Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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                    <pb chead="Primi tractatus" file="0085" n="85"/>
                  cum ſemper a. moueatur in ſexquialtero velocius
                    <lb/>
                  ipſa b. poña:  cum b. deſcripſerit vltimam quar­
                    <lb/>
                  tam pertranſibit a. adequate tres octauas: tunc
                    <lb/>
                  dico /  a tranſeundo illas tres octauas continuo
                    <lb/>
                  remittit vniformiter motum ſuum: et hoc ad non
                    <lb/>
                  gradum continuo remittendo potentiam ſuam.</s>
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                <p xml:id="N184DF">
                  <s xml:id="N184E0" xml:space="preserve">Quod ſic oſteditur / quia a. tranſeundo illas tres
                    <lb/>
                  octauas continuo vniformiter remittit motū ſuū /
                    <lb/>
                  vt patet ex prima ſuppoſitione iuncta hypotheſi:
                    <lb/>
                  et tranſeundo illas tres octauas continuo remit-
                    <lb/>
                  tit potentiam ſuaꝫ / igitur etc. </s>
                  <s xml:id="N184EB" xml:space="preserve">Minor probatur / q2
                    <lb/>
                  ſi per aliquod tempus ipſa potentia a. tranſeūdo
                    <lb/>
                  illas tres octauas ſtat, aut intenditur ſignetur il­
                    <lb/>
                  lud et ſit g. in quo a. tranſeat .ef. adequate, et b. in
                    <lb/>
                  eodem tempore g.d. partem adequate pertranſe­
                    <lb/>
                  at ad quam d. partem pars .ef. habet ꝓportiõem
                    <lb/>
                  ſexquialteram / vt patet intuēti hypotheſim: </s>
                  <s xml:id="N184FA" xml:space="preserve">Quo
                    <lb/>
                  poſito arguo ſic / latitudinis motus deperdite ab
                    <lb/>
                  ipſa b. potentia tranſeundo .ef. partem adequate
                    <lb/>
                  ad latitudinem motus deperditã ab eadem potē-
                    <lb/>
                  tia tranſeundo d. partem in g. tempore adequate
                    <lb/>
                  non eſt ꝓportio ſexquialtera nec maior: igitur la­
                    <lb/>
                  titudīs deperdite ab ipſa potētia a. inuariata vel
                    <lb/>
                  intendente potentiam ſuam tranſeundo .ef. ꝑtem
                    <lb/>
                  in g. tempore adequate ad latitudinem deperdi-
                    <lb/>
                  tam ab ipſa potentia b. tranſeundo adequate d.
                    <lb/>
                  partem in eodem tempore g. non ē ꝓportio ſexqui­
                    <lb/>
                  altera nec maior: ſed conſequens eſt falſuꝫ: igitur
                    <lb/>
                  illud ex quo ſequitur. </s>
                  <s xml:id="N18515" xml:space="preserve">Conſequentia patet / vt ſu-
                    <lb/>
                  pra in concluſione ſecunda et ſimiliter antecedēs
                    <lb/>
                  cum falſitate conſequentis: </s>
                  <s xml:id="N1851C" xml:space="preserve">Et ſic patet concluſio.
                    <lb/>
                    <note position="left" xlink:href="note-0085-01a" xlink:label="note-0085-01" xml:id="N186A3" xml:space="preserve">correla.</note>
                  </s>
                  <s xml:id="N18526" xml:space="preserve">¶ Ex quo ſequitur /  vbi aliqua potentia inuaria­
                    <lb/>
                  ta aliquod medium inuariatum tranſeundo vni-
                    <lb/>
                  formiter continuo remittit motum ſuum ad non
                    <lb/>
                  gradum: omnis potentia minor habens ad pun-
                    <lb/>
                  ctum initiatiuum eiuſdem medii ī extremo remiſ­
                    <lb/>
                  ſiori ꝓportionem maioris inequalitatis ideꝫ me­
                    <lb/>
                  dium inuariatum tranſeundo continuo vniformi­
                    <lb/>
                  ter remittit motum ſuum vſ ad non gradum in
                    <lb/>
                  aliquo puncto intrinſeco per continuam ſue po-
                    <lb/>
                  tentie remiſſionem. </s>
                  <s xml:id="N1853B" xml:space="preserve">Probatur / ſit b. potentia que
                    <lb/>
                  inuariata c. medium inuariatum vniformiter re-
                    <lb/>
                  mittit motum ſuum ad non gradum: ſit a. poña
                    <lb/>
                  minor que habeat ad punctum initiatiuum eiuſ-
