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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                <p xml:id="N1883F">
                  <s xml:id="N188D3" xml:space="preserve">
                    <pb chead="Primi partis" file="0088" n="88"/>
                  ex quarta ſuppoſitiõe huius. </s>
                  <s xml:id="N188DB" xml:space="preserve">Et ſic patet concluſio.
                    <lb/>
                    <note position="left" xlink:href="note-0088-01a" xlink:label="note-0088-01" xml:id="N18984" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N188E5" xml:space="preserve">¶ Ex quo ſequitur /  vbi aliqua potentia inuaria-
                    <lb/>
                  ta vniformiter continuo remittit motum ſuum .etc̈.
                    <lb/>
                  potentia ei equalis idem medium inuariatū tran-
                    <lb/>
                  ſeundo valet vniformiter continuo motum ſuum re­
                    <lb/>
                  mittere per ſui continuam intēſionem. </s>
                  <s xml:id="N188F0" xml:space="preserve">Probatur /
                    <lb/>
                  ſit b. potena que inuariata totnm c. medii tran-
                    <lb/>
                  ſeundo vniformiter continuo valet motum ſuū re-
                    <lb/>
                  mittere: ſit a. potentia equalis que ponatur ad
                    <lb/>
                  punctum initiatiuū vltime quarte magis reſiſten-
                    <lb/>
                  tis b. potētia poſita in extremo remiſſiori c. medii /
                    <lb/>
                  et manifeſtum eſt /  proportio b. ad punctuꝫ in quo
                    <lb/>
                  ponitur eſt dupla ad proportionem a. ad punctum
                    <lb/>
                  in quo ponitur: incipiant igtur in eodem inſtãti ab
                    <lb/>
                  illis punctis continuo moueri a: et b. b potentia cõ-
                    <lb/>
                  tinuo in duplo velociꝰ ipſa a. ponã. </s>
                  <s xml:id="N18907" xml:space="preserve">Tūc dico /  a.
                    <lb/>
                  poña illã vltimã quartã trãſeundo (quã īuariatã b.
                    <lb/>
                  potentia inuariata tranſeundo vniformiter contic­
                    <lb/>
                  nuo remittit motum ſuum) vniformiter cõtinuo re-
                    <lb/>
                  mittit motum ſuum per ſue potentie coutinuã intē-
                    <lb/>
                  ſionem. </s>
                  <s xml:id="N18914" xml:space="preserve">Quod ſic probatur / quia a. potentia conti­
                    <lb/>
                  nuo vniformiter remittit motum ſuum / vt conſtat: et
                    <lb/>
                  hoc continuo inteudendo potentiam ſuam: igitur
                    <lb/>
                  propoſitum. </s>
                  <s xml:id="N1891D" xml:space="preserve">Probatur minor: quia ſi ipſa poten-
                    <lb/>
                  tia a. per aliquod tempus ſtat inuariata aut remit­
                    <lb/>
                  tit potentiam ſuam, ſignetur illud tempus, et ſit g.
                    <lb/>
                  in quo b. potentia tranſeat .ef. partem adequate:
                    <lb/>
                  et in eodem g. tempore a potentia pertrãſeat d. par­
                    <lb/>
                  tem adequate: et cõſtat / ipſius .ef. partis ad d. par-
                    <lb/>
                  tem eſſe duplam proportionem / et ptꝫ ex hypotheſi:
                    <lb/>
                  quo poſito arguitur ſic / latitudinis motus deperdi­
                    <lb/>
                  te ab ipſa potentia b. tranſeundo .ef. partem ad la­
                    <lb/>
                  titudinem motus deperditam ab eadem potentia
                    <lb/>
                  b. tranſeundo d. partem adequate non eſt propor-
                    <lb/>
                  tio dupla: igitur latitudinis motus deperdite ab
                    <lb/>
                  ipſa b. potentia tranſeundo .ef. partem in g. tempo­
                    <lb/>
                  re adequate ad latitudinem deperditam ab a. po-
                    <lb/>
                  tentia tranſeundo d. partem in g. tempore adequa­
                    <lb/>
                  te non eſt proportio dupla: ſed conſequens eſt fal-
                    <lb/>
                  ſum: igitur illud ex quo ſequitur. </s>
                  <s xml:id="N18940" xml:space="preserve">Conſequentia ptꝫ
                    <lb/>
                  cum falſitate conſequentis ex ſuperius dictis: et ar­
                    <lb/>
                  guitur antecedens quia ipſius .ef. partis ad ipſam
                    <lb/>
                  d. partem eſt proportio dupla: et quamlibet parteꝫ
                    <lb/>
                  exceſſus minorē ipſa d. parte quo exceſſu .ef. pars
                    <lb/>
                  excedit d. partem tranſeundo b. potentia mouetur
                    <lb/>
                  cum minori reſiſtentia quam equalem partem ipſi­
                    <lb/>
                  us d. partis tranſeundo: quoniam quelibet pars
                    <lb/>
                  illius exceſſus: īmo tota .ef. pars minus reſiſtit quã
                    <lb/>
                  ipſa d. pars: igitur latitudinis motus deꝑerdite a
                    <lb/>
                  b. potentia tranſeundo .ef. partem in g. tēpore ade­
                    <lb/>
                  quate ad latitudinem motus deperditã ab eadem
                    <lb/>
                  potentia b. tranſeundo d. partem non eſt propor-
                    <lb/>
                  tio dupla. </s>
                  <s xml:id="N1895D" xml:space="preserve">Et ſic ptꝫ correlariū. </s>
                  <s xml:id="N18960" xml:space="preserve">¶ Patet etiã quibꝰ
                    <lb/>
                  modis poña equalis potētie remittēti motū ſuū cõ­
                    <lb/>
                  tinuo vniformiter īuariatū mediū trãſeundo valet
                    <lb/>
                  motū ſuū remittere.
