Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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            <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
              <div xml:id="N17BB3" level="4" n="8" type="chapter" type-free="capitulum">
                <pb chead="Primi tractatus" file="0080" n="80"/>
                <p xml:id="N17DD7">
                  <s xml:id="N17DD8" xml:space="preserve">Quod ſic ꝓbatur: q2 tēporis in quo adequate per­
                    <lb/>
                  tranſitur .ef. ab ipſa potentia a. ad tēpus in quo
                    <lb/>
                  adequate ꝑtranſitur d. pars nõ eſt ꝓportio g. nec
                    <lb/>
                  maior: ergo velocitatis deꝑdite in pertranſitiõe
                    <lb/>
                  ef. partis adequate ad velocitatē deꝑditã in ꝑtrã­
                    <lb/>
                  ſitiõe d. partis adequate nõ eſt ꝓportio g. nec ma-
                    <lb/>
                  ior: quod fuit ꝓbandū. </s>
                  <s xml:id="N17DE7" xml:space="preserve">Patet cõſequētia vt ſupra /
                    <lb/>
                  et antecedens ꝓbatur: q2 velocitas qua adequate
                    <lb/>
                  ꝑtranſitur .ef. pars eſt maior velocitate qua ꝑtrã-
                    <lb/>
                  ſitur d. pars adequate: et .ef. ad d. eſt proportio g. /
                    <lb/>
                  ergo tēporis in quo adequate ꝑtranſitur .ef. pars
                    <lb/>
                  ad tēpus in quo adequate ꝑtranſitur d. pars non
                    <lb/>
                  eſt ꝓportio g. nec maior. </s>
                  <s xml:id="N17DF6" xml:space="preserve">Cõſequentia patꝫ: quia ſi
                    <lb/>
                  velocitas qua adequate ꝑtranſitur .ef. pars eſſet
                    <lb/>
                  equalis velocitati qua ꝑtranſitur d. pars: iam tē-
                    <lb/>
                  poris in quo ꝑtranſitur .ef. ad tēpus in quo ꝑtrã-
                    <lb/>
                  ſitur d. pars eſſet ꝓportio g. (que videlicet eſt inter
                    <lb/>
                  illas partes .ef. et d. / vt conſtat) / igitur ſi velocitas
                    <lb/>
                  qua ꝑtranſitur .ef. pars eſt maior velocitate qua
                    <lb/>
                  pertranſitur d. pars adequate iam tēporis in quo
                    <lb/>
                  adequate ꝑtranſitur d. pars nõ eſt ꝓportio g. nec
                    <lb/>
                  maior. </s>
                  <s xml:id="N17E0B" xml:space="preserve">Patet hec cõſequentia / q2 minus tēpus re-
                    <lb/>
                  quiritur ad ꝑtranſeundū ſpaciū .ef. adequate ma­
                    <lb/>
                  iori velocitate quã ad ꝑtranſeundū ipſum adequa-
                    <lb/>
                  te aliqua velocitate minori. </s>
                  <s xml:id="N17E14" xml:space="preserve">Sed iam ꝓbatur an-
                    <lb/>
                  tecedens videlicet /  velocitas qua adequate per-
                    <lb/>
                  tranſitur adequate .ef. pars eſt maior velocitate
                    <lb/>
                  qua adequate ꝑtrãſitur d. pars: q2 velocitas qua
                    <lb/>
                  ꝑtranſitur adequate .e. pars ab ipſa potētia a. eſt
                    <lb/>
                  equalis vel maior velocitate qua adequate ꝑtran-
                    <lb/>
                  ſitur d. pars (cū ex hypotheſi in pertranſitione .e.
