Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
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                    <pb chead="Primi tractatus" file="0083" n="83"/>
                  b. tranſeundo .ef. partem ad latitudinem deperdi­
                    <lb/>
                  tam ab eadem potentia tranſeundo d. parteꝫ ade­
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                  quate in g. tempore nõ eſt proportio h. nec maior:
                    <lb/>
                  igitur ſi a. potentia ſtat vel intenditur in potentia
                    <lb/>
                  per g. tempus tranſeundo .ef. partem etc. / ſequēdo
                    <lb/>
                  b. potentiam latitudinis deperdite ab a. potentia
                    <lb/>
                  inuariata vel intendente potentiam ſuam tranſe­
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                  undo .ef. partem ad latitudinem deperditam a b.
                    <lb/>
                  potentia tranſeundo d. partem in g. tempore ade­
                    <lb/>
                  quate non eſt proportio h. nec maior: ſed cõſeq̄ns
                    <lb/>
                  eſt falſum / igitur et antecedens videlicet /  a. potē-
                    <lb/>
                  tia ſtat vel intenditur in potentia per g. tempꝰ trã­
                    <lb/>
                  ſeundo .ef. partem etc. / et per conſequens oppoſitū
                    <lb/>
                  conſequentis non ſtat cum antecedente / et per con-
                    <lb/>
                  ſequens conſequentia bona / quod fuit probãdum
                    <lb/>
                  </s>
                  <s xml:id="N1823A" xml:space="preserve">Conſequentia patet / quia omnes potentie inequa­
                    <lb/>
                  les idem medium tranſeuntes etc. equalem latitu-
                    <lb/>
                  dinem motus deperdunt: et ſi aliqua poña mediuꝫ
                    <lb/>
                  inuariatum tranſeundo remittat continuo motū
                    <lb/>
                  ſuum intendens potentiam ſuam: minorem latitu­
                    <lb/>
                  dinem motus deperdit quam ſi ſtaret etc. / vt ſepiꝰ
                    <lb/>
                  dictum eſt. </s>
                  <s xml:id="N18249" xml:space="preserve">Sed falſitas conſequentis probata ē
                    <lb/>
                  in ſecunda concluſione: et etiam antecedens. </s>
                  <s xml:id="N1824E" xml:space="preserve">Sed
                    <lb/>
                  iam probo ſecūdam partem minoris / quia illa po­
                    <lb/>
                  tentia a. per aliquod tempus adequate continuo /
                    <lb/>
                  ſequitur potentiam b. mouendo / tunc cum reſiſten-
                    <lb/>
                  tia minori: et per totum reſiduum precedet potētiã
                    <lb/>
                  b. mouendo continuo cum reſiſtentia maiori: et per
                    <lb/>
                  totum illud tempus in quo ſic precedit potentiam
                    <lb/>
                  b. continuo intenditur in potētia: igitur illa pars
                    <lb/>
                  vera. </s>
                  <s xml:id="N18261" xml:space="preserve">Probatur maior / quia a. potentia attinget
                    <lb/>
                  potentiã b. antea quã b. potentia deueniat ad ter­
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                  minum c. medii: et cum attigerit eam: continuo pre­
                    <lb/>
                  det eam cum continuo in h. proportione velocius
                    <lb/>
                  moueatur: igitur a. potentia per aliquod tempus
                    <lb/>
                  adequate ſequetur b. potentiam: et per totum reſi-
                    <lb/>
                  duum temporis precedet eam. </s>
                  <s xml:id="N18270" xml:space="preserve">Probatur maior
                    <lb/>
                  videlicet /  a. potentia attinget b. potentiam ante
                    <lb/>
                  terminum c. medii q2 a. in h. proportione cõtinuo
                    <lb/>
                  velocius mouetur: et a. deuenit vſ ad terminum
                    <lb/>
                  c. medii ex hypotheſi: igitur cum a. deuenit ad ter-
                    <lb/>
                  minum c. medii b. / adhuc eſt in aliquo pūcto intrin­
                    <lb/>
                  ſeco ipſius c. medii: et per conſequens aliquando
                    <lb/>
                  attingit eam: et continuo poſtea p̄cedit eam. </s>
                  <s xml:id="N18281" xml:space="preserve">Pa-
                    <lb/>
                  tet conſequentia / quia ſi eque primo eſſent in termi­
                    <lb/>
                  no c. medii vel b. ante a. iam ſpacium pertranſituꝫ
                    <lb/>
                  in totali illo tempore ab ipſa a. potentia ad ſpa-
                    <lb/>
                  cium pertranſitum ab ipſa b. potentia in eodeꝫ tē­
                    <lb/>
                  pore non eſſet proportio h. / vt patet ex hypotheſi:
                    <lb/>
                  hoc addito /  diuiſo aliquo corpore per partes ꝓ­
                    <lb/>
                  portionales proportione f. illud corpus ſe habet
                    <lb/>
                  ad totum a prima parte proportionali in propor­
                    <lb/>
                  tio .f. / vt patet ex prima concluſione quinti capitis
                    <lb/>
                  prime partis: et ex conſequenti ſequitur /  veloci-
                    <lb/>
                  tatis ipſius a. ad velocitatem ipſius b. non eſt con­
                    <lb/>
                  tinuo ꝓportio h: et per conſequens a. non cõtinuo
                    <lb/>
                  in h. proportione velocius mouetur quam b. / quod
                    <lb/>
                  eſt oppoſitum antecedentis et ſic oppoſitum cõſe-
                    <lb/>
                  quentis infert oppoſitum antecedentis / et per con­
                    <lb/>
                  ſequens conſequentia bona. </s>
                  <s xml:id="N182A4" xml:space="preserve">Sed iam probo /  a.
