Achillini, Alessandro (Achillinus, Alexander), Alexandri Achillini bononiensis De proportionibus motuum quaestio. , 1545

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              est, aut duci potest: propter mathematicos esse illos, qui Aristoteli </s>
              <s id="id.0.4.06.07">Quoddam vero moventium est divisibile: cuius virtus ad divisionem subiecti divisibilis </s>
              <s id="id.0.4.06.08">Hoc autem dupliciter est, quia si virtus motoris esset difformis in subiecto: tunc quantitativa motoris divisio per medietatem, non divideret virtutem per medium: et ad hoc advertebat Aristoteles 1 caeli, tex. com. 50 licet illa pars textus pertineret ad textum </s>
              <s id="id.0.4.06.09">De virtute igitur uniformiter extensa intelligendum est hoc </s>
              <s id="id.0.4.06.10">Sed Averrois Aristotelem restringebat 7 physicor. com. 35 ad corpora quae extrinsecus </s>
              <s id="id.0.4.06.11">Sed oportet Averroim uti etiam restrictione data scilicet virtutem corporis esse uniformiter extensam: aliter divisio corporis per medietatem eius non divideret virtutem ad movendum praecise per </s>
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              <s id="id.0.4.07.01">Moventium etiam quaedam virtutem habent in actu: sic quod diviso corpore virtus dividitur: ut gravitas plumbi in plumbo: aliquando vero non, ut Sorte et Platone moventibus navem, quam neuter illorum movere potest sine alterius adiutorio, de motore primo modo intelligitur iuxta Averroim 7 physico. com. 33 scilicet de motore in actu: non autem de motore in potentia: divisionem autem motoris specificat Averrois 7 physicor. com. 35 dicens diviso motu id est dimidiato: contingit necessario ut proportio potentiae motoris ad motum sit dupla illius proportionis, et sic velocitas erit dupla ad velocitatem: quod si contra hoc </s>
              <s id="id.0.4.07.02">Sit a. potentia movens a proportione dupla, et faciat c. motum: tunc medietas motus c. fit a medietate proportionis motoris ad motum: sed ab aequalitate non fit motus, ergo aequalitas non est medietas duplae </s>
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              <s id="id.0.4.08.01">Respondeo: Primo dictum Averro. supponit dimidiatum esse motum, et argumentum non praesupponit hoc, sed inquirit: ideo respondeo quod motus a proportione maiori quam dupla dimidiari potest: sed motus a dupla proportione, aut minori quam dupla non potest dimidiari, quia ad tam parvam proportionem res ducta est, quod medietas illius proportionis movere non potest: et sic assumptum argumenti </s>
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              <s id="id.0.4.09.01">Secundo, dico quod Averrois ex dimidiato motu concludit dimidiatam esse proportionem, quae consequentia valet, quia effectus praesupponit </s>
              <s id="id.0.4.09.02">Sed arguens ex dimidiata proportione arguit: non valet autem consequentia, dimidiata est proportio, ergo dimidiatus est motus licet aliquam valeat gratia terminorum: in quibus arguitur, ut in proportionibus magnis, puta maioribus </s>
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              <s id="id.0.4.10.01">Tertio, dico quod medietas motus intelligi potest quantitativa, et illa provenit ab eodem motore, quia facit totum motum: sed in medietate temporis: dummodo motor non fatigetur: et sit paritas ex parte resistentiae, et aliorum: et de hac intelligit Aristoteles 6 physi. dixit enim Averrois 6 physicor. commen. </s>
              <s id="id.0.4.10.02">Continuatio in istis primo invenitur in magnitudine, et propter magnitudinem invenitur in motu, et propter motum in </s>
              <s id="id.0.4.10.03">Dupliciter enim diviserat motum Aristoteles 6 physicor. tex. commen. 33 scilicet divisione temporis, et divisione </s>
              <s id="id.0.4.10.04">Alia autem est pars motus intensiva, et istam non habet motus a magnitudine, quam stat esse ita parvam, quod ipsa seorsum existere non potest, quoniam pars est in potentia, non autem in actu: et secundum istam divisionem motus intelligitur dividi proportionem secundum quantitatem suae denominationis: non tamen sic quod infinite parvus motus ab infinite parva proportione nascatur, neque oppositum supra dictum est: quia natura tantam diminutionem non tolerat: quia nulla minoritas movere potest, neque ulla aequalitas id est potentia habens ad resistentiam minoritatem vel aequalitatem movere non potest cum datis circunstantiis: sed solum potentia habens super resistentiam proportionem maioris inaequalitatis: non enim distinguo proportionem a re cuius est proportio, nisi forte ratione, ut dixi in libro </s>