                    <note position="left" xlink:href="note-0088-02a" xlink:label="note-0088-02" xml:id="N1898A" xml:space="preserve">Dubiū</note>
                  </s>
                  <s xml:id="N1896E" xml:space="preserve">Utrū autē poña aliqua vnifor­
                    <lb/>
                  miter medio īuariato remittēte cõtinuo motū ſuū,
                    <lb/>
                  valeat equalis poña cõtinuo vniformiter remitte-
                    <lb/>
                  re motū ſuū, aliqñ ītendendo poñam, aliqñ vero re­
                    <lb/>
                  mittendo: tu ipſe inq̇ras. </s>
                  <s xml:id="N18979" xml:space="preserve">Et ſi em̄ michi id īpoſſibi­
                    <lb/>
                  le eſſe appareat nichilominus demõſtratio efficax
                    <lb/>
                  non occurrit.</s>
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                <p xml:id="N18990">
                  <s xml:id="N18991" xml:space="preserve">Octaua cõcluſio. </s>
                  <s xml:id="N18994" xml:space="preserve">Ubi aliqua potētia
                    <lb/>
                  īuariata mediū īuariatū tranſeundo cõtinuo vni-
                    <lb/>
                  formiter remittit motū ſuū: aliqua maior valet cõ-
                    <lb/>
                  tinuo vniformiter: et eque velociter cū eadē motum
                    <lb/>
                  ſuū remittere per ſui continuã intenſionē. </s>
                  <s xml:id="N1899F" xml:space="preserve">Proba-
                    <lb/>
                  tur / ſit b. potentia que īuariata c. mediū inuariatū
                    <cb chead="Capitulū octauū."/>
                  trãſeundo cõtinuo vniformiter remittit motū ſuuꝫ
                    <lb/>
                  ſit a. potentia maior que ad aliquē punctū intrī-
                    <lb/>
                  ſecū ipſius c. medii habeat equalē proportionē illi
                    <lb/>
                  ꝓportioni quã habet b. potentia ad punctū initia-
                    <lb/>
                  tiuū c. medii in extremo remiſſiori: et moueãtur ille
                    <lb/>
                  potentie cõtinuo ab eadē ꝓportione: et tunc dico / 
                    <lb/>
                  ipſa a. potentia cõtinuo vniformiter et eque veloci-
                    <lb/>
                  ter cū b. potentia remittit motū ſuū illam partē c.
                    <lb/>
                  medii tranſeundo que intercipitur inter punctū ter­
                    <lb/>
                  minatiuū c. medii in extremo intenſiori et punctum
                    <lb/>
                  a quo incipit ipſa a. potentia moueri. </s>
                  <s xml:id="N189BB" xml:space="preserve">Quod ſic ꝓ-
                    <lb/>
                  batur / q2 a. potentia continuo vniformiter motum
                    <lb/>
                  ſuū: et continuo eque velociter remittit ſicut b. potē­
                    <lb/>
                  tia tranſeundo illam partē c. medii que ſignatur in
                    <lb/>
                  hypotheſi. </s>
                  <s xml:id="N189C6" xml:space="preserve">Et cõtinuo intendit potentiã ſuã: igitur
                    <lb/>
                  ꝓpoſitū. </s>
                  <s xml:id="N189CB" xml:space="preserve">Maior ꝓbatur / q2 motus ipſius a. ↄ̨tinuo
                    <lb/>
                  eſt equalis motui ipſiꝰ b. ex hypotheſi: et b. cõtinuo
                    <lb/>
                  vniformiter remittit motū ſuū datã partē c. medii
                    <lb/>
                  quã etiã pertranſit a. trãſeuudo: igitur a. continuo
                    <lb/>
                  vniformiter et eque velociter remittit motū ſuū cuꝫ
                    <lb/>
                  ipſa b. potentia tranſeundo datam partē c. medii.
