Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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              <div xml:id="N17BB3" level="4" n="8" type="chapter" type-free="capitulum">
                <pb chead="Primi tractatus" file="0081" n="81"/>
                <p xml:id="N17F4C">
                  <s xml:id="N17F4D" xml:space="preserve">Probat̄̄: ſit b. potētia que c. mediū inuariatū trã­
                    <lb/>
                  ſeūdo vniformiter cõtinuo īuariata ad nõ gradū
                    <lb/>
                  remittit motū ſuū: et ſit a. potētia maior (q̄cū ſit
                    <lb/>
                  illa) que ab eodē puncto c. medii īcipiat moueri cū
                    <lb/>
                  b. potētia a ꝓportione in h. ꝓportiõe maiori quã
                    <lb/>
                  ſit ꝓportio a qua excluſiue incipit moueri b. et cõ-
                    <lb/>
                  tinuo moueat̄̄ a. potētia per ſui variationē in h. ꝓ-
                    <lb/>
                  portione velociꝰ ipſa b. potetia / et tūc dico /  a po-
                    <lb/>
                  tētia vniformiṫ cõtinuo remittit motū ſuū ad g̈dū
                    <lb/>
                  tranſeūdo c. mediū per ſui cõtinuã intenſionē. </s>
                  <s xml:id="N17F62" xml:space="preserve">Qḋ
                    <lb/>
                  ſic ꝓbatur: q2 a. potētia ↄ̨tinuo vniformiṫ remittit
                    <lb/>
                  motū ſuū tranſeūdo c. mediū: et per nullū tempus
                    <lb/>
                  ſtat īuariata aut remittit potētiã ſuã: igit̄̄ cõtinuo
                    <lb/>
                  vniformiter remittit motū ſuū trãſeūdo c. mediū
                    <lb/>
                  per ſui cõtinuã intenſionē. </s>
                  <s xml:id="N17F6F" xml:space="preserve">Cõſequentia ptꝫ: et pro­
                    <lb/>
                  batur maior: q2 a. potentia cõtinuo in h. ꝓportiõe
                    <lb/>
                  velocius mouetur quã b. potentia: vt ptꝫ ex hypo-
                    <lb/>
                  theſi: et b. potētia cõtinuo vniformiter remittit mo­
                    <lb/>
                  tum ſuū: ergo a. potentia cõtinuo vniformiter re-
                    <lb/>
                  mittit motū ſuū. </s>
                  <s xml:id="N17F7C" xml:space="preserve">Patet cõſequentia / vt in ꝓbatiõe
                    <lb/>
                  cõcluſiõis. </s>
                  <s xml:id="N17F81" xml:space="preserve">Iam ꝓbatur minor / q2 ſi a. per aliquod
                    <lb/>
                  tēpus ſtat īuariata, aut remittit potentiã ſuã, det̄̄
                    <lb/>
                  illud tēpus: et ſit g. in quo a. potentia adequate ꝑ-
                    <lb/>
                  tranſit .ef. partē: et in eodē g. tēpore b. potētia per­
                    <lb/>
                  trãſeat d. partē: et manifeſtū eſt /  ipſius .ef. partis
                    <lb/>
                  ad partē d. eſt proportio h. cū ſemꝑ a. moueatur in
                    <lb/>
                  h. ꝓportiõe velocius / vt ptꝫ ex hypotheſi. </s>
                  <s xml:id="N17F90" xml:space="preserve">Quo po­
                    <lb/>
                  ſito arguitur ſic / latitudinis deperdite ab ipſa b.
                    <lb/>
                  potentia tranſeūdo .ef. partē adequate ad latitu-
                    <lb/>
                  dinē motus deperditã ab eadē b. potētia tranſeū-
                    <lb/>
                  do d. partē adequate in g. tēpore eſt maior ꝓpor-
                    <lb/>
                  tio quã h. / igitur latitudinis deperdite ab a. potē-
                    <lb/>
                  tia īuariata vel remittente potentiã ſuã tranſeun-
                    <lb/>
                  do .ef. partē adequate ad latitudinē deperditã ab
                    <lb/>
                  ipſa b. potētia tranſeūdo d. partē adequate in g.
