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">
                <p xml:id="N17BD1">
                  <s xml:id="N17C82" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0079" n="79"/>
                  uetur vniformiter cõtinuo intendēte motū ſuū. </s>
                  <s xml:id="N17C8E" xml:space="preserve">Et
                    <lb/>
                  conſimiliter et ex eiſdem principiis ſecundam par­
                    <lb/>
                  tem deduces.</s>
                </p>
                <p xml:id="N17C95">
                  <s xml:id="N17C96" xml:space="preserve">Secūda ſuppoſitio. </s>
                  <s xml:id="N17C99" xml:space="preserve">Si aliqua potē-
                    <lb/>
                  tia nõ variata tranſeūdo mediū nõ variatu vnifor­
                    <lb/>
                  miter cõtinuo remittit motū ſuū: maiorē latitudi-
                    <lb/>
                  nem motus deperdit tranſeundo partē magis re-
                    <lb/>
                  ſiſtentē quã ſibi equalē minus reſiſtentē. </s>
                  <s xml:id="N17CA4" xml:space="preserve">Patet / q2
                    <lb/>
                  diutius inmoratur tranſeundo partē magis reſi-
                    <lb/>
                  ſtentē quã ei equalē minus reſiſtentē: ergo ſi vnifor­
                    <lb/>
                  miter remittat motū ſuū maiorē latitudinē motꝰ
                    <lb/>
                  deperdit tranſeundo partē magis reſiſtentē quaꝫ
                    <lb/>
                  ſibi equalē minꝰ reſiſtentē: igitur ſuppoſitio vera.</s>
                </p>
                <p xml:id="N17CB1">
                  <s xml:id="N17CB2" xml:space="preserve">Tertia ſuppoſitio. </s>
                  <s xml:id="N17CB5" xml:space="preserve">Alicuiꝰ medii ſuꝑ
                    <lb/>
                  quo īuariato aliqua potentia īuariata mouēs cõ­
                    <lb/>
                  tinuo vniformiter remittit motū ſuū duabus par­
                    <lb/>
                  tibus īequalibus, ſignatis quarū vtrã in aliquo
                    <lb/>
                  tēpore adequato adequate pertranſit: et quãlibet
                    <lb/>
                  partē exceſſus per quē maior pars excedit minorē
                    <lb/>
                  illa potentia tranſeundo, cū maiori reſiſtentia cõ-
                    <lb/>
                  tinuo mouetur quã quãlibet partē equalē minoris
                    <lb/>
                  tranſeundo: maior eſt ꝓportio velocitatis deper-
                    <lb/>
                  dite a tali potentia ſuper maiori parte mouendo
                    <lb/>
                  ad velocitatē deperditã mouendo ſuper parte mi­
                    <lb/>
                  nori quã ſit taliū partiū ꝓportio: </s>
                  <s xml:id="N17CCE" xml:space="preserve">Exemplū / vt ſi a.
                    <lb/>
                  potentia ſuꝑ c. mediū mouēs vniformiter remittit
                    <lb/>
                  motū ſuū: ſignatis prima quarta c. medii et ſecun-
                    <lb/>
                  da medietate eiuſdē c. medii quaꝝ vtrã in aliquo
                    <lb/>
                  tēpore adequate peranſit: maior eſt ꝓportio quaꝫ
                    <lb/>
                  dupla (que eſt inter partes ſignatas) velocitatis
                    <lb/>
                  deperdite ab a. potentia mouēdo ſuꝑ ſecūda me-
                    <lb/>
                  dietate ad velocitatē deperditã in prima quarta
                    <lb/>
                  eiuſdē medii mouendo. </s>
                  <s xml:id="N17CE1" xml:space="preserve">Probatur / et ſit medium c.
                    <lb/>
                  ſuper quo īuariato vniformiter continuo a. poten­
                    <lb/>
                  tia remittit motū ſuū cuius vna pars minor ſit d.
                    <lb/>
                  et ſecūda maior ſit .ef. excedat .ef. ipſum d. per f.
                    <lb/>
                  partē: et quamlibet partē ipſius f. minorē d. tran-
                    <lb/>
                  ſeundo moueatur a. cū maiori reſiſtentia quã mo-
                    <lb/>
                  uetur quãlibet ſibi equalē tranſeundo cū ſuper d.