              <s id="id.0.4.10.05">Sed si infinite parvus motu; sit a proportione maiori provenit quam sit </s>
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            <p>
              <s id="id.0.4.11.01">Nota quod hoc inter has duas stellas iterum supradictum est, sed sic repertum est in </s>
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              <s id="id.0.4.12.01">Prima </s>
              <s id="id.0.4.12.02">Si aliqua potentia movet aliquam resistentiam, medietas motoris movebit medietatem mobilis, praecise eam velociter: regula est Philosophi 7 physico. tex. commen. 36 quia aequalis est proportio totius motoris supra totum mobile: et medietatis motoris supra medietatem moti, et tertii motoris supra tertiam moti, et quarti supra </s>
              <s id="id.0.4.12.03">Et mathematice imaginando, et sic in infinitum, vel naturae imaginationem confirmando, usque ad minimum naturae, et adverte quod eorum prius deducatur per divisionem ad minimum, an motor, an mobile, an motus et cetera probatur per regulam permutatim proportinabilium ex 12 diffinitione quinti geometriae </s>
              <s id="id.0.4.12.04">Qualis est proportio totius motoris ad suam medietatem, talis est proportio totius mobilis ad suam medietatem, ergo </s>
              <s id="id.0.4.12.05">Qualis est proportio totius motoris ad totum mobile, talis est proportio medietatis motoris ad medietatem </s>
              <s id="id.0.4.12.06">Sciendum quod motorum quoddam est indivisibile: ut intellectus, et tunc intellige per medietatem motoris, virtutem in duplo minus perfectam, ut praedictum est, quia illa esset praecise habens virtutem in duplo minorem quam prior motor, quia ad mathematicas imaginationes disputatio ducta est propter Mathematicos eos esse, qui Aristoteli </s>
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              <s id="id.0.4.13.01">Contra regulam arguitur per Philosophum 7 physicor. textu commenti </s>
              <s id="id.0.4.13.02">Si ab aliqua potentia provenit aliquis effectus velocitatis, non oportet quod pars illius effectus a parte motoris proveniat, ut patet de corbe millii cadente, quae sonat, et granum millii cadens nullum sonum facit, quia granum non habet potentiam velociter percutiendi medium, et praeveniendi aere in motu eius:et de gutta lapidem cavante: ut dixit Aristoteles 8 physic. textu com. </s>
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              <s id="id.0.4.14.01">Respondeo: Duplex est genus potentiarum agentium, quoddam per divisionem corrumpitur: et istis regula non applicatur, quia non assumitur medietas motoris, quia medietas rei, quae est motor, nihil habet de virtute ad </s>
              <s id="id.0.4.14.02">Quoddam autem est genus potentiae non corrumpitur per divisionem, sed medietas virtutis immediate motoris conservatur: et de isto genere potentiarum intelligitur regula: modo potentia sonandi non dividitur cum dividitur totum, sed </s>
              <s id="id.0.4.14.03">Ad confirmationem de guttis cadentibus: priores guttae praeparant ultimae, ita ut ultima gutta lapidem scindere possit: et sic totus effectus ab ultima gutta fit: inveniente tamen materiam didispositam per praecedentes guttas: ut declarat Averrois 8 physicor. comment. </s>
              <s id="id.0.4.14.04">Hic correlarie additur regula 7 physico. tex. com. </s>
              <s id="id.0.4.14.05">Si aliqua potentia movet aliquod mobile, per aliquod spatium, in aliquo tempore, ipsa movet illud mobile in medietate temporis per medietatem </s>
              <s id="id.0.4.14.06">Sermo hic intelligitur de potentia non variante proportionem suam ad motum, et sic potentia non debilitatur, neque fortificatur, neque adiuvatur magis quam prius: neque crescit, aut decrescit resistentia ex parte medii, mobilis, aut impedimenti, patet permutando, quia qualis est proportio totius temporis motus ad medietatem eius: talis est proportio totius temporis motus ad medietatem motus: ergo sicut in toto tempore totus motus completur: ita in medietate temporis medietas motus expeditur.</s>
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              Secunda </s>
