Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N1C8AF" level="3" n="2" type="other" type-free="tractatus">
              <div xml:id="N1DD6A" level="4" n="3" type="chapter" type-free="capitulum">
                <p xml:id="N204AB">
                  <s xml:id="N204AC" xml:space="preserve">
                    <pb chead="De motu locali quo ad effectū tꝑe difformi" file="0168" n="168"/>
                  ad tempus menſurari habet penes gradum mediū
                    <lb/>
                  </s>
                  <s xml:id="N204B5" xml:space="preserve">Omniſ difformiter difformis quo ad tempus pe­
                    <lb/>
                  nes reductionem ad vniformitatem ſiue penes cal-
                    <lb/>
                  culationem denominationis: et ſi in nõ nullis caſi-
                    <lb/>
                  bus difficile ſit aut impoſſibile naturaliter ad admiſ­
                    <lb/>
                  ſim infallibiliter velocitatem menſurare. </s>
                  <s xml:id="N204C0" xml:space="preserve">Hec cõ­
                    <lb/>
                  cluſio ſuum colorem apparentiam et probabilita-
                    <lb/>
                  tem ex ſuperioribus ſortitur.</s>
                </p>
                <p xml:id="N204C7">
                  <s xml:id="N204C8" xml:space="preserve">Ad rationes ante oppoſitum </s>
                  <s xml:id="N204CB" xml:space="preserve">Ad pri-
                    <lb/>
                  mam reſponſum eſt ibi vſ ad vltimam replicã ad
                    <lb/>
                  quã reſpondeo concedendo ſequelam: et negãdo fal­
                    <lb/>
                  ſitatē cõſequentis: et cū ꝓbatur / quia alias ſequere-
                    <lb/>
                  tur mobile qḋ continuo īfinite velociter intēdit mo­
                    <lb/>
                  tū ſuū infinite tarde moueri: nego illã ſequelã et ad
                    <lb/>
                  ꝓbationē admitto caſū: et ad argumentū cõcedo an­
                    <lb/>
                  tecedēs capiēdo ly infinita ī maiore et minore ſin ca­
                    <lb/>
                  thegorematice et nego cõſequētiã.
                    <note position="left" xlink:href="note-0168-01a" xlink:label="note-0168-01" xml:id="N20505" xml:space="preserve">.1. correl.</note>
                  </s>
                  <s xml:id="N204E3" xml:space="preserve">¶ Ex quo ſequit̄̄ /
                    <lb/>
                   in caſu poſito quodlibet illoꝝ īmediate poſt hoc
                    <lb/>
                  infinita tarditate mouebit̄̄ et tñ īmediate poſt hoc
                    <lb/>
                  infinita velocitate mouebitur aliquod illorū </s>
                  <s xml:id="N204EC" xml:space="preserve">Cor-
                    <lb/>
                  relarium hoc facile patet ex caſu.
                    <note position="left" xlink:href="note-0168-02a" xlink:label="note-0168-02" xml:id="N2050B" xml:space="preserve">2. correl.</note>
                  </s>
                  <s xml:id="N204F6" xml:space="preserve">¶ Sequitur ſecun­
                    <lb/>
                  do /  in caſu poſito qḋlibet iſtoꝝ īmediate poſt hoc
                    <lb/>
                  in infinitū modicū ſpacium per aliquod tempus ꝑ-
                    <lb/>
                  tranſibit: et tñ īmediate poſt hoc infinite magnum
                    <lb/>
                  ſpaciū ꝑtrãſibit aliquod illoꝝ ꝑ aliquod tempus.</s>
                </p>
                <p xml:id="N20511">
                  <s xml:id="N20512" xml:space="preserve">Patet correlariū / quia ſpacia velocitatibus cõmē­
                    <lb/>
                  ſurantur.
