Alvarus, Thomas, Liber de triplici motu, 1509

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                <pb chead="De motu locali mixto  difformi tꝑe  ſubiecto quo ad effectū" file="0170" n="170"/>
                <p xml:id="N207E2">
                  <s xml:id="N207E3" xml:space="preserve">Sed cõtra / q2 tūc ſequeretur /  ſtaret
                    <lb/>
                  ī caſu ſortē valde fatigari nitendo moueri nullo im­
                    <lb/>
                  pedimēto poſito imo ipſo ſorte habēte optimã diſ­
                    <lb/>
                  poſitionē. </s>
                  <s xml:id="N207EC" xml:space="preserve">ad currenduꝫ et ad mouēdū: et tñ nullo pa­
                    <lb/>
                  cto moueri: ſed hoc ē falſuꝫ igitur. </s>
                  <s xml:id="N207F1" xml:space="preserve">Falſitas ↄ̨ñtꝪ pꝫ /
                    <lb/>
                  q2 ſi nullū ē īpedimentū: et ſortes nitit̄̄ moueri: ſeq̇t̄̄ /
                    <lb/>
                   ipſe ſortes mouetur. </s>
                  <s xml:id="N207F8" xml:space="preserve">Itē ſortes fatigat̄̄: et nõ niſi
                    <lb/>
                  q2 mouetur: igr̄ ſortes mouetur </s>
                  <s xml:id="N207FD" xml:space="preserve">Seq̄la tñ ꝓbatur et
                    <lb/>
                  pono caſu /  ſortes ſit in naui q̄ moueat̄̄ ſus oriē-
                    <lb/>
                  tē: et ſortes nitatur moueri ſus occidentē. </s>
                  <s xml:id="N20804" xml:space="preserve">ita  ſor­
                    <lb/>
                  tes deſcribat aliquod ſpaciū in ipſa naui ita velo­
                    <lb/>
                  citer ſicut nauis mouetur adequate: et moueat̄̄ na-
                    <lb/>
                  uis ita velociter  ſortes fatigetur plurimū. </s>
                  <s xml:id="N2080D" xml:space="preserve">Quo
                    <lb/>
                  poſito arguitur ſic / ſortes fatigatur nitendo moue­
                    <lb/>
                  ri nullo īpedimēto poſito et tñ nõ mouetur igr̄. </s>
                  <s xml:id="N20814" xml:space="preserve">Mi-
                    <lb/>
                  nor ꝓbatur / q2 ſortes ſemꝑ eſt in eodē loco reſpectu
                    <lb/>
                  ſpacii fixi ex quo debet ſumi idētitas loci et īmobili­
                    <lb/>
                  tas. </s>
                  <s xml:id="N2081D" xml:space="preserve">vt patet ꝑ phm̄ quarto phiſicoꝝ dicentē locū eē
                    <lb/>
                  terminū cõtinētis īmobilē ṗmū: igitur ſortes ī tali
                    <lb/>
                  caſu nõ mouet̄̄ (nullū eī ſpaciū fixū deſcribit) / igitur</s>
                </p>
                <p xml:id="N20824">
                  <s xml:id="N20825" xml:space="preserve">Tertio prīcipalit̄̄ ↄ̨̨tra eadē ꝑtē q̄ſtio­
                    <lb/>
                  nis arguitur ſic: q2 nullꝰ eſt motꝰ mixtus. </s>
                  <s xml:id="N2082A" xml:space="preserve">g̊ illa pars
                    <lb/>
                  p̄ſupponit falſum et ꝑ ↄ̨ñs falſa. </s>
                  <s xml:id="N2082F" xml:space="preserve">Añs ꝓbatur / q2 ſi
                    <lb/>
                  eſſet aliq̇s motus mixtus maxime eſſet motus cõpo­
                    <lb/>
                  ſitus ex aſcenſu et deſcēſu: ſꝫ nullus eſt dabilis ta-
                    <lb/>
                  lis: igitur. </s>
                  <s xml:id="N20838" xml:space="preserve">Probat̄̄ minor / q2 ſi aliq̇s talis eēt dabi­
                    <lb/>
                  lis: ſeq̄retur /  dabile eēt vnū corpꝰ finitū cuius vna
                    <lb/>
                  pars aſcenderet et alia deſcenderet: et relictum ſue
                    <lb/>
                  naturali diſpoſitione ſic ꝑpetuo moueretur ↄ̨tinuo
                    <lb/>
                  vna ꝑte eiꝰ aſcendente et alia deſcendēte: ſꝫ ↄ̨ñs ē fal­
                    <lb/>
                  ſum: igr̄ illḋ ex quo ſeq̇t̄̄. </s>
                  <s xml:id="N20845" xml:space="preserve">Seq̄la ꝓbatur et pono caſū /
                    <lb/>
                   terra ſit ꝑforata ꝑ cētrū mūdi ab oriēte in occidē­
                    <lb/>
                  tē: et capiat̄̄ globꝰ terre vniformis grauitatis vĺ ali­
                    <lb/>
                  cuiꝰ alteriꝰ figure (ī idē reddit) descēdat illa terra
                    <lb/>
                  ꝑ illḋ foramē vſ. ad cētrū mūdi illo foramīe vacuo
                    <lb/>
                  exñte ꝑmittat deꝰ illã terrã moueri tãdiu ̄diu ha­
                    <lb/>
                  buerit ꝓportionē maioris ineq̈litatis ad mouēdū.