                    <lb/>
                  dem c. medii in exiremo remiſſiori ꝓportionem in
                    <lb/>
                  h. ꝓportione minorem quam ſit ꝓportio ipſiꝰ po­
                    <lb/>
                  tentie b. ad idem punctum initiatiuum ponatur
                    <lb/>
                  b. potentia in īitio ſecunde partis ꝓportionabi-
                    <lb/>
                  lis ipſius c. medii diuiſi ꝓportione h. minoribus
                    <lb/>
                  verſus extremu
                    <lb/>
                  m intenſius terminatis: et incipiãt
                    <lb/>
                  in eodem inſtanti a punctis in quibus ponuntur
                    <lb/>
                  moueri verſus extremum intenſius: ſit continuo
                    <lb/>
                  inter motus illarum potentiaruꝫ ea ꝓportio ade­
                    <lb/>
                  quate que eſt inter ꝓportionem quam habet a. ad
                    <lb/>
                  punctum initiatiuum c. medii et ꝓportionem quaꝫ
                    <lb/>
                  habet b. ad punctum initiatiuum ſecunde partis
                    <lb/>
                  ꝓportionalis ipſius c. medii diuiſi h. ꝓportione:
                    <lb/>
                  tunc dico /  a. et b. continuo vniformiter remittūt
                    <lb/>
                  motum ſuum vſ ad non gradum idem medium
                    <lb/>
                  inuariatum tranſeundo: a. continuo remittēte po­
                    <lb/>
                  tentiam ſuam. </s>
                  <s xml:id="N18568" xml:space="preserve">Quod ſic oſtenditur / quia vel pro-
                    <lb/>
                  portio ipſius a. ad punctum initiatiuum ipſius c.
                    <lb/>
                  medii eſt equalis ꝓportioni ipſius b. ad punctum
                    <lb/>
                  initiatiuum ſecunde partis ꝓportionalis c. medii
                    <lb/>
                  diuiſi etc. vel maior vel minor </s>
                  <s xml:id="N18573" xml:space="preserve">(Eſt enim altera al-
                    <lb/>
                  teri comparabilis: cum vtra ſit maioris inequa­
                    <lb/>
                  litatis ex hypotheſi) </s>
                  <s xml:id="N1857A" xml:space="preserve">Si ſit equalis ſequitur /  cõ-
                    <lb/>
                  tinuo equaliter mouebuntur ex hypotheſi: et ex cõ­
                    <lb/>
                  ſequenti cum b. fuerit in termino c. medii ī quo mo­
                    <cb chead="Capitulum octauum"/>
                  tus eius eſt remiſſus ad non gradum ex hypothe-
                    <lb/>
                  ſi a. erit in aliquo puncto intrinſeco tantum vide-
                    <lb/>
                  licet diſtante ab extremo remiſſiori c. medii quan­
                    <lb/>
                  tum diſtat extremū intenſius a puncto a quo ince­
                    <lb/>
                  pit moueri b. / vt ↄ̨ſtat (eq̄ velociṫ eī a. cū b. ↄ̨tinuo
                    <lb/>
                  mouetur) et in tali puncto a. poña remittit motum
                    <lb/>
                  ſuum ad non gradum cum nunquam moueat̄̄ ve-
                    <lb/>
                  locius aut tardius quam b. / igitur a. poña tranſe-
                    <lb/>
                  undo illam partem c. medii continuo vniformiter
                    <lb/>
                  remittit motum ſuum ad non gradum: et continuo
                    <lb/>
                  tranſeundo illam partem remittit potentiam ſuã /
                    <lb/>
                  igitur propoſitum. </s>
                  <s xml:id="N1859A" xml:space="preserve">Probatur minor videlicet / 
                    <lb/>
                  a. potentia continuo tranſeundo illam partem re­
                    <lb/>
                  mittit potentiam ſuam: quia ſi non detur tempus
                    <lb/>
                  per quod poña a. tranſeundo illam partem c. me­
                    <lb/>
                  dii ſtet inuariata, aut intendat poñam ſuam, et ſit
                    <lb/>
                  g. ſit pars pertranſita ab a. potentia in g. tem-
                    <lb/>
                  pore adequate f. et pertranſita .ab. potentia in eo­
                    <lb/>
                  dem tempore e. / quo poſito arguitur ſic. </s>
                  <s xml:id="N185AB" xml:space="preserve">maior eſt
                    <lb/>
                  latitudo motus deperdita a b. poña tranſeundo
                    <lb/>
                  e. partem quam latitudo deperdita ab eadem
                    <lb/>
                  poña b. tranſeundo f. parteꝫ adequate / vt patet ex
                    <lb/>
                  ſecunda ſuppoſitione huius capitis </s>
