Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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                    <pb chead="Primi tractatus" file="0084" n="84"/>
                  velociꝰ ipſa poña a. / vt patet ex hypotheſi / quo po­
                    <lb/>
                  ſito arguitur ſic / latitudinis motus deperdite ab
                    <lb/>
                  ipſa b. potentia tranſeundo .ef. partem in g. tem­
                    <lb/>
                  pore adequate ad latitudinem motus deperditaꝫ
                    <lb/>
                  ab eadem poña b. tranſeundo d. partem non eſt ꝓ­
                    <lb/>
                  portio quadrupla nec maior: ergo latitudinis de­
                    <lb/>
                  perdite ab b. poña tranſeundo .ef. partem in tēpo­
                    <lb/>
                  re g. ad latitudinem motus deperditam ab a. po-
                    <lb/>
                  tentia ſtante inuariata vel remittente poñam ſuã
                    <lb/>
                  tranſeundo d. partem in g. tempore adequate nõ
                    <lb/>
                  eſt proportio quadrupla nec maior quadrupla: ſꝫ
                    <lb/>
                  conſequens eſt falſum: igitur illud ex quo ſequit̄̄.
                    <lb/>
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                  <s xml:id="N18393" xml:space="preserve">Patet conſequentia / quia omnes poñe inuariate
                    <lb/>
                  idem medium tranſeuntes etc. equalem latitudinē
                    <lb/>
                  motus deperdunt. </s>
                  <s xml:id="N1839A" xml:space="preserve">et ſi aliqua poña tranſeūdo idē
                    <lb/>
                  medium īuariatum remittendo motum ſuum etc.
                    <lb/>
                  remittat poñam ſuam: ipſa maiorem latitudineꝫ
                    <lb/>
                  motus deperdit quam ſi ſtaret idem medium inua­
                    <lb/>
                  riatum tranſeundo: vt conſtat ex quarto argumē­
                    <lb/>
                  to ſexti capitis. </s>
                  <s xml:id="N183A7" xml:space="preserve">Sed falſitas conſequentis proba­
                    <lb/>
                  tur / quia ſi latitudinis deperdite ab ipſa b. poten­
                    <lb/>
                  tia tranſeundo .ef. partem in g. tempore ad veloci­
                    <lb/>
                  tatem deperditam ab a. poña tranſeundo d. par-
                    <lb/>
                  tem in eodem g. tempore non eſt ꝓportio quadru-
                    <lb/>
                  pla nec maior: et a principio latitudinis motus ip­
                    <lb/>
                  ſius b. ad latitudinem motus ipſius a. eſt ꝓportio
                    <lb/>
                  quadrupla: ſequitur /  facta tali variatione lati-
                    <lb/>
                  tudinis motus ipſius b. ad latitudinem motus ip­
                    <lb/>
                  ſius a. non eſt ꝓportio quadrupla: quod eſt cõtra
                    <lb/>
                  hypotheſim. </s>
                  <s xml:id="N183BE" xml:space="preserve">Conſequentia tamen patet ex primo
                    <lb/>
                  correlario et ſecundo quinte concluſionis ſecundi
                    <lb/>
                  capitis ſecunde partis. </s>
                  <s xml:id="N183C5" xml:space="preserve">Iam ꝓbatur antecedens
                    <lb/>
                  videlicet /  latitudinis motus deperdite a b. poña
                    <lb/>
                  tranſeundo in g. tempore .ef. partem ad latitudi-
                    <lb/>
                  nem deꝑditam ab eadem b. poña tranſeundo d. ꝑ­
                    <lb/>
                  tem nõ eſt ꝓportio quadrupla nec maior: quia ip̄i­
                    <lb/>
                  us .ef. ꝑtis ad d. partem eſt ꝓportio quadrupla ex
                    <lb/>
                  caſu: et ipſa poña b. tranſeundo quãlibet ꝑtem ex­
                    <lb/>
                  ceſſus ip̄ius .ef. ꝑtis minorem d. ꝑte: mouetur cum
                    <lb/>
                  minori reſiſtentia quam tranſeundo quamlibet ꝑ­
                    <lb/>
                  tem equalem ipſius d. ꝑtis: cum quelibet pars ex-
                    <lb/>
                  ceſſus quo .ef. pars excedit d. ꝑtem minus diſtet a
                    <lb/>
                  puncto iniciatiuo c. medii a quo incipit motus (ſi­
                    <lb/>
                  gno enim exceſſum illum verſus punctum remiſſiꝰ
                    <lb/>
                  c. medii a quo incipit motus) / ergo latitudinis de­
                    <lb/>
                  perdite ab ipſa b. poña tranſeundo .ef. ꝑtem in g.
