Alvarus, Thomas, Liber de triplici motu, 1509

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                    <pb chead="Primi tractatus" file="0086" n="86"/>
                  ſuam quia a. potentia nunquam attinget b. poten­
                    <lb/>
                  tiam precedentem: igitur continuo mouebitur cum
                    <lb/>
                  minori reſiſtentia. </s>
                  <s xml:id="N18630" xml:space="preserve">et per conſequens cõtinuo remit-
                    <lb/>
                  tit potentiam ſuam. </s>
                  <s xml:id="N18635" xml:space="preserve">Patet hec conſequentia ex ſe-
                    <lb/>
                  pius ſuperius dictis. </s>
                  <s xml:id="N1863A" xml:space="preserve">Et probatur antecedens vide­
                    <lb/>
                  delicet /  a. nūquam attinget b. quia ſi attingit de-
                    <lb/>
                  tur in quo inſtanti attingit / et ſequitur /  ſemper an­
                    <lb/>
                  tea a principio mouebatur cum minori reſiſtentia:
                    <lb/>
                  et per conſequens remittebat poñam ſuam cõtinuo
                    <lb/>
                  vt iam ſepe argutum eſt: igitur continuo manſit mi­
                    <lb/>
                  nor: et in illo tempore adequate pertranſit maius
                    <lb/>
                  ſpacium per te: q2 b. precedebat: et continuo moue-
                    <lb/>
                  batur: igitur in eodem tempore adequate mai ſpa­
                    <lb/>
                  cium pertranſit poña minor continuo manens mi-
                    <lb/>
                  nor cum eadem reſiſtentia non variata quam potē­
                    <lb/>
                  tia maior manēs maior / quod eſt impoſſibile: et per
                    <lb/>
                  conſequens illud ex quo ſequitur videlicet /  aliquã­
                    <lb/>
                  do a. attingat b. </s>
                  <s xml:id="N18657" xml:space="preserve">Et ex hoc ſatis cõſtat /  punctus il­
                    <lb/>
                  le in quo motus eius eſt remiſſus ad non graduꝫ eſt
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                  punctus intrinſecus: quia motus eius eſt remiſſus
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                  ad non gradum in eodem inſtanti in quo motus b.
                    <lb/>
                  et non in eodem puncto medii: quia iam attingeret
                    <lb/>
                  b. et b. ī extrinſeco. </s>
                  <s xml:id="N18664" xml:space="preserve">Si autem proportio ipſius a. ad
                    <lb/>
                  punctum initiatiuum c. medii eſt minor ꝓportione
                    <lb/>
                  ipſius b. ad punctum initiatiuum ſecunde partis ꝓ­
                    <lb/>
                  portionalis ipſius c. medii diuiſi ꝓportiõe h. etc. ſit
                    <lb/>
                  minor in l. ꝓportione: et ſequitur /  continuo ip̄a po­
                    <lb/>
                  tentia a. in l. ꝓportione tardius mouebitur quam
                    <lb/>
                  poña b. / et ex conſequenti cum b. fuerit in termino c.
                    <lb/>
                  medii in quo motus eius eſt remiſſus ad non gradū /
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                  ex hypotheſi a. erit in puncto aliquo intrinſeco in l.
                    <lb/>
                  ꝓportione minus diſtante ab extremo remiſſiori c.
