Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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180
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<
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<
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Additio de veteri Securi, & Bipenne.
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<
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id
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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. </
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<
s
id
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s.003063
">Primò, antiquæ ſecuris, necnon bipen
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nis figuram reſtituam. </
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<
s
id
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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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</
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<
s
id
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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. </
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>
<
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. </
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>
<
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. </
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>
<
s
id
="
s.003068
">hæc Proclus. </
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<
s
id
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s.003069
">Ex his autem poſtremis verbis deſcriptio
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nem antiquæ ſecuris, ſic puto eruendam. </
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<
s
id
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s.003070
">Ducatur primo recta A C, quæ
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place
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104
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erit inſtar manubrij ſecuris. </
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>
<
s
id
="
s.003071
">de
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inde ex centro C, interuallo. </
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>
<
s
id
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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.
<
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abbr
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cõſideremus
">conſideremus</
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>
iam,
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reliquis circulorum partibus ommiſſis, curuilineam figuram B E F, quam
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eſſe veteris ſecuris formam ex
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abbr
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ſentẽtia
">ſententia</
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>
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.</
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>
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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
<
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abbr
="
itq;
">itque</
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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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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. </
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>
<
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 </
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