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                  potentia continuo per totum illud tempus in quo
                    <lb/>
                  precedet potentiam b. continuo intendit potētiaꝫ
                    <lb/>
                  ſuam: quia per nullam partē illius temporis ſtat
                    <lb/>
                  inuariata aut remittit potentiam ſuam: et conti-
                    <lb/>
                  nuo variatur / vt patet ex quarta concluſione pre-
                    <lb/>
                  cedentis capitis. </s>
                  <s xml:id="N182B3" xml:space="preserve">igitur continuo per totum illud
                    <lb/>
                  tempus in quo ſic precedit intendit potentiam ſuã
                    <lb/>
                  </s>
                  <s xml:id="N182B9" xml:space="preserve">Iam probatur /  a. per nullam partem illius tem­
                    <lb/>
                  poris ſtat inuariata aut remittit potentiam ſuã:
                    <cb chead="Capitulum octauum"/>
                  quia ſi non: detur illḋ tꝑs: et ſit g: et in illo a. poten­
                    <lb/>
                  tia adequate pertranſeat .ef. partem: et in eodem
                    <lb/>
                  g. tempore b. poña pertranſeat d. partem: et mani­
                    <lb/>
                  feſtum eſt /  ipſius .ef. partis ad partem d. eſt pro­
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                  portio h. cum ſemper a. moueatur in h. proportio­
                    <lb/>
                  ne velocius / vt patet ex hypotheſi. </s>
                  <s xml:id="N182CB" xml:space="preserve">Quo poſito ar­
                    <lb/>
                  guitur ſic / latitudinis motus deperdite ab ipſa b.
                    <lb/>
                  poña tranſeundo .ef. partem adequate ad latitu-
                    <lb/>
                  dinem motus deperditam ab eadem b. potentia
                    <lb/>
                  tranſeundo d. partem adequate in g. tempore eſt
                    <lb/>
                  maior proportio quam h. / igitur latitudinis deꝑ-
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                  dite ab a. poña inuariata vel remittente potētiaꝫ
                    <lb/>
                  ſuam tranſeundo .ef. partem adequate in g. tēpo-
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                  re ad latitudinem deperditaꝫ ab ipſa b. poña trã­
                    <lb/>
                  ſeundo d. partem adequate in g. tempore eſt ma-
                    <lb/>
                  ior proportio quam h. </s>
                  <s xml:id="N182E2" xml:space="preserve">Conſequentia patet / vt
                    <lb/>
                  ſupra in prima concluſione: et antecedens itidem
                    <lb/>
                  cum falſitate conſequentis. </s>
                  <s xml:id="N182E9" xml:space="preserve">Et ſic patet concluſio.</s>
                </p>
                <note position="right" xml:id="N182EC" xml:space="preserve">q̈drageſi­
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                ma cõclu­
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                ſio calcu.</note>
                <p xml:id="N182F4">
                  <s xml:id="N182F5" xml:space="preserve">Quarta concluſio </s>
                  <s xml:id="N182F8" xml:space="preserve">Ubi aliqua poten­
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                  tia non variata vniformiter cõtinuo remittit mo­
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                  tum ſuum ad non gradum mediū inuariatum trã­
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                  ſeundo: aliqua minor per continuã eius intenſio-
                    <lb/>
                  nem continuo vniformiter remittit motum ſuum:
                    <lb/>
                  et hoc ad non gradum idem medium inuariatum
                    <lb/>
                  trãſeundo. </s>
                  <s xml:id="N18307" xml:space="preserve">Probatur / ſit b. poña que īuariata cõ­
                    <lb/>
                  tinuo vniformiter remittit motuꝫ ſuum ad nõ gra­
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                  dum totum c. medium tranſeundo īuariatum: ſit
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                  a. potentia que ad punctuꝫ initiatiuum vltime q̈r­
                    <lb/>
                  te puta magis reſiſtentis habeat proportionem
                    <lb/>
                  in quadruplo minorem proportione quam habet
                    <lb/>
                  b. poña ad pūctum initiatiuum c. medii: et īcipiãt ī
                    <lb/>
                  eodem inſtanti b. potentia inuariata moueri a pū­
                    <lb/>
                  cto īitiatiuo c. medii in extremo remiſſiori: et a. po­
                    <lb/>
                  tentia a puncto initiatiuo vltime quarte ipſius c.