                    <lb/>
                  parte mouetur: et vtram illarū partiū puta d. et
                    <lb/>
                  ef. in aliquo tēpore adequato adequate pertrãſit:
                    <lb/>
                  ita  in tēpore adequato in quo pertrãſit d. nichil
                    <lb/>
                  pertrãſeat ſuꝑficiale quin ſit d. aut pars illius: et
                    <lb/>
                  in tēpore in quo adequate pertrãſit .ef. nichil ſuꝑ-
                    <lb/>
                  ficiale pertranſeat quin ſit .ef. aut pars eius (ſeclu­
                    <lb/>
                  do multas alias cauillationes que nichil ꝓpoſito
                    <lb/>
                  conducūt) et ſit inter .ef. et d. ꝓportio g. moueatur
                    <lb/>
                  potentia a. pertranſeundo e. partē cū equali reſi-
                    <lb/>
                  ſtentia adequate ſicut tranſeundo d. partē vel cum
                    <lb/>
                  maiori / vt oportet / tūc dico /  velocitas deperdita
                    <lb/>
                  ab a. tranſeundo partē .ef. ſe habet in maiori pro-
                    <lb/>
                  portione ad velocitatē deperditã ab eadē potētia
                    <lb/>
                  a. tranſeundo d. partē quã ſit ꝓportio g. </s>
                  <s xml:id="N17D0C" xml:space="preserve">Quod ſic
                    <lb/>
                  ꝓbatur: q2 tēporis in quo adequate ꝑtranſitur .ef.
                    <lb/>
                  pars ab ipſa potētia a. ad tēpus in quo adequate
                    <lb/>
                  pertranſitur d. pars eſt maior ꝓportio quã g. / ergo
                    <lb/>
                  velocitatis deperdite in pertranſitione .ef. partis
                    <lb/>
                  adequate ad velocitatē deperditã in pertranſitiõe
                    <lb/>
                  d partis adequate eſt maior ꝓportio quã g. / quod
                    <lb/>
                  fuit ꝓbandū. </s>
                  <s xml:id="N17D1D" xml:space="preserve">Patet cõſequētia: q2 quãdo aliqua
                    <lb/>
                  latitudo in aliquo tēpore cõtinuo vniformiter re-
                    <lb/>
                  mittitur ſiue deperditur in qua ꝓportiõe ſe habēt
                    <lb/>
                  tēpora in eadē ſe habent latitudines deperdite: vt
                    <lb/>
                  facile ex diffinitione vniformis remiſſionis alicu-
                    <lb/>
                  ius latitudinis ptꝫ. </s>
                  <s xml:id="N17D2A" xml:space="preserve">Sed ꝓbatur antecedens: quia
                    <lb/>
                  velocitas qua pertranſitur adequate .ef. pars ve-
                    <lb/>
                  locitate qua pertranſitur d. pars eſt minor: ergo
                    <cb chead="Capitulum octauū."/>
                  tēporis in quo adequate pertrãſitur .ef. pars ade­
                    <lb/>
                  quate ad tēpus in quo pertrãſitur d. pars adequa­
                    <lb/>
                  te eſt maior ꝓportio quã g. </s>
                  <s xml:id="N17D38" xml:space="preserve">Conſequentia ptꝫ / q2 ſi
                    <lb/>
                  velocitas qua pertranſitur .ef. pars eſſet equalis
                    <lb/>
                  velocitati qua pertranſitur d. pars iam temporis
                    <lb/>
                  in quo pertrãſitur .ef. ad tēpus in quo pertrãſitur
                    <lb/>
                  ipſū d. eſſet g. ꝓportio que videlicet eſt inter illas
                    <lb/>
                  partes .ef. et d. / igitur ſi velocitas qua pertrãſitur
                    <lb/>
                  ef. pars adequate velocitate qua pertranſitur d.
                    <lb/>
                  eſt minor: iam ꝓportio tēporis in quo pertrãſitur
                    <lb/>
                  ef. pars adequate, ad tēpus in quo pertrãſitur d.