                    <lb/>
                  tempore adequate ad latitudinem deꝑditaꝫ ab ea­
                    <lb/>
                  dem b. poña tranſeundo d. ꝑtem non eſt ꝓportio
                    <lb/>
                  quadrupla nec maior: quod fuit ꝓbandum. </s>
                  <s xml:id="N183EA" xml:space="preserve">Pa-
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                  tet conſequentia ex quarta ſuppoſitione huius</s>
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                <p xml:id="N183EF">
                  <s xml:id="N183F0" xml:space="preserve">Q, autem a. poña remittit motum ſuum ad non
                    <lb/>
                  gradum: ꝓbatur / quoniam cõtinuo ex hypotheſi ī­
                    <lb/>
                  ter motum ipſius b. et motum ipſius a. eſt ꝓportio
                    <lb/>
                  quadrupla: vtro illorum motuum decreſcente:
                    <lb/>
                  et motus ipſius b. poñe tranſeuntis quatuor quar­
                    <lb/>
                  tas ipſius c. medii in extremo intenſiori eiuſdeꝫ c.
                    <lb/>
                  medii remittitur ad non gradum: igitur etiã mo-
                    <lb/>
                  tus ipſius a. poñe mouentis in quadruplo tardiꝰ
                    <lb/>
                  in eodem tempore tranſeundo vltimam quartam
                    <lb/>
                  c. medii in extremo intenſiori remittitur ad nõ gra­
                    <lb/>
                  dum. </s>
                  <s xml:id="N18407" xml:space="preserve">Patet conſequētia ex octauo correlario q̈r­
                    <lb/>
                  te concluſionis octaui capitis ſecunde ꝑtis: </s>
                  <s xml:id="N1840C" xml:space="preserve">Et ſic
                    <lb/>
                  patet concluſio. </s>
                  <s xml:id="N18411" xml:space="preserve">¶ Ex quo ſequitur /  vbi aliqua
                    <lb/>
                  poña non variata aliquod medium tranſeūdo vni­
                    <lb/>
                  formiter remittit motum ſuum: omnis minor hñs
                    <lb/>
                  ꝓportionem maioris inequalitatis ad punctū in­
                    <lb/>
                  itiatiuum eiuſdem medii in extremo remiſſiori vni­
                    <lb/>
                  formiter continuo remittit motum ſuum idē medi­
                    <lb/>
                  um tranſeundo īuariatum per continuam ſui intē­
                    <cb chead="Capitulum octauum"/>
                  ſſonem. </s>
                  <s xml:id="N18423" xml:space="preserve">Probatur / ſit b. poña que variata totuꝫ c.
                    <lb/>
                  medium inuariatum tranſeundo vniformiter re-
                    <lb/>
                  mittit motum: et a poña minor habens ad initiati­
                    <lb/>
                  uum punctum c. medii in extremo remiſſiori ꝓpor­
                    <lb/>
                  tionem maioris inequalitatis: et cum ipſa a. poña
                    <lb/>
                  habeat ad aliquem punctum intrinſecum eiuſdeꝫ
                    <lb/>
                  c. medii etiam ꝓportionem maioris inequalitatis
                    <lb/>
                  ponatur ip̄a poña a. in tali puncto et b. poña in ṗn­
                    <lb/>
                  cipio c. medii in extremo remiſſiori: et ꝓportionis
                    <lb/>
                  ipſius b. ad punctum initiatiuum c. medii ad pro-
                    <lb/>
                  portionem ipſius a. quam habet ad punctum in-
                    <lb/>
                  trinſecum ad quod ponitur ſit h. ꝓportio: et incipi­
                    <lb/>
                  at ī eodē īſtãti ab illis pūctis moueri a. et b. ſꝫ b. cõ­
                    <lb/>
                  tinuo in h. ꝓportione velocius ip̄a poña a. / et mani­
                    <lb/>
                  feſtum eſt /  non ſubito b. poña deueniet ad pūctū
                    <lb/>
                  a quo incipit moueri a. poña: capio igitur ſpaciuꝫ /
                    <lb/>
                  quod abſoluet a. poña in tempore in quo b. poña
                    <lb/>
                  deueniet ad pūctum a quo incipit moueri a. poña
                    <lb/>
                  et ſit illud ſpacium d. / et tunc dico /  tam a. quam b.
                    <lb/>
                  tranſeundo d. mediū vniformiter remittet motuꝫ
                    <lb/>
                  ſuum: et a. poña continuo d. medium tranſeundo ī­
                    <lb/>
                  tendit poñam ſuam. </s>
                  <s xml:id="N18450" xml:space="preserve">Quod ſic oſtenditur / quia a.
