur ab angulis ipſorum, in quibus M, ductæ ſint perpendiculares ad la­
                <lb/>
              tus G P, omnes cadent in idem punctum
                <foreign lang="grc">ω,</foreign>
              vt in figura;
                <expan abbr="quarũ">quarum</expan>
              vna erit M
                <foreign lang="grc">ω,</foreign>
                <lb/>
              quæ tamen cæteras omnes repreſentabit,
                <expan abbr="eisq́">eisque</expan>
              ; omnibus in volutatione axis
                <lb/>
              G K
                <foreign lang="grc">ω,</foreign>
              coincidit; erunt autem omnes æquales, quandoquidem ſunt trian­
                <lb/>
              gulorum æqualium. </s>
              <s id="s.002121">
                <expan abbr="eruntq́">eruntque</expan>
              ; in eodem eiuſdem circuli plano, & punctum
                <foreign lang="grc">ω,</foreign>
                <lb/>
              erit centrum ipſius. </s>
              <s id="s.002122">ſimilia dicta ſunt in Halone. </s>
              <s id="s.002123">Cum ergò ipſius centrum
                <lb/>
                <foreign lang="grc">ω</foreign>
              , ſit in diametro horizontis G K
                <foreign lang="grc">ω</foreign>
              P O, manifeſtum fit portionem eius, quæ
                <lb/>
              ſupra horizontem eminet, eſſe ſemicirculum, qui in figura notatur lineis
                <lb/>
              L M N. </s>
              <s id="s.002124">Atque hoc accidit Sole, vel Luna in horizonte exiſtentibus; quod
                <lb/>
              erat primo loco demonſtrandum.</s>
            </p>
            <p type="main">
              <s id="s.002125">Porrò ſciendum poſſe nos breuius polum prædictum inuenire, ſi nimirum
                <lb/>
                <figure id="id.009.01.122.1.jpg" place="text" xlink:href="009/01/122/1.jpg" number="63"/>
                <lb/>
              ad M, ducatur M P, faciens angulum K P M, æqua­
                <lb/>
              lem angulo G M K, per 23. primi, erunt enim duo
                <lb/>
              triangula
                <expan abbr="æquiãgula">æquiangula</expan>
              G P M, K P M, angulus enim
                <lb/>
              P, eſt communis, angulus verò M K P, eſt æqualis
                <lb/>
              duobus G, & G M K, per 32. primi, ergo etiam
                <lb/>
              duobus ad M, ſiue toti G M P, & reliquus K M P,
                <lb/>
              reliquo, quare per 4.6. latera circa angulos æqua­
                <lb/>
              les proportionalia erunt, & omologa G M, ad M K, ita G P, ad P M, quæ
                <lb/>
              æqualibus angulis ſubtenduntur. </s>
              <s id="s.002126">
                <expan abbr="eaſdẽ">eaſdem</expan>
              autem proprietates habebant etiam
                <lb/>
              triangula Ariſt. in figura, de qua paulò ante dicebam. </s>
              <s id="s.002127">Verba illa
                <emph type="italics"/>
              (Quæ ali­
                <lb/>
              bi quam in ſemicirculo constituuntur)
                <emph.end type="italics"/>
              ſunt perperam in antiqua tranſlatione
                <lb/>
              tranſlata, nam Græcè ſic,
                <foreign lang="grc">αι αλλοθι τοῡ ημικοκλνού συνισταμεναι,</foreign>
              transferenda
                <lb/>
              eſſent, quæ in alio circuli loco concurrunt.</s>
            </p>
            <p type="main">
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              <s id="s.002129">
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              169</s>
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            <p type="main">
              <s id="s.002130">Ibidem
                <emph type="italics"/>
              (Iterum ſit horizon quidem in quo A C. oriatur autem ſupra hunc G,
                <lb/>
              axis autem ſit nunc in quo G P. </s>
              <s id="s.002131">Alia igitur omnia ſimiliter oſtendentur vt & prius.
                <lb/>
              </s>
              <s id="s.002132">Polus autem circuli, in quo P, erit ſub horizonte eo, in quo A C, eleuato puncto,
                <lb/>
              in quo G. in eadem autem & polus, & centrum circuli, & terminantis nunc ortum,
                <lb/>
              eſt enim iſte, in quo G P. </s>
              <s id="s.002133">Quoniam autem ſupra diametrum, quæ A C, quod K G,
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              centrum vtique erit ſub horizonte priori eius, in quo A C, in linea K P, in quo
                <foreign lang="grc">ω,</foreign>
                <emph.end type="italics"/>
              </s>
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