                    <lb/>
                  medii / quam diſtet extremuꝫ a puncto a quo incepit
                    <lb/>
                  moueri b. / vt conſtat: et in tali puncto a. poña remit-
                    <lb/>
                  tit motum ſuum ad non gradum / vt patet ex ſuperi-
                    <lb/>
                  oribus et continuo vniformiter remittendo motum
                    <lb/>
                  ſuum: et hoc per continuam eius remiſſionem / igitur
                    <lb/>
                  ꝓpoſitum. </s>
                  <s xml:id="N18685" xml:space="preserve">Prima pars minoris patet ex prīa ſup­
                    <lb/>
                  poſitione huius. </s>
                  <s xml:id="N1868A" xml:space="preserve">Sed  continue remittat potētiaꝫ
                    <lb/>
                  ſuam probatur: quia ſemper mouebitur cum mino­
                    <lb/>
                  ri reſiſtentia quam b. in l. ꝓportione tardius conti-
                    <lb/>
                  nuo remittendo motum vniformiter: igitur cõtinue
                    <lb/>
                  remittit poñam ſuam: </s>
                  <s xml:id="N18695" xml:space="preserve">Conſequentia patet intelli-
                    <lb/>
                  genti modum probandi alias concluſiones: et an­
                    <lb/>
                  tecedens ſimiliter. </s>
                  <s xml:id="N1869C" xml:space="preserve">Et ſic ptꝫ correlarium.</s>
                </p>
                <p xml:id="N186A9">
                  <s xml:id="N186AA" xml:space="preserve">Sexta concluſio </s>
                  <s xml:id="N186AD" xml:space="preserve">Ubi aliqua potentia
                    <lb/>
                  inuariata aliquod medium inuariatum tranſeun-
                    <lb/>
                  do vniformiter continuo remittit motum ſuum ad
                    <lb/>
                  non gradum: omnis poña minor habens ꝓportio-
                    <lb/>
                  nem maioris inequalitatis ad punctum initiatiuū
                    <lb/>
                  c. medii in extremo remiſſiori valet motum ſuum cõ­
                    <lb/>
                  tinuo vniformiter ad non gradum remittere idem
                    <lb/>
                  medium inuariatum tranſeundo. </s>
                  <s xml:id="N186BE" xml:space="preserve">aliquando inten­
                    <lb/>
                  dendo potentiam, quando vero continuo remit-
                    <lb/>
                  tendo. </s>
                  <s xml:id="N186C5" xml:space="preserve">Probatur hec concluſio / et ſit b. poña que in­
                    <lb/>
                  uariata c. medium inuariatum tranſeundo conti-
                    <lb/>
                  nuo vniformiter remittit motū ſuū ad nõ gradū ī ex­
                    <lb/>
                  tremo intenſiori c. medii: ſit a. poña minor habēs
                    <lb/>
                  ad punctum initiatiuum c. medii in extremo remiſ-
                    <lb/>
                  ſiori ꝓportionem maioris inequalitatis in h. ꝓpor­
                    <lb/>
                  tione minorem quam ad idem punctum habeat b.
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                  potentia: et manifeſtum eſt /  ad aliquod punctum
                    <lb/>
                  intrinſecum habet a. potentia proportionem
                    <lb/>
                  equalitatis: capio igitur totam illam partem
                    <lb/>
                  c. medii a puncto videlicet initiatiuo in extremo re-
                    <lb/>
                  miſſiori vſ ad illum punctum ad quem habet pro­
                    <lb/>
                  portionem equalitatis ipſa a. poña: et diuido illaꝫ
                    <lb/>
                  partem per partes ꝓportionales ꝓportione h. et po­
                    <cb chead="Capitulum octauum"/>
                  natur a. poña in initio ſecūde partis ꝓportionalis
                    <lb/>
                  illius partis c. medii ſic diuiſi ꝓportione h. / et cõſtat
                    <lb/>
                  ꝓportionem quam habet b. ad punctum initiatiuū
                    <lb/>
                  c. medii in extremo remiſſiori ſe habere in maiori ꝓ­
                    <lb/>
                  portione quam h. ad ꝓportionem quaꝫ habet a. po­
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                  tentia minor ad illum punctum intrinſecum in quo
                    <lb/>
                  pouitur: ſit igitur illa ꝓportio l. et incipiat ab eo-
                    <lb/>
                  dem inſtanti moueri illa poñe: b. a puncto initiati-
                    <lb/>
                  uo c. medii in extremo remiſſiori: a. vero a puncto il­
                    <lb/>
                  lo in quo ponitur: et ita varietur a. /  continuo mo-
                    <lb/>
                  ueatur in l. ꝓportione tardius ipſa b. poña. </s>
                  <s xml:id="N186F9" xml:space="preserve">tunc di­
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                  co /  a. continuo vniformiter remittit motum ſuum
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                  ad non gradū, aliquando intendendo continuo po­
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                  tentiam ſuam, aliquando vero continuo remitten-
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                  do. </s>
                  <s xml:id="N18704" xml:space="preserve">Quod ſic probatur: quia a. continuo vniformi-
                    <lb/>
                  ter remittit motum ſuum vſ ad non gradum cum