                    <lb/>
                  </s>
                  <s xml:id="N20855" xml:space="preserve">Quo poſito ſic argumētor. </s>
                  <s xml:id="N20858" xml:space="preserve">illa terra ꝑpetuo moue­
                    <lb/>
                  bit̄̄ ↄ̨tinuo vna ꝑte eiꝰ aſcēdēte et alṫa deſcēdēte: igr̄
                    <lb/>
                  ꝓpoſitū </s>
                  <s xml:id="N2085F" xml:space="preserve">Probat̄̄ añs / q2 īclinatio illiꝰ ṫre ē  cētrū
                    <lb/>
                  eiꝰ ſit cētrū mūdi: cū idē ſit locꝰ totiꝰ et ꝑtꝪ prīo celi.
                    <lb/>
                  </s>
                  <s xml:id="N20865" xml:space="preserve">igr̄ illa terra ſue naturali diſpoſitioni relicta cõti­
                    <lb/>
                  nuo mouebit̄̄ quovſ (ſi fieri p̄t) cētrū eiꝰ ſit cētrum
                    <lb/>
                  mundi: ſꝫ ſic mouēdo ꝑ infinitū tp̄s mouebit̄̄ ãtea̄
                    <lb/>
                  (ſi fieri p̄t) cētrū eiꝰ fiat cētrū mūdi: igr̄ illa terra ꝑ-
                    <lb/>
                  petuo mouebit̄̄ cõtinuo vna ꝑte eiꝰ aſcendēte et alia
                    <lb/>
                  deſcēdēte: qḋ fuit ꝓbandū </s>
                  <s xml:id="N20872" xml:space="preserve">Sꝫ iam ꝓbo /  talis terra ſic
                    <lb/>
                  mouēdo ꝑ infinitū tp̄s mouebit̄̄ antea ꝙ̄ etc. cētrū eiꝰ
                    <lb/>
                  fiat cētrū mūdi. </s>
                  <s xml:id="N20879" xml:space="preserve">Qḋ ſic ꝓbat̄̄ et volo /  diuidat̄̄ illa
                    <lb/>
                  terra in q̈tuor ꝑtes eq̈les: et  vna illaꝝ ſit vltra cen­
                    <lb/>
                  trū reliq̄ vero tres ſint citra centrū: et manifeſtū eſt
                    <lb/>
                   q̈rta vltra cētrū reſiſtit tribꝰ q̈rtis citra cētruꝫ ne
                    <lb/>
                  deſcēdãt vt ↄ̨ſtat: et deſcēdūt ſiue īcipiūt deſcendere
                    <lb/>
                  illi tres q̈rte a ꝓportione tripla mouēdo vel mīori:
                    <lb/>
                  vt patet ex caſu: diuido igr̄ medietatē exceſſus quo
                    <lb/>
                  pars citra cētrū excedit ꝑtē vltra cētrū q̄ q̇dē medie-
                    <lb/>
                  tas exceſſus eſt vna q̈rta īter cētrū illius globi et cē­
                    <lb/>
                  trū mundi: et hoc ꝑ ꝑtes ꝓportionales ꝓportiõe du­
                    <lb/>
                  pla maioribꝰ ſus cētrū mūdi terminatis quo poſi­
                    <lb/>
                  to arguit̄̄ ſic q̄libet pars ꝓportionalis illius exceſ­
                    <lb/>
                  ſus descēdet: et ꝑ tãtū tꝑis vel maiꝰ mouebit̄̄ ſiue de­
                    <lb/>
                  ſcēdet q̄libet ſicut īmediate p̄cedens eã: et ſūt infini-
                    <lb/>
                  te: igr̄ ꝑ infinitꝫ tp̄s mouebitur talis terra / qḋ fuit ꝓ­
                    <lb/>
                  bãdū </s>
                  <s xml:id="N2089A" xml:space="preserve">Probat̄̄ minor / q2 ṗma illaꝝ ꝑtiū deſcendet
                    <lb/>
                  a ꝓportione tripla vel minori. </s>
                  <s xml:id="N2089F" xml:space="preserve">et ſcḋa deſcendet a ꝓ­
                    <lb/>
                  portione ſuprabiꝑtiēs tertias vel minori q̄ ē minor
                    <lb/>
                  ̄ ſubdupla ad triplã vt ↄ̨ſtat intuenti: et tertia a ꝓ­
                    <lb/>
                  portione ſuprabipartiente ſeptimas vel minori q̄
                    <lb/>
                  eſt minor ꝙ̄ ſubdupla ad ꝓportionē ſuprabipartiē­
                    <cb chead="De motu locali mixto  difformi tꝑe  ſubiecto quo ad effectū"/>
