Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

Table of handwritten notes

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              <p>
                <s xml:id="echoid-s2149" xml:space="preserve">
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                reuera locus corpori adęquatus, cum corpus in interuallum ſuperſiciale non intret,
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                quam @is interuallum corporeum ingrediatur. </s>
                <s xml:id="echoid-s2150" xml:space="preserve">Et hoc modo
                  <reg norm="nullum" type="context">nullũ</reg>
                eſt corpus, quod
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                in m@ do aut extra mundum ( dicat autem Ariſtoteles quicquid voluerit ) locum
                  <lb/>
                ſuum non habeat.</s>
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            <div xml:id="echoid-div419" type="section" level="3" n="21">
              <head xml:id="echoid-head283" style="it" xml:space="preserve">V
                <unsure/>
              trum bene Aristoteles ſenſerit de infinito.</head>
              <head xml:id="echoid-head284" xml:space="preserve">CAP. XXI.</head>
              <p>
                <s xml:id="echoid-s2151" xml:space="preserve">TRactans Ariſtoteles in fine quinti cap. lib. 3. phyſicorum de infinito ait, impoſ­
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                ſibile cum ſit inuenire locum infinitum, & omne corpus in loco cum ſit, impoſ
                  <lb/>
                ſibile quoque eſſe in rerum natura aliquod: </s>
                <s xml:id="echoid-s2152" xml:space="preserve">infinitum corpus reperiri. </s>
                <s xml:id="echoid-s2153" xml:space="preserve">Omittamus
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                quòd cum Ariſtoteles debuerit beneficio loci deſtruere infinitum, ordine peruerſo
                  <lb/>
                de infinito prius, quàm de loco diſputationem inſtituat; </s>
                <s xml:id="echoid-s2154" xml:space="preserve">ſed dicamus ipſum intelli-
                  <lb/>
                gere de infinito corporeo, & cum probauerimus corporis locum eſſe corporeum in
                  <lb/>
                teruallum, non autem ſuperficiem, neque opus ſit in definitione interualli mentio
                  <lb/>
                nem aliquam facere terminorum, vnde ipſum infinitum eſſe poteſt, neque aliqua ra
                  <lb/>
                tione de hac re dubitari poteſt; </s>
                <s xml:id="echoid-s2155" xml:space="preserve">hoc modo nullum inconueniens ſequeretur, quòd
                  <lb/>
                extra cęlum reperiri poſſit corpus aliquod infinitum, quamuis, id ipſe nulla euiden-
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                ti ratione inductus perneget. </s>
                <s xml:id="echoid-s2156" xml:space="preserve">Senſit quoque, abſque eo,
                  <reg norm="quod" type="simple">ꝙ</reg>
                aliquam rationem propo
                  <lb/>
                nat, aliquid extra cœlum reperiri quemadmodum apparet ex fine cap .9. lib. primi
                  <lb/>
                de cœlo, cum etiam ait cap .8. lib. 8. phyſicorum, infinitas partes alicuius continui eſ-
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                ſe ſolum in potentia, non item in actu, hoc non eſt illico concedendum, quia ſi omne
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                totum continuum, & re ipſa exiſtens, in actu eſt, omnis quoque eius pars erit in actu,
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                quia ſtultum eſſet credere, ea quæ actu ſunt, ex ijs, quæ potentia exiſtunt, componi.
                  <lb/>
                </s>
                <s xml:id="echoid-s2157" xml:space="preserve">Neque etiam dicendum eſt continuationem earundem partium efficere, vt poten-
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                tia ſint ipſæ partes, & omni actu priuatæ; </s>
                <s xml:id="echoid-s2158" xml:space="preserve">Sit exempli gratia linea recta
                  <var>.a.u.</var>
                continua
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                quæ deinde diuidatur in puncto
                  <var>.e.</var>
                per æqualia, dubium non eſt, quin ante
                  <reg norm="diuiſionem" type="context">diuiſionẽ</reg>
                ,
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                medietas
                  <var>.a.e.</var>
                tam in actu (licet coniuncta cum alia
                  <var>.e.u.</var>
                ) reperiretur, quàm totum .2.
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                u. licet à ſenſu diſtincta non eſſet. </s>
                <s xml:id="echoid-s2159" xml:space="preserve">Idem affirmo de medietate
                  <var>.a.e.</var>
                ideſt de quarta
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                parte totius
                  <var>.a.u.</var>
                & pariter de octaua, de milleſima, & de quauis, ita vt eſſentia actua
                  <lb/>
                lis infiniti hoc modo tutò concedi poſſit,
                  <reg norm="cum" type="context">cũ</reg>
                ita ſit in natura. </s>
                <s xml:id="echoid-s2160" xml:space="preserve">Sed peius etiam ſenſit
                  <lb/>
                Ariſtoteles eodem loco capitis quinti lib. 3. phyſicorum, negando infinitum poſſe
                  <lb/>
                connumerari inter quantitates, dicens vnam aliquam quantitatem intelligi vt cubi
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                tum, tricubitum, & cætera; </s>
                <s xml:id="echoid-s2161" xml:space="preserve">vbi non conſiderat eadem etiam ratione intelligi poſſe
                  <lb/>
                aliquam quantitatem
                  <reg norm="infinitorum" type="context">infinitorũ</reg>
                cubitorum, & in quantitatis definitione nullam eſ-
                  <lb/>
                ſe neceſſitatem terminorum, vt exempli gratia in definitione numeri, non eſt neceſ
                  <lb/>
                ſitas alicuius determinati numeri, quia multitudo, non minus infinita, quàm finita,
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                intelligi poteſt. </s>
                <s xml:id="echoid-s2162" xml:space="preserve">Vbi poſteà cap .8. libr .4. phyſicorum ait nullam eſſe differentiam
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                inter infinitum, & vacuum, reuera nihil abſurdius hoc dicere fingereue poterat.</s>
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