                    <lb/>
                  medii et moueat̄̄ a. poña cõtinuo in quadruplo tar­
                    <lb/>
                  dius ipſa b. poña. </s>
                  <s xml:id="N18320" xml:space="preserve">tunc dico /  tam a. quam b. vni-
                    <lb/>
                  formiter continuo remittit motum ſuum vltimaꝫ
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                  quartam c. medii tranſeundo vſ ad non graduꝫ
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                  et a. eſt minor b. et tranſeundo illam vltimam quar­
                    <lb/>
                  tam continuo ītendit potentiam ſuam. </s>
                  <s xml:id="N1832B" xml:space="preserve">Quod ſic
                    <lb/>
                  oſtenditur / quia a. continuo vniformiter remittit
                    <lb/>
                  motum ſuum: et a. eſt minor quam b. et continuo in­
                    <lb/>
                  tendit potentiam: et remittit motum ſuum ad non
                    <lb/>
                  gradum: igitur ꝓpoſitum. </s>
                  <s xml:id="N18336" xml:space="preserve">Conſequentia patet: et
                    <lb/>
                  probatur maior / quia a. in certa ꝓportione conti-
                    <lb/>
                  nuo tardius mouetur quaꝫ b. et b. continuo vnifor­
                    <lb/>
                  miter remittit motum ſuum / ergo et a. </s>
                  <s xml:id="N1833F" xml:space="preserve">Conſequen-
                    <lb/>
                  tia patet ex prima parte prime ſuppoſitionis hu-
                    <lb/>
                  ius: et antecedēs ex hypotheſi. </s>
                  <s xml:id="N18346" xml:space="preserve">Sed iam probatur
                    <lb/>
                  prima pars minoris / quia b. potentia ad pūctum
                    <lb/>
                  initiatiuum vltime quarte habet ꝓportionē ſub-
                    <lb/>
                  duplam ad ꝓportionem quam habet eadem potē­
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                  tia b. ad pūctum initiatuum c. medii: cum remittat
                    <lb/>
                  motum ſuum ad non gradum vniformiter c: medi­
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                  um tranſeundo. </s>
                  <s xml:id="N18355" xml:space="preserve">et ſic ī inſtanti medio totius tem-
                    <lb/>
                  poris eſt in principio vltime quarte: et tunc habet
                    <lb/>
                  ꝓportionem ſubduplam adequate ad proportio­
                    <lb/>
                  nem quam habet in principio motus / vt patet ex ṗ­
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                  mo notato tertii capitis ſecundi tractatus huius
                    <lb/>
                  partis: et ad idem punctum a. potentia habet mi-
                    <lb/>
                  norem ꝓportionem / vt patet ex hypotheſi / igit̄̄ ip-
                    <lb/>
                  ſa eſt minor b. poña / quod erat ꝓbandum. </s>
                  <s xml:id="N18366" xml:space="preserve">Secun-
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                  da pars minoris ꝓbatur / quia ſi a. per aliquod tē­
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                  pus ſtat inuariata vel remittit poñam ſuam, de-
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                  tur illud, et ſit g. et pars pertranſita ab a. in g. tem­
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                  pore ſit d: et pars pertranſita adequate in eodē g.
                    <lb/>
                  tempore ab ipſa poña b. ſit .ef. / et manifeſtum eſt / 
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                  ipſius .ef. ad ipſam d. partem eſt ꝓportio quadru­
                    <lb/>
                  pla: cum ſemper b. poña moueatur in quadruplo </s>
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