                    <lb/>
                  pars adequate eſt maior ꝓportio quã g. </s>
                  <s xml:id="N17D4D" xml:space="preserve">Ptꝫ hec
                    <lb/>
                  cõſequeatia / q2 maius tēpus requiritur ad pertrã-
                    <lb/>
                  ſeundū ſpaciū .ef. adequate minori velocitate quã
                    <lb/>
                  ad pertranſeundū ipſum adequate aliqua maiori
                    <lb/>
                  </s>
                  <s xml:id="N17D57" xml:space="preserve">Sed iam probatur antecedens: videlicet  veloci-
                    <lb/>
                  tas qua pertranſitur adequate .ef. pars velocita-
                    <lb/>
                  te qua pertranſitur d. pars minor, eſt minor: quia
                    <lb/>
                  velocitas qua pertranſitur e. pars ab ipſa poten-
                    <lb/>
                  tia a. eſt equalis vel minor velocitate qua adequa­
                    <lb/>
                  te pertraſitur ab eadem potentia d. pars cū ex hy-
                    <lb/>
                  potheſi in pertranſitione e. partis adequate mo-
                    <lb/>
                  ueatur a. potentia cum equali vel maiori reſiſten-
                    <lb/>
                  tia quã in pertrãſitione d. partis adequate: et ipſi
                    <lb/>
                  velocitati qua pertranſitur e. pars adequate addi­
                    <lb/>
                  tur extenſiue adhuc minor velocitas in pertranſi-
                    <lb/>
                  tione f. partis magis reſiſtentis / vt conſtat: igitur
                    <lb/>
                  tota velocitas qua pertranſitur .ef. pars adequa-
                    <lb/>
                  te eſt minor tota velocitate qua ꝑtranſitur d. pars
                    <lb/>
                  adequate: quod fuit inferendum. </s>
                  <s xml:id="N17D76" xml:space="preserve">Ptꝫ hec cõſequē-
                    <lb/>
                  tia: q2 ſi alicui latitudini intenſionis addatur ex-
                    <lb/>
                  tenſiue aliqua latitudo minoris intenſionis (cete-
                    <lb/>
                  ris paribꝰ) totalis illa latitudo aggregata ex ad­
                    <lb/>
                  dita et preexiſtenti efficitur minoris intenſionis: vt
                    <lb/>
                  ſi latitudini vniformiter difformi ab octauo vſ
                    <lb/>
                  ad quartū addatur vna latitudo minoris intēſio-
                    <lb/>
                  nis puta a. quatuor vſ ad ſecundū: aggregatum
                    <lb/>
                  ex eis efficitur minoris intenſionis: q2 preexiſtens
                    <lb/>
                  erat vt .6. aggregata vero ex preexiſienti et addita
                    <lb/>
                  eſt vt .5. </s>
                  <s xml:id="N17D8D" xml:space="preserve">Et ſic patet ſuppoſitio.</s>
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                <p xml:id="N17D90">
                  <s xml:id="N17D91" xml:space="preserve">Quarta ſuppoſitio. </s>
                  <s xml:id="N17D94" xml:space="preserve">Alicuius medii
                    <lb/>
                  ſuꝑ quo īuariato aliqua potentia īuariata mouēs
                    <lb/>
                  cõtinuo vniformiter remittit motū ſuū duabꝰ par­
                    <lb/>
                  tibus inequalibus ſignatis: quarū vtram in ali­
                    <lb/>
                  quo tēpore adequato adequate pertranſit: et quã-
                    <lb/>
                  libet partē exceſſus per quē maior pars excedit mi­
                    <lb/>
                  norē illa potentia tranſeundo cū minori reſiſtētia
                    <lb/>
                  cõtinuo mouetur, quã quãlibet partē equalē mino­
                    <lb/>
                  ris tranſeundo: velocitatis deperdite a. tali potē-
                    <lb/>
                  tia ſuꝑ maiore parte mouēdo ad velocitatē deper­
                    <lb/>
                  ditam mouendo ſuper parte minori: nec eſt talium
                    <lb/>
                  partiū ꝓportio nec maior. </s>
                  <s xml:id="N17DAD" xml:space="preserve">Probatur: et ſit mediū
                    <lb/>
                  c. ſuꝑ quo īuariato vniformiter cõtinuo a. potētia
                    <lb/>
                  inuariata remittit motum ſuū: cuius vna pars mi­
                    <lb/>
                  nor ſit d. et ſecunda maior ſit .ef. excedat .ef. ipſū
                    <lb/>
                  d. per f. partem: et quamlibet partem ipſius f. mi-
                    <lb/>
                  norem d. tranſeundo moueatur a. cum minori re-
                    <lb/>
                  ſiſtentia quam mouetur quamlibet ſibi equalem
                    <lb/>
                  tranſeūdo cum ſuper d. parte mouetur: et vtram
                    <lb/>
                  illarum partium puta d. et .ef. in aliquo tempore
                    <lb/>
                  adequato adequate pertranſit .etc̈. </s>
                  <s xml:id="N17DC2" xml:space="preserve">Et ſit inter .ef.
                    <lb/>
                  et d. proportio g. moueatur potentia a. tranſeū-
                    <lb/>
                  do c. partem cum equali reſiſtentia adequate ſicut
                    <lb/>
                  tranſeundo d. partem vel cum minori / vt oportet:
                    <lb/>
                  tunc dico /  velocitas deperdita ab a. tranſeundo
                    <lb/>
                  partem .ef. nun̄ ſe habet ad velocitatem deper-
                    <lb/>
                  ditam ab eadem potentia a. tranſeūdo d. partem
                    <lb/>
                  in g. proportione: nec in maiori.</s>
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