Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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                    <pb chead="Primi partis" file="0076" n="76"/>
                  poris g. ſpacium pertranſit adequate et eadem ra-
                    <lb/>
                  tione h. ſpacium in ſecunda medietate eiuſdem
                    <lb/>
                  temporis pertranſit / quod fuit probandum. </s>
                  <s xml:id="N17831" xml:space="preserve">Ma-
                    <lb/>
                  ior eſt nota / et minor probatur / quia b. potentia il-
                    <lb/>
                  lam medietatem velocitatis deperdende deper-
                    <lb/>
                  dendo adequate g. ſpacium adequate pertranſit /
                    <lb/>
                  vt patet ex hypotheſi: igitur a. potentia eandem
                    <lb/>
                  medietatem deperdendo idem g. ſpacium adequa­
                    <lb/>
                  te pertranſit: quia diuerſe potentie ſiue equales
                    <lb/>
                  ſiue inequales idem medium et eaſdem partes me-
                    <lb/>
                  dii difformis in quibus acquiritur vel deperditur
                    <lb/>
                  motus tranſeundo equalem latitudinem motus
                    <lb/>
                  acquirunt vel deperdunt / vt patet ex quarto argu-
                    <lb/>
                  mento ſexti capitis huius tractatus: igitur minor
                    <lb/>
                  vera. </s>
                  <s xml:id="N1784C" xml:space="preserve">Et eodem modo probabis ſecundam par-
                    <lb/>
                  tem concluſionis videlicet /  vbi aliqua potentia
                    <lb/>
                  etc̈. nulla minor inuariata idem medium inuaria-
                    <lb/>
                  tum tranſeundo: vniformiter continuo remittit
                    <lb/>
                  motum ſuum: quia ſi ſic: ſit illa potentia minor b.
                    <lb/>
                  et potentia que inuariata ſufficit illud c. medium
                    <lb/>
                  pertranſire continuo vniformiter remittendo mo-
                    <lb/>
                  tum ſuum ſit a. / et arguo ſic / a. pertranſeundo c. me-
                    <lb/>
                  dium vniformiter continuo remittit motum ſuum
                    <lb/>
                  et b. potentia minor idem c. medium tranſeundo
                    <lb/>
                  vniformiter continuo remittit motum ſuum: igitur
                    <lb/>
                  vbi b. potentia minor tranſeundo c. medium, vni-
                    <lb/>
                  formiter continuo remittit motum ſuum a. poten-
                    <lb/>
                  tia maior idem c. medium tranſeundo vniformi-
                    <lb/>
                  ter continuo remittit motum ſuum / quod eſt contra
                    <lb/>
                  priorem partem concluſionis. </s>
                  <s xml:id="N1786D" xml:space="preserve">Patet igitur con-
                    <lb/>
                  cluſio.
                    <note position="left" xlink:href="note-0076-01a" xlink:label="note-0076-01" xml:id="N178F9" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N17877" xml:space="preserve">¶ Ex hac cõcluſione facile ſequitur /  nulle
                    <lb/>
                  due potentie inequales nõ variate tranſeuntes idē
                    <lb/>
                  mediū adequate poſſunt ad nõ gradū ſuos motus
                    <lb/>
                  remittere. </s>
                  <s xml:id="N17880" xml:space="preserve">Probatur correlariū / quia ſi nõ ſit verū
                    <lb/>
                  detur oppoſitū videlicet /  aliquarū duarū poten­
                    <lb/>
                  tiarum inequaliū vtra idē mediū adequate tran-
                    <lb/>
                  ſeundo remittat motū ſuū ad nõ gradū / et arguitur
                    <lb/>
                  ſic / vtra potentiarū inequaliū idem mediū ade-
                    <lb/>
                  quate tranſeundo remittit motū ſuū ad nõ gradū /
                    <lb/>
                  igitur maiorē latitudinē motus deperdit potentia
                    <lb/>
                  maior quã minor idem mediū adequatū tranſeund-
                    <lb/>
                  do / ſed conſequens eſt falſum / et contra concluſionē
                    <lb/>
                  quarti argumenti ſexti capitis preallegatã: igitur
                    <lb/>
                  et antecedens. </s>
                  <s xml:id="N17897" xml:space="preserve">Sequela tamen probatur / qm̄ ſi ille
                    <lb/>
                  potentie ſunt inequales nõ variate: maior illarum
                    <lb/>
                  intenſiori latitudine motus mouetur ſupra eãdem
                    <lb/>
                  reſiſtentiã quã minor: et tamē vtra per te remittit
                    <lb/>
                  motum ſuū ad nõ gradū: igitur maiorē latitudineꝫ
                    <lb/>
                  motus perdit maior quã minor;: etc̈. igitur.
