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Version vom 2009-02-14
author Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date Thu, 02 May 2013 11:08:12 +0200
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1 <?xml version="1.0"?>
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2 <archimedes xmlns:xlink="http://www.w3.org/1999/xlink" >
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3 <info>
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4 <author>Galilei, Galilei</author>
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5 <title>De Motu Antiquiora</title>
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6 <date>1890</date>
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7 <place>Florence</place>
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8 <translator></translator>
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9 <lang>la</lang>
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10 <comments>From Archiv97</comments>
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11 <locator>083.xml</locator>
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12 </info>
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13 <text>
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14 <front></front>
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15 <body>
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16 <chap><subchap1><subchap2><p><s><pb ed="Favaro" n="251"></pb> <pb ed="manuscript" n="61r"></pb> Lationem omnem naturalem, sive deorsum sive sursum illa sit, a, propria mobilis gravitate vel levitate fieri, inferius explicaturi, rationi consentaneum duximus, ut quomodo quid alio levius vel gravius vel aeque grave dicendum sit, in medium afferremus.
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17 </s><s id="id.1.1.1.01.02">Est autem hoc determinare necessarium: saepius enim accidit ut, quae leviora sunt, graviora nuncupentur, et e converso.
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18 </s><s id="id.1.1.1.01.03">Dicimus enim interdum, magnum lignum parvo plumbo gravius esse, cum tamen plumbum ligno, simpliciter, gravius existat; et magnum plumbi frustrum pauco plumbo gravius dicimus, cum tamen plumbum plumbo gravius non sit. {1}
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19 </s><s id="id.1.1.1.01.04"><lb ed="Favaro" n="10"></lb> Quapropter, ut huiusmodi captiones aufugiamus, ea dicenda erunt inter se aeque gravia, quae, cum fuerint aequalia in mole, erunt etiam aequalia in gravitate: unde si accipiamus duo plumbi frustra, quae aequalia sint in mole, in gravitate quoque congruentia, ista vere dicenda erunt aeque ponderare.
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20 </s><s id="id.1.1.1.01.05">Unde manifestum est, quod lignum non est dicendum aeque grave ac plumbum: frustrum enim ligni, quod cum plumbi frustro aequeponderet, longe plumbeum frustrum in mole excedet.
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21 </s><s id="id.1.1.1.01.06">Deinde, illud alio gravius est nuncupandum, cuius accepta moles, alterius moli aequalis, gravior altera comperiatur: ut, verbigratia, si ex plumbo et ligno moles duas accipiamus quae inter se aequales <lb ed="Favaro" n="20"></lb> sint, moles deinde plumbi gravior sit mole ipsius ligni, tunc certe plumbum gravius esse ligno, merito asseremus.
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22 </s><s id="id.1.1.1.01.07">Quare, si ligni frustrum, quod cum frustro plumbi aequeponderet, inveniamus, non certe lignum aeque grave ac plumbum est censendum; inveniemus enim, <pb ed="Favaro" n="252"></pb> plumbi molem longe a ligni mole excedi.
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23 </s><s id="id.1.1.1.01.08">Converso demum modo de levioribus est statuendum:<pb ed="manuscript" n="61v"></pb> illud nanque levius est censendum, cuius pars accepta, alterius parti in mole aequalis, in gravitate minor esse invenietur; ut, si partes duas, alteram quidem ligni, alteram vero plumbi, accipiamus, quae in mole aequales sint, minus autem gravet lignea quam plumbea, tunc merito lignum plumbo levius esse, est statuendum.
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24 </s></p></subchap2><subchap2><p><s id="id.1.1.2.01.01">Cum ea quae naturaliter moventur, ad propria loca moveantur, et cum quae moventur aut gravia sint aut levia, videndum est, <lb ed="Favaro" n="10"></lb> quaenam gravium loca, quae vero levium, existant, et cur.
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25 </s><s id="id.1.1.2.01.02">Gravium itaque loca esse illa quae mundi centro magis accedunt, levium vero quae magis distant, sensu quidem quotidie intuemur; quare talia determinata loca illis a natura praescripta esse, non est quod dubitemus: sed in dubio quidem revocari potest, cur talem ordinem in distribuendis locis prudens natura servaverit, non autem praeposterum.
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26 </s><s id="id.1.1.2.01.03">Huius distributionis non alia, quod legerim, a philosophis affertur causa, nisi quod in aliquem ordinem erant cuncta disponenda, placuit autem Summae Providentiae in hunc distribuere; et hanc quoque causam videtur afferre Aristoteles, 8 Phys. t. 32, dum, quaerens cur gravia et <lb ed="Favaro" n="20"></lb> levia ad propria loca moveantur, subdit, causam esse quia habent a natura ut sint apta ferri aliquo, et hoc leve quidem sursum, grave autem deorsum. {1}
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27 </s><s id="id.1.1.2.01.04">Attamen, si rem accuratius spectemus, non erit profecto existimandum, nullam in tali distributione necessitatem aut utilitatem habuisse naturam, sed solum ad libitum <pb ed="manuscript" n="62r"></pb> et casu quodammodo operatam esse.
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28 </s><s id="id.1.1.2.01.05">Hoc cum de provida natura nullo pacto existimari posse perpenderem, interdum anxius fui in excogitanda, nisi necessaria, saltem congruente ac utili, aliqua causa: ac profecto, non nisi optimo iure summaque prudentia hunc elegisse ordinem naturam, comperi.
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29 </s><s id="id.1.1.2.01.06">Cum enim, ut antiquioribus philosophis placuit, una omnium corporum <lb ed="Favaro" n="30"></lb> sit materia, et illa quidem graviora sint quae in angustiori spatio plures illius materiae particulas includerent, ut iidem philosophi, inmerito <pb ed="Favaro" n="253"></pb> fortasse ab Aristotele 4 Caeli confutati, asserebant; rationi profecto consentaneum fuit, ut quae in angustiori loco plus materiae concluderent, angustiora etiam loca, qualia sunt quae centro magis accedunt, occuparent.
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30 </s><s id="id.1.1.2.01.07">Ut si, exempli gratia, intelligamus, naturam in prima mundi compagine totam elementorum communem materiam in quatuor aequas partes divisisse, deinde ipsius terrae formae suam materiam tribuisse, itidem et formae aëris suam, terrae autem formam materiam suam in angustissimo loco constipasse, aëris autem formam in amplissimo loco materiam suam reposuisse, nonne congruum erat ut natura aëri <lb ed="Favaro" n="10"></lb> magnum spatium assignaret, terrae autem minus?
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31 </s><s id="id.1.1.2.01.08">At angustiora sunt loca in sphera quo magis ad centrum accedimus, ampliora vero quo magis ab eodem recedimus: prudenter, igitur, simul et aeque terrae statuit natura locum esse qui caeteris est angustior, nempe prope centrum; reliquis deinde elementis loca eo ampliora, <pb ed="manuscript" n="62v"></pb> quo ipsorum materia rarior esset.
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32 </s><s id="id.1.1.2.01.09">Nec tamen dixerim, aquae materiam tantam esse quanta est ipsius terrae, et, ob id, aquam, cum sit terra rarior, maiora loca occupare; sed solum quod, si accipiamus partem aquae quae aequeponderet cum terrae parte, et, ob id, tanta sit aquae materia quanta est terrae, tunc profecto terra illa minorem occupabit locum quam aqua: quare merito in <lb ed="Favaro" n="20"></lb> angustiori spatio erit reponenda, nempe centro propius. {1}
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33 </s><s id="id.1.1.2.01.10">Itaque, simili modo in reliquis elementis discurrendo, congruentiam quamdam, ne dicam necessitatem, talis dispositionis gravium et levium inveniemus.
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34 </s></p></subchap2><subchap2><p><s id="id.1.1.3.01.01">Cum in superiori capite determinaverimus, et tanquam notissimum supposuerimus, ita a natura constitutum esse, ut, nempe, graviora sub levioribus maneant, nunc quomodo, quae deorsum feruntur, a gravitate moveantur, quae vero sursum, a levitate, est videndum.
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35 </s><s id="id.1.1.3.01.02">Cum enim gravia a gravitate habeant ut sub levioribus maneant (quatenus enim gravia sunt, sub levioribus a natura posita fuerunt), {2} ab eadem <lb ed="Favaro" n="30"></lb> habebunt ut, supra leviora posita, sub leviora ferantur, ne, contra naturae distributionem, leviora sub gravioribus maneant.
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36 </s><s id="id.1.1.3.01.03">Et sic a <pb ed="Favaro" n="254"></pb> levitate levia sursum ferentur, cum fuerint sub gravioribus: si enim a levitate habent ut super graviora maneant, ab eadem levitate habebunt ut sub gravioribus non maneant, nisi impediantur.
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37 </s><s id="id.1.1.3.01.04">Ex hoc autem patet, quomodo in motu non sit solum habenda ratio de mobilis levitate vel gravitate, sed de gravi<pb ed="manuscript" n="63r"></pb>tate etiam et levitate medii, per quod fit motus: nisi enim aqua levior esset lapide, tunc lapis in aqua non descenderet.
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38 </s><s id="id.1.1.3.01.05">Sed quia hic posset difficultas oriri, cur lapis in mare proiectus deorsum naturaliter feratur, cum tamen aqua maris longe gravior sit proiecto lapide, in memoriam revocandum est quod cap. .... adnotavimus: nempe, lapidem quidem aqua maris graviorem <lb ed="Favaro" n="10"></lb> esse, si tantam aquae molem accipiamus quanta est moles lapidis; et ita lapis, quatenus aqua gravior, deorsum in aqua feretur.
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39 </s><s id="id.1.1.3.01.06">At rursus difficultas insurget, cur lapidi cum tanta mole aquae quanta est propria moles, non autem cum toto mari, ratio sit habenda.
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40 </s><s id="id.1.1.3.01.07">Quam quidem difficultatem ut de medio tollamus, demonstrationes nonnullas adferre statui: ex quibus non solum haec solutio, verum etiam totum negocium, pendet.
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41 </s><s id="id.1.1.3.01.08">Cum vero media, per quae motus contingunt, sint plura, ut ignis, aër, aqua, etc., et in omnibus eadem ratio sit habenda, supponemus medium, in quo fieri debet motus, esse aquam: et, primo quidem, demonstrabimus, ea corpora quae aeque gravia sunt ac ipsa <lb ed="Favaro" n="20"></lb> aqua, in aquam demissa, demergi quidem tota, non tamen adhuc magis deorsum quam sursum ferri; 2Á, ostendemus, quae leviora sunt aqua, in aquam nedum descendere, verum etiam nec tota demergi posse; 3Á, demonstrabimus, quae sunt aqua graviora, deorsum necessario ferri.
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42 </s></p></subchap2><subchap2><p><figure id="id.1.1.4.01.00" xlink:href="FIG1/F001.jpg"></figure>
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43 <s id="id.1.1.4.01.01"><pb ed="manuscript" n="63v"></pb>Ad demonstrationes itaque accedentes, primum quidem intelligatur magnitudo aliqua aeque gravia ac aqua, hoc est cuius gravitas aequalis sit gravitati aquae cuius moles aequetur moli dictae <lb ed="Favaro" n="30"></lb> magnitudinis; sitque talis magnitudo ef: ostendendum itaque est, magnitudinem ef in aquam demissam demergi totam, non tamen magis sursum quam deorsum ferri.
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44 </s><s id="id.1.1.4.01.02">Et sit aquae status, ante quam magnitudo <pb ed="Favaro" n="255"></pb> in ipsam demittatur, abcd; et magnitudo ef, in aquam demissa, si fieri potest, non demergatur tota, sed aliqua pars extet, nempe e; demergatur autem solummodo pars f.
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45 </s><s id="id.1.1.4.01.03">Necessarium itaque est, ut, dum magnitudo f demergitur, aqua attollatur: attollatur itaque superficies aquae ao usque ad superficiem st.
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46 </s><s id="id.1.1.4.01.04">Manifestum igitur est, tantam esse molem aquae so, quanta est moles partis magnitudinis demersae, nempe f: necessarium enim est ut locus, in quem intrat magnitudo, evacuetur aqua, et tanta moles aquae removeatur quanta <lb ed="Favaro" n="10"></lb> est moles magnitudinis quae demergitur.
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47 </s><s id="id.1.1.4.01.05">Est itaque moles aquae so aequalis moli magnitudinis demersae, nempe ipsi f; quare et gravitas etiam ipsius f aequabitur gravitati aquae so.
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48 </s><s id="id.1.1.4.01.06">Et quia aqua so nititur sua gravitate deorsum redire ad pristinum suum statum, sed hoc assequi non potest nisi prius solidum ef ex aqua auferatur et ab aqua attollatur; solidum autem, ne attollatur, tota propria gravitate resistit; ponuntur autem tum solida magnitudo tum aqua in hoc statu consistentes; ergo necessarium est ut gravitas aquae so, qua sursum nititur solidum attollere, sit aequalis gravitati qua solidum resistit et <lb ed="Favaro" n="20"></lb> deorsum premit (si enim maior esset gravi<pb ed="manuscript" n="64r"></pb>tas aquae so gravitate solidi ef, attolleretur quidem ef atque expelleretur ab aqua; si vero maior esset gravitas solidi ef, attolleretur rursus aqua: quae tamen omnia ita consistentia ponuntur).
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49 </s><s id="id.1.1.4.01.07">Gravitas igitur aquae so aequatur gravitati totius ef: quod quidem est inconveniens; nam gravitas ipsius so aequatur gravitati partis f.
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50 </s><s id="id.1.1.4.01.08">Manifestum est igitur quod solidae magnitudinis ef nulla pars extabit, sed tota demergetur.
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51 </s></p><p><s id="id.1.1.4.02.01">Haec tota est demonstratio, quam quidem ita longioribus verbis explicavi, ut qui primum in ipsam inciderint, facilius intelligere possint; sed poterat etiam breviori sermone melius explicari, ita ut totum robur <lb ed="Favaro" n="30"></lb> demonstrationis tale sit.
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52 </s><s id="id.1.1.4.02.02">Demonstrandum est, magnitudinem ef, quae aeque gravis ponitur ac aqua, totam demergi.
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53 </s><s id="id.1.1.4.02.03">Nam, si non demergitur tota, aliqua illius pars extet: extet autem e; et aqua attollatur usque ad superficiem st; et, si fieri potest, in hoc statu maneant tum aqua tum magnitudo.
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54 </s><s id="id.1.1.4.02.04">Quia igitur magnitudo ef gravitate sua premit et attollit aquam so; aqua autem so, ne attollatur amplius, gravitate sua resistit; necessarium est ut tanta sit gravitas ef prementis, <pb ed="Favaro" n="256"></pb> quanta est gravitas aquae so resistentis: cum enim ita ponantur manere, non erit maior pressio quam resistentia, nec e converso.
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55 </s><s id="id.1.1.4.02.05">Gravitas igitur aquae so aequatur gravitati magnitudinis ef: quod quidem est inconveniens; cum enim moles totius ef maior sit mole ipsius so aquae, erit etiam gravitas ef magnitudinis maior gravitate aquae so.
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56 </s><s id="id.1.1.4.02.06">Manifestum igitur est, magnitudines aeque graves ac aqua totas in aquam demergi: dico insuper, non magis sursum quam deorsum ferri, sed, quocunque ponantur, ibi manere.
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57 </s><s id="id.1.1.4.02.07">Nulla enim est causa cur descendere debeant <pb ed="manuscript" n="64v"></pb>aut ascendere: cum enim aeque graves ponantur ac aqua, dicere illas in aquam descendere esset idem ac si diceremus, aquam in <lb ed="Favaro" n="10"></lb> aqua sub aquam descendere, et rursus aquam, quae super primam ascendit, deorsum iterum descendere, et sic aquam in infinitum procedere in alternatim descendendo et ascendendo; quod inconveniens est.
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58 </s></p></subchap2><subchap2><p><s id="id.1.1.5.01.01">Cum igitur in superiori capite ea demonstrata sint quae ad quietem spectant, nunc videnda sunt quae ad motum sursum faciunt.
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59 </s><s id="id.1.1.5.01.02">Dico itaque, magnitudines aqua leviores, in aquam demissas, non demergi totas, sed aliquam partem extare.
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60 </s></p><p><figure id="id.1.1.5.02.00" xlink:href="FIG1/F002.jpg"></figure>
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61 <s id="id.1.1.5.02.01">Sit <lb ed="Favaro" n="20"></lb> itaque primus aquae status, antequam magnitudo demittatur, secundum superficiem ef; magnitudo autem a, levior aqua, in aquam demissa, si fieri potest, demergatur tota, et aqua attollatur usque ad superficiem cd; et, si est possibile, maneant in hoc statu tum aqua tum magnitudo.
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62 </s><s id="id.1.1.5.02.02">Erit iam gravitas, qua magnitudo premit et attollit aquam cf, aequalis gravitati qua cf aqua premit ut magnitudinem a attollat.
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63 </s><s id="id.1.1.5.02.03">Sed etiam moles aquae cf aequatur moli magnitudinis a.
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64 </s><s id="id.1.1.5.02.04">Sunt igitur duae magnitudines, una in qua a, altera aqua cf; et gravitas ipsius a aequatur <lb ed="Favaro" n="30"></lb> gravitati ipsius cf, et moles etiam a est aequalis moli ipsius aquae cf: ergo magnitudo a est aeque gravis ac aqua: quod quidem est absurdum; nam posita est magnitudo levior quam aqua.
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65 </s><s id="id.1.1.5.02.05"><pb ed="manuscript" n="65r"></pb>Non igitur magnitudo a manebit demersa tota sub aqua; ergo necessario sursum feretur.
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66 </s></p><p><s id="id.1.1.5.03.01"><pb ed="Favaro" n="257"></pb> Patet igitur cur et quomodo motus sursum proveniat ex levitate: et, ex his quae in hoc et superiori capite tradita sunt, potest facile colligi, quod ex quae sunt aqua graviora demerguntur tota et deorsum necessario feruntur.
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67 </s><s id="id.1.1.5.03.02">Demergi quidem tota necessarium est: nisi enim tota demergerentur, essent iam, contra suppositum, leviora aqua; leviora enim esse aqua quae non tota demerguntur, ex converso mox allatae demonstrationis constat.
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68 </s><s id="id.1.1.5.03.03">Eadem vero deorsum ferri oportet.
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69 </s><s id="id.1.1.5.03.04">Nisi enim deorsum ferrentur, aut quiescerent, aut sursum moverentur: non autem quiescerent; quiescere, enim, nec magis <lb ed="Favaro" n="10"></lb> sursum quam deorsum ferri, in praecedenti, ea quae aeque gravia sunt ac aqua, demonstratum est: sursum vero ferri quae aqua sunt leviora, mox apparuit.
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70 </s><s id="id.1.1.5.03.05">Ex his igitur omnibus satis percipi potest, eo quod necessarium sit ea quae deorsum moventur esse graviora medio per quod feruntur, quomodo gravia a gravitate deorsum moveantur; et quomodo lapidi in mare proiecto non cum tota maris aqua ratio sit habenda, sed tantum cum illa particula quae a loco, in quem intrat lapis, est dimovenda.
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71 </s><s id="id.1.1.5.03.06">Sed, quia haec omnia quae in superioribus his duobus capitibus tradita sunt, minus adhuc mathematice, et magis physice, declarari possunt, reducendo ea ad lancis considerationem, <lb ed="Favaro" n="20"></lb> placuit in sequenti capite convenientiam explicare, quam mobilia haec naturalia cum bilan<pb ed="manuscript" n="65v"></pb>cis ponderibus servant: et hoc ad uberiorem eorum quae tradentur cognitionem, et ad exactiorem legentium cognitionem.
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72 </s></p></subchap2><subchap2><p><s id="id.1.1.6.01.01">Quae igitur in lance contingunt prius examinabimus, ut omnia deinde in naturalibus mobilibus contingere ostendamus.
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73 </s></p><p><figure id="id.1.1.6.02.00" xlink:href="FIG1/F003.jpg"></figure>
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74 <s id="id.1.1.6.02.01">Intelligatur itaque bilanx ab linea, cuius centrum, super quod fiat motus, sit c, lineam ab bifariam dispescens; <lb ed="Favaro" n="30"></lb> sint autem duo pondera suspensa ex punctis a, b, quae sint e, o.
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75 </s><s id="id.1.1.6.02.02">In pondere itaque e tria possunt contingere: aut quiescere, aut moveri sursum, aut moveri deorsum.
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76 </s><s id="id.1.1.6.02.03">Si igitur pondus e gravius <pb ed="Favaro" n="258"></pb> fuerit pondere o, tunc e deorsum feretur: quod si e fuerit minus grave, sursum profecto movebitur; et hoc, non quia non habeat gravitatem, sed quia maior est gravitas o.
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77 </s><s id="id.1.1.6.02.04">Ex quo patet quod in lance tam motus sursum quam motus deorsum proveniunt ex gravitate, sed diverso modo: nam motus sursum continget ipsi e propter gravitatem ipsius o, motus vero deorsum propter gravitatem suam.
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78 </s><s id="id.1.1.6.02.05">Quod si gravitas ponderis e aequabitur gravitati ipsius o, tunc e non movebitur quidem sursum neque deorsum: deorsum enim non movebitur e, nisi pondus quod attollere debet, nempe o, sit minus grave; nec sursum feretur idem e, nisi pondus o, a quo trahi debet, sit gravius. <lb ed="Favaro" n="10"></lb>
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79 </s></p><p><s id="id.1.1.6.03.01"><pb ed="manuscript" n="66r"></pb>His in lance inspectis, ad naturalia mobilia revertentes, universaliter hoc proponere possumus: nempe, gravius non posse attolli a minus gravi.
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80 </s><s id="id.1.1.6.03.02">Quo supposito, facile est intellectu, cur solida quae leviora sunt ac aqua non demergantur tota.
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81 </s><s id="id.1.1.6.03.03">Nam si, verbigratia, in aquam demittamus trabem, tunc, si trabes demergenda est, necessarium est ut aqua exeat ex loco in quam intrat trabes, et sursum attollatur, hoc est dimoveatur a centro mundi.
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82 </s><s id="id.1.1.6.03.04">Si igitur aqua, quae attollenda est, gravior erit ipsa trabe, tunc profecto non poterit a trabe attolli: sed si trabes demergitur tota, tunc necesse est ut ex loco, in quem intrat trabes, removeatur tanta aqua quanta <lb ed="Favaro" n="20"></lb> est moles ipsiusmet trabis: sed tanta aqua in mole, quanta est moles trabis, gravior est ipsa trabe (ponitur enim trabes aqua levior): non ergo possibile erit, trabem demergi totam.
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83 </s><s id="id.1.1.6.03.05">Hoc autem ei correspondet quod in lance dictum est, nempe minus pondus non posse maius attollere.
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84 </s><s id="id.1.1.6.03.06">Quod si trabes aeque gravis esset ac aqua, hoc est si aqua, quae a trabe demergenda attollitur, non fuerit gravior sed aeque gravis ac trabes, trabes tunc profecto tota demergetur, cum resistentiam aquae attollendae non habeat; non tamen adhuc, tota sub aqua existens, magis sursum quam deorsum feretur: et hoc proportione respondet ei quod in lance dictum est de ponderibus aequalibus, <lb ed="Favaro" n="30"></lb> quorum alterum nec sursum nec deorsum fertur.
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85 </s><s id="id.1.1.6.03.07"><pb ed="manuscript" n="66v"></pb>Quod si, rursus, trabes gravior fuerit aqua illa quae a trabe est attollenda, hoc est si trabes gravior fuerit tanta aqua, quanta est sua moles propria (attollitur enim a trabe demersa, ut saepius dictum est, tanta moles aquae quanta est suamet moles), tunc trabes certe deorsum feretur: quod quidem proportione respondet ei quod in lance dictum est, <pb ed="Favaro" n="259"></pb> nempe tunc pondus unum deorsum ferri et alterum attollere, quando eo fuerit gravius.
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86 </s><s id="id.1.1.6.03.08">Insuper, in mobilibus etiam naturalibus, sicut et in ponderibus lancis, potest motuum omnium, tam sursum quam deorsum, causa reduci ad solam gravitatem.
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87 </s><s id="id.1.1.6.03.09">Quando enim quid fertur sursum, tunc attollitur a gravitate medii; ut, si trabes aqua levior vi sub aqua comprimeretur, tunc, quia trabes demersa tantam aquae molem extulit quanta est suamet moles, tanta autem moles aquae quanta est moles trabis gravior est ipsa trabe, tunc, dubio procul, a gravitate illius aquae attolletur trabes, et sursum impelletur: et sic <lb ed="Favaro" n="10"></lb> motus sursum fiet a gravitate medii et levitate mobilis; motus vero deorsum, a gravitate mobilis et levitate medii. {1}
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88 </s><s id="id.1.1.6.03.10">Et ex his, contra Aristotelem p.Á Caeli 89, facile quispiam colligere poterit, quomodo quae moventur, moveantur, quodammodo, vi et per extrusionem medii: nam aqua trabem, vi demersum, extrudit violenter, cum, descendendo, ad propriam redit regionem, nec pati vult ut, quod se levius est, sub se maneat; et, pari pacto, lapis extruditur ac deorsum impellitur quia gravior est medio.
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89 </s><s id="id.1.1.6.03.11">Patet igitur, talem motum posse dici violentum; quamvis communiter lignum in aqua sursum, et lapidem deorsum, naturaliter ferri, dicantur.
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90 </s><s id="id.1.1.6.03.12">Nec valet Aristotelis argumentum, dum dicit, <lb ed="Favaro" n="20"></lb> Si esset violentus in fine remitteretur, non autem, ut facit, augeretur: nam motus violentus tunc remittitur quando mobile extra manum moventis fuerit, non autem dum motori est coniunctum.
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91 </s></p><p><s id="id.1.1.6.04.01">Patet igitur, quomodo naturalium mobilium motus ad ponderum in lance motum congrue reducatur: ita ut, nempe, mobile naturale unius ponderis in lance vicem gerat; tanta autem moles medii, quanta est mobilis moles, alterum in lance pondus repraesentet.
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92 </s><s id="id.1.1.6.04.02">Ita ut si tanta moles medii, quanta est mobilis moles, gravior erit mobili,<pb ed="manuscript" n="85r"></pb> mobile autem levius, tunc mobile, tanquam levius pondus, sursum feretur: quod si mobile eadem medii mole gravius erit, tunc, tanquam gravius <lb ed="Favaro" n="30"></lb> pondus, descendet: et si, demum, moles dicta medii aequabitur etiam in gravitate ipsi mobili, mobile nec sursum nec deorsum feretur; sicut in lance aequalia pondera, ad invicem, nec deprimuntur nec attolluntur.
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93 </s><s id="id.1.1.6.04.03">Et quia valde commode naturalia mobilia ad lancis <pb ed="Favaro" n="260"></pb> pondera comparantur, in sequentibus congruentiam hanc in omnibus, quae de naturali motu dicentur, ostendemus: quae profecto non modice ad intelligentiam conferet. {1}
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94 </s></p></subchap2><subchap2><p><s id="id.1.1.7.01.01"><pb ed="manuscript" n="67r"></pb>Cum in superioribus satis abunde explicatum sit, quomodo motus naturales proveniant a gravitate et levitate, nunc videndum est unde accidat maior aut minor ipsius motus celeritas.
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95 </s><s id="id.1.1.7.01.02">Quod quidem ut facilius assequi possimus, distinguendum hoc est: quod, scilicet, dupliciter accidit inaequalitas inter motus tarditates et celeritates: vel <lb ed="Favaro" n="10"></lb> enim est idem mobile in diversis mediis motum; vel idem est medium, diversa vero mobilia.
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96 </s><s id="id.1.1.7.01.03">In utroque motu ex: eadem causa pendere tarditatem et celeritatem, nempe ex maiori vel minori gravitate mediorum et mobilium, mox demonstrabimus; {2} ubi primum causam quae, talis effectus, tradita est ab Aristotele, insufficientem esse, ostenderimus.
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97 </s></p><p><s id="id.1.1.7.02.01">Aristoteles igitur, 4 Phys. t. 71, scripsit, idem mobile citius moveri in medio subtiliori quam in crassiori, et, ideo, tarditatis motus causam esse crassitiem medii, velocitatis autem subtilitas; et hoc non alia ratione confirmavit nisi ab experientia, quia, nempe, videmus mobile aliquod velocius moveri in aëre quam in aqua.
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98 </s><s id="id.1.1.7.02.02">Verum hanc <lb ed="Favaro" n="20"></lb> causam non sufficientem esse, proclive erit demonstrare.
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99 </s><s id="id.1.1.7.02.03">Si enim motus velocitas ex subtilitate medii provenit, idem mobile semper citius <pb ed="Favaro" n="261"></pb> movebitur per media subtiliora: quod quidem falsum est; nam multa sunt mobilia quae naturali motu velocius moventur in mediis crassioribus quam in subtilioribus, ut, verbigratia, in aqua quam in aëre.
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100 </s><s id="id.1.1.7.02.04">Si enim accipiamus, exempli gratia, tenuissimam vessicam inflatam, haec in aëre motu naturali tarde descendet; quod si ex aquae profundo demittatur,<pb ed="manuscript" n="67v"></pb> citissime sursum, motu itidem naturali, advolabit.
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101 </s><s id="id.1.1.7.02.05">Sed hic scio, aliquem posse respondere, vessicam in aëre quidem moveri et velociter deorsum ferri; in aqua vero, nedum citius, verum etiam non descendere.
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102 </s><s id="id.1.1.7.02.06">Cui ego e contra responderem, vessicam in aqua sursum <lb ed="Favaro" n="10"></lb> citissime ferri, in aëre deinde non moveri.
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103 </s><s id="id.1.1.7.02.07">Sed, ne disputationem in longum protraham, dico, in mediis subtilioribus velociorem contingere non omnem motum, sed tantum motum deorsum; motum vero sursum citiorem fieri in mediis crassioribus.
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104 </s><s id="id.1.1.7.02.08">Et hoc rationabiliter quidem accidit: necessarium enim est, ut ubi difficile fit motus deorsum, ibi facile fiat motus sursum.
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105 </s><s id="id.1.1.7.02.09">Manifestum est igitur, insufficienter ab Aristotele dictum fuisse, tarditatem motus naturalis ob medii crassitiem contingere.
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106 </s><s id="id.1.1.7.02.10">Quapropter, ipsius opinione derelicta, ut veram tarditatis et celeritatis motus causam afferamus, attendendum est, celeritatem non distingui a motu: qui enim ponit motum, ponit necessario <lb ed="Favaro" n="20"></lb> celeritatem; et tarditas nihil aliud est quam minor celeritas.
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107 </s><s id="id.1.1.7.02.11">A quo igitur provenit motus, ab eodem provenit etiam celeritas: cum itaque a gravitate et levitate motus proveniat, ab eadem ut tarditas vel celeritas proveniant, necessarium est; a maiori quidem mobilis gravitate, maior celeritas<pb ed="manuscript" n="68r"></pb> illius motus qui a gravitate mobilis fit, ut motus deorsum; a minori vero gravitate, eiusdem motus tarditas; et, rursus, a maiori mobilis levitate maior manabit celeritas illius motus qui a levitate mobilis fit, nempe motus sursum.
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108 </s><s id="id.1.1.7.02.12">Manifestum est itaque, quomodo diversitas celeritatis et tarditatis motus contingat in diversis mobilibus in eodem medio motis: si enim motus sit deorsum, quod <lb ed="Favaro" n="30"></lb> gravius erit citius movebitur, quam quod minus grave; si vero motus erit sursum, illud velocius movebitur quod levius erit.
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109 </s><s id="id.1.1.7.02.13">Sed utrum duo mobilia in eodem medio lata in motuum celeritate proportionem servent quam suae gravitates habent, ut credidit Aristoteles, inferius examinabitur.
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110 </s><s id="id.1.1.7.02.14">De celeritate deinde et tarditate eiusdem mobilis in diversis mediis similiter accidit ut mobile citius in medio illo deorsum <pb ed="Favaro" n="262"></pb> moveatur in quo gravius erit, quam in alio in quo minus grave; citius vero in medio illo ascendat in quo levius fuerit, quam in alio in quo minus leve. {1}
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111 </s><s id="id.1.1.7.02.15">Quare manifestum est, quod, si invenerimus in quibus mediis idem mobile gravius extiterit, inventa erunt media in quibus citius descendet; quod si, rursus, demonstremus, quantum idem mobile gravius sit in hoc medio quam in illo, erit, rursus, demonstratum, quanto citius in hoc quam in illo deorsum movebitur: et, converso modo de levi perscrutantes, cum invenerimus in quonam medio idem mobile levius erit, inventum erit medium in quo citius ascendet mobile; quod si comperiamus quanto in hoc, quam in illo medio, idem <lb ed="Favaro" n="10"></lb> mobile sit levius, erit iam compertum quanto citius in hoc, quam illo medio, ascendat mobile.
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112 </s><s id="id.1.1.7.02.16">Verum, ut haec omnia in quolibet particulari motu exactius depraehendi valeant, primum quidem de illis <pb ed="manuscript" n="68v"></pb>motibus discurrentes qui a diversis mobilibus in eodem medio fiunt, ostendemus quam proportionem servent inter se eorum motus, quo ad tarditatem et celeritatem; deinde, de motibus qui ab eodem mobili in diversis mediis fiunt inquirentes, demonstrabimus similiter quam in huiusmodi motibus proportionem servent.
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113 </s></p></subchap2><subchap2><p><s id="id.1.1.8.01.01">Ut igitur ea quae sunt pertractanda facilius absolvantur, considerandum est, primum, diversitatem inter duo mobilia dupliciter posse contingere: vel enim sunt eiusdem speciei, ut, verbigratia , ambo plumbea aut ferrea; differunt autem in mole: vel sunt diversae speciei, ut ferreum unum, ligneum alterum; differunt autem inter se aut mole et gravitate, aut gravitate et non mole, aut mole et non gravitate. {2}
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114 </s><s id="id.1.1.8.01.02">De illis mobilibus quae sunt eiusdem speciei dixit Aristoteles, <pb ed="Favaro" n="263"></pb> illud velocius moveri quod maius est: et hoc in 4 Caeli t. 26, ubi scripsit, quamlibet magnitudinem ignis sursum ferri, et velocius quae maior esset; et sic quamlibet terrae magnitudinem deorsum moveri, et, similiter, velocius quae maior esset.
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115 </s></p><p><figure id="id.1.1.8.02.00" xlink:href="FIG1/F004.jpg"></figure>
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116 <s id="id.1.1.8.02.01">Et idem, 3 Caeli t. 26, inquit: Sit mobile grave in quo b, et feratur per lineam ce, quae dividatur in puncto d; si itaque mobile b dividatur secundum proportionem qua dividitur linea ce in puncto d, manifestum est, in quo tempore <pb ed="manuscript" n="69r"></pb>totum fertur per totam lineam ce, in eodem partem moveri per lineam cd.
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117 </s><s id="id.1.1.8.02.02"><lb ed="Favaro" n="10"></lb> Ex quo apertissime constat, velle Aristotelem mobilia eiusdem generis inter se eam servare in velocitate motus proportionem, quam habent ipsae mobilium magnitudines: et apertissime hoc dicit 4 Caeli t. 16, dicens magnum aurum citius ferri quam paucum. {1}
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118 </s><s id="id.1.1.8.02.03">Quae quidem opinio quam sit ridiculosa, luce clarius patet: quis enim unquam credet, si, exempli gratia, ab orbe lunae duae sphaerae plumbeae demitterentur, quarum altera centies altera maior esset, quod, si maior in una hora ad terram usque deveniret, minor centum horarum spacium in motu suo consumeret? aut, si ex alta turri duos lapides, quorum alter altero sit duplus in mole, eodem momento <lb ed="Favaro" n="20"></lb> proiciantur, quod, minore existente in dimidia turre, maior iam terram sit assecutus?
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119 </s><s id="id.1.1.8.02.04">Aut, rursus, si ex profundo maris eodem tempore ascendere incipiant maxima trabes et parvum ex eadem trabe frustrum, ita ut trabes centies maior sit ipso ligno, quis unquam dixerit, trabem centies velocius ad summum usque aquae ascensuram esse? {2}
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120 </s></p><p><s id="id.1.1.8.03.01">Sed, ut semper rationibus magis quam exemplis utamur (quaerimus enim effectuum causas, quae ab experientia non traduntur), sententiam nostram in medium afferemus, ex cuius comprobatione corruet Aristotelis opinio.
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121 </s><s id="id.1.1.8.03.02">Dicimus ergo, mobilia eiusdem speciei (eiusdem autem speciei vocentur quae ex eadem materia, ut plumbo vel ligno etc., <lb ed="Favaro" n="30"></lb> conflantur), quamvis mole differant, tamen eadem cum celeritate moveri, nec citius descendere maior lapis quam minor.
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122 </s><s id="id.1.1.8.03.03">Qua conclusione qui mirantur, mirabuntur etiam, tam maximam trabem quam parvum <pb ed="Favaro" n="264"></pb> lignum aquae supernatare posse: eadem enim est ratio; ut, si mente conciperemus aquam, cui supernatant trabes et modicum eiusdem trabis frustrum, paulatim et successive leviorem fieri, ita ut tandem aqua levior evadat ligno et ligna incipiant tarde descendere, <pb ed="manuscript" n="69v"></pb>quis unquam dixerit, trabem aut prius aut citius descensuram quam parvum lignum?
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123 </s><s id="id.1.1.8.03.04">Quamvis enim magna trabes sit ligno parvo gravior, tamen trabi cum multo aquae a se attollendae, ligno vero parvo cum paululo aquae, est ratio habenda: et quia a trabe est attollenda tanta aquae moles quanta est propria sua moles, et a ligno parvo similiter, moles istae duae aquae, quae scilicet a lignis attolluntur, eandem inter <lb ed="Favaro" n="10"></lb> se in gravitate proportionem habebunt quam suae moles habent (partes enim homogeneorum sunt inter se in gravitate sicut in mole; quod demonstrari oporteret), {1} hoc est quam habent inter se moles trabis et parvi ligni: ergo eandem habebit proportionem gravitas trabis ad gravitatem aquae a se attollendae, quam gravitas parvi ligni ad gravitatem aquae a se attollendae; et eadem facilitate a magna trabe superabitur repugnantia multae aquae, qua a parvo ligno parvae aquae resistentia vincetur.
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124 </s><s id="id.1.1.8.03.05">Et si, rursus, mente concipiamus magnam, verbigratia, cerae molem aquae supernatantem, quam ceram aut arena aut aliquo graviori commisceamus, ita ut tandem aqua gravior evadat <lb ed="Favaro" n="20"></lb> et vix descendere tardissime incipiat, quis unquam crediderit, si particulam talis cerae accipiamus, utpote centesimam, aut non descensuram aut centies tardius quam tota cera?
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125 </s><s id="id.1.1.8.03.06">Nemo profecto.
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126 </s><s id="id.1.1.8.03.07">Et hoc idem in lance experiri licebit: si enim utrinque pondera aequalia et maxima imponantur, deinde alteri eorum quid grave superaddatur, sed modicum quidem, iam gravius descendet, sed non citius quam si pondera illa essent parva.
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127 </s><s id="id.1.1.8.03.08">Pari ratione et in aqua: trabes enim rationem habet unius ponderis in lance, <pb ed="manuscript" n="70r"></pb>alterum vero pondus repraesentatur a tanta mole aquae quanta est trabis moles: quod si haec aquae moles aequeponderet cum trabe, iam trabes non descendet; <lb ed="Favaro" n="30"></lb> quod si trabes paululum ingravetur ita ut descendat, non iam citius descendet quam parvum ex eodem ligno frustrum, quod cum parva aqua aequeponderaret, deinde paululum gravius redderetur.
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128 </s></p><p><s id="id.1.1.8.04.01">Sed libet hoc idem alio argumento confirmare.
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129 </s><s id="id.1.1.8.04.02">Et prius hoc supponatur: scilicet, si fuerint duo mobilia quorum alterum altero velocius <pb ed="Favaro" n="265"></pb> moveatur, compositum ex utrisque tardius quidem moveri quam pars illa quae altera velocius movebatur, citius vero quam reliqua pars quae, sola, altera tardius ferebatur: {1} ut, exempli gratia, si intelligamus duo mobilia, ut cerae frustrum et vessicam inflatam, quae ex profundo aquae sursum ambo ferantur, tardius tamen cera quam vessica, petimus ut concedatur, quod si ambo componantur, compositum tardius ascensurum esse quam vessica sola, citius vero quam cera sola.
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130 </s><s id="id.1.1.8.04.03">Quod quidem apertissimum est: cui enim dubium est, quod tarditas cerae minuetur a velocitate vessicae, et, rursus, <lb ed="Favaro" n="10"></lb> velocitas vessicae a tarditate cerae retardabitur, et fiet motus quidam medius inter tarditatem cerae et velocitatem vessicae?
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131 </s><s id="id.1.1.8.04.04">Similiterque, si duo mobilia, rursus, descendant, quorum alterum altero tardius feratur, ut, verbigratia, si alterum sit lignum, alterum vessica, quae in aëre descendant, et citius quidem lignum quam vessica, hoc supponimus: si componantur, compositum tardius quidem descensurum quam lignum solum, citius vero quam sola vessica.
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132 </s><s id="id.1.1.8.04.05">Manifestum est enim quod celeritas ligni a tarditate vessicae tardabitur, tarditas vero vessicae a velocitate ligni accelerabitur; et fiet similiter motus quidam medius inter tardita<pb ed="manuscript" n="70v"></pb>tem vessicae et celeritatem ligni.
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133 </s><s id="id.1.1.8.04.06"><lb ed="Favaro" n="20"></lb> Hoc supposito, sic arguo: probando, mobilia eiusdem speciei, mole inaequalia eadem ferri cum celeritate. {2}
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134 </s></p><p><figure id="id.1.1.8.05.00" xlink:href="FIG1/F005.jpg"></figure>
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135 <s id="id.1.1.8.05.01">Sint duo mobilia eiusdem speciei, a quidem maius, b vero minus; et, si fieri potest per adversarium, ab citius moveatur quam b.
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136 </s><s id="id.1.1.8.05.02">Sunt igitur duo mobilia quorum alterum citius movetur; ergo, ex suppositione, compositum ex utrisque tardius movebitur ex parte quae, sola, altera citius movebatur.
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137 </s><s id="id.1.1.8.05.03">Si ergo a, b componantur, compositum tardius movebitur quam a solum: sed compositum ex a et b maius est quam a solum: ergo, contra adversarios, maius mobile tardius movebitur quam minus; quod quidem esset inconveniens.
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138 </s><s id="id.1.1.8.05.04"><lb ed="Favaro" n="30"></lb> Quid ergo clarius exquirimus de falsitate opinionis Aristotelis?
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139 </s><s id="id.1.1.8.05.05">Sed, <pb ed="Favaro" n="266"></pb> quaeso, cui, simpliciter et naturaliter hoc intuenti, veritas non statim cognoscitur?
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140 </s><s id="id.1.1.8.05.06">Si enim supponamus, a et b mobilia aequalia esse et esse ad invicem propinquissima, iam, omnium consensu, aequa celeritate movebuntur: quod si intelligamus, ea, dum moventur, uniri, cur, quaeso, ut voluit Aristoteles, celeritatem motus duplicabunt aut eam augebunt?
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141 </s><s id="id.1.1.8.05.07">Satis igitur confirmatum sit, non esse causam, per se, cur mobilia eiusdem speciei inaequali ad invicem velocitate moveri debeant, sed certe ut aequali.
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142 </s><s id="id.1.1.8.05.08">Quod si aliqua esset causa per accidens, ut, verbigratia, mobilis figura, haec inter causas per se non erit reponenda: et adde quod parum iuvat, aut impedit, motum figura, ut <lb ed="Favaro" n="10"></lb> suo loco ostendemus.
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143 </s><s id="id.1.1.8.05.09">Neque etiam, ut multi solent, statim deveniendum est ad extrema, accipientes, verbigratia, maximam <pb ed="manuscript" n="71r"></pb>plumbi molem, et, rursus, minimam ex eodem lamillam seu bracteam, quae interdum etiam aquae supernatet: cum enim tam aëris quam aquae partium sit quaedam cohaerentia et (ut ita loquar) tenacitas atque viscositas, haec a minima gravitate non potest vinci.
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144 </s><s id="id.1.1.8.05.10">Intelligenda itaque est conclusio de mobilibus illis quorum minoris tanta sit gravitas et moles, ut a parva illa medii tenacitate non impediatur; qualis esset, verbigratia, globus plumbi unius librae.
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145 </s><s id="id.1.1.8.05.11">Adde quod etiam cavillatoribus huiusmodi, qui fortasse Aristotelem tueri posse sibi persuadem, hoc quidem accidit si <lb ed="Favaro" n="20"></lb> ad extrema devenient, quod eo magis laborandum erit quo mobilia magis ad invicem differentia capient: si enim accipiant mobile unum quod altero millies maior sit, antequam illud millies alterum in velocitate superet ostendant, sudandum profecto erit et laborandum.
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146 </s></p><p><s id="id.1.1.8.06.01">Sed, ut ad ea quae restant deveniamus, sequitur nunc ut videamus, mobilia diversa specie, in eodem medio mota, quamnam in suis motibus proportionem servent.
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147 </s><s id="id.1.1.8.06.02">Quae quidem mobilia licet inter se tripliciter differre possint; vel enim differunt mole et non gravitate, vel gravitate et non mole, vel mole et gravitate; de illis tantummodo est inquirendum, quae differunt gravitate et non mole.
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148 </s><s id="id.1.1.8.06.03">Proportiones enim <lb ed="Favaro" n="30"></lb> eorum quae duobus aliis modis differunt, ad hanc reduci possunt: ut, si mobilia differant mole et non gravitate, si ex maiori accipiatur pars quae aequalis sit minori, erunt iam mobilia differentia gravitate et non mole; et quam proportionem servabit pars illa, ablata a maiori mobili, cum alio mobili, eandem servabit etiam totum <pb ed="manuscript" n="71v"></pb>illud integrum <pb ed="Favaro" n="267"></pb> mobile (demonstratum est enim, mobilia eiusdem generis, quamvis mole differant, eadem velocitate moveri): et similiter, si mobilia differant mole et gravitate, sumpta, ex maiori, parte quae aequetur mobili minori, habebimus rursus duo mobilia quae different gravitate et non mole; et eandem proportionem servabit in motu pars illa cum altero mobili, quam totum etiam mobile alterum integrum (eadem enim, rursus, cum celeritate mobilium eiusdem speciei movetur pars et totum).
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149 </s><s id="id.1.1.8.06.04">Patet igitur quomodo, data proportione motuum eorum mobilium quae differunt tantum gravitate et non mole, dentur etiam <lb ed="Favaro" n="10"></lb> proportiones eorum, quae quovis alio modo differant.
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150 </s><s id="id.1.1.8.06.05">Ut {1} igitur proportionem hanc inveniamus et, contra Aristotelis sententiam, ostendamus, nullo pacto mobilia, etiam si diversae speciei, proportionem suarum gravitatum servare, ea demonstrabimus ex quibus non solum huius quaestionis, verum etiam et quaestionis de proportione motuum eiusdem mobilis in diversis mediis, exitus pendet; et utramque quaestionem simul examinabimus.
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151 </s></p><p><s id="id.1.1.8.07.01">Quare ad proportionem eiusdem mobilis in diversis mediis <pb ed="Favaro" n="268"></pb> exquirendam deveniamus: et prius quidem examinemus, utrumnam Aristotelis de hoc sententia verior sit quam altera supra exposita, nec ne.
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152 </s></p><p><figure id="id.1.1.8.08.00" xlink:href="FIG1/F006.jpg"></figure>
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153 <s id="id.1.1.8.08.01">Credidit itaque Aristoteles, motus eiusdem mobilis in diversis mediis eam in celeritate proportionem inter se servare, quam subtilitates mediorum inter se habent; et hoc quidem aperte scripsit 4 Physicorum t. 71, dum dixit: Medium magis impedit, quod crassius est: ut a movebitur per spacium b in tempore c, per spacium autem d, cum sit subtilius tempore e, secundum proportionem impedientis, si aequalis sit longitudo; ut, si b sit aqua, d vero aër, quanto ergo subtilior est aër aqua, tanto citius a <pb ed="manuscript" n="72v"></pb>per d movebitur quam per b.
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154 </s><s id="id.1.1.8.08.02">Habet ergo velocitas ad <lb ed="Favaro" n="10"></lb> velocitatem eam proportionem secundum quam distat aër ab aqua: quare, si in duplo subtilior aër quam aqua, in duplo tempore transibit a lineam b quam lineam d; et erit tempus c duplum temporis e.
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155 </s><s id="id.1.1.8.08.03">Haec sunt verba Aristotelis, quae falsam certe sententiam includunt: quod quidem ut luce clarius appareat, hanc formabo demonstrationem.
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156 </s></p><p><figure id="id.1.1.8.09.00" xlink:href="FIG1/F007.jpg"></figure>
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157 <s id="id.1.1.8.09.01">Si velocitas ad velocitatem eam habet proportionem quam medii subtilitas ad subtilitatem, esto mobile quidem o, et medium a, cuius subtilitas sit 4, et sit, verbigratia, aqua; medii vero b subtilitas sit 16, maior <lb ed="Favaro" n="20"></lb> nempe subtilitate a, et sit b, exempli gratia, aër; et mobile o tale sit ut in aqua non descendat; eiusdem vero mobilis in b medio celeritas sit 8. {1}
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158 </s><s id="id.1.1.8.09.02">Quia ergo mobilis o in medio b celeritas est 8, in medio vero a est nulla, poterit certe inveniri aliquod medium in quo mobilis o celeritas sit 1.
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159 </s><s id="id.1.1.8.09.03">Sit autem tale medium c.
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160 </s><s id="id.1.1.8.09.04">Quia igitur o citius movetur in medio b quam in medio c, necesse est ut subtilitas ipsius c sit minor subtilitate ipsius b, sitque, <pb ed="Favaro" n="269"></pb> per adversarium, tanto minor quanto celeritas in ipso medio c minor est celeritate in medio b: posita autem est celeritas in medio b octupla celeritatis in medio c: ergo subtilitas etiam medii b erit octupla subtilitatis medii c: quare subtilitas ipsius c erit 2.
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161 </s><s id="id.1.1.8.09.05">Movetur ergo mobile o cum celeritate 1 in subtilitate medii c, quae est 2: positum autem est non moveri in subtilitate medii a, quae est 4: ergo mobile o non movebitur in maiori subtilitate, cum tamen in minori moveatur: quod est absurdissimum.<pb ed="manuscript" n="73r"></pb>
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162 </s><s id="id.1.1.8.09.06">Patet igitur, motuum velocitates non servare inter se subtilitatum mediorum <lb ed="Favaro" n="10"></lb> proportiones.
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163 </s><s id="id.1.1.8.09.07">Sed, absque alia demonstratione, nonne quisque intueri potest falsitatem opinionis Aristotelis?
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164 </s><s id="id.1.1.8.09.08">Si enim motus servant mediorum proportionem, ergo et, conversim, media servabunt motuum proportionem: quia igitur lignum in aëre quidem descendit, in aqua vero minime, et, consequenter, motus in aëre ad motum in aqua nullam habet proportionem, ergo et raritas aëris ad raritatem aquae nullam habebit proportionem: quo quid absurdius?
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165 </s><s id="id.1.1.8.09.09">At ne quis forte sibi satis meo argumento respondisse videretur, si diceret, Quamvis lignum non moveatur deorsum in aqua, movetur tamen sursum, et quam proportionem habet motus sursum in aqua ad motum deorsum in aëre, hanc habet <lb ed="Favaro" n="20"></lb> raritas aquae ad raritatem aëris; et ob id dextre Aristotelem salvasse existimaret; hoc quoque subterfugium auferemus: accipiendo, scilicet, corpus quod in aqua neque sursum neque deorsum moveatur, ut esset, exempli gratia, ipsamet aqua, quae tamen satis velociter in aëre movetur.
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166 </s></p><p><s id="id.1.1.8.10.01">Merito, igitur, posthabita Aristotelis sententia, inquiramus iam, quam servent proportionem motus ab eodem mobili in diversis mediis facti: et, prius quidem, de motu sursum ostendamus, solidas magnitudines aqua leviores, in aquam impulsas, ferri sursum tanta vi, quanto aqua, cuius moles aequetur moli demersae magnitudinis, ipsa magnitudine <lb ed="Favaro" n="30"></lb> gravior erit.
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167 </s></p><p><figure id="id.1.1.8.11.00" xlink:href="FIG1/F008.jpg"></figure>
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168 <s id="id.1.1.8.11.01">Sit itaque primus aquae status, antequam magnitudo in eam demittatur, secundum superficiem ab; et demittatur in eam, vi, solida magnitudo cd; et attollatur aqua usque ad superficiem ef: et quia aqua, quae attollitur, eb habet molem aequalem moli totius magnitudinis demersae, et magnitudo ponitur<pb ed="manuscript" n="73v"></pb> aqua levior, erit aquae eb gravitas maior gravitate cd.
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169 </s><s id="id.1.1.8.11.02">Intelligatur itaque pars aquae tb, cuius gravitas aequetur gravitati magnitudinis cd: demonstrandum itaque erit, magnitudinem cd <pb ed="Favaro" n="270"></pb> sursum ferri tanta vi, quanta est gravitas aquae tf (secundum enim hanc gravitatem aqua eb gravior est gravitate aquae tb, hoc est gravitate magnitudinis cd).
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170 </s><s id="id.1.1.8.11.03">Quia itaque gravitas aquae tb aequalis est gravitati cd, tanta vi premet sursum aqua tb ut magnitudinem attollat, quanta resistet magnitudo ne attollatur.
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171 </s><s id="id.1.1.8.11.04">Gravitas itaque partis aquae prementis, nempe tb, aequatur resistentiae solidae magnitudinis: sed gravitas totius aquae prementis ex superat gravitatem aquae tb secundum gravitatem aquae tf: ergo <lb ed="Favaro" n="10"></lb> gravitas totius aquae eb superabit resistentiam solidi cd secundum gravitatem tf aquae.
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172 </s><s id="id.1.1.8.11.05">Gravitas itaque totius aquae prementis sursum impellet solidam magnitudinem tanta vi, quanta est gravitas partis aquae tf: quod fuit demonstrandum.
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173 </s></p><p><s id="id.1.1.8.12.01">Ex hac demonstratione patet, primo, quomodo, ut supra dictum fuit, motus sursum fiat etiam a gravitate, non quidem mobilis, sed medii: 2Á, colligitur nostrae quaestionis intentum.
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174 </s><s id="id.1.1.8.12.02">Quia enim quaerimus, quanto citius idem mobile ascendat per hoc medium quam per alterum, quotiescunque noverimus quanta celeritate per utrumque feratur, sciemus etiam discrimen inter utrasque celeritates: et hoc est quod quaerimus.
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175 </s><s id="id.1.1.8.12.03"><lb ed="Favaro" n="20"></lb> Si igitur hoc lignum, verbigratia, cuius gravitas est 4, fertur in aqua <pb ed="manuscript" n="74r"></pb>sursum, et tantae molis aquae; quanta est moles ligni, gravitas est 6, feretur iam lignum celeritate ut 2: quod si, rursus, idem lignum feratur sursum in medio aqua graviori, ita ut tantae molis huius secundi medii, quanta est moles ligni, gravitas sit 10, iam lignum in hoc feretur sursum celeritate ut 6.
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176 </s><s id="id.1.1.8.12.04">In altero autem ferebatur celeritate ut 2: ergo istae duae celeritates erunt inter se sicut et 2; non autem ut gravitates aut crassities mediorum, ut volebat Aristoteles, quae sunt inter se ut 10 et 6.
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177 </s><s id="id.1.1.8.12.05">Patet igitur, universaliter, celeritates inter se motuum sursum, esse, sicut excessus gravitatis unius medii super gravitatem <lb ed="Favaro" n="30"></lb> mobilis se habet ad excessum gravitatis alterius medii super gravitatem eiusdem mobilis.
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178 </s><s id="id.1.1.8.12.06">Quare, si statim voluerimus cognoscere celeritates eiusdem mobilis in duobus mediis, accipiamus ex utroque medio duas moles aequales moli mobilis, et gravitas mobilis ex utriusque medii gravitate subtrahatur; et remanentes numeri erunt inter se sicut <pb ed="Favaro" n="271"></pb> motuum celeritates. {1}
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179 </s><s id="id.1.1.8.12.07">Colligitur etiam exitus alterius quaestionis: nempe, quam proportionem servent in celeritate motuum diversa mobilia, aequalia mole, et gravitate inaequalia.
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180 </s><s id="id.1.1.8.12.08">Si enim unumquodque fertur sursum tanta vi, quanto <pb ed="manuscript" n="74v"></pb>tanta moles medii, quanta est mobilis moles, gravior est ipso mobili, subtractis, ex dictae medii molis gravitate, mobilium gravitatibus, remanentes numeri eam inter se habebunt proportionem, quam celeritates: ut si, verbigratia, unius mobilis gravitas sit quatuor, alterius vero 6, medii vero 8, erit iam mobilis, cuius gravitas est 4, celeritas 4, alterius vero mobilis <lb ed="Favaro" n="10"></lb> celeritas 2.
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181 </s><s id="id.1.1.8.12.09">Istae autem celeritates, 4 et 2, non sunt inter se sicut mobilium levitates, quae sunt 6 et 4: nunquam enim excessus unius numeri super duos alios erunt inter se sicut illi duo numeri; neque excessus duorum numerorum super alium numerum erunt inter se sicut numeri excedentes.
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182 </s><s id="id.1.1.8.12.10">Apertissimum igitur est, quod, in motu sursum, mobilium diversorum motus non sunt inter se sicut levitates mobilium.
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183 </s></p><p><s id="id.1.1.8.13.01">Restat igitur ut ostendamus, neque in motu deorsum mobilium celeritates esse inter se sicut gravitates mobilium, et ut, simul, ostendamus proportionem quam servant celeritates eiusdem mobilis in diversis mediis: quae omnia ex hac demonstratione facile <lb ed="Favaro" n="20"></lb> haurientur.
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184 </s><s id="id.1.1.8.13.02">Dico igitur, solidam magnitudinem aqua graviorem deorsum ferri tanta vi quanto aqua, molem habens aequalem moli ipsius magnitudinis, levior est ipsa magnitudine.
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185 </s></p><p><figure id="id.1.1.8.14.00" xlink:href="FIG1/F009.jpg"></figure>
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186 <s id="id.1.1.8.14.01">Sit itaque primus aquae status secundum superficiem de; magnitudo autem solida bl, aqua gravior, in aquam demittatur, et attollatur aqua ad superficiem ab; sit autem aqua ae, quae molem ipsius magnitudinis moli aequalem habeat: et quia solida magnitudo ponitur aqua gravior, erit aquae gravitas minor gravi<pb ed="manuscript" n="75r"></pb>tate solidae magnitudinis.
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187 </s><s id="id.1.1.8.14.02">Intelligatur itaque moles aquae ao, quae aequalem habeat gravitatem gravitati bl: et quia aqua ae levior est ao secundum gravitatem do, demonstrandum <lb ed="Favaro" n="30"></lb> est, magnitudinem bl deorsum ferri tanta vi, quanta est gravitas aquae do.