                    <lb/>
                  tēpore eſt maior ꝓportio quã h. / ſed conſequens eſt
                    <lb/>
                  falſum: igitur illud ex quo ſequitur. </s>
                  <s xml:id="N17FA7" xml:space="preserve">Cõſequentia
                    <lb/>
                  ptꝫ vt ſupra: et antecedens ſimiliter cum falſitate
                    <lb/>
                  conſequentis. </s>
                  <s xml:id="N17FAE" xml:space="preserve">Patet igitur correlarium.</s>
                </p>
                <note position="left" xml:id="N17FB1" xml:space="preserve">q̈drageſi­
                  <lb/>
                ma ſecū-
                  <lb/>
                da cõclu-
                  <lb/>
                ſio calcu.</note>
                <p xml:id="N17FBB">
                  <s xml:id="N17FBC" xml:space="preserve">Secūda ↄ̨̨cluſio. </s>
                  <s xml:id="N17FBF" xml:space="preserve">Ubi aliqua potētia
                    <lb/>
                  nõ variata tranſeūdo aliquod mediū īuariatum
                    <lb/>
                  vniformiter cõtinuo ad nõ gradū remittit motum
                    <lb/>
                  ſuū: aliqua potentia maior per cõtinuã eiꝰ remiſ-
                    <lb/>
                  ſionē tranſeūdo idē mediū remittit motū ſuū vni-
                    <lb/>
                  formiter cõtinuo ad nõ gradū. </s>
                  <s xml:id="N17FCC" xml:space="preserve">Probatur: ſit b. po­
                    <lb/>
                  tentia que nõ variata c. mediū īuariatū tranſeūdo
                    <lb/>
                  vniformiter cõtinuo motū ſuū remittat ad nõ gra­
                    <lb/>
                  dum: et ſit a. potentia que habet in duplo maiorē
                    <lb/>
                  ꝓportionē ad punctū initiatiuū c. medii in extre-
                    <lb/>
                  mo remiſſiori quã habeat b. potentia ad punctuꝫ
                    <lb/>
                  mediū eiuſdem c. medii: et ponatur b. potentia ad
                    <lb/>
                  punctū mediū ipſius c. medii: et a. potētia in pūcto
                    <lb/>
                  initiatiuo eiuſdē c. medii remiſſiori: et incipiant in
                    <lb/>
                  eodē inſtanti moueri ab illis punctis verſus extre­
                    <lb/>
                  mū intēſius: et taliter varietur a.  cõtinuo mouea­
                    <lb/>
                  tur in duplo velocius quã ipſa b. potentia: et tunc
                    <lb/>
                  dico /  ipſa potentia a. cõtinuo vniformiter motū
                    <lb/>
                  ſuū et hoc vſ ad nõ gradū remittit per continuã
                    <lb/>
                  eius remiſſionē. </s>
                  <s xml:id="N17FEB" xml:space="preserve">Quod ſic ꝓbatur: q2 a. potētia cõ­
                    <lb/>
                  tinuo remittit motū ſuū vniformiter c. mediū trã-
                    <lb/>
                  ſeundo: et per nullū tēpus ſtabit īuariata in poten­
                    <lb/>
                  tia aut intendet potentiã ſuã: igitur a. potētia trã­
                    <lb/>
                  ſeūdo c. mediū īuariatū cõtinuo vniformiter remit­
                    <lb/>
                  tit motū ſuū per continuã eius remiſſionē. </s>
                  <s xml:id="N17FF8" xml:space="preserve">Cõſequē­
                    <lb/>
                  tia ptꝫ ex ſe: et maior iam arguta eſt in precedenti
                    <lb/>
                  concluſione: et minor ꝓbatur / q2 ſi per aliquod tē-
                    <lb/>
                  pus potentia a. ſtat inuariata, aut intendit potē-
                    <lb/>
                  tiam ſuã, detur illud tēpus, et ſit g. in quo a. poten­
                    <lb/>
                  tia pertranſeat adequate .ef. partē: et b. potentia
                    <cb chead="Capitulum octauū."/>
                  d. partem adequate: et manifeſtum eſt /  ipſius .ef.