                    <note position="left" xlink:href="note-0168-03a" xlink:label="note-0168-03" xml:id="N205D1" xml:space="preserve">.3. correl:</note>
                  </s>
                  <s xml:id="N2051C" xml:space="preserve">¶ Sequitur tertio /  īmediate poſt hoc in­
                    <lb/>
                  finita tarditate mouebitur aliquod illorum: et nul­
                    <lb/>
                  lum iſtorum īmediate poſt hoc mouebitur ita tarde
                    <lb/>
                  ſicut a. et a. mouebitur: et ipſuꝫ a. nõ īmediate pꝰ hoc
                    <lb/>
                  infinita tarditate mouebitur. </s>
                  <s xml:id="N20527" xml:space="preserve">Probatur correlari­
                    <lb/>
                  um et pono caſum /  ſint infinita mobilia a. b.c. etc. et
                    <lb/>
                  incipiat a. moueri ab octauo vſ ad non gradum ī
                    <lb/>
                  hora vniformiter difformiter: et b. a gradu duplo
                    <lb/>
                  vſ ad non graduꝫ in prima medietate: et c. adhuc
                    <lb/>
                  a gradu duplo ad illum in prima quarta hore vſ
                    <lb/>
                  ad non gradum. </s>
                  <s xml:id="N20536" xml:space="preserve">et d. a gradu duplo a quo incipit c.
                    <lb/>
                  in prima octaua hore vſ ad non gradum et ſic in ī­
                    <lb/>
                  finitum </s>
                  <s xml:id="N2053D" xml:space="preserve">Quo poſito ſequitur /  immediate pꝰ hoc
                    <lb/>
                  infinita tarditate mouebitur aliquod iſtoruꝫ: quia
                    <lb/>
                  immediate poſt hoc erit aliquod iſtorum prope nõ
                    <lb/>
                  gradum motus: et aliud in duplo propinquius non
                    <lb/>
                  gradui: et aliud in quadruplo: et ſic conſequenter / et
                    <lb/>
                  nullum iſtorum immediate poſt hoc mouebitur ita
                    <lb/>
                  tarde ſicut a. quoniam quodlibet illorum incipit ve­
                    <lb/>
                  locius moueri quã a. dempto a. et quodlibet illoruꝫ
                    <lb/>
                  immediate poſt hoc per aliquod tempus mouebi-
                    <lb/>
                  tur velocius quã a. / ergo nullum iſtorum immedia-
                    <lb/>
                  te poſt hoc mouebitur ita tarde ſicut a. in eodem tē-
                    <lb/>
                  pore </s>
                  <s xml:id="N20556" xml:space="preserve">Et  a. nõ immediate poſt hoc infinita tardi-
                    <lb/>
                  tate mouetur. </s>
                  <s xml:id="N2055B" xml:space="preserve">Probatur / quia immediate poſt hoc
                    <lb/>
                  mouetur maiori quã vt .6. / igitur non infinita tardi­
                    <lb/>
                  tate mouebitur. </s>
                  <s xml:id="N20562" xml:space="preserve">Et ſic patet correlariū. </s>
                  <s xml:id="N20565" xml:space="preserve">¶ Ad ṗmaꝫ
                    <lb/>
                  confirmationē reſponſum eſt ibi vſ ad vltimaꝫ re­
                    <lb/>
                  plicam: ad quã reſpondeo negando ſequelam im-
                    <lb/>
                  mo dico /  poſſibile eſt  eque velociter geometrice
                    <lb/>
                  intendatur vnus motus in tempore finito ſicut al-
                    <lb/>
                  ter remittitur ipſis in principio exiſtentibus equa-
                    <lb/>
                  libus: ſed oportet illum qui intenditur infinitam ve­
                    <lb/>
                  locitatem acquirere in illo tempore finito in quo al­
                    <lb/>
                  ter motus remittitur ad non gradum. </s>
                  <s xml:id="N20578" xml:space="preserve">et ad proba-
                    <lb/>
                  tionem ſequele dico /  rñſio loquit̄̄ de motu q̇ vſ
                    <lb/>
                  ad certū gradū finite intenditur: et de tali bene con­