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188 </s><s id="id.1.1.8.14.03">Intelligatur altera solida magnitudo, aqua levior, primae <pb ed="Favaro" n="272"></pb> coniuncta, cuius quidem moles sit ao aquae moli aequalis, gravitas autem eius sit aequalis gravitati aquae ae; sitque dicta magnitudo lm: et quia moles bl aequatur moli ae, moles autem lm aequatur moli ao, ergo moles compositarum magnitudinum bl, lm aequatur moli compositae aquae ea, ao.
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189 </s><s id="id.1.1.8.14.04">Sed gravitas magnitudinis aquae ae aequatur gravitati magnitudinis lm: gravitas autem aquae ao aequatur gravitati magnitudinis bl: tota ergo gravitas ambarum <lb ed="Favaro" n="10"></lb> magnitudinum bl, lm aequatur gravitati aquae oa, ae.
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190 </s><s id="id.1.1.8.14.05">Sed etiam moles magnitudinum demonstrata est aequalis moli aquae oa, ae; ergo, per primam propositionem, magnitudines ita compositae neque sursum neque deorsum ferentur.
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191 </s><s id="id.1.1.8.14.06">Tanta ergo erit vis magnitudinis bl deorsum prementis, quanta est vis magnitudinis lm sursum impellentis: sed, per praemissam, magnitudo lm sursum impellit tanta vi, quanta est gravitas aquae do: ergo magnitudo bl deorsum feretur tanta vi, quanta est gravitas aquae do.
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192 </s><s id="id.1.1.8.14.07">Quod fuit demonstrandum.
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193 </s></p><p><s id="id.1.1.8.15.01">Hac igitur demonstratione percepta, quaestionum exitus facile <lb ed="Favaro" n="20"></lb> dignosci potest.
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194 </s><s id="id.1.1.8.15.02">Constat enim, idem mobile in diversis mediis descendens eam, in suorum motuum cele<pb ed="manuscript" n="75v"></pb>ritate, servare proportionem, quam habent inter se excessus quibus gravitas sua mediorum gravitates excedit: ut si mobilis gravitas sit 8, molis autem unius medii, aequalis moli mobilis, gravitas sit 6, erit iam illius celeritas ut 2; quod si molis alterius medii, aequalis mobilis moli, gravitas sit 4, erit iam mobilis celeritas, in hoc medio, ut 4.
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195 </s><s id="id.1.1.8.15.03">Patet ergo quod istae celeritates erunt inter se sicut 2 et 4; non autem ut mediorum crassities aut gravitates, ut volebat Aristoteles, quae inter se sunt ut 6 et 4.
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196 </s><s id="id.1.1.8.15.04">Exitus itidem alterius quaestionis patet: quam, scilicet, proportionem servent inter <lb ed="Favaro" n="30"></lb> se mobilium, aequalium mole, inaequalium vero gravitate, in eodem medio, velocitates.
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197 </s><s id="id.1.1.8.15.05">Erunt enim inter se talium mobilium velocitates, ut excessus quibus gravitates mobilium gravitatem medii excedunt: ut, exempli gratia, si fuerint duo mobilia mole aequalia, gravitate vero inaequalia, quorum alterius gravitas sit 8, alterius vero 6, molis autem medii, aequalis moli alterius mobilis, sit gravitas 4, <pb ed="Favaro" n="273"></pb> illius quidem mobilia celeritas erit 4, huius vero 2.
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198 </s><s id="id.1.1.8.15.06">Servabunt igitur hae velocitates proportionem quae est 4 ad 2; non illam quae est inter gravitatem nempe 8 ad 6.
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199 </s><s id="id.1.1.8.15.07">Atque ex his omnibus quae tradita sunt, haud arduum erit proportionem quoque depraehendere, quam diversa, specie, mobilia in diversis mediis servabunt.
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200 </s><s id="id.1.1.8.15.08">Scrutetur enim, quam servent proportionem, in celeritate, utraque in eodem medio; quod, uti faciendum sit, patet ex superioribus: {1} deinde inquiratur, quam celeritatem habeat alterum eorum in alio medio, per ea itidem quae supra tradita sunt: et habebimus quod quaeritur.
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201 </s><s id="id.1.1.8.15.09">Ut, <lb ed="Favaro" n="10"></lb> verbigratia, si fuerint duo mobilia, <pb ed="manuscript" n="76r"></pb>mole quidem aequalia, gravitate vero diversa, et sit huius quidem gravitas 12, illius vero 8, et quaeramus proportionem inter celeritatem illius, cuius gravitas 12, in aqua descendentis, et celeritatem illius, cuius gravitas 8, in aëre descendentis; videatur, primo, quanto 12 velocius descendat in aqua quam 8, deinde videatur quanto citius 8 fertur in aëre quam in aqua: et habebimus intentum; aut, e contra, videatur quanto 12 citius in aëre descendat quam 8, deinde 12 quanto tardius feratur in aqua quam in aëre.
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202 </s></p><p><s id="id.1.1.8.16.01">Hae, igitur, universales sunt regulae proportionum motuum <lb ed="Favaro" n="20"></lb> mobilium, sive eiusdem sive non eiusdem speciei, in eodem vel in diversis mediis, sursum aut deorsum motorum.
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203 </s><s id="id.1.1.8.16.02">Sed animadvertendum est, quod magna hic oritur difficultas: quod proportiones istae, ab eo qui periculum fecerit, non observari comperientur.
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204 </s><s id="id.1.1.8.16.03">Si enim duo diversa mobilia accipiet, quae tales habeant conditiones ut alterum altero duplo citius feratur, et ex turri deinde demittat, non certe velocius, duplo citius, terram pertinget: quin etiam, si observetur, id quod levius est, in principio motus praeibit gravius et velocius erit.
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205 </s><s id="id.1.1.8.16.04">Quae quidem diversitates et, quodammodo, prodigia unde accidant (per accidens enim haec sunt), non est hic locus inquirendi: <lb ed="Favaro" n="30"></lb> praevidenda enim nonnulla sunt, quae nondum inspecta fuere.
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206 </s><s id="id.1.1.8.16.05">Videndum enim prius est, cur motus naturalis tardior sit in principio.<pb ed="manuscript" n="77r"></pb>
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207 </s></p></subchap2><subchap2><p><s id="id.1.1.9.01.01">Quando quis veritatem alicuius rei nactus est, et non nisi summo labore comparavit, deinde, sua inventa diligentius inspiciens, saepius cognoscit quomodo ea, quae magno negocio invenit, poterant facillime percipi.
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208 </s><s id="id.1.1.9.01.02">Habet enim hoc veritas, ut non adeo, ut multi crediderunt, latitet; sed eius vestigia diversis locis splendent, multi sunt calles per quos ad eam inceditur: nobis tamen saepius accidit ut ex non cernamus quae propinquiora et clariora sunt.
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209 </s><s id="id.1.1.9.01.03">Et de hoc <lb ed="Favaro" n="10"></lb> exemplum prae manibus manifestum habemus: ea enim omnia quae supra satis ardue demonstrata et declarata fuerunt, nobis a natura adeo aperta et manifesta exponuntur, ut nihil clarius, nil apertius.
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210 </s></p><p><s id="id.1.1.9.02.01">Quod quidem ut cuique appareat, consideremus, primo, quomodo et cur ex quae feruntur sursum, ferantur tanta vi, quanto tanta moles medii, per quod feruntur, quam tanta est moles mobilis, gravior est ipso mobili.
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211 </s><s id="id.1.1.9.02.02">Intelligamus itaque lignum quod in aqua ascendat et aquae supernatet: iam manifestum est quod lignum fertur sursum tanta vi, quanta esset necessaria ad illud vi sub aquam demergendum.
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212 </s><s id="id.1.1.9.02.03">Si itaque inveniamus, quanta vis necessaria sit ad illud sub <lb ed="Favaro" n="20"></lb> aquam comprimendum, habebimus intentum: sed lignum nisi esset levius aqua, hoc est si esset grave ut tanta moles aquae quanta est sua moles, iam certe demergeretur, et non attolleretur supra aquam: tanta ergo vis, quanta est gravitas secundum quam ligni gravitas superatur a gravitate dictae molis aquae,<pb ed="manuscript" n="77v"></pb> sufficit ad lignum demergendum.
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213 </s><s id="id.1.1.9.02.04">Inventa est ergo quanta gravitas requiratur ad lignum demergendum: sed mox determinatum fuit quod lignum sursum fertur tanta vi, quanta requiritur ad illud demergendum; requiritur autem ad illud demergendum gravitas mox inventa: ergo lignum fertur sursum tanta vi, quanta est gravitas qua tanta moles aquae, quanta est <lb ed="Favaro" n="30"></lb> moles ligni, excedit gravitatem ligni: quod quaerebatur.
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214 </s></p><p><s id="id.1.1.9.03.01">Pari ratione de motu deorsum est ratiocinandum.
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215 </s><s id="id.1.1.9.03.02">Quaerimus igitur, sphera plumbea quanta vi deorsum feratur in aqua.
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216 </s><s id="id.1.1.9.03.03">Patet igitur, primo, <pb ed="Favaro" n="275"></pb> quod sphera plumbea fertur deorsum tanta vi, quanta requireretur ad illam sursum attrahendam: sed si sphera plumbea esset aquea, nulla vis esset necessaria ad illam sursum attrahendam, aut certe minima omnium virium: resistit ergo, ne sursum trahatur sphaera, tanta gravitas, quanta sphaera plumbea sphaeram aqueam sibi aequalem excedit.
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217 </s><s id="id.1.1.9.03.04">Sed eadem vi, qua sphaera plumbea resistit ne sursum trahatur, deorsum etiam fertur: ergo sphaera plumbea fertur deorsum tanta vi, quanta est gravitas qua excedit gravitatem sphaerae aqueae.
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218 </s><s id="id.1.1.9.03.05">Hoc autem idem licet in lancis ponderibus intueri.
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219 </s><s id="id.1.1.9.03.06">Si enim pondera aeque <lb ed="Favaro" n="10"></lb> ponderantia fuerint, et alteri eorum aliquod grave imponatur, tunc id deorsum feretur; sed non secundum totam suam gravitatem, sed tantum ea gravitate qua alterum pondus excedit: quod idem est ac si dicamus, pondus hoc deorsum ferri tanta vi quanto aliud pondus est eo levius.
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220 </s><s id="id.1.1.9.03.07">Et pari ratione alterum pondus feretur sursum tanta vi, quanto alterum est eo gravius.
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221 </s></p><p><s id="id.1.1.9.04.01"><pb ed="manuscript" n="78r"></pb>Ex his quae in hoc et superiori capite tradita sunt, colligitur universaliter, mobilia diversae speciei eandem in suorum motuum celeritatibus servare proportionem, quam habent inter se gravitates ipsorum mobilium, dum fuerint aequales mole; et hoc quidem non simpliciter, <lb ed="Favaro" n="20"></lb> sed in eo medio ponderata in quo fieri debet motus.
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222 </s></p><p><figure id="id.1.1.9.05.00" xlink:href="FIG1/F010.jpg"></figure>
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223 <s id="id.1.1.9.05.01">Ut, verbigratia, sint duo mobilia, mole aequalia, inaequalia gravitate, a, b; et gravitas a in aëre sit 8, gravitas vero b in aëre sit 6: istorum mobilium in aqua celeritates non servabunt, ut iam dictum est, proportionem quae est 8 ad 6.
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224 </s><s id="id.1.1.9.05.02">Si enim accipiamus molem aquae c, quae aequetur moli alterius mobilis, sit eius gravitas 4: celeritas ergo mobilis a erit ut 4, celeritas vero b erit ut 2; quae celeritates erunt inter se in dupla proportione, non autem in sesquitertia, ut sunt gravitates mobilium in aëre ponderatorum.
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225 </s><s id="id.1.1.9.05.03">Attamen eorundem <lb ed="Favaro" n="30"></lb> mobilium in aqua gravitates quoque erunt in proportione dupla: gravitas enim a in aqua esset tantum 4.
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226 </s><s id="id.1.1.9.05.04">Quod sic patet.
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227 </s><s id="id.1.1.9.05.05">Si gravitas a in aëre esset 4, in aqua esset nulla.
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228 </s><s id="id.1.1.9.05.06">Esset enim tunc a aeque grave ac aqua, cum positum sit tantae molis aquae quanta est moles a, nempe c, in aëre gravitatem esse 4: gravitas autem e in aqua esset nulla; <pb ed="Favaro" n="276"></pb> non enim aut sursum aut deorsum ferretur: ergo etiam a in aqua gravitas esset nulla, si in aëre esset 4.
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229 </s><s id="id.1.1.9.05.07">Sed quia in aëre est 8, in aqua erit 4: et, eadem ratione, gravitas b in aqua esset 2: quare eorum gravitates essent in dupla proportione, sicut et motuum celeritates.
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230 </s><s id="id.1.1.9.05.08">Pari ratione de levi est discurrendum.
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231 </s><s id="id.1.1.9.05.09"><pb ed="manuscript" n="78v"></pb>Colligitur etiam, quomodo, datis duorum ponderum gravitatibus in aëre, statim gravitates eorundem in aqua cognosci possunt: ex utroque enim subtracta gravitate tantae aquae molis quanta est eorum moles, remanebunt gravitates eorum in aqua.
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232 </s><s id="id.1.1.9.05.10">Et sic de aliis mediis.
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233 </s><s id="id.1.1.9.05.11">Et ex supradictis unicuique manifestum esse potest, quod nullius rei propriam suam gravitatem habemus: si enim, <lb ed="Favaro" n="10"></lb> verbigratia, duo pondera ponderentur in aqua, quis dixerit gravitates, quas tunc videbimus, veras esse gravitates eorum ponderum, quorum deinde, in aëre ponderatorum, diversae ab his gravitates apparebunt, et aliam inter se proportionem servabunt?
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234 </s><s id="id.1.1.9.05.12">Quae si rursus in alio medio, ut, verbigratia, igne, ponderari possent, essent itidem diversae gravitates, aliamque proportionem inter se habentes: et hoc semper, pro mediorum diversitate, variabunt.
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235 </s><s id="id.1.1.9.05.13">Quod si in vacuo ponderari possent, tunc certe, ubi nulla medii gravitas ponderum gravitatem minueret, eorum exactas perciperemus gravitates.
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236 </s><s id="id.1.1.9.05.14">Sed quia Peripatetici, cum principe suo, dixerunt, in vacuo nullos fieri posse motus et ideo omnia aeque <lb ed="Favaro" n="20"></lb> ponderare, forte non absonum erit hanc opinionem examinare, et eius fundamenta et demonstrationes perpendere: haec enim quaestio est una eorum quae de motu sunt.<pb ed="manuscript" n="79v"></pb>
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237 </s></p></subchap2><subchap2><p><s id="id.1.1.10.01.01">Aristoteles, 4 Phys., nitens tollere vacuum, multa facit argumenta; quorum quae a t. 64 sunt, ex motu sunt deprompta.
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238 </s><s id="id.1.1.10.01.02">Quia enim ponit motum in instanti fieri non posse, demonstrare contendit, si vacuum daretur, motum in eo in instanti contingere: quod quidem cum <lb ed="Favaro" n="30"></lb> impossibile sit, vacuum etiam impossibile esse, necessario concludit.
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239 </s><s id="id.1.1.10.01.03">Nos autem cum de motu agamus, statuimus exquirere utrum verum sit <pb ed="Favaro" n="277"></pb> quod, si daretur vacuum, motus in eo in instanti fieret: et cum determinaturi simus, in vacuo motum fieri in tempore, prius contrariam opinionem examinabimus et illius argumenta.
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240 </s></p><p><s id="id.1.1.10.02.01">Et, primo quidem, argumentorum ab Aristotele allatorum, nullum profecto est quod necessitatem habeat; sed unum quidem est quod necessitatem habere, prima fronte, videtur: et hoc illud est quod t. 71 et 72 scribitur, in quo ad inconveniens illud deducit, si motus in tempore fiat in vacuo, quod, scilicet, eodem tempore movebitur idem mobile in pleno et vacuo.
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241 </s><s id="id.1.1.10.02.02">Quod quidem argumentum ut melius diluere <lb ed="Favaro" n="10"></lb> possimus, nunc in medium afferre statuimus.
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242 </s><s id="id.1.1.10.02.03">Supposuit itaque hoc, primum, Aristoteles, cum vidisset idem mobile per subtiliora media citius ferri quam per crassiora: eandem proportionem servare motus velocitatem in uno medio ad alterius motus velocitatem in altero medio, quam medii unius subtilitas ad alterius medii subtilitatem.
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243 </s></p></subchap2></subchap1><subchap1><subchap2><p><figure id="id.1.1.1.0.03.00" xlink:href="FIG1/F011.jpg"></figure>
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244 </p></subchap2><subchap2><p><s id="id.1.1.10.03.01">Deinde sic est argumentatus: Transeat mobile a medium b in tempore c; medium autem subtilius ipso, nempe d, transeat <pb ed="manuscript" n="80br"></pb>in tempore e: manifestum est, sicut crassities b ad crassitiem d, ita se habere tempus c ad tempus e.
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245 </s><s id="id.1.1.10.03.02">Sit deinde f vacuum; et mobile a, si fieri possit, transeat ipsum f, non in instanti, sed tempore g; et sicut tempus e se habet ad <lb ed="Favaro" n="20"></lb> tempus g, ita se habeat crassities medii d ad alterius medii crassitiem.
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246 </s><s id="id.1.1.10.03.03">Tunc, ex his quae constituta sunt, mobile a per medium nunc inventum movebitur in tempore g, cum medium d ad medium nunc inventum eandem habeat proportionem quam e tempus ad tempus g: sed eodem tempore g movetur a etiam per vacuum f: ergo a eodem tempore movebitur per duo spatia aequalia, quorum <lb ed="Favaro" n="30"></lb> unum sit plenum, alterum vero vacuum; quod quidem est impossibile.
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247 </s><s id="id.1.1.10.03.04">Non ergo mobile movebitur per vacuum in tempore; ergo in instanti.
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248 </s></p><p><s id="id.1.1.10.04.01">Haec est Aristotelis demonstratio: quae quidem optime et necessario conclusisset, si ea, quae assumpsit, demonstrasset Aristoteles, aut, si non demonstrata, fiussent saltem vera; sed in hoc deceptus {1} est, quod ea tanquam nota axiomata assumpsit, quae non solum non sunt <pb ed="Favaro" n="278"></pb> sensui manifesta, verum nec unquam demonstrata, nec etiam demonstrabilia, cum prorsus falsa existant.
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249 </s><s id="id.1.1.10.04.02">Posuit enim eiusdem mobilis motus in diversis mediis eam, in celeritate, inter se proportionem servare, quam habent mediorum subtilitates: quod quidem falsum esse, supra abunde demonstratum est.
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250 </s><s id="id.1.1.10.04.03">Ad cuius etiam confirmationem hoc unum addam: si subtilitas aëris ad aquae subtilitatem eam proportionem habet quam celeritas eiusdem mobilis in aëre ad celeritatem ipsius in aqua, cum igitur gutta <pb ed="manuscript" n="80bv"></pb>aut quaelibet alia pars aquae in aëre quidem velociter descendat, in aqua vero nec hilum quidem deorsum moveatur, cum celeritas in aëre ad celeritatem in aqua <lb ed="Favaro" n="10"></lb> nullam habeat proportionem, iam, ex ipsomet Aristotele, subtilitas aëris ad subtilitatem aquae nullam proportionem servabit: quod ridiculum est. {1}
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251 </s><s id="id.1.1.10.04.04">Patet igitur quod sit Aristoteli respondendum, cum ita argumentatur: primum, enim, falsum est, ut supra est ostensum, differentiam tarditatis et velocitatis eiusdem mobilis ex maiori aut minori crassitie et subtilitate medii provenire; quod etiam si concederetur, falsum etiam est, mobile in motibus eam servare proportionem quam mediorum subtilitates.
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252 </s></p><p><s id="id.1.1.10.05.01">Et quod eodem loco scribit AristoteIes, quod impossibile est numerum ad numerum eam habere proportionem quam numerus ad <lb ed="Favaro" n="20"></lb> nihil, verum quidem est de proportione geometrica, et non solum in numeris sed in omni quantitate.
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253 </s><s id="id.1.1.10.05.02">Cum in proportionibus geometricis necessarium sit ut minor quantitas possit toties multiplicari, ut tandem quamcunque magnitudinem excedat, oportet dictam quantitatem esse aliquid et non nihil; nihil enim semper in se multiplicatum nullam tamen quantitatem excedet.
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254 </s><s id="id.1.1.10.05.03">Attamen hoc non est necessarium in proportionibus arithmeticis: potest enim in his numerus ad numerum eam habere proportionem quam numerus ad nihil.
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255 </s><s id="id.1.1.10.05.04">Cum enim numeri illi sint in eadem arithmetica proportione cum maiorum super minoribus excessus fuerint aequales, poterit <lb ed="Favaro" n="30"></lb> profecto numerus ad numerum eandem habere proportionem quam alius numerus ad nihil: ut si dicamus, <pb ed="manuscript" n="81r"></pb>20 ad 12 est sicut 8 ad 0; <pb ed="Favaro" n="279"></pb> excessus enim 20 super 12, qui est 8, est idem cum excessu ipsius 8 super 0.
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256 </s><s id="id.1.1.10.05.05">Quare si, ut volebat Aristoteles, motus inter se eam geometrice haberent proportionem quam subtilitas ad subtilitatem, bene conclusisset quod in vacuo non contingeret motus in tempore; tempus enim in pleno ad tempus in vacuo non potest habere proportionem quam subtilitas pleni ad subtilitatem vacui, cum vacui subtilitas nulla sit: sed si celeritas ad celeritatem non geometrice sed arithmetice dictam proportionem servaret, iam nullum absurdum sequeretur.
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257 </s><s id="id.1.1.10.05.06">At certe quidem celeritas ad celeritatem eam, arithmetice, proportionem <lb ed="Favaro" n="10"></lb> servat, quam levitas medii ad medii levitatem; cum celeritas ad celeritatem se habeat, non sicut levitas medii ad medii levitatem, sed, ut demonstratum est, sicut excessus gravitatis mobilis super huius medii gravitatem ad excessum gravitatis eiusdem mobilis super alterius medii gravitatem.
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258 </s></p><p><s id="id.1.1.10.06.01">Quod quidem ut clarius appareat, ecce exemplum.
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259 </s></p></subchap2></subchap1><subchap1><subchap2><p><figure id="id.1.1.1.0.07.00" xlink:href="FIG1/F012.jpg"></figure>
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260 </p></subchap2><subchap2><p><s id="id.1.1.10.07.01">Sit mobile a, cuius gravitas sit 20; duo autem media inaequalia in gravitate sint bc, de; et moles b aequalis moli a, et moles d aequalis moli itidem a; et, quia loquimur nunc de motu deorsum qui in vacuo fit, sint media leviora mobili, et ipsius b sit gravitas 12, ipsius vero d sit gravitas 6: <lb ed="Favaro" n="20"></lb> manifestum igitur <pb ed="manuscript" n="81v"></pb>est, ex supra demonstratis, quod celeritas mobilis a in medio bc ad celeritatem mobilis eiusdem in medio de erit sicut exessus gravitatis ipsius a super gravitatem ipsius b ad excessum gravitatis ipsius a super gravitatem d, hoc est sicut 8 ad 14.
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261 </s><s id="id.1.1.10.07.02">Sit ergo celeritas a in medio bc ut 8, celeritas vero eiusdem a in medio de sit 14: {1} apparet iam celeritas 14 ad celeritatem 8 non eam geometrice servare <lb ed="Favaro" n="30"></lb> proportionem, quam levitates mediorum.
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262 </s><s id="id.1.1.10.07.03">Levitas enim medii de dupla est levitatis medii bc (cum enim gravitas b sit 12, gravitas vero d sit 6, hoc est cum gravitas b sit dupla gravitatis d, erit <pb ed="Favaro" n="280"></pb> levitas d dupla levitatis b); attamen celeritas 14 est minus quam dupla celeritatis 8.
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263 </s><s id="id.1.1.10.07.04">Sed habet certe celeritas 14 ad celeritatem 8 eandem arithmetice proportionem quam levitas d ad levitatem b; cum excessus 14 super 8 sit 6, et 6 etiam excessus levitatis d 12 super levitatem b 6.
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264 </s><s id="id.1.1.10.07.05">Quod si, rursus, medium de levius sit, ita ut gravitas ipsius d sit 5, erit iam celeritas f 15 (15 enim erit excessus gravitatis mobilis a super gravitatem medii d); et erit, rursus, celeritatis 15 ad celeritatem 8 eadem proportio quae erit gravitatis medii b 12 ad gravitatem me<pb ed="manuscript" n="82r"></pb>dii d 5, hoc est levitatis d ad levitatem b: utrinque enim excessus erit 7.
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265 </s><s id="id.1.1.10.07.06">Quod si, rursus, <lb ed="Favaro" n="10"></lb> gravitas d sit tantum 4, erit celeritas f 16; et erit celeritatis 16 ad celeritatem 8 (cuius excessus est 8) eadem itidem arithmetica proportio quae erit gravitatis b 12 ad gravitatem d 4, hoc est levitatis d ad levitatem b, quarum excessus est itidem 8.
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266 </s><s id="id.1.1.10.07.07">Quod si, rursus, medium de sit levius et gravitas d sit tantum 3, erit iam celeritas f 17; et erit celeritatis f 17 ad celeritatem 8 (cuius excessus est 9) eadem arithmetica proportio quae est gravitatis b 12 ad gravitatem d 3, hoc est levitatis d ad levitatem b.
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267 </s><s id="id.1.1.10.07.08">Quod si, rursus, medium de sit levius et sit gravitas ipsius d tantum 2, erit iam celeritas f 18; et illius proportio arithmetica ad celeritatem <lb ed="Favaro" n="20"></lb> 8 erit eadem quae est gravitatis b 12 ad gravitatem d 2, hoc est levitatis d ad levitatem b: utrinque enim excessus erit 10.
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268 </s><s id="id.1.1.10.07.09">Quod si, rursus, medium de sit levius et gravitas d sit tantum 1, erit iam celeritas f 19; quae ad celeritatem 8 eandem habebit arithmeticam proportionem, quam habet gravitas b 12 ad gravitatem d 1, hoc est levitas d ad levitatem b: utrinque enim excessus erit 11.
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269 </s><s id="id.1.1.10.07.10">Quod si, demum, gravitas d sit 0, ita ut excessus gravitatis a mobilis super medium d sit 20, erit celeritas f 20; eritque celeritatis f 20 ad celeritatem 8 eadem arithmetice proportio quae est gravitatis b 12 super gravitatem d 0: utrinque enim excessus erit 12. <lb ed="Favaro" n="30"></lb><pb ed="manuscript" n="82v"></pb>
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270 </s></p><p><s id="id.1.1.10.08.01">Patet ergo quomodo celeritas ad celeritatem, non geometrice sed arithmetice, eam servet proportionem quam medii levitas ad medii levitatem: et cum non sit absurdum, in arithmetica proportione, quantitatem ad quantitatem ita se habere sicut quantitas ad nihil, non erit <pb ed="Favaro" n="281"></pb> similiter profecto absurdum, celeritatem ad celeritatem ita arithmetice posse se habere sicut raritas ad nihil.
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271 </s><s id="id.1.1.10.08.02">Quapropter in vacuo quoque eadem ratione movebitur mobile, qua in pleno.
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272 </s><s id="id.1.1.10.08.03">In pleno enim mobile movetur celeriter secundum excessum suae gravitatis super medii, per quod movetur, gravitatem; et ita in vacuo movebitur secundum excessum suae gravitatis super vacui gravitatem: quae cum nulla sit, erit excessus gravitatis mobilis super gravitatem vacui tota ipsius mobilis gravitas; quare celeriter movebitur secundum totam suam gravitatem.
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273 </s><s id="id.1.1.10.08.04">In pleno autem nullo tam celeriter moveri poterit, cum <lb ed="Favaro" n="10"></lb> mobilis gravitatis excessus supra gravitatem medii sit minor quam tota mobilis gravitas: quare etiam minor erit celeritas, quam si secundum totam suam gravitatem moveretur.
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274 </s></p><p><s id="id.1.1.10.09.01">Ex quo manifeste colligi potest, quomodo in pleno, ut apud nos, nulla ponderantur secundum eorum propriam naturalemque gravitatem; sed semper eo erunt leviora quo in medio graviori extiterint, et erunt quidem leviora tantum quanta esset gravitas molis talis medii aequalis moli illius rei in vacuo: ita ut sphaera quidem plumbea in aqua erit tanto levior quam in va<pb ed="manuscript" n="83r"></pb>cuo, quanta est gravitas sphaerae aqueae, aequalis sphaerae plumbeae, in vacuo; et sic sphaera plumbea in aëre est tanto <lb ed="Favaro" n="20"></lb> levior quam in vacuo, quanta esset gravitas sphaerae aëreae, mole aequalis sphaerae plumbeae, in vacuo; et sic in igne, et ceteris.
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275 </s><s id="id.1.1.10.09.02">Et quia ex gravitate quam habet mobile in medio, in quo movetur, sequitur motus celeritas, eo erit celerior motus quo gravius erit idem mobile pro diversitate mediorum.
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276 </s><s id="id.1.1.10.09.03">Nec tamen valet hoc argumentum: Vacuum est medium omni pleno medio infinite levius; ergo in ipso continget motus infinite celerior quam in medio pleno; ergo in instanti.
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277 </s><s id="id.1.1.10.09.04">Nanque verum est quod vacuum infinite levius est quovis medio: nec tamen dicendum est, tale medium esse infinitae gravitatis; sed ita est intelligendum, ut possunt esse inter aëris, verbigratia, levitatem et vacuum <lb ed="Favaro" n="30"></lb> infinita media, leviora aëre, vacuo vero graviora.
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278 </s><s id="id.1.1.10.09.05">Quod si ita intelligatur, etiam inter celeritatem in aëre et celeritatem in vacuo possunt esse infinitae celeritates, maiores celeritate quae contingit in aëre, minores vero celeritate in vacuo: sic et inter gravitatem mobilis in aëre et gravitatem eiusdem in vacuo possunt esse infinitae gravitates mediae, maiores quidem gravitate in aëre, minores vero <pb ed="Favaro" n="282"></pb> gravitate in medio.
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279 </s></p></subchap2></subchap1><subchap1><subchap2><p><figure id="id.1.1.1.0.10.00" xlink:href="FIG1/F013.jpg"></figure>
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280 </p></subchap2><subchap2><p><s id="id.1.1.10.10.01">Et hoc contingit in omni continuo: ut inter lineas a, b, quarum a maior, possunt esse infinitae lineae mediae, minores quidem a, maiores vero d (cum enim excessus, quo a superat b, sit linea, erit infinite divisibilis): non tamen dicen<pb ed="manuscript" n="83v"></pb>dum est, lineam a infinite excedere lineam b, ita ut, etiam si b infinite multiplicetur, non componat tandem lineam maiorem ipsa a.
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281 </s><s id="id.1.1.10.10.02">Et ita, pari ratione, si intelligamus a esse celeritatem in vacuo, b vero celeritatem in aëre, poterunt quidem esse inter a et b infinitae celeritates, maiores quam b et minores quam a: nec tamen concludendum erit, a infinite <lb ed="Favaro" n="10"></lb> excedere ipsam b, ita ut tempus in suo fit celeritas a, in se quantumlibet multiplicatum, nunquam tamen possit excedere tempus celeritatis b, et, ideo, celeritas temporis a sit instantanea.
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282 </s><s id="id.1.1.10.10.03">Patet ergo quomodo intelligendum sit: Levitas vacui infinite excedit levitatem medii, ergo celeritas in vacuo infinite excedet celeritatem in pleno.
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283 </s><s id="id.1.1.10.10.04">Conceditur totum.
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284 </s><s id="id.1.1.10.10.05">Ergo celeritas in vacuo erit in instanti, negatur.
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285 </s><s id="id.1.1.10.10.06">Potest enim esse in tempore, sed breviori quidem quam tempus celeritatis in pleno; ita ut inter tempus in pleno et tempus in vacuo possint infinita tempora intercedere, hoc quidem maiora, illo vero minora: et ita non est necessarium, motum in vacuo <lb ed="Favaro" n="20"></lb> fieri in instanti, sed in tempore minori quam sit tempus motus in quovis pleno.
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286 </s></p></subchap2></subchap1><subchap1><subchap2><p><figure id="id.1.1.1.0.11.00" xlink:href="FIG1/F014.jpg"></figure>
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287 </p></subchap2><subchap2><p><s id="id.1.1.10.11.01">Quare, ut uno verbo dicam, hoc totum est meum intentum: ut si sit grave a, cuius gravitas propria et naturalis sit 1000, huius in quovis medio pleno gravitas minor erit quam mille, et, ideo, celeritas sui motus in quocunque pleno minor erit quam <pb ed="manuscript" n="84r"></pb>mille.
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288 </s><s id="id.1.1.10.11.02">Ut si intelligamus medium, cuius tantae molis, quanta est moles a, gravitas sit tantum 1, erit in hoc medio gravitas a 999; quare etiam sua celeritas 999: et solum celeritas ipsius d erit mille in medio ubi illius gravitas sit mille; et hoc nullibi erit nisi in vacuo. <lb ed="Favaro" n="30"></lb>
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289 </s></p><p><s id="id.1.1.10.12.01">Haec est solutio argumenti Aristotelis: ex qua satis intelligi potest, quomodo in vacuo nullo pacto requiratur motus instantaneus.
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290 </s><s id="id.1.1.10.12.02">Cetera argumenta Aristotelis nullius sunt roboris et nullam habent necessitatem.
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291 </s><s id="id.1.1.10.12.03">Nam dicere, exempli gratia, in vacuo non magis huc quam illuc, aut sursum quam deorsum, movebitur mobile, quia non magis versus sursum quam deorsum cedit vacuum sed undique aequaliter, puerile <pb ed="Favaro" n="283"></pb> est: nam hoc idem dicam de aëre; cum enim lapis est in aëre, quomodo magis cedit deorsum quam sursum, aut sinistrorsum quam dextrorsum, si aëris ubique eadem est raritas?
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292 </s><s id="id.1.1.10.12.04">Hic diceret forsan aliquis, ex Aristotele, aërem gravare in sua regione, et ob id magis iuvare motum deorsum: sed has chimaerulas capite sequenti examinabimus, ubi inquiremus utrum elementa in proprio loco gravitent.
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293 </s><s id="id.1.1.10.12.05">Similiter etiam cum dicunt, In vacuo non est neque sursum neque deorsum; quis hoc somniavit?
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294 </s><s id="id.1.1.10.12.06">Nonne, si vacuus esset aër, vacuum prope terram esset centro propinquius vacuo quod esset prope ignem?
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295 </s><s id="id.1.1.10.12.07">Argumentum <lb ed="Favaro" n="10"></lb> etiam quod facit Aristoteles de proiectis, dicens: Proiecta in vacuo non possunt moveri, nam proiecta, cum extra manum moventis sunt, moventur ab aëre vel alio medio corporeo circumambiente et moto, quod quidem desideratur in vacuo; <pb ed="manuscript" n="84v"></pb>similiter nullius est momenti: ponit enim proiecta a medio vehi; quod quidem falsum esse, suo loco demonstrabimus.
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296 </s><s id="id.1.1.10.12.08">Falsum similiter quod addit argumento, de diversis mobilibus in eodem medio: ponit, enim, in pleno quidem graviora velocius ferri, quod fortius scindant medium, et hanc solam esse celeritatis causam; quae resistentia cum in vacuo non sit, inducit motus omnes futuros esse in vacuo in eodem tempore et eadem cum <lb ed="Favaro" n="20"></lb> celeritate: quod quidem impossibile esse asserit.
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297 </s><s id="id.1.1.10.12.09">Et, primo, Aristoteles peccat in hoc, quod non ostendit quomodo absurdum sit, in vacuo diversa mobilia eadem celeritate moveri: sed magis peccat cum ponit, motuum celeritates diversorum mobilium ex eo pendere, quod graviora mobilia melius medium dividant.
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298 </s><s id="id.1.1.10.12.10">Non enim ex hoc spectanda est mobilium celeritas, ut supra demonstratum est, sed ex maiori excessu gravitatis mobilium super gravitatem medii; celeritates enim talium excessuum proportionem secuntur: sed diversorum mobilium gravitatis non idem est excessus super eiusdem medii gravitatem (essent enim mobilia aeque gravia): quare nec celeritates erunt aequales.
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299 </s><s id="id.1.1.10.12.11">Ut <lb ed="Favaro" n="30"></lb> mobilis, cuius gravitas est 8, super gravitatem vacui, quae nulla est, excessus est 8; quare 8 erit celeritas: mobilis vero, cuius gravitas est 4, excessus super vacuum similiter erit 4; quare et illius celeritas 4.
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300 </s><s id="id.1.1.10.12.12">In vacuo demum eadem demonstratione utentes quam in <pb ed="Favaro" n="284"></pb> pleno posuimus; demonstrabimus, mobilia specie eadem, mole vero diversa, eadem celeritate moveri in vacuo.
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301 </s><s id="id.1.1.10.12.13">Et de hoc satis.<pb ed="manuscript" n="85r"></pb>
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302 </s></p><p><s id="id.1.1.10.13.01">Tanta {1} est veritatis vis, ut doctissimi etiam viri et Peripatetici huius sententiae Aristotelis falsitatem cognoverint, quamvis eorum nullus commode Aristotelis argumenta diluere potuerit.
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303 </s><s id="id.1.1.10.13.02">Nec certe ullus unquam argumentum, quod 4Á Phys. t. 71 et 72 scribitur, evertere potuit: nunquam enim adhuc illius fallacia observata fuit; et quamvis Scotus, D. Thomas, Philoponus et alii nonnulli contrariam Aristoteli teneant sententiam, attamen veritatem fide potius quam vera demonstratione, aut quod Aristoteli responderint, sunt consecuti. <lb ed="Favaro" n="10"></lb>
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304 </s><s id="id.1.1.10.13.03">Et, quidem, nullus sit qui speret posse se Aristoteli respondere et illius demonstrationem evertere, si eam proportionem concedat, quae ab eo ponitur inter velocitates eiusdem mobilis in diversis mediis.
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305 </s><s id="id.1.1.10.13.04">Ponit enim, ita se habere velocitatem in uno medio ad velocitatem in alio, sicut subtilitas unius medii ad subtilitatem in altero: hanc nullus hucusque negare ausus est.
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306 </s><s id="id.1.1.10.13.05">Nec quicquam roboris habet quod a praedictis ponitur, nempe duplex: illa resistentia mobilis ad motum: altera, scilicet, extrinseca, proveniens ex medii crassitie; altera vero intrinseca, ratione determinatae gravitatis mobilis.
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307 </s><s id="id.1.1.10.13.06">Hoc enim fictitium quiddam est: non enim, si accurate consideremus, differunt inter se istae <lb ed="Favaro" n="20"></lb> duae resistenstiae.
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308 </s><s id="id.1.1.10.13.07">Ut enim supra declaratum est, crassities seu (ut rectius loquar) gravitas medii facit levitatem mobilis, et medii levitas mobilis gravitatem praestat; et idem mobile modo gravius modo levius est, prout in leviori vel graviori medio erit.
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309 </s><s id="id.1.1.10.13.08">Nihil igitur addunt novi, ponentes duplicem illam resistentiam; cum tantummodo augeatur et minuatur pro decremento vel incremento gravitatis vel crassitiei medii.
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310 </s><s id="id.1.1.10.13.09">Quod si rursus concedant, augeri et minui in ea proportione in qua gravitates medii variantur, frustra tentabunt Aristotelis argumentum evertere.
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311 </s></p></subchap2><subchap2><p><s id="id.1.1.11.01.01">Methodus quam in hoc tractatu servabimus ea erit, ut semper dicenda ex dictis pendeant; nec unquam (si licebit) declaranda supponam tanquam vera.
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312 </s><s id="id.1.1.11.01.02">Quam quidem methodum mathematici mei me docuere: nec satis quidem a philosophis quibusdam servatur, qui saepius, physica elementa docentes, ea quae seu ill libris De anima, seu in libris De caelo, quin et in Metaphysicis, tradita, supponunt; nec etiam <lb ed="Favaro" n="10"></lb> hoc sufficit, sed etiam, docentes logicam ipsam, continue ea in ore habent quae in ultimis Aristotelis libris tradita sunt; ita ut, dum discipulos prima docent, supponunt eos omnia scire, doctrinamque tradunt non ex notioribus, verum ex ignotis simpliciter et inauditis.
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313 </s><s id="id.1.1.11.01.03">Accidit autem ita addiscent<pb ed="manuscript" n="85v"></pb>ibus, ut nunquam quicquam per causas sciant, sed tantum ut fide credant, quia, nempe, hoc dixerit Aristoteles.
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314 </s><s id="id.1.1.11.01.04">Utrum deinde verum sit quod dixerit Aristoteles, pauci sunt qui quaerant: sufficit enim his, quod eo doctiores habebuntur, quo plures Aristotelis locos prae manibus habebunt.
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315 </s><s id="id.1.1.11.01.05">Sed, his omissis, ad propositum revertentes, videndum est, utrum aër et aqua vere in propriis <lb ed="Favaro" n="20"></lb> locis habeant gravitatem: haec enim quaestio, solis his quae tradita sunt suppositis, explicari potest.
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316 </s></p><p><s id="id.1.1.11.02.01">Aristoteles, nedum aquam in proprio loco gravem esse, verum etiam aërem, scripsit 4 Caeli t. 30; dicens, in sua regione omnia gravitatem habere praeter ignem, aërem etiam ipsum.
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317 </s><s id="id.1.1.11.02.02">De aëre autem statim probat a signo; dicens, quia magis trahit uter inflatus quam non inflatus, signum igitur aërem in utre habere gravitatem.
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318 </s><s id="id.1.1.11.02.03">Hoc idem repetit t. 39 eiusdem libri, inquiens, in sua regione unumquodque eorum, quae gravitatem habent ac levitatem, gravitatem habere: ponit enim, aërem et aquam in relatione quidem ad alia <lb ed="Favaro" n="30"></lb> elementa nunc esse gravia nunc quidem levia, sed absolute et in propria regione gravare tantum.
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319 </s><s id="id.1.1.11.02.04">Quidam vero recentiores philosophi, animadvertentes id quod Aristoteles scripsit 3Á Caeli t. 28, nempe aërem utrumque motum iuvare; quatenus, scilicet, levis est, iuvare motum <pb ed="Favaro" n="286"></pb> sursum, quatenus vero gravis, motum deorsum; aliud argumentum efformarunt, dicentes: Aër magis iuvat motum deorsum, quia facilius fert gravia deorsum, quam motum sursum, quia difficilius fert levia sursum.
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320 </s><s id="id.1.1.11.02.05">Conclu<pb ed="manuscript" n="86r"></pb>serunt, aërem necessario gravem esse censendum in regione sua.
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321 </s><s id="id.1.1.11.02.06">Hoc tamen omnino falsum esse, mox innotescet: et demonstrabimus, aërem et aquam in regione sua nec gravia esse nec levia; {1} demonstrabimus deinde, recentiorum philosophorum argumentum oppositum simpliciter concludere ei quod ipsi probare contendunt, nec potuisse illos argumentum invenire quod magis sibi contrariaretur. <lb ed="Favaro" n="10"></lb>
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322 </s></p><p><s id="id.1.1.11.03.01">Et, primo quidem, omnino inexcogitabile videtur, quomodo aër et aqua in proprio loco gravitent.
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323 </s><s id="id.1.1.11.03.02">Nanque aliqua pars aquae in loco aëris, hoc est in aëre ipso, gravitat, et deorsum quidem fertur quia gravitat; sed quis unquam mente concipiet, aliquam partem aquae in aqua descendere?
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324 </s><s id="id.1.1.11.03.03">Si enim descendet, quando erit in fundo, necesse est ut locus, in quem intrat, iam evacuetur ab alia aqua, quae coacta erit ascendere unde alia recessit; et sic iam illa pars aquae erit levis in proprio loco.
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325 </s><s id="id.1.1.11.03.04">2Á, Si aliqua pars aquae in aqua est gravis, vocetur, verbigratia, a: quia ergo pars aquae a in aqua est gravis et descendit, si accipiamus aliam aquae partem quae in mole aequetur ipsi a, <lb ed="Favaro" n="20"></lb> necessario a gravior erit quam altera pars aquae; et sit aqua erit gravior quam aqua: quo quid ineptius excogitari potest?
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326 </s><s id="id.1.1.11.03.05">Ad exemplum autem Aristotelis de utre, respondeo quod, si foramen utris seu follis inflati sit apertum, ita ut aër, non vi compressus, in folle detineatur, non erit iam uter gravior quam non inflatus: sed si vi multum aëris in eo comprimatur, <pb ed="manuscript" n="86v"></pb>cui dubium erit quod gravitabit?
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327 </s><s id="id.1.1.11.03.06">Aër enim tunc, vi constrictus, gravior est aëre libero et vaganti: sicut si uter lana repleatur, deinde vero alterum tantum lanae superaddatur, vi comprimendo, quis anceps erit an gravior fiet uter necne?
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328 </s></p></subchap2></subchap1><subchap1><subchap2><p><figure id="id.1.1.1.1.04.00" xlink:href="FIG1/F015.jpg"></figure>
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329 </p></subchap2><subchap2><p><s id="id.1.1.11.04.01">Pari ratione, si, verbigratia, intelligamus partem aëris in qua <lb ed="Favaro" n="30"></lb> sit a, aliam vero partem aëris, in qua b, esse duplam ipsius a, tunc aër b in loco ignis, verbigratia, duplo gravior erit aëre a: si ergo {2} aër b vi <pb ed="Favaro" n="287"></pb> coarctetur, ita ut fiat moles aequalis moli a, erit iam aër b quodammodo alia aëris species gravior quam sit aër a; quid ergo mirum si aër b in aëre, cuius pars est a, descendet?
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330 </s><s id="id.1.1.11.04.02">Patet igitur ratio cur uter inflatus magis trahat: aër enim qui in ipso est, gravior est aëre circumfuso, eo quod in angustiori loco plus eiusdem materiae compraehendat.
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331 </s><s id="id.1.1.11.04.03">Manifestum itaque est, nullius esse roboris argumentum de utre; cum, volens ostendere aërem liberum et rarum, ut sua est natura, gravem esse, in exemplo deinde assumat aërem vi condensatum et in angusto loco compressum.
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332 </s></p><p><s id="id.1.1.11.05.01"><lb ed="Favaro" n="10"></lb> Ad argumentum deinde dicentium, aërem ideo esse gravem quia facilius fert gravia deorsum quam levia sursum, respondeo, formam istam argumentandi esse ex diametro contra argumentantes.
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333 </s><s id="id.1.1.11.05.02">Si enim illud medium grave existimandum est quod facilius fert gravia deorsum, aër erit iam gravior aqua: ea enim quae deorsum feruntur, facilius et citius de<pb ed="manuscript" n="87r"></pb>scendunt in aëre quam in aqua.
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334 </s><s id="id.1.1.11.05.03">Adde: supra demonstratum est, gravia quae in aqua deorsum feruntur, tanta vi descendere, quanto eorum gravitas gravitatem molis aquae eorum moli aequalis excedit.
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335 </s></p></subchap2></subchap1><subchap1><subchap2><p><figure id="id.1.1.1.1.06.00" xlink:href="FIG1/F016.jpg"></figure>
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336 </p></subchap2><subchap2><p><s id="id.1.1.11.06.01">Si ergo fuerit corpus aliquod grave, ut, verbigratia, corpus in quo a, cuius gravitas sit 8, gravitas autem <lb ed="Favaro" n="20"></lb> aquae b, cuius moles aequetur moli a, sit 4, tunc solidum a in aqua feretur deorsum ita celeriter et facile ut 4; si vero deinde idem corpus ferretur per medium levius quam medium b, ita ut talis medii tanta moles quanta est moles ipsius b haberet tantum 3 gravitatis, tunc a in tali medio moveretur ita celeriter et facile ut 5.
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337 </s><s id="id.1.1.11.06.02">Patet, igitur, quod idem corpus a facilius deorsum movetur per media leviora quam per graviora: ergo necessario sequitur, quod medium eo levius existimandum sit, quo gravia in eo facilius deorsum moventur; cuius contrarium ipsi affirmabant.
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338 </s><s id="id.1.1.11.06.03">Cui igitur iam non apertissimum est <lb ed="Favaro" n="30"></lb> quod, si aër adhuc levior esset, gravia deorsum facilius moverentur?
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339 </s><s id="id.1.1.11.06.04">Quod si sic est, sequitur, aërem ideo levem esse, quia gravia in eo facile deorsum feruntur.
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340 </s><s id="id.1.1.11.06.05">Opposito autem modo de levibus ratiocinantes, colligemus, medium illud grave existimandum esse, per quod levia facilius sursum feruntur; illud vero leve, per quod levia difficile ascendunt.
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341 </s><s id="id.1.1.11.06.06">Ergo, tum quia in aëre levia difficilius sursum moventur, tum quia in eodem gravia facilius deorsum moventur, sequitur aërem <pb ed="Favaro" n="288"></pb> magis levem quam gravem esse existimandum.
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342 </s><s id="id.1.1.11.06.07">Sed hoc solum concludam <pb ed="manuscript" n="87v"></pb>eorum modo argumentando; qui si bonus erit, videant ipsi quid colligatur: attamen dixerim ego, elementa in propriis locis nec gravia esse nec levia.
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343 </s><s id="id.1.1.11.06.08">Si enim pars aquae in aqua esset gravis, descenderet; quod non facit: et si gravis esset, quomodo, in profundo natantes, vastissimae molis aquae gravitatem non sentiremus?
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344 </s><s id="id.1.1.11.06.09">Ad hoc responderent ipsi: quia partes aquae super partes haerent, sicut lateres muri super lateribus incumbunt; unde, dicunt, accidit, murem existentem in muro lapidum pondus non sentire. {1}
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345 </s><s id="id.1.1.11.06.10">Quae quidem comparatio non satis accommodata videtur.
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346 </s><s id="id.1.1.11.06.11">Primo, enim, comparant aquam <lb ed="Favaro" n="10"></lb> fluidam et labentem muro solido et consistenti: deinde, quod lateres non super humerum muris consistant, signum est, quod, ablato mure, remanet foramen ubi erat mus, nec in eo lateres labuntur; sed, ablato pisce aut homine ex aqua, non remanet locus ubi erat homo, sed statim ab aqua repletur, quod indicat, aquam inniti super pisces aut homines.
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347 </s><s id="id.1.1.11.06.12">Quomodo ergo solvetur problema, nisi dicamus, aquam et aërem non gravare in suis regionibus?
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348 </s><s id="id.1.1.11.06.13">Ita ut talis sit tota problematis explicatio: tunc dicimur gravari, quando super nos incumbit aliquod pondus quod sua gravitate deorsum tendit, nobis autem opus est nostra vi resistere ne amplius descendat; illud autem resistere est <lb ed="Favaro" n="20"></lb> quod gravari appellamus.
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349 </s><s id="id.1.1.11.06.14">At quia demonstratum est, corpora quae sunt aqua graviora, in aquam <pb ed="manuscript" n="88r"></pb>demissa, descendere, et esse in aqua gravia quidem, attamen minus gravia quam in aëre; leviora autem aqua ostensa sunt, vi sub aquam impulsa, sursum attolli; quae vero sunt aeque gravia ac aqua neque sursum neque deorsum ferri, sed ibi manere ubi collocantur, dummodo tota fuerint sub aqua; ex hoc patet quod si nobis sub aqua existentibus incumbat aliquod corpus aqua gravius, ut lapis, gravabimur quidem, sed minus quam si essemus in aëre, quia lapis in aqua est minus gravis quam in aëre: si vero nobis in aqua manentibus corpus aqua levius alligatum fuerit, <lb ed="Favaro" n="30"></lb> nedum gravabimur, verum etiam attollemur ab illo; ut patet in natantibus cum cucurbita, cum alioquin, in aëre existentes, a cucurbita gravemur; et hoc quia cucurbita in aquam impulsa fertur sursum et allevat, in aëre vero fertur deorsum et gravat: si autem in aqua existentibus aliquod corpus aeque grave ac aqua nobis immineat, neque <pb ed="Favaro" n="289"></pb> ab illo gravabimur neque attollemur, quia neque sursus neque deorsum tale corpus feretur.
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350 </s><s id="id.1.1.11.06.15">At non invenitur corpus aliquod, quod magis aquae in gravitate aequetur quam ipsamet aqua: non ergo mirum est si aqua in aqua non descendat et gravet; diximus enim, gravari esse resistere nostra vi corpori deorsum petenti.
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351 </s><s id="id.1.1.11.06.16">Et eadem prorsus ratio de aere habenda est.
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352 </s></p><p><s id="id.1.1.11.07.01">Haec, meo iudicio, quicquid dicant alii, est vera problematis explicatio.
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353 </s><s id="id.1.1.11.07.02">Cum igitur nec aër nec aqua deorsum in suis <pb ed="manuscript" n="88v"></pb>regionibus ferantur neque sursum, ne dicantur esse aut gravia aut levia; cum <lb ed="Favaro" n="10"></lb> gravia definiantur ea esse quae deorsum feruntur, levia vero quae sursam.
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354 </s><s id="id.1.1.11.07.03">Et cum de motu loquimur, semper non solum gravitatis aut levitatis mobilis, sed gravitatis et levitatis medii etiam, ratio est habenda: non grave deorsum movebitur, nisi medio per quod ferri debet gravius erit; nec leve ascendet, nisi levius fuerit medio per quod movetur.
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355 </s><s id="id.1.1.11.07.04">Quod cum ita sit, aqua non descendet in aqua, cum aqua gravior non sit quam aqua; et cum non descendat, non erit aqua in aqua grans.
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356 </s><s id="id.1.1.11.07.05">Quod si, non ut consideravit Aristoteles, sed per se, simpliciter et absolute, nullo habito respectu, quaëratur utrum elementa gravia sint, respondemus, nedum aquam aut terram aut <lb ed="Favaro" n="20"></lb> aërem, verum etiam et ignem, et si quid igne sit levius, gravitatem habere, et demum onmia quae cum substantia quantitatem et materiam habeant coniunctam.
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357 </s><s id="id.1.1.11.07.06">Sed quia hic contrariatur Aristoteles, ponens simpliciter leve quod nullibi gravat, examinandam iudicamus esse talem opinionem: quod quidem capite sequenti exequemur.
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358 </s></p></subchap2><subchap2><p><s id="id.1.1.12.01.01">Grave et leve non nisi in comparatione ad minus gravia vel levia <lb ed="Favaro" n="30"></lb> considerarunt qui ante Aristotelem; et hoc quidem, meo iudicio, iure optimo: Aristoteles autem, 4 Caeli, opinionem antiquorum confutare nititur, suamque huic contrariam confirma<pb ed="manuscript" n="89r"></pb>re.
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359 </s><s id="id.1.1.12.01.02">Nos autem, antiquorum <pb ed="Favaro" n="290"></pb> in hoc opinionem secuturi, tum Aristotelis confutationes, tum etiam suas confirmationes, examinabimus, confutationes quidem confirmando, confirmationes vero confutando; et hoc quidem tunc praestabimus, cum Aristotelis opinionem exposuerimus.
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360 </s></p><p><s id="id.1.1.12.02.01">Definit itaque, primo, Aristoteles, illud se appellare gravissimum simpliciter, quod omnibus substat et semper ad medium fertur; levissimum vero appellat id, quod omnibus supereminet et semper sursum, nunquam vero deorsum, movetur: et haec scribit 4 Caeli t. 26 et 31.
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361 </s><s id="id.1.1.12.02.02">Dicit deinde, gravissimum esse terram, et levissimum ignem; et hoc t. 32 et aliis in locis.
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362 </s><s id="id.1.1.12.02.03">Tunc, contra ponentes in igne aliquam <lb ed="Favaro" n="10"></lb> gravitatem, sic argumentatur: Si ignis habet aliquam gravitatem, ergo alicui substabit; at hoc non videtur; ergo [etc.]. {1}
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363 </s><s id="id.1.1.12.02.04">Argumentum hoc non concludit.
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364 </s><s id="id.1.1.12.02.05">Nam ad hoc ut aliquid alicui immineat, sufficit ut eo, cui imminere debet, sit minus grave; non autem necesse est, ut omni gravitate careat: sicut ad hoc ut lignum aquae supernatet, non requiritur necessario ut lignum omni gravitate careat, sed satis est ut sit aqua minus grave; et ita, pari ratione, ad hoc ut ignis aëri immineat, sat est quod aëre sit minus gravis, nec est necessarium ut omni careat gravitate.
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365 </s><s id="id.1.1.12.02.06">Quare patet, nullam necessitatem habere hoc argumentum. <lb ed="Favaro" n="20"></lb>
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366 </s></p><p><s id="id.1.1.12.03.01">Argumentatur etiam hoc pacto: Si ignis aliquam habet gravitatem, ergo multus ignis gravior erit pauco; quare tardius ascendet multum ignis in aëre quam paucum: et ira, si terra habet aliquam levitatem, multum terrae, quod plus habebit levitatis, tardius descendet quam pauca terra: experientia tamen contrarium <pb ed="manuscript" n="89v"></pb>ostendit; videmus enim, multum ignem citius ascendere pauco, sicut et multam terram citius descendere: signum ergo est quod in igne est tantum levitas; et cum in multo igne plus sit levitatis, citius ascendit.
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367 </s><s id="id.1.1.12.03.02">Hoc quoque argumentum infirmum est.
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368 </s><s id="id.1.1.12.03.03">Et, primo quidem, limites transcendit. {2}
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369 </s><s id="id.1.1.12.03.04">Non enim valet consequentia, Si ignis absolute consideratus habet gravitatem, ergo <lb ed="Favaro" n="30"></lb> <pb ed="Favaro" n="291"></pb> multum ignis in aëre gravius erit pauco: ignis enim in aëre nullam habet gravitatem.
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370 </s><s id="id.1.1.12.03.05">Sed ita est argumentandum: Ignis, absolute consideratus, habet gravitatem: ergo ubi ignis habet gravitatem, multum ignis multam habebit gravitatem; et ubi ignis habet levitatem, ut in aëre, ibi multum ignis multam habebit levitatem, paucum vero paucam.
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371 </s><s id="id.1.1.12.03.06">Constat ergo Aristotelis fallacia in argumentando.
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372 </s><s id="id.1.1.12.03.07">2Á: falsum est quod asserit, nempe, multum ignem citius ascendere quam paucum, aut multam terram velocius descendere quam paucam; ut supra: demonstravimus.
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373 </s></p><p><s id="id.1.1.12.04.01"><lb ed="Favaro" n="10"></lb> 3Á, argumentatur: Si ignis habet gravitatem, erit iam multum ignis pauco aëre gravius: quod quidem pro absurdo maximo ponit, sicut si dicamus, si terra habet levitatem aliquam, erit aliqua pars terrae levior aliqua parte aquae: quod falsum inquit esse, quia videmus, quamlibet terrae particulam sub aquam descendere, et quamlibet ignis portionem in aëre sursum ferri.