                    <lb/>
                  partis adequate moueatur a. potētia cū equali vĺ
                    <lb/>
                  minori reſiſtentia quã in pertranſitione d. partis
                    <lb/>
                  adequate) et ipſi velocitati qua ꝑtranſitur .e. pars
                    <lb/>
                  adequate additur extēſiue adhuc maior velocitas
                    <lb/>
                  in pertranſitione f. partis minus reſiſtentis / vt cõ­
                    <lb/>
                  ſtat: igitur tota velocitas qua ꝑtranſitur .ef. pars
                    <lb/>
                  adequate eſt maior tota velocitate qua pertranſi-
                    <lb/>
                  tur d. pars adequate: quod fuit oſtēdendū. </s>
                  <s xml:id="N17E33" xml:space="preserve">Patet
                    <lb/>
                  hec cõſequentia: q2 ſi alicui latitudini intenſionis
                    <lb/>
                  addatur extēſiue aliqua latitudo maioris intēſio­
                    <lb/>
                  nis .etc̈. totalis illa latitudo aggregata ex addita
                    <lb/>
                  et preexiſtenti efficitur maioris intēſionis: vt ſi la-
                    <lb/>
                  titudini vniformiter difformi q̈rto vſ ad octa-
                    <lb/>
                  uum addatur vna alia maioris intēſiõis puta ab
                    <lb/>
                  octauo vſ ad duodecimū: aggregatū ex eis effi-
                    <lb/>
                  cit̄̄ maioris intēſiõis / vt cõſtat. </s>
                  <s xml:id="N17E46" xml:space="preserve">Et ſic ptꝫ ſuppoſitio</s>
                </p>
                <note position="left" xml:id="N17E49" xml:space="preserve">q̈drageſi­
                  <lb/>
                ma ṗma
                  <lb/>
                ↄ̨cĺo. cal.</note>
                <p xml:id="N17E51">
                  <s xml:id="N17E52" xml:space="preserve">His ſuppoſitis. </s>
                  <s xml:id="N17E55" xml:space="preserve">Sit prima concluſio
                    <lb/>
                  </s>
                  <s xml:id="N17E59" xml:space="preserve">Ubi aliqua potentia non variata vniformiter re-
                    <lb/>
                  mittit motū ſuū ad nõ gradū mediū īuariatū trã-
                    <lb/>
                  ſeūdo: aliqua maior ꝑ ſui cõtinuã intenſionē idem
                    <lb/>
                  mediū īuariatū trãſeūdo valet motū ſuū vniformi­
                    <lb/>
                  ter ad gradū remittere. </s>
                  <s xml:id="N17E64" xml:space="preserve">Probat̄̄: ſit b. potētia que
                    <lb/>
                  īuariata c. mediū īuariatū trãſeūdo vniformiter
                    <lb/>
                  ad nõ gradū motū ſuū remittat: ſit a. potentia
                    <lb/>
                  maior q̄ ab eodē puncto c. medii incipiēdo moueri
                    <lb/>
                  cū ipſo b. ab in duplo maiori ꝓportiõe īcipiat mo­
                    <lb/>
                  ueri quã b. et cõtinuo in duplo velociꝰ moueat̄̄ quã
                    <lb/>
                  b. ꝑ variationē ipſiꝰ a. potētie (q2 alias medio īua­
                    <lb/>
                  riato hoc nequit fieri / vt ptꝫ ex quarta ↄ̨cluſiõe pre­
                    <lb/>
                  cedētis capitis): tūc dico /  a. potētia ↄ̨tinuo vni-
                    <lb/>
                  formiter remittit motū ſuū ad gradū ↄ̨tinuo intē-
                    <lb/>
                  tendo potentiã ſuã. </s>
                  <s xml:id="N17E7B" xml:space="preserve">Quod ꝓbatur ſic: q2 a. poten-
                    <lb/>
                  tia cõtinuo vniformiter remittit motū ſuū trãſeū-
                    <lb/>
                  do illud mediū: et per nullū tēpus ſtabit inuariata
                    <lb/>
                  aut remittet potentiã ſuã idē mediū trãſeūdo: igit̄̄
                    <lb/>
                  cõtinuo vniformiter remittit motū ſuū, cõtinuo in­
                    <lb/>
                  tendendo potentiã ſuã. </s>
                  <s xml:id="N17E88" xml:space="preserve">Cõſequētia ptꝫ ex ſe: et ꝓba­
                    <lb/>
                  tur maior / q2 a. potentia cõtinuo in duplo velocius
                    <cb chead="Capitulū octauū."/>
                  mouetur quam b. potentia / vt ptꝫ ex hypotheſi: et b.