                    <lb/>
                  poña tranſeundo d. medium continuo vniformi-
                    <lb/>
                  ter remittit motum ſuum / vt ſupra in concluſione
                    <lb/>
                  quarta probatum eſt: et ipſa a. poña continuo trã­
                    <lb/>
                  ſeundo d. ꝑtem intendit poñam ſuam: igitur ꝓpo­
                    <lb/>
                  poſitum. </s>
                  <s xml:id="N1845D" xml:space="preserve">Probatur minor / quia ſi a. per aliquod
                    <lb/>
                  tempus d. medium inuariatum tranſeundo ſtat ī-
                    <lb/>
                  uariata vel remittit potentiam ſuam. </s>
                  <s xml:id="N18464" xml:space="preserve">detur illud
                    <lb/>
                  tempus et ſit g. et pars pertranſita ab a. in g. tēpo­
                    <lb/>
                  re adequate ſit e. et pars pertranſita adequate in
                    <lb/>
                  eodem g. tempore ab ip̄a poña b. ſit .ef. / et manife-
                    <lb/>
                  ſtum eſt /  ip̄ius .ef. partis ad e. partem eſt ꝓportio
                    <lb/>
                  h. quia continuo potentia b. in h. ꝓportione velo-
                    <lb/>
                  cius mouetur quaꝫ ipſa potentia a. / vt patet ex hy­
                    <lb/>
                  potheſi. </s>
                  <s xml:id="N18475" xml:space="preserve">Quo poſito arguitur ſic / latitudinis mo-
                    <lb/>
                  tus deperdite ab ipſa b. potentia tranſeundo .ef.
                    <lb/>
                  partem in g. tempore adequate ad latitudinē mo­
                    <lb/>
                  tus deperditam ab eadeꝫ potentia b. tranſeundo
                    <lb/>
                  e. partem non eſt proportio h. nec maior: ergo la-
                    <lb/>
                  titudinis deperdite ab ip̄a b. poña tranſeundo .ef:
                    <lb/>
                  ꝑtem in g. tempore adequate ad latitudinem mo-
                    <lb/>
                  tus deperditam ab a. potentia ſtãte inuariata vel
                    <lb/>
                  remittente potentiam ſuam tranſeundo e. parteꝫ
                    <lb/>
                  in g. tempore adequate non eſt ꝓportio h. nec ma­
                    <lb/>
                  ior: ſed conſequens eſt falſum: igitur illud ex quo
                    <lb/>
                  ſequitur. </s>
                  <s xml:id="N1848E" xml:space="preserve">Conſequentia patet cum antecedente ex
                    <lb/>
                  ꝓbatione concluſionis: et ſimiliter falſitas conſe­
                    <lb/>
                  quentis </s>
                  <s xml:id="N18495" xml:space="preserve">Patet igitur correlarinm.</s>
                </p>
                <note position="right" xml:id="N18498" xml:space="preserve">q̈drageſi­
                  <lb/>
                ma q̈rta
                  <lb/>
                ↄ̨clu. cal.</note>
                <p xml:id="N184A0">
                  <s xml:id="N184A1" xml:space="preserve">Quinta concluſio </s>
                  <s xml:id="N184A4" xml:space="preserve">Ubi aliqua poten­
                    <lb/>
                  tia inuariata inuariarum medium tranſeundo
                    <lb/>
                  vniformiter continuo remittit motum ſuum ad nõ
                    <lb/>
                  gradum: aliqua minor per cõtinuam ſui remiſſio­
                    <lb/>
                  nem continuo vniformiter remittit motum ſuum
                    <lb/>
                  ad non gradum in aliquo puncto intrinſeco dati
                    <lb/>
                  medii idem medium inuariatum trãſeundo </s>
                  <s xml:id="N184B3" xml:space="preserve">Pro­
                    <lb/>
                  batur / ſit b. poña que vniformiter continuo remit­
                    <lb/>
                  tit motum ſuum totum c. medium tranſeundo vſ
                    <lb/>
                  ad nõ gradum: ſit a. poña minor que habeat ad
                    <lb/>
                  punctum initiatiuum c. medii in extremo remiſſio­
                    <lb/>
                  ri ꝓportionem in ſexquialtero maiorem quam b.
                    <lb/>
                  poña habeat ad punctum initiatiuum vltime q̈r-
                    <lb/>
                  te magis reſiſtentis: ponatur a. poña in puncto
                    <lb/>
                  initiatiuo c. medii in extremo remiſſiori: et b. poña
                    <lb/>
                  in puncto initiatiuo vltime quarte magis reſiſten­
                    <lb/>
                  tis: et in eodem inſtanti incipiant ab illis punctis
                    <lb/>
                  moueri a. cõtinuo in ſexquialtero velocius ip̄o b.
                    <lb/>
                  quo ad b. deueniat ad extremum intenſius c. medii
                    <lb/>
                  in quo habet non gradum motus: et manifeſtū eſt / </s>
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