Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.003214">
                <pb pagenum="191" xlink:href="009/01/191.jpg"/>
              uertuntur ad D; hinc flectunt per H, vſque ad E, & per G, angulum iterum
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              deſcendunt ad M, à quo recta tendunt in F, hinc per 2. deducunt ad 3. à quo
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              foramine, per foramen 4. reflexum faciunt ad 5. à quo iterum per B, deſcen­
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              dunt ad angulum K,
                <expan abbr="ibiq́">ibique</expan>
              ; alterum funis extremum deſinit:
                <expan abbr="hocq́">hocque</expan>
              ; modo duo
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              anguli A, & K, reſtis habent capita, & reſtes extenſæ ſunt non diametrali­
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              ter, ſed tranſuerſim.</s>
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              <s id="s.003215">Notandum autem, quod reſtes æquales ſunt cum ſuis curuaturis. </s>
              <s id="s.003216">v. g. re­
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              ſtis A B, cum ſua curuatura B C, æqualis eſt reſti C D, vnà cum eius curua­
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              tura D H, & aliæ eodem modo ſe habent, quia eadem demonſtratio omni­
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              bus accommodari poteſt: quia enim figura A B G M, parallelogrammum
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              eſt, æqualia enim ſunt latera B G, A M, & quot foramina ſunt in vno, tot
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              etiam ſunt in altero,
                <expan abbr="eaq́">eaque</expan>
              ; inuicem æquidiſtant, ſequitur omnes reſtes eſſe
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              parallelas, & æquales, per 33, primi. </s>
              <s id="s.003217">ex qua etiam ſequitur prædictas cu­
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              ruaturas, B C, D H, E G, eſſe æquales. </s>
              <s id="s.003218">quare manifeſtum eſt in dimidio le­
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              ctulo tot eſſe reſtes æquales reſti A B, quot ſunt foramina in dimidio latere
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              B G, vel in dimidio F B, hoc eſt eſſe quatuor. </s>
              <s id="s.003219">porrò oportet quantitatem
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              harum omnium reſtium perſcrutari, vt eam cum quantitate reſtium diame­
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              traliter extenſarum conferamus, quod geometricè hoc modo aſſeque mur:
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              triangulum enim B G K, rectangulum eſt, ergò per 47. primi, quadrata la­
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              terum B G, G K, æqualia ſunt quadrato lineæ B K: latus B G, eſt trium pe­
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              dum, quemadmodum etiam latus G K quadratus autem numerus ternarij
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              eſt 9. ergo duo quadrati numeri 9. ſiue 18. æquales ſunt quadrato lineæ B K,
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              ergò linea B K, eſt radix quadrata numeri 18. quæ radix non poteſt exactè
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              in numeris repræſentari, eſt enim, vt aiunt, radix ſurda. </s>
              <s id="s.003220">verumtamen per
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              radicum extractionem,
                <expan abbr="atq;">atque</expan>
              approximationem ea poni poteſt eſſe 41/4. ideſt
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              quatuor pedum cum vna quarta. </s>
              <s id="s.003221">cum igitur in toto lecto ſint huiuſmodi
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              octo reſtes, erit omnium ſumma pedum 34. ferè. </s>
              <s id="s.003222">ſi autem ſeeundum diame­
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              trum extendantur reſtes, vti factum eſt in lectulo A B C D, neutiquam re­
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              ſtes omnes ſimul ſuperiori quantitati adæquabuntur, ſed illam longè ſupe­
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                <figure id="id.009.01.191.1.jpg" place="text" xlink:href="009/01/191/1.jpg" number="114"/>
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              rabunt. </s>
              <s id="s.003223">Sit igitur lectus A B­
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              C D, in quo diametraliter du­
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              ctæ ſint reſtes B D, E H, & re­
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              liquæ, vt in figura. </s>
              <s id="s.003224">harûm quan­
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              titas ſi per 47. primi, & per ra­
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              dicis quadratæ extractionem
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              inueniatur, erit ſumma earum
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              pedum quadraginta cum dimi­
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              dio; quæ quantitas præcedenti
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              maior eſt ſex pedibus cum di­
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              midio.</s>
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              <s id="s.003225">
                <expan abbr="Atq;">Atque</expan>
              hic eſt ſenſus Ariſt. quamuis tex. ipſius propter nimiam tam in græ­
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              cis, quàm in latinis codicibus corruptionem, totus reſtitui nequiuerit.</s>
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