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374 </s><s id="id.1.1.12.04.02">Quod quidem argumentum magis infirmum est ceteris omnibus quis autem est adeo stultus, ut non credat, multum aquae gravius esse pauca terra, et multum aëris pauca aqua, et multum ignis pauco aëre?
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375 </s><s id="id.1.1.12.04.03">Neque obstat quod dicit Aristoteles: Videmus terram in aqua descendere.
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376 </s><s id="id.1.1.12.04.04">Nam, <lb ed="Favaro" n="20"></lb> cum haec dicit, iam non sibi constat: nanque, cum dicimus aquam habere gravitatem, non dicimus <pb ed="manuscript" n="90r"></pb>habere gravitatem in sua regione, ubi, ut demonstratum est, nullam habet aut gravitatem aut levitatem; sed dicimus, multum aquae gravius esse pauca terra in loco ubi aqua etiam habeat gravitatem, ut, verbigratia, in aëre.
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377 </s><s id="id.1.1.12.04.05">Nam si valeret illa argumentandi ratio, concluderem etiam, paucum plumbi gravius esse maxima trabe, quia plumbum in aqua descendit, trabes autem non: at verum quidem est quod plumbi paucum gravius est trabe in loco ubi trabes nullam habeat gravitatem; sed si volumus loqui de gravitate trabis, oportet ponere trabem in loco ubi habeat <lb ed="Favaro" n="30"></lb> gravitatem.
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378 </s><s id="id.1.1.12.04.06">Similiter, cum dicit, Quaelibet particula aquae in aëre descendit, ergo quantumvis aëris levius est particuIa aquae; hoc verum erit in eo loco, ubi aër nullam habet gravitatem, aqua vero habet: sed hoc non erit loqui de gravitate absoluta, ut loquimur.
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379 </s><s id="id.1.1.12.04.07">Nanque, si ponamus multum aëris in loco ubi aër etiam gravet, ut in igne aut vacuo, ibi profecto gravius erit pauca aqua.
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380 </s><s id="id.1.1.12.04.08">Neque concludatur, Ergo velocius descendet: qui enim ita concluderet, <pb ed="Favaro" n="292"></pb> ostenderet se ignorare, unde tarditas et velocitas motus oriatur.
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381 </s><s id="id.1.1.12.04.09">Non enim valet, Saccus stuppa confertus in aëre gravior est pauco plumbo, ergo in aëre citius descendet: stultus enim non haec diceret, nec ullus qui quae supra dicta sunt intellexerit.
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382 </s><s id="id.1.1.12.04.10">Sic de igne est ratiocinandum: multum enim ignis gravius erit pauco aëre; non tamen in aëre, ubi ignis nullam habet gravitatem, sed in alio loco ubi ignis quoque gravet, ut esset in vacuo aut in medio levi<pb ed="manuscript" n="90v"></pb>ori quam sit ignis.
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383 </s></p><p><s id="id.1.1.12.05.01">Hic mehercule taedet et pudet, quod verba sint iactanda ad solvenda tam puerilia argumenta tanquam crassas subtilitates, quales illae sunt, quas, contra antiquos, toto 4 Caeli inculcat Aristoteles: <lb ed="Favaro" n="10"></lb> nihil enim roboris, nihil doctrinae, nihil concinnitatis aut venustatis habentes, et quarum fallacias quisque cognoscet, si quae supra dicta sunt intellexerit.
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384 </s><s id="id.1.1.12.05.02">Sicut cum dicit, Videmus terram omnibus substrare, ignem vero superesse; oportet, Aristotelem habuisse Lyncei oculos, si vidit utrum in visceribus terrae sit aliquid quod terra sit gravius necne, et an super ignem sit aliquod corpus levius.
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385 </s><s id="id.1.1.12.05.03">Sed, absque Lyncei oculis, caecus videre poterit, multa esse terra graviora, ut metalla omnia, quibus liquefactis terra supernatat, ut ipsi argento, quod dicunt, vivo; et non solum est argento vivo levior terra, sed plusquam decies levior.
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386 </s><s id="id.1.1.12.05.04">Quomodo ergo metalla accipiunt gravitatem suam a terra, si <lb ed="Favaro" n="20"></lb> quam terra longe sunt graviora; cum tamen, si ex terra, aqua, aëre et igne constarent, longe leviora esse deberent quam sola terra?
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387 </s><s id="id.1.1.12.05.05">Patet ergo, multa esse terra graviora.
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388 </s><s id="id.1.1.12.05.06">Cum ergo dicit: Duo sunt loca contraria, medium et extremum, accipiens pro extremo lunae concavum; ergo oportet, quae in illis sunt esse contraria; quod non erit, nisi terra ponatur omni carens levitate, ignis vero ab omni gravitate vacuus: argumentum nullam habet necessitatem; quam etiam si haberet, centro contrariatur etiam eodem pacto concavum aquae et aër, sicut concavum xxx; nec, tamen, quae sub concavo aëris sunt, omni carent gravitate. {1}
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389 </s><s id="id.1.1.12.05.07">Quod vero <pb ed="manuscript" n="91r"></pb>de levitate ignis scribit, dicens quod, si submoveatur <lb ed="Favaro" n="30"></lb> aër, ignis non descendet, ut aër submota aqua, demonstratione indiget: quod non probavit Aristoteles, nisi dicas quod dixerit, Sicut terra non ascendit in medicorum cucurbitulis quia gravissima est, ita ignis non descendet quia levissimus.
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390 </s><s id="id.1.1.12.05.08">Sed non valet proportio: quia, non quod <pb ed="Favaro" n="293"></pb> terra sit gravissima, non ascendit, sed quia non est fluida; nam neque lignum ascenderet, cum tamen sit levius aqua, quae ascendit; ascenderet tamen mercurius, quamvis terra gravior, quia fluidus; et sic ignis descenderet, quia non solidus sed fluens habetur. {1}
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391 </s><s id="id.1.1.12.05.09">Sed, amabo, si elementa, ut ipse vult, ad invicem transmutantur, quando ex aëre gravi fit ignis, quid de illa gravitate aëris?
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392 </s><s id="id.1.1.12.05.10">An forsan adnihilatur?
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393 </s><s id="id.1.1.12.05.11">Sed, si adnihilatur, cum rursus ex igne fit terra, unde manat gravitas? an forsan gravitas, quae aliquid est, eg non gravitate, quae nihil est?
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394 </s><s id="id.1.1.12.05.12">Sed amplius: si ignis omni caret gravitate, ergo et omni <lb ed="Favaro" n="10"></lb> densitate carebit; densum enim consequitur grave: sed quod omni caret densitate, id vacuum est: ergo ignis vacuum.
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395 </s><s id="id.1.1.12.05.13">At quid absurdius?
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396 </s><s id="id.1.1.12.05.14">Sed, demum, quomodo unquam poterit quis ignem imaginari substanitiam cum quantitate coniunctam gravitatem non habere?
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397 </s><s id="id.1.1.12.05.15">Hoc profecto omnino irrationabile videtur.
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398 </s><s id="id.1.1.12.05.16">Et cum dicimus, terram omnium esse gravissimam, quia omnibus substat, cogimur, velimus nolimus, dicere terram ideo esse gravissimam, respectu aliorum, quia omnibus substat.
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399 </s><s id="id.1.1.12.05.17">Substare enim omnibus et omnium esse gravissimum, idem sunt: et hoc patet; quia, si gravissimum <pb ed="manuscript" n="91v"></pb>est quod omnibus substat, si omnia auferantur, non poterit amplius gravissimum dici, cum nulli <lb ed="Favaro" n="20"></lb> substet.
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400 </s><s id="id.1.1.12.05.18">Dicitur ergo gravissimum in comparatione minus gravium, quibus substat; et idem de levitate ignis dicendum est.
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401 </s><s id="id.1.1.12.05.19">Concludimus igitur, non posse aliquid dici gravissimum nulla habita ratione aliorum quae minus gravia sunt, cum gravissimum non possit definiri aut mente concipi nisi quatenus minus gravibus substat; et, ita, levissimum non posse dici nisi in comparatione ad minus levia, quibus supereminet; nec corpus levissimum esse id quod omni careat gravitate, hoc enim est vacuum non corpus aliquod, sed id quod illis, quae habent gravitatem, est minus grave.
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402 </s><s id="id.1.1.12.05.20">Nec tamen dixerim, non inveniri in rerum natura aliquid quod omnibus sit gravius, et aliquid <lb ed="Favaro" n="30"></lb> quod omnibus sit levius, hoc est minus grave; sed solum haec duo negamus, id posse considerari absolute, non habita ratione aliorum, et, etiam, talia esse terram et ignem.
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403 </s><s id="id.1.1.12.05.21">Multa enim sunt graviora quam <pb ed="Favaro" n="294"></pb> terra, quae quidem videmus: et possent etiam esse aliqua igne leviora, ut exhalationes aliquae, quae super ignem advolarent; sed hoc non possumus audacter affirmare, quia super ignem non fuimus.
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404 </s><s id="id.1.1.12.05.22">Quod si ignis est, non tamen omni caret gravitate; hoc enim vacui est: quare etiam ignis, si submoveatur aër, descendet, si vacuum sub ipso relinquatur aut aliquod aliud medium igne levius.
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405 </s><s id="id.1.1.12.05.23">Descendunt enim omnia, <pb ed="manuscript" n="92r"></pb>dummodo medio, per quod ferri debent, sint graviora, ut supra est ostensum; nec repugnat in vacuo fieri motus, ut similiter declaratum est.
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406 </s><s id="id.1.1.12.05.24">At nunc non descendit ignis, quia aër, per quem ferri deberet, gravior est ipso igne, et non quia ignis nullam habeat <lb ed="Favaro" n="10"></lb> gravitatem: sicut nec aër descendit, quia ferri deberet per aquam, quae, cum sit aëre gravior, hoc non patitur; nec, quia aër non descendit, dicendum est aërem omni carere gravitate.<pb ed="manuscript" n="92v"></pb>
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407 </s></p></subchap2><subchap2><p><s id="id.1.1.13.01.01">Themistius, Aristotelis opinionem sequens, de vacuo loquendo, haec super t. 74 4i Phys., scribit: Cum vacuum itaque cedat aequaliter, sed neque cedat quidem (cum enim id nihil sit, subtilis hominis est putare vacuum cedere), ita fit ut differentiae gravium et levium, idest <lb ed="Favaro" n="20"></lb> rerum momenta, tollantur, et, quod sequens est, omnibus quae moventur aequalis et indiscriminata velocitas accidat.
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408 </s><s id="id.1.1.13.01.02">Quanto autem haec falsa sint mox innotescet, cum, quomodo in solo vacuo possint vera gravitatum et motuum discrimina dari, et in pleno nullo haec inveniri posse, declaraverimus.
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409 </s></p><p><s id="id.1.1.13.02.01">Et, primo quidem, sicut inter philosophos variae de eadem re opiniones certo testantur testimonio, eorum nullum veritatem detegisse (si enim semel ab aliquo inventa esset, statim et nulla controversia, quae sua ex natura, omnibus se videri et cognosci permisisset), sic etiam in mediis variis variae eorundem corporum gravitatum proportiones, a <lb ed="Favaro" n="30"></lb> nullo medio vera et naturalia pondera determinari, firmo arguunt argumento.
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410 </s><s id="id.1.1.13.02.02">Quo enim medium gravius est, eo maior inter gravitates solidorum est differentia.
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411 </s><s id="id.1.1.13.02.03">Quod quidem ut adhuc facilius intelligatur, ea, <pb ed="Favaro" n="295"></pb> quae supra demonstrata sunt, in memoriam reducantur.
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412 </s></p></subchap2></subchap1><subchap1><subchap2><p><figure id="id.1.1.1.3.03.00" xlink:href="FIG1/F017.jpg"></figure>
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413 </p></subchap2><subchap2><p><s id="id.1.1.13.03.01">Demonstratum est itaque, verbigratia, solidum aliquod minus in aqua quam in aëre ponderare, quanta est gravitas in aëre <pb ed="manuscript" n="93r"></pb>molis aquae aequalis solidi moli: ut si sint duo solida a, b, gravitas autem a in aëre sit 8, gravitas vero b sit 6, sint autem eorum moles aequales, quibus etiam aequetur moles aquae c, cuius gravitas in aëre sit 3, patet, ex supra dictis, gravitatem a in aqua esse 5, b vero gravitatem esse 3.
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414 </s><s id="id.1.1.13.03.02">In aqua igitur gravitatum a, b maius erit discrimen, sicut inter 5 et 3 maior est <lb ed="Favaro" n="10"></lb> discrepantia quam inter 8 et 6.
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415 </s><s id="id.1.1.13.03.03">Quod si, rursus, fuerit aliquod medium gravius aqua, cuius gravitas sit, verbigratia, 5, erit in eo gravitas a 3, gravitas vero b 1.
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416 </s><s id="id.1.1.13.03.04">Et sic patet quomodo in mediis gravioribus maior semper est differentia gravitatum; in aëre enim gravitas a est sesquitertia gravitatis b; in aqua, superbipartiens tertias, in alio medio graviori, tripla: at quis dicet, magis in hoc quam in illo medio veras solidorum esse gravitates?
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417 </s><s id="id.1.1.13.03.05">Nullus profecto: sed verius certe dicetur, in nullo eorum pondera exacta haberi.
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418 </s><s id="id.1.1.13.03.06">Cum enim in omni medio gravium gravitates tantum imminuantur, quantum illius medii pars aequalis moli solidi ponderaret, patet quod in illo solum medio <lb ed="Favaro" n="20"></lb> integrae et non imminutae solidorum habebuntur gravitates, cuius nulla fuerit gravitas: tale autem solum est vacuum.
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419 </s><s id="id.1.1.13.03.07">In caeteris autem mediis gravia tantum solummodo ponderant et gravant, quantum graviora sunt mediis illis (si enim essent aeque gravia ac medium <pb ed="manuscript" n="93v"></pb>aliquod, in tali medio nihil gravarent): quod cum in vacuo, similiter, tantum gravent solida, quantum eorum gravitates vacui gravitatem superant; superent secundum totam suam gravitatem, cum vacui nulla sit gravitas; sequitur quidem, necessario, in vacuo solo posse veras gravium gravitates haberi: quare et talium gravitatum discrimina ibi solum erunt.
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420 </s></p><p><s id="id.1.1.13.04.01">Similiter etiam de motuum velocitatibus et earum proportionibus <lb ed="Favaro" n="30"></lb> est sentiendum.
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421 </s><s id="id.1.1.13.04.02">Quis enim eas in mediis plenis inveniri dicet, si alia est mobilis velocitas in hoc medio, alia in illo, alia in alio, et in alio etiam nulla, ut ligni in aqua? estque, similiter, alia proportio velocitatum in aëre, alia in aqua, alia in medio graviori, alia in medio leviori; ut facile quisque ex his, quae supra scripta sunt, invenire poterit?
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422 </s><s id="id.1.1.13.04.03">Ac demum, cum velocitates mobilium, in medio in quo <pb ed="Favaro" n="296"></pb> moventur, gravitates; et proportiones consequenter velocitatum, gravitatum proportiones, sequantur; haecque non nisi in vacuo dari contingat; in vacuo etiam solo velocitatum discrimina vera et naturalia contingere, dubio procul est asserendum.<pb ed="manuscript" n="94r"></pb>
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423 </s></p></subchap2></subchap1><subchap1><subchap2><p><s id="id.1.2.1.01.01">Quaestio, quam nunc explicaturi sumus, a philosophis nullis, quod sciam, pertractata est: attamen, cum de motu sit, necessario examinanda videtur illis, qui de motu non mancam tractationem tradere <lb ed="Favaro" n="10"></lb> profitentur.
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424 </s><s id="id.1.2.1.01.02">Est autem quaestio non minus necessaria, quam elegans et subtilis.
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425 </s><s id="id.1.2.1.01.03">Quaeritur enim cur idem mobile grave, naturaliter descendens per plana ad planum horizontis inclinata, in illis facilius et celerius movetur quae cum horizonte angulos recto propinquiores continebunt; et, insuper, petitur proportio talium motuum in diversis inclinationibus factorum.
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426 </s><s id="id.1.2.1.01.04">Huius quaestionis exitus, cum primum exquirere tentassem, visus est non omnino faciles habere explicatus: attamen, cum diligentius rem examinarem eiusque demonstrationem in sua principia resolvere conarer, tandem comperi, huius demonstrationem, sicut et aliorum quae prima fronte nimis ardua videntur, ex notis <lb ed="Favaro" n="20"></lb> et manifestis naturae principiis ortum ducere.
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427 </s><s id="id.1.2.1.01.05">Quae quidem notiones, tanquam ad illius explicationem necessarias, nunc primum exponemus.
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428 </s></p><p><s id="id.1.2.1.02.01">Et primo, ut melius omnia intelligantur, quaesitum exemplo declaremus.
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429 </s></p><p><figure id="id.1.2.1.03.00" xlink:href="FIG1/F018.jpg"></figure>
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430 <s id="id.1.2.1.03.01">Sit itaque linea ab, ad centrum mundi tendens, quae ad planum horizonti aequidistans sit perpendicularis; in plano autem horizonti aequidistanti sit linea bc; ex puncto autem b educantur lineae quotcunque, quae cum linea <pb ed="manuscript" n="94v"></pb>bc angulos acutos contineant, sintque lineae bd, be.
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431 </s><s id="id.1.2.1.03.02">Quaeritur igitur cur mobile, descendens, <lb ed="Favaro" n="30"></lb> citissime descendat per lineam ab per lineam vero bd, citius quam per be, tardius tamen quam per ba; et per lineam be, tardius <pb ed="Favaro" n="297"></pb> quam per bd: quaeritur insuper quanto velocius per ba quam per bd, et hic quam per be, mobile descendat.
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432 </s><s id="id.1.2.1.03.03">Ut igitur haec consequi possimus, prius hoc est considerandum, quod etiam supra animadvertimus: scilicet, quod manifestum est, grave deorsum ferri tanta vi, quanta esset necessaria ad illud sursum trahendum; hoc est, fertur deorsum tanta vi, quanta resistit ne ascendat.
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433 </s></p><p><figure id="id.1.2.1.04.00" xlink:href="FIG1/F019.jpg"></figure>
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434 <s id="id.1.2.1.04.01">Si itaque inveniamus quanto minori vi trahitur sursum grave per lineam bd quam per lineam ba, erit iam inventum quanto maiori vi descendat idem grave per lineam ab quam per lineam bd; et, similiter, si <lb ed="Favaro" n="10"></lb> inveniamus quanto maior vis requiritur ad sursum impellendum mobile per lineam bd quam per be, erit iam compertum quanto maiori vi descendet per bd quam per be.
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435 </s><s id="id.1.2.1.04.02">Sed tunc sciemus quanto minor vis requiratur ad sursum trahendum mobile per bd quam per be, quando cognoverimus quanto eiusdem mobilis maior erit gravitas in plano secundum lineam bd, quam in plano secundum lineam be.
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436 </s><s id="id.1.2.1.04.03">Procedamus itaque ad inquisitionem talis gravitatis.
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437 </s><s id="id.1.2.1.04.04">Et {1} intelligatur libra cd, cuius centrum a, et in puncto c pondus aequale ponderi alii quod sit in puncto d.
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438 </s><s id="id.1.2.1.04.05">Si itaque intelligamus, lineam ad, manente puncto a, moveri versus b, <lb ed="Favaro" n="20"></lb> in primo puncto d descensus mobilis erit veluti per lineam ef; quare per lineam ef descensus mobilis erit secundum gravitatem mobilis in puncto d.
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439 </s><s id="id.1.2.1.04.06">Rursus, quando mobile erit in puncto s, in primo puncto s suus descensus erit veluti per lineam gh; quare mobilis per lineam gh motus erit secundum gravitatem quam habet mobile in puncto s.
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440 </s><s id="id.1.2.1.04.07">Et rursus, quando <lb ed="Favaro" n="30"></lb> mobile erit in puncto r, tunc illius descensus in primo puncto r erit veluti per lineam tn; quare mobile per lineam tn movebitur secundum gravitatem quam habet in puncto r.
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441 </s><s id="id.1.2.1.04.08">Si <pb ed="Favaro" n="298"></pb> itaque ostendamus, mobiles in puncto s minus esse grave quam in puncto d, erit iam manifestum quod illius motus erit tardior per lineam gh quam per ef: quod si, rursus, ostendamus, in r mobile adhuc minus esse grave quam in puncto s, erit iam manifestum quod tardior erit motus per lineam nt quam per gh.
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442 </s><s id="id.1.2.1.04.09">Atque iam manifestum est, mobile in puncto r minus gravare quam in puncto si et in s, quam in d.
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443 </s><s id="id.1.2.1.04.10">Pondus enim in puncto d aequeponderat ponderi in puncto c, cum distantiae ca, ad sint aequales: sed pondus in puncto s non aequiponderat ponderi c.
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444 </s><s id="id.1.2.1.04.11">Ducta enim linea ex puncto s perpendiculari super cd, pondus in s, respectu ponderis in c, est ac si <lb ed="Favaro" n="10"></lb> penderet ex p; sed pondus in p minus gravat quam pondus in c, cum distantia pa sit minor distantia ac.
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445 </s><s id="id.1.2.1.04.12">Et, similiter, pondus in r minus gravat quam pondus in s: quod itidem patebit ducta perpendiculari ex r super ad, quae secabit ipsam ad inter puncta a, p.
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446 </s><s id="id.1.2.1.04.13">Manifestum est igitur quod mobile maiori vi descendet per lineam ef quam per lineam gh, et per gh quam per nt.
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447 </s><s id="id.1.2.1.04.14">Sed quanto maiori vi moveatur per ef quam per gh, ita innotescet: extensa, scilicet, linea ad extra circulum, quae secet lineam gh in puncto q.
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448 </s><s id="id.1.2.1.04.15">Et quia tanto facilius descendit mobile per lineam ef quam per gh, quanto gravius est in puncto d quam in puncto s; est autem tanto gravius in puncto d <lb ed="Favaro" n="20"></lb> quam in s, quanto longior est linea da quam linea ap; ergo mobile eo facilius descendet per lineam ef quam per gh, quo linea da longior est ipsa pa.
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449 </s><s id="id.1.2.1.04.16">Eandem ergo proportionem d habebit celeritas in ef ad celeritatem in gh, quam linea da ad lineam pa.
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450 </s><s id="id.1.2.1.04.17">Est autem sicut da ad ap ita qs ad sp, hoc est obliquus descensus ad rectum descensum: constat igitur, tanto minori vi trahi sursum idem pondus per inclinatum ascensum quam per rectum, quanto rectus ascensus minor est obliquo; et, consequenter, tanto maiori vi descendere idem grave per rectum descensum quam per inclinatum, quanto maior est inclinatus descensus quam rectus.
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451 </s><s id="id.1.2.1.04.18">Sed haec demonstratio intelligenda <lb ed="Favaro" n="30"></lb> est nulla existente accidentali resistentia (aut mobilis, aut plani inclinati, asperitas; vel etiam mobilis figura): sed supponendum est, planum esse quodammodo incorporeum, vel saltem exactissime expolitum et durum, ne, dum mobile super planum gravat, inclinaret planum, et, quodammodo tanquam in fovea, in eo quiesceret.
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452 </s><s id="id.1.2.1.04.19">Necesse est etiam, mobile esse expolitissimum, et figura quae motui non resistat, qualis <pb ed="Favaro" n="299"></pb> esset perfecta sphaerica, et, item, materia durissima, aut fluida ut aqua.
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453 </s><s id="id.1.2.1.04.20">Quae omnia si ita disposita fuerint, quodcunque mobile super planum horizonti aequidistans a minima vi movebitur, imo et a vi minori quam quaevis alia vis.
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454 </s><s id="id.1.2.1.04.21">Et hoc, quia videtur satis creditu difficile, demonstrabitur hac demonstratione.
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455 </s></p><p><figure id="id.1.2.1.05.00" xlink:href="FIG1/F020.jpg"></figure>
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456 <s id="id.1.2.1.05.01">Sit itaque circulus, cuius centrum a, et libra bc mobilis super centro a, et horizonti aequidistans, a centro vero a ducta sit perpendicularis ad, ad mundi centrum tendens; et ex puncto d imaginetur pendens quodcunque pondus.
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457 </s><s id="id.1.2.1.05.02">Manifestum est iam quod pondus in d, dum <lb ed="Favaro" n="10"></lb> movetur versus c, necessario ascendit.
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458 </s><s id="id.1.2.1.05.03">Dico igitur, quamcunque vim puncto b impositam posse movere pondus in d, et necessario movere.
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459 </s><s id="id.1.2.1.05.04">Intelligatur enim aliquod pondus, quantumvis parvum, ex puncto b pendens, et sicut pondus in d ad pondus in b, ita fiat linea ba ad aliam, cui aequalis ponatur linea ae.
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460 </s><s id="id.1.2.1.05.05">Si itaque d pendeat ex puncto c, tunc aequeponderabit cum pondere in b; nec alterum ab altero movebitur, nec lanx inclinabitur.
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461 </s><s id="id.1.2.1.05.06">At pondus in d ex a pendens levius est quam pendens ex e, quia non solum centro est propinquius appensum, verum ex <lb ed="Favaro" n="20"></lb> ipso centro pendens: necesse est ut pondus in d, pendens ex a, a pondere in b moveatur, et lanx inclinetur ex parte b, et d ascendat.
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462 </s><s id="id.1.2.1.05.07">Ergo, si a quacunque vi quodcunque pondus in d, nedum movetur, verum etiam attollitur, quid ergo mirum est, idem pondus d ab eadem vel minori vi, quam sit vis in b, in plano non ascendente moveri?
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463 </s><s id="id.1.2.1.05.08">Amplius: mobile, nullam extrinsecam habens resistentiam, in plano sub horizonte quantulumcunque inclinato naturaliter descendet, nulla adhibita vi extrinseca; ut patet in aqua: et idem mobile in plano quantulumcunque super horizontem erecto non nisi violenter ascendit: ergo restat, quod in ipso horizonte nec naturaliter nec violenter <lb ed="Favaro" n="30"></lb> moveatur.
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464 </s><s id="id.1.2.1.05.09">Quod si non violenter movetur, ergo a vi omnium minima moveri poterit.
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465 </s><s id="id.1.2.1.05.10">Quod etiam aliter demonstrare possumus: nempe, quodcunque mobile, nullam extrinsecam resistentiam patiens, a vi quae minor sit quacunque vi proposita, in plano quod nec sursum nec deorsum tendat, moveri posse.
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466 </s><s id="id.1.2.1.05.11">Ad cuius demonstrationem hoc supponimus: nempe, mobile grave quodcunque a minori vi moveri <pb ed="Favaro" n="300"></pb> posse per planum aequidistans horizonti, quam per planum supra horizontem inclinatum.
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467 </s></p><p><figure id="id.1.2.1.06.00" xlink:href="FIG1/F021.jpg"></figure>
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468 <s id="id.1.2.1.06.01">Sit itaque planum horizonti aequidistans secundum lineam ab, cui ad rectos angulos sit bc; et mobile sit sphaera e; sit autem quaecunque vis f: dico, sphaeram e, nullam extrinsecam et accidentalem resistentiam habentem, posse per planum ab moveri a minori vi quam sit vis f.
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469 </s><s id="id.1.2.1.06.02">Sit vis n, quae potest sursum trahere pondus e; et sicut vis n ad vim f; ita sit ad linea ad lineam db.
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470 </s><s id="id.1.2.1.06.03">Ex his, itaque, quae supra <lb ed="Favaro" n="10"></lb> demonstrata sunt, poterit sphaera e sursum trahi per planum ad a vi f: ergo per planum ab a minori vi, quam sit f, movebitur sphaera e.
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471 </s><s id="id.1.2.1.06.04">Quod fuit demonstrandum. {1}
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472 </s></p><p><s id="id.1.2.1.07.01">Hic autem non me praeterit, posse aliquem obiicere, me ad has demonstrationes tanquam verum id supponere quod falsum est: nempe, suspensa pondera ex lance, cum lance angulos rectos continere; cum tamen pondera ad centrum tendentia concurrerent.
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473 </s><s id="id.1.2.1.07.02">His responderem, me sub suprahumani Archimedis (quem nunquam absque admiratione nomino) alis memet protegere.
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474 </s><s id="id.1.2.1.07.03">Ipse enim hoc idem in sua Parabolae quadratura supposuit; et hoc, fortasse, ut eo longius alios se excedere <lb ed="Favaro" n="20"></lb> ostenderet, quo etiam ex falsis vera haurire posset: nec tamen dubitandum est, ipsum concludere falsum, cum conclusionem eandem prius geometrica alia demonstratione probasset.
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475 </s><s id="id.1.2.1.07.04">Quare, aut dicendum est, suspensa pondera vere cum lance rectos continere angulos, aut nihil referre si rectos contineant, sed tantum sufficere ut aequales sint; quod forte probabilius erit: nisi velimus dicere, hanc potius esse geometricam licentiam; sicut dum idem Archimedes supponit, superficies habere gravitatem, et alteram altera graviorem esse, cum tamen revera omni sint expertes gravitate.
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476 </s><s id="id.1.2.1.07.05">Et haec quae demonstravimus, ut etiam supra diximus, intelligenda sunt de mobilibus ab omni <lb ed="Favaro" n="30"></lb> <pb ed="Favaro" n="301"></pb> extrinseca resistentia immunibus: quae quidem cum forte impossibile sit in materia invenire, ne miretur aliquis, de his periculum faciens, si experientia frustretur, et magna sphaera, etiam si in plano horizontali, minima vi non possit moveri.
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477 </s><s id="id.1.2.1.07.06">Accedit enim, praeter causas iam dictas, etiam haec: scilicet, planum non vere posse esse horizonti aequidistans.
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478 </s><s id="id.1.2.1.07.07">Superficies enim terrae sphaerica est, cui non potest aequidistare planum: quare, plano in uno tantum puncto sphaeram contingente, si a tali puncto recedamus, necesse est ascendere: quare merito a tali puncto non quacunque minima vi poterit removeri <lb ed="Favaro" n="10"></lb> sphaera.
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479 </s></p><p><s id="id.1.2.1.08.01">Et ex his quae demonstrata sunt, facile erit aliquorum problematum solutionem assequi: qualia haec sunt.
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480 </s><s id="id.1.2.1.08.02">Primo: datis duobus planis inclinatis, quorum rectus descensus idem sit, invenire proportionem celeritatum in eis eiusdem mobilis.
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481 </s></p><p><figure id="id.1.2.1.09.00" xlink:href="FIG1/F022.jpg"></figure>
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482 <s id="id.1.2.1.09.01">Sit enim rectus descensus ab, et planum horizontis sit bd, et sint obliqui descensus ac, ad: quaeritur iam, quam proportionem habeat celeritas in ca ad celeritatem in ad.
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483 </s><s id="id.1.2.1.09.02">Et, quia sicut tarditas in ad ad tarditatem in ab, ita est linea da ad lineam ab, ut supra ostensum est, sicut autem ab linea ad lineam ac, ita tarditas <lb ed="Favaro" n="20"></lb> in ab ad tarditatem in ac; erit, ex aequali, sicut tarditas in ad ad tarditatem in ac, ita da linea ad lineam ac: quare et sicut celeritas in ac ad celeritatem in ad, ita linea da ad lineam ac.
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484 </s><s id="id.1.2.1.09.03">Constat ergo, eiusdem mobilis in diversis inclinationibus celeritates esse inter se permutatim sicut obliquorum descensuum, aequales rectos descensus compraehendentium, longitudines.
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485 </s><s id="id.1.2.1.09.04">Rursus, possumus plana inclinata invenire, in quibus mobile idem datam in celeritatibus servet proportionem.
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486 </s></p><p><figure id="id.1.2.1.10.00" xlink:href="FIG1/F023.jpg"></figure>
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487 <s id="id.1.2.1.10.01">Sit enim data proportio quam habet linea e ad f; et sicut e ad f, in <lb ed="Favaro" n="30"></lb> praecedenti figura ita fiat da ad ac: erit iam absolutum quod quaerebatur.
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488 </s><s id="id.1.2.1.10.02">Possunt etiam alia similia problemata resolvi: ut, datis duobus diversi generis mobilibus, mole aequalibus, planum ita inclinatum constituere, ut quod velocius, motu recto, altero movebatur, in hoc plano eadem velocitate descendat qua alterum motu recto.
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489 </s><s id="id.1.2.1.10.03">Sed quia haec et similia ab his, qui quae supra <pb ed="Favaro" n="302"></pb> dicta sunt intellexerint, facile inveniri possunt, prudentes omittimus: hoc solum animadvertentes, quod, sicut supra dictum de motu recto, ita etiam in his motibus super planis accidit non servari has proportiones quas posuimus, tum propter causas mox allatas, tum etiam quod per accidens est quod mobile levius in principio sui motus citius <pb ed="manuscript" n="98v"></pb>descendat quam gravius: quod unde accidat, suo loco declarabimus; quaestio enim haec ex illa pendet, in qua quaeritur cur motus naturalis intendatur celeritas.
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490 </s><s id="id.1.2.1.10.04">Sed, ut saepius diximus, hae demonstrationes supponunt, nulla esse extrinseca impedimenta, seu mobilis figurae, seu plani aut mobilis asperitatis, seu medii in contrarias aut in easdem <lb ed="Favaro" n="10"></lb> partes moti, seu extrinseci motoris virtutis urgentis aut retardantis motum, et similia: de his enim accidentibus, eo quod innumeris modis accidere possint, regulae tradi nequeunt.
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491 </s><s id="id.1.2.1.10.05">Simili ratione considerandum erit de motu sursum.
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492 </s></p><p><s id="id.1.2.1.11.01">Et haec de motu in planis inclinatis dicta sufficiant.
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493 </s><s id="id.1.2.1.11.02">Restat autem ut capite sequenti aliquid de motu circulari dicamus; quaerendo, primum, utrum proportionalis sit motui recto necne, et utrum sit violentus an naturalis.
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494 </s></p></subchap2><subchap2><p><s id="id.1.2.2.01.01">Aristotelem parum in geometria fuisse versatum, multis in locis suae philosophiae apparet; sed in hoc potissimum, ubi asserit, motum circularem motui recto non esse proportionatum, quia, scilicet, recta linea curvae non est proportionata aut comparabilis: quod quidem mendacium (indignum enim est nomine opinionis), nedum intima et magis recondita geometriae inventa, Aristotelem ignorasse, verum et minima etiam principia huius scientiae, demonstrat.
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495 </s><s id="id.1.2.2.01.02">Nanque, quomodo dixit rectam et circularem non esse proportionatas, si ad hoc, ut quantitates inter se proportionem habeant, sufficit ut minor possit <lb ed="Favaro" n="30"></lb> toties multiplicari <pb ed="manuscript" n="99r"></pb>ut alteram excedat? {1}
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496 </s><s id="id.1.2.2.01.03">An forsan chorda arcus, quae <pb ed="Favaro" n="303"></pb> arcu minor est, in se saepius multiplicata, arcus longitudinem non excedet?
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497 </s><s id="id.1.2.2.01.04">At si excedet, cur dicitur ab Aristotele, arcum et chordam non esse proportionata?
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498 </s></p><p><s id="id.1.2.2.02.01">Non tamen adhuc desunt qui contendant Aristotelem salvare, dicentes, Aristotelem hoc solum sibi voluisse, nempe, curvum et rectum non esse inter se comparabilia.
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499 </s><s id="id.1.2.2.02.02">Sed isti sunt geometriae longe imperitiores quam Aristoteles, quandoquidem, dum conantur ipsum non errasse ostendere, errorem illi tribuunt qui longe gravior est illo, a quo ipsum purgatum reddere conantur.
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500 </s><s id="id.1.2.2.02.03">Et primo quidem, quonam loci in <lb ed="Favaro" n="10"></lb> geometria invenerunt, mentionem fieri de proportione aut non proportione curvi et recti, cum proportio non inveniatur nisi ubi maius et minus est, hoc est ubi quantitas est?
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501 </s><s id="id.1.2.2.02.04">Curvum autem aut rectum quis unquam quantitates dixerit?
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502 </s><s id="id.1.2.2.02.05">At quam ineptiam maiorem potuisset unquam excogitare Aristoteles, quam dicere, curvum et rectum non esse proportionatos aut comparabiles?
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503 </s><s id="id.1.2.2.02.06">Esset enim hoc ut si quis diceret, trigonum et quadratum non esse comparabiles, quia trigonus habet tantum tres angulos, quadratum vero quatuor.
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504 </s><s id="id.1.2.2.02.07">Sed haec ad quid? cum Aristoteles hoc non voluisset, quod ipsi volunt.
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505 </s><s id="id.1.2.2.02.08">Dicit enim haec verba, 7 Phys. t. 24: Si recta et curva sunt comparabiles, accidit rectam esse <lb ed="Favaro" n="20"></lb> aequalem circulo; sed comparabiles non sunt.
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506 </s><s id="id.1.2.2.02.09">Haec sunt illius verba.
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507 </s><s id="id.1.2.2.02.10">Verum, ut eos convincam ut nunquam aufugere possint, hoc pacto dicam.
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508 </s><s id="id.1.2.2.02.11">Non certe negabunt, planam superficiem ad aliquam sui partem habere proportionem: quod si sic est, iam habeo intentum.
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509 </s><s id="id.1.2.2.02.12">Circulus, enim, quadrato inscriptus, est illius quadrati aliqua pars; ergo quadratum ad circulum habet aliquam proportionem: sed quadratum ad circulum sibi inscriptum <pb ed="manuscript" n="99v"></pb>est sicut quadrati peripheria ad circuli circumferentiam: quare quadrati peripheria, quae est ex lineis rectis, ad circuli curvam circumferentiam habet proportionem.
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510 </s><s id="id.1.2.2.02.13">Sed quid ulterius progredior?
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511 </s><s id="id.1.2.2.02.14">Aristoteles temere dicit, Non datur recta aequalis circuli <lb ed="Favaro" n="30"></lb> circumferentiae: quod falsum esse demonstratur a divino Archimede in suis Lineis spiralibus, propositioneƒ; ubi circumferentiae circuli circa spiralem primae revolutionis recta linea aequalis invenitur.
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512 </s><s id="id.1.2.2.02.15">Neque dicas: Hoc latuit Aristotelem, quia Archimedes Aristotele est multo recentior.
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513 </s><s id="id.1.2.2.02.16">Nam, si Aristotelem latuit demonstratio inveniendae rectae curvae aequalis, latuit etiam demonstratio probans non dari rectam curvae <pb ed="Favaro" n="304"></pb> aequalem; quare non debebat temere asserere, non dari talem rectam.
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514 </s><s id="id.1.2.2.02.17">Sed amplius: quis est tam caecus, cui lateat quod, si fuerint duo rectae aequales, quarum altera incurvetur, erit illa curva rectae aequalis?
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515 </s><s id="id.1.2.2.02.18">Aut, si circulus super lineam rectum circumducatur, quis dubitabit, circulum in una revolutione lineam rectam pertransire suae circumferentiae aequalem?
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516 </s><s id="id.1.2.2.02.19">Quare motum rectum curvo esse aequalem et in quavis proportione proportionatum, non amplius dubitemus.<pb ed="manuscript" n="100r"></pb>
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517 </s></p></subchap2><subchap2><p><s id="id.1.2.3.01.01">De motu circulari aliqua dicturi, primo ipsum ita distinguemus.
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518 </s><s id="id.1.2.3.01.02">Motus itaque circularis vel fit super mundi centrum, vel extra.
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519 </s><s id="id.1.2.3.01.03">Nunc autem videamus, an qui fit circa mundi centrum sit violentus nec ne; ut, verbigratia, si marmorea sphaera esset in mundi centro, ita ut centrum eius a mundi centro non differret.
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520 </s><s id="id.1.2.3.01.04">Huius quaesiti solutionem habebimus, si quid sit naturalis et quid violentus motus declaretur.
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521 </s></p><p><s id="id.1.2.3.02.01">Motus itaque naturalis est dum mobilia, incedendo, ad loca propria accedunt; violentus vero est dum mobilia, quae moventur, a proprio loco recedunt.
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522 </s><s id="id.1.2.3.02.02">Haec cum ita se habeant, manifestum est, sphaeram super mundi centrum circumvolutam neque naturali neque violento <lb ed="Favaro" n="20"></lb> motu moveri.
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523 </s><s id="id.1.2.3.02.03">Cum enim sphaera gravis sit, et gravium locus sit centrum, moveanturque gravia secundum suae gravitatis centrum; si iam sphaerae esset centrum gravitatis in centro mundi, in quo, dum sphaera circumducitur, maneret; manifestum est quod neque naturaliter nec violenter moveretur, cum ad proprium locum nec accederet nec recederet.
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524 </s><s id="id.1.2.3.02.04">Ubi animadvertendum est, quod si sphaera esset consimilium partium, ita ut centrum gravitatis et magnitudinis idem esset, tunc illius centrum a centro mundi non differret; quod si dissimilium esset partium, ita ut centrum suae gravitatis a centro magnitudinis differret, tunc centrum gravitatis esset idem cum centro mun<pb ed="manuscript" n="100v"></pb>di, <lb ed="Favaro" n="30"></lb> centrum vero magnitudinis diversum.
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525 </s><s id="id.1.2.3.02.05">Sed, quomodocunque se haberet, dummodo centrum gravitatis esset idem cum centro mundi, sphaera in centro mundi nec naturaliter nec violenter circumduceretur.
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526 </s><s id="id.1.2.3.02.06"><pb ed="Favaro" n="305"></pb> Unumquodque enim eorum, quae moventur, secundum gravitatis suae centrum movetur: quod si centrum gravitatis non differat a centro mundi, tunc sphaera, super centro suae gravitatis circumvoluta, nec naturaliter nec violenter movebitur.
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527 </s></p><p><s id="id.1.2.3.03.01">Sed hic duo quaeri possunt: primo, utrum sphera heterogenearum partium, cuius centrum magnitudinis esset in centro mundi, centrum vero gravitatis a mundi centro distaret, utrum, inquam, talis sphaera violenter moveretur nec ne; 2Á, si sphaera esset in centro mundi, nec naturaliter nec violenter circumageretur, quaeritur, utrum, accepto <lb ed="Favaro" n="10"></lb> motus principio ab externo motore, perpetuo moveretur nec ne.
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528 </s><s id="id.1.2.3.03.02">Si enim non praeter naturam movetur, videtur quod perpetuo moveri deberet; sed si non secundum naturam, videtur quod tandem quiescere debeat.
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529 </s></p><p><s id="id.1.2.3.04.01">Ad primum itaque redeuntes, dicimus, sphaeram heterogenearum partium, cuius centrum gravitatis a magnitudinis centro differret, praeter naturam quidem et vi ita manere, ut eius centrum magnitudinis esset in centro mundi, centrum vero gravitatis distaret; non autem praeter naturam et vi moveri.
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530 </s></p><p><figure id="id.1.2.3.05.00" xlink:href="FIG1/F024.jpg"></figure>
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531 <s id="id.1.2.3.05.01">Ut, verbigratia, sit sphaera, cuius magnitudinis centrum sit a, quod a centro mundi non <lb ed="Favaro" n="20"></lb> differat; sit autem heterogenea, ut, verbigratia, si sphaera esset lignea, sed tamen, ex parte in qua o, esset plumbi frustrum; centrum autem gravitatis talis sphaerae esset inter centrum a et o, ut, verbigratia, in c.
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532 </s><s id="id.1.2.3.05.02">Manifestum est, quod in tali loco non nisi violenter retinebitur.
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533 </s><s id="id.1.2.3.05.03">Cum enim gravia appetant centrum, et ad ipsum secundum suae <pb ed="manuscript" n="101r"></pb>gravitatis centrum moveantur, ergo sphaerae centrum gravitatis c naturaliter ad centrum mundi a moveretur: quare extra illud violenter detinebitur.
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534 </s><s id="id.1.2.3.05.04">Non tamen extra mundi centrum violenter circumageretur: nanque, in tali circulatione, centrum gravitatis circa mundi <lb ed="Favaro" n="30"></lb> centrum circulum describeret, ad ipsum nec accedendo nec recedendo.
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535 </s><s id="id.1.2.3.05.05">Quod cum ita sit, nec naturaliter nec violenter circumgirabitur: naturaliter enim, ut supra etiam diximus, tunc moveretur, quando in motu ad centrum mundi accederet; violenter vero, si, dum movetur, ab eodem recederet.
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536 </s><s id="id.1.2.3.05.06">Ex quo patet error quorumdam dicentium, Si caelo una adderetur stella, caeli motus aut cessaret aut tardior <pb ed="Favaro" n="306"></pb> evaderet.
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537 </s><s id="id.1.2.3.05.07">Horum enim neutrum accideret: cum enim, ex eorum etiam sententia, caeli circumvolutio circa mundi centrum fiat, addita stella aut aliud grave pondus superadditum nec iuvabit nec retardabit motum; cum tale pondus, in tali circulatione, nec acquirat nec amittat de accessu aut recessu a centro, ad quod sua gravitate ferretur.
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538 </s><s id="id.1.2.3.05.08">Decipiuntur, ergo, talia dicentes, in hoc: quod, primo, statuunt, vim motricis intelligentiae esse ita resistentiae caeli proportionatam, ut ipsum hac, qua nunc movet, celeritate movere possit, nec maiori; quod si, additione alicuius stellae, augeatur caeli resistentia, tunc, inquiunt, caeli motus ab eadem vi motrice segnior causabitur.
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539 </s><s id="id.1.2.3.05.09">Ducuntur autem, <lb ed="Favaro" n="10"></lb> meo iudicio, ad hoc ita credendum, quia vident apud nos ut qui magnam rotam movet, si ex altera parte magnum superaddatur pondus, tunc magis laborabit, aut motus tardior evadet: non autem animadvertunt, causam talis effectus esse <pb ed="manuscript" n="101v"></pb>quia rota movetur extra centrum mundi; ita ut, quando pondus superadditum ex imo rotae loco ad supremum ferri debet, tunc praeter naturam movetur, cum sursum tendat, a mundi centro recedens.
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540 </s><s id="id.1.2.3.05.10">Quod si rota super mundi centrum circumageretur, quis unquam dixerit eam a pondere impediri, cum pondus in circulatione nec accedat aut recedat a mundi centro?
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541 </s><s id="id.1.2.3.05.11">Pari ratione de caelo est iudicandum.
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542 </s><s id="id.1.2.3.05.12">Tunc enim stella motum retardare <lb ed="Favaro" n="20"></lb> poterit, quando a loco in quem naturaliter tenderet removebitur: sed nunquam hoc in circulatione facta circa mundi centrum contingit, quia nunquam sursum et nunquam deorsum movetur: non ergo ex stellae additione motus tardabitur.
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543 </s></p><p><s id="id.1.2.3.06.01">Ad secundum, quod supra quaerebatur, non est hic responsionis locus; videndum enim prius est, a quo moveantur quae non naturaliter moventur.
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544 </s></p><p><s id="id.1.2.3.07.01">In motu itidem circulari qui extra mundi centrum fit, est distinguendum de mobili: an, scilicet, consimilium sit partium, vel dissimilium.
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545 </s><s id="id.1.2.3.07.02">Et si mobile sit consimilium partium, ut, verbigratia, sphaera <lb ed="Favaro" n="30"></lb> marmorea, quae super axem moveatur, motus iste nec naturalis erit nec violentus; cum sphaerae gravitatis centrum nec accedat nec recedat a mundi centro, et tanta sit gravitas partium sphaerae ascendentium quanta est partium descendentium, ita ut semper sphaera sit in aequilibrio.
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546 </s><s id="id.1.2.3.07.03">Attamen per accidens est quod talis circulatio sit <pb ed="Favaro" n="307"></pb> violenta: quia, scilicet, est axium super cardinibus resistentia.
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547 </s><s id="id.1.2.3.07.04">Cum enim contingat sphaeram extra proprium locum esse, contingit etiam ipsam gravare et <pb ed="manuscript" n="102r"></pb>substentaculo egere; quare axis sphaerae extremitates, super cardinibus gravantes, motum impediunt.
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548 </s><s id="id.1.2.3.07.05">Verum quo magis axis extrema subtilia et expolita fuerint, eo minus resistentiam patientur: ita ut si imaginabimur indivisibilia esse, tunc ab illis nulla resistentia proveniet.
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549 </s><s id="id.1.2.3.07.06">Accidit etiam, talem motum a superficie sphaerae retardari, si superficies rudis et scabrosa extet: aër enim circumfluus, et in superficiei concavitatibus retentus, motum impediet, non autem <lb ed="Favaro" n="10"></lb> iuvabit, ut aliquis credidit; quod suo loco explicabitur.
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550 </s><s id="id.1.2.3.07.07">Quod si sphaera heterogenea fuerit, ita ut habeat centrum gravitatis extra centrum molis, circumducatur autem super centrum magnitudinis, hic, praeter ceteras causas per accidens supra allatas, erit etiam causa per se cur motus talis sit non, ut alter, nec naturalis nec violentus, sed nunc naturalis nunc vero sit violentus.
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551 </s><s id="id.1.2.3.07.08">Cum enim centrum gravitatis circa centrum magnitudinis in tali circulatione circulum describat, quando ex imo ad supremum locum ascendet, vi movebitur, cum a centro mundi recedat; cum vero ex supremo in imum tendit, natura certe feretur.
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552 </s><s id="id.1.2.3.07.09">Sed quia non quantum natura descendit, tantum vi potest <lb ed="Favaro" n="20"></lb> attolli ab impetu accepto (cuius causa suo loco explicabitur), hinc fit ut maior sit difficultas in ascensu quam propensio in descensu: ex quo sequitur, tum ex hoc tum propter alias causas per accidentia, ut magis violenti naturam sapiat quam naturalis.<pb ed="manuscript" n="103r"></pb>
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553 </s></p></subchap2><subchap2><p><s id="id.1.2.4.01.01">Aristoteles, sicut fere in omnibus quae de motu locali scripsit, in hac etiam quaestione, vero contrarium scripsit: et profecto non mirum hoc est; quis enim ex falsis vera colliget?
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554 </s><s id="id.1.2.4.01.02">Non poterat Aristoteles tueri, motorem debere esse coniunctum mobili, nisi diceret, proiecta ab aëre moveri.
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555 </s><s id="id.1.2.4.01.03">De hac itaque sua opinione multis in locis testimonium fecit, {1} <pb ed="Favaro" n="308"></pb> quam, quia a nobis confutanda est, in medium afferemus; eamque (fusius enim ab expositoribus declaratur) sic breviter perstringemus.
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556 </s></p><p><s id="id.1.2.4.02.01">Vult igitur Aristoteles, motorem, ut, verbigratia, proicientem lapidem, priusquam lapidem relinquat, pellere etiam partes aëris contiguas, quas, inquit, similiter movere alias partes, has alias, et sic successive; lapidem autem, a proiciente relictum, deinde ferri a partibus illis aëris; et sic fieri motum quendam lapidis discontinuum, et non esse unicum motum sed plures. {1}
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557 </s><s id="id.1.2.4.02.02">Huc conatus est aufugere Aristoteles et eius sectatores, qui sibi suadere non potuerunt quomodo posset mobile a virtute impressa moveri, aut quid ista esset virtus.
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558 </s><s id="id.1.2.4.02.03">Verum, <lb ed="Favaro" n="10"></lb> ut altera opinio verissima innotescat, hanc prius Aristotelis funditus evertere conabimur; alteram vero de virtute impressa, quoad licuerit, declarabimus et exemplis illustrabimus.
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559 </s></p><p><s id="id.1.2.4.03.01">Contra igitur Aristotelem sic arguo.
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560 </s><s id="id.1.2.4.03.02">Sint partes aëris, quae mobile movent, A, B, C, D, E; quarum motori contigua sit A.
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561 </s><s id="id.1.2.4.03.03">Aut igitur partes istae moventur omnes simul, aut una post aliam: si A, B, C, D, E moventur omnes simul, peto, quiescente motore, a quo moveantur; et sic deveniendum erit ad virtutem impressam: si prius movetur A quam B, similiter peto, quiescente A, a quo moveatur B.
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562 </s><s id="id.1.2.4.03.04">Rursus, motus violentus, ex eodem Aristotele, {2} velocior est in medio quam in principio: <lb ed="Favaro" n="20"></lb> ergo pars aëris C, a B impulsa, velocius movetur quam B; ergo et idem C velocius impellet D, quam <pb ed="manuscript" n="103v"></pb>A, B, C, D, E ipsa a B impulsa fuerint; quare D velocius quoque impellet E, quam ipse a C impulsus fuit; et sic consequenter: quare motus violentus semper augebitur.
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563 </s><s id="id.1.2.4.03.05">2Á: argumentum est de sagitta a chorda impulsa, et etiam contra spirantem boream, quae tamen citissime volat.
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564 </s><s id="id.1.2.4.03.06">Huic argumento nil aliud adversarii respondent, nisi quod, quamvis alte spiret aura, tamen aër contra ventum fertur, accepto impetu ab arcu: nec pudet eos talia puerilia iactare.
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565 </s><s id="id.1.2.4.03.07">At quid ad simile argumentum dicent?
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566 </s><s id="id.1.2.4.03.08">Quando triremis contra nitentem fluvium remis impellitur, et, exemptis ex <lb ed="Favaro" n="30"></lb> aqua remis, cymba adhuc per magnum spatium contra decursum aquae invehitur, quis tam caecus est qui aquam impetu quam maximo ad contrarias ruere non aspiciat? aquam, inquam, naviculae contiguam, <pb ed="Favaro" n="309"></pb> nec hilum quidem, ob navis impetum, a naturali cursu deflectentem? {1}
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567 </s><s id="id.1.2.4.03.09">3Á: si medium est quod defert mobilia, unde est quod, cum quis eodem tormento iaculat globum ferreum cum quo tamen etiam feratur lignum sive stuppa aut aliquid leve, ita tamen ut grave praecedat; unde, inquam, accidit quod ferrum per longissimum spacium cietur, stuppa autem, postquam per aliquod spacium ferrum prosequuta fuerit, sistitur ac in terram decidit?
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568 </s><s id="id.1.2.4.03.10">Si ergo est medium quod utrumque portat, cur plumbum vel ferrum longissime portat, stuppam vero non item?
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569 </s><s id="id.1.2.4.03.11">An ne facilius est aëri movere gravissimum ferrum quam <lb ed="Favaro" n="10"></lb> levissimam stuppam aut lignum?
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570 </s><s id="id.1.2.4.03.12">4Á: non bene sibi constare videtur Aristoteles.
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571 </s><s id="id.1.2.4.03.13">Nam, 3Á Caeli t. 27, inquit: Si quod movetur neque grave neque leve fuerit, vi movebitur; et quod vi movetur, nullam gravitatis aut levitatis resistentiam habens, in infinitum movetur.
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572 </s><s id="id.1.2.4.03.14">Textu autem sequenti inquit, proiecta a medio ferri: cum igitur aër nec gravitatem habeat nec <pb ed="manuscript" n="103,2r"></pb>levitatem, a proiciente motus in infinitum movebitur, et semper eadem velocitate; ergo etiam in infinitum portabit proiecta, nec fatigabitur, cum semper eadem vi moveatur.
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573 </s><s id="id.1.2.4.03.15">Huius tamen contrarium experientia docet.
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574 </s><s id="id.1.2.4.03.16">5Á: intelligatur sphaera marmorea exacte rotunda et expolita, quae super axe, duobus <lb ed="Favaro" n="20"></lb> cardinibus inhaerente, moveri possit; deinde accedat motor, qui utrasque axis extremitates extremis digitis contorqueat.
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575 </s><s id="id.1.2.4.03.17">Tunc certe sphaera per longum tempus girabit: et tamen nec aër a motore fuit commotus; nec potest aër in sphaeram agere, illam impellendo, cum nunquam locum mutet et, cum sit expolita, nullas habeat cavitates in quas possit aër irruere: quin aër penitus immotus circa spheram manebit; ut patet si lumen sphaerae appropinquetur, qui nec extinguetur nec movebitur.
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576 </s></p><p><s id="id.1.2.4.04.01">Hae sint rationes quibus satis superque confutari credimus ineptam illam sententiam, quam, qui sibi suadere non possunt quid sit <lb ed="Favaro" n="30"></lb> illa virtus impressa, tueri conantur.
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577 </s><s id="id.1.2.4.04.02">Nunc autem, ut sententiam nostram explicemus, inquiramus, primo, quid sit ista virtus motiva, quae a proiciente in proiecto imprimitur.
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578 </s><s id="id.1.2.4.04.03">Dicimus ergo, illam esse <pb ed="Favaro" n="310"></pb> privationem gravitatis, cum mobile sursum impellitur; cum vero deorsum, esse privationem levitatis.
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579 </s><s id="id.1.2.4.04.04">Quomodo autem proiciens possit, sursum dirigendo grave, ipsum gravitate privare et leve reddere, non mirabitur is qui non miratur quomodo ignis possit privare ferrum frigiditate, introducendo calorem.
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580 </s><s id="id.1.2.4.04.05">Movetur, igitur, sursum mobile a proiciente, dum in manu illius est et gravitate privatur; movetur, similiter, motu alterativo ferrum ad calorem, dum ferrum est in igne et ab eo privatur frigiditate: virtus motiva, nempe levitas, <pb ed="manuscript" n="103,2v"></pb>conservatur in lapide, non tangente qui movit; calor conservatur in ferro ab igne remoto: virtus impressa successive remittitur in proiecto a <lb ed="Favaro" n="10"></lb> proiciente absente; calor remittitur in ferro, igne absente: lapis tandem reducitur ad quietem; ferrum, similiter, ad naturalem frigiditatem redit: motus ab eadem vi magis imprimitur in mobili magis resistenti quam in eo quod minus resistit, ut in lapide magis quam in pumice levi: et calor, similiter, acrius imprimitur ab eodem igne in durissimo et frigidissimo ferro quam in tenui et minus frigido ligno.
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581 </s><s id="id.1.2.4.04.06">Ridendus esset qui diceret, aërem excalefactum iam ab igne, igne extincto aut procul remoto, in ferro conservare calorem; cum etiam in frigidissimo aëre candescat ferrum: plusque ridendus est qui ab aëre immoto et saepius in contrarium nitente mobilitatem in <lb ed="Favaro" n="20"></lb> proiecto conservari crediderit.
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582 </s><s id="id.1.2.4.04.07">At quis non dicet, ferrum in aëre frigido ab eius frigiditate citius refrigerari? at quis sanae mentis non dicet, aërem, aut manentem aut in contrarium nitentem, motum impedire?
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583 </s></p><p><s id="id.1.2.4.05.01">Sed esto aliud pulcrius exemplum.
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584 </s><s id="id.1.2.4.05.02">Miraris quid ex manu proicientis exeat et in proiectum imprimatur; et non miraris quid e malleo exeat et in horologii campanam transferatur, et unde tantus sonus e silente malleo in silentem campanam traducatur, et quomodo in ea, absente qui percussit, conservetur?
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585 </s><s id="id.1.2.4.05.03">Pulsatur a pulsante campana; movetur a movente lapis: privatur campana silentio; privatur <lb ed="Favaro" n="30"></lb> lapis quiete: introducitur in campanam qualitas sonora contraria eius naturali silentio; introducitur <pb ed="manuscript" n="104r"></pb>in lapidem qualitas motiva contraria illius quieti: conservatur in campana sonus, absente qui pulsavit; conservatur in lapide motus, absente qui movit: remittitur successive in campana qualitas sonora; gradatim remittitur in lapide <pb ed="Favaro" n="311"></pb> qualitas motiva.