                    <lb/>
                  continuo in l. ꝓportione tardius moueatur ꝙ̄ ipſa
                    <lb/>
                  potentia b. continuo vniformiter remittens motuꝫ
                    <lb/>
                  ſuum vſ ad non gradum in eodem tempore adeq̈-
                    <lb/>
                  te: et per totum tempus quo precedet a. poña, ipſam
                    <lb/>
                  potentiam b. (quia precedit ex hypotheſi) ipſa con-
                    <lb/>
                  tinuo intendet poñam ſuaꝫ: et per totum tempꝰ quo
                    <lb/>
                  ſequetur b. potentiam, ipſa continuo remittit po-
                    <lb/>
                  tentiam ſuam: igitur a. potentia continuo vniformi­
                    <lb/>
                  ter remittit motum ſuum ad non gradum aliquãdo
                    <lb/>
                  continuo intendendo poñam et aliquando cõtinuo
                    <lb/>
                  remittendo. </s>
                  <s xml:id="N1871F" xml:space="preserve">Conſequentia patet: et probatur ante-
                    <lb/>
                  cedens: ꝓbando primum /  a. poña aliquando p̄ce­
                    <lb/>
                  det: et aliquando ſequitur b. poñam: quia b. poten-
                    <lb/>
                  tia deueniet ad punctum ad quem habet a. potētia
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                  ꝓportioneꝫ equalitatis in principio motus: et tunc
                    <lb/>
                  a. poña ſequetur eam: igitur a. poña aliquando ſe-
                    <lb/>
                  quetur b. poñam: et aliquando precedet / vt patet ex
                    <lb/>
                  hypotheſi: igitur per aliquod tempus precedet / et ꝑ
                    <lb/>
                  aliquod ſequetur: </s>
                  <s xml:id="N18732" xml:space="preserve">Sed ꝓbatur /  cum b. erit ad pū­
                    <lb/>
                  ctum ad quem a principio motus a. habet propor-
                    <lb/>
                  tionem equalitatis. </s>
                  <s xml:id="N18739" xml:space="preserve">ipſa b. potentia precedet a. / q2
                    <lb/>
                  ſi continuo b. potentia moueretur velocius in h. ꝓ-
                    <lb/>
                  portione quam a. cum reſiduo hypotheſis: eque pri­
                    <lb/>
                  mo a. et b. deuenirent ad illum punctum ad quem a.
                    <lb/>
                  potentia habet proportionem equalitatis a prin-
                    <lb/>
                  cipio motus: quoniam tunc pertranſirent in eodem
                    <lb/>
                  tempore adequate ſpacia ſe habentia in h. ꝓportio­
                    <lb/>
                  ne / vt patet ex hypotheſi: iuuamine prime concluſio­
                    <lb/>
                  nis quinti capitis prime partis: ſed b. modo conti-
                    <lb/>
                  nuo in maiori ꝓportione velocius mouetur ip̄a po­
                    <lb/>
                  tentia a. / quam tunc ceteris omnibus paribus: igi-
                    <lb/>
                  tur citius modo et prius b. potentia attinget illū pū­
                    <lb/>
                  ctum quam a. potentia: et per conſequens cuꝫ b. erit
                    <lb/>
                  ad punctum ad quem a principio motus a. habet ꝓ­
                    <lb/>
                  portionem equalitatis: ipſa b. potentia precedet a. /
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                  quod fuit probandum. </s>
                  <s xml:id="N1875A" xml:space="preserve">Et iſto probato iam probo
                    <lb/>
                  primam partem minoris videlicet /  per illud tem-
                    <lb/>
                  pus quo precedet a. potentia ipſaꝫ poñam b. ip̄a a.
                    <lb/>
                  poña continuo intendit poñam ſuam: quia per nul­
                    <lb/>
                  lam partem talis temporis ipſa poña a. ſtat inua-
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                  riata, aut remittit poñam ſuam: igitur continuo in­
                    <lb/>
                  tendit poñam ſuam. </s>
                  <s xml:id="N18769" xml:space="preserve">Probatur antecedens: quia ſi
                    <lb/>
                  per aliquam partem illius temporis poña a. ſtat in­
                    <lb/>
                  uariata, aut remittit poñam ſuam: ſignetur illud. </s>
                  <s xml:id="N18770" xml:space="preserve">et
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                  ſit g. et pars pertranſita adequate in eodem g. tem­
                    <lb/>
                  pore ab ipſa potentia b. ſit .ef. et pars ꝑtranſita ab
                    <lb/>
                  a. poña in eodem d. tꝑe ſit d. / et manifeſtum eſt /  ip-
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                  ſius .ef. partis ad d. partem eſt ꝓportio l. cum ſem-
                    <lb/>
                  per b. poña in l. proportione velocius moueatur ip­
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                  ſa a. poña / vt patet ex hypotheſi. </s>
                  <s xml:id="N1877F" xml:space="preserve">Quo poſito argui­
                    <lb/>
                  tur ſic / latitudinis motus deperdite ab ipſa poña
                    <lb/>
                  b. tranſeundo .ef. parteꝫ in g. tempore adequate ad
                    <lb/>
                  latitudinem motus deperditam ab eadem potētia </s>
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