                    <lb/>
                  potētia cõtinuo vniformiter remittit motū ſuum:
                    <lb/>
                  igitur a potētia idem mediū tranſeūdo vniformi-
                    <lb/>
                  ter remittit motū ſuū cõtinuo. </s>
                  <s xml:id="N17E96" xml:space="preserve">Patet hec cõſequē-
                    <lb/>
                  tia ex ſecūda parte prime ſuppoſitionis. </s>
                  <s xml:id="N17E9B" xml:space="preserve">Iam pro­
                    <lb/>
                  batur minor / q2 ſi a. per aliquod tēpus ſtat īuaria-
                    <lb/>
                  ta vel remittit potentiã ſuam: detur illud et ſit g. et
                    <lb/>
                  pars pertranſita ab ipſa .a. potentia in g. tēpore
                    <lb/>
                  adequate ſit .ef. et pars ꝑtranſita ab ipſa b. poten­
                    <lb/>
                  tia in eodē g. tēpore ſit d. / et manifeſtū eſt /  ipſius
                    <lb/>
                  ef. ad ipſam d. partē eſt ꝓportio dupla, cū ſemper
                    <lb/>
                  a. moueatur in duplo velocius ipſa potentia b. / vt
                    <lb/>
                  ptꝫ ex hypotheſi: quo poſito arguitur ſic: latitudi­
                    <lb/>
                  nis motus deperdite ab ipſa b. potētia tranſeūdo
                    <lb/>
                  ef. partē adequate, ad latitudinē motus deꝑditã
                    <lb/>
                  ab ipſa b. potētia tranſeūdo d. partē adequate in
                    <lb/>
                  g. tēpore eſt maior ꝓportio quã dupla que eſt īter
                    <lb/>
                  illas partes .ef. et d. / ergo latitudinis deperdite ab
                    <lb/>
                  a. potētia ſtante vel remittente potentiã ſuam trã-
                    <lb/>
                  ſeundo .ef. partē in g. tēpore adequate ad velocita­
                    <lb/>
                  tem deperditã ab ipſa b. potentia tranſeundo d.
                    <lb/>
                  partē adequate in g. tēpore eſt maior ꝓportio quã
                    <lb/>
                  dupla: ſed cõſequens eſt falſum: igitur illud ex quo
                    <lb/>
                  ſequitur. </s>
                  <s xml:id="N17EC4" xml:space="preserve">Probatur cõſequentia: q2 oēs potentie
                    <lb/>
                  īuariate idem mediū īuariatū trãſeūtes .etc̈. equa-
                    <lb/>
                  lem latitudinē motus deꝑdunt: et ſi aliqua potētia
                    <lb/>
                  trãſeundo mediū īuariatū remittendo motū ſuum
                    <lb/>
                  etc̈. et remittat potentiã: ipſa maiorē latitudinem
                    <lb/>
                  motus deperdit quã ſi ſtaret idem mediū tranſeū-
                    <lb/>
                  do / vt conſtat: et ptꝫ ex quarto argumento ſexti ca-
                    <lb/>
                  pitis huius. </s>
                  <s xml:id="N17ED5" xml:space="preserve">Sed falſitas cõſequentis ꝓbatur: q2
                    <lb/>
                  ſi latitudinis motus deperdite ab ipſa a. potētia
                    <lb/>
                  in g. tēpore ad latitudinē motꝰ deperditã ab ipſa
                    <lb/>
                  b. potentia in eodē g. tēpore eſt maior ꝓportio quã
                    <lb/>
                  dupla: et a principio latitudinis motus ipſius a.