                  <s xml:id="N185B6" xml:space="preserve">(Magis eni3
                    <lb/>
                  reſiſtit e. quam f. / vt patet intuenti) / ergo maior eſt
                    <lb/>
                  latitudo motus deperdita ab ipſa poña b. tranſe­
                    <lb/>
                  undo e. partem in g. tempore adequate quã ſit la-
                    <lb/>
                  titudo deperdita ab a. poña ſtante inuariata vel ī­
                    <lb/>
                  tendente continuo poñam ſuam f. partem tranſe-
                    <lb/>
                  undo in eodem g. tempore adequate: ſed cõſequēs
                    <lb/>
                  eſt falſum / igitur illud ex quo ſequitur: </s>
                  <s xml:id="N185C7" xml:space="preserve">Patet hec
                    <lb/>
                  conſequentia / quia potentie inequales inuariate
                    <lb/>
                  idem medium etc. tranſeundo equalem latitudinē
                    <lb/>
                  motus deperdunt. </s>
                  <s xml:id="N185D0" xml:space="preserve">et ſi aliqua potentia tranſeūdo
                    <lb/>
                  idem medium inuariatum remittendo motum ſuuꝫ
                    <lb/>
                  etc. intendo motum ſuum etc. intendat potentiam
                    <lb/>
                  ſuam: minorem latitudinem motus deperdit quã
                    <lb/>
                  ſi ſtaret idem medium inuariatum tranſeundo / vt
                    <lb/>
                  patet ex quarto argumento ſexti capitis ſepius
                    <lb/>
                  allegato. </s>
                  <s xml:id="N185DF" xml:space="preserve">Sed falſitas conſequentis probatur: q2
                    <lb/>
                  ſi latitudo motus deperdita ab ipſa b. potētia e.
                    <lb/>
                  ꝑtē trãſeūdo ī g. tꝑe adeq̈te ē maior quã latitudo
                    <lb/>
                  deperdita ab eadē b. poña trãſeūdo f. ꝑtē in g. tꝑe
                    <lb/>
                  adeq̈te: et a prīcipio motus ipſiꝰ b. eſt eq̈lis motui
                    <lb/>
                  ipſius a. / ergo ſequitur /  facta tali variatione la­
                    <lb/>
                  titudo motus ipſius b. non eſt equalis latitudini
                    <lb/>
                  motus ipſius a. / quod eſt contra hypotheſim. </s>
                  <s xml:id="N185F0" xml:space="preserve">Cõ-
                    <lb/>
                  ſequentia patet ex primo correlario quinte cõclu­
                    <lb/>
                  ſionis ſecundi capitis ſecunde partis. </s>
                  <s xml:id="N185F7" xml:space="preserve">Si autē ꝓ-
                    <lb/>
                  portio a. ad punctum initiatiuum c. medii eſt ma-
                    <lb/>
                  ior ꝓportione b. ad punctum initiatiuum ſecunde
                    <lb/>
                  partis ꝓportionalis c. medii diuiſi per partes ꝓ­
                    <lb/>
                  portionales ꝓportione h. ſit maior in l. ꝓportio-
                    <lb/>
                  ne / et ſequitur /  cõtinuo in l. ꝓportione ipſa potē-
                    <lb/>
                  tia a. velocius mouebitur quaꝫ potentia b. / et ex cõ­
                    <lb/>
                  ſequenti cū b. fuerit in termino c. medii in quo mo­
                    <lb/>
                  tus eius eſt remiſſus ad non gradum / ex hypothe-
                    <lb/>
                  ſi a. erit in aliquo puncto in l. ꝓportione magꝪ di­
                    <lb/>
                  ſtante ab extremo remiſſiori c. medii quam diſtat
                    <lb/>
                  extremum intenſius a puncto a quo a. poña ince-
                    <lb/>
                  pit moueri: et in tali puncto remittit motū ſuū ad
                    <lb/>
                  non gradum / vt facile ex octauo correlario quar-
                    <lb/>
                  te concluſionis octaui capitis ſecunde partis ar-
                    <lb/>
                  gui poteſt eo modo quo ſepius argutum eſt: et con­
                    <lb/>
                  tinuo deueniendo vſ ad illud punctum vniformi­
                    <lb/>
                  ter remittit motum ſuum: quemadmodum ſepius
                    <lb/>
                  argutum eſt: et continuo remittit potentiam ſuam
                    <lb/>
                  et punctus ille in quo motus eius remiſſns ē ad nõ
                    <lb/>
                  gradum eſt intrinſecus: igitur propoſitum. </s>
                  <s xml:id="N18622" xml:space="preserve">Sed
                    <lb/>
                  probatur /  a. poña continuo remittit potentiam </s>
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