                    <lb/>
                  </s>
                  <s xml:id="N189D9" xml:space="preserve">Patet cõſequentia: quoniã ſi ab equalibus equa-
                    <lb/>
                  lia demas remanētia ſunt equalia. </s>
                  <s xml:id="N189DE" xml:space="preserve">Et demo rema­
                    <lb/>
                  nentes motus a. motibus deperditis. </s>
                  <s xml:id="N189E3" xml:space="preserve">Iam ꝓbatur
                    <lb/>
                  minor: quoniã ſi per aliquod tēpus a. potentia ſtat
                    <lb/>
                  inuariata, aut remittit potentiã ſuã: ſignetur illud
                    <lb/>
                  et ſit g. in quo b. potentia pertranſeat adequate d.
                    <lb/>
                  partē c. medii et a. potentia in eodē g. tēporē pertrã­
                    <lb/>
                  ſeat e. partē adequate. </s>
                  <s xml:id="N189F0" xml:space="preserve">Et manifeſtū eſt /  ipſius e.
                    <lb/>
                  ad d. eſt ꝓportio equalitatis / vt patet ex hypotheſi
                    <lb/>
                  </s>
                  <s xml:id="N189F6" xml:space="preserve">Quo poſito arguitur ſic / latitudinis motus deper­
                    <lb/>
                  dite ab ipſa b. potentia tranſeundo e. partē ad la-
                    <lb/>
                  titudinē motus deperditam ab eadem b. potentia
                    <lb/>
                  tranſeundo d. partem in g. tēpore adequate non eſt
                    <lb/>
                  ꝓportio equalitatis: igitur latitudinis motus de-
                    <lb/>
                  perdite ab a. poteutia ſtante aut remittente poten­
                    <lb/>
                  tiam ſuã tranſeundo e. partē in g. tēpore adequate
                    <lb/>
                  ad latitudinē motus deperditã a b. potentia tran-
                    <lb/>
                  ſeundo d. partē in eodem g. tēpore adequate nõ eſt
                    <lb/>
                  proportio equalitatis. </s>
                  <s xml:id="N18A0B" xml:space="preserve">Conſequens eſt falſum: vt
                    <lb/>
                  patet ex probatione maioris: igitur illud ex quo
                    <lb/>
                  ſequitur. </s>
                  <s xml:id="N18A12" xml:space="preserve">Conſequentia patet per locum a maiori
                    <lb/>
                  auxiliante quarto argumento ſexti capitis huius
                    <lb/>
                  tractatus: vbi habetur /  omnes potentie inuari-
                    <lb/>
                  ate idem medium inuariatum tranſeuntes .etc̈. </s>
                  <s xml:id="N18A1B" xml:space="preserve">An-
                    <lb/>
                  tecedens autem patet manifeſte ex ſecunda ſuppo-
                    <lb/>
                  ſitione huius capitis: hoc addito /  e. pars magis
                    <lb/>
                  reſiſtit ꝙ̄ d. quia a. continuo mouetur in parte ma-
                    <lb/>
                  gis reſiſtente ex hypotheſi. </s>
                  <s xml:id="N18A26" xml:space="preserve">Et ſic patet concluſio.</s>
                </p>
                <p xml:id="N18A29">
                  <s xml:id="N18A2A" xml:space="preserve">¶ Ex quo ſequitur /  vbi aliqua potentia non va-
                    <lb/>
                  riata continuo vniformiter remittit motum ſuum
                    <lb/>
                  ad non gradum medium inuariatum tranſeundo:
                    <lb/>
                  omnis potentia maior per ſui continuam intenſi-
                    <lb/>
                  onem idem medium inuariatum tranſeundo valet
                    <lb/>
                  motum ſuum continuo vniformiter remittere. </s>
                  <s xml:id="N18A37" xml:space="preserve">Et
                    <lb/>
                  hoc continuo ꝙ̄ data potentia inuariata velocius
                    <lb/>
                  remittendo. </s>
                  <s xml:id="N18A3E" xml:space="preserve">Prima pars huius correlarii eſt pri-
                    <lb/>
                  mum correlarium prime concluſionis huius capi-
                    <lb/>
                  tis. </s>
                  <s xml:id="N18A45" xml:space="preserve">Et ſecunda probatur: ſuppoſſto hypotheſi pre­
                    <lb/>
                  dicti correlarii videlicet /  a. potentia maior ipſa
                    <lb/>
                  b. potentia continuo moueatur velocius in h. pro-
                    <lb/>
                  portione ꝙ̄ eadem b. potentia. </s>
                  <s xml:id="N18A4E" xml:space="preserve">Et tunc dico /  a. po­
                    <lb/>
                  tentia continuo velocius remittit motum ſuum ̄
                    <lb/>
                  ipſa b. potentia. </s>
                  <s xml:id="N18A55" xml:space="preserve">Quod ſic probatur: quia a. potē-
                    <lb/>
                  tia continuo velocius in h. ꝓportione remittit mo­
                    <lb/>
                  tum ſuū ꝙ̄ b. / igitur continuo velocius remittit mo-
                    <lb/>
                  tum ſuū ꝙ̄ b. ↄ̨ña patet. </s>
                  <s xml:id="N18A5E" xml:space="preserve">Et probatur añs / q2 motus
                    <lb/>
                  b. et a. continuo remittuntur cõtinuo ſe habentes </s>
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