Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.001059">
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              diſciplinis, idem tamen apud græcos
                <foreign lang="grc">μαθηματα</foreign>
              ſunt, ac apud latinos diſci­
                <lb/>
              plinæ; verbum autem
                <foreign lang="grc">μαθηματα</foreign>
              vſurpat hoc loco Ariſtoteles. </s>
              <s id="s.001060">Porrò non
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              eſt in mathematicis, ſicut in alijs paralogiſmus, quia in omni demonſtra­
                <lb/>
              tione maius extremum dicitur de omni medio, & rurſus medium dicitur de
                <lb/>
              omni minori extremo, ac ſi diceret mathematicæ demonſtrationes ſunt in
                <lb/>
              primo modo, qui barbarè à latinis recentioribus Barbara appellatur. </s>
              <s id="s.001061">Hæc
                <lb/>
              eſt autem pulcherrima mathematicarum commendatio, quippe præclarum
                <lb/>
              eſt à laudato laudari. </s>
              <s id="s.001062">In mathematicis, inquit, non accidit ſimiliter para­
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              logiſmus, ideſt, tam frequenter, quemadmodum in ſyllogiſmis dialecticis,
                <lb/>
              quia modus argumentandi mathematicarum eſt perfectiſſimus, quippe in
                <lb/>
              primo modo primæ figuræ.</s>
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              <s id="s.001063">
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              46</s>
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              <s id="s.001065">Eodem tex.
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              (Contingit autem quoſdam non ſyllogiſticè dicere, & quod ex vtriſ­
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              que conſequentia accipiunt, quemadmodum & Cæneus facit, quod ignis in multi­
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              plici proportione: etenim ignis celeriter gignitur, vt ait: & hæc est proportio. </s>
              <s id="s.001066">ſic
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              autem non eſt ſyllogiſmus, niſi celerrimam proportio ſequatur multiplex: & ignem
                <lb/>
              celerrima in motu proportio)
                <emph.end type="italics"/>
              verba illa (in multiplici proportione) græcè ſic
                <lb/>
              ſe habent,
                <foreign lang="grc">εν τῃ πολλαπλασιονι αναλογιᾳ,</foreign>
              quod melius redditur latinè in mul­
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              tiplici proportione, quemadmodum fecimus, quam in multiplicata, quem­
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              admodum in vulgata editione. </s>
              <s id="s.001067">porrò quid inter multiplicem, & multipli­
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              catam rationem interſit, optimè declarat noſter Clauius ad 4. definit. </s>
              <s id="s.001068">lib. 5.
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              Elem. ex quo etiam loco pauca decerpam, quæ huic loco declarando con­
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              ducunt. </s>
              <s id="s.001069">Proportio igitur multiplex eſt habitudo inter duas quantitates in­
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              æquales, quarum maior continet minorem, bis, vel ter, vel quater, &c. </s>
              <s id="s.001070">vn­
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              de proportio multiplex habet ſub ſe genera infinita, quando enim maior
                <lb/>
              continet minorem bis, dicitur Dupla: quando ter, Tripla: quando quater,
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              Quadrupla: & ſic in infinitum: v. g. 2. ad 1. eſt proportio dupla; 3. ad 1. tri­
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              pla; 4. ad 1. quadrupla, &c. </s>
              <s id="s.001071">omnes tamen continentur ſub genere multipli­
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              cis rationis. </s>
              <s id="s.001072">porrò ſi quępiam proportio ex genere multiplici progrediatur
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              per plures terminos, v. g. proportio quadrupla progrediatur hoc modo,
                <lb/>
              1. 4. 16. 64. 256. &c. </s>
              <s id="s.001073">fit, vt ſubſequentes termini mirum in modum augean­
                <lb/>
              tur. </s>
              <s id="s.001074">hic vides primum ipſam quadruplam rationem in diſpoſitis terminis
                <lb/>
              progredi, quia quilibet ſequens terminus ad præcedentem eſt quadruplus.
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              </s>
              <s id="s.001075">cernis etiam in paucis terminis, quinque ſcilicet magnum factum eſſe incre­
                <lb/>
              mentum, cum
                <expan abbr="vſq;">vſque</expan>
              ad 256. excreuerint. </s>
              <s id="s.001076">Cæneus igitur dicens ignem augeri
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              ſecundum multiplicem rationem, vnam ex prædictis intelligebat aliquam,
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              quia quælibet illarum magnopere creſcit, ſi propagetur, vt ad 10. quinti
                <lb/>
              definit. </s>
              <s id="s.001077">traditur: & vt paulo ante exemplo licuit perſpicere. </s>
              <s id="s.001078">argumentaba­
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              tur igitur Cæneus in hunc modum; quod in multiplici ratione augetur, ce­
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              lerrimè augetur: ignis celerrimè augetur, ergo ignis in multiplici ratione
                <lb/>
              augetur, quæ argumentatio vitioſa eſt, ex duabus quippe affirmatiuis in ſe­
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              cunda figura procedens, vt colligitur ex verbis illis tex.
                <emph type="italics"/>
              (Ex viriſque conſe­
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              quentia accipiunt
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              ) ex his mathematica huius locis patere ſatis poſſunt.</s>
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              47</s>
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              <s id="s.001081">Ibidem (
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              Conuertuntur autem magis, quæſunt in mathematicis, quoniam nul­
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              lum accidens accipiunt (in quo quidem ijs præſtăt, quæ diſputationibus traduntur)
                <lb/>
              ſed definitiones
                <emph.end type="italics"/>
              ) Hæc eſt altera mathematicarum laus, vnde earum quoque
                <lb/>
              præſtantia elucet, quia ſcilicet mathematicæ pro medijs vtuntur </s>
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          </chap>
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