Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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figuram non deſtruit, quamuis diuidat. </
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<
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partiuntur. </
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<
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">At cæteræ lineæ, quæ per lineas compoſitam figuram ſecant, eam cor
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rumpunt: committitur enim rectilinea figura in angulis, vel ſecundum angulos)
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Vt rectè problema hoc percipiamus, proponenda eſt figura rectilinea, &
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vna ex ijs, quæ parallelogramma dicuntur, vt ſunt Quadratum, Quadrila
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terum, Rhombus, Rhomboides, cuiuſmo
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di eſt præſens, aliter verba Ariſt. illi non
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ſemper quadrarent, quia illarum diameter
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illas ſemper bifariam non ſe caret. </
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<
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modum videre eſt in trapezio. </
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">& pentagono
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etiam æquilatero. </
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nibus lineis, quæ quadrilaterum A B C D,
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bifariam diuidunt, quales ſunt E F, G H, &
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D B. ſola D B, quæ ab angulo ad angulum
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ducta eſt, mœruit appellari diameter. </
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<
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">Reſpondet autem, eam fortè appel
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lationem hanc præ cæteris inde promeruiſſe, quòd, quamuis aliæ omnes
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æquè parallelogrammum dimetiantur, ſola tamen ipſa D B, ipſum non de
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ſtruit, nec ſcindit, cùm ei nouam aliquam diuiſionem non inferat, ſed id per
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angulos ſecet, vbi prius laterum commiſſuræ
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: reliquæ verò omnes no
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uas figuræ ſectiones inferunt, cùm eius latera in punctis E, F, G, H,
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,
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vbi nulla prius erat diuiſio; quapropter ipſam quodammodo deſtruunt,
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corrumpunt. </
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<
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(Angulis enim
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constant, quæ rectis lineis continentur)
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malè græco textui
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ευθυγραμμον κατὰ τας γωνίας,</
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reſpondere, qui ſic latinè reddendus eſt: com
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ponitur enim rectilineum iuxta angulos; quæ interpretatio vera eſt, quia
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anguli ſunt laterum commiſſuræ, vt dictum eſt.</
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338</
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(cur diameter ita eſt appellata? </
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partitò figuram diuidat? </
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bus in flexa coarctatur, cùm cæteræ per latera diuidant?)
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præſentis problematis
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expoſitio petatur ex præcedentis expoſitione.</
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339</
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<
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">In problemate 3.
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(Cur homines omnes tam Græci, quàm Barbari ad decem
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numerare conſueuere, & c. </
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<
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">Vtrum quod denarius numerus perfectus ſit: con
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tinet enim omnia numerorum genera. </
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<
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">vt par, impar, quadratum, quadrantale, lon
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gum, planum, primum, compoſitum)
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Cur omnes nationes miro quodam con
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ſenſu ſuos numeros in denas, veluti in gradus quoſdam diuidant, Ariſtoteles
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cauſam indagaturus, reſpondet primò id fortè accidiſſe ob denarij numeri
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perfectionem: cuius perfectionis hoc eſt indicium, quod denarius contineat
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omnes numerorum ſpecies. </
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<
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">quæ quidem omnes numerorum ſpecies in defi
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nitionibus 7. Elem. exponuntur, quas conſulere debes. </
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<
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contineri numeros pares, ac impares, per ſe patet. </
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<
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">continetur etiam in eo
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quadratus numerus, imò duo quadrati numeri, nam, & quaternarius eſt
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numerus quadratus, quippe qui ex ductu binarij in binarium producatur:
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item nouenarius eſt quadratus, quippe qui ex multiplicatione ternarij in
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ternarium gignitur. </
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<
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">Porrò pro quadrantali numero intelligendus eſt nume
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rus cubus, erat. </
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<
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<
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co textu voci huic quadrantali, reſpondet
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ideſt, cubus. </
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<
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