                    <lb/>
                  ad latitudinem motus ipſius b. erat proportio
                    <lb/>
                  duplo: ſequitur /  facta tali deperditione: latitu-
                    <lb/>
                  dinis motus ipſius a. ad latitudinem motus ipſi-
                    <lb/>
                  us b. eſt minor ꝓportio quam dupla: quod eſt con-
                    <lb/>
                  tra hypotheſim. </s>
                  <s xml:id="N17EEA" xml:space="preserve">Conſequentia tamen ptꝫ / ex ſecū-
                    <lb/>
                  da parte quinti correlarii quarte ↄ̨cluſionis octa­
                    <lb/>
                  ui capitis ſecunde partis. </s>
                  <s xml:id="N17EF1" xml:space="preserve">Iam ꝓbatur antecedēs
                    <lb/>
                  videlicet /  latitudinis deperdite ab b. potētia trã­
                    <lb/>
                  ſeundo .ef. partē adequate ad velocitatē deperdi-
                    <lb/>
                  tam etc̈. q2 ipſius .ef. partis ad d. partē eſt propor­
                    <lb/>
                  tio dupla ex caſu: et ipſa potētia b. tranſeūdo quã­
                    <lb/>
                  libet partem exceſſus ipſius .ef. partis minoreꝫ d.
                    <lb/>
                  parte mouetur cū maiori reſiſtentia quã tranſeun­
                    <lb/>
                  do quãlibet partē equalē ipſius d. partis (cū que-
                    <lb/>
                  libet pars exceſſus quo .ef. pars excedit d. partem
                    <lb/>
                  magis diſtat a puncto initiatiuo c. medii a quo in­
                    <lb/>
                  cipit motus quam aliqua pars ipſius d. partis q2
                    <lb/>
                  per totum illum exceſſum ad minus a potentia b.
                    <lb/>
                  potentiam precedit) / ergo latitudinis deperdite a
                    <lb/>
                  b. potentia tranſeundo .ef. partem adequate ad ve­
                    <lb/>
                  locitatem deperditam ab ipſa b. potentia tranſe-
                    <lb/>
                  undo d. partem adequate in g. tempore eſt maior
                    <lb/>
                  proportio quam dupla: quod fuit inferendū. </s>
                  <s xml:id="N17F14" xml:space="preserve">Pa­
                    <lb/>
                  tet conſequentia ex tertia ſuppoſitione huius. </s>
                  <s xml:id="N17F19" xml:space="preserve">Q,
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                  vero a. potentia remittat motum ſuuꝫ ad gradum
                    <lb/>
                  in extremo intenſiori / patet ex ſecundo correlario
                    <lb/>
                  quarte concluſionis ſeptimi capitis huius tracta­
                    <lb/>
                  tus, auxiliante loco a maiori: quia illa potētia cõ­
                    <lb/>
                  tinuo intenditur. </s>
                  <s xml:id="N17F26" xml:space="preserve">Et ſic patet concluſio.
                    <note position="right" xlink:href="note-0080-01a" xlink:label="note-0080-01" xml:id="N17F42" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N17F2E" xml:space="preserve">¶ Ex quo
                    <lb/>
                  ſequitur. </s>
                  <s xml:id="N17F33" xml:space="preserve">Q, vbi aliqua potentia non variata vni­
                    <lb/>
                  formiter continuo remittit motum ſuum ad non
                    <lb/>
                  gradū mediū īuariatū trãſeūdo: oīs potentia ma­
                    <lb/>
                  ior ꝑ ſui ↄ̨tinuã ītenſionē idē mediū īuariatū tran-
                    <lb/>
                  ſeūdo valet motū ſuū vniformiṫ ad g̈dū remittere.</s>
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