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586 </s><s id="id.1.2.4.05.04">At quis sanae mentis dicet, esse aërem qui continue campanam pulsat?
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587 </s><s id="id.1.2.4.05.05">Nanque, primo, movetur a malleo unica tantum aëris particula: verum si quis manum super campanam imponat, et in contrarias partes mallei, sentiet statim torporem quendam acrem et mordacem per totum metallum pervagantem.
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588 </s><s id="id.1.2.4.05.06">2Á: si aër pulsat et sonat in campana, cur flante maximo vento silet ea?
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589 </s><s id="id.1.2.4.05.07">An mollius verberat auster, qui mare totum turres moeniaque subvertit, quam parvus malleus, qui vix movetur?
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590 </s><s id="id.1.2.4.05.08">3Á: si esset aër in aëre, non autem aes in aëre, quod sonaret, iam omnes campanae eiusdem figurae idem <lb ed="Favaro" n="10"></lb> emitterent sonum; quin etiam lignea vel saltem plumbea vel marmorea, ut aerea, streperet campana.
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591 </s><s id="id.1.2.4.05.09">Sed, demum, sileant qui dicunt, aërem esse qui sonat vel sonum defert: tremit enim campana dum sonum emittit, et, absente pulsante, tremor motus et sonus in ea remanet et conservatur; quod quidem aëri tribuere, ut tantam molem moveat a malleo vix motus, omnem excedit rationem.
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592 </s><s id="id.1.2.4.05.10">Ad rem igitur revertendo, cur mirantur illi, quomodo possit a movente in mobili imprimi qualitas motiva, non autem quomodo a malleo possit imprimi sonus et motus quidam trepidationis in campana?
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593 </s></p><p><s id="id.1.2.4.06.01">Sed, amplius, dicunt illi, se non posse mente concipere, quomodo <lb ed="Favaro" n="20"></lb> gravissimus lapis <pb ed="manuscript" n="104v"></pb>possit evadere levis, virtute motiva a proiciente accepta: quae quidem, cum sit levitas, leve, mobili inhaerens, ipsum reddet: attamen dicunt ipsi, ridiculum prorsus esse credere, lapidem post motum sursum levem evasisse et minus ponderare quam antea.
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594 </s><s id="id.1.2.4.06.02">Verum isti de rebus non iudicant sano ac rationali discursu.
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595 </s><s id="id.1.2.4.06.03">Nanque neque ego dixerim, lapidem, post motum, levem factum esse, sed suam primam ac naturalem gravitatem retinere: sicut etiam ferrum candens frigiditate caret; post autem calorem, suam eandemque frigiditatem resumit.
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596 </s><s id="id.1.2.4.06.04">Et non est quod miremur, lapidem, dum movetur, levem esse: nanque inter lapidem in actu illo motus existentem et quodcunque aliud leve, nulla <lb ed="Favaro" n="30"></lb> differentia assignari poterit; cum enim leve illud dicamus quod sursum fertur, lapis autem sursum fertur, ergo lapis levis est dum sursum fertur.
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597 </s><s id="id.1.2.4.06.05">Sed dices, leve illud esse quod sursum naturaliter fertur; non autem, quod vi.
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598 </s><s id="id.1.2.4.06.06">Ego autem dicam, leve id naturaliter esse quod sursum naturaliter fertur; leve autem id praeternaturaliter aut per accidens aut vi esse, quod sursum praeter naturam per accidens et vi <pb ed="Favaro" n="312"></pb> fertur.
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599 </s><s id="id.1.2.4.06.07">Talis autem est lapis a virtute impulsus: et in lapide sua nativa et intrinseca gravitas eo deperditur modo, quo deperditur etiam dum in mediis se gravioribus ponitur.
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600 </s><s id="id.1.2.4.06.08">Nam lapis qui, verbigratia, mercurio supernatat nec descendit, omnem amittit suam gravitatem; imo et adeo gravitatem amittit et levitatem induit, ut multae etiam extrinsecae gravitati advenienti (ut si quis eum deorsum premat) strenue resistat: et lignum quoque adeo in aqua fit leve, ut non nisi vi deorsum comprimi possit.
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601 </s><s id="id.1.2.4.06.09">Attamen nec lapis nec lignum <pb ed="manuscript" n="105r"></pb>suam naturalem gravitatem deperdunt, verum, e gravioribus illis mediis exempta, propriam gravitatem resumunt: sic proiectum, a vi <lb ed="Favaro" n="10"></lb> impellente liberatum, suam veram et intrinsecam gravitatem, descendendo, prae se fert.
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602 </s></p><p><s id="id.1.2.4.07.01">Dubitant, amplius, qui contrarias tuentur partes, in qua mobilis parte recipiatur illa virtus, in superficie, nempe, vel in centro, vel in alia particula.
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603 </s><s id="id.1.2.4.07.02">His breviter respondeo, ut mihi prius declarent in qua parte ferri recipiatur calor; et ego deinde illis dicam ubi virtus recipiatur motiva? eamque ponam ubi ponunt calorem: et si calor recipiatur in superficie tantum, in sola superficie dicam recipi virtutem; et si in centro, in centro; et si dixerint, recipi calorem ubi prius erat frigiditas, dicam ego, levitatem extraneam eas ingredi <lb ed="Favaro" n="20"></lb> partes, in quibus antea domestica gravitas insidebat.
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604 </s></p><p><s id="id.1.2.4.08.01">Mirantur, demum, adversarii, quomodo eadem manus facultatem habeat, modo levitatem, modo gravitatem, modo autem etiam id quod neque grave neque leve videtur, imprimendi.
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605 </s><s id="id.1.2.4.08.02">At cur non potius mirantur, quomodo nunc quicquam velint, paulo autem post idem nolint; et hoc credant, et de eodemmet nunc haesitent et dubitent, interdum etiam non credant?
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606 </s><s id="id.1.2.4.08.03">Verum si, ut haec, ex voluntate pendet posse nunc brachium attollere, mox deprimere, inde in diversas movere, et habet brachium, a voluntate gubernatum, ut nunc gravet, nunc allevet; cur mirandum est, id quod a brachio gravatur gravitatem <lb ed="Favaro" n="30"></lb> recipere, id autem quod allevatur levitate indui?
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607 </s></p><p><s id="id.1.2.4.09.01">Verum, postquam non a nostro proposito <pb ed="manuscript" n="105v"></pb>dissonat, non sileam errorem quendam fere communem: eorum, nempe, qui credunt, aërem et aquam, quia fluida sunt, facillime et citissime, aëremque <pb ed="Favaro" n="313"></pb> praesertim, posse moveri; quo ducti crediderunt, proicientem magis aërem quam proiectum movere, et aërem proiecta portare.
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608 </s><s id="id.1.2.4.09.02">Verum longe aliter se res habet: ut etiam interdum ipsi fatentur, qui, cum principe suo Aristotele, nunc, ut proiecta possit ferre, dicunt aërem ob levitatem suam celerrime moveri, cum fere nullam resistentiam habeat; nunc autem dicunt, ea quae nec gravitatem nec levitatem habent non posse moveri, quia oportet quod movetur resistere: atque, ita dicentes, eadem nunc credunt nunc negant, prout suae intentioni melius quadrant.
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609 </s><s id="id.1.2.4.09.03">Res tamen ita se habet, ut mobile, quo levius erit, <lb ed="Favaro" n="10"></lb> eo quidem facilius movetur dum motori est coniunctum, sed, a movente relictum, brevi tempore impetum acceptum retinet: ut patet si quis iaculetur pinnam, tantam adhibens vim quantam si deberet iaculari libram plumbi; nam facilius quidem movebit pinnam quam plumbum; attamen diutius in plumbo servabitur virtus impressa quam in pinna, et multo longius iaculabitur.
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610 </s><s id="id.1.2.4.09.04">Quod si aër esset qui proiectum portaret, quis unquam credet, aërem facilius plumbum quam pinnam laturum esse?
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611 </s><s id="id.1.2.4.09.05">Videmus itaque, quo quicquam levius fuerit, eo quidem facilius moveri, sed minus impetum acceptum retinere: quare, cum aër, ut supra demonstratum est, nullam in proprio loco habeat gravitatem, <lb ed="Favaro" n="20"></lb> facillime quidem movebitur, sed tamen impetum acceptum minime servabit.
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612 </s><s id="id.1.2.4.09.06">Cur autem levia impetum non retineant, inferius demonstra<pb ed="manuscript" n="106r"></pb>bimus.
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613 </s></p><p><s id="id.1.2.4.10.01">Nec est ullius momenti exemplum, quod tradunt, de calculo in lacum proiecto; a quo, dicunt, aquam motam in circulum per longissima spacia moveri.
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614 </s><s id="id.1.2.4.10.02">Falsum enim est, primo, quod aqua moveatur: ut patet si in aqua fuerint ligna vel paleae supernatantes, quae ab aquae vorticibus de loco minime movebuntur, sed tantum paululum attollentur ab undis, nec circulorum circumferentias sequentur.
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615 </s><s id="id.1.2.4.10.03">2Á: non valet comparatio in aëre, cuius a proiciente non movetur superficies, sicut sola aquae superficies a calculo est quae movetur; <lb ed="Favaro" n="30"></lb> quae etiam aquae extrema superficies ideo attollitur et deprimitur, quia resistentiam habet ne attollatur et in locum aëris feratur: verum in medio aëre non potest virtus motiva imprimi, quia tunc aër nullam habet resistentiam, cum ex loco in locum alterius medii non trudatur.
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616 </s><s id="id.1.2.4.10.04">Et hoc contingeret etiam in medio aquae, quae impetum acceptum non conservaret, cum illius motus nullam habeat inclinationem; non, enim, naturalem, quia non moveretur ad locum suum, <pb ed="Favaro" n="314"></pb> cum iam ibi sit; nec violentam, cum non trudatur in locum alterius medii.
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617 </s></p><p><s id="id.1.2.4.11.01">Hic fuit communis error eorum qui dixerunt, proiecta a medio moveri.
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618 </s><s id="id.1.2.4.11.02">Contingit autem non nunquam, opiniones quasdam inter homines, quamvis falsas, diu remanere; quia prima fronte aliquam veritatis speciem prae se ferunt, et ob id nullus est qui accuratius scrutari curet, an sit ut creditur.
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619 </s><s id="id.1.2.4.11.03">Tale quiddam est quod creditur de rebus sub aqua existentibus, quas communis opinio asserit <pb ed="manuscript" n="106v"></pb>maiores, quam vere sint, apparere. {1}
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620 </s><s id="id.1.2.4.11.04">Cum autem talis effectus causam invenire non possem, tandem, ad experientiam accedens, inveni, nullo modo <lb ed="Favaro" n="10"></lb> denarium in aquae profundo manens maius apparere, sed potius minus: quare arbitror ego, eum, qui primus hanc protulit sententiam, in hanc deductum fuisse opinionem aestivo tempore, cum interdum pruna vel alii fructus in vitreo calice aqua pleno, cuius figura conoidis superficiem referat, imponuntur; quae quidem, aspicientibus ita ut radii per vitrum transmittantur, longe maiora quam sint appareant.
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621 </s><s id="id.1.2.4.11.05">Verum non aqua, sed calicis figura, talis effectus causa; ut fusius in commentariis super Magnam Ptolemaei Constructionem declaravimus, quae (Deo favente) brevi edentur. {2}
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622 </s><s id="id.1.2.4.11.06">Signum autem huius est, quod, oculo super aquam posito, ita ut non intercedente medio vitro prunum <lb ed="Favaro" n="20"></lb> intueri queat, non maius apparet.
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623 </s></p><p><s id="id.1.2.4.12.01">Concludamus igitur tandem, proiecta nullo modo moveri a medio, sed a virtute motiva impressa a proiciente.
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624 </s><s id="id.1.2.4.12.02">Nunc autem prosequamur ostendere, hanc virtutem successive diminui; nec posse in motu violento duo puncta assignari, in quibus eadem fuerit virtus motiva.
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625 </s></p></subchap2><subchap2><p><s id="id.1.2.5.01.01"><pb ed="manuscript" n="107r"></pb>Cum itaque, in capite superiori, proiecta a virtute impressa moveri, determinatum sit, patet motum violentum esse unum et continuum, <pb ed="Favaro" n="315"></pb> non autem plures et interruptos, ut credidit Aristoteles.
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626 </s><s id="id.1.2.5.01.02">Quod cum ita sit, nec motus violentus infinitus sit, sequitur necessario, virtutem illam, a proiciente impressam, continue in proiecto remitti; nec posse dari in eo motu duo puncta temporis, in quibus eadem virtus motiva sit et non debilior.
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627 </s><s id="id.1.2.5.01.03">Quod ut adhuc clarius appareat, hac utar demonstratione: supponendo prius, idem mobile ab eadem virtute, in eodem medio et super eandem lineam, eadem cum velocitate moveri.
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628 </s></p><p><figure id="id.1.2.5.02.00" xlink:href="FIG1/F025.jpg"></figure>
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629 <s id="id.1.2.5.02.01">Hoc supposito, sit linea, super quam fit motus, linea ab; et motus fiat ex a in b; et, si fieri potest, inveniantur in linea ab duo puncta in quibus <lb ed="Favaro" n="10"></lb> eadem sit virtus impellens, sintque c, d.
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630 </s><s id="id.1.2.5.02.02">Quia igitur tam in c quam in d eadem est virtus motiva et idem est medium, idemque est mobile et eadem linea in qua fit motus, ergo mobile ex puncto d eadem velocitate movebitur, qua ex puncto c motum est: verum ex puncto c ita motum est, ut ex c ad d eadem semper velocitate latum sit, nec virtus debilior evasit: ergo ex d quoque, per lineam aequalem lineae cd, eadem cum velocitate ciebitur, eadem manente virtute impressa.
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631 </s><s id="id.1.2.5.02.03">Non enim maior est ratio cur ex c in d eadem maneat virtus, non autem ex d in linea, versus b, aequali lineae cd; cum eadem sit virtus, idem mobile, idem medium, eademque linea motus.
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632 </s><s id="id.1.2.5.02.04"><lb ed="Favaro" n="20"></lb> Quare, eadem argumentatione repetita, demonstrabitur, motum d violentum nunquam remitti, sed eadem velocitate semper et in c infinitum ferri, eadem semper manente virtute motiva: quod certe <pb ed="manuscript" n="107v"></pb>absurdissimum est: non ergo verum est, in motu violento posse a duo puncta assignari, in quibus eadem maneat virtus impellens.
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633 </s><s id="id.1.2.5.02.05">Quod demonstrandum fuit.
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634 </s></p></subchap2><subchap2><p><s id="id.1.2.6.01.01">Magis certe inventu quam explicatu difficilis est causa, cur <lb ed="Favaro" n="30"></lb> naturalis motus velocitas in fine augeatur; eamque aut nullus hucusque invenit, aut, siquis interdum eam innuit, mancam quidem et defectuosam tradidit, et quae etiam a communibus philosophis recepta non <pb ed="Favaro" n="316"></pb> fuit.
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635 </s><s id="id.1.2.6.01.02">Huius tamen, non dicam admirabilis, sed necessarii effectus, causam cum interdum disquirerem (nunquam, enim, quae ab Aristotele traditur {1} arrisit), diu anxius fui, nec quod plene satisfaceret inveniebam.
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636 </s><s id="id.1.2.6.01.03">Verum, causa (meo tamen iudicio) verissima reperta, prima quidem fronte laetatus sum: verum, cum eam diligentius examinarem, non nulla difficultate carere suspicatus sum: sed tandem, omni difficultate temporis progressu exempta, exactam eam quidem et certissimam: nunc in medium afferam.
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637 </s><s id="id.1.2.6.01.04">Sed prius, de more nostro, quid roboris in se habeat causa quae ab Aristotele redditur, prius perpendemus.
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638 </s></p><p><s id="id.1.2.6.02.01">Et, primo, sciendum est, recentiores quosdam asserere, hanc causam <lb ed="Favaro" n="10"></lb> Aristotelem tribuere aëris partibus, quae terga mobilis verberant, eo ad replendum vacuum recurrentes: a qua verberatione, inquiunt ipsi, motus naturalis augumentatur.
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639 </s><s id="id.1.2.6.02.02">Atque hoc non sensisse Aristotelem aperte ex his quae <pb ed="manuscript" n="108r"></pb>leguntur p.Á Caeli 89 colligere est, ubi apertis verbis inquit: Naturalis motus non per extrusionem , ut quidam crediderunt, iuvatur; nam hoc pacto esset motus violentus, qui in fine remittitur, non autem augetur, ut naturalis.
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640 </s><s id="id.1.2.6.02.03">Patet ergo quomodo Aristoteles hanc opinionem non modo non teneat, verum respuat: et merito quidem est respuenda.
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641 </s><s id="id.1.2.6.02.04">Nam, quod dicunt de vacuo, aut relinquitur post terga mobilis vacuum, aut non: <lb ed="Favaro" n="20"></lb> si non, cur dicunt decurrere aërem ad vacuum replendum? at si relinquitur, cur non dicunt mobile quoque retrocedere ad vacuum replendum, et sic potius a tali causa retardari motum, non autem iuvari?
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642 </s><s id="id.1.2.6.02.05">2Á: accipiatur mobile aliquod, de quo non possit dubitari a tergo ab aëre impelli; quale esset rombus solidus ex duobus conis constans, utrinque in acutissimam cuspidem desinens.
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643 </s><s id="id.1.2.6.02.06">Hoc certe non poterit ab aëre impelli, cum illius figura non habeat in quod percutiat aër.
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644 </s><s id="id.1.2.6.02.07">3Á: ea, quae violentia moventur, non citius moventur quam id a quo moventur: verum aër, dum ad terga mobilis movetur, vi movetur (in sua enim regione natura quiescit): non ergo citius <lb ed="Favaro" n="30"></lb> moveri potest quam id a quo movetur.
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645 </s><s id="id.1.2.6.02.08">Movetur autem a corpore illo descendente; ergo non velocius movebitur aër quam mobile descendens: quod si non velocius movetur, illud certe impellere non poterit; <pb ed="Favaro" n="317"></pb> necessarium enim est ut, si quis currentem ad easdem partes, ad quas currit, impellere voluerit, ut velocius eo currat, et ad easdem partes, ad quas <pb ed="manuscript" n="108v"></pb>currens, concitetur.
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646 </s></p><p><figure id="id.1.2.6.03.00" xlink:href="FIG1/F026.jpg"></figure>
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647 <s id="id.1.2.6.03.01">Hoc autem in naturali mobili non accidit, imo aër ad contrarias partes movetur: ut si sphaera abc descendat, circumfluus aër, ex partibus b, c ad terga mobilis a decurrens, sursum, respectu motus sphaerae deorsum, movebitur.
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648 </s><s id="id.1.2.6.03.02">Quod etiam ipsi fatentur, dum dicunt medium motui resistere, quia est scindendum: si ergo scindendum est medium, non certe medium ad easdem <lb ed="Favaro" n="10"></lb> partes, ad quas mobile, movebitur.
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649 </s><s id="id.1.2.6.03.03">Ergo aut quiescet, aut ad contrarias, aut saltem tardius, si velimus ad easdem moveri, quam mobile, movebitur: quod cum ita sit, quomodo motum iuvabit?
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650 </s><s id="id.1.2.6.03.04">4Á: isti causam per se motus accelerationis non quaerunt, sed tantum causam per accidens adducunt; per accidens, enim est, quod mobile in pleno moveatur, et quod illius velocitas aut impediatur aut iuvetur a medio: nos autem quaerimus, cur mobile naturale, ut naturaliter movetur a propria gravitate, nulla habita ratione medii, velocius in fine quam in medio, et hic quam in principio, moveatur; et quomodo de ratione motus necessarium sit, in <lb ed="Favaro" n="20"></lb> principio segniorem esse.
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651 </s><s id="id.1.2.6.03.05">Haec contra huius opinionis sequaces.
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652 </s></p><p><s id="id.1.2.6.04.01">Alii dixerunt, mobile ideo in fine velocius moveri, quia pauciores medii partes sunt illi scindendae; et ideo, cum minorem habeat resistentiam, velocius ferri crediderunt.
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653 </s><s id="id.1.2.6.04.02">Verum ridicula, nedum falsa, est haec sententia: nam, si hoc esset verum, sequeretur, lapidem ab altissima turri descendentem tardius in medio turris moveri, quam si idem ab humillimo loco in terram decideret, et ob id minorem <pb ed="manuscript" n="109r"></pb>etiam ictum facere.
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654 </s></p><p><figure id="id.1.2.6.05.00" xlink:href="FIG1/F027.jpg"></figure>
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655 <s id="id.1.2.6.05.01">Quod ut clarius intelligatur, sit linea abc, sitque ac longe maior quam cb: dico igitur quod si ex a descenderet lapis, tardius moveretur cum esset circa c, quam, si idem lapis ex c <lb ed="Favaro" n="30"></lb> dimitteretur, prope b; quia, scilicet, pauciores partes aëris mobili c scindendae essent cum esset circa b, ex c demissus, quam cum esset circa c, ex a veniens.
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656 </s><s id="id.1.2.6.05.02">Addi etiam potest, quod lapis descendens ex a eodem impetu in terram irrueret, quo si ex c descenderet: et ratio est quia, ex a descendens, quando erat paulo sub c, non velocius movebatur quam ex c descendens, cum esset paulo sub c, quia non pauciores tunc restabant scindendae partes aëris quam nunc; ex qua <pb ed="Favaro" n="318"></pb> scissione inquiunt ipsi pendere motus celeritatem.
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657 </s><s id="id.1.2.6.05.03">Haec autem omnia quam sint absona, nullus est qui ignoret.
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658 </s></p><p><s id="id.1.2.6.06.01">Verum, caeterorum omissis sententiis, ut veram, quam credimus, huius effectus causam indagemus, hac resolutiva methodo utemur.
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659 </s><s id="id.1.2.6.06.02">Quia igitur grave mobile (loquamur autem de motu naturali deorsum, a gravitate proveniente: nam, hoc cognito, contrario discurrentes modo de motu sursum iudicabimus) descendens, tardius movetur in principio, ergo necessarium est, illud minus esse grave in principio sui motus quam in medio vel in fine; cum certo sciamus, ex demonstratis in primo libro, velocitatem et tarditatem, gravitatem et levitatem sequi.
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660 </s><s id="id.1.2.6.06.03">Si <lb ed="Favaro" n="10"></lb> igitur inventum fuerit, quomodo mobile et cur in principio motus sit minus grave, erit certe causa inventa cur tardius descendat.
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661 </s><s id="id.1.2.6.06.04">Verum naturalis et intrinseca mobilis gravitas certe non est diminuta, quia nec diminuta est moles nec densitas <pb ed="manuscript" n="109v"></pb>illius: restat ergo, imminutionem illam gravitatis esse praeternaturalem et accidentariam.
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662 </s><s id="id.1.2.6.06.05">Si ergo invenerimus, quomodo praeternaturaliter et extrinsece mobilis gravitas minuatur, erit certe inventum propositum.
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663 </s><s id="id.1.2.6.06.06">At gravitas illa non imminuitur ob medii gravitatem; nam tam in principio motus quam in medio idem est medium: restat ergo, a violentia aliqua extrinseca et de foris adveniente mobilis gravitatem diminutam esse (his duobus <lb ed="Favaro" n="20"></lb> tantum modis mobile per accidens leve evadere contingit). {1}
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664 </s><s id="id.1.2.6.06.07">Si igitur, rursus, inveniamus, quomodo a vi extrinseca possit allevari mobile, erit, rursus, inventa causa tarditatis.
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665 </s><s id="id.1.2.6.06.08">At virtus impressa a proiiciente non solum interdum minuit gravis gravitatem, verum etiam saepius adeo leve ipsum reddit, ut magna velocitate sursum advolet: videamus ergo et diligenter perscrutemur, an forte virtus ista sit causa diminuendae gravitatis mobilis in principio sui motus.
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666 </s><s id="id.1.2.6.06.09">At illa certe est virtus, inquam, a proiciente impressa, quae motum naturalem segniorem in principio facit: qua ratione autem id praestare possit, <pb ed="Favaro" n="319"></pb> ad declarandum properemus.
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667 </s><s id="id.1.2.6.06.10">Mobile grave ad hoc ut violenter sursum moveri possit, necessaria est virtus impellens maior gravitate resistenti; alioquin gravitas resistens non posset vinci, nec, consequenter, grave sursum ferri.
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668 </s><s id="id.1.2.6.06.11">Fertur, ergo, sursum mobile, dum motiva virtus impressa maior est gravitate resistente.
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669 </s><s id="id.1.2.6.06.12">Cum autem ista virtus, ut demonstratum est, continue debilitetur, deveniet tandem adeo diminuta, ut mobilis gravitatem non amplius vincet, et tunc non ulterius impellet mobile: sed tamen non ideo in fine motus violenti erit adnihilata virtus illa <pb ed="manuscript" n="110r"></pb>impressa, sed tantum adeo erit diminuta, ut non <lb ed="Favaro" n="10"></lb> amplius gravitatem mobilis superet, sed illi aequabitur; et, ut uno verbo dicam, in mobili non amplius dominabitur virtus sursum impellens, quae est levitas, sed ad paritatem cum mobilis gravitate redacta erit: et tunc, in ultimo puncto motus violenti, nec grave nec leve erit mobile.
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670 </s><s id="id.1.2.6.06.13">Sed amplius, suo more decrescente virtute impressa, incipit praedominari gravitas mobilis; quare et mobile descendere aggreditur.
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671 </s><s id="id.1.2.6.06.14">Sed quia in principio talis descensus superest adhuc multa virtus sursum impellens (licet non amplius maior sit gravitate mobilis), quae est levitas, hinc fit ut gravitas propria mobilis ab hac levitate minuatur, et, consequenter, motus tardior sit in principio.
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672 </s><s id="id.1.2.6.06.15">Et, <lb ed="Favaro" n="20"></lb> rursus, quia extrinseca illa virtus amplius debilitatur, minorem gravitas mobilis resistentiam habens augetur, et mobile velocius adhuc movetur.
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673 </s></p><p><s id="id.1.2.6.07.01">Et hanc veram existimo causam accelerationis motus: quam quidem cum excogitassem, et, post duos menses, forte quae ab Alexandro de hac re scribuntur legerem, ex eo intellexi, hanc quoque fuisse sententiam doctissimi illius philosophi a doctissimo viro laudati, a Ptolemaeo, nempe, a quo magni habetur et summis laudibus per totum suae Magnae Constructionis contextum extollitur Hipparchus.
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674 </s><s id="id.1.2.6.07.02">Hanc itaque, referente Alexandro, credidit Hipparchus quoque causam <lb ed="Favaro" n="30"></lb> esse accelerationis motus naturalis: verum, quia nihil amplius addidit supra id quod diximus, manca quidem visa haec est opinio, et, ob id, digna ut re<pb ed="manuscript" n="110v"></pb>praehendatur a philosophis est habita; quippe quae tantummodo locum habeat in motibus illis naturalibus quibus violentus praecesserit, nec tribui possit illi motui qui violentum non sequitur.
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675 </s><s id="id.1.2.6.07.03">Verum non contenti sunt ipsam tanquam mancam respuere, verum <pb ed="Favaro" n="320"></pb> etiam tanquam falsam, nec etiam in motu, cui violentus praecesserit, veram.
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676 </s><s id="id.1.2.6.07.04">Nos vero et ea quae ab Hipparco explicata non sunt addemus, ostendendo, quomodo etiam in motu, cui non praecessit violentus, causa eadem locum habeat; ipsamque ab omni calumnia purgatam reddere conabimur.
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677 </s><s id="id.1.2.6.07.05">Nec tamen dixerim, omnino repraehensione indignum esse Hipparcum; scopulum enim magni momenti indetectum reliquit: sed solum ea quae desunt superaddam, veritatisque fulgorem ostendam.
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678 </s></p><p><s id="id.1.2.6.08.01">Dico igitur, eandem ob causam motus etiam, quibus non praecessit motus violentus, tardius in principio moveri.
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679 </s><s id="id.1.2.6.08.02">Nanque etiam in motibus quibus violentus praecessit, mobile a statu quietis, non a <lb ed="Favaro" n="10"></lb> violento motu, moveri, incipit.
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680 </s><s id="id.1.2.6.08.03">Ut lapis sursum proiectus, quando incipit deorsum moveri ab extremo illo puncto in quo aequalitas inter virtutem impellentem et gravitatem resistentem contingit, quod est quietis status, incipit descendere; quod idem est ac si de manu alicuius decideret.
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681 </s><s id="id.1.2.6.08.04">Quando enim etiam de manu, nulla vi sursum impellente impressa, decidit lapis, cum tanta virtute impressa discedit, quanta est sua gravitas.
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682 </s><s id="id.1.2.6.08.05">Nam quando lapis in manu alicuius quiescit, tunc non est dicendum, lapidem habentem, nullam vim in lapide imprimere: quia enim lapis sua gravitate deorsum premit, necesse est ut altera tanta vi a manu sursum impellatur, nec <lb ed="Favaro" n="20"></lb> maiori nec minori.
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683 </s><s id="id.1.2.6.08.06">Nam si virtus, qua manus sursum impellit lapidem, maior esset quam gravitas lapidis, resistens lapis a manu attolleretur; non autem quiesceret, <pb ed="manuscript" n="111r"></pb>ut supponimus: contra, vero, si lapis magis gravaret quam manus allevaret, lapis deorsum peteret; supponimus autem, lapidem in manu quiescere: ergo in lapide, a manu vel a quocunque alio a quo regitur, tanta virtus sursum impellens imprimitur, quanta est gravitas lapidis deorsum tendens; nec tamen lapis attollitur, quia, ut diximus, virtus illa impellens superare non potest gravitatem resistentem, cum ea non sit maior.
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684 </s><s id="id.1.2.6.08.07">Patet ergo, quomodo, quando lapis ex manu egreditur, cum tanta virtute impressa discedit, <lb ed="Favaro" n="30"></lb> quanta est suamet gravitas: non secus ac accidit quando lapis, absoluto motu sursum, deorsum petere aggreditur; tunc enim etiam, quando de statu quietis recedit, cum tanta virtute discedit, quanta est sua gravitas: quare eandem ob causam, sicut in hoc, in illo etiam motu, tardius in principio movetur.
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685 </s></p><p><s id="id.1.2.6.09.01"><pb ed="Favaro" n="321"></pb> Verum, ut adhuc totum hoc negocium clarius explicetur, exemplum particulare in medium afferam.
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686 </s></p><p><figure id="id.1.2.6.10.00" xlink:href="FIG1/F028.jpg"></figure>
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687 <s id="id.1.2.6.10.01">Sit linea ab, super quam fit motus violentus ex a in ab, naturalis vero ex b in a; sit autem mobile c, cuius gravitas sit 4.
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688 </s><s id="id.1.2.6.10.02">Oportet igitur, ad hoc ut mobile c sursum moveatur, ut in eo virtus motiva imprimatur maior quam sit illius gravitas: ab aequali enim virtute non moveretur; nam nec grave esset nec leve, cum sua gravitas aequaretur virtuti impressae, quae est levitas.
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689 </s><s id="id.1.2.6.10.03">Sit ergo virtus, quae c usque ad b impellere potest, 8: et quia virtus motiva, ut supra demonstravimus, continue remittitur, <lb ed="Favaro" n="10"></lb> nec potest c movere nisi maior fuerit mobilis gravitate, patet quod, quando c erit in b, virtus impressa erit tanta <pb ed="manuscript" n="111v"></pb>quam est gravitas c.
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690 </s><s id="id.1.2.6.10.04">Non enim erit minor, quia non impulisset usque ad b; nec maior, quia adhuc ulterius impelleret: restat ergo necessario ut sit aequalis.
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691 </s><s id="id.1.2.6.10.05">Quando ergo e est in b, habet tantam virtutem impressam quanta est sua gravitas, nempe 4: quae virtus, quia adhuc successive debilitatur, statim atque diminui incipit, c se ad motum deorsum convertit.
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692 </s><s id="id.1.2.6.10.06">Quando igitur ex primo puncto b descendere incipit, c recedit cum tanta virtute impressa quanta est sua gravitas; quare b tardissime in principio talis motus movebitur: verum quo magis <lb ed="Favaro" n="20"></lb> virtus contraria remittitur et, consequenter, gravitas augetur, motus quoque velocior contingit.
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693 </s><s id="id.1.2.6.10.07">Rursus, si 8 virtutis impressae pellunt c usque ad b, patet quod potest imprimi tanta virtus quae, tantum usque ad d, c impellat: quae certe minor erit quam 8, sed tamen maior quam 4; tanta enim est gravitas c resistens.
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694 </s><s id="id.1.2.6.10.08">Amplius, potest etiam imprimi tanta virtus quae tantummodo usque ad e pellat c: quae, rursus, minor erit quam illa quae usque ad d impellit, sed tamen maior erit quam 4; nam ab aequali 4 c non movetur.
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695 </s><s id="id.1.2.6.10.09">Et, similiter, poterit tantundem virtutis imprimi, quae c per minima quaeque spacia, in linea ae <lb ed="Favaro" n="30"></lb> sumpta, sursum impellat.
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696 </s><s id="id.1.2.6.10.10">Verumtamen haec virtus, cum sursum moveat, semper erit maior quam 4: et virtus omnis quae minor fuerit quam 4, non solum c sursum non impellit, verum nec illi resistere potest quominus descendat, cum a gravitate maiori superetur: restat ergo necessario, ut virtus impressa, quae sit 4, <pb ed="manuscript" n="112r"></pb>solummodo c substineat: <pb ed="Favaro" n="322"></pb> quare, quando c quiescet, erit in eo virtus sursum impellens impressa, quae erit 4.
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697 </s><s id="id.1.2.6.10.11">Quod si ab imprimente virtute derelinquatur, cum 4 virtutis impressae recedet: non ergo sursum post talem recessum movebitur; verum tardissime descendet in principio, et eo citius deinde movebitur, quo magis virtus contraria debilitabitur.
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698 </s></p><p><s id="id.1.2.6.11.01">Haec vera propria potissimaque est causa, qua indubitanter asserimus, naturalem motum in principio tardiorem esse; quam qui recte et aequa mente examinabunt, dubio procul amplectentur et tanquam verissimam sequentur.
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699 </s><s id="id.1.2.6.11.02">Verum poterant haec eadem faciliori methodo consequi?
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700 </s><s id="id.1.2.6.11.03">Poterant, certe? et naturaliter discurrenti facile innotescere: <lb ed="Favaro" n="10"></lb> nanque, amabo, nonne in idem coincidunt hae 2 propositiones, Motus violentus tardus est in fine, Ergo motus naturalis tardus est in principio?
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701 </s><s id="id.1.2.6.11.04">Motus enim naturalis violentum sequitur, et finis violenti cum principio naturalis est coniunctus: sed tarditatis motus violenti in fine causa est modicus excessus, quo virtus impellens gravitatem resistentem, hoc est quo causa motus violenti causam motus naturalis, excedit: ergo, pari pacto, tarditatis motus naturalis in principio causam censendum est esse modicum excessum quo causa motus naturalis causam motus violenti, hoc est gravitas deorsum premens levitatem, idest virtutem impressam, sursum impellentem, superat.
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702 </s><s id="id.1.2.6.11.05">Videatis, ergo, quam bene vera inter se <lb ed="Favaro" n="20"></lb> congruant.
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703 </s><s id="id.1.2.6.11.06">Ex hoc autem discursu facile quispiam intelligere poterit, quomodo isti 2 motus non vere sint contrarii, sed potius motus quidam ex violento et naturali compositus: nanque motus isti <pb ed="manuscript" n="112v"></pb>locales ex motibus aliis quibusdam alterativis quodammodo pendent, dum in mobili propria gravitas et extranea levitas (levitatem enim deinceps appellabimus virtutem impressam) permiscentur.
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704 </s><s id="id.1.2.6.11.07">Es tali mixtione sequitur, et quodammodo per accidens, ut nunc sursum nunc deorsum moveatur mobile: cum enim in mixtione plus fuerit levitatis quam gravitatis, ex ea effectus levitatis orietur, nempe motus sursum; quod si in mobili, diminuta levitate, plus fuerit gravitatis, effectus gravitatis, <lb ed="Favaro" n="30"></lb> nempe motus deorsum, emanabit.
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705 </s><s id="id.1.2.6.11.08">Verum motus iste alterativus, dum mobile ex levitate ad gravitatem movetur, est unus et continuus motus: ut cum aqua ex calida per accidens fit frigida, unico motu ad frigiditatem movetur, nec motus ex calida in tepidam est alius a motu ex tepida in frigidam; sic et dum ex levi fit nec grave nec leve, non est motus disiunctus a motu dum ex nec gravi nec levi fit grave.
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706 </s><s id="id.1.2.6.11.09"><pb ed="Favaro" n="323"></pb> Tantum, ergo, abest ut isti motus sint contrarii, ut etiam unum tantum, continuum, et ad eundem terminum, sint: quare et effectus qui ex hisce causis manant contrarii vere non erunt appellandi, cum effectus contrarii ex causis contrariis pendeant: quare motus sursum consequenti motui deorsum, qui motus ex motu mixtionis levitatis et gravitatis manant, vere contrarius non erit dicendus.
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707 </s><s id="id.1.2.6.11.10">Et ex hoc facile etiam deduci potest, quomodo in puncto reflexionis quies non intercedat.
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708 </s><s id="id.1.2.6.11.11">Nam, si tunc esset quies, necessarium esset, quietem etiam contingere in motu illo mixtionis gravitatis <pb ed="manuscript" n="113ar"></pb>et levitatis, quando levitas ad <lb ed="Favaro" n="10"></lb> aequalitatem cum gravitate devenisset; mobile enim tunc solum quiescere potest, quando virtus impellens nec vincit nec vincitur: verum, ut iam declaravimus, motus ille, dum ex levi fit grave, est unus et continuus, ut cum ex calido fit frigidum, quod in tempore non quiescit: quare et motus locales, qui ex eo manant, erunt unus et continuus.
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709 </s><s id="id.1.2.6.11.12">Sed, quia haec sententia communi opinioni adversatur (creditur communiter, in punto reflexionis dari quietem), in sequens caput transferetur; ubi prius adversa sententia examinabitur et confutabitur, nostraque opinio adhuc validior reddetur.
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710 </s></p></subchap2><subchap2><p><s id="id.1.2.7.01.01">Crediderunt Aristoteles et qui Aristoteli credunt, duos motus contrarios (vocat autem contrarios qui ad contrarios terminos tendunt) nullo posse modo continuari; et, idcirco, quando lapis sursum impellitur et inde per eandem lineam retrocedit, eum necessario in puncto reflexionis quiescere.
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711 </s><s id="id.1.2.7.01.02">Potissimum autem argumentum, quo Aristoteles id probare contendit, {1} tale est: Quod {2} movetur ad aliquod punctum accedendo et <pb ed="Favaro" n="324"></pb> ab eodem recedendo, ac ut fine et principio utendo, non recedet nisi in eo constiterit: at quod ad extremum lineae punctum movetur et ab eodem reflectitur, utitur eo ut fine et principio: inter accessum, ergo, et recessum ut stet, est necessarium.
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712 </s><s id="id.1.2.7.01.03">Maiorem propositionem sic probat Aristoteles: Nam qui utitur aliquo ut principio et fine, quod unum numero est, duo ratione facit; quemadmodum qui mente cogitat, qui eundem numero punctum, qui unus numero est, facit duo ratione, nempe finem huius, principium vero alterius: verum si uno tanquam duobus utitur, ut in eo stet est necessarium, inter duo, enim, tempus est.
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713 </s></p><p><s id="id.1.2.7.02.01">Haec est argumentatio Aristotelis; quae quidem quantum infirma <lb ed="Favaro" n="10"></lb> <pb ed="Favaro" n="325"></pb> sit, mox apparebit.
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714 </s><s id="id.1.2.7.02.02">Nam, sicut ipse vult, quod movetur utitur in linea sui motus puncto uno, numero, pro duobus, ratione, ut pro principio et pro fine; et tamen inter haec duo linea non intercedit, cum unum tantum sint numero: cur etiam idem mobile , eodem modo, in tempore sui motus non utetur eodem instanti, numero, pro duobus, ratione, nempe pro fine <pb ed="manuscript" n="113bv"></pb>temporis accessus et pro principio temporis recessus, ita ut inter haec duo instantia, ratione, non sit tempus, cum unum tantum, numero, sint?
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715 </s><s id="id.1.2.7.02.03">Hoc cur non fieri debeat, ratio nulla urget; ac praesertim cum idem Aristoteles <lb ed="Favaro" n="10"></lb> doceat, quae lineae competunt, tempori etiam et motui eadem convenire.
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716 </s><s id="id.1.2.7.02.04">Si, ergo, in eadem linea idem, numero, punctus ist finis est huius motus et principium alterius , nec tamen inter hoc principium et finem illum ut mediet linea necesse est; sic et idem instans numero, ratione fiet finis huius temporis et principium alterius, nec tamen ut tempus intercidat necesse erit.
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717 </s><s id="id.1.2.7.02.05">Constat igitur, quomodo Aristotelis argumenti solutio ex eiusdem argumenti propositionibus apte hauriri possit: quare, cum nos amplius non urgeat, videamus an in contrarium magis acriusque urgentia argumenta construere possimus.
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718 </s></p><p><s id="id.1.2.7.03.01"><lb ed="Favaro" n="20"></lb> <pb ed="manuscript" n="114r"></pb>Haec contra Aristotelem: verum, ut aliis argumentis in puncto reflexionis non intercedere quietem ostendamus, nec sit inter contrarios motus necessaria quies, alia haec sint argumenta.
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719 </s></p><p><figure id="id.1.2.7.04.00" xlink:href="FIG1/F029.jpg"></figure>
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720 <s id="id.1.2.7.04.01">2Á: moveatur aliquod continuum, ut linea ab tota, ad partes b motu violento simili, qui continue remittatur: et dum ita fertur linea, aliquod mobile, ut puta c, moveatur super lineam eandem contrario motu, ex b in a; sed hic motus sit naturali similis, qui scilicet, augeatur: sed motus lineae in principio sit velocior motu c in principio.
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721 </s><s id="id.1.2.7.04.02">Manifestum iam est, quod in principio c movebitur ad easdem partes ad quas linea <lb ed="Favaro" n="30"></lb> fertur, quia illius motus, quo in contrarias fertur, <pb ed="manuscript" n="114v"></pb>tardior est motu lineae; attamen, quia motus lineae remittitur, motus vero c augetur, movebitur aliquando c vere ad partes sinistras, et sic faciet transitum de motu ad dextram ad motum ad sinistram et super lineam eandem; nec tamen in puncto regressus quiescet per aliquod tempus.
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722 </s><s id="id.1.2.7.04.03">Et ratio est quia non potest quiescere, nisi tanta velocitate moveatur linea ad partes dextras, quanta mobile c ad sinistras fertur: <pb ed="Favaro" n="326"></pb> verum nunquam accidet quod per aliquod temporis spatium duret haec aequalitas, cum alter motus continue remittatur, alter vero continue intendatur: ergo, necessario, ex motu uno ad contrarium transibit c, nulla intercedente quiete.
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723 </s><s id="id.1.2.7.04.04">3um argumentum desumi potest a motu quodam recto, quem ex duobus circularibus motibus Nicolaus Copernicus in suis Revolutionibus componit.
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724 </s><s id="id.1.2.7.04.05">Sunt enim duo circuli, quorum alter in alterius circumferentia fertur, cuius signum unum, dum alter altero citius movetur, in recta fertur linea et per eandem continue regreditur; nec tamen dici potest, illud in extremis quiescere, cum continue a circuli circumferentia circumducatur.
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725 </s><s id="id.1.2.7.04.06">4um est vulgatum <lb ed="Favaro" n="10"></lb> argumentum de magno lapide ex turri descendente, qui a calculo sursum vi impulso non firmabitur, ad hoc ut sinat calculum aliquantisper quiescere: quare calculus certe in ultimo puncto sui motus sursum non quiescet, et, invito Aristotele, utetur ultimo puncto pro terminis duobus, scilicet motus sursum et motus deorsum; et est ultimum instans bis sumptum, pro fine, scilicet, unius temporis et pro principio alterius.
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726 </s><s id="id.1.2.7.04.07">Verum, ut hoc aufugiant adversarii, dicunt, magnum illum lapidem quiescere; et ita <pb ed="manuscript" n="115r"></pb>sibi satis argumento fecisse suadent.
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727 </s><s id="id.1.2.7.04.08">Verum, ut in posterum (nisi pervicacissimi omnino fuerint) hoc non credant, hoc addam argumento: isti lapides, qui contrarii moventur <lb ed="Favaro" n="20"></lb> motibus, non sursum et deorsum, sed in plana horizonti aequidistante superficie ferantur, alter quidem magno impetu, alter vero tardius, et ex contrariis in contraria moveantur; in medio autem motu mutuo occurrant: tunc dubio procul debilior a fortiori reicietur et retro ferri cogetur; at quomodo in puncto illo conflictus quietem intercedere dicent?
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728 </s><s id="id.1.2.7.04.09">Si enim semel quiescerent, semper deinde quiescerent, cum causam movendi non habeant: sicut magnus ille lapis, ab alto veniens, si a calculo sisteretur, tamen, post quietem, ambo concordes descenderent, a propria gravitate moti; at cum in plano horizonti aequidistanti fuerint, nulla motus, post quietem, habetur causa.
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729 </s><s id="id.1.2.7.04.10"><lb ed="Favaro" n="30"></lb> Ultimum sit argumentum: ante cuius explicationem haec duo supponantur.
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730 </s><s id="id.1.2.7.04.11">Primum, quod suppono, est, tunc solum posse mobile extra locum proprium quiescere, quando virtus prohibens descensum aequabitur gravitati suae deorsum prementi: quod certe manifestum est; nam si virtus impressa esset maior gravitate resistente, mobile adhuc <pb ed="Favaro" n="327"></pb> sursum moveretur; quod si esset minor, iam descenderet.
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731 </s><s id="id.1.2.7.04.12">Suppono, secundo, idem mobile ab aequalibus virtutibus per aequalia temporis spatia in eodem loco substineri posse.
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732 </s><s id="id.1.2.7.04.13">Tunc sic insto: si in puncto reflexionis, ut cum lapis a motu sursum violento ad motum deorsum convertitur, datur quies, quae aliquod temporis spatium duret, dabitur <pb ed="manuscript" n="115v"></pb>et per idem tempus aequalitas inter vim impellentem et gravitatem resistentem: quod quidem est impossibile, cum vim impellentem continue remitti capite superiori sit demonstratum; est enim motus, quo lapis ex levi per accidens ad gravitatem movetur, motus <lb ed="Favaro" n="10"></lb> unus continuus, sicut dum ferrum ex calore movetur ad frigiditatem: non ergo quiescere poterit lapis.
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733 </s></p><p><figure id="id.1.2.7.05.00" xlink:href="FIG1/F030.jpg"></figure>
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734 <s id="id.1.2.7.05.01">Amplius: moveatur lapis ex a in b violenter, ex b in a naturaliter; si, ergo, lapis in b per aliquod temporis spacium quiescit, sit tale tempus, cuius extrema momenta sint cd.
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735 </s><s id="id.1.2.7.05.02">Si ergo mobile quiescit tempus cd, ergo virtus estrinseca impellens aequalis est gravitati mobilis per tempus cd: sed naturalis gravitas semper est eadem: ergo virtus in momento c est aequalis virtuti in momento d.
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736 </s><s id="id.1.2.7.05.03">Estque idem lapis, idemque locus; ergo per aequalia temporis spacia a virtutibus aequalibus substinebitur: sed virtus in momento c per cd tempus substinet: <lb ed="Favaro" n="20"></lb> ergo virtus in momento d substinebit eundem lapidem per spacium temporis aequale spacio cd.
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737 </s><s id="id.1.2.7.05.04">Quiescet igitur lapis per duplum temporis cd: quod est inconveniens; ponebatur enim quiescens solum per tempus cd.
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738 </s><s id="id.1.2.7.05.05">Eadem vero argumentandi ratione servata, demonstrabitur etiam, lapidem in b semper quiescere.
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739 </s><s id="id.1.2.7.05.06">Neque perturberis ab hoc, quod, scilicet, si aliquando gravitas et virtus impellens aequantur, debeat etiam mobile aliquando quiescere: nanque aliud est dicere, mobilis gravitatem aliquando ad aequalitatem cum vi impellente devenire; aliud vero, eam in tali aequalitate per temporis spatium commorari.
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740 </s><s id="id.1.2.7.05.07">Hoc autem inde fit <lb ed="Favaro" n="30"></lb> manifestum: nam, cum mobile movetur, eo quod (ut dictum est) virtus impellens semper remittitur, gravi<pb ed="manuscript" n="116r"></pb>tas vero intrinseca semper eadem manet, sequitur necessario ut, antequam ad proportionem aequalitatis pervenerint, innumerae aliae proportiones intercedant: attamen vim et gravitatem in aliqua istarum proportione per aliquod tempus manere, est impossibile; cum demonstratum sit, nunquam virtutem impellentem per aliquod temporis spacium in eodem statu consistere, <pb ed="Favaro" n="328"></pb> cum semper remittatur.
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741 </s><s id="id.1.2.7.05.08">Verum itaque est, vim et gravitatem per proportionem, verbigratia, duplam, sesquialteram, sesquitertiam, et alias innumeras, transire; quod autem per aliquod tempus in una earum maneant, hoc falsum et impossibile: sic etiam ad aequalitatem quandoque deveniunt, sed in aequalitate non sistunt.
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742 </s><s id="id.1.2.7.05.09">Quod cum ita sit, et ad motum istum alterativum transmutationis de levi per accidens ad grave per se consequatur motus localis sursum et deorsum; ita ut ab excessu virtutis impressae sequatur sursum, a defectu deorsum, ab aequalitate vero quies; cum aequalitas per temporis spatium non duret, et quies ut non duret necessarium est. <lb ed="Favaro" n="10"></lb>
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743 </s></p></subchap2><subchap2><p><s id="id.1.2.8.01.01">Existimavit Aristoteles (ut videre est p.Á Caeli t. 88), motum naturalem non solum semper accelerari donec ad proprium locum pervenerit mobile, verum etiam, si infinite motus continuari posset, infinite etiam auctum iri eius gravitatem et motus celeritatem.
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744 </s><s id="id.1.2.8.01.02">Ita enim scribit, dum ostendere contendit, quae moventur, ad aliquem locum determinatum ferri: Si terra, dum deorsum movetur, non ad determinatum <lb ed="Favaro" n="20"></lb> locum sed in infinitum moveretur, infinite <pb ed="manuscript" n="116v"></pb>etiam augeretur illius gravitas et velocitas; verum infinita gravitas et infinita velocitas dari non potest; ergo non in infinitum movetur quod fertur deorsum.
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745 </s><s id="id.1.2.8.01.03">Haec igitur est opinio Aristotelis: nos autem, quae his ex diametro adversantur vera esse, manifestabimus; nempe, neque semper augeri velocitatem, neque, etiam si semper augeretur et in infinitum extendi posset motus, necessario deveniendum esse ad infinitam gravitatem et instantaneam celeritatem, ostendemus.
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746 </s></p><p><s id="id.1.2.8.02.01">Quod igitur ad primum attinet, facile quispiam intelligere poterit ex his quae supra scripta sunt, percepta causa accelerationis motus <lb ed="Favaro" n="30"></lb> naturalis in fine, cur tandem ista acceleratio desinere debeat.
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747 </s><s id="id.1.2.8.02.02">Cum enim ideo mobile acceleretur quia virtus contraria continue remittitur, <pb ed="Favaro" n="329"></pb> gravitas vero naturalis acquiritur, rationi quidem consentaneum erit ut tandem tota virtus contraria deperdatur, naturalisque resumatur gravitas, atque, iccirco, remota causa, acceleratio desinat.
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748 </s><s id="id.1.2.8.02.03">Nec tamen dixerim, ideo totam absumi virtutem contrariam, quia forte crediderim necessarium esse, omne quod semper imminuitur tandem adnihilari (hoc enim necessarium non esse non me latet, ut inferius dicetur); sed solum dicam eam absumi, quia experientia id ostendere nobis videtur.
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749 </s><s id="id.1.2.8.02.04">Primo, enim, si quid non admodum grave ex alto veniens aspiciemus, qualis esset vel lanae globus vel pinna vel quid tale, <lb ed="Favaro" n="10"></lb> videbimus tardius quidem in principio moveri, sed tamen, paulo post, motum uniformem observare.
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750 </s><s id="id.1.2.8.02.05">Cur autem id in minus gravibus manifestius appareat, ratio est quia, cum incipiunt moveri, eo quod tantum virtutis contrariae habeant quanta est propria gravitas, sintque ipsa modicum gravia, modica, ergo, etiam erit virtus impressa contra<pb ed="manuscript" n="117r"></pb>ria, quare et citius absumetur; qua absumpta, motu uniformi movebuntur: et cum tarde etiam moveantur, facilius erit talis motus uniformitatem observare quam in his quae citissime descendunt.
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751 </s><s id="id.1.2.8.02.06">In rebus autem gravioribus, cum multa in eorum descensu absumenda sit virtus contraria, maius etiam tempus ad eam absumendam requiretur; <lb ed="Favaro" n="20"></lb> in quo tempore, cum cito ferantur, per magnum spatium descendent: quae magna spatia cum apud nos haberi non possint, unde gravia demittantur, non mirum est si lapis, ex sola turris altitudine demissus, usque ad terram accelerari videbitur; hoc enim breve spacium breveque tempus motus non sufficit ad totam virtutem contrariam deperdendam.
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752 </s><s id="id.1.2.8.02.07">2a experientia desumi potest ex aliis motibus alterativis, in quibus tandem omnino deperditur qualitas contraria; ut cum, ex candente, ferrum fit frigidissimum, totusque penitus adnihilatur calor.
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753 </s><s id="id.1.2.8.02.08">Eadem ergo ratione, dum lapis ex levi fit grave, ut totam perdat extraneam levitatem, iudicandum est; quod cum factum fuerit, <lb ed="Favaro" n="30"></lb> cessabit velocitatis intensio.
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754 </s><s id="id.1.2.8.02.09">3Á: ratione et experientia comprobari etiam potest, non solum motus non semper accelerari dum mobile a statu quietis recesserit; verum etiam, si in principio motus ab externo motore magna imprimatur vis deorsum impellens, hanc quoque destrui.
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755 </s><s id="id.1.2.8.02.10">Et ratio quidem est, quia tunc mobilis gravitas haberet rationem levitatis, eo quod ipsamet libera et simplex tardius descenderet, quam cum impetu coniuncta; violentiae itaque deorsum impellentis <pb ed="Favaro" n="330"></pb> resisteret propria et naturalis tarditas descendentis.
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756 </s><s id="id.1.2.8.02.11">Exemplo etiam manifestum est, quod urinatoribus et natantibus saepius accidit.
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757 </s><s id="id.1.2.8.02.12">Eorum enim tanta est naturalis gravitas, ut descendant, <pb ed="manuscript" n="117v"></pb>si voluerint, ad imum usque maris, et tunc solum, a propria gravitate tracti, demergentur: quod si ab externo motore, quantumvis maxima vi, deorsum impellantur, ut si ab excelso loco, qualis esset summitas mali navis, praecipitentur, in principio quidem in aqua motus erit valde concitatus et supranaturalis; attamen a gravitate propria absoluta, quae tunc, respectu gravitatis cum impetu accepto coniunctae, est levitas, retardabitur motus, et eo usque donec descendens ad <lb ed="Favaro" n="10"></lb> naturalem tarditatem devenerit; atque si aqua satis fuerit profunda, non maiorem in fundo laesionem patietur, quam si ex aquae summitate proprio naturalique motu descendisset.
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758 </s><s id="id.1.2.8.02.13">Et ex his sic ratio hauriri potest: si enim descendens semper acceleraretur in motu, capax esset cuiuscunque celeritatis, ut celeritas nulla esset illi supranaturalis; ergo et impetum acceptum deorsum ab externo motore non deperderet ac respueret, cum ad eundem impetum tandem naturaliter etiam devenisset: at contrarium accidere experientia docet: patet ergo unicuique, naturali motu descendenti determinatam statutamque celeritatem praescriptam esse. {1} <lb ed="Favaro" n="20"></lb>
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759 </s></p><p><s id="id.1.2.8.03.01">Verum quod, et si semper celeritas intenderetur et infinitum esset spatium motus, non tamen sequeretur, motum tandem ad infinitam celeritatem devenire et mobile ad infinitam gravitatem, non difficile erit eis intelligere, qui in mathematicis versati fuerint.
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760 </s><s id="id.1.2.8.03.02">Simile enim hoc est ei quod illis fere omnibus impossibile videtur, qui demonstrationis non sunt capaces: quod, scilicet, inve<pb ed="manuscript" n="118r"></pb>niri possint duo lineae, quae, in infinitum protractae, semper appropinquentur, nunquam tamen concurrant; ita ut distantia, quae inter eas est, semper in infinitum minuatur, nunquam tamen absumatur.
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761 </s><s id="id.1.2.8.03.03">Verum tales lineas dari, omnes norunt qui aut in asymptotos hyperboles in Conicis Apollonii Pergaei, <lb ed="Favaro" n="30"></lb> aut in primam lineam conchoidem Nicomedis, apud Eutocium <pb ed="Favaro" n="331"></pb> Ascalonitam in Commentariis super librum secundum inimitabilis Archimedis De sphaera et cylindro, inciderint: sunt enim hae duae lineae (et multae etiam aliae excogitari possent), quae, in infinitum protractae, semper magis accedunt, verum ut aliquando concurrant impossibile est; minuitur ergo semper eorum distantia, nunquam tamen absumitur.
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762 </s><s id="id.1.2.8.03.04">Et si linea ad rectos angulos super lineam rectam quae conchoidi subiacet, vel super asymptotum, excitetur, et hanc ponamus moveri, semper manentibus angulis rectis, in infinitum versus partes ad quas in infinitum extenduntur lineae non concurrentes; in hac linea ad rectos <lb ed="Favaro" n="10"></lb> angulos, punctus, quo ab hyperbole vel conchoide secatur, semper versus alteram extremitatem movebitur ad eam accedendo, nunquam tamen perveniet ad ultimum punctum.
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763 </s><s id="id.1.2.8.03.05">Pari etiam pacto de celeritate accidit: potest enim semper tarditas motus imminui et, consequenter, celeritas augeri, nec tamen aliquando absumi.
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764 </s><s id="id.1.2.8.03.06">Ut, exempli causa, sit tarditas ab, quam si totam mobile absumeret, motus in instanti contingeret: dico, non esse necessarium, quamvis semper in infinitum minuatur, ut tandem absumatur.
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765 </s></p><p><figure id="id.1.2.8.04.00" xlink:href="FIG1/F031.jpg"></figure>
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766 <s id="id.1.2.8.04.01">Incipiat enim motus, qui in infinitum intendi potest: sit autem talis ut in prima unius milliarii distan<pb ed="manuscript" n="118v"></pb>tia adeo acceleretur, ut imminuat octavam partem tarditatis ab, ut <lb ed="Favaro" n="20"></lb> puta ac; in secundo vero milliario minuat octavam partem residuae cb; in alio vero milliario minuat alterius residui partem octavam.
