Alvarus, Thomas, Liber de triplici motu, 1509

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                <pb chead="De motu rarefactionis  cõdēnaitonis." file="0202" n="202"/>
                <p xml:id="N23E22">
                  <s xml:id="N23E23" xml:space="preserve">¶ Ex hiis duabus opinionibꝰ elige quã malueris
                    <lb/>
                  </s>
                  <s xml:id="N23E27" xml:space="preserve">Et per hoc pꝫ reſponſio ad dubiū
                    <note position="left" xlink:href="note-0202-01a" xlink:label="note-0202-01" xml:id="N23E38" xml:space="preserve">Calcula.</note>
                  </s>
                  <s xml:id="N23E2F" xml:space="preserve">Uide illud latius
                    <lb/>
                  in calculatore in capitulo de raritate et denſitate.</s>
                </p>
                <p xml:id="N23E3E">
                  <s xml:id="N23E3F" xml:space="preserve">¶ His poſitis ſit cõcluſio vniuerſalis reſponſiua
                    <lb/>
                  queſtionis raritas et denſitas ſunt poſſibiles / pꝫ cõ­
                    <lb/>
                  cluſio ex his que ſuperius dicta ſunt.</s>
                </p>
                <p xml:id="N23E46">
                  <s xml:id="N23E47" xml:space="preserve">¶ Ad rationes ante oppoſitū. </s>
                  <s xml:id="N23E4A" xml:space="preserve">Ad primã duplicit̄̄
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                  reſpõdeo prīo ſecūdū opiniõeꝫ recitatã in prīo no-
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                  tabili q̄ tenet /  dicunt̄̄ poſitiue et ſunt qualitates et
                    <lb/>
                  cum ꝓbatur  nõ: quia eque velociter et eque ꝓpor-
                    <lb/>
                  tionabiliter ſicut denſitas auget̄̄ ita raritas dimi-
                    <lb/>
                  nuitur:
                    <note position="left" xlink:href="note-0202-02a" xlink:label="note-0202-02" xml:id="N23F0A" xml:space="preserve">Calcula.</note>
                  igit̄̄ raritas et denſitas nõ dicunt̄̄ poſitiue
                    <lb/>
                  negatur añs ſcḋm hanc opinionē et etiã aliq̇ negãt
                    <lb/>
                  idem añs ſcḋm alteram quorū prīceps eſt calcula-
                    <lb/>
                  tor in quodã dubio / et ſic patet ſecūda reſponſio ſi-
                    <lb/>
                  militer qm̄ ſcḋm aliã opinionem hoc etiã negatur
                    <lb/>
                  </s>
                  <s xml:id="N23E65" xml:space="preserve">¶ Ad quatuor cõfirmatiões ſimul reſpondeo bre-
                    <lb/>
                  uiter /  procedūt cõtra opinionē que recitata eſt in
                    <lb/>
                  primo notabili et ibi reſpõſum eſt ad illas .8. confir­
                    <lb/>
                  mationes. </s>
                  <s xml:id="N23E6E" xml:space="preserve">¶ Ad ſcḋam rationem reſponſum eſt in
                    <lb/>
                  ſecundo notabili. </s>
                  <s xml:id="N23E73" xml:space="preserve">¶ Ad tertiam rationē dictum eſt
                    <lb/>
                  ibi vſ ad vltimã replicã. </s>
                  <s xml:id="N23E78" xml:space="preserve">ad quã reſpondeo conce­
                    <lb/>
                  dendo quod infert̄̄ videlicet /  oīa intermedia mu­
                    <lb/>
                  tantur localiter dato /  nullū intermediorū cõden­
                    <lb/>
                  ſetur. </s>
                  <s xml:id="N23E81" xml:space="preserve">Nec hoc eſt incõueniēs: ſꝫ prout michi nūc ap­
                    <lb/>
                  paret videt̄̄ neceſſariū naturaliter. </s>
                  <s xml:id="N23E86" xml:space="preserve">Si autē malue­
                    <lb/>
                  ris /  ſemꝑ vbicun eſt cauſa condēſationis ibi eſt
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                  cauſa rarefactiõis et ecõtra et hoc ex ordine natu-
                    <lb/>
                  rali nõ video rationē fortē in oppoſitū. </s>
                  <s xml:id="N23E8F" xml:space="preserve">Poſſet em̄
                    <lb/>
                  non abſ ratiõe dici /  vbi ſit cõdenſatio a cauſis
                    <lb/>
                  particularibꝰ fiat a cãis vĺibꝰ rarefactio et eↄ̈ ne va­
                    <lb/>
                  cuū aut dimēſionū penetratio naturaĺr ſeq̈t̄̄. </s>
                  <s xml:id="N23E98" xml:space="preserve">¶ Ad
                    <lb/>
