Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <pb pagenum="180" xlink:href="009/01/180.jpg"/>
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              <s id="s.003061">
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              Additio de veteri Securi, & Bipenne.
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              </s>
            </p>
            <p type="main">
              <s id="s.003062">Libet etiam huic tractationi de ſecuri nonnulla addere, quæ olim oc­
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              caſione ex Proclo accepta in tenebris diu deliteſcentia in lucem re­
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              ſtituimus, ſunt autem hæc. </s>
              <s id="s.003063">Primò, antiquæ ſecuris, necnon bipen­
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              nis figuram reſtituam. </s>
              <s id="s.003064">Secundò, oſtendam angulum ſecuris, qui
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              curuilineus eſt, æqualem eſſe angulo trianguli æquilateri, qui rectilineus eſt.
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              </s>
              <s id="s.003065">Proclus igitur in comm. 23. primi Euclidis, ſic ait: oſtenſum fuit ab anti­
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              quis, ſcilicet Geometris, quod angulus figuræ illius, quæ ſecuri ſimilis eſt,
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              æqualis eſt angulo rectilineo, quippe qui duabus tertijs anguli recti æqualis
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              eſt. </s>
              <s id="s.003066">hanc anguli ſecuris affectionem, cum nec ille, nec alij, quod ſciam de­
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              monſtrent, ego paulò poſt demonſtrabo. </s>
              <s id="s.003067">deinde ſubdit; fit autem huiuſmo­
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              di ſecuralis figura, quæ pelecoides vocatur duobus circulis per centra ſe
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              mutuò ſecantibus. </s>
              <s id="s.003068">hæc Proclus. </s>
              <s id="s.003069">Ex his autem poſtremis verbis deſcriptio­
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              nem antiquæ ſecuris, ſic puto eruendam. </s>
              <s id="s.003070">Ducatur primo recta A C, quæ
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                <figure id="id.009.01.180.1.jpg" place="text" xlink:href="009/01/180/1.jpg" number="104"/>
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              erit inſtar manubrij ſecuris. </s>
              <s id="s.003071">de­
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              inde ex centro C, interuallo. </s>
              <s id="s.003072">v. g.
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              C B, deſcribatur circulus B F; ſi­
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              militer eodem interuallo B D, ex
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              centro D, deſcribatur circulus
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              B E; tandem ex B, centro, atque
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              eodem interuallo ducatur alius
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              circulus D E F C, qui priores duos ſecabit in punctis E F.
                <expan abbr="cõſideremus">conſideremus</expan>
              iam,
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              reliquis circulorum partibus ommiſſis, curuilineam figuram B E F, quam
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              eſſe veteris ſecuris formam ex
                <expan abbr="ſentẽtia">ſententia</expan>
              Proclinon eſt dubitandum, cum cir­
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              culis ſe mutuò per centra ſecantibus conſtituatur, vt vult ipſe, & præterea
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              habeat angulos E F, tantos, quantos ipſe tradit, vt mox patebit; linea au­
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              tem A B C, ſecuris manubrium refert.</s>
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              <s id="s.003073">Quod autem tam angulus E, quàm angulus F, ſint æquales duabus tertijs
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              vnius anguli recti, ſiue quod idem eſt angulo trianguli æquilateri, manife­
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              ſtum erit hoc modo. </s>
              <s id="s.003074">Deſcribatur iterum ſecuralis figura prædicto modo,
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              ſ
                <expan abbr="itq;">itque</expan>
              ea A B C. ducantur præterea ad ſingulos angulos tres rectæ A B, B C,
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              C A, quæ conſtituunt triangulum æquilaterum A B C, tria enim ipſius late­
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                <figure id="id.009.01.180.2.jpg" place="text" xlink:href="009/01/180/2.jpg" number="105"/>
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              ra ſubtendunt tres arcus æquales A B, B C, C A,
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              ſunt enim tres ſextantes æqualium circulorum,
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              ut facilè colligi poteſt ex 15. 4. ex quo etiam ſe­
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              quitur tres illas circulorum portiones, quas re­
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              ctè cum ſuis arcubus conſtituunt eſſe inuicem
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              æquales, & ſimiles portiones nimirum A B E,
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              B C D, C A F. hinc pręterea ſequitur angulos ip­
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              ſarum eſſe inuicem æquales, angulos, v.g. A B E,
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              C B D, mixtos eſſe æquales, quod facilè eſt per imaginariam ſuperpoſitio­
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              nem demonſtrare. </s>
              <s id="s.003075">cum igitur prædicti duo anguli ſint æquales, ſitque inter
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              eos medius alius angulus E B C, qui pariter mixtus eſt, ſi ipſe addatur tam
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              angulo C B D, quàm angulo A B E, inuicem æqualibus, erunt duo anguli </s>
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