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767 </s><s id="id.1.2.8.04.02">Et sic semper poterit produci in infinitum haec diminutio, cum semper residuae septem octavae partes in octo aequales di vidi possint; et mobile per infinita milliaria moveri poterit, in unoquoque milliario de tarditate absumendo: nec tamen ut tarditas omnino absumatur, necessarium est.
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768 </s></p><p><s id="id.1.2.8.05.01">Verum amplius: illi qui cum Aristotele crediderunt, si semper minuatur tarditas, tandem ad infinitam celeritatem esse veniendum quid dicent si illis ostendetur, non solum non esse necessarium ad <lb ed="Favaro" n="30"></lb> infinitam celeritatem devenire, verum etiam demonstretur, posse mobile semper accelerari, nec tamen adeo intendi celeritatem ut finitae cuidam celeritati aequetur, nedum excedat?
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769 </s></p><p><figure id="id.1.2.8.06.00" xlink:href="FIG1/F032.jpg"></figure>
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770 <s id="id.1.2.8.06.01">Et, ut clarius loquar, moveatur aliquid, cuius in principio motus celeritas sit ab; sit autem alia celeritas cd maior ab: dico, mobile, in infinitum motum, posse in infinitum celeritatem suam ab augere , quae tamen, in infinitum <pb ed="Favaro" n="332"></pb> aucta, nunquam tanta erit quanta est celeritas cd.
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771 </s><s id="id.1.2.8.06.02">Ut accideret si mobile, a quiete recedens, in primo milliario sui motus acquirat celeritatem ab, quae sit duo tertiae celeritatis cd; in secundo autem milliario augeatur illius celeritas secundum tertiam partem celeritatis ab; in tertio augeatur secundum tertiam partem tertiae partis celeritatis ab; in quarto augeatur <pb ed="manuscript" n="119r"></pb>secundum tertiam partem tertiae partis unius tertiae partis ab; et sic in infinitum fiat augumentum per singula milliaria secundum tertiam partem augumenti praecedentis milliarii: et semper certe augebitur celeritas, numquam tamen tanta erit quanta <lb ed="Favaro" n="10"></lb> est cd, sed semper deficiet dimidium {1} ultimi augumenti.
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772 </s><s id="id.1.2.8.06.03">Huius autem demonstratio sit haec.
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773 </s></p><p><figure id="id.1.2.8.07.00" xlink:href="FIG1/F033.jpg"></figure>
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774 <s id="id.1.2.8.07.01">Sint quotcunque celeritates continuae in tripla proportione ab, bc, cd; quarum maxima sit ab, cuius sesquialtera sit ca.
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775 </s><s id="id.1.2.8.07.02">Dico, omnes magnitudines ab, bc, cd, simul cum dimidia cd, aequales esse ipsi ea.
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776 </s><s id="id.1.2.8.07.03">Quia enim ea sesquialtera est ab, erit ab cum sua medietate aequalis ae; et quia ab est tripla bc, erit bc cum sua medietate aequalis dimidiae ab: at demonstratum est ab cum sua medietate aequari ae: ergo abc cum medietate bc aequatur ipsi ae.
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777 </s><s id="id.1.2.8.07.04">Simili autem modo, quia bc tripla est cd, erit cd cum sua medietate aequalis dimidiae bc: verum tota ac cum dimidia bc demonstrata est <lb ed="Favaro" n="20"></lb> aequalis ae: ergo et tota ad cum dimidia dc aequabitur ae.
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778 </s><s id="id.1.2.8.07.05">Et eadem demonstratione semper repetita, demonstrabitur, celeritates, quotcunque illae fuerint, in tripla proportione continue proportionales, simul sumptas, una cum medietate earum minimae, aequales esse ei celeritati quae earum maximae celeritatis sesquialtera fuerit.
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779 </s><s id="id.1.2.8.07.06">Quod si ita est, patet, celeritates omnes, in tripla proportione, sumptas simul, minores esse quam celeritas illa, quae earum maximae sesquialtera fuerit, cum semper ab ea deficiant per dimidium minimae celeritatis.
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780 </s><s id="id.1.2.8.07.07">Constat ergo quomodo celeritas ab <pb ed="manuscript" n="119v"></pb> possit in infinitum semper augeri; nec tamen unquam[ 30] aequetur celeritati ae.
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781 </s><s id="id.1.2.8.07.08">Concludamus igitur, in mobili, ob rationes prius allatas, non semper augeri velocitatem; sed deveniri ad motum quendam, quo velociorem naturaliter non patitur eius terminata <pb ed="Favaro" n="333"></pb> gravitas: quod si etiam concederetur, eius velocitatem semper intendi in infinitum, non tamen ad infinitam velocitatem deveniendum esset.
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782 </s></p><p><s id="id.1.2.8.08.01">Ex his quae hactenus scripta sunt, facile erit unicuique causam invenire, cur gravia in suis naturalibus motibus non servent proportiones illas quas, cum de hoc ageremus, illis assignavimus; proportiones, inquam , suarum gravitatum, quas habent in medio per quod moventur.
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783 </s><s id="id.1.2.8.08.02">Cum enim in principio motus non secundum gravitatem suam moveantur, cum a virtute contraria impediantur, mirum profecto non erit, si gravitatum proportiones non servent celeritates; imo <lb ed="Favaro" n="10"></lb> vero, quod certe mirabile videtur, leviora gravioribus citius in principio descendant.
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784 </s><s id="id.1.2.8.08.03">Cuius mirabilis effectus causam etiam alii assignare tentarunt; quam, eo quod non sint assecuti, capite sequenti confutabimus, veramque causam afferre conabimur.
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785 </s></p></subchap2><subchap2><p><s id="id.1.2.9.01.01">Non minus venusta certe quam difficilis extat haec quaestio: cuius solutionem alii quoque explicare tentarunt, ut Averroes et qui eum secuntur; at, quae mea est opinio, in vanum laboraverunt, deformes <lb ed="Favaro" n="20"></lb> quasdam hypotheses statuendo.
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786 </s><s id="id.1.2.9.01.02">Dicunt enim, {1} aërem in propria regione gravem <pb ed="manuscript" n="120r"></pb>esse; ex quo sequitur, ea quae plus aëris habuerint, in loco aëris graviora esse (et haec etiam est opinio Aristotelis): ex quo fit, quia, verbigratia, lignea sphaera plus in se aëris habet quam plumbea, ut habeat tria gravantia, nempe aërem, aquam et terram; plumbum vero, quia modicum in se aëris habet, quasi 2 tantum gravantia habeat: unde fit, ligneam sphaeram citius descendere quam plumbeam. {2}
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787 </s><s id="id.1.2.9.01.03">Dicunt etiam, hoc non contenti, plumbum rarum ideo denso ferro esse gravius in aëre, quia plures partes aëris sunt in raro plumbo quam in denso ferro.
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788 </s><s id="id.1.2.9.01.04">Haec solutio quot et quantas difficultates habeat, <pb ed="Favaro" n="334"></pb> nemo est qui non videat.
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789 </s><s id="id.1.2.9.01.05">Et primo, aërem nec gravem esse nec levem {1} in sua regione, quis est qui ignoret? eundemque, quod consequens est, nec sursum nec deorsum ferri?
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790 </s><s id="id.1.2.9.01.06">Hoc enim supra demonstratum est.
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791 </s><s id="id.1.2.9.01.07">2Á: si velocitas motus mobilis gravitatem sequitur, ut omnes volunt, et plumbea sphaera loco aëris partium, quae in lignea sunt, habet terram et aquam, et terra et aqua sunt aëre graviora, ut facile est credere, nonne plumbum gravius erit, et velocius descendet?
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792 </s><s id="id.1.2.9.01.08">Quod autem, ut aërem gravare ostendant, de ferro et plumbo dicunt, si plumbum gravius est, quia plus habet aëris, ergo lignum et ferro et plumbo gravius erit, cum plus utroque habeat <lb ed="Favaro" n="10"></lb> aëris.
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793 </s><s id="id.1.2.9.01.09">3Á: si multum aëris, quod in ligno est, illud velocius facit, ergo semper velocius, dum fuerit in aëre, movebitur.
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794 </s><s id="id.1.2.9.01.10">Experientia tamen contrarium ostendit: verum enim est, lignum in principio sui motus ocius ferri plumbo; attamen paulo post adeo acceleratur motus plumbi, ut lignum post se relinquat, et, si ex alta turri demittantur, per magnum spatium praecedat: et de hoc saepe periculum feci.
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795 </s><s id="id.1.2.9.01.11"><pb ed="manuscript" n="120v"></pb>Firmiorem igitur causam ex firmioribus hypothesibus ut hauriamus, tentandum est.
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796 </s></p><p><s id="id.1.2.9.02.01">Oh, quam facile ex veris principiis verae extrahuntur demonstrationes!
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797 </s><s id="id.1.2.9.02.02">Si verum est, quod diximus, mobilia, dum a statu quietis <lb ed="Favaro" n="20"></lb> recedunt, cum tanta contraria vi impressa recedere, quanta est eorum gravitas; ergo quae graviora fuerint, cum maiori virtute contraria coniuncta recedent: quod si gravioribus plus de virtute ad contrarias partes impellente est absumendum quam levioribus, graviora certe ut tardius moveantur necesse erit, cum maiorem patiantur resistentiam.
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798 </s><s id="id.1.2.9.02.03">Et si, rursus, haec vera sunt, sequitur ut graviora, postquam tantum de resistentia contraria absumpserint ut non amplius tanto impediantur quanto leviora, ocius descendere debeant: quod certe rursus experientia monstrat.
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799 </s></p><p><s id="id.1.2.9.03.01">Hic autem silentio non est dissimulanda magna, quae oritur, <lb ed="Favaro" n="30"></lb> difficultas.
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800 </s><s id="id.1.2.9.03.02">Nam, licet graviora plus de qualitate contraria quam leviora consumere habeant, attamen habent etiam maiorem gravitatem, qua illam destruere possint; quod cum ita sit, rationi consentaneum esse videtur, ut aequali tantum velocitate in principio moveantur: causa <pb ed="Favaro" n="335"></pb> autem cur minus gravia citius moveri debeant, nondum apparet.
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801 </s><s id="id.1.2.9.03.03">Magni certe momenti est obiectio ista; sed, tamen, non adeo est potens, ut veritatis splendorem offuscare valeat.
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802 </s><s id="id.1.2.9.03.04">Ut autem ipsam de medio tollamus, est animadvertendum, in mobili qualitatem illam contrariam non ideo remitti, quia a gravitate eiusdem mobilis oppugnetur; gravitas enim, cum in mobili contraria qualitate conferto <pb ed="manuscript" n="121r"></pb>nulla penitus sit, idem praestare non potest; sed qualitas illa per se debilitatur, et mobile relinquit: sicut etiam dum candens ferrum frigefit, non ideo in eo calor remittitur, quia a contraria frigiditate reluctetur; nulla enim <lb ed="Favaro" n="10"></lb> tunc in ferro est frigiditas; sed suapte natura ex ferro paulatim recedit.
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803 </s><s id="id.1.2.9.03.05">Est, secundo, animadvertendum, qualitatem contrariam eo facilius et citius recedere, quo in leviori mobili impressa fuerit: quod quidem exemplis multis comprobare licet.
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804 </s><s id="id.1.2.9.03.06">Ut si eodem tormento et eodem tempore simul iaculentur duae glandulae, plumbea una, altera lignea, tunc, dubio procul, eadem in utrisque virtus imprimetur; et tamen acrius et diutius in plumbo conservabitur quam in ligno: cuius signum est, quod longius et diutius motu violento movebitur plumbum.
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805 </s><s id="id.1.2.9.03.07">Et hoc idem etiam patet, si quis, eadem manu, eodem tempore, simul, sursum 2 frustra, ligni unum, alterum ferreum, proiciat; quorum <lb ed="Favaro" n="20"></lb> ferreum vel plumbeum per longius spatium movebitur: quod quidem indicat, virtutem motivam acrius ferro inhaerere et diutius in eo conservari quam in ligno.
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806 </s><s id="id.1.2.9.03.08">Hoc idem patet si ex duobus filis aequalibus suspendantur duo pondera, ligneum alterum, alterum plumbeum, et, impetu ex aequali a perpendiculo distantia accepto, derelinquantur; quorum plumbeum per longius temporis spatium certe huc illuc movebitur.
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807 </s><s id="id.1.2.9.03.09">Et tandem, qualitates omnes contrarias diutius, quo in graviori ac densiori et magis eis contraria materia impressae fuerint, conservari, in omnibus manifestum est.
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808 </s><s id="id.1.2.9.03.10">Si enim lignum et plumbum calefiant, ita ut amborum aequalis sit in principio calor, tamen in <lb ed="Favaro" n="30"></lb> plumbo diutius conservabitur; <pb ed="manuscript" n="121v"></pb>licet maior plumbi frigiditas magis calori contrarietur quam modica ligni frigiditas.
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809 </s><s id="id.1.2.9.03.11">Et hoc manifeste patet in aëre, qui, praesente igne valdeque excalefactus, statim, si removeatur ignis vel cineribus obtegatur, frigefit aër: si autem aqua ab igne excalefiat, non dicam ut ferveat, sed solum ut calida <pb ed="Favaro" n="336"></pb> tantum sit quantum erat aër, per longum profecto temporis spatium calorem servabit; licet aquae frigiditas longe peius odio habeat calorem quam aër.
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810 </s><s id="id.1.2.9.03.12">Patet etiam, aestivo tempore multo magis excalefieri lapides vel ferrum quam aër, cum lapidis calorem vix manus substinere valeant, eumque diu conservant; iidem vero lapides hieme longe frigidiores evadunt ipsomet aëre.
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811 </s><s id="id.1.2.9.03.13">Ex his itaque omnibus patet, qualitates omnes contrarias fortius in graviori ac densiori materia haerere, tardiusque ex eadem recedere.
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812 </s><s id="id.1.2.9.03.14">His autem constitutis patet iam problematis solutio.
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813 </s><s id="id.1.2.9.03.15">Nam si in ligno et plumbo eadem proportione remitterentur qualitates contrariae, verum quidem esset <lb ed="Favaro" n="10"></lb> quod in principio naturalis motus eadem moverentur velocitate: verum, quia qualitas contraria facilius et citius in minus gravi materia consumitur, hinc fit ut in ligno citius deperdatur, et a ligno recedat, virtus impressa; quod cum ita fuerit, necessario velocius movebitur.
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814 </s><s id="id.1.2.9.03.16">Verum, quia, amissa qualitate contraria, non tantam gravitatem acquirit lignum quantam plumbum, cum, simpliciter et libere, plumbum ligno sit gravius, hinc fit ut plumbum lignum deinde assequatur et longe praecedat.
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815 </s></p><p><s id="id.1.2.9.04.01">Verum exemplo adhuc facilius haec declarentur.
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816 </s></p><p><figure id="id.1.2.9.05.00" xlink:href="FIG1/F034.jpg"></figure>
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817 <s id="id.1.2.9.05.01"><pb ed="manuscript" n="122r"></pb>Sintque duo mobilia, mole aequalia; alterum vero sit ligneum, plumbeum <lb ed="Favaro" n="20"></lb> alterum: sitque plumbi gravitas 20, ligni vero 4; et ambo substineantur a linea ab.
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818 </s><s id="id.1.2.9.05.02">Primo, itaque, manifestum est, tanta vi deorsum premere ipsa mobilia, quanta vi sursum impellit linea ab.
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819 </s><s id="id.1.2.9.05.03">Nam, si magis premerent, linea ab illos non regeret, sed deorsum, invita linea, ferrentur: nunc autem ipsa mobilia non feruntur deorsum in aëre, quia in aëre, per quod ferri debent, non gravant (nec, ut demonstratum est, quicquam deorsum fertur, ni medio, per quod ferri debet, gravius fuerit), sed in ab gravant; et, cum non magis gravent quam ipsa substineat, necessario quiescunt.
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820 </s><s id="id.1.2.9.05.04">Cum autem a linea <lb ed="Favaro" n="30"></lb> derelinquuntur, in primo puncto recessus retinent adhuc qualitatem contrariam sursum impellentem impressam, quae non in instanti sed successive remittitur; plumbumque 20 qualitatis contrariae, lignum vero 4, consumendum habent.
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821 </s><s id="id.1.2.9.05.05">Quae qualitates si aequaliter in utroque remitterentur, ita ut, quando in plumbo 1 qualitatis recesserit, in ligno <pb ed="Favaro" n="337"></pb> etiam 1 abierit, et, quod consequens est, 1 gravitatis resumpsissent, ambo, dubio procul, eadem moverentur velocitate: sed, quia in eo tempore in quo e plumbo recessit 1 qualitatis, e ligno plus quam unum egressum est, et, per consequens, quando plumbum unum tantum gravitatis resumpsit, lignum plus quam unum acquisivit, hinc fit quod lignum tunc velocius motum est; et, rursus, <pb ed="manuscript" n="122v"></pb>quia, quando in ligno recesserat 2 qualitatis, in plumbo minus quam 2 abierat, factum inde est, plumbum tunc tardius moveri.
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822 </s><s id="id.1.2.9.05.06">Verum, quia tandem plus gravitatis acquirit plumbum quam lignum, sequitur, plumbum <lb ed="Favaro" n="10"></lb> etiam tunc multo velocius ferri.
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823 </s></p></subchap2><subchap2><p><s id="id.1.2.10.01.01">Hanc non levem difficultatem ex his quae supra, cum de motu super diversas ad horizontem inclinationes ageremus, scripsimus, quispiam haurire posset.
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824 </s><s id="id.1.2.10.01.02">Cum enim ex illis colligatur, eo facilius grave sursum impelli posse, quo planum, super quod fit motus, acutiores angulos cum horizonte continebit; nunc autem contrarium afferre videamus; merito alicui dubitandi ansa praebetur.
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825 </s><s id="id.1.2.10.01.03">Quae difficultas ut, quatenus <lb ed="Favaro" n="20"></lb> cum superioribus pugnare videtur, auferatur, est animadvertendum: cum in superioribus dictum fuit, gravia eo facilius moveri sursum, quo planum, super quod fit motus, magis fuerit inclinatum, intelligendum esse de his, quae super solidum planum feruntur; nunc autem de his, quae non ab alio substentata, verum in aëre suspensa, a sola virtute impressa et substinentur et impelluntur; ut cum ex muralibus tormentis ferrei globi extruduntur, quos certe constat per longius spatium in eadem linea recta ferri, quo linea motus minus acutos cum horizonte angulos efformaverit.
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826 </s><s id="id.1.2.10.01.04">Cuius effectus, quicquid dicant alii, ut veram causam inveniamus, est animadvertendum, quemadmodum etiam supra <lb ed="Favaro" n="30"></lb> notavimus, virtutem impellentem acrius longe <pb ed="manuscript" n="123r"></pb>imprimi in eo quod magis resistit, dummodo virtus ob debilitatem non languescat: quod si rationem aliquam invenire possemus, ut idem grave plus nunc <pb ed="Favaro" n="338"></pb> quam antea resisteret, nunc, dubio procul, fortius a virtute movebitur.
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827 </s><s id="id.1.2.10.01.05">Verum magis resistit quod contra nititur, quam quod aut quiescit aut ad eadem fertur: in eo, ergo, quod contra nititur, arctius virtus imprimitur; quod experientia docti qui follibus ludunt, ab aliquo contra se follem deici volunt, ut in eo reluctante et magis resistente plus virtutis motivae imprimatur.
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828 </s><s id="id.1.2.10.01.06">Verum, ut iam diximus, id soli praestare possunt, qui robusto fortique brachio praediti sunt: qui vero languidi sunt viribus, nec contra impetum niti possunt, contra quiescentem vel non ad contrarias tendentem follem moventur: quod si ad easdem moveatur follis, paululum, ut quisque novit, impellitur.
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829 </s><s id="id.1.2.10.01.07">Cuius effectus <lb ed="Favaro" n="10"></lb> causa quidem est, quia quod quiescit, a maxima virtute percussum, movetur antequam tota virtus imprimatur, cum illius mobilitas impressionem tantae virtutis non expectet: quod non accidit in eo quod in contrarias cietur; nam, aucta per motum suae gravitatis resistentia, magis resistit, nec ante totius virtutis impressionem retrocedit.
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830 </s><s id="id.1.2.10.01.08">Et hoc idem experimur omnes, cum lapidem ante proicere volumus: prius enim eum manu retro celeriter portamus ad hoc, ut, ad contrarias motus, magis virtuti imprimendae non solum ipse verum etiam manus resistat: quod si, cum retro latus est, manum sisteremus et lapis, retro motus, quiesceret, multo minus iaculari posset, ut unicuique patet. <lb ed="Favaro" n="20"></lb>
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831 </s><s id="id.1.2.10.01.09">Oportet igitur, lapidem, retro latum, in puncto <pb ed="manuscript" n="123v"></pb>regressus non quiescere, ad hoc ut maiori impetu iaculari possit.
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832 </s><s id="id.1.2.10.01.10">Et idem patet in illis qui funda proiciunt lapidem: prius enim fundam bis aut ter in orbem girant, ad hoc ut velocius moveatur; in extremo autem talem motum in motum retro convertuntur, ut tunc in lapide reluctante maior imprimatur vis.
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833 </s></p><p><s id="id.1.2.10.02.01">His animadversis, geminam causam propositae quaestionis affero: et primum dico, quod, quamvis virtus motiva in tormentis sit eadem, tamen eo plus de eadem virtute in sphaera ferrea imprimitur, quo tormentum magis erectum fuerit.
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834 </s><s id="id.1.2.10.02.02">Cui causa est, quia sphaera tunc magis virtuti resistit: difficilius enim in cavitate bombardae movetur <lb ed="Favaro" n="30"></lb> cum sursum, tanquam in plano magis erecto, est impellenda, quam cum magis inclinata fuerit; quare etiam magis virtuti imprimendae resistit.
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835 </s><s id="id.1.2.10.02.03">Quando enim tormentum inclinatum fere iacet, tunc sphaera virtutem imprimendam non expectat, sed ante totam impressionem <pb ed="Favaro" n="339"></pb> eicitur: verum, cum erectum fuerit tormentum, gravitate globus nigrum pulverem premit, et motui super plano erecto magis obstat, multaeque virtutis impressionem ante discessum expectat.
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836 </s><s id="id.1.2.10.02.04">Nec est de virtute impellente verendum, ne languida et impotens sit: tanta enim est, ut, si globus adeo arcte constipatus in bombarda fuerit ut expelli nequeat, in frusta comminuetur tormentum; tanta enim moles ignis, in angusto illo spatio compressa, carceres illos aereos nedum solveret, verum etiam si centies solidiores essent; ut patet quando vallos, moenia, integraque propugnacula, <pb ed="manuscript" n="124r"></pb>ad sidera tollit.
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837 </s><s id="id.1.2.10.02.05">Quanta autem sit moles illa <lb ed="Favaro" n="10"></lb> ignis quae in angusta tunc cavitate concluditur, ex quantitate nigri pulveris, qui interdum ad 8 vel 10 libras pondere accedit, totusque, nullis fere relictis cineribus aut ignium excrementis, in ignem convertitur, diiudicari potest.
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838 </s><s id="id.1.2.10.02.06">Quanta enim sit ignis moles, cuius gravitas ad 10 libras accedit, excogitent praesertim illi qui in igne nullam ponunt gravitatem.
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839 </s><s id="id.1.2.10.02.07">Haec prima esto causa.
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840 </s></p><p><s id="id.1.2.10.03.01">Secunda est quia, quando globus sursum ad perpendiculum horizontis fertur, non potest ab illa linea recta deflectere, cum per eandem ut revertatur necesse sit, nisi prius qualitas sursum impellens omnino recesserit: quod non accidit cum per lineam horizonti inclinatam <lb ed="Favaro" n="20"></lb> fertur.
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841 </s><s id="id.1.2.10.03.02">Tunc, enim, quando a linea recta deflecti incipit, ut virtus impellens absumpta sit, non est necessarium: virtuti enim violenter impellenti sufficit ut mobile a principio motus removeat; quod bene praestare potest dum in linea horizonti inclinata fertur, licet aliquantulum in motu inclinetur.
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842 </s><s id="id.1.2.10.03.03">Tunc, enim, motus ille, cum globus declinare incipit, non est motui recto contrarius; quare ad illum mobile se convertere poterit, absque eo quod virtus impellens recedat: hoc autem fieri non potest dum mobile sursum ad perpendiculum cietur, quia linea inclinationis est eadem cum linea motus violenti.
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843 </s><s id="id.1.2.10.03.04">Quando igitur mobile in inclinatione ad locum, unde a virtute impressa expellitur, <lb ed="Favaro" n="30"></lb> non accedit, sinit virtus mobile declinare; sufficit enim illi ut mobile a termino, unde recessit, removeat; et eo <pb ed="manuscript" n="124v"></pb>libentius illud declinare sinet, quo minus declinatio illa recessum a termino a quo impediet.
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844 </s></p></subchap2></subchap1><subchap1><subchap2><p><figure id="id.1.2.1.0.04.00" xlink:href="FIG1/F035.jpg"></figure>
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845 </p></subchap2><subchap2><p><s id="id.1.2.10.04.01">Verum, si fertur per lineam perpendicularem ab, ab ea nullo modo mobile declinare potest, nisi, super eadem recedendo, ad terminum, a quo recessit, accedat; hoc autem, dum vivet, nunquam patietur <pb ed="Favaro" n="340"></pb> virtus impellens: cum autem mobile per lineam ac fertur, quia adhuc inclinatio ad terminum a quo tendit, nisi valde debilitata eam non sinet virtus motiva: cum autem fertur per ae horizonti fere aequidistantem, potest quantumlibet cito inclinari incipere mobile; inclinatio enim haec recessum a termino non impedit.
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846 </s><s id="id.1.2.10.04.02">Oppositum autem huius accidit, dum mobile super diversas planorum inclinationes movetur: in planis enim magis inclinatis longius ab eadem vi per rectam lineam movetur mobile, quam in planis magis erectis.
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847 </s><s id="id.1.2.10.04.03">Ratio <lb ed="Favaro" n="10"></lb> est quia, quo magis planum fuerit inclinatum, eo minus gravat in eo mobile, quia pars illius gravitatis a plano substinetur; unde fit ut a motore facilius moveri possit: et, cum in dictis planis non possit mobile a motu deflectere nisi per eandem lineam retrocedendo, in illis planis longius recta movebitur, in quibus gravitas mobilis impellendi minor fuerit.
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848 </s></p></subchap2></subchap1></chap><chap><subchap1><subchap2><p><s id="id.2.0.1.01.01"><pb ed="Favaro" n="341"></pb> <pb ed="manuscript" n="133r"></pb>Lationem {1} omnem naturalem ab excessu vel defectu gravitatis fieri, inferius explicaturi, rationi consentaneum esse duximus, prius quid magis, quid minus, quidve aeque grave dicendum sit, in medium afferre.
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849 </s><s id="id.2.0.1.01.02">Est enim hoc determinare necessarium: saepius enim accidit ut, quae minus gravia sunt, graviora, quae autem magis, minus gravia, nuncupentur.
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850 </s><s id="id.2.0.1.01.03">Interdum, nanque, magnum lignum parvo plumbo gravius esse dicimus, cum tamen plumbum ligno, simpliciter, gravius existat; et magnum plumbi frustrum pauco plumbo gravius dicimus, cum tamen plumbum plumbo gravius non sit.
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851 </s><s id="id.2.0.1.01.04">Quapropter, ut huiusmodi <lb ed="Favaro" n="10"></lb> captiones aufugiamus, ea inter se aeque gravia dicenda erunt, quae, cum fuerint aequalia in mole, erunt etiam aequalia in gravitate: unde si duo plumbi frustra, quae, in mole aequalia, in gravitate quoque congruant, inveniamus, ista vere aeque ponderare dicenda erunt.
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852 </s><s id="id.2.0.1.01.05">Unde, lignum aeque ac plumbum gravare non esse dicendum, manifestum est: frustrum enim ligni cum plumbi frustro aequeponderans, in mole plumbeum frustrum longe excedet.
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853 </s><s id="id.2.0.1.01.06">Deinde, illud alio gravius est nuncupandum, cuius accepta moles, alterius moli aequalis, ea gravior comperiatur: ut, verbigratia, si ex plumbo et ligno moles duas inter se aequales accipiamus, sitque plumbi moles gravior, tunc <lb ed="Favaro" n="20"></lb> certe plumbum ligno esse gravius, merito asseremus.
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854 </s><s id="id.2.0.1.01.07">Quare, si ligni frustrum, quod cum frustro plumbi aequeponderet, accipiamus, non tamen lignum aeque grave ac plumbum est censendum: plumbi enim molem longe a ligni mole excedi inveniemus.
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855 </s><s id="id.2.0.1.01.08">Converso demum modo de minus gravibus est statuendum: minus nanque grave censendum est illud, cuius pars accepta, alterius parti in mole aequalis, in gravitate minor extiterit; ut, si solida duo, ligneum unum, plumbeum alterum, quae in mole aequalia sint, accipiamus, minus autem ligneum gravet quam plumbeum, tunc lignum plumbo minus grave esse, est censendum.<pb ed="manuscript" n="133v"></pb>
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856 </s></p></subchap2><subchap2><p><s id="id.2.0.2.01.01">Huc usque gravia et minus gravia, non autem gravia et levia, diximus; sicut centro propinquius et centro remotius, non autem deorsum et sursum: inferius enim explicaturi sumus, non esse leve, hoc est carens gravitate; nec esse locum, qui tantum sursum, non autem etiam deorsum, sit.
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857 </s><s id="id.2.0.2.01.02">Attamen si interdum, ut communiter loquar (parum enim interest ad propositum nostrum de nominibus contentio), grave et leve et sursum et deorsum dixero, hoc pro minus et magis grave, et pro centro propinquius et remotius, intelligatur; donec, <lb ed="Favaro" n="10"></lb> occasione superveniente, de his distinctius determinare liceat.
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858 </s><s id="id.2.0.2.01.03">Quod autem ad praesens negocium attinet, cum ea, quae naturaliter moventur, ad propria moveantur loca, et cum gravia aut levia sint quae moventur, videndum est, quaenam gravium loca, et quae levium, existant, et cur.
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859 </s><s id="id.2.0.2.01.04">Verum, quod ad primum attinet, gravium loca ea esse quae magis centro accedunt, levium vero quae magis distant, sensu quidem quotidie intuemur; quare talia determinata loca illis a natura praescripta esse, non est quod dubitemus: verum in dubium revocari potest, cur talem ordinem in distribuendis locis, non autem praeposterum, prudens natura servaverit. <lb ed="Favaro" n="20"></lb>
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860 </s></p><p><s id="id.2.0.2.02.01">Huius distributionis non alia, quod legerim, a philosophis affertur causa, nisi quod in aliquem erant ordinem cuncta distribuenda, in hunc autem Summae Prudentiae distribuere placuit; et simile quiddam Aristoteles, 8 Phys. 32, afferre videtur, dum, quaerens cur gravia et levia ad propria moveantur loca, subdit, causam esse quia habent a natura ut sint apta ferri aliquo, et hoc leve quidem sursum, grave autem deorsum.
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861 </s><s id="id.2.0.2.02.02">Ptolamaeus autem, in principio 7i capitis primi <pb ed="manuscript" n="134r"></pb>libri suae Magnae Constructionis, inquit frustra inquiri cur gravia ad medium ferantur; cum demonstrasset terram, ad quam feruntur, in medio esse.
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862 </s><s id="id.2.0.2.02.03">Verum haec difficultatem non tollunt: dato, enim, ferri ad medium <lb ed="Favaro" n="30"></lb> quia ad terram ferantur, rursus, cur terra in medio non autem in loco ignis posita fuit, quaerimus.
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863 </s><s id="id.2.0.2.02.04">Quod si rem accuratius spectemus, non erit profecto existimandum, nullam in tali distributione <pb ed="Favaro" n="343"></pb> necessitatem aut utilitatem habuisse naturam, sed solum ad libitum et casu quodammodo operatam fuisse.
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864 </s><s id="id.2.0.2.02.05">Hoc cum de provida natura nullo pacto existimari posse perpenderem, in excogitanda, nisi necessaria, saltem utili et congruente, aliqua causa interdum anxius fui: ac profecto, non nisi optimo iure summaque prudentia hunc naturam elegisse ordinem, comperi.
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865 </s><s id="id.2.0.2.02.06">Cum enim una omnium corporum sit materia, et illa quidem graviora sint quae in angustiori spatio plures illius materiae particulas includunt, rationi profecto consentaneum fuit, ut quae in angustiori loco plus materiae concluderent, angustiora etiam <lb ed="Favaro" n="10"></lb> loca, qualia sunt quae centro magis accedunt, occuparent.
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866 </s><s id="id.2.0.2.02.07">Ut si, exempli gratia, intelligamus , naturam in prima mundi compagine totam elementorum communem materiam in quatuor partes divisisse; deinde ipsius terrae formae suam materiam tribuisse, itidem et formae aëris suam; terrae autem formam materiam suam in angustissimo loco constipasse, aëris autem formam in amplissimo loco materiam suam reposuisse; nonne congruum erat ut aëri natura magnum spatium assignaret, terrae autem minus?
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867 </s><s id="id.2.0.2.02.08">At in sphaera angustiora sunt loca quo magis ad centrum accedunt, ampliora vero quo ab eodem magis dis<pb ed="manuscript" n="134v"></pb>tant: prudenter, igitur, simul et aeque terrae statuit natura locum <lb ed="Favaro" n="20"></lb> esse qui caeteris est angustior, nempe prope centrum; reliquis deinde elementis loca eo ampliora, quo ipsorum materia rarior esset.
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868 </s><s id="id.2.0.2.02.09">Nec tamen dixerim, aquae materiam tantam esse quanta est ipsius terrae, et ob id aquam, cum sit terra rarior, maiora loca occupare; sed solum quod, si partem aquae cum terrae parte aequeponderantem accipiamus, et ob id tanta sit aquae materia quanta terrae, tunc profecto terra illa minorem occupabit locum quam aqua: quare merito in angustiori spatio erit reponenda.
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869 </s><s id="id.2.0.2.02.10">Et, similiter, tanta materia, quantam terrae forma in angusto loco compraehendebat, forma aëris amplissimum spatium replebat: ergo aëri natura ampliorem, quam <lb ed="Favaro" n="30"></lb> terrae, locum assignare debuit; ergo, a centro remotiorem.
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870 </s><s id="id.2.0.2.02.11">Similique modo de igne etiam discurrendo, congruentiam quamdam, ne dicam necessitatem, talis dispositionis gravium et levium inveniemus.
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871 </s></p></subchap2></subchap1></chap><chap><subchap1><subchap2><p><s id="id.3.0.1.01.01"><pb ed="manuscript" n="43r"></pb>Vastissimae caelestis excrementa sphaerae, post illius mirabilem compaginem, divinus Opifex, ne forte immortalium beatorumque spirituum offenderent intuitum, in eiusdem globi centrum extrusit atque abscondidit: verum; cum satis amplum et capax sub ultimi concava superficie orbis relictum spacium densissima gravissimaque illa materia mole sua non expleret, ne magnum spacium otiosum atque vacuum esset, quae, pressa gravitate sui, onerosam illam indigestamque massam, in angustis se cancellis concluserat, distraxit; et ex illius innumeris <lb ed="Favaro" n="10"></lb> particulis plus minusve rarefactis quatuor illa efformavit corpora, quae postea elementa diximus.
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872 </s><s id="id.3.0.1.01.02">Quorum quod gravissimum densissimumque, ut prius erat, remansit, e loco in quem antea confugerat non removit; et sic relicta est terra in centro: et, simili ratione, quae densiora fuerant, terrae viciniora constituta sunt.
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873 </s><s id="id.3.0.1.01.03">Eorum vero quae ex hac materia constituta sunt corpora, densiora illa dicta sunt quae, sub eadem mole, plures eiusdem materiae particulas coëgere; {2} densiora, autem, graviora fuere. {3}
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874 </s></p><p><s id="id.3.0.1.02.01">In hunc, itaque, ordinem a natura distributa fuisse corpora, ut, scilicet, quae gra<pb ed="manuscript" n="43v"></pb>viora essent, centro propinquiora manerent, <lb ed="Favaro" n="20"></lb> continua nobis declarat experientia verum in dubium revocari potest, cur talem ordinem in distribuendis locis, non autem praeposterum, prudens natura servaverit.
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875 </s><s id="id.3.0.1.02.02">Huius distributionis non alia, quod legerim, a philosophis adfertur causa, nisi quod in aliquem erant ordinem cuncta disponenda, in hunc autem Summae Prudentiae <pb ed="Favaro" n="345"></pb> distribuere placuerit.
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876 </s><s id="id.3.0.1.02.03">Simile quiddam Aristoteles, 8 Phys. 32, adferre videtur, dum, quaerens cur gravia et levia ad propria moveantur loca, subdit, causam esse quia habent a natura ut sint apta ferri aliquo, et hoc leve quidem sursum, grave autem deorsum.
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877 </s><s id="id.3.0.1.02.04">Ptolemaeus autem, in principio 7i cap. p.i libri suae Magnae Constructionis, inquit frustra inquiri cur gravia ad medium ferantur; cum demonstrasset terram, ad quam feruntur, in medio esse.
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878 </s><s id="id.3.0.1.02.05">Verum haec difficultatem non tollunt: dato, enim, ferri ad medium quia ad terram ferantur, rursus cur terra in medio non autem in loco ignis posita fuit, quaerimus.
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879 </s><s id="id.3.0.1.02.06">Quod si rem <lb ed="Favaro" n="10"></lb> accuratius spectemus, non erit profecto existimandum, nullam in tali distributione necessitatem aut saltem utilitatem habuisse naturam, sed solum ad libitum et casu quodammodo operatam fuisse.
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880 </s><s id="id.3.0.1.02.07">Hoc cum de provida natura nullo posse pacto existimari perpenderem, in excogitanda, nisi necessaria, saltem utili et congruente, aliqua causa interdum anxius fui: ac profecto, non nisi optimo iure hunc naturam <pb ed="manuscript" n="44r"></pb>elegisse ordinem, comperi.
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881 </s><s id="id.3.0.1.02.08">Cum enim una omnium corporum sit materia, et illa quidem graviora sint quae in angustiori spatio plures illius materiae particulas includunt, rationi profecto consentaneum fuit, ut quae in angustiori spatio plus materiae continerent, angustiora etiam loca, <lb ed="Favaro" n="20"></lb> qualia sunt quae centro magis accedunt, occuparent.
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882 </s><s id="id.3.0.1.02.09">Ut si, exempli gratia, intelligamus, naturam in prima mundi compagine totam elementorum communem materiam in 4 partes divisisse; deinde ipsius terrae formae suam materiam tribuisse, itidem et formae aëris suam; terrae autem formam materiam suam in angustissimo loco constipasse, aëris autem formam in amplissimo loco materiam suam reposuisse; nonne congruum erat ut aëri natura maius spatium, terrae autem minus, assignaret?
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883 </s><s id="id.3.0.1.02.10">At in sphaera angustiora sunt loca quo magis centro appropinquantur, ampliora vero quo ab eodem magis distant: prudenter, igitur; simul et aeque terrae statuit natura locum esse qui caeteris est <lb ed="Favaro" n="30"></lb> angustior, nempe prope centrum; reliquis deinde elementis loca eo ampliora, quo ipsorum materia rarior esset.
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884 </s><s id="id.3.0.1.02.11">Nec tamen dixerim (ut credidit Aristoteles), aquae materiam tantam esse quanta est ipsius terrae, et ob id aquam, cum sit terra rarior, maiora loca occupare; sed solum quod, si partem aquae cum terrae parte aequeponderantem accipiamus, et ob id tanta sit aquae materia quanta terrae, tunc profecto terra <pb ed="Favaro" n="346"></pb> illa minorem occupabit locum quam aqua: quare merito in angustiori spatio <pb ed="manuscript" n="44v"></pb>erit reponenda.
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885 </s><s id="id.3.0.1.02.12">Et, similiter, tanta materiae mole, quantam terrae forma in angusto loco compraehendebat, forma aëris amplissimum spatium replebat: ergo aëri natura ampliorem, quam terrae, locum assignare debuit; ergo, centro remotiorem.
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886 </s><s id="id.3.0.1.02.13">Similique modo de igne etiam discurrendo, congruentiam quamdam, ne dicam necessitatem, talis dispositionis inveniemus.
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887 </s></p><p><s id="id.3.0.1.03.01">Ex his colligi potest, nullius esse momenti Aristotelis argumentum, quo probare contendit, elementorum materias inter se esse aequales; dum dicit: Si ignis materia excederet materiam aëris et aquae, iam <lb ed="Favaro" n="10"></lb> aër et aqua, ab igne exusta, in ignem conversa fuissent. {1}
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888 </s><s id="id.3.0.1.03.02">Nanque, etiam si ponamus ignem vel millies aërem excedere, non tamen verendum est, aërem in ignis naturam converti posse: cum enim locus omnis sub concavo xxx iam expletus sit, et, si aër ignis evaderet, longe ampliore, quam nunc occupat, loco egeret, constat, eo quod careat spatio in quo consisteret, in igneam non posse transire naturam.
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889 </s><s id="id.3.0.1.03.03">Et sic de caeteris censendum est elementis.
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890 </s></p></subchap2><subchap2><p><s id="id.3.0.2.01.01">Proprissimam naturalis descensus causam esse excessum gravitatis <lb ed="Favaro" n="20"></lb> mobilis super gravitatem medii per quod ferri debet, tunc mihi ostendisse persuasero, cum duo haec demonstrata fuerint: primo, impossibile esse, corpora quaecunque, si medio aliquo fuerint graviora, in eo (non impedita) non descendere; 2Á, nullum posse haberi corpus, quod, si medio aliquo fuerit minus grave, in eo naturaliter descendat.
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891 </s><s id="id.3.0.2.01.02">Horum itaque confirmatio ex his, quae superiori capite declarata atque supposita fuere, commode hauriri potest.
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892 </s><s id="id.3.0.2.01.03"><pb ed="manuscript" n="45r"></pb>Cum enim natura constitutum sit, graviora sub minus gravibus manere, quatenus igitur graviora sunt, sub minus gravibus quiescunt: ergo causa cur graviora sub minus gravibus consistant est excessus gravitatis.
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893 </s><s id="id.3.0.2.01.04">Verum id quod dat manere sub <lb ed="Favaro" n="30"></lb> <pb ed="Favaro" n="347"></pb> minus gravibus, dat etiam supra minus gravia non manere: est autem supra minus gravia non manere idem quod sub minus gravia ferri ergo excessus gravitatis mobilis super gravitatem medii naturalis descensus causa est; et quaecunque medio per quod ferri debent fuerint graviora, sub eo, nisi impediantur, descendent, ne, contra naturae institutum, graviora super minus gravia maneant.
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894 </s><s id="id.3.0.2.01.05">Haec cum ita se habeant, sequitur necessario, quaecunque medio minus gravia fuerint, descendere non posse naturaliter: nam quae naturaliter moventur, moventur eo, ubi naturaliter quiescant; at minus gravia sub gravioribus <lb ed="Favaro" n="10"></lb> naturaliter quiescere non possunt; ergo, nec naturaliter descendere.
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895 </s><s id="id.3.0.2.01.06">Ex his itaque constat, posito gravitatis excessu, semper (ablatis externis impedimentis) sequi motum deorsum, et, eodem ablato excessu, semper auferri naturalem descensum: ergo sequitur, dictum excessum gravitatis naturalis descensus causam esse.
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896 </s></p><p><s id="id.3.0.2.02.01">Verum hic merito posset quis ambigere, quomodo mobile, quod deorsum fertur naturaliter, semper medio per quod ferri debet gravius sit; praesertim cum videamus lapillum in magna aquae copia descendere, qua certe longe minus gravis est.
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897 </s><s id="id.3.0.2.02.02">Quare, ut difficultatem hanc et quascunque alias de <pb ed="manuscript" n="45v"></pb>medio tollamus, et quae dicta sunt clarius <lb ed="Favaro" n="20"></lb> explicentur, demonstrationes nonnullas conscribemus, ex quibus totius negocii exitus apparebit.
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898 </s><s id="id.3.0.2.02.03">Itaque prius eos explicabimus terminos qui explicatione egent, eaque supponam axiomata quae ad demonstrationes necessaria erunt; deinde ad ipsas properabimus demonstrationes.
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899 </s></p></subchap2><subchap2><p><s id="id.3.0.3.01.01">Prius itaque quid magis, quid minus, quidve aeque grave dicendum est, in medium afferamus.
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900 </s><s id="id.3.0.3.01.02">Est enim hoc determinare necessarium: saepius enim accidit ut, quae minus gravia sunt, graviora, quae autem magis, minus gravia, nuncupentur.
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901 </s><s id="id.3.0.3.01.03">Interdum, nanque, magnum lignum parvo plumbo gravius esse dicimus, cum tamen plumbum ligno, simpliciter, <lb ed="Favaro" n="30"></lb> gravius existat; et magnum plumbi frustrum pauco plumbo gravius appellamus, cum tamen plumbum plumbo gravius non sit.
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902 </s><s id="id.3.0.3.01.04">Quapropter, ut huiusmodi captiones aufugiamus, ea inter se aeque gravia dicenda erunt, quae, cum fuerint aequalia in mole, erunt etiam aequalia in <pb ed="Favaro" n="348"></pb> gravitate: unde si 2 frustra, argenteum unum, chalybeum alterum, inveniamus, quae, in mole aequalia, in gravitate quoque congruant, ista vere aeque ponderare dicenda erunt.
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903 </s><s id="id.3.0.3.01.05">Unde lignum aeque ac plumbum gravare, dicendum non est: frustrum <pb ed="manuscript" n="46r"></pb>enim ligni cum plumbi frustro aequeponderans, in mole plumbeum frustrum longe excedet.
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904 </s><s id="id.3.0.3.01.06">Deinde, illud alio gravius est nuncupandum, cuius accepta moles, alterius moli aequalis, ea gravior comperiatur: ut, verbigratia, si ex plumbo et ligno moles duas inter se aequales accipiamus, sitque plumbi moles gravior, tunc plumbum ligno esse gravius, merito asseremus.
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905 </s><s id="id.3.0.3.01.07">Quare, si ligni frustrum, quod cum plumbi frustro aequeponderet, ponamus, non <lb ed="Favaro" n="10"></lb> tamen lignum aeque ac plumbum grave est censendum: plumbi enim molem longe a ligni mole excedi inveniemus.
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906 </s><s id="id.3.0.3.01.08">Converso demum modo de minus gravibus est censendum: minus nanque grave statuendum est illud, cuius pars accepta, alterius parti in mole aequalis, in gravitate minor extiterit; ut, si solida duo, ligneum unum, plumbeum alterum, quae in mole aequalia sint, capiamus, minus autem lignum gravet quam plumbum, tum lignum plumbo minus esse grave, est asserendum.
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907 </s></p><p><s id="id.3.0.3.02.01">Haec sunt quae de terminorum definitionibus dicenda erant.
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908 </s><s id="id.3.0.3.02.02">Verum ut ad ea quae demonstranda sunt commodius descendere possimus, <lb ed="Favaro" n="20"></lb> ponatur axioma hoc: scilicet, id quod gravius est a minus gravi, si cetera sint paria, non posse attolli.
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909 </s><s id="id.3.0.3.02.03">Verum, ad ea quae dicenda sunt, egemus etiam sequenti lemmate.
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910 </s></p></subchap2><subchap2><p><s id="id.3.0.4.01.01">Gravitates inaequalium molium corporum aeque gravium eam inter se habent proportionem, quam ipsae moles.
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911 </s></p><p><figure id="id.3.0.4.02.00" xlink:href="FIG1/F036.jpg"></figure>
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912 <s id="id.3.0.4.02.01"><pb ed="manuscript" n="46v"></pb>Sint itaque aeque gravium corporum moles inaequales a, b, quarum maior sit a; erit iam a gravior ipsa b.
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913 </s><s id="id.3.0.4.02.02">Sit itaque ipsius a gravitas c, ipsius vero b sit gravitas d: dico, eandem proportionem habere c gravitatem ad gravitatem d, quam habet a moles ad molem b.
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914 </s><s id="id.3.0.4.02.03">Multiplicentur enim <lb ed="Favaro" n="30"></lb> moles a, b secundum quascunque multiplicationes; sitque molis a multiplex moles efg, molis autem b multiplex sit moles hk, ita tamen ut moles efg molem hk excedat: et quoties moles efg est multiplex ipsius a, <pb ed="Favaro" n="349"></pb> toties nop gravitas sit multiplex gravitatis c; quoties autem hk moles molis b est multiplex, toties gravitas lm gravitatis d multiplex accipiatur.
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915 </s><s id="id.3.0.4.02.04">Quia itaque moles efg et gravitas nop aeque multiplices sunt ipsarum a et c, quot moles sunt in efg, aequales moli a, tot gravitates erunt in nop, ipsi c, gravitati aequales: et quia gravitas c est aequalis gravitati molis a, et gravitas c aequatur gravitati n, et moles a moli g, erit <lb ed="Favaro" n="10"></lb> gravitas n aequalis gravitati molis g.
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916 </s><s id="id.3.0.4.02.05">Similiter ostendetur, gravitatem o aequari gravitati molis f, et p gravitatem gravitati molis e: quare totius molis efg gravitas erit nop.
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917 </s><s id="id.3.0.4.02.06">Simili autem modo ostendetur, <pb ed="manuscript" n="47r"></pb>gravitatem lm aequari gravitati molis hk.
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918 </s><s id="id.3.0.4.02.07">Verum posita est moles efg maior mole hk: ergo etiam gravitas ipsius efg, hoc est gravitas nop, maior erit gravitate molis hk, nempe gravitate lm.
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919 </s><s id="id.3.0.4.02.08">Similiter autem ostendemus, secundum quamcunque multiplicationem, si moles efg maior fuerit mole hk, gravitatem quoque nop maiorem esse gravitate lm; et si efg minor vel aequalis fuerit hk, ipsam etiam nop minorem vel aequalem esse ipsi lm: <lb ed="Favaro" n="20"></lb> et sunt efg, nop ipsarum a, c aeque multiplices; et hk, lm ipsarum b, d, secundum quamcunque multiplicationem, aeque multiplices: ergo, per definitionem aequalis proportionis, sicut moles a ad molem b ita gravitas c ad gravitatem d.
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920 </s><s id="id.3.0.4.02.09">Quod demonstrandum erat.
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921 </s></p><p><s id="id.3.0.4.03.01">His ita inspectis, accedamus iam ad explicandum quomodo causa motus deorsum sit excessus gravitatis mobilis super gravitatem medii: quod, ut supra etiam innuimus, tunc manifestum erit, cum ostensum fuerit, nullum, medium in gravitate non excedens, posse deorsum moveri naturaliter; et nullum, in gravitate excedens medium, in eo non descendere, nisi impediatur.
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922 </s><s id="id.3.0.4.03.02">Quia autem media, per quae fiunt motus, <lb ed="Favaro" n="30"></lb> multa sunt, quia aqua aptissima est in qua intelligi possint motus tam sursum quam deorsum , de motibus tanquam in ea factis speculabimur: et, primo quidem, demonstrabimus, solida corpora quaecunque aeque gra<pb ed="manuscript" n="47v"></pb>via fuerint ac aqua, in aquam demissa, demergi quidem tota; non tamen adhuc deorsum in aqua moveri.
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923 </s><s id="id.3.0.4.03.03">Revocetur autem in memoriam quod supra dictum fuit, nempe ea corpora inter <pb ed="Favaro" n="350"></pb> se aeque gravia tunc esse, cum, existentia aequalia in mole, aeque ponderant: quare si aliquod fuerit corpus quod cum tanta aqua, quanta est sua moles, aeque ponderet, illud aeque grave erit ac aqua.
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924 </s></p></subchap2><subchap2><p><figure id="id.3.0.5.01.00" xlink:href="FIG1/F037.jpg"></figure>
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925 <s id="id.3.0.5.01.01">Intelligatur itaque corpus aliquod aeque grave ac aqua, sitque illud in quo ef; aqua autem sit aobc, secundum superficiem ao antequam corpus ef in eam demittatur: dico solidum ef, in aquam demissum, demergi quidem totum, non tamen adhuc <lb ed="Favaro" n="10"></lb> deorsum ferri.
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926 </s><s id="id.3.0.5.01.02">Demittatur itaque; et, si fieri potest, non demergatur totum, sed illius aliqua pars ex aqua extet, quae sit pars e.
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927 </s><s id="id.3.0.5.01.03">Necessarium itaque est, dum solidum ef demergitur, aquam attolli: locus enim, in quem intrat solidum, ut aqua evacuetur oportet.
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928 </s><s id="id.3.0.5.01.04">Dum itaque solidum demergitur, <pb ed="manuscript" n="48r"></pb>attollatur aqua usque ad superficiem st; et, si fieri potest, in hoc statu maneant tum aqua tum solidum.
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929 </s><s id="id.3.0.5.01.05">Et quia solidum ef premens gravitate sua extulit aquam so, non erit aqua so gravior solido ef; positum est enim, <lb ed="Favaro" n="20"></lb> graviora a levioribus non posse attolli: verum neque erit etiam solidum ef gravius aqua so; nam, si gravius esset, adhuc premeret et attolleret, et, quod consequens est, demergeretur amplius, cum tamen ponatur in hoc statu consistens: restat ergo ut tanta sit gravitas qua aqua so resistit ne amplius attollatur, quanta est gravitas qua solidum ef premit et aquam attollit.
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930 </s><s id="id.3.0.5.01.06">Premit autem solidum tota sua gravitate, aqua autem similiter so tota sua gravitate resistit; ergo gravitas solidi ef aequatur gravitati aquae so.
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931 </s><s id="id.3.0.5.01.07">Rursus: moles aquae so est minor mole totius solidi ef; nam aequatur moli tantummodo quae sub aqua est demersa.
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932 </s><s id="id.3.0.5.01.08">Patet enim hoc: nam tanta moles aquae de loco, in quem <lb ed="Favaro" n="30"></lb> intravit solidum, expulsa fuit, quanta est moles solidi quae demersa est; ergo moles aquae so aequatur moli partis solidi demersae, nempe parti f.
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933 </s><s id="id.3.0.5.01.09">Sunt itaque 2 corpora, aqua so unum, alterum solidum ef, <pb ed="Favaro" n="350"></pb> et gravitas aquae so demonstrata est aequalis gravitati totius solidi ef: moles autem solidi ef est maior mole aquae so: ergo corpus ef est minus grave quam aqua (duorum enim corporum aequalium in gravitate, in mole vero inaequalium, maius in mole est minus grave).
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934 </s><s id="id.3.0.5.01.10"><pb ed="manuscript" n="48v"></pb>Hoc autem est contra positionem; positum enim fuit solidum ef aeque grave ac aqua: quare ipsius ef nulla pars extabit extra aquam: ergo totum demergetur.
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935 </s><s id="id.3.0.5.01.11">Quod primo fuit ostendendum.
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936 </s><s id="id.3.0.5.01.12">Dico insuper, non adhuc, in aqua totum existens, deorsum ferri.
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937 </s><s id="id.3.0.5.01.13">Cum enim aeque grave sit ac aqua, dicere illud in aquam descendere idem esset ac si <lb ed="Favaro" n="10"></lb> diceremus, aquam in aqua sub aquam descendere, et rursus aquam, quae super primam ascendit, deorsum iterum descendere, et sic aquam in infinitum procedere in alternatim descendendo et ascendendo; quod inconveniens esset.
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938 </s></p><p><s id="id.3.0.5.02.01">Postquam itaque inspeximus, corpora medio, per quod ferri deberent, aeque gravia non descendere, sequitur ut ostendamus, ea quae minus gravia sunt, nullo similiter posse modo deorsum moveri: et erit iam prima pars nostrae propositionis demonstrata; scilicet, impossibile esse quicquam deorsum ferri, quod medium, per quod ferri debet, in gravitate non excedat.
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939 </s></p></subchap2><subchap2><p><figure id="id.3.0.6.01.00" xlink:href="FIG1/F038.jpg"></figure>
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940 <s id="id.3.0.6.01.01">Sit itaque primus aquae status, antequam corpus in eam demittatur, secundum superficiem ef; corpus autem aliquod a, minus grave quam aqua, in aquam demissum, si fieri potest, demergatur totum, et aqua attollatur usque ad superficiem cd.
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941 </s><s id="id.3.0.6.01.02">Quia itaque corpus a, <pb ed="manuscript" n="49r"></pb>sua premens gravitate, potuit aquam cf sursum attollere, non erit solidum a minus grave aqua cf <lb ed="Favaro" n="30"></lb> (positum enim est, minus gravia non posse graviora attollere): sed moles a aequatur moli cf: sunt itaque duo corpora, a et cf, et gravitas ipsius a non est minor gravitate ipsius cf, moles autem a moli cf aequatur: ergo corpus a non <pb ed="Favaro" n="352"></pb> erit minus grave quam aqua: quod est contra hypothesim; posuimus enim corpus a aqua minus grave.
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942 </s><s id="id.3.0.6.01.03">Quare constat, impossibile esse corpora medio aliquo minus gravia posse demergi tota; quare etiam multo minus poterunt deorsum moveri.
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943 </s></p><p><s id="id.3.0.6.02.01">His itaque demonstratis, indubitanter primam propositionis partem, quam demonstrandam suscepimus, asserere possumus: nempe, impossibile esse aliquid deorsum moveri, medium per quod ferri debet in gravitate non excedens.
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944 </s><s id="id.3.0.6.02.02">Secundam autem partem, nempe corpora, quaecunque medio graviora fuerint, in eo, nisi impediantur, necessario descendere, ex dictis similiter confirmatam habebimus. <lb ed="Favaro" n="10"></lb>
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945 </s><s id="id.3.0.6.02.03">Primo, enim, ita confirmabitur: sunt quaedam quae moventur deorsum, ut quotidie videmus; et quae moventur deorsum, necessario medium gravitate excedunt: ergo, convertendo, quaecunque medium gravitate excedunt, deorsum movebuntur.
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946 </s><s id="id.3.0.6.02.04">2Á: si quae gravitate medium excedunt non moventur deorsum, aut supernatabunt medio, aut ita demergentur ut non adhuc descendant.
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947 </s><s id="id.3.0.6.02.05">Si non demer<pb ed="manuscript" n="49v"></pb>guntur, erunt, contra hypothesim, medio minus gravia: quod si tota demergantur, ita tamen ut non adhuc deorsum ferantur, erunt aeque gravia ac medium; quod similiter est contra id quod positum est: restat ergo, ut necessario deorsum moveantur.
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948 </s><s id="id.3.0.6.02.06">Quae omnia cum ita se habeant, <lb ed="Favaro" n="20"></lb> verissime nobis attestantur, causam motus naturalis deorsum esse excessum gravitatis mobilis super gravitatem medii per quod fertur: quod confirmandum susceperamus.
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949 </s></p><p><s id="id.3.0.6.03.01">Postquam autem hactenus, quoad licuit, causam naturalis motus deorsum investigavimus et explicuimus, ut inventionem causae motus sursum aggrediamur, superest.