                  quartã rationē reſpõſum eſt ibi vſ ad penultimã
                    <lb/>
                  replicã. </s>
                  <s xml:id="N23E9F" xml:space="preserve">ad quã dico dupliciter prīo. </s>
                  <s xml:id="N23EA2" xml:space="preserve">vt dictū eſt ibi
                    <lb/>
                  hoc addito /  nõ fiat mutatio materie de vna par-
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                  te corꝑis in reliquã manēte eadē ̄titate: q2 iſto mõ
                    <lb/>
                  nec cõdenſabit̄̄ nec rarefiet: vt pꝫ ex ṗmo dubio. </s>
                  <s xml:id="N23EAB" xml:space="preserve">Di­
                    <lb/>
                  co ſcḋo /  tale denſum difforme põt reduci ad vni-
                    <lb/>
                  formitatē gradus medii ſine rarefactione et condē­
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                  ſatione. </s>
                  <s xml:id="N23EB4" xml:space="preserve">Et hoc remouēdo medietatē exceſſus mate­
                    <lb/>
                  rie abuna medietate et addendo alteri ſiue acq̇ſitio­
                    <lb/>
                  ne aut deperditione ̄titatis in aliqua illarū me-
                    <lb/>
                  dietatū: vt ptꝫ ex argumēto ī oppoſitū primi dubii
                    <lb/>
                  </s>
                  <s xml:id="N23EBE" xml:space="preserve">¶ Ad vltimã vero replicam reſpõdeo breuiter negã­
                    <lb/>
                  do / hanc ↄ̨ſequentiã ꝑ maiorē partē cõtinuo erit ra­
                    <lb/>
                  rarefactio ꝙ̄ condenſatio: igit̄̄ hoc cõtinuo rarefit
                    <lb/>
                  </s>
                  <s xml:id="N23EC6" xml:space="preserve">Et ad probationē nego ſimilitudinē ſicut eam eſſe
                    <lb/>
                  negandã docet penultima replica. </s>
                  <s xml:id="N23ECB" xml:space="preserve">¶ Ad ↄ̨firmatio­
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                  nē negatur añs: immo dico /  tale inſtans eſt dabi­
                    <lb/>
                  le: et nego /  ſit inſtans mediū. </s>
                  <s xml:id="N23ED2" xml:space="preserve">Ad minꝰ dico /  non
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                  oportet /  ſit inſtans medi
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                  ̀ / vt ꝓbat argumētū: q2
                    <lb/>
                  aliquãdo rarefit tale corpus ante inſtans medium.
                    <lb/>
                  </s>
                  <s xml:id="N23EDC" xml:space="preserve">Et dicit calculator /  vbicū calculauerit illud in-
                    <lb/>
                  ſtans erat ante inſtans mediū totius tꝑis. </s>
                  <s xml:id="N23EE1" xml:space="preserve">Et ſi tu
                    <lb/>
                  queras / quod eſt illud inſtans añ inſtans medium.
                    <lb/>
                    <note position="left" xlink:href="note-0202-03a" xlink:label="note-0202-03" xml:id="N23F10" xml:space="preserve">Calcula.</note>
                  </s>
                  <s xml:id="N23EED" xml:space="preserve">Reſpondeo tibi cum eodē calculatore  huiuſcemo­
                    <lb/>
                  di inquiſitio talis inſtantis maioris laboris et an­
                    <lb/>
                  xietatis eſſet ꝙ̄ vtilis: ſufficit em̄ pro ſolutiõe argu-
                    <lb/>
                  menti oſtēdere /  nec per totū tp̄s condēſat̄̄: ſꝫ ꝑ ali­
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                  quã partē tēporis cõdenſatur: et ꝑ aliquam rarefit
                    <lb/>
                    <note position="left" xlink:href="note-0202-04a" xlink:label="note-0202-04" xml:id="N23F16" xml:space="preserve">phūs .2°.
                      <lb/>
                    metha. et
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                    1. ethicoꝝ</note>
                  </s>
                  <s xml:id="N23EFF" xml:space="preserve">Ip̄m eī exactū nõ in oībus eſt expetendū quēadmo­
                    <lb/>
                  dū nec in cõpotis auctoritate philoſophi prīo ethi­
                    <lb/>
                  corum: et ſecundo methaphiſices in calce.</s>
                </p>
                <p xml:id="N23F20">
                  <s xml:id="N23F21" xml:space="preserve">¶ Ad quintam rationem ſufficienter reſpondet ter­
                    <lb/>
                  tium notabile / quod ꝓpter hãc rõnē fuit adductum.
