Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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              <div xml:id="N16983" level="4" n="6" type="chapter" type-free="capitulum">
                <p xml:id="N17455">
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                    <pb chead="Primi tractatus" file="0074" n="74"/>
                  illatum / quia aut illud medium d. eſt medium pri-
                    <lb/>
                  mo modo puta trahens mobile cuiuſmodi eſt na-
                    <lb/>
                  uis aut aqua trahens natantem / et ſic ego nego ſe­
                    <lb/>
                  quelam. </s>
                  <s xml:id="N174B7" xml:space="preserve">Dico enim /  tale mobile quod ꝑ tale me­
                    <lb/>
                  dium mouetur: mouetur tota velocitate qua mo-
                    <lb/>
                  uetur ipſum mediū et inſuper velocitate propria:
                    <lb/>
                  et ſic aggregatum ex illis duabus velocitatibus
                    <lb/>
                  conſtituit velocitatem maiorē velocitate qua mo-
                    <lb/>
                  uetur ipſum mobile per rarefactionem. </s>
                  <s xml:id="N174C4" xml:space="preserve">Et ſic põt
                    <lb/>
                  ſemper pertingere quamdiu mouetur: aliqḋ pun­
                    <lb/>
                  ctum precedens ipſuꝫ. </s>
                  <s xml:id="N174CB" xml:space="preserve">quoniam quãdiu mouetur
                    <lb/>
                  intenſiori velocitate (computatis vtriuſ velocita­
                    <lb/>
                  tibus) mouetur quã aliquod punctum precedens
                    <lb/>
                  ipſum. </s>
                  <s xml:id="N174D4" xml:space="preserve">Sed cū motu proprio deuenerit ad nõ gra­
                    <lb/>
                  dum mouebitur a medio dūtaxat / et ſemper mane­
                    <lb/>
                  bit in eodem puncto medii. </s>
                  <s xml:id="N174DB" xml:space="preserve">Si vero medium d. ſit
                    <lb/>
                  medium ſecundo modo non trahens ipſum mobi­
                    <lb/>
                  le concedo illatum / et ad probationem dico /  non
                    <lb/>
                  habeo pro inconuenienti quando vna illarum re­
                    <lb/>
                  ſiſtentiarum mouetur et alia quieſcit </s>
                  <s xml:id="N174E6" xml:space="preserve">Ibi enim ce­
                    <lb/>
                  tera non ſunt paria. </s>
                  <s xml:id="N174EB" xml:space="preserve">¶ Hec argumenta partim
                    <lb/>
                  ſunt ex calculatore traducta: que ideo huic operi ī­
                    <lb/>
                  terſerui quoniam aliquid ſubtilitatis et difficul-
                    <lb/>
                  tatis pre ſe ferunt. </s>
                  <s xml:id="N174F4" xml:space="preserve">Tum etiam vt redderetur ipſe
                    <lb/>
                  calculator peruius et vadis plenus.</s>
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              <div xml:id="N17509" level="4" n="7" type="chapter" type-free="capitulum">
                <head xml:id="N1750E" xml:space="preserve">Septimum capitulum / in quo inquiri­
                  <lb/>
                tur: vtrum aliqua potentia non varia-
                  <lb/>
                riata per medium vniforme aut diffor-
                  <lb/>
                me, vniformiter ad non gradum vel ad
                  <lb/>
                gradum ſuum motum remittere aut in­
                  <lb/>
                tendere valeat.</head>
                <p xml:id="N1751B">
                  <s xml:id="N1751C" xml:space="preserve">ÃTea materia que ī titulo hu­
                    <lb/>
                  ius capitis tangitur valeat clare expe­
                    <lb/>
                  diri: ponam aliquas concluſiones qui­
                    <lb/>
                  bus probandis vnicam duobus correlariis adiū­
                    <lb/>
                  ctam ſuppoſitionem premittam. </s>
                  <s xml:id="N17527" xml:space="preserve">Que talis eſt.</s>
                </p>
                <p xml:id="N1752A">
                  <s xml:id="N1752B" xml:space="preserve">Si b. latitudo motus minor  a. ma­
                    <lb/>
                  ior diminuantur vniformiter in tempore equali
                    <lb/>
                  vel inequali perdendo adequate equalem latitu-
                    <lb/>
                  dinem motus: maior eſt proportio motus b. in pri­
                    <lb/>
                  ma medietate temporis in quo ipſum b. diminui-
                    <lb/>
                  tur ad ſeipſum in ſecunda medietate eiuſdem tem­
                    <lb/>
                  poris, quam ſit motus a. in prima medietate tem­
                    <lb/>
                  poris in quo ipſum a. diminuitur ad ſeipſum ī ſe-
                    <lb/>
                  cunda medietate eiuſdem tēporis. </s>
                  <s xml:id="N1753E" xml:space="preserve">Patet hec ſup­
                    <lb/>
                  poſitio ex ſecunda parte ſecundi correlarii prime
                    <lb/>
                  concluſionis vltimi capitis ſecunde partis / hoc ad­
                    <lb/>
                  dito /  motus vniformiter difformis et vniformi-
                    <lb/>
                  ter remiſſus correſpondet motui exiſtēti in medio
                    <lb/>
                  inſtanti temporis / in quo remittitur vniformiter:
                    <lb/>
                  quia talis motus eſt ſuus gradus medius.