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950 </s><s id="id.3.0.6.03.02">Verum, quia sententiae nostrae de motu sursum longe aliae sunt ab illis quae de ipso ab Aristotele et Peripateticis traditae sunt, antequam illius causam inquiramus, primo, contra Peripateticorum opinionem, motum sursum omnem praeternaturalem esse, demonstrabimus. <lb ed="Favaro" n="30"></lb>
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951 </s></p></subchap2><subchap2><p><s id="id.3.0.7.01.01">Ut igitur hanc nostram opinionem commodius explicare et confirmare valeamus, inspiciendum est, quaenam conditiones motui alicui <pb ed="Favaro" n="353"></pb> requirantur ad hoc, ut naturalis appellari possit: quae si in motu sursum inerunt, naturalis erit; sin minus, naturalis non erit.
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952 </s><s id="id.3.0.7.01.02">Conditiones autem 2 sunt: una quidem quae sumitur ex parte solius motus, ut motus est, nulla habita ratione vel ad mobile vel ad medium; altera est ex parte mobilis.
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953 </s><s id="id.3.0.7.01.03">Conditio ex parte motus, ut purus motus est, est ut non possit in infinitum esse et ad inde<pb ed="manuscript" n="50r"></pb>terminatum, sed ut sit finitus et terminatus: {1} nam ea quae natura moventur, feruntur ad aliquem terminum, in quo naturaliter quiescere possint.
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954 </s><s id="id.3.0.7.01.04">Conditio ex parte mobilis est, ut non ab extrinseca, sed intrinseca, moveatur <lb ed="Favaro" n="10"></lb> causa. {2}
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955 </s><s id="id.3.0.7.01.05">Harum conditionum nulla est in motu qui est a medio; ergo non potest dici naturalis.
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956 </s><s id="id.3.0.7.01.06">De prima conditione prius disquiremus, de secunda autem paulo post. {3}
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957 </s></p><p><s id="id.3.0.7.02.01">Dico itaque, motum sursum, ratione qua elongatio quaedam est a centro, non posse esse naturalem: quod sic probo.
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958 </s><s id="id.3.0.7.02.02">Ipsius motus naturalis est aliquis terminus: sed motus sursum nullus est terminus: ergo motus sursum non est naturalis.
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959 </s><s id="id.3.0.7.02.03">Maior manifesta est: natura enim non movet eo, quo nunquam pertingere possit; ergo, in aliquem terminum.
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960 </s><s id="id.3.0.7.02.04">Minor, nempe ipsius motus sursum non esse terminum, sic probatur: ille est terminus alicuius motus, a quo recedi <lb ed="Favaro" n="20"></lb> non potest eodem motu cuius est terminus; at in motu sursum assignari non potest terminus, a quo removeri non possit eodem motu, nempe sursum; ergo motus ipsius sursum non est terminus.
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961 </s><s id="id.3.0.7.02.05">Maior manifesta est: si enim ab eo recedere possemus eodem motu incedentes, iam non esset ille illius motus terminus; ut, verbigratia, Roma non dicetur terminus motus ad meridiem, quia, postquam meridiem versus moti Romam venimus, possumus ab eadem urbe recedere eodem motu procedentes, nempe motu meridiem versus.
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962 </s><s id="id.3.0.7.02.06"><pb ed="manuscript" n="50v"></pb>Minor itidem verissima est: nam, assignato quocunque loco in ipso sursum, possumus ab eo removeri eodem motu procedentes, nempe motu sursum, <lb ed="Favaro" n="30"></lb> recedendo a centro; nulla enim tanta est distantia a centro, ut ea maior <pb ed="Favaro" n="354"></pb> distantia intelligi nequeat.
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963 </s><s id="id.3.0.7.02.07">Caret itaque sursum termino; ergo sursum nihil moveri potest naturaliter.
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964 </s></p><p><s id="id.3.0.7.03.01">Verum dum naturalitatem a motu sursum excludimus, consideremus quam apte eadem motui deorsum accommodetur.
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965 </s><s id="id.3.0.7.03.02">In motu enim deorsum est terminus, nempe centrum, a quo recedi non potest quicquam eadem specie motus qua accesserat: accesserat enim motu deorsum; quod si removeri velit, sursum feretur.
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966 </s><s id="id.3.0.7.03.03">Longinquitas a medio est indeterminata et infinita; sed propinquitas est terminata, ab ipso nempe centro: si ergo erit aliquid hac facultate praeditum, ut medium fugiat, hoc certe in infinitum moveri aptum erit; quo quid <lb ed="Favaro" n="10"></lb> absurdius?
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967 </s><s id="id.3.0.7.03.04">Rationabiliter itaque motum ad medium naturalem, a medio autem praeter naturam, esse dicemus.
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968 </s></p><p><s id="id.3.0.7.04.01">Neque obiicias vulgatum illud axioma: Posito in rerum natura uno contrario, ponitur etiam reliquum: sed datur motus naturalis deorsum; ergo dabitur etiam naturalis motus sursum.
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969 </s><s id="id.3.0.7.04.02">Nam, dato axiomate, respondeo, primo, aliud esse dicere, Dato in natura uno contrario, datur et alterum; aliud si dicamus, Unum contrariorum est secundum naturam, ergo et reliquum, similiter, ut secundum naturam sit, est necessarium.
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970 </s><s id="id.3.0.7.04.03">Primum concedimus, secundum negamus.
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971 </s><s id="id.3.0.7.04.04">Datur itaque motus deorsum: in natura; datur etiam in natura motus <lb ed="Favaro" n="20"></lb> <pb ed="manuscript" n="51r"></pb>sursum, eius contrarium.
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972 </s><s id="id.3.0.7.04.05">Quod si addas, Motus deorsum est secundum naturam, ergo motus sursum erit secundum naturam; hoc negatur.
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973 </s><s id="id.3.0.7.04.06">Immo, argumentum retorquentes, ita argumentabimur: Dato uno contrariorum in natura, datur etiam alterum; sed in natura datur motus unus naturalis deorsum; ergo dabitur illius oppositum, qui erit motus praeternaturalis sursum. {1}
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974 </s></p><p><s id="id.3.0.7.05.01"><pb ed="Favaro" n="355"></pb> Haec sunt ex quibus satis manifestum esse potest, motum a medio, ut motus est, nulla vel ad mobile vel ad media, per quae fit motus, ratione habita, naturalem esse non posse.
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975 </s><s id="id.3.0.7.05.02">Ut autem argumenta quae ex parte mobilis sumuntur explicari possint, prius corpora gravitatem habere, est videndum.
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976 </s></p></subchap2><subchap2><p><s id="id.3.0.8.01.01">De levi hucusque ne verbum quidem diximus, sed tantum de gravi et minus gravi; quare, iurene an iniuria hoc a nobis factum sit, locus hic examinandi praebet ansam.
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977 </s><s id="id.3.0.8.01.02">Si itaque Aristoteles et caeteri <lb ed="Favaro" n="10"></lb> philosophi pro levi accipere id quod nos minus grave appellamus contenti essent, hanc levis appellationem nos quoque admittere non gravati essemus: verum quia voluerunt (non contenti se pro levi id quod minus grave est intelligere) dari etiam leve quoddam corpus, quod tale simpliciter esset et omni careret gravitate, id cane peius et angue abhorrentes, omnimode et funditus usque ipsum leve evertere conati sumus.
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978 </s><s id="id.3.0.8.01.03">Quapropter, in hoc antiquorum opinionem, quam frustra Aristoteles 4Á Caeli destruere tentat, sequentes, Aristotelis eo loci tum confutationes, tum etiam suas confirmationes, confutata quidem confirmando, confirmata vero confutando, examinabimus; et hoc tunc <lb ed="Favaro" n="20"></lb> praestabimus, cum Aristotelis opinionem <pb ed="manuscript" n="52r"></pb>exposuerimus.
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979 </s></p><p><s id="id.3.0.8.02.01">Voluit itaque Aristoteles, dari aliquod corpus quod simpliciter gravissimum esset, quod nullo unquam modo leve posset dici et quo nihil gravius haberi posset; similiter, et dari huic contrarium, quod simpliciter leve esset, nullam in se gravitatem habens, et quo nihil levius inveniri posset.
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980 </s><s id="id.3.0.8.02.02">Et primo quidem, gravissimum definiens, <pb ed="Favaro" n="356"></pb> simpliciter gravissimum, inquit, illud dicimus quod omnibus substat et semper ad medium fertur; levissimum vero appellat id, quod omnibus supereminet et semper sursum, nunquam vero deorsum, movetur: et haec scribit 4 Caeli t. 26 et 31.
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981 </s><s id="id.3.0.8.02.03">Dicit deinde, gravissimum esse terram, levissimum ignem: et hoc t. 32 et aliis in locis.
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982 </s><s id="id.3.0.8.02.04">Tunc, contra ponentes in igne aliquam gravitatem, sic argumentatur: Si ignis habet aliquam gravitatem, alicui substabit; at hoc non videtur; ergo [etc.].
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983 </s><s id="id.3.0.8.02.05">Argumentum hoc non concludit.
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984 </s><s id="id.3.0.8.02.06">Nam ad hoc ut aliquid alicui immineat, sufficit ut eo, cui imminere debet, sit minus grave; non autem necesse est, ut omni careat gravitate: sicut ad hoc ut lignum aquae <lb ed="Favaro" n="10"></lb> supernatet, non requiritur necessario ut omni careat gravitate, sed satis est ut sit aqua minus grave; et ita, pari ratione, ad hoc ut ignis aëri immineat, sat est quod aëre sit minus gravis, nec est necessarium ut omni careat gravitate.
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985 </s><s id="id.3.0.8.02.07">Quare patet, argumentum hoc nullam habere necessitatem.
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986 </s></p><p><s id="id.3.0.8.03.01">Argumentatur etiam hoc pacto: Si ignis aliquam habet gravitatem, ergo multus ignis gravior erit pa<pb ed="manuscript" n="52v"></pb>uco; quare tardius ascendet in aëre multum ignis quam paucum: et ita, si terra habet aliquam levitatem, multum terrae, eo quod plus habebit levitatis, tardius descendet quam pauca: experientia tamen contrarium ostendit; videmus enim, multum <lb ed="Favaro" n="20"></lb> ignem citius ascendere pauco, sicut et multam terram citius descendere: signum ergo est quod in igne est tantum levitas; et cum in multo igne plus sit levitatis, citius ascendit.
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987 </s><s id="id.3.0.8.03.02">Hoc quoque argumentum infirmissimum est.
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988 </s><s id="id.3.0.8.03.03">Primo, enim, non sibi constat Aristoteles: loquens enim de gravitate et levitate absoluta, nulla ad aliud habita ratione, subdit exemplum ex quo nihil aliud colligi potest, nisi ignem aëre esse minus gravem, et terram aqua vel aëre graviorem.
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989 </s><s id="id.3.0.8.03.04">Non enim bona est consequentia ista, Si ignis absolute consideratus gravitatem haberet, multum ignis in aëre pauco esset gravius: ignem enim in aëre gravem esse non dicimus, sed solum esse gravem.
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990 </s><s id="id.3.0.8.03.05">Sed ita est argumentandum: Ignis, <lb ed="Favaro" n="30"></lb> absolute consideratus, habet gravitatem: ergo ubi ignis habet gravitatem, multum ignis multam habebit gravitatam; et ubi ignis habet levitatem, ut in aëre, ibi multum ignis multam habebit levitatem, paucum vero paucam.
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991 </s><s id="id.3.0.8.03.06">Constat ergo Aristotelis fallacia in argumentando.
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992 </s><s id="id.3.0.8.03.07">Quod si valeret modus ille argumentandi, possemus etiam demonstrare, quodlibet lignum nullam habere gravitatem, hoc pacto <pb ed="Favaro" n="357"></pb> inducendo: Si lignum aliquam habet gravitatem, ergo magnum lignum gra<pb ed="manuscript" n="53r"></pb>vius erit pauco; quare tardius ascendet in aqua magnum lignum parvo: cuius tamen contrarium experientia ostendit; magnum enim lignum ex imo aquae maiori impetu sursum irruit parvo.
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993 </s><s id="id.3.0.8.03.08">At quis unquam dixerit lignum, ut lignum est, nulla habita ratione ad medium in quo ascendit, omni carere gravitate?
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994 </s><s id="id.3.0.8.03.09">Sicut itaque lignum aquae imminet, non eo quod absolute omni careat gravitate, sed solum quia minus est grave quam aqua; ita, pari pacto, ignis aëri imminet, non quod simpliciter nullam habeat gravitatem, sed quia minus gravis <lb ed="Favaro" n="10"></lb> est ipso aëre.
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995 </s><s id="id.3.0.8.03.10">2Á: quod supponit tanquam verissimum Aristoteles, nempe multum ignem citius ascendere quam paucum, aut multam terram pauca velocius descendere, fortasse falsum est; ut suo loco demonstrabimus.
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996 </s></p><p><s id="id.3.0.8.04.01">3Á, argumentatur: Si ignis habet gravitatem, erit iam multum ignis pauco aëre gravius: quod absurdissimum est, sicut si dicamus, Si terra habet levitatem aliquam, erit aliqua pars terrae levior aliqua parte aquae: quod falsum est, quia videmus, quamlibet terrae particulam sub aquam descendere, et quamlibet ignis portionem in aëre sursum ferri.
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997 </s><s id="id.3.0.8.04.02">Verum argumentum hoc caeteris aliis infirmius est: nam <lb ed="Favaro" n="20"></lb> qui adeo mente captus est, ut non credat, multum aquae gravius esse pauca terra, et multum aëris pauca aqua, et multum ignis pauco aëre?
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998 </s><s id="id.3.0.8.04.03">Neque obstat quod dicit Aristoteles: Videmus terram in aqua descendere.
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999 </s><s id="id.3.0.8.04.04">Nam, cum <pb ed="manuscript" n="53v"></pb>haec dicit, iam non sibi constat: nam, loquens de gravitate absoluta, exemplum ponit de gravitate in ratione ad minorem gravitatem medii.
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1000 </s><s id="id.3.0.8.04.05">Nanque, cum dicimus aquam habere gravitatem et, inde, magnam aquae molem graviorem esse pauca terra, non dicimus aquam gravitatem habere in sua regione, nec multam aquam pauca terra esse graviorem in aqua, ubi aqua nullam habet gravitatem, ut inferius demonstrabitur; sed asserimus, multum aquae <lb ed="Favaro" n="30"></lb> gravius esse pauca terra in loco ubi aqua etiam gravitatem habeat, ut, verbigratia, in aëre.
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1001 </s><s id="id.3.0.8.04.06">Amplius: non bene deducit consequentiam, Quaelibet particula terrae in aqua descendit, ergo particula illa terrae, ut quacunque mole aquae sit gravior oportet: nam, ut supra demonstratum est, ad hoc ut particula terrae descendat in aqua, sufficit ut gravior sit tanta aquae mole quanta suamet moles extat.
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1002 </s><s id="id.3.0.8.04.07">Idem de igne est dicendum: cuius magna pars pauco aëre gravior erit, sed <pb ed="Favaro" n="358"></pb> non in loco aëris, ubi ignis gravitatem suam exercere non potest, sed in loco ubi ignis etiam gravet.
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1003 </s><s id="id.3.0.8.04.08">Quod si necessitatem haberet argumentum Aristotelis, concluderem etiam, paucum plumbi maxima trabe gravius esse, quia, scilicet, plumbum in aqua aliquam habet gravitatem et deorsum fertur, trabes autem nequaquam: at verum quidem est, plumbi paucum gravius esse trabe in loco ubi trabes nullam habet gravitatem; at si loqui velimus de gravitate trabis, <pb ed="manuscript" n="54r"></pb>ut illam ponamus oportet in loco ubi gravitatem suam ostendere possit.
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1004 </s><s id="id.3.0.8.04.09">Similiter, cum dicit, Quaelibet particula aquae in aëre descendit, ergo quantumvis aëris levius est particula aquae; hoc verum erit in eo <lb ed="Favaro" n="10"></lb> loco, ubi aër nullam habet gravitatem, aqua vero habeat: sed hoc non erit loqui de gravitate absoluta, ut loquimur.
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1005 </s><s id="id.3.0.8.04.10">Nam, si ponamus multum aëris in loco ubi aër etiam gravet, ut in igne, ibi profecto gravius erit pauca aqua.
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1006 </s><s id="id.3.0.8.04.11">Neque ob id inferat Aristoteles, Ergo multum aëris velocius descendet pauca aqua.
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1007 </s><s id="id.3.0.8.04.12">Non enim valet consequentia, hoc illo est quomodocunque gravius, ergo velocius descendet: nanque magna vessica inflata pauco plumbo in aëre gravior erit; non tamen velocius descendet.
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1008 </s><s id="id.3.0.8.04.13">Sed de hoc fusius, ubi de causis maioris et minoris velocitatis agemus.
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1009 </s><s id="id.3.0.8.04.14">Pari etiam pacto, non eo quod ignis multus gravior sit pauco aëre, dicemus ignem velocius esse descensurum. <lb ed="Favaro" n="20"></lb>
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1010 </s></p><p><s id="id.3.0.8.05.01">4Á, argumentatur: Duo sunt loca contraria, medium et extremum, accipiens pro extremo concavum xxx ergo oportet, quae in illis sunt esse contraria; quod non erit, nisi terra ponatur omni carens levitate, ignis vero ab omni gravitate vacuus.
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1011 </s><s id="id.3.0.8.05.02">Argumentum pluribus de causis nullius est roboris.
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1012 </s><s id="id.3.0.8.05.03">Primo, enim, nec terra est in centro nec ignis in concavo xxx centrum enim locus non est, cum indivisibile sit punctum; ex igne autem sola convexa superficies est in concavo xxx quare ex hoc nihil <pb ed="manuscript" n="54v"></pb>aliud concludi potest, nisi centrum terrae contrarium esse convexae superficiei ignis: at centrum terrae nulla pars est ipsius, sicut convexa superficies ignis nulla ignis est pars: ergo ex hoc inferri <lb ed="Favaro" n="30"></lb> non potest quicquam de terra et igne.
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1013 </s><s id="id.3.0.8.05.04">Amplius: terra non magis est in centro quam in concavo aquae et aëris, sicut ignis etiam est in convexa aëris superficie: quare ostendendum erat, quomodo concava aëris superficies convexae contrariaretur.
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1014 </s><s id="id.3.0.8.05.05">Quod si sic sit, erit aër qui inter ambas continetur superficies in locis contrariis; et aër (si argumentandi ratio Aristotelis concludit) qui est sub convexa sui <pb ed="Favaro" n="359"></pb> superficie, contrarius, erit aëri qui est supra suam concavam superficiem.
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1015 </s><s id="id.3.0.8.05.06">Amplius: ut bene scripsit Plato in Timaeo, centro contrariatur etiam eodem pacto concavum aquae et aëris, sicut concavum xxx nec, tamen, quae sub concavo aëris sunt, illis quae circa centrum sunt, contrariantur.
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1016 </s><s id="id.3.0.8.05.07">Patet igitur, nullius esse momenti tale argumentum.
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1017 </s></p><p><s id="id.3.0.8.06.01">5Á, arguit Aristoteles: Si submoveatur aër, ignis non descendet, sicut aër submota aqua; signum ergo est, ignem gravitatem non habere.
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1018 </s><s id="id.3.0.8.06.02">Antecedens demonstratione indiget: quod non probavit Aristoteles, nisi dicas quod dixerit, Sicut terra non ascendit in medicorum cucurbitulis <lb ed="Favaro" n="10"></lb> quia gravissima, ita ignis non descendet quia levissimus.
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1019 </s><s id="id.3.0.8.06.03">Sed non valet proportio: quia, non quod sit gravissima, terra non ascendit, sed quia non est fluida; nam neque lignum ascenderet, cum tamen sit aqua levius, quae ascendit; <pb ed="manuscript" n="55v"></pb>ascenderet tamen mercurius, quamvis terra gravior, quia fluidus est; et sic ignis descenderet, quia non solidus et durus, sed fluens, est.
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1020 </s></p><p><s id="id.3.0.8.07.01">Haec Aristoteles contra antiquos, et nos pro antiquis; sed iam contra ipsum procedamus.
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1021 </s><s id="id.3.0.8.07.02">Primo, itaque, grave et leve per deorsum et sursum definit Aristoteles: si ergo datur simpliciter grave et simpliciter leve, quod omni careat gravitate, ergo ut dentur simpliciter deorsum et <lb ed="Favaro" n="20"></lb> simpliciter sursum oportet, quo nihil magis sursum haberi possit.
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1022 </s><s id="id.3.0.8.07.03">At simpliciter sursum, quo nihil magis sursum, et quod etiam ut deorsum esse non possit, non solum actu non datur, verum neque ipsa cogitatione concipi potest: de deorsum autem, quamvis sit aliquod ita deorsum ut aliud quicquam magis deorsum esse non possit, tamen illud tale non est ut in eo aliquod corpus esse possit, cum indivisibile punctum sit.
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1023 </s><s id="id.3.0.8.07.04">Quare cum ista non dentur, non dabitur etiam quicquam adeo grave ut eo aliud gravius dari non possit, nec quicquam gravitate ab omni immune.
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1024 </s><s id="id.3.0.8.07.05">2Á: si elementa, ut ipse vult, ad invicem transmutantur , quando ex aëre gravi fit ignis, quid de illa <lb ed="Favaro" n="30"></lb> gravitate aëris?
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1025 </s><s id="id.3.0.8.07.06">An forsan adnihilatur?
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1026 </s><s id="id.3.0.8.07.07">Sed, si adnihilatur, cum rursus ex igne fit terra, unde manat gravitas? an forsan gravitas, quae aliquid est, ex non gravitate, quae nihil est?
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1027 </s><s id="id.3.0.8.07.08">3Á: si ignis caret omni gravitate, ergo et omni densitate carebit; densum enim consequitur grave: sed quod omni caret densitate, id vacuum est: ergo ignis vacuum.
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1028 </s><s id="id.3.0.8.07.09">At quid absurdius?<pb ed="manuscript" n="55v"></pb>
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1029 </s><s id="id.3.0.8.07.10">Sed, demum, quomodo unquam poterit <pb ed="Favaro" n="360"></pb> quis ignem imaginari, substantiam cum quantitate coniunctam, gravitatem non habere?
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1030 </s><s id="id.3.0.8.07.11">Hoc profecto omnino irrationabile est.
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1031 </s><s id="id.3.0.8.07.12">Et cum dicimus, ignem omnium levissimum et terram omnium esse gravissimam, cogimur, velimus nolimus, dicere terram ideo esse gravissimam, in respectu aliorum omnium, quia omnibus substat.
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1032 </s><s id="id.3.0.8.07.13">Substare enim omnibus et omnium esse gravissimum, idem sunt: et hoc patet; quia, si gravissimum est quod omnibus substat, si omnia auferantur, non poterit amplius gravissimum dici, cum nulli substet.
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1033 </s><s id="id.3.0.8.07.14">Dicitur ergo gravissimum in comparatione minus gravium, quibus substat; et idem de levitate ignis est dicendum. {1} <lb ed="Favaro" n="10"></lb>
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1034 </s></p><p><s id="id.3.0.8.08.01">Concludamus itaque, gravitatis nullum corpus expers esse, sed gravia esse omnia, haec quidem magis, haec autem minus, prout eorum materia magis constipata et compressa, vel diffusa et extensa, fuerit: ex quo sequitur, non posse dici ignem esse simpliciter leve, hoc est quod omni careat gravitate; hoc enim vacui est.
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1035 </s><s id="id.3.0.8.08.02">Non tamen dixerim, non inveniri in rerum natura aliquod corpus quo nullum aliud gravius inveniatur, similiter et aliud quo nullum sit minus grave; nam hoc concedimus, cum sciamus de facto non esse infinita corpora, alterum altero gravius: sed dicimus, ea non esse talia quibus adhuc magis et minus gravia esse non possent alia, et ideo non posse illa dici <lb ed="Favaro" n="20"></lb> simpliciter gravia, aut simpliciter levia, quod omni careant gravitate.
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1036 </s><s id="id.3.0.8.08.03">Dicimus etiam, haec, quae ceteris magis minusve gravia sunt, non esse fortasse terram <pb ed="manuscript" n="56r"></pb>et ignem.
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1037 </s><s id="id.3.0.8.08.04">Nam de terra, quod non sit gravissima omnium, iam experientia docet: ipsa enim metallis liquatis omnibus supernatat, ut argento quod dicunt vivo; ex quo patet, metalla graviora esse ipsa terra.
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1038 </s><s id="id.3.0.8.08.05">Similiter erunt fortasse exhalationes aliquae minus graves quam sit ignis, super igne natantes: verum hoc audacter non asserimus, quia super ignem non fuimus.
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1039 </s><s id="id.3.0.8.08.06">Verum si cometae exhalationes sunt <pb ed="Favaro" n="361"></pb> ardentes, ut ipsi testantur Peripatetici, hoc certum est, oportuisse exhalationes ipsas super ignem evolasse; cum cometae nonnullae longe prima, {1} quam ponunt ipsi, aëris regione altiores conspectae sint.
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1040 </s></p><p><s id="id.3.0.8.09.01">His igitur ita explicatis, ad ea quae pro superioris quaestionis exitu pronuncianda restabant, revertamur.
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1041 </s></p></subchap2><subchap2><p><s id="id.3.0.9.01.01">Ex parte itaque mobilis, motus sursum naturales esse non posse in iis quae causam externam omnibus conspicuam habent, ut cum vi expulsus lapis sursum in aëre fertur, nullus est qui dubitet: talem <lb ed="Favaro" n="10"></lb> enim motum naturalem non esse constat, quia non tendit eo ubi mobile quiescat; nam mobile statim se ad motum deorsum sibi proprium sua sponte convertitur.
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1042 </s><s id="id.3.0.9.01.02">Quaestio itaque est de motu illo sursum, quando mobile eo fertur ubi quiescit; ut cum lignum et aër sursum in aqua, et ignis in aëre, feruntur: de quo, licet contra Peripateticorum omnium sententiam, <pb ed="manuscript" n="56v"></pb>ita decrevimus, ut vere naturalem dici non posse assereremus; et hanc conclusionem ex parte ipsius motus, nulla seu mobilis seu medii ratione habita, quoad licuit, confirmavimus; quam similiter nunc ex parte mobilis confirmare conabimur.
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1043 </s></p><p><s id="id.3.0.9.02.01">Primo, itaque, illud naturaliter moveri dici non potest, quod sui <lb ed="Favaro" n="20"></lb> motus intrinsecam non habet causam, sed externa eget: talia autem sunt corpora quaecunque sursum moventur: ergo praeter naturam moventur.
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1044 </s><s id="id.3.0.9.02.02">Maior patet: nam quae ab externa moventur causa per accidens, ab alio et non ex sui natura moventur.
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1045 </s><s id="id.3.0.9.02.03">Minor quoque patet: cum enim corpus omne internam motus deorsum causam, nempe gravitatem, habeat, ut contrarii motus contrariam causam habeat, impossibile est.
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1046 </s><s id="id.3.0.9.02.04">Neque dicas, sicut excessus gravitatis mobilis super gravitatem medii est per se et intrinseca motus deorsum causa, ita defectum gravitatis mobilis, in respectu ad gravitatem medii, esse per se et intrinsecam motus sursum causam: nam motus deorsum per se <lb ed="Favaro" n="30"></lb> est causa gravitas mobilis absoluta; per accidens autem est ut dicta gravitas debeat medii gravitatem excedere, sicut per accidens est <pb ed="Favaro" n="362"></pb> mobile moveri deorsum in medio quod aliquam habeat gravitatem.
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1047 </s><s id="id.3.0.9.02.05">Grave enim, licet medium nullam haberet gravitatem, et propterea sua gravitas non esset medii gravitatem excedens, tamen deorsum moveretur, quia intrinsecam habet causam descensus: <pb ed="manuscript" n="57r"></pb>at non sic iudicare licet de defectu gravitatis; cum enim gravitatis defectus, nempe ipsum non grave, nihil sit, requiritur necessario medium quod mobili ipso sit gravius, ad hoc ut mobile dici possit in gravitate deficiens.
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1048 </s><s id="id.3.0.9.02.06">Cum igitur mobile non possit esse non grave, nisi adsit medium gravius (nullum enim corpus ex se est gravitatis expers), constat mobilis non gravitatem omnino ex gravitate medii pendere (si enim medium <lb ed="Favaro" n="10"></lb> grave non adsit, mobile non erit amplius non grave, sed grave remanebit): quod cum ita sit, extrinseca erit mobili ipsa non gravitas, et ab alio proveniens, et externa egens gravitate.
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1049 </s><s id="id.3.0.9.02.07">Quare, si ipsa non gravitas est causa motus sursum, extrinseca erit et mobili ab alio proveniens: quod cum mobile intrinsecam motus causam non habeat, ut secundum naturam moveatur, impossibile erit.
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1050 </s></p><p><s id="id.3.0.9.03.01">Disparitas itaque est inter motum sursum et deorsum: quia in motu deorsum mobile non eget medio, a quo causam motus recipiat; habet enim intrinsecam gravitatem motus deorsum causam; immo a medio impeditur suus motus, cum a medio sua gravitas minuatur, <lb ed="Favaro" n="20"></lb> ut inferius demonstrabitur: motus autem sursum causa adeo a medio gravi pendet, ut in medio non gravi quicquam nullo pacto moveri sursum possit, cum mobilis non gravitas omnino e gravitate medii proveniat. {1}
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1051 </s><s id="id.3.0.9.03.02">Sed quid pluribus opus est?
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1052 </s><s id="id.3.0.9.03.03">Omnium corporum una est materia, eaque in omnibus gravis: sed eiusdem gravitatis non possunt esse contrariae inclinationes naturales: ergo, si una est naturalis inclinatio, ut contraria sit praeter naturam opus est: naturalis autem gravitatis inclinatio est ad centrum: ergo necesse est, quae a centro praeter naturam esse.
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1053 </s></p><p><s id="id.3.0.9.04.01">Crediderim autem, errorem eorum, qui motum a medio secundum <lb ed="Favaro" n="30"></lb> naturam esse existimarunt, ex eo ortum duxisse, quia non potuerunt externam causam, a qua mobilia moverentur, invenire; et ideo coactos <pb ed="Favaro" n="363"></pb> fuisse, intrinsecam ponere, eamque levitatem appellare.
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1054 </s><s id="id.3.0.9.04.02">Quapropter, ut huiusmodi deleamus erratum, properemus iam ad explicandum, quomodo quae sursum feruntur, ab extrinseca moveantur causa, nempe ab ipso medio per extrusionem.
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1055 </s></p></subchap2><subchap2><p><s id="id.3.0.10.01.01">Si itaque quae sursum moventur, praeter naturam moventur, ut externam sui motus causam habeant necesse est.
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1056 </s><s id="id.3.0.10.01.02">Hanc autem dicimus esse medii extrusionem: quae ita contingit.
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1057 </s></p><p><s id="id.3.0.10.02.01"><lb ed="Favaro" n="10"></lb> Primo, igitur, ut quae sursum moventur, medio, per quod feruntur, minus sint gravia, necesse est.
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1058 </s><s id="id.3.0.10.02.02">Demonstratum enim est, ea quae medio aliquo fuerint graviora, deorsum in eo ferri; et ea quae fuerint aeque gravia, neque sursum neque deorsum moveri, sed in <pb ed="manuscript" n="58r"></pb>eo quiescere: quae, ergo, corpora sursum feruntur, ut minus sint gravia, de necessitate sequitur.
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1059 </s><s id="id.3.0.10.02.03">Quando, igitur, in medio aliquo corpus aliquod ipso medio minus grave demersum fuerit, circumflui medii partes, gravitate sua prementes, tentant ex inferiori loco corpus illud expellere, ut ipsaemet humiliores occupent regiones.
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1060 </s><s id="id.3.0.10.02.04">Quod si minor fuerit resistentia quam in corpore illo offenderint, quam sit vis qua ipsae <lb ed="Favaro" n="20"></lb> premunt, vincunt illudque extrudunt: at minor erit resistentia mobilis ne attollatur, quotiescunque sua gravitas gravitate medii prementis fuerit minor: ergo tunc extrudetur.
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1061 </s></p></subchap2></subchap1><subchap1><subchap2><p><figure id="id.3.0.1.0.03.00" xlink:href="FIG1/F039.jpg"></figure>
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1062 </p></subchap2><subchap2><p><s id="id.3.0.10.03.01">Verum ut totum negocium melius intelligatur, exemplum in medium afferamus.
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1063 </s><s id="id.3.0.10.03.02">Intelligatur itaque corpus aliquod a, quod medio, ut puta ipsa aqua, sit minus grave; sit autem aquae superficies, antequam corpus a demergatur, secundum lineam bc; demerso autem a, extollatur aqua usque ad superficiem de.
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1064 </s><s id="id.3.0.10.03.03">Manifestum itaque est, quod si corpus a ibi non detineretur, <lb ed="Favaro" n="30"></lb> aqua dc in locum suum declinaret.
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1065 </s><s id="id.3.0.10.03.04">Premit itaque aqua dc tentans gravitate sua corpus a expellere, ut ipsa inferiorem occupet locum; resistit autem a gravitate <pb ed="Favaro" n="364"></pb> sua, ne attollatur.
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1066 </s><s id="id.3.0.10.03.05">Quod si gravitas aquae dc maior fuerit gravitate ipsius a, superabit ipsa, et ipsum a extrudet: at cum moles aquae dc aequalis sit moli ipsius a ponaturque corpus a aqua minus grave, erit aquae <pb ed="manuscript" n="58v"></pb>dc gravitas maior gravitate ipsius a: quare a ab aqua extrudetur et sursum expelletur.
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1067 </s></p><p><s id="id.3.0.10.04.01">Modus, quo medium corpora se minus gravia exprimere ac extrudere potest, huiuscemodi est.
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1068 </s><s id="id.3.0.10.04.02">Verum contra haec, quae diximus, quaedam obici possunt.
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1069 </s><s id="id.3.0.10.04.03">Obiciemus itaque, ut ex eorum solutionibus exactius veritas eorum quae diximus appareat.
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1070 </s><s id="id.3.0.10.04.04">Primo, itaque, si res ita se habet, cur plumbi massa de mari profundo non extruditur, cum mare <lb ed="Favaro" n="10"></lb> longe gravius sit ipso?
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1071 </s><s id="id.3.0.10.04.05">Respondeo ad hoc: ut possit lamina plumbi a mari extrudi, necesse est ut tanta moles aquae, quanta est moles plumbi, gravior sit ipso plumbo.
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1072 </s><s id="id.3.0.10.04.06">Nam pars aquae, quae plumbum extrudere potest, non est nisi ea cuius locum plumbum occupat, et quae, extrudendo, locum, in quo erat antea plumbum, ingredi potest: nam aqua quae a plumbo est iniuriam passa, dum illius locus a plumbo occuparetur, non est nisi tanta mole quanta est moles plumbi; et haec sola, extrudendo, est quae in locum a plumbo relictum ingredi potest.
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1073 </s><s id="id.3.0.10.04.07">Quod si huius aquae gravitas gravitatem plumbi non superet, certe ipsum attollere non valebit: at supponitur, gravius esse <lb ed="Favaro" n="20"></lb> plumbum: mirum itaque non est si non extruditur.
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1074 </s><s id="id.3.0.10.04.08">Quod si fuisset corpus aqua minus grave, ut si, gratia exempli, intelligas ligneam sphaeram in profundo putei aqua pleni, tunc partes aquae ipsi sphaerae circumfluae compriment, et in locum, ubi <pb ed="manuscript" n="59r"></pb>nunc est sphaera, ingredi tentabunt: tentabit autem tantummodo tanta aqua, quantam locus qui a sphaera, dum ascendit, relinquitur, capere potest; haec autem est quanta est sphaerae moles.
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1075 </s><s id="id.3.0.10.04.09">Quod si aqua premens minorem offenderit resistentiam in sphera, quam sua, qua exprimit, fuerit vis (quod tunc accidet, quando sphaera fuerit quam aqua minus gravis), dubio procul sphaeram ipsam expellet atque extrudet. <lb ed="Favaro" n="30"></lb>
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1076 </s></p><p><s id="id.3.0.10.05.01">Obiicies, 2Á: Si elementa in regione sua non habent gravitatem (ut supra pollicitus sum me demonstraturum), ergo non poterit corpus grave a medii gravitate extrudi.
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1077 </s><s id="id.3.0.10.05.02">Respondeo, aliud esse elementa in sua regione non habere gravitatem, aliud gravitatem exercere non posse.
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1078 </s><s id="id.3.0.10.05.03">Primum falsum est; nam eorundem corporum eadem semper <pb ed="Favaro" n="365"></pb> est gravitas: secundum autem verum est; nam non semper gravia gravitatem suam exercere possunt.
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1079 </s><s id="id.3.0.10.05.04">Hoc autem patet in ligno; quod grave quidem semper est, sed, si ponatur in aqua, tunc gravitatem exercere, hoc est deorsum ferri, non potest, quia a maiori aquae gravitate impeditur.
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1080 </s><s id="id.3.0.10.05.05">Sic elementa in regione sua gravitatem exercere non possunt: quia nulla eorum pars descendere potest, cum locus, in quem ferri deberet, ab alia sit iam preoccupatus aqua, quae non minus est gravis quam sit superior; et quamvis superiores partes inferiores premant, tamen eas non extrudunt, quia tanta gravitate resistunt quanta <lb ed="Favaro" n="10"></lb> impelluntur.
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1081 </s><s id="id.3.0.10.05.06">Verum non sic evenit, si in aqua cor<pb ed="manuscript" n="59v"></pb>pus aliud, aqua minus grave, fuerit.
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1082 </s><s id="id.3.0.10.05.07">Tunc enim tanta aqua, quantam caperet locus quem corpus illud occupat, eo gravior existens, dum supra illud fuerit, iam extra propriam regionem erit (in propria enim regione ea solummodo sunt, quae super minus gravibus non sunt; cum, ut dictum est, sic a natura constitutum sit, ut graviora sub minus gravibus maneant): quare, gravitatem suam exercendo, minorem in corpore illo gravitatem, ac proinde resistentiam, {1} offendens, ipsum, modo iam explicato extrudet et fugabit.
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1083 </s></p><p><s id="id.3.0.10.06.01">Obiicies, 3Á, cum Aristotele p.Á Caeli 89: Quae moventur per <lb ed="Favaro" n="20"></lb> extrusionem violentia moventur; et quae violentia moventur, tardius in fine motus moventur: si ergo quae sursum feruntur, per extrusionem moverentur, tardius in fine moverentur: quod tamen non sic se habet.
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1084 </s><s id="id.3.0.10.06.02">Respondeo, non in omnibus quae moventur violentia, ut in fine tardius moveantur necesse esse, sed tantum in illis quae separata ab eo, qui impulit, violenter feruntur: ut cum lapis ab homine sursum iaculatur, cuius motus in fine remittitur, postquam a proiciente divisus et separatus fuit; {2} at si proiciens non extra manum demitteret, posset etiam in fine velocius movere.
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1085 </s><s id="id.3.0.10.06.03">Verum quae sursum moventur per extrusionem, non separantur in motu suo a motore; sed <lb ed="Favaro" n="30"></lb> semper est coniunctus qui pellit: quare ut in fine debilitetur motus, necesse non est.
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1086 </s><s id="id.3.0.10.06.04">Dices: Quamvis non remittatur, tamen non deberet <pb ed="Favaro" n="366"></pb> intendi; at quae sursum, ut ignis, moventur, velocius in fine moventur.
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1087 </s><s id="id.3.0.10.06.05">Ad hoc respondeo, falsum esse quod assu<pb ed="manuscript" n="60r"></pb>munt, nempe velocitatem motus sursum augeri: nam semper uniformis est; nec deprehendere possum, quonam pacto potuerit Aristoteles, quae sursum moventur, velocitari in fine animadvertere.
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1088 </s></p></subchap2></subchap1></chap><chap><subchap1><subchap2><p><s id="id.4.0.0.01.01"><pb ed="Favaro" n="367"></pb> <pb ed="manuscript" n="4r"></pb>AL. Quo {1} tam celeri pede, carissime Dominice?
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1089 </s></p><p><s id="id.4.0.0.02.01"> DO. Ehem, salve, dulce caput!
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1090 </s></p><p><s id="id.4.0.0.03.01">AL. Siste, quaeso, tantisper gradum; nanque, in te sectando, sum adeo defessus, ut vix vitalem auram excalefacto cordi, quantum idem avet, subministrare valeam.
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1091 </s></p><p><s id="id.4.0.0.04.01">DO. Ego autem, quamvis celeri gradu procedam, obsistens tamen frigus vincere nequeo; et male in me verificatur tritum illud dictum, Motus est causa caloris.
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1092 </s><s id="id.4.0.0.04.02">Quapropter, quantum placet, tarde incedamus, atque ad deambulandum extra urbem, de more nostro, proficiscamur, <lb ed="Favaro" n="10"></lb> quo etiam vel solus proficisci decreveram.
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1093 </s><s id="id.4.0.0.04.03">Sed qui nostri sermones erunt in hoc mane?
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1094 </s></p><p><s id="id.4.0.0.05.01">AL. Quodcunque primum sive tibi sive mihi in mentem venerit, de quo tamen verba facere iniocundum non sit, de eodem sermonem habeamus.
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1095 </s></p><p><s id="id.4.0.0.06.01">DO. De eo itaque quod nuper memoravi.
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1096 </s></p><p><s id="id.4.0.0.07.01">AL. At quid?
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1097 </s></p><p><s id="id.4.0.0.08.01">DO. Dixeram enim, tritum illud dictum...
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1098 </s></p><p><s id="id.4.0.0.09.01">AL. Ah ah, iam in memoriam redivit.
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1099 </s></p><p><s id="id.4.0.0.10.01">DO. De motu itaque sermonem non iniucundum esse arbitror. {2}
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1100 </s><s id="id.4.0.0.10.02"><lb ed="Favaro" n="20"></lb> Attamen de quocunque motu in universali, deque eiusdem essentia et de singulis ipsius accidentibus, disserere nimis longum esset, quin etiam et supervacaneum.
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1101 </s><s id="id.4.0.0.10.03">De hac enim materia, cum exactissimam tractationem voluero, ipsummet Aristotelem, <pb ed="manuscript" n="4v"></pb>in suo Physico Auditu, omnesque illius interpretes, consulam.
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1102 </s><s id="id.4.0.0.10.04">Itaque ad unam tantummodo motus speciem me constringam, nempe ad motum gravium et levium.
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1103 </s><s id="id.4.0.0.10.05">Sed tamen, quia etiam de hoc exacte a compluribus actum est, exactissime autem a Ieronimo Borrio, ceteris omnibus omissis, circa particularia <pb ed="Favaro" n="368"></pb> quaedam sententiam tuam cognoscere gratum erit, quorumdamve problematum solutionem tuam audire, de quibus ad opinionem et solutionem aliorum animus meus non satis quiescit.
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1104 </s><s id="id.4.0.0.10.06">Sunt autem et ipsa huiusmodi:
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1105 </s></p><p><s id="id.4.0.0.11.01">Primum: utrum verum existimes, quod in puncto reflexionis motus requiratur quies;
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1106 </s></p><p><s id="id.4.0.0.12.01">2Á: quam causam afferas de hoc, quod, scilicet, si fuerint duo corpora aequalia in mole, quorum alterum sit, verbigratia, ligneum, alterum ferreum, et ob id alterum altero gravius, si ab aliquo excelso loco eodem tempore demittantur, citius per aërem fertur ligneum <lb ed="Favaro" n="10"></lb> quam ferreum, hoc est levius quam gravius; si tamen hoc tanquam verum admittas;
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1107 </s></p><p><s id="id.4.0.0.13.01">3Á: undenam accidat quod motus naturalis velocior in fine quam in medio vel in principio, violentus vero velocior in principio quam in medio, et hic quam in fine, existat;
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1108 </s></p><p><s id="id.4.0.0.14.01">4Á: cur idem corpus citius in aëre quam in aqua descendat; quin imo et nonnulla corpora in aëre descendant, quae tamen in aqua non demerguntur;
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1109 </s></p><p><s id="id.4.0.0.15.01">5Á (et est quaesitum <pb ed="manuscript" n="5r"></pb>amicissimi nostri Dionigii Fontis, equitis dignissimi): quamnam causam reddas de eo, quod tormenta, tum <lb ed="Favaro" n="20"></lb> muralia tum manualia, longius per rectam lineam plumbeas sphaeras iaciunt, si eas ad rectos angulos horizonti proiciant, quam si per lineam eidem horizonti parallelam; cum tamen primus motus magis naturali motui contrarietur;
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1110 </s></p><p><s id="id.4.0.0.16.01">6Á: cur eadem tormenta globos graviores celerius ex longius iaculent quam leviores, utpote ferreos quam ligneos, cum tamen leviores minus vi impellenti resistant.
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1111 </s></p><p><s id="id.4.0.0.17.01">Tuam itaque sententiam de his et de similibus, quae ab istis pendent, audire gratissimum erit: scio enim te in hac materia aut nihil dicturum, aut aliquid novi et veritati ipsi propinquissimum in medium <lb ed="Favaro" n="30"></lb> allaturum.
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1112 </s><s id="id.4.0.0.17.02">Cum enim certissimis, clarissimis atque subtilissimis mathematicis demonstrationibus sis assuetus, utpote divini Ptolemaei et divinissimi Archimedis, crassioribus quibusdam rationibus nullo pacto assentiri potes: cumque haec, quae proposui, non longe a mathematicis considerationibus distent, abs te aliquid pulcri arrectis auribus expecto.
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1113 </s></p><p><s id="id.4.0.0.18.01"><pb ed="Favaro" n="369"></pb> AL. Non poterat Dominicus noster, elati ingenii sui indigna in medium proferre.
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1114 </s></p><p><s id="id.4.0.0.19.01">Ut autem meam de his opinionem recensere possim, prius quaedam ponenda sunt.
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1115 </s><s id="id.4.0.0.19.02">In motu itaque, quatenus ad praesens negocium spectat, tria consideranda sunt: haec autem sunt movens, mobile, et medium per quod fit motus.
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1116 </s><s id="id.4.0.0.19.03">Duo postrema tam in naturali quam in violento motu sunt eadem; primum, nempe, <pb ed="manuscript" n="5v"></pb>movens, non idem est in utroque motu: in motu enim naturali est propria gravitas vel levitas; in violento est virtus quaedam impressa a movente; in medio....
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1117 </s></p><p><s id="id.4.0.0.20.01"><lb ed="Favaro" n="10"></lb> DO. Sine, sine: oportet nos gradatim procedere, ne forte domus super instabilibus fundamentis erecta, cum tectum superponere velles, tota corrueret.
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1118 </s><s id="id.4.0.0.20.02">Dixisti itaque nuper, in motu naturali mobile moveri a gravitate vel levitate, in violento vero a virtute impressa: quae duo, antequam a me concedantur vel credantur, declaratione egent.
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1119 </s><s id="id.4.0.0.20.03">Et primum, qua ratione innixus audacter asseris, in motu violento mobile moveri a virtute impressa a movente, cum tamen Aristoteles aliam huius motus causam afferat, nempe moveri a medio? {1}
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1120 </s><s id="id.4.0.0.20.04">Putasne ergo, falsam de hoc esse Aristotelis sententiam?
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1121 </s></p><p><s id="id.4.0.0.21.01">AL. Sententiam istam, quas Aristoteli adscribunt, quamve <lb ed="Favaro" n="20"></lb> complurimi tuentur vel potius tueri contendunt, me quoque sectari nulla est necessitas; cum etiam altera opinio suos habeat sectatores, eosque doctissimos.
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1122 </s><s id="id.4.0.0.21.02">Attamen, si quibus rationibus motus Aristotelis sententiam respuam audire cupis, rationes nonnullas ipsam destruentes, easque non fictas et ex maioribus chimaeris pendentes, sed ab ipsamet sensu depromptas, in medium adducam.
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1123 </s></p><p><s id="id.4.0.0.22.01">DO. Non minus <pb ed="manuscript" n="6r"></pb>iocundum erit haec audire, quam problematum solutiones; quas si tempus non suppetierit perferre antequam sit prandendi hora, in crastinam diem reservabimus.
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1124 </s><s id="id.4.0.0.22.02">At fortasse non absonum erit, nosmetipsos usque ad littus maris conferre, ibique a piscatoribus <lb ed="Favaro" n="30"></lb> et nautis aliquid esui accommodatum accipere, et ad multam diem commorari; cum praesertim, sole altius super horizonte ascendente; subcalescit adeo aër, ut brumalem rigorem minus obnoxium reddat: atque ita, satis ocii suppetente, quicquid exopto, abs te audire potero.
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1125 </s></p><p><s id="id.4.0.0.23.01"><pb ed="Favaro" n="370"></pb> AL. Eamus iam quolubet.
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1126 </s></p><p><s id="id.4.0.0.24.01">DO. Tu autem, hoc interim, tuas rationem perferre ne graveris.
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1127 </s></p><p><s id="id.4.0.0.25.01">AL. Antequam ad rationem deveniam, sententiam prius eorum declarare expediet, qui Aristotelis opinionem sectant. {1}
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1128 </s><s id="id.4.0.0.25.02">Dicunt enim: quando mobile a proiciente, ut, verbigratia, lapis ab homine, proicitur, tunc a moventis manu prius impellitur aër sibi contiguus, qui et reliquas partes aëris movet; dum postea mobile a manu relinquitur in aëre, aër iam commotus secum defert mobile.
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1129 </s><s id="id.4.0.0.25.03">Haec est Aristotelis causa: nonnulli {2} addunt etiam quod, cum mobile movetur, partes aëris ad replendum vacuum, quod post se relinqueret, <lb ed="Favaro" n="10"></lb> succedunt; ex quarum concursu posteriores partes mobilis impelluntur.
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1130 </s><s id="id.4.0.0.25.04">Hanc tamen sententiam esse falsissimam, his rationibus ostendere conabor.
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1131 </s></p><p><s id="id.4.0.0.26.01">Prima itaque ratio sit: si mobile a medio movetur, mobile <pb ed="manuscript" n="6v"></pb>necessario ad easdem partes, ad quas medium, movebitur; huius tamen contrarium saepius videmus; ergo [etc.].
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1132 </s><s id="id.4.0.0.26.02">Minor patet: si enim, flante quocunque validissimo vento, contra ipsum, mobile proiciatur, quamvis ventus ab austro spiret, ad austrum tamen, si eo dirigatur, feretur mobile; ex quo patet, mobile non a medio, sed ab alio movente, moveri.
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1133 </s><s id="id.4.0.0.26.03">Neque est dicendum, quamvis sentiamus ventum in contrarium ferri, <lb ed="Favaro" n="20"></lb> tamen partes aëris quae sunt mobili propinquissimae ad easdem cum mobili ferri partes: nam ecce de hoc manifestissimum exemplum.
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1134 </s><s id="id.4.0.0.26.04">Nonne aspicis naviculam istam, quae ab unico nauta Pisas, contra aquae decursum, impellitur?
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1135 </s><s id="id.4.0.0.26.05">Videmus enim illam, semel a nauta impulsam, per aliquod inde spacium contra nitentem aquam invehi: partes tamen aquae naviculam tangentes in contrarium ferri, oculis ipsis manifestissime apparent.
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1136 </s><s id="id.4.0.0.26.06">Neque credas fortasse quod ultimae partes aquae, quae puppim tantum navis contingunt, navem impellant, quamvis caeterae partes aquae videantur in contrarium moveri: nam, praeter quam quod hoc ridiculum est, contrarium etiam <lb ed="Favaro" n="30"></lb> experientia docet.
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1137 </s><s id="id.4.0.0.26.07">Si quis enim, supra puppim manens, lignum filo suspendat quantumlibet parvum, et in aquam demittat, clare videbit <pb ed="Favaro" n="371"></pb> ipsum in contrarium vehi, et filo trahenti resistere: cuius tamen contrarium sequeretur, si aqua ad easdem partes moveretur ad quas navicula impellitur.
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1138 </s></p><p><s id="id.4.0.0.27.01">2a: si medium est quod defert mobilia, unde est quod, cum quis eodem tormento iaculat globum ferreum, cum quo etiam feratur lignum sive stuppa aut aliquid leve, ita tamen <pb ed="manuscript" n="7r"></pb>ut grave praecedat; unde, inquam, accidit quod ferrum per longissimum spacium ciebitur; stuppa autem, postquam per aliquod spacium ferrum prosecuta fuerit, sistitur et in terram decidit?
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1139 </s><s id="id.4.0.0.27.02">Si ergo est medium quod utrumque <lb ed="Favaro" n="10"></lb> portat, cur plumbum seu ferrum longissime portat, stuppam vero non item?
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1140 </s><s id="id.4.0.0.27.03">Anne forsan facilius erit gravissimum ferrum impellere, quam levissimam stuppam aut lignum?
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1141 </s></p><p><s id="id.4.0.0.28.01">3a: si mobile a medio movetur, illud mobile celerius et per longius spacium feretur, cui plures aderint partes impellentes: huius tamen contrarium experientia demonstrat.
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1142 </s><s id="id.4.0.0.28.02">Nam si ab arcu impellatur subtilissimum telum utrinque acutum, hoc per longius spatium feretur quam aliud lignum crassum, ab eodem arcu iaculatum, quod tamen sit eiusdem ponderis cum telo: attamen pauciores partes aëris acutam teli cuspidem impellunt.
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1143 </s></p><p><s id="id.4.0.0.29.01"><lb ed="Favaro" n="20"></lb> DO. Ad hoc facilis esset responsio: nam, cum telum sit acutum, aptius est ad scindendum medium quam lignum obtusum; ergo minus illi resistet aër.
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1144 </s></p><p><s id="id.4.0.0.30.01">AL. Putasne fortasse, ceteros quoque huius sententiae sectatores ita ad argumentum responsuros esse?
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1145 </s></p><p><s id="id.4.0.0.31.01">DO. Ita profecto; et mihi quoque videtur optima solutio.
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1146 </s></p><p><s id="id.4.0.0.32.01">AL. Quo pacto ergo non fateberis, medium non moveri ad easdem partes, ad quas fertur mobile?
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1147 </s><s id="id.4.0.0.32.02">Si enim ad easdem ferretur, non esset a mobili scindendus aër.
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1148 </s><s id="id.4.0.0.32.03">Luce ergo clarius patet, medium esse scindendum, ex eo quod acuta facilius ferantur quam obtusa: ex quo <lb ed="Favaro" n="30"></lb> deinde sequitur, medium non moveri quo tendit mobile.
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1149 </s><s id="id.4.0.0.32.04">Restat itaque tantummodo demonstrandum, quod mobile non movetur etiam a medio, eo <pb ed="manuscript" n="7v"></pb>quia medium, succedens in partes vacuas, illud impellat.
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1150 </s><s id="id.4.0.0.32.05">Nanque si partes aëris moventur ad replendum vacuum relictum a mobili, cur non etiam pari pacto retrocedit mobile ad idem vacuum replendum?
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1151 </s><s id="id.4.0.0.32.06">Item sit, verbigratia, quod movetur, pars cylindri, et una <pb ed="Favaro" n="372"></pb> illius basis praecedat; moveatur autem versus septemtrionem.
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1152 </s><s id="id.4.0.0.32.07">Perspicuum est quod partium aëris aliae ab oriente, aliae autem ab occidente, in vacuum decurrent; nullae autem ab austro.
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1153 </s><s id="id.4.0.0.32.08">Nam locus in quem anteriores partes cylindri ingrediuntur, debet evacuari aëre, ne detur corborum penetratio; quae partes aëris debent ingredi in locum qui a cylindro relinquitur: sed locus quem cylindrus ab aëre evacuat, est semper aequalis loco quem cylindrus post se relinquit: ergo ad hunc explendum sufficiunt partes quae nunc praecedebant cylindrum; quae, ab extrema circumferentia basis illius in vacuum intrantes, omnes vel ab oriente vel occidente proveniunt.
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1154 </s><s id="id.4.0.0.32.09">Quod si ita sit, <lb ed="Favaro" n="10"></lb> quomodo impellent cylindrum ad septemtrionem?
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1155 </s><s id="id.4.0.0.32.10">His rationibus aliam adde: si intelligamus moveri conum, cuius basis praecedat, cuspis vero subsequatur, tunc nullae partes aëris poterunt moveri ad replendum vacuum.
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1156 </s><s id="id.4.0.0.32.11">Demum, et hoc sit potissimum argumentum, intelligatur sphera marmorea seu ferrea, exacte rotunda et expolita, quae super axe, duobus cardinibus inhaerente, moveri possit; deinde accedat motor, qui utrasque axium extremitates extremis digitis contorqueat: tunc certe sphaera per longum tempo<pb ed="manuscript" n="8r"></pb>ris spacium girabit; et tamen nec aër a motore fuit commotus, nec potest unquam medium succedere in partes a mobili relictas, cum nunquam sphaera locum <lb ed="Favaro" n="20"></lb> mutet.
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1157 </s><s id="id.4.0.0.32.12">Quid ergo de hoc violento motu dicendum? a quo movebitur sphaera, cum extra manus moventis fuerit? quid dicendum, nisi a virtute impressa moveri?
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1158 </s></p><p><s id="id.4.0.0.33.01">DO. Non possum tuis rationibus non dare manum: attamen de hac ultima, quam tu videris praecipuam censere, est quod aliquid dubitare possim.
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1159 </s><s id="id.4.0.0.33.02">Nanque qui contrarias partes tuentur, forsan huiusmodi argumento ita respondere possent, dicentes motum illum non esse violentum, cum sit circularis.
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1160 </s><s id="id.4.0.0.33.03">Cum enim motui violento contrarietur naturalis, motui vero circulari motus contrarius sit nullus, circularis motus violentus nullo pacto erit: et cum non sit violentus, <lb ed="Favaro" n="30"></lb> consequentia, quam ex motu sphaerae deducis, nullius erit momenti.
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1161 </s></p><p><s id="id.4.0.0.34.01">AL. Hanc responsionem impugnare nullius erit negocii.
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1162 </s><s id="id.4.0.0.34.02">Cum enim dicunt motum violentum fieri a medio, non intelligunt tantum de motu illo qui naturali ex diametro opponitur, sed de quocunque motu qui naturalis non sit, idest de violento et mixto.
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1163 </s><s id="id.4.0.0.34.03">Nanque dicere, <pb ed="Favaro" n="373"></pb> verbigratia, lapidem ad rectos horizontis angulos proiectum, quia motus erit ex diametro naturali oppositus, moveri, cum fuerit extra manum, a medio; si tamen idem lapis proiciatur ad angulum inclinatum, tunc moveri a diverso movente; esset penitus puerile et ridiculum: et tamen secundus motus erit mixtus ex naturali et violento.
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1164 </s><s id="id.4.0.0.34.04">Sub motu ergo proiectorum <pb ed="manuscript" n="8v"></pb>motus omnes, quicunque a naturali diversi fuerint, compraehenduntur; sed motus talis sphaerae, quam diximus, non est naturalis, sed mixtus; ergo [etc.]. {1}
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1165 </s><s id="id.4.0.0.34.05">Quod sit mixtus, probatur: motus mixtus est qui componitur ex naturali et violento; sed talis est <lb ed="Favaro" n="10"></lb> motus sphaerae; ergo [etc.].