                    <lb/>
                  </s>
                  <s xml:id="N23F27" xml:space="preserve">¶ Ad ſextã rationē reſpõſum eſt ibi nec replica ꝓce­
                    <lb/>
                  dit / vt patet ibi. </s>
                  <s xml:id="N23F2C" xml:space="preserve">¶ Ad cõfirmationē reſpõſum eſt ibi
                    <lb/>
                  vſ ad replicam ad quam reſpondeo concedendo
                    <lb/>
                  ſequelam / vt ptꝫ ex ſecundo dubio vbi hec materia
                    <cb chead="De motu rarefactionis  cõdēnaitonis."/>
                  reſoluitur. </s>
                  <s xml:id="N23F36" xml:space="preserve">Sed q2 hoc argumentū querit quomo-
                    <lb/>
                  do vnū pedale infinite denſum difformiter poteſt
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                  reduci ad vniformitatē: et videt̄̄ /  oporteat ṗmã ꝑ­
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                  tē ꝓportionalē in infinitū condenſari: et ſic videtur /
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                   ipſa rediget̄̄ ad nõ ̄tum et pari ratione q̄libet
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                  alia. </s>
                  <s xml:id="N23F43" xml:space="preserve">Et ideo dico /  illud corpus non debet reduci
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                  ad vniformitatē nec aliqua pars ꝓportionalis eiꝰ
                    <lb/>
                  debet effici in infinite denſa ꝑ ſui cõdēſatione ſine
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                  mīo rationem: ſed per acquiſitionē materie ſtante
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                  ̄titate / vt dictum eſt in primo dubio in argumēto
                    <lb/>
                  ad oppoſitū facto.
                    <note position="right" xlink:href="note-0202-05a" xlink:label="note-0202-05" xml:id="N24004" xml:space="preserve">bonū cor­
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                    relarium</note>
                  </s>
                  <s xml:id="N23F55" xml:space="preserve">¶ Ex quo ſequit̄̄ /  motꝰ augmē­
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                  tationis non ſequitur motū rarefactionis: nec mo­
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                  tus diminutionis ſeq̇tur motū condēſatiõis neceſ-
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                  ſario. </s>
                  <s xml:id="N23F5E" xml:space="preserve">Ad ſecūdã cõfirmationē rñdet tertiū dubium
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                  </s>
                  <s xml:id="N23F62" xml:space="preserve">¶ Ad ſeptimã rationē reſpondeo negando ſeque-
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                  lam ſicut nec in ſimili ſequitur de remiſſione. </s>
                  <s xml:id="N23F67" xml:space="preserve">Et ſi
                    <lb/>
                  queras ꝙ̄ rarū eſt illud: dico /  eiꝰ raritas diiudi-
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                  cari debet ex eius denſitate. </s>
                  <s xml:id="N23F6E" xml:space="preserve">Eiꝰ autem denſitas pꝫ
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                  ex argumento. </s>
                  <s xml:id="N23F73" xml:space="preserve">Et ad cõfirmationē priorē reſpõdeo
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                  negando ſequelã: et ad ꝓbationē concedo /  illud
                    <lb/>
                  corpus eſt infinite denſum / vt patet ex ſecunda con­
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                  cluſione q̄ſtionis: et nego /  ſit rarū: et ad ꝓbatio-
                    <lb/>
                  nē nego illam ſimilitudinē qm̄ ille modus arguen-
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                  do valet in poſitiuis: et non in priuatiuis / vt patet
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                  de remiſſione. </s>
                  <s xml:id="N23F82" xml:space="preserve">Ad poſteriorem cõfirmationē reſpõ­
                    <lb/>
                  deo negando ſequelã videlicet / quod ſequeretur il-
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                  lud eſſe infinite denſum: et ad ꝓbationē nego cõſe-
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                  quentiam: nec eſt ſimile quãdo illnd corpus diuidi­
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                  tur ꝓportione dupla: et denſitates continuo ſe ha-
                    <lb/>