                    <note position="left" xlink:href="note-0076-02a" xlink:label="note-0076-02" xml:id="N178FF" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N178A9" xml:space="preserve">¶ Sequi­
                    <lb/>
                  tur ſecūdo /  ſi aliqua potētia nõ variata tranſeū-
                    <lb/>
                  do aliquod mediū nõ variatū remittit motum ſuū
                    <lb/>
                  ad nõ gradum: oīs potentia maior nõ variata re-
                    <lb/>
                  mittens in eodem medio motum ſuū remittit illum
                    <lb/>
                  ad gradū. </s>
                  <s xml:id="N178B6" xml:space="preserve">et oīs minor remittit ad nõ gradū in ali-
                    <lb/>
                  quo puncto medii intrinſeco. </s>
                  <s xml:id="N178BB" xml:space="preserve">Probat̄̄ prima pars /
                    <lb/>
                  qm̄ illa potentia maior remittit ibi motum ſuū et
                    <lb/>
                  nõ remittit ad non gradum / vt patet ex antecedenti
                    <lb/>
                  correlario: igitur remittit illū ad gradum. </s>
                  <s xml:id="N178C4" xml:space="preserve">Secun-
                    <lb/>
                  da pars probatur / qm̄ oīs minor potētia in aliquo
                    <lb/>
                  puncto intrinſeco deueniet ad proportionem equa­
                    <lb/>
                  litatis: igitur in aliquo puncto intrinſeco remittet
                    <lb/>
                  motū ſuum ad nõ gradū. </s>
                  <s xml:id="N178CF" xml:space="preserve">Patet hoc etiã facile exē-
                    <lb/>
                  plo / quoniã ſi ſit aliqua potentia vt .4. et incipiat re­
                    <lb/>
                  mittere motum ſuum et remittat ad non gradū ali-
                    <lb/>
                  quod medium pertranſeundo: neceſſe eſt cum ipſa
                    <lb/>
                  ſit inuariata medium illud in ſuo extremo intenſio­
                    <cb chead="Capitulū ſeptimū."/>
                  ri reſiſtere vt .4. et in nullo puncto alio ãteriori tan­
                    <lb/>
                  tum reſiſtere quoniã alias iam in tali puncto motꝰ
                    <lb/>
                  ad non gradum deueniret et ſic non pertranſiret to­
                    <lb/>
                  tum: capiatur tunc alia potentia minor vt tria vel
                    <lb/>
                  vt duo (in idem redit) remittens in eodē medio mo-
                    <lb/>
                  tum ſuum / tunc manifeſtum eſt /  illa potētia ad nõ
                    <lb/>
                  gradum remittet motum ſuum cum deueneret ad
                    <lb/>
                  punctum reſiſtentie vt duo vel ad punctum reſiſten­
                    <lb/>
                  tie vt tria ſi ipſa fuerit vt tria: et tale punctū eſt pun­
                    <lb/>
                  ctum intrinſecum / vt ſatis patet quoniam extrinſe­
                    <lb/>
                  cum reſiſtit et .4. / igitur talis potentia minor ad nõ
                    <lb/>
                  gradum remittet motum ſuum in aliquo puncto in­
                    <lb/>
                  trinſeco / quod fuit probandum.</s>
                </p>
                <note position="right" xml:id="N17905" xml:space="preserve">Trigeſi-
                  <lb/>
                ma .9. cõ­
                  <lb/>
                cluſio cal­
                  <lb/>
                culatorꝪ</note>
                <p xml:id="N1790F">
                  <s xml:id="N17910" xml:space="preserve">Quinta concluſio. </s>
                  <s xml:id="N17913" xml:space="preserve">Si aliqua poten-
                    <lb/>
                  tia non variata in aliquo medio difformi non va-
                    <lb/>
                  riato vniformiter ad non gradum motum ſuum re­
                    <lb/>
                  mittit: omnis potentia maior inuariata idem me-
                    <lb/>
                  dium tranſeundo inuariatum in infinitum veloci-
                    <lb/>
                  ter remittit motum ſuum verſus extremum inten-
                    <lb/>
                  ſius eiuſdem medii deueniēdo. </s>
                  <s xml:id="N17922" xml:space="preserve">Probatur / ſit b. po-
                    <lb/>
                  tentia minor que inuariata c. medium inuariatum
                    <lb/>
                  tranſeundo: vniformiter remittit motum ſuum ad
                    <lb/>
                  non gradum continuo d. gradu velocitatis. </s>
                  <s xml:id="N1792B" xml:space="preserve">ſit a.