                  tē tertias / vt patet aſpiciēti: et quarta deſcendet a ꝓ­
                    <lb/>
                  portione ſuprabipartiente quīdecimas vel minori
                    <lb/>
                  q̄ eſt minor ꝙ̄ ſubdupla ad ꝓportioneꝫ ſuprabipar­
                    <lb/>
                  tientē ſeptimas / et ſic ↄ̨̨ñter repperies  q̄libet pars
                    <lb/>
                  ꝓportionalis medietatis illius exceſſus ſequēs de­
                    <lb/>
                  ſcendit a ꝓportione ſubdupla vel minor ad ꝓpor-
                    <lb/>
                  tionē a qua īcipit deſcendere pars īmediate prece-
                    <lb/>
                  dens: et ille ꝑtes ꝓportionales cõtinuo ſe hñt in pro­
                    <lb/>
                  portione dupla: igr̄ ꝑ tãtū tꝑis vel maius mouebit̄̄
                    <lb/>
                  ſiue descēdet q̄libet pars ꝓportionalis ſicut īmedi­
                    <lb/>
                  ate p̄cedēs eã: vel ſaltē ſequitur ꝑ infinitum tp̄s mo­
                    <lb/>
                  uebitur talis terra / qḋ ꝓbare intendimus.</s>
                </p>
                <p xml:id="N208C3">
                  <s xml:id="N208C4" xml:space="preserve">In oppoſitū tñ arguit̄̄ ſic / q2 penes ali­
                    <lb/>
                  quid menſnrãda ē tã̄ penes effectū velocitas motꝰ
                    <lb/>
                  difformis ſcḋm tp̄s et ſubiectum ſimul et ēt motꝰ mix­
                    <lb/>
                  ti: et nõ niſi penes id qḋ dr̄ ī titulo q̄ſtiõis: igr̄ qõ a</s>
                </p>
                <p xml:id="N208CD">
                  <s xml:id="N208CE" xml:space="preserve">Pro enucleatione huius parue q̄ſtio-
                    <lb/>
                  nis notãdū eſt primo:  ī oī motu difformi quo ad
                    <lb/>
                  tp̄s et ſubiectū ſimul velocitas mēſurãda ē penes re­
                    <lb/>
                  ductionē ad vniformitatē ſaltē denoīationis vt ſu­
                    <lb/>
                  perius dicebat̄̄ ī ſecūdo capite huiꝰ tractatꝰ </s>
                  <s xml:id="N208D9" xml:space="preserve">¶ Hoc
                    <lb/>
                  tñ vnū aduertendū eſt  motus difformis quo ad tē­
                    <lb/>
                  pus et ſubiectū ſimul aliqñ fit ſecluſo alio motu ſub­
                    <lb/>
                  iecti puta rarefactionis aut ↄ̨dēſatiõis etc / vt cuꝫ ro­
                    <lb/>
                  ta nõ rarefacta aut cõdēſata cõtinuo circulariṫ ve-
                    <lb/>
                  locius et velocius mouet̄̄ aut tardius et tardius. </s>
                  <s xml:id="N208E6" xml:space="preserve">Ali­
                    <lb/>
                  quando vero fit talis motus cõcomitante rarefacti­
                    <lb/>
                  one aut condēſatione ſiue augmentatione etc. </s>
                  <s xml:id="N208ED" xml:space="preserve">Pri-
                    <lb/>
                  mo mõ debet mēſurari talis motꝰ velocitas penes
                    <lb/>
                  velocitatem qua mouet̄̄ pūctꝰ medius aut velociſ-
                    <lb/>
                  ſime motꝰ ſcḋm diuerſitatē opinionuū eo mõ quo ſu­
                    <lb/>
                  perius dicebatur de motu difformi quo ad ſubiectū
                    <lb/>
                  tm̄ </s>
                  <s xml:id="N208FA" xml:space="preserve">Et ēt mēſurãda ē velocitas illiꝰ motus penes li-
                    <lb/>
                  neã deſcriptã a pūcto medio talis corꝑis vel velo-
                    <lb/>
                  ciſſime moto: ſed tale pūctū duplici motu mouetur
                    <lb/>
                  motu vcꝫ locali et rarefactionis ſiue cõdēſatiõis etc.