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1166 </s><s id="id.4.0.0.34.06">Componitur autem giratio; sphaerae ex naturali et violento motu: quia aliquae illius partes recedunt a centro mundi, ad quem naturaliter fertur sphaera; aliquae ad idem accedunt.
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1167 </s><s id="id.4.0.0.34.07">Neque dicas, partes sphaerae, quae deorsum moventur, sursum trahere partes quae ascendunt; et hoc, quia, cum sphaera sit in aequilibrio, partes ascendentes non resistunt partibus descendentibus.
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1168 </s><s id="id.4.0.0.34.08">Hoc enim nihil est: nanque si partes sphaerae sunt omnes aeque graves, non erit maior ratio, ut dextrae partes potius sinistras, quam e contra, attollant.
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1169 </s><s id="id.4.0.0.34.09">Deinde accipiatur sphera cuius partes non aeque ponderent: in cuius motu videbis partes graviores a levioribus attolli, et <lb ed="Favaro" n="20"></lb> tamen in motu isto erit resistentia.
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1170 </s><s id="id.4.0.0.34.10">At quid? nonne semper in tali motu est resistentia axium, qui, super cardinibus sphaerae pondere gravati, motui resistunt?
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1171 </s><s id="id.4.0.0.34.11">Demum, hoc ut animadvertas velim: quod, quando dicitur motum circularem non esse violentum, intelligitur de illo motu circulari qui fit circa centrum mundi, qualis est motus caeli.
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1172 </s><s id="id.4.0.0.34.12">Si itaque marmorea sphae<pb ed="manuscript" n="9r"></pb>ra existeret in centro mundi, ita ut centrum mundi et centrum sphaerae essent idem, deinde initium motus sphaerae a motore externo daretur, tunc sphaera fortasse non moveretur motu violento sed naturali; cum nulla ibi esset axium resistentia, nec partes sphaerae centro mundi accederent aut recederent.
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1173 </s><s id="id.4.0.0.34.13">Dixi <lb ed="Favaro" n="30"></lb> autem, fortasse: quia si talis motus non esset violentus, perpetuo duraret; ista autem motus aeternitas ab ipsius terrae natura longe abesse videtur, cui quies iocundior quam motus esse videtur.
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1174 </s><s id="id.4.0.0.34.14">Ex rationibus <pb ed="Favaro" n="374"></pb> itaque omnibus allatis satis perspicuum esse videtur, medium, nedum iuvare motum, quin imo et motui magis obstare.
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1175 </s><s id="id.4.0.0.34.15">Concludendum itaque est, mobile, dum motu praeternaturali movetur, moveri a virtute impressa a motore; quid autem sit ista virtus, nobis absconditum esse. {1}
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1176 </s></p><p><s id="id.4.0.0.35.01">DO. Satis tandem sit ista opinio confutata; et, postquam rationibus tuis sum convictus, concedatur, mobile non a medio sed a virtute impressa moveri.
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1177 </s><s id="id.4.0.0.35.02">Nunc autem, antequam de medio quicquam dicas, ut mihi explanes velim, quomodo intelligas, in naturali motu mobile a gravitate vel levitate moveri.
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1178 </s></p><p><s id="id.4.0.0.36.01">AL. Quae de movente naturali et de medio, quatenus ad praesens <lb ed="Favaro" n="10"></lb> negocium spectat, dicenda sunt, simul declarari commode possunt.
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1179 </s><s id="id.4.0.0.36.02">Supponatur itaque, primo, sic a natura constitutum esse, ut graviora sub levioribus maneant: quod qui<pb ed="manuscript" n="9v"></pb>dem ita esse, sensui manifestissimum est.
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1180 </s></p><p><s id="id.4.0.0.37.01">DO. Hoc quod supponis, verissimum quidem esse sensu depraehendimus; sed causam cur talem ordinem servaverit natura, et non potius conversum, intelligere vellem.
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1181 </s></p><p><s id="id.4.0.0.38.01">AL. Causam talis ordinis reddere, cum ita rem se habere manifestum sit, ad nostrum intentum nil conducere potest; eamque potissimam reddere, forte difficillimum esset: nec aliam reddere possem, <lb ed="Favaro" n="20"></lb> nisi quod in aliquem ordinem erant res disponendae, placuit autem naturae in hunc disponere. {2}
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1182 </s><s id="id.4.0.0.38.02">Nisi forte velimus dicere, graviora centro propinquiora esse quam leviora, quia videntur quodammodo ea esse graviora, quae in angustiori loco plus materiae continent: {3} ut, verbigratia, si fuerit saccus lana plenus, quae in eo nulla vi sit constipata, deinde magna cum violentia multo plus lanae in eodem comprimatur, tunc gravior erit quam antea, quia in eodem spatio plus materiae cumulabitur.
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1183 </s><s id="id.4.0.0.38.03">Cum, itaque, spatia quae centro mundi sunt propinquiora, semper angustiora sint iis quae a centro magis recedunt, {4} rationi consentaneum fuit ut ea replerentur materia, cuius <lb ed="Favaro" n="30"></lb> maior gravitas, quam alterius, angustiora spatia occuparet.
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1184 </s></p><p><s id="id.4.0.0.39.01"><pb ed="Favaro" n="375"></pb> DO. Ratio ista, quamvis talis elementorum dispositionis existimanda non sit potissima, attamen nonnullam in se habet veritatis speciem, cui animus libenter adsentitur: ita ut, tum quia per se clarissimum est quod petis, tum quia de eodem ea quae nuper dixisti causam quodammodo reddunt, graviora sub levioribus a natura constituta esse, aequo animo concedam.
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1185 </s><s id="id.4.0.0.39.02">Quare, si libet, ad ea quae dicenda restant, te conferas.
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1186 </s></p><p><s id="id.4.0.0.40.01"><pb ed="manuscript" n="10r"></pb>AL. Nunc autem animadvertendum est, gravia vel levia non dici nisi in comparatione. {1}
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1187 </s></p><p><s id="id.4.0.0.41.01"><lb ed="Favaro" n="10"></lb> <pb ed="manuscript" n="102r"></pb>DO. Siste, quaeso; gradatim nobis est incedendum.
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1188 </s><s id="id.4.0.0.41.02">Dicis enim tu, non dari grave vel leve absolute, sed tantum gravius et levius in comparatione: hoc primum a me non concedetur, quia praesertim est in contrarium opinio Aristotelis in toto 4 Caeli, ubi terram simpliciter gravem, ignem vero simpliciter levem, contra antiquorum sententiam, ostendit.
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1189 </s><s id="id.4.0.0.41.03">Quare, nisi prius auferas quae ab Aristotele ponuntur, tuam nunquam opinionem amplectar.
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1190 </s></p><p><s id="id.4.0.0.42.01">AL. Nimis longus noster erit sermo, si in omnibus, quae contra Aristotelis sententiam a me proponentur, rationibus confutandus erit Aristoteles.
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1191 </s></p><p><s id="id.4.0.0.43.01"><lb ed="Favaro" n="20"></lb> DO. Nimis brevis erit noster sermo, si casu fundamenta struere velis, opiniones tuas sine ratione in medium afferens: nam te amplius <pb ed="Favaro" n="376"></pb> audire non curo.
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1192 </s><s id="id.4.0.0.43.02">Quare, nisi qua ratione ductus Aristotelem refellas explanabis, finem dicendi facere potes: surdo enim (ut aiunt) verba faceres.
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1193 </s></p><p><s id="id.4.0.0.44.01">AL: Postquam hanc suscepi provinciam, ut tibi morem geram, brevius quam potero, quae causae me impulerint ad Aristotelis sententiam respuendam, adferam.
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1194 </s><s id="id.4.0.0.44.02">Primo, itaque, posuit Aristoteles, terram esse omnium gravissimam: scripsit enim, 4 Caeli t. 29, omnia habere levitatem praeter terram, mixta vero eo plus habere gravitatis quo plus terrae continebunt.
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1195 </s><s id="id.4.0.0.44.03"><pb ed="manuscript" n="102v"></pb>Si ergo terra est omnium gravissima, manifestum est quod mixtorum nullum gravius erit ipsa terra; <lb ed="Favaro" n="10"></lb> cum componantur etiam ex aqua aëre et igne, quae minorem habent gravitatem quam terra.
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1196 </s><s id="id.4.0.0.44.04">Hoc autem est falsum: nam cui non patet quod metalla omnia graviora sunt ipsa terra, ut, verbigratia, mercurius, in quo terra supernatat? et quod alii supereminet, ex ipsomet Aristotele, levius est illo cui insidet.
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1197 </s><s id="id.4.0.0.44.05">Et quis dubitabit, vas plumbo plenum gravius esse quam terra refertum?
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1198 </s><s id="id.4.0.0.44.06">Qui ergo terra omnium: est gravissima?
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1199 </s><s id="id.4.0.0.44.07">Adfert etiam Aristoteles aliud signum de gravitate terrae, dicens: Si dimoveatur aër aut aqua, terra nunquam ascendet in locum aëris aut aquae; ut patet in medicorum cucurbitulis, quae aquam et carnem attrahunt, terram vero minime: ergo terra est <lb ed="Favaro" n="20"></lb> gravissima.
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1200 </s><s id="id.4.0.0.44.08">Quid autem magis puerile potest excogitari?
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1201 </s><s id="id.4.0.0.44.09">Si enim terra non est corpus fluidum, quo modo pars illius super alteram attolletur?
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1202 </s><s id="id.4.0.0.44.10">Hoc igitur non ex absoluta terrae gravitate provenit, sed es eius soliditate: nam neque etiam aqua congelata attolletur, neque incudo intumescet, quae non erit terra; attolletur quidem argentum vivum, quamvis terra sit longe gravius, quia fluidum est.
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1203 </s><s id="id.4.0.0.44.11">Dicere deinde, Medium contrariatur extremo; quare rationi consentaneum est, ut quae sunt in medio sint contraria eis quae in extremis, et hoc non erit nisi terra ponatur simpliciter gravissima, ignis vero levissimus; est quaedam ratio quae non solum necessi<pb ed="manuscript" n="103v"></pb>tatem non habet, sed, <lb ed="Favaro" n="30"></lb> meo iudicio, est parvi momenti.
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1204 </s><s id="id.4.0.0.44.12">Nam si accipit pro extremo concavum xxx, pro medio vero centrum mundi, tunc profecto centro mundi non magis contrariabitur concavum xxx, quam concavum aëris et aquae: {1) <pb ed="Favaro" n="377"></pb> et si ita sumenda sit locorum contrarietas, terra ipsa erit in locis contrariis, cum in centro et in concavo aëris et aquae existat.
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1205 </s><s id="id.4.0.0.44.13">Simili modo de igne argumentatur Aristoteles, dicens quod, si submoveatur aër, ignis non descendet, ut aër submota aqua.
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1206 </s><s id="id.4.0.0.44.14">Hoc demonstratione indiget; quod non probavit Aristoteles.
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1207 </s><s id="id.4.0.0.44.15">Nisi forte credas, probationem esse id quod t. 39 eiusdem libri ponit, dicens, ignem non descensurum, quia nullam habet gravitatem: sed hoc esset probare idem per idem, si, dum conatur demonstrare, ignem nullam habere gravitatem eo quod non descendit, probaret ipsum non descendere quia <lb ed="Favaro" n="10"></lb> nullam habeat gravitatem.
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1208 </s><s id="id.4.0.0.44.16">Eget itaque hoc demonstratione; et eo amplius, quia nec ipse Aristoteles, quod credam, periculum fecit, an descendat ignis remoto aëre.
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1209 </s><s id="id.4.0.0.44.17">Quod autem non sit aliquid igne levius, unde scivit Aristoteles?
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1210 </s><s id="id.4.0.0.44.18">Nonne possunt esse exhalationes aliquae, quae super ignem advolent?
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1211 </s><s id="id.4.0.0.44.19">Sed, demum, quomodo unquam poterit quis ignem imaginari, substantiam cum quantitate coniunctam, gravitatem non habere?
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1212 </s><s id="id.4.0.0.44.20">Hoc profecto omnino mihi <pb ed="manuscript" n="104r"></pb>irrationabile videtur.
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1213 </s><s id="id.4.0.0.44.21">Et cum dicimus, terram omnium esse gravissimam, quia omnibus substat, cogimur, velimus nolimus, dicere terram ideo esse gravissimam, respectu aliorum, quia omnibus substat; et ideo omnibus <lb ed="Favaro" n="20"></lb> substat, quia gravior est his quibus substat.
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1214 </s><s id="id.4.0.0.44.22">Et hoc patet: quia, si gravissimum est quod omnibus substat, si omnia auferantur, non poterit amplius gravissimum dici, cum nulli substet.
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1215 </s><s id="id.4.0.0.44.23">Dicitur ergo gravissimum in comparatione minus gravium; et idem de igne dicendum est.
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1216 </s><s id="id.4.0.0.44.24">Neque dicas, Si ignis haberet gravitatem, descenderet.
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1217 </s><s id="id.4.0.0.44.25">Nanque aër nonne habet gravitatem? nec tamen descendit sub aqua: ita et ignis habet gravitatem, nec tamen descendit sub aëre; quia minorem habet gravitatem quam aër.
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1218 </s><s id="id.4.0.0.44.26">Quapropter, <pb ed="manuscript" n="104v"></pb>ut rem paucis constringam, dico aliquid esse in rerum natura quod omnium sit gravissimum, et aliquid quod omnium sit levissimum, hoc est minima gravitate praeditum: <lb ed="Favaro" n="30"></lb> nego autem, ista necessario esse terram et ignem; sicuti etiam nego, posse dici simpliciter gravissimum vel levissimum, nulla ratione habita ad minus gravia vel levia, sed solum id esse gravissimum omnium quae sunt gravia, non autem eorum quae possent esse.
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1219 </s><s id="id.4.0.0.44.27">Et haec pauca dicta velim ad opinionem meam confirmandam.
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1220 </s></p><p><s id="id.4.0.0.45.01">DO. Rationes tuae omnino satisfaciunt, et eo magis, quod haec quaestio est parvi momenti, an scilicet terra sit gravis absolute utrum <pb ed="Favaro" n="378"></pb> respective; et quod credam, quomodocunque ponatur, non multum ad praesens negocium refert.
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1221 </s><s id="id.4.0.0.45.02">Quapropter ad reliqua procedamus.
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1222 </s></p><p><s id="id.4.0.0.46.01">AL. Dico ita, gravia et levia non dici nisi in comparatione.
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1223 </s><s id="id.4.0.0.46.02"><pb ed="manuscript" n="10r"></pb>Ista autem comparatio dupliciter accidit: vel enim comparamus inter se duo corpora quae in eodem existant medio, vel comparamus corpus aliquod cum medio in quo movetur.
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1224 </s><s id="id.4.0.0.46.03">In prima, itaque, comparatione ea dicuntur esse aeque gravia, quae, cum sint aequalis molis et in eodem medio, eiusdem erunt gravitatis.
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1225 </s><s id="id.4.0.0.46.04">Ex quo patet quod si accipiamus duo frustra, ligneum, verbigratia, unum, alterum ferreum, quae aequalia sint in gravitate, non tamen ista appellanda <lb ed="Favaro" n="10"></lb> erunt aeque gravia: frustrum enim ligneum multo maius erit in mole frustro ferreo.
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1226 </s><s id="id.4.0.0.46.05">Illud, deinde, corpus dicetur alio corpore gravius, cuius moles, aequalis moli alterius, gravior est quam illo, si in eodem medio ponderentur.
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1227 </s><s id="id.4.0.0.46.06">Illud autem corpus, cuius accepta moles aequalis alterius corporis moli, et in eodem medio cum illa ponderata, levior altera extiterit, levius appellatur.
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1228 </s><s id="id.4.0.0.46.07">Pari etiam ratione media quoque, inter se comparata, graviora vel leviora dicentur; et corpora solida cum medio in quo moventur comparata, itidem graviora vel leviora dicentur.
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1229 </s><s id="id.4.0.0.46.08">Media autem, per quae fieri potest motus, sunt omnia elementa, excepta terra, quae, cum sit solidissima, non potest ab alio <lb ed="Favaro" n="20"></lb> corpore scindi: reliqua vero elementa, nempe aqua aër et ignis, cum sint liquida, motum in se fieri admittunt.
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1230 </s></p><p><s id="id.4.0.0.47.01"><pb ed="manuscript" n="11r"></pb>His autem declaratis, proclive erit mente concipere, quomodo gravia moveantur a gravitate, levia vero a levitate.
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1231 </s><s id="id.4.0.0.47.02">Ea enim corpora quae medio, per quod moventur, sunt graviora, deorsum moventur: nam ita a natura constitutum est, ut graviora sub levioribus maneant; si vero aliquod corpus aqua gravius super aquam permaneret, tunc levius sub gravius existeret.
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1232 </s><s id="id.4.0.0.47.03">Moventur itaque gravia deorsum, quatenus medio, per quod moventur, sunt graviora: ergo eorum gravitas respectu medii, est causa talis motus deorsum.
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1233 </s><s id="id.4.0.0.47.04">Simili etiam <lb ed="Favaro" n="30"></lb> ratione et de levioribus medio est intelligendum.
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1234 </s></p><p><s id="id.4.0.0.48.01">DO. Haec, quae nunc dixisti, non adhuc penitus satisfaciunt; et ratio dubitandi mihi est.
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1235 </s><s id="id.4.0.0.48.02">Nam si, verbigratia, accipiamus tenuissimum calculum et in mare proiciamus, ille, procul dubio, per medium aquae deorsum feretur: calculus autem aqua maris qua ratione gravior <pb ed="Favaro" n="379"></pb> existimandus, nullo modo depraehendo; cum praesertim aqua ipsa maris innumeris fere calculis gravior certe existat.
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1236 </s></p><p><s id="id.4.0.0.49.01">AL. Esne tam cito oblitus nuper a me dictorum?
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1237 </s><s id="id.4.0.0.49.02">Nonne dixeram ego, tunc corpus corpore alio gravius esse, cuius aequalis moles moli alterius ea gravior fuerit?
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1238 </s><s id="id.4.0.0.49.03">Si itaque accipiamus partem <pb ed="manuscript" n="11v"></pb>aquae, cuius moles aequalis sit moli ipsius calculi, inveniemus postea, calculum ipsum aqua graviorem esse: quod cum ita sit, non est mirandum si calculus in medio aquae descendat.
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1239 </s></p><p><s id="id.4.0.0.50.01">DO. Hoc totum verum est: sed tamen, qua ratione calculo existenti <lb ed="Favaro" n="10"></lb> in aqua sit tantummodo habenda ratio cum tanta mole aquae quanta: est ipsius calculi moles, non autem cum tota aqua, nondum intelligo.
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1240 </s></p><p><s id="id.4.0.0.51.01">AL. Demum aufugere nequeo, quin tibi nonnulla theoremata demonstrem, ex quorum intelligentia non modo id quod petis apertissime intelliges, verum etiam et quam proportionem habeant corpora, tum gravia tum levia, ad celeritatem vel tarditatem sui motus, quaeve sit proportio gravitatum et levitatum unius et eiusdem corporis, si illud in diversis mediis ponderemus: quae omnia demonstranda fuerunt, cum veram rationem invenire tentassem, qua possimus, in mixto ex duobus metallis, singuli metalli exactissimam portionem assignare.
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1241 </s><s id="id.4.0.0.51.02"><lb ed="Favaro" n="20"></lb> Quorum theorematum (licet non dissimilia ab Archimede demonstrata sint) demonstrationes minus mathematicas et magis physicas in medium afferam; positionibus utar clarioribus et sensui manifestioribus, quam eae sint quas <pb ed="manuscript" n="12r"></pb>Archimedes accepit.
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1242 </s></p><p><s id="id.4.0.0.52.01">DO. Veram igitur rationem qua dicitur Archimedes aurificis furtum in corona aurea depraehendisse, te quoque excogitasse asseris? at nonne eadem scripta a plurimis, et praesertim a Vitruvio?
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1243 </s></p><p><s id="id.4.0.0.53.01">AL. Modum illum vulgatum, quem dicunt de vase aqua pleno etc., fallacissimum esse demonstrare possem; illum vero quem adinveni, exactissimum, et quem eundem cum illo Archimedis existimem, tum <lb ed="Favaro" n="30"></lb> quia exquisitissimus est, tum quia ab ipsius Archimedis demonstrationibus pendens.
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1244 </s></p><p><s id="id.4.0.0.54.01">DO. At si pulcra ista tua inventio demonstrationibus a te mox explanandis innititur, eam quoque audire, si tempus suppetierit, gratissimum erit.
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1245 </s><s id="id.4.0.0.54.02">Nunc autem, si linearibus figuris opus fuerit ad tua <pb ed="Favaro" n="380"></pb> demonstranda, ecce minutissimae arenae expolita lataque planities, in qua virgula ista dextre designare poteris.
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1246 </s></p><p><figure id="id.4.0.0.55.00" xlink:href="FIG1/F040.jpg"></figure>
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1247 <s id="id.4.0.0.55.01">AL. Antequam itaque ad descriptionem accedam, hoc advertendum est: quod, licet, ut dixi, sint tria media praecipua per quae fit motus, tamen, quia ignis a nobis nimium distat, et quia in aëre non prae manibus habemus quae sursum ascendant, in medio aquae demonstrationes adferam: quae vero de aqua demonstrantur, de aliis quoque mediis vera esse nemo inficias ibit. {1}
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1248 </s><s id="id.4.0.0.55.02">Dico igitur, primum, quod solida magnitudo quae ac aliqua pars aquae, cuius moles dictae magnitudinis moli sit aequalis, aeque gravis est, in aquam demis<pb ed="manuscript" n="12v"></pb>sa, <lb ed="Favaro" n="10"></lb> tota demergitur; non tamen adhuc, tota sub aqua existente, magis sursum quam deorsum fertur: quod idem est ac si dicamus, solidas magnitudines aeque graves ac aqua, in aquam demissas, totas demergi, non tamen adhuc deorsum ferri magis quam sursum.
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1249 </s><s id="id.4.0.0.55.03">Sit itaque primus aquae status, antequam magnitudo in eam demittatur, ced; magnitudo autem ab, quae aeque gravis sit ac aqua, in aquam demissa, si fieri potent, non demergatur tota, sed aliqua illius pars extet extra aquam, nempe a; et superficies aquae cd attollatur usque ad fg, et in hoc situ consistat tum aqua tum magnitudo.
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1250 </s><s id="id.4.0.0.55.04">Manifestum est itaque, quod moles aquae a superficiebus tg, cd contenta, quae <lb ed="Favaro" n="20"></lb> [3812] attolitur, est aequalis moli partis illius magnitudinis quae sub aqua est demersa, nempe b.
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1251 </s><s id="id.4.0.0.55.05">Hoc enim clarissimum est: quia moles dicta aquae non potest esse minor, nam daretur corporum penetratio; nec potest esse maior, ne quis locus vacuus derelinquatur.
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1252 </s><s id="id.4.0.0.55.06">Quia itaque aqua fg, cd superficiebus contenta nititur sua gravitate deorsum redire ad pristinum suum statum, sed hoc assequi non potest nisi prius solidum ab ex aqua auferatur et ab aqua attollatur; solidum autem, ne attollatur, tota propria gravitate <lb ed="Favaro" n="10"></lb> resistit; ponuntur autem tum solida magnitudo tum aqua in hoc statu consistentes; ergo necessarium est ut gravitas aquae fgcd, qua sursum nititur solidum attollere, sit aequalis gravitati qua solidum resistit et deorsum premit (si enim maior esset gravitas aquae fgcd gravitate solidae magnitudinis ab, solidum <pb ed="manuscript" n="13r"></pb>ab attolleretur atque expelleretur ab aqua; si vero maior esset gravitas solidi ab, attolleretur rursus aqua: quae tamen omnia ita consistentia ponuntur).
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1253 </s><s id="id.4.0.0.55.07">Si itaque gravitas portionis aquae fgcd aequatur gravitati totius solidi ab, erit etiam moles aquae portionis fgcd aequalis moli totius solidi ab: quod quidem esse non potest.
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1254 </s><s id="id.4.0.0.55.08">Nam moles aquae fgcd <lb ed="Favaro" n="20"></lb> aequatur moli illius portionis solidi quae sub aqua est, nempe portioni b; b autem minor est ipso ba.
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1255 </s><s id="id.4.0.0.55.09">Non ergo verum est quod aliqua pars solidae magnitudinis extra aquam extet; ergo tota demergetur.
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1256 </s><s id="id.4.0.0.55.10">Non tamen, in aqua existens tota, deorsum descendet; sed, quo loci ponatur, eo manebit.
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1257 </s><s id="id.4.0.0.55.11">Nulla enim est causa cur descendere debeat: nam, cum aeque gravis ponatur ac aqua, dicere illam in aquam descendere esset idem ac si diceremus, aquam in aqua sub aquam descendere, et rursum aquam, quae super primam ascendit, deorsum iterum descendere, et sic aquam in infinitum procedere in alternatim descendendo et ascendendo; quod inconveniens est.
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1258 </s></p><p><figure id="id.4.0.0.56.00" xlink:href="FIG1/F041.jpg"></figure>
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1259 <s id="id.4.0.0.56.01"><lb ed="Favaro" n="30"></lb> Hoc itaque demonstrato, sequitur ut ostendamus, solidas magnitudines aqua leviores, in aquam demissas, non demergi totas, sed earum aliquam partem extare ex aqua.
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1260 </s><s id="id.4.0.0.56.02">Oportet igitur meminisse, quod tunc solida magnitudo dicitur alia levior, si, existens cum ea aequalis in mole, sit eadem in gravitate levior.
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1261 </s><s id="id.4.0.0.56.03"><pb ed="manuscript" n="13v"></pb>Sit primus aquae status ef, antequam solida magnitudo in eam demittatur; sit autem ab magnitudo in aquam demissa, aqua levior: dico itaque, ipsam <pb ed="Favaro" n="382"></pb> solidam magnitudinem non demergi totam.
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1262 </s><s id="id.4.0.0.56.04">Si enim fieri potest, demergatur tota, et aqua attollatur usque ad superficiem cd; erit igitur moles aquae cf aequalis moli magnitudinis ab: et, si fieri potest, maneant in hoc statu cum magnitudo tum aqua.
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1263 </s><s id="id.4.0.0.56.05">Et quia tanta est gravitas qua aqua cf deorsum premit, ut solidam magnitudinem attollat; quanta est gravitas qua magnitudo ab, deorsum premens, resistit ne attollatur (ponuntur enim ita consistentes); estque insuper moles aquae cf moli magnitudinis ab aequalis; ergo magnitudo solida <lb ed="Favaro" n="10"></lb> est aeque gravis ac aqua: quod est inconveniens; ponebatur enim levior.
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1264 </s><s id="id.4.0.0.56.06">Non ergo magnitudo ab tota demergetur, sed aliqua illius pars ex aqua extabit.
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1265 </s></p><p><figure id="id.4.0.0.57.00" xlink:href="FIG1/F042.jpg"></figure>
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1266 <s id="id.4.0.0.57.01">Demonstrato igitur, solidas magnitudines aqua leviores non demergi totas, expedit nunc ostendere, quaenam illarum partes demergantur.
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1267 </s><s id="id.4.0.0.57.02">Dico igitur, quod solidae magnitudines aqua leviores, in aquam demissae, usque eo demerguntur, ut tanta moles aquae, quanta est moles partis demersae magnitudinis, eandem quam tota magnitudo habeat gravitatem.
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1268 </s><s id="id.4.0.0.57.03">Sit primus aquae status superficies ab; solida autem magnitudo cd, aqua levior, in aquam demittatur: manifestum <lb ed="Favaro" n="20"></lb> est igitur ex praecedenti, quod non demergetur tota.
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1269 </s><s id="id.4.0.0.57.04">Demer<pb ed="manuscript" n="14r"></pb>gatur igitur pars d, et aqua attollatur usque ad superficiem et: dico igitur, tantam molem aquae, quanta est moles partis demersae magnitudinis, eandem quam tota magnitudo habere gravitatem.
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1270 </s><s id="id.4.0.0.57.05">Quia enim tanta gravitate premit aqua eb, quanta resistit magnitudo cd (ponuntur enim ita consistentes), est ergo gravitas aquae eb aequalis gravitati totius magnitudinis cd: sed moles aquae eb aequatur moli partis magnitudinis demersae, nempe d: ergo tanta <lb ed="Favaro" n="30"></lb> moles aquae, quanta est moles partis demersae magnitudinis, eandem quam tota magnitudo habet gravitatem.
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1271 </s><s id="id.4.0.0.57.06">Quod fuit demonstrandum.
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1272 </s></p><p><figure id="id.4.0.0.58.00" xlink:href="FIG1/F043.jpg"></figure>
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1273 <s id="id.4.0.0.58.01">Nunc autem, antequam ad demonstrationem solidorum aqua graviorum accedamus, demonstrandum est, quanta vi solida magnitudo aqua levior sursum feratur, si tota, vi, sub aquam demergatur.
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1274 </s><s id="id.4.0.0.58.02">Dico igitur, solidas magnitudines aqua leviores, in aquam impulsas, ferri <pb ed="Favaro" n="383"></pb> sursum tanta vi, quanto aqua, cuius moles aequetur moli demersae magnitudinis, ipsa magnitudine gravior erit.
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1275 </s><s id="id.4.0.0.58.03">Sit itaque primus aquae status, antequam magnitudo solida in eam demittatur, secundum superficiem ab; et demitta<pb ed="manuscript" n="14v"></pb>tur in eam, vi, solida magnitudo cd; et attollatur aqua usque ad superficiem ef: et quia aqua, quae attollitur, eb habet molem aequalem moli totius magnitudinis demersae, et magnitudo ponitur aqua levior, erit aquae eb gravitas maior gravitate cd solidi.
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1276 </s><s id="id.4.0.0.58.04">Intelligatur itaque pars aquae tb, <lb ed="Favaro" n="10"></lb> cuius gravitas aequetur gravitati solidi cd: demonstrandum igitur est, magnitudinem solidam sursum ferri tanta vi, quanta est gravitas aquae tf (secundum enim hanc gravitatem, aqua eb gravior est gravitate aquae tb, hoc est gravitate solidi cd).
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1277 </s><s id="id.4.0.0.58.05">Quia itaque gravitas aquae tb aequalis est gravitati solidae magnitudinis cd, tanta vi premet sursum aqua tb ut solidum attollat, quanta resistet solidum ne attollatur.
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1278 </s><s id="id.4.0.0.58.06">Gravitas itaque partis aquae prementis, nempe tb, aequatur resistentiae solidae magnitudinis sed gravitas totius aquae prementis eb superat gravitatem aquae tb <lb ed="Favaro" n="20"></lb> secundum gravitatem aquae tf: ergo gravitas totius aquae eb superabit resistentiam solidi cd secundum gravitatem tf aquae.
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1279 </s><s id="id.4.0.0.58.07">Gravitas igitur totius aquae prementis sursum impellet solidam magnitudinem tanta vi, quanta est gravitas partis aquae tf: quod fuit demonstrandum.
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1280 </s></p><p><figure id="id.4.0.0.59.00" xlink:href="FIG1/F044.jpg"></figure>
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1281 <s id="id.4.0.0.59.01"><pb ed="manuscript" n="15r"></pb>Ex his autem quae demonstrata sunt satis perspicuum est, solidas magnitudines aqua graviores deorsum ferri, si in aquam demittantur.
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1282 </s><s id="id.4.0.0.59.02">Nisi enim feruntur deorsum, aut earum aliqua pars extabit, aut sub aqua manebunt, nec sursum aut deorsum ferentur.
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1283 </s><s id="id.4.0.0.59.03">At earum nulla pars extabit; essent enim, uti demonstratum est, aqua leviores: nec in aqua manebunt; quia essent aeque graves ac aqua: restat ergo <lb ed="Favaro" n="30"></lb> quod deorsum ferantur.
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1284 </s><s id="id.4.0.0.59.04">Nunc autem quanta vi deorsum ferantur, ostendamus.
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1285 </s><s id="id.4.0.0.59.05">Dico igitur, solidas magnitudines aqua graviores, in aquam demissas, ferri deorsum tanta vi, quanto aqua, molem habens moli ipsius magnitudinis aequalem, levior est ipsa magnitudine.
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1286 </s><s id="id.4.0.0.59.06">Sit itaque primus aquae status secundum superficiem de; magnitudo autem solida bl, aqua gravior, in aquam demittatur, et attollatur aqua ad superficiem ab; sit autem aqua ae, quae molem ipsius <pb ed="Favaro" n="384"></pb> magnitudinis moli aequalem habeat: et quia solida magnitudo ponitur aqua gravior, erit aquae ae gravitas minor gravitate solidae magnitudinis.
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1287 </s><s id="id.4.0.0.59.07">Intelligatur itaque moles aquae ao, quae aequalem habeat gravitatem gravitati bl: et quia aqua ae levior est ao secundum gravitatem do, demonstrandum est, magnitudinem solidam bl deorsum ferri tanta vi, quanta est gravitas aquae do.
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1288 </s><s id="id.4.0.0.59.08">Intelligatur altera solida magnitudo, aqua levior, primae coniuncta, cuius quidem moles sit ao aquae moli aequalis, gravitas autem eius sit aequalis gravitati aquae ae; sitque dicta magnitudo lm: et quia moles bl <lb ed="Favaro" n="10"></lb> <pb ed="manuscript" n="15v"></pb>aequatur moli ae, moles autem lm aequatur moli ao, ergo moles compositarum magnitudinum bl, lm aequatur moli compositae aquae ea, ao.
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1289 </s><s id="id.4.0.0.59.09">Sed gravitas magnitudinis aquae ae aequatur gravitati magnitudinis lm: gravitas autem aquae ao aequatur gravitati magnitudinis bl: tota ergo gravitas ambarum magnitudinum bl, lm aequatur gravitati aquae oa, ae.
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1290 </s><s id="id.4.0.0.59.10">Sed et moles quoque magnitudinum ml, lb demonstrata est aequalis moli aquae oa, ae; ergo, per primam propositionem, magnitudines ita <lb ed="Favaro" n="20"></lb> compositae neque sursum neque deorsum ferentur.
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1291 </s><s id="id.4.0.0.59.11">Tanta ergo erit vis magnitudinis bl deorsum prementis, quanta est vis magnitudinis ml sursum impellentis: sed, per praemissam, magnitudo ml sursum impellit tanta vi, quanta est gravitas aquae do: ergo magnitudo bl deorsum feretur tanta vi, quanta est gravitas aquae do.
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1292 </s><s id="id.4.0.0.59.12">Et ex hoc manifeste colligitur, quod solidum aqua gravius est in aqua tanto levius quam in aëre, quanta est in aëre gravitas aquae molem habentis ipsius solidi moli aequalem.
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1293 </s><s id="id.4.0.0.59.13">Nam solidum bl in aëre fertur deorsum ea gravitate, quae ponitur aequalis gravitati aquae ao; in aqua autem fertur deorsum tanta gravitate, quanta est gravitas do: gravitas <lb ed="Favaro" n="30"></lb> autem do exceditur a gravitate ao secundum gravitatem ae: <pb ed="manuscript" n="16r"></pb>quae est gravitas aquae molem habentis aequalem moli solidi bl.
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1294 </s><s id="id.4.0.0.59.14">Haec autem omnia quae de aqua demonstrata sunt, de aëre quoque intelligenda erunt.
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1295 </s><s id="id.4.0.0.59.15">Ex quo universaliter patet, corpora illa deorsum ferri, quae medio, per quod ferri debent, graviora sunt; ea vero sursum ferri, quae medio, per quod ferri debent, leviora fuerint.
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1296 </s></p><p><s id="id.4.0.0.60.01"><pb ed="Favaro" n="385"></pb> DO. Ex demonstrationibus istis certissimis manifestissimisque adeo perfectam exquisitamque horum motuum intelligentiam acquisivi, ut nunquam de illis mihi amplius dubitandum sit, de quibus antea dubitaveram, eo quod nunquam, nisi confuso quodam modo, intellexeram.
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1297 </s></p><p><s id="id.4.0.0.61.01">AL. Sequitur etiam, gravia eo facilius deorsum ferri, quo medium, per quod moveri debent, levius fuerit; levia vero, eo facilius sursum ferri, quo medium, per quod feruntur, gravius erit.
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1298 </s></p><p><s id="id.4.0.0.62.01">DO. Falsum ergo erit quod fere omnes asserunt philosophi, dum, conantes demonstrare aërem magis gravem esse quam levem, dicunt, <lb ed="Favaro" n="10"></lb> ideo aërem magis gravem quam levem esse existimandum, quia facilius fert gravia deorsum quam levia sursum. {1}
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1299 </s></p><p><figure id="id.4.0.0.63.00" xlink:href="FIG1/F045.jpg"></figure>
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1300 <s id="id.4.0.0.63.01">AL. Oh ridiculae chimaerae! o hominum ineptae sententiae, quae non solum veritati non adpropinquantur, sed veritati ipsi adversantur!
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1301 </s><s id="id.4.0.0.63.02">At, Dii immortales, quo pacto, quaeso, ipsorum chimaeris credendum erit, quibus naturae abditissima arcana explanare profitentur, si in rebus sensui quasi apertissimis veritati contraria temere asserunt?
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1302 </s><s id="id.4.0.0.63.03">Et quis, quaeso, somniavit, ea media esse magis gravia quam levia, quae gravia facilius deorsum quam levia sursum portent, cum e converso penitus res se <pb ed="manuscript" n="16v"></pb>habeat?
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1303 </s><s id="id.4.0.0.63.04">Sin enim ista consequentia valeret, aër <lb ed="Favaro" n="20"></lb> profecto gravior esset ipsa aqua: nam, quodcunque grave sit illud quod deorsum moveatur, facilius semper et celerius feretur in aëre quam in aqua; imo et multa sunt corpora illa, quae in aëre celerrime et facillime deorsum moventur, quae in aqua, nedum deorsum feruntur, sed aquae supernatant et, in aquam vi impulsa, sursum feruntur.
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1304 </s><s id="id.4.0.0.63.05">Hoc autem exemplo pateat: nam cucurbita, verbigratia, facile deorsum fertur in aëre, quae deinde in aqua non nisi difficillime et summa cum violentia deorsum impelletur; ergo, quia aër facilius fert corpora deorsum quam aqua, erit aqua gravior existimandus.
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1305 </s><s id="id.4.0.0.63.06">Oh absurda! oh absurda!
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1306 </s><s id="id.4.0.0.63.07">Sed attende, quaeso.
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1307 </s><s id="id.4.0.0.63.08">Demonstratum est, gravia quae in <lb ed="Favaro" n="30"></lb> aqua deorsum feruntur, tanta vi descendere, quanto eorum gravitas gravitatem aquae molis eorum moli aequalis excedit.
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1308 </s><s id="id.4.0.0.63.09">Si ergo fuerit corpus aliquod grave, ut, verbigratia, corpus in quo a, cuius quidem <pb ed="Favaro" n="386"></pb> gravitas sit, exempli gratia, 8; gravitas autem aquae b, cuius moles aequetur moli a, sit 4; tunc solidum a feretur deorsum ita celeriter et facile ut 4: si vero deinde idem corpus a ferretur per medium levius, ita ut talis medii molis c, quae esset aequalis moli a, gravitas esset ut 2, tunc profecto solidum a in hoc secundo medio ferretur deorsum facile et celeriter ut 6.
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1309 </s><s id="id.4.0.0.63.10">Patet igitur, quod idem corpus a facilius deorsum movetur per media leviora quam per graviora: <pb ed="manuscript" n="17r"></pb>ergo sequitur, quod medium eo levius existimandum sit, quo gravia in eo facilius deorsum moventur; cuius tamen contrarium plurimum opinio <lb ed="Favaro" n="10"></lb> affirmat.
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1310 </s><s id="id.4.0.0.63.11">Cui igitur iam non apertissimum est quod, si aër adhuc levior esset, gravia deorsum facilius moverentur?
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1311 </s><s id="id.4.0.0.63.12">Quod si sic est, sequitur, aërem ideo levissimum esse, quia gravia facile in eo deorsum feruntur.
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1312 </s><s id="id.4.0.0.63.13">Opposito autem huic modo ratiocinandum est de levibus, quae sursum moventur: et colligetur, medium illud grave existimandum esse, per quod levia facilius sursum feruntur; illud vero leve, per quod levia difficile sursum moventur.
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1313 </s><s id="id.4.0.0.63.14">Ergo, tum quia in aëre levia difficilius sursum moventur, tum quia in eodem gravia facilius deorsum moventur, sequitur aërem magis levem quam gravem existimandum esse.
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1314 </s><s id="id.4.0.0.63.15">Attamen quae dixi, tantummodo dicta velim ad <lb ed="Favaro" n="20"></lb> confutationem opinionis eorum, qui dixerunt aërem esse magis gravem quam levem.
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1315 </s></p><p><s id="id.4.0.0.64.01">DO. Quae ergo est tua sententia de gravitate aut levitate elementorum? {1}
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1316 </s></p><p><s id="id.4.0.0.65.01">AL. Si loquamur de gravitate vel levitate absoluta, dico, corpora omnia, sive mixta sive immixta sint illa, habere gravitatem: si vero de gravitate vel levitate respectiva sermonem habeamus, dico, corpora omnia itidem habere gravitatem, alia tamen maiorem, alia minorem; istam autem minorem gravitatem esse quam levitatem appellamus.
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1317 </s><s id="id.4.0.0.65.02">Et sic dicimus, ignem leviorem esse aëre, non quia gravitate <lb ed="Favaro" n="30"></lb> careat, sed quia minorem habet gravitatem quam habeat aër; aërem vero, eodem modo, leviorem aqua dicimus.<pb ed="manuscript" n="17v"></pb>
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1318 </s></p><p><s id="id.4.0.0.66.01">DO. At, quaeso, si ponis gravitatem in igne, qua ratione tueberis, ignem non descendere, cum gravia sint illa quae deorsum feruntur?
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1319 </s><s id="id.4.0.0.66.02"><pb ed="Favaro" n="387"></pb> Ab omnibus, tamen, ignem descendere impossibile existimatur, etiam si illi submoveretur aër.
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1320 </s></p><p><s id="id.4.0.0.67.01">AL. Ah, ah! novae chimaerae, nova figmenta.
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1321 </s><s id="id.4.0.0.67.02">Ea deorsum feruntur, quae medio, per quod ferri debent, sunt graviora: at ignis non est aëre gravior; et ideo non potest deorsum ferri.
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1322 </s><s id="id.4.0.0.67.03">At si submoveretur illi aër, ita ut vacuum sub igne relinqueretur, cui dubium est, ignem in locum aëris descensurum esse?
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1323 </s><s id="id.4.0.0.67.04">Nam, cum in vacuo nihil sit, id quod est aliquid, gravius est nihilo: cum igitur ignis sit aliquid, dubio procul descenderet sub nihilo; a natura enim <lb ed="Favaro" n="10"></lb> constitutum est, graviora sub levioribus manere.
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1324 </s><s id="id.4.0.0.67.05">Nec tamen credas, ignem descensurum ad replendum vacuum: nam, cum descenderet, relinqueret vacuum sub concavo lunae; ad quod replendum non amplius ascendere posset, cum graviora super leviora non ascendant.
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1325 </s></p><p><s id="id.4.0.0.68.01">DO. Sed si asseris, elementum aëris, sicut etiam et ignis et aquae, omnia gravia esse, quomodo possumus nos pondus aëris substinere? sicut etiam, sub aqua natantes, vastissimam aquae molem, a qua nil gravari sentimus?
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1326 </s></p><p><s id="id.4.0.0.69.01">AL. Facillima est huius dubii solutio, et ex his quae supra demonstravimus pendens: solutiones autem aliorum non admodum satisfaciunt.
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1327 </s></p><p><s id="id.4.0.0.70.01"><lb ed="Favaro" n="20"></lb> Dicunt enim aliqui, {1} pisces et homines in aqua esse sicut mus in muro, <pb ed="manuscript" n="18r"></pb>ubi laterum pondus non sentiunt, quia lateres super lateribus inhaerent, non autem super mures: quae solutio quam sit inepta, luce clarius patet.
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1328 </s><s id="id.4.0.0.70.02">Nam, quaeso, quaenam est proportio inter corpora solida et consistentia, ut lapides, et corpora liquida et fluida, ut aqua?
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1329 </s><s id="id.4.0.0.70.03">Nam, si removeamus mures e muro, ibi adhuc remanebit foramen, in quo mus erat; ex quo manifestum fit, lapides non super mures insistere, sed super alios lapides: at si removeamus piscem ex aqua, putasne ibi remansurum esse locum, in quo manebat? nonne eo statim aqua affluet?
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1330 </s><s id="id.4.0.0.70.04">Quod quidem apertissimum est indicium, aquam super pisces <lb ed="Favaro" n="30"></lb> insistere.
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1331 </s></p><p><s id="id.4.0.0.71.01">Alii autem dixerunt, elementa in proprio loco neque gravia neque levia esse, et ideo natantes in aqua ab ea non gravari.
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1332 </s><s id="id.4.0.0.71.02">Qui autem ita dicunt, nondum solvunt dubitationem.
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1333 </s><s id="id.4.0.0.71.03">Nanque, primum, demonstrandum erit hoc quod supponunt, nempe elementa in proprio <pb ed="Favaro" n="388"></pb> loco neque gravia esse neque levia.
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1334 </s><s id="id.4.0.0.71.04">Quod si sic sit, cur dicunt postea, aërem esse magis gravem quam levem?
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1335 </s><s id="id.4.0.0.71.05">Quod si tueri velint, quanam ratione defendent, aquam non esse gravissimam?
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1336 </s><s id="id.4.0.0.71.06">Deinde, etiam si hoc concedatur, nondum tamen solvitur dubium.
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1337 </s><s id="id.4.0.0.71.07">Si enim elementa in proprio loco non sunt neque gravia neque levia, peto ab eis, quis sit proprius aquae locus.
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1338 </s><s id="id.4.0.0.71.08">Respondent (ut arbitror), sub aëre.
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1339 </s><s id="id.4.0.0.71.09">Sed, si ascendamus in altissimam turrim, in cuius <pb ed="manuscript" n="18v"></pb>summitate sit balneus, in eo existentibus idem accidet quod si in mare intraremus: ab aqua enim non gravabimur, licet ea, habens sub se aërem, extra proprium locum sit.
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1340 </s><s id="id.4.0.0.71.10">Totus itaque illorum error inde manavit, quia de medii <lb ed="Favaro" n="10"></lb> gravitate, per quod gravia ferri debent, rationem non habuerunt, sed solummodo de propria mobilium gravitate vel levitate.
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1341 </s><s id="id.4.0.0.71.11">Sed, ut tuo quaesito satisfaciam, solutionem meam attende.
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1342 </s></p><p><s id="id.4.0.0.72.01">Tunc dicimur gravari, quando super nos incumbit aliquod pondus quod sua gravitate deorsum tendit, nobis autem opus est nostra vi resistere ne amplius descendat; illud autem resistere est quod gravari appellamus.
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1343 </s><s id="id.4.0.0.72.02">At, quia demonstratum est, corpora quae sunt aqua graviora, in aquam demissa, descendere, et esse in aqua gravia quidem, attamen minus gravia quam in aëre, quanta est gravitas molis aquae aequalis moli illius corporis; leviora autem aqua ostensa sunt, vi sub <lb ed="Favaro" n="20"></lb> aquam impulsa, sursum attolli tanta vi, quanto moles aquae, aequalis moli illius corporis in aëre, gravior est eodem corpore; quae autem sunt aeque gravia ac aqua demonstrata sunt, in aqua submersa, neque sursum neque deorsum ferri, sed ibi manere ubi collocantur, si tamen tota fuerint sub aqua; ex hoc patet, quod si nobis sub aqua existentibus incumbat aliquod <pb ed="manuscript" n="19r"></pb>corpus aqua gravius, gravabimur quidem, sed minus quam si essemus in aëre, quia lapis in aqua est minus gravis quam in aëre: si vero nobis in aqua manentibus corpus aqua levius alligatum fuerit, nedum gravabimur, verum etiam attollemur ab illo; ut patet in natantibus cum cucurbita, cum alioquin, in aëre <lb ed="Favaro" n="30"></lb> existentes, a cucurbita gravemur; et hoc quia cucurbita, sub aquam impulsa, fertur sursum et allevat, in aëre vero fertur deorsum et gravat: si autem in aqua existentibus aliquod corpus aeque grave ac aqua nobis immineat, neque ab illo gravabimur neque attollemur, quia neque <pb ed="Favaro" n="389"></pb> sursum neque deorsum ferretur tale corpus.
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1344 </s><s id="id.4.0.0.72.03">At non invenitur corpus quod magis aquae in gravitate vel levitate aequetur, quam ipsamet aqua: non ergo est mirum si aqua in aqua non descendat et gravet, nec ascendat et attollat; diximus autem, gravari esse resistere nostra vi corpori deorsum petenti.
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1345 </s><s id="id.4.0.0.72.04">Et eadem prorsus ratio de aëre habenda est.
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1346 </s></p><p><s id="id.4.0.0.73.01">DO. Oh pulcrum inventum! certissima et verissima solutio!
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1347 </s><s id="id.4.0.0.73.02">Tu sermonibus tuis adeo nebulas omnes inscitiae praeripuisti, ut nullum amplius de hisce rebus dubitationi locum reliqueris.
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1348 </s><s id="id.4.0.0.73.03">At quid de problematibus meis?
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1349 </s></p><p><s id="id.4.0.0.74.01"><lb ed="Favaro" n="10"></lb> AL. Ex animadversionibus his, quae circa media, mobilia et motus posuimus, unius tantummodo problematis tui solutio manifeste apparet; ceterorum vero <pb ed="manuscript" n="19v"></pb>explicationes, cum ex constitutis animadversionibus, tum ex constituendis, mox innotescent.
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1350 </s><s id="id.4.0.0.74.02">Ad problema igitur cur idem mobile citius in aëre quam in aqua descendat, patet responsio.
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1351 </s><s id="id.4.0.0.74.03">Inter gravitatem, enim, mobilis et gravitatem aëris maior est proportio, quam inter eiusdem mobilis gravitatem et gravitatem aquae; aqua enim gravior est quam aër: ex quo sequitur, idem mobile maiori vi descendere in aëre quam in aqua.
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1352 </s></p><p><s id="id.4.0.0.75.01">DO. Huius solutionem prius optime perceperam ex tuis constitutis <lb ed="Favaro" n="20"></lb> et demonstratis animadversionibus.
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1353 </s><s id="id.4.0.0.75.02">Sed quod quaesitum de puncto reflexionis motus....
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1354 </s></p><p><figure id="id.4.0.0.76.00" xlink:href="FIG1/F046.jpg"></figure>
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1355 <s id="id.4.0.0.76.01">AL. Ante quam ad meae de hoc sententiae explicationem deveniam, sunt nonnulla inspicienda.
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1356 </s><s id="id.4.0.0.76.02">Primo itaque, posito hoc, ut supra satis comprobavimus, mobile, dum motu praeternaturali movetur, moveri a virtute impressa a movente, supponatur, idem mobile, ab aequalibus virtutibus proiectum, per lineas rectas, aequales cum horizonte angulos continentes, semper per aequalia spatia moveri.
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1357 </s><s id="id.4.0.0.76.03">Supponatur, 2Á, mobile, a virtute impressa finita motum, per spatium infinitum motu violento moveri non posse. {1}
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1358 </s><s id="id.4.0.0.76.04"><pb ed="manuscript" n="20r"></pb>Supponatur, 3Á, mobile non moveri <lb ed="Favaro" n="30"></lb> motu violento, nisi virtus impellens sit maior resistentia propriae gravitatis eiusdem mobilis; si vero maior fuerit resistens gravitas quam <pb ed="Favaro" n="390"></pb> vis impellens, tunc mobile non amplius moveri motu violento, sed ad naturalem se convertere.
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1359 </s><s id="id.4.0.0.76.05">Ex quo aperte sequitur, {1} dum corpus quiescit, tunc propriam gravitatem aequari virtuti impellenti si enim maior esset gravitas, tunc corpus descenderet; si vero maior esset vis impellens, tunc corpus motu violenter moveretur.
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1360 </s><s id="id.4.0.0.76.06">Ex quo manifestum est, tandiu mobile quiescere, quam diu manet aequalitas inter gravitatem resistentem et virtutem impellentem.
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1361 </s><s id="id.4.0.0.76.07">Supponatur, 4Á, idem corpus grave ab aequalibus virtutibus per aequalia temporis spatia substineri.
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1362 </s><s id="id.4.0.0.76.08">His autem positis demonstratur, virtutem impressam a motore successive in motu violento debilitari, nec posse assignari in eodem <lb ed="Favaro" n="10"></lb> motu duo puncta, in quibus eadem fuerit virtus impellens.
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1363 </s><s id="id.4.0.0.76.09">Sit enim linea ab, super quam fiat motus violentus ex a in b a virtute finita; et quia talis motus, ex positione, non potest esse infinitus, terminetur in puncto b, nec ulterius moveatur mobile.
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1364 </s><s id="id.4.0.0.76.10">Dico itaque, virtu<pb ed="manuscript" n="20r"></pb>tem impellentem semper in tali motu debilitari, nec posse assignari in linea ab duo puncta, in quibus eiusdem roboris sit virtus impellens.
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1365 </s><s id="id.4.0.0.76.11">Nam, si fieri potest, esto duo puncta c, d, et virtus in d non sit debilior b quam in c: erit, ergo, aut eadem aut fortior.
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1366 </s><s id="id.4.0.0.76.12">Sit, primo, eadem.
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1367 </s><s id="id.4.0.0.76.13">Quia itaque mobile est idem, virtus autem impellens eadem in d et in c, linea autem supra quam fit motus, cum sit eadem, idem <lb ed="Favaro" n="20"></lb> angulum continet cum horizonte, ergo mobile per aequalia spatia d movebitur ex punctis c et d: at ex c movetur usque ad b: ergo ex d movebitur supra b: quod est absurdum; positum est enim, non ulterius quam b moveri.
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1368 </s><s id="id.4.0.0.76.14">Et maius absurdum sequeretur, si diceremus, virtutem in d esse maiorem quam in c.
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1369 </s><s id="id.4.0.0.76.15"><pb ed="manuscript" n="20v"></pb>Si itaque in motu ab assignari non possunt duo puncta in quibus aequalis fuerit virtus impellens, patet quod nec in tempore, in quo fit talis motus, poterunt assignari duo momenta in quibus aequalis fuerit virtus impellens.
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1370 </s><s id="id.4.0.0.76.16">His positis et demonstratis, sequitur necessario, in puncto reflexionis non dari quietem.
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1371 </s><s id="id.4.0.0.76.17">Nanque, si datur quies quae <lb ed="Favaro" n="30"></lb> aliquod temporis spatium duret, dabitur etiam aequalitas inter gravitatem mobilis et virtutem impellentem per aliquod spatium temporis durans: at demonstratum est, virtutem impellentem semper et <pb ed="Favaro" n="391"></pb> successive remitti: impossibile est ergo, ut per aliquod temporis spacium in statu aequalitatis virtus cum gravitate mobilis maneat; et, ob id, impossibile est, ut mobile per aliquod spacium temporis quiescat.
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1372 </s></p><p><figure id="id.4.0.0.77.00" xlink:href="FIG1/F047.jpg"></figure>
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1373 <s id="id.4.0.0.77.01">Hoc autem clarius ex ista demonstratione apparebit, descripta eadem figura quae supra.
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1374 </s><s id="id.4.0.0.77.02">Nam, si quando mobile est in b, per aliquod temporis spacium quiescit, sit tale tempus, cuius extrema momenta sint cd.
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1375 </s><s id="id.4.0.0.77.03">Si ergo mobile quiescit tempus cd, ergo virtus impellens aequalis est gravitati mobilis per <lb ed="Favaro" n="10"></lb> totum tempus cd: sed gravitas mobilis semper est eadem: ergo virtus in momento c est aequalis virtuti in d.
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1376 </s><s id="id.4.0.0.77.04">Estque idem corpus grave; ergo per aequalia temporis spatia a virtutibus aequalibus substinebitur: sed virtus in momento c substinet per cd spatium temporis: ergo virtus in momento d substinebit <pb ed="manuscript" n="21r"></pb>idem corpus per spatium temporis aequale spatio cd.
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1377 </s><s id="id.4.0.0.77.05">Quiescet igitur mobile per duplum temporis cd: quod est inconveniens; nam ponebatur quiescens per spatium cd.
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1378 </s><s id="id.4.0.0.77.06">Eadem vero argumentandi ratione servata, demonstrabitur etiam, mobile in puncto b semper <lb ed="Favaro" n="20"></lb> quiescere; cum tamen ponatur se convertens ad motum naturalem. {1}
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1379 </s></p><p><s id="id.4.0.0.78.01">DO. Non possum non fateri, demonstrationes istas necessario concludere, cum ex principiis manifestissimis et certissimis, quae nullo modo negari possint, pendeant.
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1380 </s><s id="id.4.0.0.78.02">Attamen adhuc nescio quid mentem perturbat: nam si ponis, aliquando virtutem impellentem aequari gravitati resistenti, quomodo etiam non pones, aliquando corpus quiescere?
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1381 </s></p><p><s id="id.4.0.0.79.01">AL. Dubitationem hanc facile erit removere.
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1382 </s><s id="id.4.0.0.79.02">Aliud enim est dicere, mobilis gravitatem aliquando ad aequalitatem cum vi impellente devenire; aliud vero, eam in tali aequalitate per temporis spatium <lb ed="Favaro" n="30"></lb> commorari.
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1383 </s><s id="id.4.0.0.79.03">Hoc autem exemplo manifestabitur.
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1384 </s><s id="id.4.0.0.79.04">Nam, cum mobile movetur, eo quod (ut demonstratum est) virtus impellens semper remittitur, gravitas vero semper eadem manet, sequitur necessario ut, antequam ad proportionem aequalitatis pervenerint, innumerae aliae <pb ed="Favaro" n="392"></pb> proportiones intercedant: attamen vim et gravitatem in aliqua istarum proportione per aliquod tempus manere, est impossibile; cum demontratum [= demonstratum] sit, nunquam virtutem impellentem per ali quod temporis spacium in eodem statu manere, cum semper remittatur.
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1385 </s><s id="id.4.0.0.79.05">Verum itaque est, vim et gravitatem per proportionem, verbigratia, duplam, sesquialteram, sesquitertiam, et alias innumeras, transire; quod autem in una earum proportione per aliquod tempus maneant, hoc falsissimum est.
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1386 </s><s id="id.4.0.0.79.06">Sicut <pb ed="manuscript" n="21v"></pb>etiam si intelligamus aliquod mobile per superficiem aliquam moveri, tunc illud omnes superficiei lineas tanget, et per eas transibit: quod autem in aliqua earum per aliquod temporis spacium <lb ed="Favaro" n="10"></lb> maneat, est falsum; cum nunquam quiescat, sed semper moveatur.
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1387 </s><s id="id.4.0.0.79.07">Pari etiam ratione verum est, vim et gravitatem aliquando pervenire ad aequalitatis proportionem, sicut et ad innumeras alias; nec tamen sequitur, ob id in tali proportione quiescere et per aliquod temporis spacium commorari, sicut nec in aliis proportionibus.