                    <lb/>
                  cedo  nõ eſt poſſibile ipſū eque velociter ꝓportio-
                    <lb/>
                  nabiliter intēdi ſicut alter motus ad non gradū re­
                    <lb/>
                  mittit̄̄. </s>
                  <s xml:id="N20585" xml:space="preserve">¶ Ad ſecundã confirmationem que facilis ē:
                    <lb/>
                  rñdeo negãdo ſequelã īmo dico /  qñ vnus eſt remiſ­
                    <lb/>
                  ſus ad ſubduplū alter eſt remiſſus ad nõ gradū. </s>
                  <s xml:id="N2058C" xml:space="preserve">Et
                    <lb/>
                  cū ꝓbatur /  non q2 qñ vnus eſt remiſſus ad ſubdu­
                    <cb chead="De motu locali quo ad effectū tꝑe difformi"/>
                  plum perdidit proportioneꝫ duplam: et alter remit­
                    <lb/>
                  titur in duplo velocius adequate: ergo debuit per­
                    <lb/>
                  didiſſe proportionem quadruplam preciſe q̄ eſt du­
                    <lb/>
                  pla duple: nego conſequentiam. </s>
                  <s xml:id="N2059A" xml:space="preserve">Et ratio eſt / q2 illḋ
                    <lb/>
                  mobile non ſufficit ad illum motum remitti in du-
                    <lb/>
                  plo velocius altero qnia hic non loquimur de velo­
                    <lb/>
                  citate geometrica ſed arithmetica que debet attē-
                    <lb/>
                  di penes latitudinem deperditam: et non penes ꝓ-
                    <lb/>
                  portionem deperditam et ſic debet ſemper capi quã­
                    <lb/>
                  do dicitur eque velociter, ſi non addatur propor-
                    <lb/>
                  tionabiliter aut geometrice. </s>
                  <s xml:id="N205AB" xml:space="preserve">¶ Ad tertiam confir-
                    <lb/>
                  mationem reſpondeo negando ſequelam: et cum ꝓ­
                    <lb/>
                  batur / quia ſemper a. in duplo velocius acquiret la­
                    <lb/>
                  titudinem quã b. et hec intenſio procedit in infinituꝫ
                    <lb/>
                  etc. / igitur aliquando a. erit duplus motus ad b. ne-
                    <lb/>
                  go conſequentiam: et cum probatur conſequentia.
                    <lb/>
                  </s>
                  <s xml:id="N205B9" xml:space="preserve">quia per infinituꝫ latitudo acquiſita ipſi a. excedet
                    <lb/>
                  latitudinem acquiſitam ipſi b. / ergo aliquando mo­
                    <lb/>
                  tus a. erit duplus ad motum b. conceſſo anteceden-
                    <lb/>
                  te nego conſequentiam / vt argumentum probat eã
                    <lb/>
                  negandam eſſe. </s>
                  <s xml:id="N205C4" xml:space="preserve">¶ Ad quartam confirmationem reſ­
                    <lb/>
                  ponſum eſt vſ ad vltimam replicam ad quam reſ­
                    <lb/>
                  pondet ſeptima propoſitio primi notabilis huius
                    <lb/>
                  queſtionis cum annotationibus ibi poſitis.</s>
                </p>
                <p xml:id="N205D7">
                  <s xml:id="N205D8" xml:space="preserve">Ad ſecundam rationem reſpondeo cõ­
                    <lb/>
                  cedēdo ſequelã et negando falſitatem conſequentis
                    <lb/>
                  et ad ꝓbationem concedo  illi motus ſunt equales
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                  in principio et equales in fine et equalem latitudinē
                    <lb/>
                  deperdunt in totali illo tēpore cathegorematice: et
                    <lb/>
                  cū infertur / ergo in toto illo tꝑe ſunt equales: nego
                    <lb/>
                  illã conſequentiam: quia non mediantibus eis eq̈-
                    <lb/>
                  le ſpaciū pertranſitur / vt patet ex tertia concluſiõe
                    <lb/>
