Alvarus, Thomas, Liber de triplici motu, 1509

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              <div xml:id="N20F2E" level="4" n="1" type="chapter" type-free="capitulum">
                <p xml:id="N228F8">
                  <s xml:id="N22921" xml:space="preserve">
                    <pb chead="De motu rarefactionis et condenſationis." file="0190" n="190"/>
                  homo eſſet cecus ſecundum vnum oculum et vidēs
                    <lb/>
                  ſecundum alterum: adhuc talis homo eſſet videns
                    <lb/>
                  </s>
                  <s xml:id="N2293E" xml:space="preserve">Item ſecundum hanc opinionem intenſio raritatis
                    <lb/>
                  aut denſitatis non debet ſumi aut meuſurari pe-
                    <lb/>
                  nes denſitates partium vt oſtendit tertium notabi­
                    <lb/>
                  le huius dubii. </s>
                  <s xml:id="N22947" xml:space="preserve">intenſio autem calidi aut frigidi po­
                    <lb/>
                  teſt meuſurari ex intenſionibus partium: et ideo il-
                    <lb/>
                  la ſimilitudo nnllo pacto quadrat huic propoſito.</s>
                </p>
                <p xml:id="N2294E">
                  <s xml:id="N2294F" xml:space="preserve">Ad tertiam rationem reſpondeo con-
                    <lb/>
                  cedēdo ſequelam ſicut probat argumentum: et nego
                    <lb/>
                  falſitatem conſequentis: et ad ꝓbationem nego con­
                    <lb/>
                  ſequentiam: et ad ꝓbationem conſequentie: nego ſi­
                    <lb/>
                  militudinem ꝓpter rationem dictam in ſolutione
                    <lb/>
                  ſecunde rationis.</s>
                </p>
                <p xml:id="N2295C">
                  <s xml:id="N2295D" xml:space="preserve">Ad quartam rationem reſpondeo ne-
                    <lb/>
                  gando ſequelam: immo dico /  in aliquibus talibꝰ
                    <lb/>
                  caſibus poteſt facile reperiri adequata materia in
                    <lb/>
                  aliquibus vero non ſaltem naturaliter ab intelle-
                    <lb/>
                  ctu finite capacitatis / vt dictum ē tertio notabili hu­
                    <lb/>
                  ius dubii </s>
                  <s xml:id="N2296A" xml:space="preserve">In primo tamen caſu huius argumenti vi­
                    <lb/>
                  delicet  prima pars ꝓportionalis ſit aliqualiter
                    <lb/>
                  rara: et ſecunda in duplo: et tertia in triplo: et ſic con­
                    <lb/>
                  ſequenter diuiſione facta per partes ꝓportiõales
                    <lb/>
                  proportione dupla: et proportione quãtitatis prīe
                    <lb/>
                  partis proportionalis ad ſuam materiam exiſten-
                    <lb/>
                  te dupla tunc materie illarum partium proportio­
                    <lb/>
                  nalium continuo ſe habent in proportione quadru­
                    <lb/>
                  pla: et ſic ſcita materia prime partis proportiona-
                    <lb/>
                  lis facile ſcietur totalis materia: in infinitis tamen
                    <lb/>
                  caſibus vbi variatur proportio illud a finito inge-
                    <lb/>
                  nio et intellectu percipi non poteſt.</s>
                </p>
                <p xml:id="N22983">
                  <s xml:id="N22984" xml:space="preserve">Ad quintam rationem reſpondeo ne-
                    <lb/>
                  gando ſequelam: et cum petitur ratio quare potiꝰ
                    <lb/>
                  raritas dicitur priuatiue quam poſitiue ſecnndum
                    <lb/>
                  hanc opiniouem reſpondeo /  ideo dicitur potius
                    <lb/>
                  priuatiue quam poſitiue: quia raritas intenditur
                    <lb/>
                  ad deperditionem ſiue remiſſionem alicuius poſiti­
                    <lb/>