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1388 </s></p><p><s id="id.4.0.0.80.01">DO. Iam omnis sublata est dubitatio, et cogor demonstrationibus tuis annuere.
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1389 </s><s id="id.4.0.0.80.02">Sed quid ad argumentationes Aristotelis?
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1390 </s></p><p><s id="id.4.0.0.81.01">AL. Potissima erat Aristotelis argumentatio haec.
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1391 </s><s id="id.4.0.0.81.02">Dicebat enim: Si in puncto reflexionis non datur quies, sequitur duos contrarios motus esse continuos, et, ob id, unum tantum, cum unus eorum sit <lb ed="Favaro" n="20"></lb> terminus; quod quidem absurdum esset.
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1392 </s><s id="id.4.0.0.81.03">At ad hoc respondetur, tales motus esse contiguos, non autem continuos; ex quo nullus sequitur error; et inter terminum motus sursum et terminum motus deorsum nihil intercedere: talis nanque contiguorum, es ipsomet Aristotele, est natura.
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1393 </s><s id="id.4.0.0.81.04">Sed aliquis adhuc nonnunquam obstitit, ex sententia ipsius Aristotelis, dicens, aërem etiam esse in causa cur grave in puncto reflexionis quiescat: cum enim mobile in tali puncto valde sit debilitatum, ab aëre resistentiam patitur, qui motui eius resistit.
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1394 </s><s id="id.4.0.0.81.05">Ad hoc enim dico, meas non esse partes respondere: quia, quamvis in puncto reflexionis, talem ob causam tantum, quies continge<pb ed="manuscript" n="22r"></pb>ret, non <lb ed="Favaro" n="30"></lb> tamen ob id dicendum esset, in puncto dicto necessariam esse quietem; haec causa esset per accidens.
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1395 </s><s id="id.4.0.0.81.06">Quod si Aristoteles existimasset, contrarios motus hoc a natura contrariorum habere, ut simul coniungi possent, et ideo, quod ex eorum natura esset, quod in puncto reflexionis intercedens non requireretur quies, utique dixisset, absolute in puncto reflexionis non dari quietem: quod si deinde per aëris <pb ed="Favaro" n="393"></pb> intercessionem atque resistentiam quies contingeret, hanc inter causas per accidens reposuisset, et, cum de contrariorum motuum natura disputasset, omnino praeteriisset.
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1396 </s><s id="id.4.0.0.81.07">Attamen, et ne fortasse crederet quis hanc ob causam vere in puncto reflexionis quietem contingere, eam omnino de medio tollendam esse statui, declarando quod nec per accidens requiratur quies.
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1397 </s><s id="id.4.0.0.81.08">Primo, nanque, in contrarium esset adversariorum inconstantia: qui, pro ut opus illis est, dicunt, motum iuvari a medio, eundemque a medio impediri, quia, nempe, medium obstat.
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1398 </s><s id="id.4.0.0.81.09">At si medium iuvat motum, quomodo in puncto reflexionis illum <lb ed="Favaro" n="10"></lb> destruit?
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1399 </s><s id="id.4.0.0.81.10">2Á: sicut se habet motus ad motum, ita resistentia medii ad resistentiam; ita ut quo magis motus fuerit velox et concitatus, magis medium resistet, cum citius sit scindendum: ergo a commutata proportione, motus semper eodem se habebit modo ad medii resisistentiam; ita ut quo tardior fuerit <pb ed="manuscript" n="22v"></pb>motus, eo minor erit resistentia.
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1400 </s><s id="id.4.0.0.81.11">Itaque, cum in puncto reflexionis tardissimus sit motus, minima quoque erit medii resistentia; et sicut celerrimus motus maximam resistentiam vincit, ita et minimus motus resistentiam superabit minimam, cum motus ad resistentiam semper eodem se habeat modo.
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1401 </s><s id="id.4.0.0.81.12">3Á: attendas, quaeso, quam infirmus sit adversariorum argumentandi modus; <lb ed="Favaro" n="20"></lb> eo quod dum motum tollere conantur; eundem necessario supponunt.
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1402 </s><s id="id.4.0.0.81.13">Nanque aut aër resistit mobili dum quiescit, aut dum movetur.
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1403 </s><s id="id.4.0.0.81.14">Non utique dum quiescit: cum enim resistere, ipsi aëri sit quoddam pati, aër nil profecto patitur a quiescente corpore, sed a corpore quod movetur; ergo aër non resistet motui, nisi dum fit motus.
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1404 </s><s id="id.4.0.0.81.15">Si enim aër resisteret, et resisteret ante motum, motus utique fieret nunquam: quapropter dicendum est, aërem resistere dum mobile movetur.
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1405 </s><s id="id.4.0.0.81.16">Necessario igitur sequitur, ut qui dicunt in puncto reflexionis medium resistere mobili, mobile in motu existens supponant; et ita tum conantur tollere motum, eundem concedant: quo quid ineptius?
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1406 </s><s id="id.4.0.0.81.17"><lb ed="Favaro" n="30"></lb> Possem etiam ex eiusdem Aristotelis sententia argumenta efformare: qui profecto ponit, non fieri posse motum absque medii resistentia; ita ut in vacuo neget motum, cum ibi nulla sit resistentia medii, dicens, Si esset vacuum, motus certe fieret in ipso instantaneus.
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1407 </s><s id="id.4.0.0.81.18"><pb ed="manuscript" n="23r"></pb>At quia alia est mea opinio, allatis argumentis contentus ero.
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1408 </s></p><p><s id="id.4.0.0.82.01">DO. Satis superque sententia tua de motu in puncto reflexionis, <pb ed="Favaro" n="394"></pb> tum demonstrationibus, tum ex reiectione argumentorum in contrarium, est confirmata: sed postquam casu de vacuo verba fecisti, de eodem aliquid dicere ne graveris.
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1409 </s></p><p><figure id="id.4.0.0.83.00" xlink:href="FIG1/F048.jpg"></figure>
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1410 <s id="id.4.0.0.83.01">AL. De vacuo plura in medium afferre possem; quae tamen omittam, ne talis disputatio a nostro fine nos averteret, et id tantum adferam, quod ex superioribus pendet.
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1411 </s><s id="id.4.0.0.83.02">Dico itaque, quod in vacuo motus non fieret in instanti: quod ex his quae demonstrata sunt innotescit.
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1412 </s><s id="id.4.0.0.83.03">Ostensum est enim, eorum quae moventur, tantam esse celeritatem, quanta est gravitas qua excedunt medium per quod moventur.
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1413 </s><s id="id.4.0.0.83.04">Ut si sit mobilis moles ipsa a, <lb ed="Favaro" n="10"></lb> moles autem medii per quod ferri debet, b, aequetur moli a, gravitas autem a sit 8, gravitas vero b sit ut 3, velocitas profecto qua descendet erit ut 5: quod si gravitas b esset 2, velocitas a esset 6: si vero gravitas b esset 1, velocitas esset 7: quod si gravitas b esset nulla, velocitas a esset 8, non autem infinita.
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1414 </s><s id="id.4.0.0.83.05">Gravitas enim a excedit gravitatem, quae nulla est, per totam gravitatem suam, quae est finita: sed qualis est gravitas excedens, talis est motus celeritas: gravitas autem est finita: ergo et velocitas motus erit terminata, non autem infinita.
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1415 </s><s id="id.4.0.0.83.06"><pb ed="manuscript" n="23v"></pb>Itaque tunc esset velocitas infinita et instantanea, quando gravitas esset infinita, et tunc, <lb ed="Favaro" n="20"></lb> tam in vacuo quam in pleno, motus esset instantaneus; in pleno, tamen, penetrabili et non infinitae resistentiae.
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1416 </s><s id="id.4.0.0.83.07">Itaque iure optimo dicemus, gravitatem infinitam, quocunque moveatur, in instanti moveri; gravitatem vero finitam, quoquo loci, finita celeritate cieri.
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1417 </s><s id="id.4.0.0.83.08">Quapropter sicut qui contra nos ita argumentantur, In vacuo si fieret motus fieret in instanti; sed motus non fit in istanti, ergo in vacuo non fieret motus; ita et nos modo converso sic ratiocinabimur: In vacuo si motus contingeret, non utique fiet in instanti; sed motus contingit, dummodo in tempore fiat; ergo in vacuo fiet motus.
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1418 </s><s id="id.4.0.0.83.09">Ex quo etiam colligi potest, medium non iuvare motum, sed eundem <lb ed="Favaro" n="30"></lb> prorsus impedire; cum ubi medium non esset, concitatior motus fieret.
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1419 </s><s id="id.4.0.0.83.10">2Á: libet etiam ex eorundemmet adversariorum argumento, quo vacuum dari tollere conantur, id ipsum elicere: nempe in vacuo motum fieri in tempore.
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1420 </s><s id="id.4.0.0.83.11">Dicunt enim ipsi, quod si accipias duos lapides exactissime expolitos, quorum superficies ita congruant, inter se <pb ed="Favaro" n="395"></pb> aptatae, ut nihil diversi generis inter ipsas relinquatur, tunc si conatus eris eas ad invicem separare, ita tamen ut semper aequidistent, te operam perditurum; natura enim vacuum, quod aliquando inter ipsas relinqueretur, nimium horret: ex quo colligunt, vacuum non dari posse.
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1421 </s><s id="id.4.0.0.83.12">At si hoc verum est, uti <pb ed="manuscript" n="24r"></pb>certe verissimum extat, tunc sic arguo: Lapides non possunt separari; ergo motus in instanti non fit in vacuo.
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1422 </s><s id="id.4.0.0.83.13">Nam si lapides non possunt separari, ne quis locus vacuus relinquatur, iam separari poterunt cum vacuum non relinquatur: nam aër circumfluus in vacuum in instanti advolabit, et ita vacuus <lb ed="Favaro" n="10"></lb> nunquam erit locus.
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1423 </s><s id="id.4.0.0.83.14">Attamen quia lapides adhuc non disseparantur, signum est quod per aliquod tempus inter eas relinqueretur vacuum: quod quidem vacuum, ex eo quod per aliquod temporis spatium duraret, satis superque demonstrat, in se non instantaneum fieri motum sed successivum. {1}
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1424 </s><s id="id.4.0.0.83.15">Haec autem de vacuo veluti per transennam dicta velim, cum praesertim ad primum nostrum intentum non conferant.
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1425 </s></p><p><s id="id.4.0.0.84.01">DO. Et haec quoque audire gratissimum fuit, cum, me iudice, veritatem assequantur. {2}
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1426 </s><s id="id.4.0.0.84.02"><pb ed="manuscript" n="27v"></pb>In hoc itaque disserendo diutius commorari, <pb ed="Favaro" n="396"></pb> quaeso, ne graveris.
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1427 </s><s id="id.4.0.0.84.03">Hoc enim quod petam, abs te audire cupio.
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1428 </s><s id="id.4.0.0.84.04">Si igitur vera est tua opinio, ut demonstrationes tuae confirmare videntur, falsa necessario erit opinio contraria: ex quo necessario sequitur, in aliquem errorem impegisse Aristotelem, cum contrarium demonstrare contenderet; quod sane fecit 4 Physicorum.
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1429 </s><s id="id.4.0.0.84.05">At quia demonstratione quasi geometrica est <pb ed="manuscript" n="28r"></pb>usus, miror quidem in ea captiones inesse: quapropter te etiam atque etiam rogatum velim, ut eius fallaciam detegas.
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1430 </s></p><p><figure id="id.4.0.0.85.00" xlink:href="FIG1/F049.jpg"></figure>
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1431 <s id="id.4.0.0.85.01">AL. Si Aristotelis demonstrationem exacte examinare velimus, longior fiet sermo, et primum nostrum intentum transcendens.
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1432 </s><s id="id.4.0.0.85.02">Sed, <lb ed="Favaro" n="10"></lb> postquam lubet, illius captiones adaperiam; quae ut lucidius appareant, ipsius demonstrationem in medium adferam.
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1433 </s><s id="id.4.0.0.85.03">Praemittit itaque, primo, e haec: tarditatem et celeritatem motus ex duplici causa pendere; nempe aut ex ipso mobili, aut ex ipso medio.
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1434 </s><s id="id.4.0.0.85.04">Ex ipso quidem mobili: nam mobile gravius per idem medium citius quam minus grave movebitur.
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1435 </s><s id="id.4.0.0.85.05">Ratione autem medii dupliciter inquit contingere tarditatem aut celeritatem: semel quidem eodem medio spectato, seu manenti, seu in contrarias, sive in easdem cum mobili partes, irruente; velocior enim erit eiusdem mobilis motus si ad easdem feratur partes medium quam si maneat, et si maneat quam si ad contrarias <lb ed="Favaro" n="20"></lb> moveatur: 2Á, diversis acceptis mediis, mobile per id quod subtilius erit citius quam per crassius movebitur, ut per aërem quam per aquam.
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1436 </s><s id="id.4.0.0.85.06">His, primo, notatis, quia videbat idem pondus per subtiliora media citius ferri quam per crassiora, supposuit, 2Á, eandem proportionem servare velocitatem motus ad velocitatem, quam medii unius subtilitas ad alterius medii subtilitatem.
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1437 </s><s id="id.4.0.0.85.07">His autem constitutis, ad <pb ed="manuscript" n="28v"></pb>demonstrationem se convertens, ita est argumentatus: Transeat mobile a medium b in tempore c; medium autem subtilius ipso, <lb ed="Favaro" n="30"></lb> nempe d, transeat in tempore e: manifestum est, sicut crassities b ad crassitiem d, ita se habere tempus c ad tempus e.
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1438 </s><s id="id.4.0.0.85.08">Sit deinde f vacuum; et mobile a, si fieri possit, transeat ipsum f in tempore g: habebit igitur eandem rationem vacuum ad <pb ed="Favaro" n="397"></pb> plenum, quam habet g ad e.
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1439 </s><s id="id.4.0.0.85.09">Intelligatur deinde aliud medium subtilius ipso d, ad cuius crassitiem ipsius d crassities eam habeat proportionem quam tempus e ad tempus g.
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1440 </s><s id="id.4.0.0.85.10">Tunc, ex his quae constituta sunt, mobile a per medium nunc inventum movebitur in tempore g, cum medium d ad medium nunc inventum eandem habeat proportionem quam e tempus ad tempus g: sed in eodem tempore g, movetur a etiam per vacuum f: ergo a eodem tempore movebitur per duo spatia aequalia, quorum unum sit plenum, alterum vero sit vacuum; quod quidem est inconveniens.
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1441 </s></p><p><s id="id.4.0.0.86.01"><lb ed="Favaro" n="10"></lb> Haec est Aristotelis demonstratio: quae quidem optime et necessario conclusisset, quoad formam demonstrationis, {1} si ea, quae assumpsit, demonstrasset Aristoteles, aut, si non demonstrata, fuissent saltem vera; sed in hoc deceptus est (meo tamen iudicio) Aristoteles, quod ea tanquam nota axiomata assumpsit, quae non solum non sunt sensui <pb ed="manuscript" n="29r"></pb>nota, verum nec unquam demonstrata, nec etiam demonstrabilia, cum prorsus falsa existant.
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1442 </s><s id="id.4.0.0.86.02">Quod ut luce clarius appareat, singulas illius hypotheses examinabimus.
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1443 </s></p><p><s id="id.4.0.0.87.01">Primo, itaque, supponit celeritatis et tarditatis motus causam esse subtilitatem aut crassitiem medii, per quod fit motus: quae quidem <lb ed="Favaro" n="20"></lb> positio falsa est, tum ex demonstratis supra; ubi gravitatem medii, non crassitiem aut subtilitatem, motus tarditatis aut celeritatis causam esse, ostensum est; tum etiam ex his quae nunc addemus.
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1444 </s><s id="id.4.0.0.87.02">Nanque, amabo, si subtilitas medii est causa motus celeritatis, profecto in subtiliori medio velocior fiet motus: nunc, ex ipsomet Aristotele, aër subtilior est aqua: attamen nonnulla velocius moventur in aqua quam in aëre.
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1445 </s><s id="id.4.0.0.87.03">Ut si, verbigratia, accipiamus vessicam inflatam, haec in aëre tardius motu naturali movebitur quam in aqua: si enim in aquae profundo vi comprimeretur et alligaretur, tunc, vinculis solutis, citissime sursum advolaret vessica; quod si adhuc levius quoddam <lb ed="Favaro" n="30"></lb> acciperemus corpus, id in aëre tardius, in aqua vero velocius, moveretur; ita ut devenire possemus ad aliquod, quod in aëre vix moveretur, in aqua vero citissime.
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1446 </s><s id="id.4.0.0.87.04">Quin etiam hoc addam: si enim intelligamus aliquod corpus adeo leve quod in aëre ascendat, hoc profecto levius erit quam vessica; si itaque tale corpus sub aqua vi detineatur, mox autem relinquatur, cui <pb ed="manuscript" n="29v"></pb>dubium erit ipsum longe citius in aqua, quam <pb ed="Favaro" n="397"></pb> deinde in aëre, ascensurum esse, cum tamen aër subtilior sit ipsa aqua?
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1447 </s><s id="id.4.0.0.87.05">Quomodo ergo verum erit unquam, motum naturalem necessario velociorem esse in medio subtiliori quam in crassiori? {1}
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1448 </s></p><p><s id="id.4.0.0.88.01">Hic autem non me praeterit, magnum esse moderniorum philosophantium numerum, qui ea quae scire profitentur, magis fide et aliorum authoritate quam demonstratione sciunt: qui, si talia audirent, statim respondere conarentur, et satis illis esset si duo verba, etiam si nihil ad rem facientia, in medium afferrent; subiungerent enim paulo post, Satis superque abunde superius talis opinio confutata est; et similia verba ampullata, quibus solis sibi ipsis et <lb ed="Favaro" n="10"></lb> audientibus se imperitioribus opiniones suas persuadent.
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1449 </s><s id="id.4.0.0.88.02">Istis, si argumenta mea audirent, et responderent meas rationes non concludere, quia mox loquor de motu sursum mox de deorsum, quod est contra Aristotelis intentionem, aut similia verba nullius roboris in medium afferrent; his, inquam, satis superque opinio mea confutata videretur.
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1450 </s><s id="id.4.0.0.88.03">At de his hactenus: satis mihi sit, talem illis responsionem praeripuisse, cum adderem secundum exemplum, in quo de uno tantum motu loquitur.
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1451 </s><s id="id.4.0.0.88.04">Concludendum itaque est, falsum omnino illud esse, quod scilicet tarditas aut celeritas motus ex crassitie aut subtilitate medii proveniat.
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1452 </s></p><p><s id="id.4.0.0.89.01">Secundo: tanquam notum assumpsit Aristoteles, eandem habere <lb ed="Favaro" n="20"></lb> proportionem motus veloci<pb ed="manuscript" n="30r"></pb>tatem ad alterius motus velocitatem, quam habet subtilitas medii ad alterius medii subtilitatem.
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1453 </s><s id="id.4.0.0.89.02">Hoc non demonstravit Aristoteles, et dextre quidem hoc aufugit: frustra enim laborasset, cum indemonstrabile sit, et, nedum indemonstrabile, verum etiam falsum.
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1454 </s><s id="id.4.0.0.89.03">Nam, etiam si concedatur subtilitatem esse causam celeritatis, sequetur quidem ut in maiori subtilitate maior erit celeritas; non tamen adhuc sequetur, secundum eandem proportionem augeri celeritates et subtilitates.
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1455 </s><s id="id.4.0.0.89.04">Et, ut secundum Aristotelem loquar, subtilitas aëris ad subtilitatem aquae nullam haberet proportionem: nam, verbigratia, lignum in aëre descendit, in aqua vero non; quare <lb ed="Favaro" n="30"></lb> celeritas in aëre ad celeritatem in aqua null am habebit proportionem. {2}
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1456 </s><s id="id.4.0.0.89.05"><pb ed="manuscript" n="35r"></pb>Quod quidem ut luce clarius appareat, primo quidem, <pb ed="Favaro" n="399"></pb> demonstratione omnino simili illi qua contendebat Aristoteles demonstrare motum in vacuo contingere in instanti, ostendam, motus non servare, inter se, quoad velocitatem, proportionem subtilitatum mediorum; deinde etiam ostendam quam proportionem servent, ut apertius veritas innotescat.
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1457 </s></p><p><figure id="id.4.0.0.90.00" xlink:href="FIG1/F050.jpg"></figure>
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1458 <s id="id.4.0.0.90.01">Si igitur, ut ipse dicebat, velo<pb ed="manuscript" n="35v"></pb>citas ad velocitatem eam habet proportionem quam subtilitas medii ad alterius medii subtilitatem, esto mobile quidem o; duo autem media sint a, b, quorum a sit, verbigratia, aqua, b vero aër; <lb ed="Favaro" n="10"></lb> subtilitas autem aëris, quae sit 8, sit maior subtilitate aquae, quae sit 2; et mobile non descendat in aqua sed supernatet, in aëre vero sit illius celeritas ut 4; et fiat sicut subtilitas b aëris, quae est 8, ad subtilitatem a aquae, quae est 2, ita celeritas in aëre, quae posita est 4, ad aliam celeritatem, quae profecto non erit nulla, sed erit 1.
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1459 </s><s id="id.4.0.0.90.02">Quia itaque mobile o in subtilitate b movetur cum 4 celeritatis; sicut autem subtilitas b ad subtilitatem a, ita celeritas ut 4 ad celeritatem ut 1; manifestum est ergo, quod celeritas mobilis o in subtilitate a erit ut 1: posita tamen fuit <lb ed="Favaro" n="20"></lb> esse nulla; quod quidem est inconveniens.
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1460 </s><s id="id.4.0.0.90.03">Quare non erit ut subtilitas ad subtilitatem, ita velocitas ad velocitatem, ut posuit Aristoteles.
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1461 </s></p><p><figure id="id.4.0.0.91.00" xlink:href="FIG1/F051.jpg"></figure>
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1462 <s id="id.4.0.0.91.01">Sed libet quoque aliam adferre demonstrationem.
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1463 </s><s id="id.4.0.0.91.02">Sint enim eadem ut supra; et subtilitas b sit ut 16, subtilitas vero a sit ut 4; et mobile o non moveatur in a, sed supernatet; eiusdem vero mobilis in b medio celeritas sit ut 8.
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1464 </s><s id="id.4.0.0.91.03">Sit rursus alia velocitas, quae sit ut 1; ut autem celeritas 8 ad celeritatem 1, ita se habeat subtilitas b <lb ed="Favaro" n="30"></lb> ad subtilitatem aliam, quae sit c: erit iam subtilitas c ut 2.
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1465 </s><s id="id.4.0.0.91.04">Et quia sicut subtilitas b ad subtilitatem c, ita se habet velocitas 8 ad velocitatem 1; mobile autem o in subtilitate b <pb ed="Favaro" n="400"></pb> movetur cum celeritate 8; ergo idem mobile o in subtilitate c movebitur cum celeritate ut 1.
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1466 </s><s id="id.4.0.0.91.05">Movebitur itaque o in medio c: sed medium c est crassius medio a (est enim medii a subtilitas 4 maior subtilitate c, quae est ut 2); in medio autem a positum est non moveri mobile o: mobile igitur o movebitur quidem per medium crassius, per subtilius vero minime: quod est absurdissimum et omnino indignum Aristotele.
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1467 </s></p><p><figure id="id.4.0.0.92.00" xlink:href="FIG1/F052.jpg"></figure>
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1468 <s id="id.4.0.0.92.01">Patet ergo, motuum velocitates non servare inter se subtilitatum mediorum proportiones.
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1469 </s><s id="id.4.0.0.92.02">Sed ut quasnam servent proportiones innotescat, <pb ed="manuscript" n="30r"></pb>accipiamus veram causam tarditatis atque celeritatis motus eiusdem mobilis; quam supra demonstravimus esse medii levitatem <lb ed="Favaro" n="10"></lb> aut gravitatem respectu mobilis.
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1470 </s><s id="id.4.0.0.92.03">Et sit mobile a, medium autem c sit in duplo levius medio b: non utique tempus in quo a movetur per b erit duplum temporis in quo a movetur per c; hoc est, celeritas in c non erit dupla celeritatis in b. {1}
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1471 </s><s id="id.4.0.0.92.04">Sit enim tempus, in quo a movetur per b ipsum, d; et tempus, quo a movetur per c, sit e.
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1472 </s><s id="id.4.0.0.92.05">Et quia celeritas a in b spatio tanta erit, quantus est excessus in quo gravitas a excedit gravitatem b, ut supra demonstratum est; si gravitas a sit 20, gravitas vero b sit 8, erit utique celeritas d 12: sed, eandem ob causam, si gravitas c <lb ed="Favaro" n="20"></lb> sit 4, erit celeritas e ut 16: celeritas ergo e non erit dupla <pb ed="manuscript" n="30v"></pb>celeritatis d.
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1473 </s><s id="id.4.0.0.92.06">Quare, cum spatia b, c sint aequalia in longitudine, non erit tempus d duplum temporis e.
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1474 </s><s id="id.4.0.0.92.07">Patet ergo, quod velocitas in medio c non est tanta, quantam esse volebat Aristoteles, sed multo minor: nam, ex illius sententia, velocitas e debuit esse, respectu velocitatis d, 24; est autem 16.
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1475 </s><s id="id.4.0.0.92.08">Manifestum est igitur quod, quo quidem levius erit medium, eo velocior erit motus proveniens ex gravitate.
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1476 </s><s id="id.4.0.0.92.09">Sed quia sub minori proportione semper respicit velocitas velocitatem, quam raritas raritatem, sequitur, quando raritas pleni respexerit raritatem vacui secundum <lb ed="Favaro" n="30"></lb> maximam omnium proportionum, non tamen velocitatem in pleno ad velocitatem in vacuo eam debere proportionem retinere; ut falso ratus est Aristoteles.
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1477 </s></p><p><s id="id.4.0.0.93.01"><pb ed="Favaro" n="401"></pb> Ex his etiam quae supra posita sunt sequitur, quod celeritas ad celeritatem semper servet arithmetice proportionem levitatis medii ad alterius medii, non tamen geometrice.
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1478 </s><s id="id.4.0.0.93.02">Si enim, rursus, gravitas c sit 2, ita ut ipsius levitas sit quadrupla levitatis b, celeritas e non erit profecto quadrupla celeritatis d, sed sesquialtera erit; nanque celeritas e, ut 18: attamen eandem arithmeticam habebit proportionem quam c ad b, cum excessus sint aequales, nempe 6.
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1479 </s><s id="id.4.0.0.93.03">Quod si, rursus, gravitas c sit 1, ut c levitas sit octupla gravitatis b, non erit profecto celeritas e octupla celeritatis d, sed longe minor <pb ed="manuscript" n="31r"></pb>quam octupla, <lb ed="Favaro" n="10"></lb> nempe super septem partiens 12; erit enim celeritas e ut 19: et erit eadem arithmetica proportio quae est levitatis ad levitatem, cum idem sit excessus, nempe 7.
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1480 </s><s id="id.4.0.0.93.04">Quod si nulla sit gravitas c, ita ut nullam habeat proportionem c levitas ad levitatem b, erit e celeritas ut 20, eandem proportionem arithmeticam habens ad d quam 8 ad 0: celeritatis enim 20 super celeritatem 12 idem est excessus, quo 8 excedit 0, nempe 8.
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1481 </s><s id="id.4.0.0.93.05">Et sic, contra id quod dicit Aristoteles, non inconveniens est, numerum ad numerum eandem habere proportionem, quam numerus ad nihil, si tamen loquamur de proportione arithmetica: 20 ad 12 eam habet proportionem, quam 8 ad 0; excessus enim 20 <lb ed="Favaro" n="20"></lb> super 12 est idem cum excessu 8 super 0.
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1482 </s></p><p><s id="id.4.0.0.94.01">DO. Ho subtile inventum, oh pulcherrimum excogitatum!
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1483 </s><s id="id.4.0.0.94.02">Sileant profecto, sileant, qui philosophiam consequi posse autumant absque divinae mathematicae cognitione.
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1484 </s><s id="id.4.0.0.94.03">Ecquis unquam negabit, hac sola duce verum a falso dignosci posse, huius auxilio ingenii acumen excitari, hac denique duce quicquid inter mortales vere scitur percipi et intelligi posse? {1}
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1485 </s></p><p><s id="id.4.0.0.95.01">AL. Audias, quaeso.
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1486 </s><s id="id.4.0.0.95.02">Aristoteles ex hypothesibus suis secundum argumentum hauriebat: nempe, quod si in vacuo motus fieret in tempore, eadem cum celeritate moverentur leviora ac graviora, cum tam <lb ed="Favaro" n="30"></lb> levioribus quam gravioribus nulla esset medii resistentia; {2} quod tamen est inconveniens.
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1487 </s><s id="id.4.0.0.95.03">In quo argumento similiter <pb ed="manuscript" n="31v"></pb>deceptus est Aristoteles, eo quod posuerit celeritatem et tarditatem motus ex medii tantum resistentia oriri, cum tamen ex gravitate vel levitate medii et <pb ed="Favaro" n="402"></pb> mobilis totum negocium pendeat.
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1488 </s><s id="id.4.0.0.95.04">Dico itaque, quod in vacuo graviora citius descenderent quam leviora; quia excessus graviorum super medium maior esset excessu leviorum. {1}
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1489 </s></p><p><figure id="id.4.0.0.96.00" xlink:href="FIG1/F053.jpg"></figure>
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1490 <s id="id.4.0.0.96.01">Neque etiam verum est quod Aristoteles dixit de proportione motuum respectu mobilium gravitatum: quod, scilicet, celeritas ad celeritatem eandem habeat proportionem in eodem medio, quam habet gravitas ad gravitatem; ut si, verbigratia, a esset duplo gravius ipso b, quod etiam celeritas ipsius a esset dupla celeritatis b.
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1491 </s><s id="id.4.0.0.96.02">Nam eodem modo, quo supra, demonstrabimus hoc.
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1492 </s><s id="id.4.0.0.96.03">Si enim gravitas a sit 4, gravitas vero b sit 2, et a in medio aquae descendat, et sit eius <lb ed="Favaro" n="10"></lb> celeritas 2, b vero non descendat; tunc aperte constat quod celeritas a non erit dupla celeritatis b, cum b non moveatur.
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1493 </s><s id="id.4.0.0.96.04">Sed hic quoque arithmetica servabitur proportio inter celeritates, hoc est secundum excessum gravitatum super gravitatem medii; ut si a sit 4, b vero 2, medium autem 1 in gravitate, tunc celeritas a erit 3 respectu celeritatis b, quae erit ut 1.
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1494 </s><s id="id.4.0.0.96.05">Quapropter, ut in summa dicam, tarditas et velocitas <pb ed="manuscript" n="32r"></pb>omnis motus deorsum provenit, primo et per se, ex propria mobilium gravitate; quae deinde gravitas quia a mediorum gravitate minor fit, hinc est quod debilior fit motus.
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1495 </s><s id="id.4.0.0.96.06">Si vero et medii fuerit tanta gravitas quanta est mobilium, tunc, eo quod mobilium in tali <lb ed="Favaro" n="20"></lb> medio nulla est gravitas, motus fit nullus; quod si, rursus, maior sit medii gravitas, tunc mobilium gravitas respectu medii gravitatis fit levitas, et mobile fertur sursum; quod si medii nulla sit gravitas, tunc mobilia movebuntur secundum simplicem suam gravitatem, et eam in motu proportionem servabunt quam propriae gravitates inter se habebunt.
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1496 </s><s id="id.4.0.0.96.07">Et ex hoc patet alius gravis error; quod Aristoteles contrario prorsus modo senserit ab eo, quod sentiendum erat.
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1497 </s><s id="id.4.0.0.96.08">Dicebat enim, gravia in pleno eam in suis motibus servare proportionem quam gravitates; in vacuo vero minime, sed omnia eodem tempore moveri.
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1498 </s><s id="id.4.0.0.96.09">Sed, e contra, in vacuo servabunt proportiones suarum gravitatum, <lb ed="Favaro" n="30"></lb> cum excessus super medium sint totae gravitates mobilium; in pleno, vero, hanc proportionem non servabunt, ut supra demonstratum est.
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1499 </s><s id="id.4.0.0.96.10">Sed, ut supra saepius dictum est, oportet ut semper intelligas atque <pb ed="Favaro" n="403"></pb> supponas, ista diversa mobilia, de quibus loquimur, differre tantum in gravitate, cum <pb ed="manuscript" n="32v"></pb>in mole sint aequalia; ne forte ita diceres: Sit verbigratia, mobile, cuius gravitas sit 8; molis autem aquae aequalis moli dicti mobilis sit gravitas 3; manifestum est itaque, ex his quae dicta sunt, quod celeritas mobilis dicti erit ut 5: quod si aliud mobile accipias, quale esset c, cuius quidem moles esset dupla ipsius a, gravitas autem eius minor quam dupla gravitas a, esset nempe 12, molis autem aquae aequalis ipsi c gravitas esset 6, tunc <lb ed="Favaro" n="10"></lb> celeritas c esset ut 6.
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1500 </s><s id="id.4.0.0.96.11">Non tamen dicendum est, c velocius descensurum quam a; quia tunc non valeret proportio, cum mobilia differant in mole.
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1501 </s><s id="id.4.0.0.96.12">Sed si volumus ut ratio valeat, accipiamus dimidium c, ita ut eius moles aequetur moli a; erit iam gravitas c, 6: dimidiae vero aquae gravitas erit 3, ita ut dimidii c velocitas erit 3, respectu velocitatis a, quae erit 5: velocius itaque descendet a quam totum c (totum enim celeritate eadem movetur quam sui dimidium).
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1502 </s><s id="id.4.0.0.96.13">Verum itaque erit dicere, a celeritatem esse 5 respectu celeritatis dimidii c, quae erit 3; seu celeritatem totius c esse 6 respectu celeritatis dupli a, quae erit 10.
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1503 </s><s id="id.4.0.0.96.14">Patet <lb ed="Favaro" n="20"></lb> ergo quod, cum ratiocinamur de celeritate vel tarditate mobilium, oporteat intelligere de mobilibus illis, quorum <pb ed="manuscript" n="33r"></pb>differentia ex sola pendeat gravitate, cum tamen in mole sint aequalia.
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1504 </s><s id="id.4.0.0.96.15">Cum deinde velocitatum proportio inter haec collecta fuerit, haec eadem proportio servabitur inter mobilia eiusdem generis, quamvis deinde mole quantumvis differant: tanta enim cum velocitate descendit plumbi frustrum cuius gravitas sit 100 libras, quam plumbi frustrum cuius gravitas sit 100 libras.
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1505 </s></p><p><s id="id.4.0.0.97.01">DO. Hoc profecto mirabile videtur, et est contra Aristotelis opinionem. {1}
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1506 </s><s id="id.4.0.0.97.02">Arduum enim erit mihi illud credere, nisi aliquo modo persuadeas.
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1507 </s></p><p><figure id="id.4.0.0.98.00" xlink:href="FIG1/F054.jpg"></figure>
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1508 <s id="id.4.0.0.98.01"><lb ed="Favaro" n="30"></lb> AL. Ad hoc tibi suadendum satis deberent esse demonstrationes supra allatae; {2} quae etiam si non explicite hoc demonstrent, ex illis tamen pendet: at, si non tibi sufficiunt illae, alias in medium <pb ed="Favaro" n="404"></pb> afferam.
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1509 </s><s id="id.4.0.0.98.02">Utque ad intentum deveniam, hoc ut mihi concedas abs te peto: nempe, quod si fuerint duo mobilia, quorum alterum celerius altero moveatur, ista mobilia coniuncta movebuntur quidem celerius quam id solum quod tardius movebatur, tardius vero eo quod celerius mo vebatur.
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1510 </s><s id="id.4.0.0.98.03">Ut si, verbigratia, mobile a moveatur velocius quam b, dico, compositum ex ambobus a, b, tardius descensurum esse quam a solum, citius vero quam b solum.
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1511 </s><s id="id.4.0.0.98.04">Quod quidem luce clarius patet: cui enim dubium est, quod tarditas b retardabit celeritatem a, et, e contra, quod celeritas a intendet motum 6, et ita fiet motus quidam medius inter celeritatem ipsius a et tarditatem b? <lb ed="Favaro" n="10"></lb>
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1512 </s></p><p><s id="id.4.0.0.99.01">DO. Hoc negare nunquam <pb ed="manuscript" n="33v"></pb>ausus ero.
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1513 </s></p></subchap2><subchap2><p><figure id="id.4.0.0.1.00.00" xlink:href="FIG1/F055.jpg"></figure>
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1514 </p><p><s id="id.4.0.0.100.01">AL. Hoc supposito, si fieri potest per adversarios, moles magna citius moveatur quam moles parva (sint autem eiusdem materiae); et sit moles quidem magna a, moles vero parva sit b.
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1515 </s><s id="id.4.0.0.100.02">Si ergo b tardius movetur quam a, ergo, ex his quae supra posita sunt, compositum ex ambobus a, b tardius movebitur quam a solum: et sunt a, b eiusdem materiae: ergo moles maior eiusdem materiae tardius movebitur quam moles minor eiusdem materiae; quod quidem ex diametro illis opponitur, et est contra suppositum.
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1516 </s><s id="id.4.0.0.100.03">Non est ergo verum, quod moles magna citius moveatur quam parva, si eiusdem sint materiae; <lb ed="Favaro" n="20"></lb> quod, in toto progressu 4 De caelo, contra antiquos, tanquam notum supposuit Aristoteles.
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1517 </s><s id="id.4.0.0.100.04">Vide ergo quam firmis fundamentis innixus eorum confutaverit opinionem, qui non ponebant (uti vere non est ponendum) simpliciter grave et simpliciter leve, sed tantum levius et gravius in comparatione; et, consequenter, intueri potes quod habeant robur rationes illius, quibus absolutam gravitatem et levitatem in terra et igne, quin imo et gravitatem aquae et aëris in propriis locis, tribuere conatus est.
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1518 </s><s id="id.4.0.0.100.05">Sed, his omissis, ad propositum rediens, dico, eandem etiam in vacuo rationem habendam esse; nempe, mobilia quae fuerint eiusdem materiae, licet inaequalia magnitudine, eadem ferri <lb ed="Favaro" n="30"></lb> celeritate: quod eodem prorsus modo, quo in pleno, demonstrabitur.
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1519 </s></p><p><s id="id.4.0.0.101.01"><pb ed="manuscript" n="24v"></pb>DO. Ad reliquorum problematum solutionem regredi potes, quam auribus arrectis expecto.
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1520 </s></p></subchap2><subchap2><p><figure id="id.4.0.0.1.02.00" xlink:href="FIG1/F056.jpg"></figure>
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1521 </p><p><s id="id.4.0.0.102.01">AL. Nunc illius problematis meam accipito solutionem, quae ex solis supra positis innotescere potest: illius, nempe, in quo causa <pb ed="Favaro" n="405"></pb> expetebatur, cur naturalis motus velocior in fine quam in medio, et hic quam in principio, existat.
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1522 </s><s id="id.4.0.0.102.02">Memoria itaque repetendum est, quod supra fuit declaratum; nempe mobile, dum motu violento movetur, moveri quousque virtus a motore impressa fuerit maior gravitate resistente: ex quo sequitur ut, quando grave desinit ascendere, virtus in eo impressa aequetur eius gravitati; ex quo aperte sequitur ut, cum grave incipit moveri deorsum, tunc non moveatur simpliciter motu naturali.
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1523 </s><s id="id.4.0.0.102.03">Nanque in principio talis motus est adhuc in ipso mobili de virtute impressa, quae illud sursum impellebat: quae quidem, eo quod minor <lb ed="Favaro" n="10"></lb> est ipsa mobilis gravitate, ipsum amplius sursum non impellit; <pb ed="manuscript" n="25r"></pb>attamen adhuc resistit gravi deorsum petenti, eo quod adhuc non sit adnihilita.
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1524 </s><s id="id.4.0.0.102.04">Demonstratum est enim ipsam successive remitti; et hinc fit ut mobile in principio sui naturalis motus tarde moveatur: quia deinde virtus contraria remittitur ac debilitatur, movens, minorem inveniens resistentiam, celerius movetur.
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1525 </s><s id="id.4.0.0.102.05">Ut si, exempli causa, intelligamus mobile quod ex a in b motu violento moveatur, cuius gravitas sit 4, manifestum est quod virtus, quae ipsum impellit, b 4 erit in quolibet puncto ab lineae, a motu violento descriptae, maior quam 4: in ipso autem b non erit maior quam 4 (si enim <lb ed="Favaro" n="20"></lb> esset maior, ipsum mobile ultra b ab ea impelleretur); nec etiam erit minor (nanque ante b fuisset aequalis; at demonstrata est quod semper fuit maior); ergo virtus in b erit aequalis gravitati mobilis, nempe erit 4.
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1526 </s><s id="id.4.0.0.102.06">Cum ergo mobile recedit a b, virtus quae erat ut 4 incipit remitti, et, ob id, mobile incipit minorem habere resistentiam suae gravitati; quae resistentia eo quod continue remittatur, hinc fit quod motus naturalis continue intendatur.
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1527 </s></p><p><s id="id.4.0.0.103.01">DO. Haec solutio satis superque arridet: attamen videtur tantum locum habere in illo naturali motu, cui violentus praecesserit.
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1528 </s><s id="id.4.0.0.103.02">Sed quando quis habens lapidem in manu, quem non sursum impellat, sed <lb ed="Favaro" n="30"></lb> tantum derelinquat, in hoc motu, cui non praecessit violentus, quae erit causa intensionis?
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1529 </s></p></subchap2><subchap2><p><figure id="id.4.0.0.1.04.00" xlink:href="FIG1/F057.jpg"></figure>
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1530 </p><p><s id="id.4.0.0.104.01">AL. Isthaec dubitatio mihi quoque in mentem venerat, cum problematis explicationem excogitarem; quam cum accuratius intuerer, parvi esse mo<pb ed="manuscript" n="25v"></pb>menti depraehendi.
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1531 </s><s id="id.4.0.0.104.02">Intensio itaque in utroque motu, tam in eo cui praecessit quies, quam in eo cui motus naturalis praeivit, eandem ob causam accidit: nam etiam in motu naturali cui <pb ed="Favaro" n="406"></pb> praecessit violentus, mobile recedit a proportione aequalitatis, quae est proportio quietis.
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1532 </s><s id="id.4.0.0.104.03">Quod ut apertius intelligas, attende.
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1533 </s><s id="id.4.0.0.104.04">Sit mobile o, cuius gravitas sit 4: linea autem super quam fit motus violentus sit oe.
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1534 </s><s id="id.4.0.0.104.05">Manifestum est itaque, quod in mobile o potest imprimi tanta virtus, quae ipsum moveat usque ad r; quae virtus necessario erit maior quam 4, quae est gravitas mobilis potest etiam imprimi virtus, quae illud moveat tantum usque ad t; quae etiam erit maior quam 4, et minor ea quae impellebat usque ad r: potest etiam imprimi tanta vis, quae moveat molem usque ad s tantum; quae tamen erit maior quam 4, minor autem quam <lb ed="Favaro" n="10"></lb> illa quae impellebat usque ad t: et sic in infinitum potest 4 semper imprimi vis, quae per quaecunque minima spatia impellat mobile; attamen virtus illa semper erit maior quam 4.
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1535 </s><s id="id.4.0.0.104.06">Restat ergo ut illa virtus sit 4, quae mobile per nullum spatium motu impellit violento: ex quo patet ut, quando mobile o recedit ex manu, recedit cum tanta virtute, quae est ut 4; quae deinde a gravitate successive cum absumatur, motus intensionis est causa.
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1536 </s><s id="id.4.0.0.104.07">Et hoc, quod dixi, lucidius etiam apparebit si considerabimus quod, quando quod grave in manu quiescit, cum sua gravitate deorsum premat, oportet quod ab aliquo, nempe a manu, tanta vi sursum impellatur, quanta <lb ed="Favaro" n="20"></lb> est <pb ed="manuscript" n="26r"></pb>sua gravitas deorsum premens: alioquin, nisi ab altera tanta virtute sursum impellente impediretur, deorsum peteret, si minor esset resistentia; sursum vero, si maior.
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1537 </s><s id="id.4.0.0.104.08">Patet igitur quod, cum a substinente relinquitur, grave discedit ipsum tanta virtute impressa, quanta est propria gravitas; ex quo sequitur etc.
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1538 </s></p><p><s id="id.4.0.0.105.01">DO. Haec quae dicis admodum satisfaciunt; attamen adhuc restat nescio quid, quod mentem perturbat.
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1539 </s><s id="id.4.0.0.105.02">Nam si ex resistentia impressae virtutis accidit tarditas motus naturalis in principio, ipsa quidem aliquando absumetur, cum asseras eam continue remitti; ergo motus naturalis, quando dicta virtus erit adnihilata, non ulterius concitatior <lb ed="Favaro" n="30"></lb> fiet: quod tamen multorum opinioni adversatur.
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1540 </s></p></subchap2><subchap2><p><figure id="id.4.0.0.1.06.00" xlink:href="FIG1/F058.jpg"></figure>
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1541 </p><p><s id="id.4.0.0.106.01">AL. Quod hoc multorum opinioni adversetur, nil mea refert, dummodo rationi et experientiae congruat, et licet experientia contrarium potius interdum ostendat.
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1542 </s><s id="id.4.0.0.106.02">Si enim ab alta turri lapis descendat, illius celeritas semper augeri videtur: hoc tamen accidit quia lapis, respectu <pb ed="Favaro" n="407"></pb> medii per quod fertur, nempe aëris, est gravissimus; et cum discedat cum tanta virtute impressa, quanta est sua gravitas, discedit profecto cum multa virtute impressa, ad quam absumendam non sufficit motus ex altitudine turris: ex quo fit, ut per spatium unius turris semper intendatur celeritas.
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1543 </s><s id="id.4.0.0.106.03">Quod si acciperemus aliquod grave, cuius gravitas non tam longe aëris gravitatem superaret, tunc profecto oculis ipsis cerneremus, ipsum, paulo post principium motus, semper uniformiter moveri, existente tamen aëre tranquillissimo.
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1544 </s><s id="id.4.0.0.106.04">Et idem etiam in lapide <pb ed="manuscript" n="26v"></pb>accidere perspiceremus, si et ex locis altissimis de <lb ed="Favaro" n="10"></lb> mitteretur, et ita essemus constituti, ut semper eadem sub ratione lineam motus perspiceremus.
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1545 </s><s id="id.4.0.0.106.05">Nanque etiam noster situs impedit, quominus motus uniformitatem depraehendamus.
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1546 </s><s id="id.4.0.0.106.06">Fiat enim motus uniformis ex b in f, et sint bc, cd, de, ef spatia aequalia; oculus autem aspicientis sit in a, et ducantur lineae visuales ab, ac, ad, ae, af: et quia motus ponitur uniformis, et sunt bc, cd, de, ef spatia aequalia, transibit ergo mobile per ea in temporibus aequalibus.
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1547 </s><s id="id.4.0.0.106.07">Tempus ergo transitus ex b in c erit aequale tempori transitus <lb ed="Favaro" n="20"></lb> ex c in d: motus tamen ex c in d velocior inspicienti apparebit, cum et spacium cd maius appareat spacio bc (sub maiori nanque angulo spectatur).
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1548 </s><s id="id.4.0.0.106.08">Et ita motus ex d in e velocior apparebit quam qui ex c in d, cum spacium de maius appareat quam cd, et aequali in tempore transeatur a mobili: et simili ratione, motus ex e in f velocior apparebit motu ex d in e.
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1549 </s><s id="id.4.0.0.106.09">Quare et totus motus bf difformis apparebit, et semper in fine velocior, cum tamen uniformis supponatur.
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1550 </s><s id="id.4.0.0.106.10">Oportet igitur ad diiudicandum motus uniformitatem et difformitatem, ut spacium sit adeo amplum ut in ipso possit mobile <lb ed="Favaro" n="30"></lb> virtutem resistentem absumere, et ut oculus ita sit dispositus ut ab angulorum disparitate minime decipiatur.
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1551 </s></p><p><s id="id.4.0.0.107.01">DO. Satis superque pulcherrima tua elicatio a <pb ed="manuscript" n="27r"></pb>me percepta est.
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1552 </s><s id="id.4.0.0.107.02">Itaque circa materiam hanc non nisi unum tantum inquirendum mihi restat; et hoc est utrum credas, an grave quod deorsum demittatur et a movente aliqua vi deiciatur, in motu suo acceleretur sicut et <pb ed="Favaro" n="408"></pb> illud grave quod, descendens, a movente nullam vim deorsum impellentem recepit.
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1553 </s></p><p><s id="id.4.0.0.108.01">AL. Ex his quae supra posita sunt patet quod grave descendens, et ex statu quietis recedens, eo usque in motu acceleratur, quousque virtus impressa resistens adnihiletur; quod si virtus illa ab externo motore extinguatur, tunc non amplius in motu accelerabitur.
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1554 </s><s id="id.4.0.0.108.02">Ut, verbigratia, si grave, cuius gravitas sit 4, a statu quietis descendat, recedet profecto cum 4 resistentiae; quae cum a mobilis gravitate sit destruenda, segnior in principio fiet naturalis motus: quod si dicta virtus ut 4 ab externo motore absumatur, imprimendo in mobili <lb ed="Favaro" n="10"></lb> virtutem quae deorsum premat ut 4, tunc dubio procul grave non accelerabitur amplius in motu, cum in principio a nulla resistente virtute retardetur.
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1555 </s><s id="id.4.0.0.108.03">At si ab externo motore virtus imprimatur deorsum impellens quae minor sit quam 4, hoc est quam virtus quae impressa erat in mobili dum quiesceret, tunc profecto mobile accelerabitur; cum sit consumendum aliquid de virtute contraria, quae ab externo motore non tota ablata fuit.
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1556 </s><s id="id.4.0.0.108.04">Quod si mobili imprimatur virtus deorsum pellens maior quam 4, tunc velocior erit in principio naturalis motus: nam movebitur motu supranaturali, et quod excedat motum requisitum suae propriae gravitatis.
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1557 </s><s id="id.4.0.0.108.05">Ita ut <pb ed="manuscript" n="27v"></pb>suamet gravitas tunc haberet <lb ed="Favaro" n="20"></lb> rationem levitatis, eo quod ipsamet libera et simplex tardius descenderet quam cum impetu coniuncta: violentiae itaque deorsum impellenti resisteret propria et naturalis tarditas descendentis.
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1558 </s><s id="id.4.0.0.108.06">Et hoc exemplo manifestabitur, quod unicuique natanti saepius accidit.
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1559 </s><s id="id.4.0.0.108.07">Constat enim, quod homo in aqua existens, si voluerit, tanta est illius gravitas, quod descendet ad imum usque ipsius aquae; et tunc, a propria gravitate tractus, uniformi motu demergetur: quod si ab externo motore, quantumvis maxima vi, deorsum impellatur, ut si ab excelso loco praecipitetur, in principio quidem in aqua motus erit valde concitatus et supranaturalis; attamen a gravitate propria absoluta, <lb ed="Favaro" n="30"></lb> quae tunc, respectu gravitatis, quae cum impetu accepto est coniuncta, est veluti levitas, retardabitur motus, et eo usque donec descendens ad naturalem tarditatem devenerit; atque ita, si aqua satis fuerit profunda, non maiorem in fundo laesionem patietur, quam si ex aquae summitate proprio naturalique motu descendisset.
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1560 </s></p></subchap2></subchap1></chap><chap><subchap1><subchap2><p><s id="id.5.0.1.01.01">Non valet quod dicit Aristoteles, 4 Caeli t. 32: Impossibile est ignem habere gravitatem, quia alii substaret.
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1561 </s><s id="id.5.0.1.01.02">Si elementa transmutantur sd invicem, quomodo ignis non habebit gravitatem, quando fit ex aëre gravi? {2}
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1562 </s></p></subchap2><subchap2><p><s id="id.5.0.12.01.01">Vide Aristotelem, 1 Caeli t. 88, ubi dicit, naturalis motus semper augeri velocitatem, et, si in infinitum moveretur, infinite quoque augeretur velocitas.
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1563 </s></p><p><s id="id.5.0.12.02.01">Vide et t. 89, ubi dicit, maiorem terram citius ferri minore, nec motum naturalem accelerari ob extrusionem aëris: nam sic maior terra tardius moveretur quam parva, quia difficilius extruderetur; nec in motu acceleraretur, quia motus esset violentus, qui remittitur.
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1564 </s></p><p><s id="id.5.0.12.03.01">Benedictus Pererius, in lib. 14 cap. 3 prope finem, ita scribit: Nec dubitanter dixerim, si spacium aëris, per quod saxum fertur deorsum, <lb ed="Favaro" n="20"></lb> esset infinitum, eius saxi motum semper celeriorem et vehementiorem fore, nec ullam tamen eius ponderi factum iri accessionem.
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1565 </s><s id="id.5.0.12.03.02">Animadverte autem Pererii in sequentibus verbis errorem.
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1566 </s><s id="id.5.0.12.03.03">Dicit enim: Non recte concludit Aristoteles, Quia in motu naturali crescit velocitas, etiam in mobili crescere debere gravitatem: nam si lapis moveatur per spacium aliquod, priori parte densius atque crassius, posteriori autem tenuius et rarius, procul dubio motus erit velocior in fine, idque accidet non propter incrementum gravitatis.
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1567 </s></p></subchap2><subchap2><p><s id="id.5.0.13.01.01"><pb ed="Favaro" n="412"></pb> Iulius Scaliger, in opere suo adversus Cardanum, exercitat.e 28, adfert argumenta quaedam contra dicentes, proiecta ab aëre moveri.
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1568 </s></p></subchap2><subchap2><p><s id="id.5.0.18.01.01"><pb ed="Favaro" n="413"></pb> Quod fortius imprimatur virtus contraria in gravioribus, patet ex his quae, filo suspensa, huc illuc moventur: diutius enim, quo graviora fuerint, movebuntur.
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1569 </s></p><p><s id="id.5.0.18.02.01">Solidiora, graviora ac densiora diutius, acrius, faciliusque qualitates contrarias conservant omnes; ut lapides, qui in hieme longe frigidiores fiunt quam aër, in aestate vero calidiores.
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1570 </s></p></subchap2><subchap2><p><s id="id.5.0.26.01.01">Longinquitas a medio est infinita; sed propinquitas est finita et ab ipsomet centro determinata: si ergo erit aliquid hac facultate donatum, ut medium fugiat, hoc certe in infinitum moveri aptum erit. <lb ed="Favaro" n="20"></lb>
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1571 </s><s id="id.5.0.26.01.02">Quo quid absurdius?
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1572 </s></p><p><s id="id.5.0.26.02.01">Ille non potest esse naturalis motus, cui terminus assignari non potest: sed motui sursum terminus assignari non potest: ergo motus sursum non est naturalis.
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1573 </s><s id="id.5.0.26.02.02">Minor probatur: ibi terminatur motus, unde eodem motu recedere non licet (nam si ulterius eodem motu progredi posset, non esset ibi terminus): at motus sursum nullibi ita terminatur, ut inde eodem motu, nempe sursum, elongari non liceat: ergo motus sursum nullibi terminatur; ergo caret termino; ergo non potest esse naturalis.
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1574 </s><s id="id.5.0.26.02.03">Quod autem motus sursum nullibi possit statui terminus, a quo eodem motu elongari non liceat, patet: nam, <lb ed="Favaro" n="30"></lb> assignato quocunque loco, potest ab eo recedi ascendendo, et assignari alius qui eo magis a centro distet.
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1575 </s></p></subchap2></subchap1></chap><chap><subchap1><subchap2><p><s id="id.6.0.0.01.01"><pb ed="Favaro" n="418"></pb> Quaeri {1} potest, an gravia vere ad centrum moveantur; de quo Ptolemaeus, c. 7. p.i lib. Al.
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1576 </s></p><p><s id="id.6.0.0.02.01">Utrum virtus impressa, tempore vel gravitate mobilis consumetur.
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1577 </s></p><p><s id="id.6.0.0.03.01">Motus naturalis a quo fiat.
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1578 </s></p><p><s id="id.6.0.0.04.01">Motus violentus a quo fiat.
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1579 </s></p><p><s id="id.6.0.0.05.01">Utrum medium sit necessarium ad motum.
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1580 </s></p><p><s id="id.6.0.0.06.01">An detur simpliciter grave et simpliciter leve. {2}
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1581 </s></p><p><s id="id.6.0.0.07.01">An elementa in proprio loco sint gravia aut levia.
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1582 </s></p><p><s id="id.6.0.0.08.01">De proportione motuum eiusdem mobilis in diversis mediis.
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1583 </s></p><p><s id="id.6.0.0.09.01">De proportione motuum diversorum mobilium in eodem medio. <lb ed="Favaro" n="10"></lb>
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1584 </s></p><p><s id="id.6.0.0.10.01">De causa tarditatis et velocitatis motus.
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1585 </s></p><p><s id="id.6.0.0.11.01">An in puncto reflexionis detur quies.
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1586 </s></p><p><s id="id.6.0.0.12.01">An motus naturalis semper intendatur et cur intendatur.
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1587 </s></p><p><s id="id.6.0.0.13.01">Utrum tarditas et celeritas motus naturalis sit a raritate vel de.... me....
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1588 </s><s id="id.6.0.0.13.02">
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1589 </s><s id="id.6.0.0.13.03">In motu 3 considerantur: mobile, medium et movens.
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1590 </s></p><p><s id="id.6.0.0.14.01">Quid prosit aut obsit figura mobilium motui.
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1591 </s></p><p><s id="id.6.0.0.15.01">De proportione gravitatum eiusdem gravis in diversis mediis, es qua pendet quaestio de proportione motuum.
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1592 </s></p><p><s id="id.6.0.0.16.01">Data medii gravitate et velocitate mobilis, datur etiam gravitas <lb ed="Favaro" n="20"></lb> mob....
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1593 </s></p><p><s id="id.6.0.0.17.01">Data gravitate mobilis et medii, datur velocitas motus.
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1594 </s></p><p><s id="id.6.0.0.18.01">Data velocitate et gravitate mobilis, datur gravitas medii. {3}
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1595 </s></p><p><s id="id.6.0.0.19.01">De motu circulari.
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1596 </s></p><p><s id="id.6.0.0.20.01">Considerandum est de proportione motuum super planos inclinatos, et an forte leviora citius in principio descendant; sicut in lance, quo minora fuerint pondera, eo facilius fit motus.
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1597 </s></p><p><s id="id.6.0.0.21.01">Medium retardat motum naturalem hoc modo: ut, quando campana descendit, est quodammodo corpus solidum constans ex aëre incluso.... metallo, et ideo est levior quam si non adesset aër.
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1598 </s></p><p><s id="id.6.0.0.22.01">Mobilia leviora facile quidem moventur, dum moventi fuerint con....; sed, extra moventis manum, parum temporis impetum....
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1599 </s></p><p><s id="id.6.0.0.23.01">Argumentum dicentium, ideo motum in fine accelerari quia pau.... habet locum in his quae tota simul scindenda... non autem in his quorum partes tantum scindenti contiguae.... per in terebrando ligno.
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1600 </s></p></subchap2></subchap1></chap>
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1601 </body>
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1602 </text>
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1603 </archimedes>