                  tertii notabilis: et ex deductione argumēti. </s>
                  <s xml:id="N205EB" xml:space="preserve">Et hec ē
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                  ſolutio ibi poſita. </s>
                  <s xml:id="N205F0" xml:space="preserve">Et ad replicam conceditur ſeque­
                    <lb/>
                  la: et negatur falſitas ↄ̨ñtis vt docet argumentum:
                    <lb/>
                  et ſecundum correlarium tertie propoſitionis ter-
                    <lb/>
                  tii notabilis.</s>
                </p>
                <p xml:id="N205F9">
                  <s xml:id="N205FA" xml:space="preserve">Ad tertiam rationeꝫ reſpondeo negã­
                    <lb/>
                  do ſequelam. </s>
                  <s xml:id="N205FF" xml:space="preserve">immo dico /  dabitur certa intenſio ī
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                  caſu poſito in argumento. </s>
                  <s xml:id="N20604" xml:space="preserve">ſed non erit rationalis
                    <lb/>
                  ad intenſionem velocitatis prime partis: </s>
                  <s xml:id="N20609" xml:space="preserve">Nec hoc
                    <lb/>
                  requiritur. </s>
                  <s xml:id="N2060E" xml:space="preserve">Quod tamen totalis ille motus ſit intē­
                    <lb/>
                  ſior motu vt ſex vniformi probatur / quia ſi hora eēt
                    <lb/>
                  diuiſa in duas partes equales et in prima illarum
                    <lb/>
                  mobile moueretur vt octo. et in ſecunda vt quatuor
                    <lb/>
                  totus motus eſſet vt ſex (vt notum eſt) ſed motus iſte
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                  de quo fit mentio in caſu argumenti eſt intenſior:
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                  cū maior pars quã medietas ſit vt octo et reſidua vt
                    <lb/>
                  4. / ergo ſequitur /  ille motus eſt intenſior quã mo-
                    <lb/>
                  tus vt ſex / quod fuit probandum. </s>
                  <s xml:id="N20621" xml:space="preserve">Et ad primam re-
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                  plicam dictum eſt ibi. </s>
                  <s xml:id="N20626" xml:space="preserve">Ad vltimam vero reſpondeo
                    <lb/>
                  negando conſequentiam ſicut docet eam negandã
                    <lb/>
                  ſecunda concluſio huius capitis vide eam ibi.</s>
                </p>
                <p xml:id="N2062D">
                  <s xml:id="N2062E" xml:space="preserve">Ad quartam rationem reſponſum eſt
                    <lb/>
                  ibi vſ ad replicam ad quam replicam cum ſuis cõ­
                    <lb/>
                  firmationibus patet reſponſio ex duodecima con-
                    <lb/>
                  cluſione huius capitis cuꝫ ſuis correlariis: </s>
                  <s xml:id="N20637" xml:space="preserve">Uide eã
                    <lb/>
                  </s>
                  <s xml:id="N2063B" xml:space="preserve">Et hec de queſtione et capitulo tertio.</s>
                </p>
              </div>
              <div xml:id="N2063E" level="4" n="4" type="chapter" type-free="capitulum">
                <head xml:id="N20643" xml:space="preserve">Capitulum quartum in
                  <lb/>
                quo diſputatiue īquiritur
                  <lb/>
                quõ motus difformis quo
                  <lb/>
                ad ſubiectū et tp̄s ſimul: pa­
                  <lb/>
                riter motus mixti veloci­
                  <lb/>
                tas cognoſci debeat.</head>
                <p xml:id="N20650">
                  <s xml:id="N20651" xml:space="preserve">ABſoluta ſuperioribus capiti-
                    <lb/>
                  bus doctrina perſcrutande motus dif-
                    <lb/>
                  mis quo ad ſubiectū et difformis quo ad </s>
                </p>
              </div>
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