                    <lb/>
                  partis ad ipſam d. partē eſt proportio dupla cum
                    <lb/>
                  a. potētia continuo moueatur in duplo velociꝰ b. /
                    <lb/>
                  ex hypotheſi </s>
                  <s xml:id="N1800E" xml:space="preserve">Quo poſito arguitur ſic / latitudinis
                    <lb/>
                  motus deperdite ab ipſa potentia b. tranſeundo
                    <lb/>
                  ef. partem ad latitudinē deperditam ab eadē po-
                    <lb/>
                  tētia b. tranſeūdo d. partem adequate in g. tēpo-
                    <lb/>
                  re nõ eſt proportio dupla nec maior: igitur latitu-
                    <lb/>
                  dinis deperdite ab a. potentia inuariata vel inten­
                    <lb/>
                  dente potentiã ſuam tranſeundo .ef. partem ad la­
                    <lb/>
                  titudinē deperditam a b. potentia tranſeundo d.
                    <lb/>
                  partem in g. tempore adequate non eſt proportio
                    <lb/>
                  dupla nec maior: ſed conſequēs eſt falſum: igitur
                    <lb/>
                  illud ex quo ſequitur. </s>
                  <s xml:id="N18025" xml:space="preserve">Cõſequentia probatur / quia
                    <lb/>
                  oēs potentie inuariate idem mediū īuariatū tran­
                    <lb/>
                  ſeuntes .etc̈. equalē latitudinem motus deperdunt
                    <lb/>
                  et ſi aliqua potentia mediū inuariatum tranſeun-
                    <lb/>
                  do remittat motum ſuū intendens potentiã ſuam:
                    <lb/>
                  minorem latitudinem motus deperdit quam ſi ſta­
                    <lb/>
                  ret idem mediū tranſeundo .etc̈. / vt conſtat: et argu-
                    <lb/>
                  tum eſt ſupra. </s>
                  <s xml:id="N18036" xml:space="preserve">Sed falſitas conſequētis probatur /
                    <lb/>
                  quia ſi latitudinis motus deperdite ab ipſa a. po­
                    <lb/>
                  tentia tranſeundo .ef. partem in g. tempore ade-
                    <lb/>
                  quate ad latitudinem deperditam ab ipſa b. potē­
                    <lb/>
                  tia tranſeundo d. partem adequate in eodē g. tem­
                    <lb/>
                  pore nõ eſt proportio dupla nec maior dupla: et a
                    <lb/>
                  principio latitudinis motus ipſius a. potentie ad
                    <lb/>
                  latitudinē motus ipſius b. potentie quarū vtra
                    <lb/>
                  remittitur erat ꝓportio dupla: ergo facta tali re-
                    <lb/>
                  miſſione latitudinis motus ipſius a. ad latitudinē
                    <lb/>
                  motus ipſius b. nõ eſt proportio dupla: quod eſt
                    <lb/>
                  contra hypotheſim. </s>
                  <s xml:id="N1804F" xml:space="preserve">Cõſequentia patet ex primo
                    <lb/>
                  correlario quinte concluſionis ſecundi capitis ſe-
                    <lb/>
                  cunde partis. </s>
                  <s xml:id="N18056" xml:space="preserve">Iam probatur antecedens videlicet /
                    <lb/>
                   latitudinis deperdite ab ipſa potentia b. tran-
                    <lb/>
                  ſeundo .ef. partem ad latitudineꝫ deperditam ab
                    <lb/>
                  eadem potentia b. in g. tempore adequate non eſt
                    <lb/>
                  proportio dupla, aut maior dupla: quia ipſiꝰ .ef.