                    <note position="left" xlink:href="note-0074-01a" xlink:label="note-0074-01" xml:id="N175CD" xml:space="preserve">1. correl.</note>
                  </s>
                  <s xml:id="N17552" xml:space="preserve">¶ Ex
                    <lb/>
                  quo ſequitur primo /  ſi b. potentia minor in ali-
                    <lb/>
                  quo tempore c. medium tranſeundo vniformiter
                    <lb/>
                  remittet motū ſuum. </s>
                  <s xml:id="N1755B" xml:space="preserve">et a. potentia maior in tempo­
                    <lb/>
                  re minori (vt opꝫ) idē c. mediū trãſeūdo vniformiṫ
                    <lb/>
                  remittit motum ſuum: maior eſt ꝓportio velocita­
                    <lb/>
                  tis ipſius b. in prima medietate tēporis in quo b.
                    <lb/>
                  vniformiter remittit motum ſuum ad velocitateꝫ
                    <lb/>
                  ſecunde medietatis eiuſdem temporis quam velo­
                    <lb/>
                  citatis ipſius a. ī prima medietate temporis ī quo
                    <lb/>
                  idem a. vniformiter remittit motum ſuum ad velo­
                    <lb/>
                  citatem ſecunde medietatis eiuſdē temporis. </s>
                  <s xml:id="N1756E" xml:space="preserve">Pa­
                    <lb/>
                  tet hoc correlarium ex ſuppoſitione / quia quando
                    <lb/>
                  b. potentia minor vniformiter remittit motū ſuū
                    <lb/>
                  in aliquo tempore c. medium tranſeundo: et a po-
                    <lb/>
                  tentia maior in tempore minori etiam vniformi-
                    <lb/>
                  ter remittit motum ſuum: iam latitudo motꝰ qua
                    <lb/>
                  mouetur b. potentia minor et latitudo motus ma­
                    <cb chead="Capitulum ſeptimum"/>
                  ior qua mouetur a. potentia maior in tempore eq̈­
                    <lb/>
                  li vel inequali diminuuntur vniformiter equalem
                    <lb/>
                  latitudinem adequate deperdendo / ergo maior ē
                    <lb/>
                  proportio motus ſiue velocitatis ipſius b. / in pri-
                    <lb/>
                  ma medietate temporis in quo ipſum b. vniformi­
                    <lb/>
                  ter remittit motum ſuum ad motum / quo idem b.
                    <lb/>
                  mouetur in ſecunda medietate eiuſdem temporis /
                    <lb/>
                  quam ſit proportio motus ipſius a. / in prima me-
                    <lb/>
                  dietate temporis in quo vniformiter remittit mo­
                    <lb/>
                  tum ſuum ad motum in ſecunda medietate eiuſdē
                    <lb/>
                  temporis. </s>
                  <s xml:id="N17594" xml:space="preserve">Conſequentia patet ex ſuppoſitione et
                    <lb/>
                  antecedens ex iſta concluſione. </s>
                  <s xml:id="N17599" xml:space="preserve">Diuerſe potentie
                    <lb/>
                  inuariate idem medium inuariatum tranſeuntes
                    <lb/>
                  </s>
                  <s xml:id="N1759F" xml:space="preserve">(Nam de inuariatis potentiis et medio inuaria-
                    <lb/>
                  to eſt ſermo) / in quo medio acquiritur aut deperdi­
                    <lb/>
                  tur motus equalem latitudinem motus acquirūt
                    <lb/>
                  vel deperdunt.
                    <note position="right" xlink:href="note-0074-02a" xlink:label="note-0074-02" xml:id="N175D3" xml:space="preserve">2. correl.</note>
                  </s>
                  <s xml:id="N175AD" xml:space="preserve">¶ Ex quo ſequitur ſecundo /  ſi b.