              <s id="id.0.4.15.03">Si aliqua potentia movet aliquod mobile, ipsa movet resistentiam in duplo minorem praecise in duplo velocius, et hoc sive moveat a proportione dupla, sive a maiori quam dupla, sive a minori quam dupla, quia in duplo maius est dominium totius supra medietatem mobilis quam supra totum </s>
              <s id="id.0.4.15.04">Istam voluit Aristoteles 7 physicorum, tex. commen. </s>
              <s id="id.0.4.15.05">Adverte tamen accidens potens regulam impedire: ut si medietas resistentiae seorsum existere non </s>
              <s id="id.0.4.15.06">Contra excessus potentiae supra medietatem est plus quam duplus ad excessum potentiae supra totum: ergo velocitas supra medietatem est plus quam dupla ad velocitatem supra totum: data enim proportione sesquialtera, praecise duplus est excessus super medietate ad excessum super toto: ut 3 excedunt duo per unum, et 3 excedunt unum per </s>
              <s id="id.0.4.15.07">Data autem proportione minori quam sit sesquialtera, quae sit maioritas, tunc excessus potentiae supra resistentiam est minus quam medietas excessus potentiae supra medietatem resistentiae; ut quatuor excedunt tria per unum, et excedunt unum medium per duo </s>
              <s id="id.0.4.15.08">Sed data proportione maiori quam sesquialtera excessus potentiae supra medietatem est minus quam duplus ad excessum potentiae supra resistentiam: ut 2 excedunt 1 per 1 et 2 excedunt medietatem unius per </s>
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              <s id="id.0.4.16.01">Secundo stat proportionem motoris supra medietatem resistentiae esse minus quam duplam ad proportionem motoris supra resistentiam: ut fit motor: ut 8 sit totum mobile, ut 2 sit meditas [=medietas] mobilis, ut unum: tunc octupla est minus quam dupla ad quadruplam: quia praecise est sesquialtera illi, quia octupla est tres duplae, quia 8. 4. 2. 1 tantum tres duplas claudunt, et quadrupla est duae duplae.</s>
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              <s id="id.0.4.17.01">Tertio sequitur Sortem proiicientem ad certam distantiam, mediocrem lapidem totis viribus proiicere medietatem illius ad duplam distantiam, quod est contra </s>
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              <s id="id.0.4.18.01">Ad primum: negatur consequentia, quia non sequitur proportio velocitatum proportionem excessuum: sed proportionem geometricam dominiorum agentium supra </s>
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              <s id="id.0.4.19.01">Ad secundum negatur assumptum, immo octupla est quatuor duplae quia 2 est denominator duplae: et 2 quater clauditur in 8 quae sunt denominator </s>
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              <s id="id.0.4.20.01">Ad tertium negatur consequentia: quia ex parte agentis accipi habent omnia quae iuvant, et quantum iuvant agens: et ex parte resistentiae, omnia quae impediunt aut resistunt, a proximatione enim augetur proportio 4 caeli, commen. 44 et </s>
              <s id="id.0.4.20.02">Imaginatur enim periferia virtutis agentis, et in parti distantiore virtus est minus potens, et in propinquiore magis </s>
              <s id="id.0.4.20.03">Et in centro periferiae virtus est </s>
              <s id="id.0.4.20.04">In circunferentia vero ad non gradum: exempli gratia </s>
              <s id="id.0.4.20.05">Est autem Sortes mediatum movens post separationem lapidis a manu: quia movit, non quia moveat: in initio enim motus movet Sortes medium et lapidem: et si aer sit medium, aer impulsus movetur a se, et portat lapidem, ut 3 de elementis dixi: neque oportet lapidem in duplo minorem esse, ita bene proportionatum virtuti impellenti, sicut erat lapis in duplo </s>
              <s id="id.0.4.20.06">Tum etiam melius vincitur resistentia medii a lapide maiori quam minori: plus enim de gravitate secum affert maior quantitas stante aequali densitate, et non multum variata figura quam minor, ergo plus habet de virtute ad medium dividendum maior quantitas quam </s>
              <s id="id.0.4.20.07">Tum etiam stat non ita bene applicari manum parvo lapidi, sicut applicatur lapidi aliquantulum </s>
              <s id="id.0.4.20.08">Addunt aliqui circulos in aere aut aqua faciendos et cetera et vide Averroim octavo physicorum commento </s>
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              Tertia </s>
              <s id="id.0.4.21.03">Si aliqua potentia movet aliquod mobile: dupla potentia movebit illud mobile in duplo velocius: quia duplum ad potentiam, habet supra mobile proportionem praecise in duplo </s>