                    <lb/>
                  partis ad ipſam d. parteꝫ eſt proportio dupla ex
                    <lb/>
                  caſu: et ipſa potentia b. tranſeundo quãlibet par-
                    <lb/>
                  tem exceſſus quo .ef. excedit d. minorē ipſa d. par-
                    <lb/>
                  te mouetur cum minori reſiſtentia quam quãlibet
                    <lb/>
                  partem equalem ipſius d. partis tranſeundo: cum
                    <lb/>
                  q̄libet pars exceſſus quo .ef. pars excedit d. partē
                    <lb/>
                  minꝰ diſtet a. puncto remiſſiori initiatiuo c. medii
                    <lb/>
                  quã aliqua pars ipſiꝰ d. partꝪ. </s>
                  <s xml:id="N18071" xml:space="preserve">(Signo em̄ exceſſū
                    <lb/>
                  ſus punctū īitiatiuū c. medii minꝰ reſiſtentē quē
                    <lb/>
                  exceſſū ſemꝑ voco f) / igit̄̄ latitudīs deꝑdite ab ipſa
                    <lb/>
                  b. potētia trãſeūdo .ef. partē adeq̈te ad latitudinē
                    <lb/>
                  deꝑditã ab eadē potētia trãſeūdo d. partē adeq̈te
                    <lb/>
                  in g. tꝑe nõ eſt ꝓportio dupla aut maior dupla / qḋ
                    <lb/>
                  fuit īferendū. </s>
                  <s xml:id="N18080" xml:space="preserve">Ptꝫ ↄ̨ña ex quarta ſuppoſitiõe huiꝰ
                    <lb/>
                  </s>
                  <s xml:id="N18084" xml:space="preserve">Sed q2 cõcluſio ſupponit potētiã a. eſſe maiorē b. /
                    <lb/>
                  ideo reſtat illud ꝓbare. </s>
                  <s xml:id="N18089" xml:space="preserve">Qḋ ſic ꝓbo / q2 a. ꝑ ↄ̨tinuã
                    <lb/>
                  ſui remiſſionē ꝑtrãſit totū c. mediū in tēpore ī quo
                    <lb/>
                  adequate b. ꝑtrãſit eiuſdē c. medii īuariati medie-
                    <lb/>
                  tatē: igitur ipſa a. potentia eſt maior b. potentia.
                    <lb/>
                  </s>
                  <s xml:id="N18093" xml:space="preserve">Patet conſequentia ex ſe / et antecedens probatur /
                    <lb/>
                  quia a. in duplo velocius cõtinuo mouetur quam
                    <lb/>
                  b. / vt patet ex hypotheſi: et a. incipit moueri a. pun-
                    <lb/>
                  cto iniciatiuo c. medii: et b. a puncto medio eiuſdeꝫ
                    <lb/>
                  c. medii in eodē inſtanti cum ceteris poſitꝪ in caſu:
                    <lb/>
                  igitur eque cito erunt in termino ipſius c. medii: et
                    <lb/>
                  per conſequens in tēpore in quo adequate b. per-
                    <lb/>
                  tranſit vnam medietatem c. medii inuariati a. ꝑ-
                    <lb/>
                  trãſit totū c. mediū / quod fuit ꝓbandū. </s>
                  <s xml:id="N180A6" xml:space="preserve">Q, autē a.
                    <lb/>
                  potētia remittat motū ſuū ad nõ gradū / ꝓbat̄̄ / qm̄
                    <lb/>
                  cõtinuo ex hypotheſi inter motū ipſius a. et motū
                    <lb/>
                  ipſius b. eſt proportio dupla vtro illorū motuū </s>
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