                  bent in proportione dupla aſcendendo: ſed ad hoc
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                   eſſet ſimile oportet /  partes continuo ſe habe-
                    <lb/>
                  rent in ꝓportiõe decupla in dēſitate ita  ſicut ꝑs
                    <lb/>
                  ſequens eſt in decuplo mīor īmediate p̄cedēte: ita
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                  etiam ſit decuplo denſior. </s>
                  <s xml:id="N23F97" xml:space="preserve">¶ Ad octauã rationē di-
                    <lb/>
                  ctum eſt ibi vſ ad replicã. </s>
                  <s xml:id="N23F9C" xml:space="preserve">ad quã reſpõdeo /  den­
                    <lb/>
                  ſitas illius corporis adequata eſt incõmēſurabilis
                    <lb/>
                  denſitati prime partis ꝓportiõalis / vt michi ꝓ nūc
                    <lb/>
                  apparet nec aliq̇s intellectꝰ finile capacitatis da-
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                  to /  illa eēt mēſurabilis p̄t illã cõmenſurare ꝓpter
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                  infinitã variationē ꝓportiõis. </s>
                  <s xml:id="N23FA9" xml:space="preserve">Ad primã et ſecūdaꝫ
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                  confirmationē ſimul reſpõdeo concedendo /  in ca­
                    <lb/>
                  ſibus ibi poſitis dabilis eſt certa dēſitas talis cor­
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                  poris: ſed credo illam eſſe incõmēſurabilē denſita-
                    <lb/>
                  ti prime partis ꝓportionalis: et ſi ipſa ſit cõmēſu-
                    <lb/>
                  rabilis eius adequata ꝓportio ab intellectu finite
                    <lb/>
                  capacitatis minime īueniri poteſt eo /  īfinita va-
                    <lb/>
                  rietas ꝓportionū eſt inter denſitates illarū partiū
                    <lb/>
                  proportionalium. </s>
                  <s xml:id="N23FBC" xml:space="preserve">¶ Ad nonã rationē reſpondeo
                    <lb/>
                  negando ſequelã: et ad ꝓbationē nego /  in fine ho-
                    <lb/>
                  re illud ſit denſius immo eſt rarius. </s>
                  <s xml:id="N23FC3" xml:space="preserve">et ad ꝓbationē
                    <lb/>
                  nego hanc conſequētiã infinite partes illius ſunt dē­
                    <lb/>
                  ſiores ꝙ̄ erant antea etc̈. / q2 ſtat  vna ſola acq̇rat
                    <lb/>
                  tantū de ̄titate vel plus ꝙ̄ ille infinite omnes de­
                    <lb/>
                  perdant. </s>
                  <s xml:id="N23FCE" xml:space="preserve">Ad cõfirmationē rēſpõdeo admiſſo caſu
                    <lb/>
                  negando añs. </s>
                  <s xml:id="N23FD3" xml:space="preserve">immo dico /  in illo cãu in fine hore
                    <lb/>
                  illud corpus nõ eſt rarius nec denſius ꝙ̄ eſt in prin­
                    <lb/>
                  cipio. </s>
                  <s xml:id="N23FDA" xml:space="preserve">Et ad ꝓbationē nego hanc cõſequentiam pri­
                    <lb/>
                  ma pars ꝓportionalis eſt maior ꝙ̄ erat antea: et
                    <lb/>
                  aggregatū ex ipſa et ſecunda eſt maius ꝙ̄ erat an­
                    <lb/>
                  tea et aggregatū ex ip̄a ſecūda et tertia ē maiꝰ ꝙ̄ erat
                    <lb/>
                  antea: et aggregatū ex ip̄a ſecūda tertia et quarta
                    <lb/>
                  ſimiliter: et ſic cõſequenter aggregatū ex quotcū
                    <lb/>
                  finitis cõputata prima eſt maius ꝙ̄ erat antea: igi-
                    <lb/>
                  tur illud totum eſt maius ꝙ̄ erat antea. </s>
                  <s xml:id="N23FEB" xml:space="preserve">¶ Ad deci-
                    <lb/>
                  mã reſponſum eſt ibi vſ ad replicam ad quã etiã
                    <lb/>
                  reſpondeo concedendo illatum. </s>
                  <s xml:id="N23FF2" xml:space="preserve">Illlud em̄ in nõ cõ­
                    <lb/>
                  uenit. </s>
                  <s xml:id="N23FF7" xml:space="preserve">ſꝫ eſt correlariū ſequēs vt ꝓbat argumentuꝫ
                    <lb/>
                  </s>
                  <s xml:id="N23FFB" xml:space="preserve">Et hec de totali queſtiõe: et per cõſequens de tota
                    <lb/>
                  materia de denſitate et raritate.</s>
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