Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.000840">
                <pb pagenum="44" xlink:href="009/01/044.jpg"/>
              autem terminum mathematicum colligitur manifeſtè ex Proelo, qui lib. 3.
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              in comm. Elem. Euclidis ad primam propoſitionem primi Elementi, pag.
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              </s>
              <s id="s.000841">121. ſic ait, Abductio verò eſt tranſitus à propoſito problemate, vel theo­
                <lb/>
              remate ad aliud, quo cognito, aut comparato Propoſitum quoque perſpi­
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              cuum eſt. </s>
              <s id="s.000842">Exempli cauſa, cum cubi duplicatio propoſita eſſet ad inueſti­
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              gandam quæſtionem in aliud tranſtulere, quod illud propoſitum conſequi­
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              tur, ad duarum nempe mediarum linearum inuentionem tranſlata eſt quæ­
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              ſtio, & ſic quærebant deinceps, quonam modo datis duabus rectis lineis,
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              duæ mediæ proportionales reperirentur. </s>
              <s id="s.000843">Primum autem dicunt Hippocra­
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              tem Chium prędictorum titulorum, Abductionem feciſſe, qui & lunulæ qua­
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              dratum fecit æquale, & alia multa in Geometria inuenit. </s>
              <s id="s.000844">hæc Proclus. </s>
              <s id="s.000845">vbi
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              non diſſimulandum nos reſtituiſſe verbum, Abductionem, cuius loco inter­
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              pres Procli vtitur inductionis voce, ſequuti & rationem, & græcum textum,
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              qui noſtram hanc expoſitionem euidenter poſtulat,
                <foreign lang="grc">απαγωγὴ</foreign>
              enim valet &
                <lb/>
              inductionem, & abductionem, ſed abductio omnino rei propoſitæ quadrat.</s>
            </p>
            <p type="main">
              <s id="s.000846">Notandum præterea Hippocratem Chium fuiſſe auctorem huius Abdu­
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              ctionis,
                <expan abbr="eumq́">eumque</expan>
              ; feciſſe Abductionem à propoſito Problemate quadrandi cir­
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              culi, vnde manifeſtè apparet, Ariſtotelem ex Mathematicis hunc terminum
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              mutuò accepiſſe, quandoquidem ex ijſdem accepit etiam exemplum Abdu­
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              ctionis Mathematicæ, imò etiam exemplum ipſius authoris Abductionis
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              Mathematicæ. </s>
              <s id="s.000847">ſyllogiſmus autem Hippocratis, quo oſtendebat circuli qua­
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              draturam reducebatur ad has propoſitiones, omnis rectilinea figura qua­
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              dratur, ſed circulus reducitur ad figuram rectilineam, ergo circulus qua­
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              dratur. </s>
              <s id="s.000848">in probatione minoris facta eſt Abductio, cum enim ipſe vellet re­
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              ctificare circumferentiam circuli per lunulas, nec valeret, alij per lineam,
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              quandam quadratricem, vt eſt apud Pappum
                <expan abbr="Alexandrinũ">Alexandrinum</expan>
              , & apud P. Cla­
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              uium in fine ſexti Elem. & alij aliter fruſtra conarentur, facta eſt Abductio
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              circa probationem minoris, in qua adhuc Mathematici verſantur; quæ pro­
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              batio, ſi tandem inueniri poſſet, mox ſequeretur principale
                <expan abbr="propoſitũ">propoſitum</expan>
              pro­
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              blema, nimirum circulus quadraretur; vide quæ ſcripſimus in cap. 3. Præ­
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              dicam. de hac re, quia plurimum hunc conferunt. </s>
              <s id="s.000849">ſed iam ad textus expli­
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              cationem veniamus.</s>
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            <p type="main">
              <s id="s.000850">
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              </s>
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            <p type="margin">
              <s id="s.000851">
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              17</s>
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            <p type="main">
              <s id="s.000852">Ex eodem cap.
                <emph type="italics"/>
              (Veluti ſi K, eſſet quadrari, in quo autem E, rectilineum, in
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              quo verò F, circulus, ſi ipſius E F, vnum ſolum eſſet medium, hoc, quod eſt, cum
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              lunulis æqualem fieri circulum rectilineo, eſſe poſſet propè ipſum cognoſcere, cum
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              vero B C, neque credibilius ſit, quam A C,
                <expan abbr="neq;">neque</expan>
              pauca media, non dico Abductio­
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              nem:
                <expan abbr="neq;">neque</expan>
              quando B C, ſit immediatum, tale enim ſcientia est)
                <emph.end type="italics"/>
              Aduerte figuram
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              vulgatæ editionis eſſe mendoſam, & propterea reſtituendam eſſe, qualis pri­
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              ma ſequens ex Simplicio ad tex. 11. primi Phyſic. hoc modo Hippocrates
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              Chius conabatur circulum ad quadrum redigere; fit circulus A B G C, qua­
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              drandus; conſtituatur
                <expan abbr="itaq;">itaque</expan>
              ſuper diametro eius B C, quadratum B C D F,
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              cuius diameter B D, ſecatur bifariam in G, à circumferentia circuli dati,
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              quod patet ducta ſemidiametro H G, perpendiculari ex B C, quæ ſuo extre­
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              mo puncto G, ſecat bifariam, &
                <expan abbr="diametrũ">diametrum</expan>
              B D, & circumferentiam B G C.
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              facto ergo centro G, deſcribatur alter circulus per puncta B C D F,
                <expan abbr="conne-ctaturq́">conne­
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                ctaturque</expan>
              ; recta G C. in triangulo orthogonio B C D, latus B D, ſubtenditur </s>
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