Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.000729">
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              bus vltimis, non prætereundum. </s>
              <s id="s.000730">reliquas duas logicæ partes, Topicam ſci­
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              licet, & Elenchos, quæ ſyllogiſmos probabilem, & apparentem docent, no­
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              luit appellare reſolutorios, quamuis inuentionem mediorum doceant, quia
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              iam mos iſte inoleuerat apud Philoſophos, & Mathematicos, vt illa ſola
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              pars, quæ ex materia neceſſaria doceret ſyllogiſmum demonſtratiuum con­
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              ſtruere, diceretur reſolutio: cum Mathematici, qui primi de reſolutione
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              ſcripſerunt, talem materiam ſolum conſiderent.</s>
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              5</s>
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              <s id="s.000733">Ex cap. 23. ſecti primi lib. 1.
                <emph type="italics"/>
              (Vt quod diameter incommenſurabilis eo, quod
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              imparia æqualia paribus fiant, ſi fuerit poſita commenſurabilis. </s>
              <s id="s.000734">æqualia igitur fieri
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              imparia paribus ratiocinantur, diametrum vtrò incommenſurabilem eſſe ex ſuppo­
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              ſitione
                <expan abbr="monſtrãt">monſtrant</expan>
              , quoniam falſum accidit propter contradictionem)
                <emph.end type="italics"/>
              Euclides pri­
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              mis duabus definitionibus 10. elem. </s>
              <s id="s.000735">definit, quæ nam ſint magnitudines
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              commenſ. </s>
              <s id="s.000736">& quæ incommenſ. </s>
              <s id="s.000737">ſic; commenſ. </s>
              <s id="s.000738">magnitudines dicuntur, quas
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                <figure id="id.009.01.037.1.jpg" place="text" xlink:href="009/01/037/1.jpg" number="3"/>
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              eadem menſura metitur, vt ſi fuerint duæ magnitu­
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              dines, A, & B, quas eadem menſura C, ideſt quan­
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              titas C, metiatur, ideſt
                <expan abbr="quãtitas">quantitas</expan>
              C, applicata quan­
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              titati A, & per ipſam aliquoties replicata ipſam ad­
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              æquatè abſumat, vt ſi linea C, quinquies ſuper li­
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              neam A, replicata eam præcisè, & perfectè omninò
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              adæquaret: & eadem linea C, applicata lineæ B, & ſuper illam ter, v.g. re­
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              petita ipſam conſumeret, diceretur
                <expan abbr="vtranq;">vtranque</expan>
              metiri, & proinde duas lineas
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              A, & B, eſſe comm. definit poſtea
                <expan abbr="incommẽſ">incommenſ.</expan>
              hoc modo, incomm. autem, qua­
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              rum nullam contingit communem menſuram reperiri; vt ſi duarum linea­
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                <figure id="id.009.01.037.2.jpg" place="text" xlink:href="009/01/037/2.jpg" number="4"/>
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              rum, A, B, nunquam poſſet reperiri aliqua menſu­
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              ra, quæ
                <expan abbr="vtranq;">vtranque</expan>
              adæquatè metiretur, v. g. ſi linea
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              C, menſuraret A, quater ſumpta, ter autem ſumpta
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              non adæquaret omnino
                <expan abbr="lineã">lineam</expan>
              B, ſed deficeret, vel ex­
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              cederet aliquantulum,
                <expan abbr="atq;">atque</expan>
              hoc fieret in quauis alia
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              menſura, loco ipſius C, aſſumpta, ſiue maior, ſiue
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              minor ipſa C, vt
                <expan abbr="vtranq;">vtranque</expan>
              nunquam perfectè metiretur, eſſent duæ illæ lineæ
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              incommenſ. </s>
              <s id="s.000739">Extare porrò tales lineas, & ſuperficies, & corpora,
                <expan abbr="eaq́">eaque</expan>
              ; quam­
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              plurima, ac penè infinita ex 10. Elem. manifeſtum eſt. </s>
              <s id="s.000740">inuentum autem hu­
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              ius aſymmetriæ, quod Pythagoricis veteres attribuunt, mihi ſemper viſum
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              eſt omni maius admiratione, cum nulla experientia,
                <expan abbr="nullusq́">nullusque</expan>
              ; effectus in ip­
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              ſius cognitionem potuerit priſcos illos Geometras inducere. </s>
              <s id="s.000741">Quapropter
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              non immeritò diuinus ille Plato lib. 7. de legib. </s>
              <s id="s.000742">huius aſymmetriæ ignora­
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              tionem, adeo deteſtatus eſt, vt eam non hominum, ſed ſuum, pecorumque
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              ignorantiam cenſuerit. </s>
              <s id="s.000743">inter lineas incommenſ. ſunt diameter, & latus eiuſ­
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              dem quadrati, quia nulla poteſt reperiri menſura quantumuis exigua, vti
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                <figure id="id.009.01.037.3.jpg" place="text" xlink:href="009/01/037/3.jpg" number="5"/>
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              eſt lineola E, in præſenti quadrato, etiamſi illam in
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              infinitum ſubdiuidas, quæ
                <expan abbr="vtranq;">vtranque</expan>
              lineam, diame­
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              trum ſcilicet A C, & latus quoduis ex quatuor, v.g.
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              latus B C, præcisè omnino metiatur. </s>
              <s id="s.000744">theorema
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              iſtud demonſtratur in vltima 10. Elem. eodem me­
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              dio, quod ab Ariſtotele hic innuitur; Euclides ex
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              ſuppoſitione alterius partis contradictionis ipſius </s>
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