                    <lb/>
                  potentia maior que inuariata ipſum c. medium in­
                    <lb/>
                  uariatum totaliter pertranſeat remittendo motuꝫ
                    <lb/>
                  ſuuꝫ procedendo continuo per eandem lineam per
                    <lb/>
                  quam ꝓcedit b. </s>
                  <s xml:id="N17936" xml:space="preserve">(Semper enim hoc modo intelligo
                    <lb/>
                  et ſi propter breuiloquium id non explicem) / tunc di­
                    <lb/>
                  co /  a. potentia maior verſus extremum intenſius
                    <lb/>
                  c. medii deueniendo in infinitum velociter remittit
                    <lb/>
                  motum ſuum. </s>
                  <s xml:id="N17941" xml:space="preserve">Quod ſic probatur / quia a. verſus ex­
                    <lb/>
                  tremum intenſius c. medii deueniendo in infinitum
                    <lb/>
                  velocius remittit motum ſuum quam b. et b. conti-
                    <lb/>
                  nuo certe velociter remittit motum ſuum puta
                    <lb/>
                  d. gradu / ergo a. in infinitum velociori gradu re-
                    <lb/>
                  mittit motum ſuum quam ſit d. gradus / et per con-
                    <lb/>
                  ſequens in infinitum velociter remittit motum ſuū /
                    <lb/>
                  quod eſt probandū. </s>
                  <s xml:id="N17952" xml:space="preserve">Conſequentie ſunt manifeſte et
                    <lb/>
                  minor ex hypotheſi patet / et maior arguitur / quia
                    <lb/>
                  a. et b. cum ſint potentie inuariate idem medium in­
                    <lb/>
                  uariatum traſeuntes eaſdem partes eiuſdem me-
                    <lb/>
                  dii tranſeundo equales latitudines motus deper-
                    <lb/>
                  dunt adequate / vt iam ſepius argutum eſt / ſed a.
                    <lb/>
                  verſus extremū ītēſiꝰ c. medii deueniendo in infini­
                    <lb/>
                  tum velocius pertranſibit aliquam partem ipſius
                    <lb/>
                  c: medii quam b. pertranſibit eandem / ergo a. in in-
                    <lb/>
                  finitum velocius remittet motum ſuum verſus ex-
                    <lb/>
                  tremum intenſius c. medii deueniendo quã b. / quod
                    <lb/>
                  fuit probandum. </s>
                  <s xml:id="N1796B" xml:space="preserve">Patet hec conſequentia / quoniã
                    <lb/>
                  ita velociter ſicut a. pertranſit aliquam partem c.
                    <lb/>
                  medii ita velociter remittit motum ſuū deperden-
                    <lb/>
                  dum in illa parte medii et b. ſimiliter: ſed in infini-
                    <lb/>
                  tum velocius pertranſibit a. aliquam partem ipſi-
                    <lb/>
                  us c. medii quam b. pertranſibit eandem: igitur in
                    <lb/>
                  infinitum velocius a. remittet motum ſuum verſus
                    <lb/>
                  extremum intenſius c. medii deueniendo quam b.
                    <lb/>
                  </s>
                  <s xml:id="N1797D" xml:space="preserve">Sed iam probatur minor / et capio proportionem /
                    <lb/>
                  quam habet a. ad extremum intenſius c. medii que
                    <lb/>
                  ſit f. / et arguo ſic: continuo a. mouebitur a propor-
                    <lb/>
                  tione f. vĺ a. maiori: et b. ab īfinite modica propor-
                    <lb/>
                  tione mouebitur tranſeundo illud medium: ergo
                    <lb/>
                  ab in infinitū maiori proportione tranſeundo ali-
                    <lb/>
                  quam partem c. medii mouebitur a. quam b. ean-
                    <lb/>
                  dem partem tranſeundo: igitur a. verſus extremū
                    <lb/>
                  intenſiꝰ c. medii deueniēdo in īfinitū velociꝰ ꝑtrã-
                    <lb/>
                  ſibit aliquã partē eiuſdē c. medii quã b. ꝑtranſibit </s>
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