                    <lb/>
                  </s>
                  <s xml:id="N20904" xml:space="preserve">Et ideo tale pūctū tantã lineã deſcribit ac ſi moue-
                    <lb/>
                  retur ṗmo mõ: et in ſuꝑ deſcribit illã lineã ꝑ quã plꝰ
                    <lb/>
                  diſtat ſi rarefiat: aut minus ſi condenſetur: a cētro
                    <lb/>
                  talis motꝰ ꝙ̄ antea diſtabat a principio motꝰ. </s>
                  <s xml:id="N2090D" xml:space="preserve">vt ſi
                    <lb/>
                  rota moueat̄̄ ī hora cõtinuo rarefiēdo: ita  ꝑ rare­
                    <lb/>
                  factionē acq̇rat pūctus penes cuiꝰ motū debet attē­
                    <lb/>
                  di velocitas rote pedalē diſtãtiã a cētro ſupra diſtã­
                    <lb/>
                  tiã iã habitã: et moueat̄̄ talis pūctus motu circula-
                    <lb/>
                  ri cõtinuo velociꝰ et velociꝰ: tūc dico /  velocitas ta-
                    <lb/>
                  lis motus mēſurãda eſt penes lineã quã deſcriberet
                    <lb/>
                  motu illo circulari ſi non rarefieret: et penes illã li-
                    <lb/>
                  neã pedalē quã motu rarefactionis deſcribit</s>
                </p>
                <p xml:id="N20920">
                  <s xml:id="N20921" xml:space="preserve">Hic tñ tu aduerte /  nõnū̄ mouet̄̄ aliqḋ mobile et
                    <lb/>
                  motu recto er circulari et rarefactionis ſimul: ita
                    <lb/>
                   cõtinuo cētrū illiꝰ corꝑis moueatur: quēadmodū
                    <lb/>
                  contingit ſi pila vel aliqḋ aliud corpꝰ ſpericū vel al­
                    <lb/>
                  teriꝰ figure moueat̄̄ motu recto et circulari continuo
                    <lb/>
                  rotando continuo rarefiendo et ī hoc et ſimili caſu
                    <lb/>
                  velocitas talis mobilis iudicãda eſt penes velocita­
                    <lb/>
                  tē cētri mobilis. </s>
                  <s xml:id="N20932" xml:space="preserve">Nõ eī video quo° certiꝰ et cõmodius
                    <lb/>
                  talis motꝰ velocitas ↄ̨mēſurari dēat. </s>
                  <s xml:id="N20937" xml:space="preserve">¶ Ex his faci­
                    <lb/>
                  le pꝫ ↄ̨ſiderãti  tot modꝪ tīgit corpꝰ moueri motu
                    <lb/>
                  difformi quo ad tp̄s et ſubiectū ſimul quot ↄ̨tīgit ip­
                    <lb/>
                  ſū moueri motu difformi quo ad tp̄s dūtaxat. </s>
                  <s xml:id="N20940" xml:space="preserve">Põt
                    <lb/>
                  eī pūctꝰ penes cuiꝰ velocitatē attendi d3 talis motꝰ
                    <lb/>
                  velocitas in q̊libet illoꝝ triū modoꝝ moueri ī prīa
                    <lb/>
                  ꝑte ꝓportionali hore ̄uis ꝓportione ꝑtite aliquã­
                    <lb/>
                  tula velocitate. </s>
                  <s xml:id="N2094B" xml:space="preserve">et in ſcḋa in duplo velociꝰ: et ī tertia
                    <lb/>
                  ī triplo velociꝰ ꝙ̄ ī ṗma: et ſic ↄ̨ñter. </s>
                  <s xml:id="N20950" xml:space="preserve">vel quouis alio°
                    <lb/>
                  et tūc ī iſto et ſiĺibꝰ caſibus velocitas et ſpaciū ꝑtran­
                    <lb/>
                  ſitū mediãte tali velocitate ex his q̄ dcã ſūt p̄ceden-
                    <lb/>
                  tibus captis cõmode menſuratur inſpectis theore-
                    <lb/>
                  matibus ibidem demonſtratis</s>
                </p>
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