                    <lb/>
                  potētia minor in d. tempore c. medium tranſeūdo
                    <lb/>
                  vniformiter remittit motū ſuū: et a. potētia maior
                    <lb/>
                  in e. tempore mouendo equalem latitudinem mo-
                    <lb/>
                  tus vniformiter deperdit adequate ſicut b. / tunc ſi
                    <lb/>
                  velocitatis b. in prima medietate d. temporis ad
                    <lb/>
                  velocitatem eiuſdē b. in ſecunda medietate eiuſdē
                    <lb/>
                  temporis ſit f. proportio: minor proportio erit ve­
                    <lb/>
                  locitatis a. in prima medietate e. temporis ad ve-
                    <lb/>
                  locitatem a. in ſecunda medietate eiuſdē temporis
                    <lb/>
                  quam f. ꝓportio. </s>
                  <s xml:id="N175C4" xml:space="preserve">Patet hoc correlarium ex ſup-
                    <lb/>
                  poſitione.</s>
                </p>
                <p xml:id="N175D9">
                  <s xml:id="N175DA" xml:space="preserve">His premiſſis ſit prima cõcluſio. </s>
                  <s xml:id="N175DD" xml:space="preserve">Ali­
                    <lb/>
                  qua potentia non variata ſemper tranſeundo re-
                    <lb/>
                  ſiſtentiam vniformē: vniformiter continuo remit-
                    <lb/>
                  tit motum ſuum ad non gradum et ad gradum.</s>
                </p>
                <p xml:id="N175E6">
                  <s xml:id="N175E7" xml:space="preserve">Probatur hec concluſio / et volo /  ſit aliquod me­
                    <lb/>
                  dium vniforme reſiſtens vt .4. et potentia vt .8. q̄
                    <lb/>
                  non variata moueatur per illud: ſic tamen  illḋ
                    <lb/>
                  medium creſcat in reſiſtentia vniformiter ꝓportio­
                    <lb/>
                  nabiliter per totum. </s>
                  <s xml:id="N175F2" xml:space="preserve">ita  inequalibus tempori-
                    <lb/>
                  bus equales proportiones reſiſtentiarum acqui-
                    <lb/>
                  rat per totum / quo ad ſit reſiſtentia vt .8. / quo poſi-
                    <lb/>
                  to illud mobile tranſeundo illud medium remit-
                    <lb/>
                  tit motum ſuum vniformiter primo ad certū gra-
                    <lb/>
                  dum deinde ad non gradum / igitur concluſio ve-
                    <lb/>
                  ra. </s>
                  <s xml:id="N17601" xml:space="preserve">Antecedens probatur / quoniam reſiſtentia creſ­
                    <lb/>
                  ſcit ſemper eque proportionabiliter / igitur poten­
                    <lb/>
                  tia non variata mouens per eam vniformiter mo­
                    <lb/>
                  tum ſuū / remittit ſiue ad gradum ſiue ad non gra-
                    <lb/>
                  dum. </s>
                  <s xml:id="N1760C" xml:space="preserve">Patet conſequētia ex ſexta et quarta ſuppo­
                    <lb/>
                  ſitionibus quīti capitis huius tractatus coniunc­
                    <lb/>
                  tis. </s>
                  <s xml:id="N17613" xml:space="preserve">¶ Hic tamen tu aduerte /  quãuis illa potētia
                    <lb/>
                  non variata ſemꝑ mouetur per medium vniforme /
                    <lb/>
                  hoc eſt per medium / quod in quolibet īſtanti tem-
                    <lb/>
                  poris in quo mouetur eſt vniforme: per nullum ta­
                    <lb/>
                  men mediū aliqua vniformitate vniforme ſemper
                    <lb/>
                  mouetur / quia illḋ medium continuo habet aliam
                    <lb/>
                  et aliaꝫ vniformitatē.
                    <note position="right" xlink:href="note-0074-03a" xlink:label="note-0074-03" xml:id="N1763C" xml:space="preserve">corelar.</note>
                  </s>
                  <s xml:id="N17627" xml:space="preserve">¶ Ex quo ſequitur /  aliqua
                    <lb/>
                  potentia non variata ſemper tranſeūdo medium /
                    <lb/>
                  quod in quolibet inſtanti temporis in quo moue-
                    <lb/>
                  tur eſt vniforme: vniformiter intendit motum ſuuꝫ
                    <lb/>
                  </s>
                  <s xml:id="N17631" xml:space="preserve">Patet / ſi illa potentia vt .8. incipiat moueri per
                    <lb/>
                  reſiſtentiam vt .8. vniformiter proportionabili-
                    <lb/>
                  ter in reſiſtentia decreſcentem per totum.</s>
                </p>
                <p xml:id="N17642">
                  <s xml:id="N17643" xml:space="preserve">Secunda concluſio </s>
                  <s xml:id="N17646" xml:space="preserve">Aliqua potentia
                    <lb/>
                  non variata pertranſeundo mediuꝫ difforme: vni­
                    <lb/>
                  formiter remittit motum ſuum et ad gradum et ad
                    <lb/>
                  non gradum. </s>
                  <s xml:id="N1764F" xml:space="preserve">Probatur hec concluſio et capio
                    <lb/>
                  duo media equalia quorum vtrū ſit reſiſtētie vt
                    <lb/>
                  4. per totum: et volo /  fiat de vno illorum omni-
                    <lb/>
                  no eodem modo ſicut ponitur in precedenti cõclu­ </s>
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