              <s id="id.0.4.21.04">Istam voluit Aristoteles 7 physi. tex. com. </s>
              <s id="id.0.4.21.05">Sive movet potentia a proportione dupla, sive a maiori proportione quam dupla, sive a </s>
              <s id="id.0.4.21.06">Corollarium, movens plusquam duplum ad potentiam moventem, plusquam in duplo velocius </s>
              <s id="id.0.4.21.07">Corollarium secundum, movens plusquam duplum ad potentiam moventem, movet medietatem resistentiae plusquam in duplo velocius: partem huius regulae ponit Averrois 8 physicor, commen. </s>
              <s id="id.0.4.21.08">Si maior magnitudo fuerit dupla minoris, erit tempus motionis illius, huius </s>
              <s id="id.0.4.21.09">Contra sequitur, quod quocunque dato habente adminus se maioritatem, quaecunque fuerit maioritas: ad idem habebit duplum proportionem praecise in duplo </s>
              <s id="id.0.4.21.10">Secundo, quocunque movente a proportione dupla, dabile est duplo tardius movens ex 6. physicor. tex. com. 15 immo in quadruplo: et sic in infinitum: infinite enim parvum spatium pertransiens in certo tempore, imaginatur aliquid quod localiter movetur: et tamen, non in infinitum maius est a dupla proportione movens: ergo non aequalis est proportio moventium in medio: talis est proportio </s>
              <s id="id.0.4.21.11">Tertio diminuatur potentia usque ad aequalitatem resistentiae: tunc infinite parvus aliquando erit motus, et nunquam infinite parvus erit motor: ergo non qualis est proportio motorum: talis est proportio </s>
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              <s id="id.0.4.22.01">Ad primum, conceditur consequens, ad quodcunque enim quatuor comparentur in aliqua proportione se habentia: ad illud in duplo maiorem proportionem habent 8 quam 4 ut patet consideranti proportiones denominationum 4 ad 1 sunt quadruplum 8 vero octuplum: 4 ad 2 sunt duplum. 8 vero quadruplum. 4 ad 3 sunt sesquitertia. 8 vero sunt dupla superbitertia. 4 ad 4 sunt aequale. 8 vero ad 4 sunt duae aequalitates: dictum enim est, quod quemadmodum 2 est duplum ad 1 ita dupla est aequalitati </s>
              <s id="id.0.4.22.02">Idem patet in minoritatibus, quia 4 ad 6 sunt duae tertiae. 8 vero sunt quatuor </s>
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              <s id="id.0.4.23.01">Ad secundum negatur </s>
              <s id="id.0.4.23.02">Ad probationem non dixit Aristoteles in duplo vel triplo tardius: ideo concesso dicto Aristotelis negatur assumptum argumenti: conceditur tamen quod imaginabile est illud, quia naturae continuorum non </s>
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              <s id="id.0.4.24.01">Ad tertium negatur assumptum, scilicet infinite parvus aliquando erit motus, quia dantur minima in </s>
              <s id="id.0.4.24.02">Sed conceditur quod non infinite parvus erit motor, sed tamen infinite parvum erit dominium, respectu huius resistentiae, sed non similiter: et licet dominium et motor sint idem, ratione tamen differunt, et sic stat infinite minorari unum et non </s>
              <s id="id.0.4.24.03">Sciendum tamen quod quantitas motoris absolute accipi potest, et respectu determinatae resistentiae, sit exempli gratia motor, ut 8 resistentia vero ut 4 et alio numero signatur motor, puta ut 8 et proportionis denominator: ut puta 2 et neuter istorum numerorum deducitur ad non quantum: sed numerus virtutis motoris deducitur ad non excedere resistentiam </s>
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              Quarta </s>
              <s id="id.0.4.25.03">Si aliqua potentia movet suum mobile aeque velociter cum alia: tunc illae potentiae congregatae moverent mobilia congregata aeque velociter sicut prius movebat una illarum suum mobile, quia ab eadem proportione movent ambae sicut una earum quia aeque proportionalia coniunguntur: iuxta decimamtertiam propositionem quinti geomatriae Euclidis: et etiam iuxta primam propositionem eiusdem quinti: propositio decimatertia quinti, si fuerit quotlibet quantitatum ad totidem alias proportio una: erit quoque quae proportio unius ad unam eadem proportio omnium pariter acceptarum ad alias pariter acceptas.</s>
              <s id="id.0.4.25.04">Istam vult Philosophus 7 physicor. tex. com. </s>
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              <s id="id.0.4.25.06">Sit a. grave in aere velociter descendens: ut 4.b. vero sit leve aequaevelociter ascendens, et </s>
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