                  ni puta materie ſine acquiſitione alicuius poſitiui
                    <lb/>
                  quod nū̄ eſt verum etiam de aliquo poſitiuo. </s>
                  <s xml:id="N22995" xml:space="preserve">Quod ve-
                    <lb/>
                  ro ita fiat: aut poteſt fieri: volo /  diminuatur ſiue
                    <lb/>
                  dematur materia alicuius pedalis ſucceſſiue ad nõ
                    <lb/>
                  gradum nullo pacto maiorata quantitate: quo po­
                    <lb/>
                  ſito iam patet /  ibi nullum poſitum acquiritur: ſꝫ
                    <lb/>
                  contiuuo deperditur: nichilominus continuo pro-
                    <lb/>
                  portio quantitatis ad materiam maiorabitur: et
                    <lb/>
                  ſic continuo raritas intenditur. </s>
                  <s xml:id="N229A6" xml:space="preserve">Sed quia hec ra-
                    <lb/>
                  tio eque bene concludit denſitatem dici priuatiue
                    <lb/>
                  quēadmodū et raritatem. </s>
                  <s xml:id="N229AD" xml:space="preserve">quoniam per diminutio-
                    <lb/>
                  nem continuam quantitatis ſiue acquiſitione mate­
                    <lb/>
                  rie intenditur ipſa denſitas. </s>
                  <s xml:id="N229B4" xml:space="preserve">ideo cum queris cau­
                    <lb/>
                  ſam quare raritas potius priuatiue dicitur quam
                    <lb/>
                  denſitas. </s>
                  <s xml:id="N229BB" xml:space="preserve">Reſpondeo /  eſt illa quãtū in argumēto
                    <lb/>
                  aſſumis videlicet quia non poteſt reperiri infinita
                    <lb/>
                  raritas in ſubiecto ſiue corpore finito: ſi tamen dice­
                    <lb/>
                  retur poſitiue poſſet infinita raritas in ſubiecto fi-
                    <lb/>
                  nito reperiri / vt patet de omni poſitiuo magis et mi­
                    <lb/>
                  nus ſuſcipiente. </s>
                  <s xml:id="N229C8" xml:space="preserve">Et per hoc patet reſponſio ad du-
                    <lb/>
                  bium.</s>
                </p>
                <note position="left" xml:id="N229CD" xml:space="preserve">Opinio
                  <lb/>
                coīs</note>
                <p xml:id="N229D3">
                  <s xml:id="N229D4" xml:space="preserve">Notandem eſt tertio tangēdo opinio­
                    <lb/>
                  nem commuuem quam calculator in capitulo de ra­
                    <lb/>
                  ritate inſequitur. </s>
                  <s xml:id="N229DB" xml:space="preserve">et communiter moderni. </s>
                  <s xml:id="N229DE" xml:space="preserve"> ſecun-
                    <lb/>
                  dum hanc opinioneꝫ aliter deſcribendi ſunt iſti ter­
                    <lb/>
                  mini: rarum: denſum: rarefieri: condenſari quam ſe­
                    <lb/>
                  cundum opiniones precedentes.
                    <note position="left" xlink:href="note-0190-01a" xlink:label="note-0190-01" xml:id="N22A90" xml:space="preserve">q̇d raruꝫ</note>
                  </s>
                  <s xml:id="N229EC" xml:space="preserve">Rarum enim eſt il-
                    <lb/>
                  lud quod ſub magna quantitate continet modicuꝫ
                    <lb/>
                  de materia
                    <note position="left" xlink:href="note-0190-02a" xlink:label="note-0190-02" xml:id="N22A96" xml:space="preserve">q̇d dēſuꝫ</note>
                  </s>
                  <s xml:id="N229F8" xml:space="preserve">Denſum vero eſt illud quod ſnb modi-
                    <cb chead="De motu rarefactionis et condenſationis."/>
                  ca quantitate multum continet de materia.
                    <note position="right" xlink:href="note-0190-03a" xlink:label="note-0190-03" xml:id="N22A9C" xml:space="preserve">q̇d ↄ̨dēſa­
                      <lb/>
                    ri.</note>
                  </s>
                  <s xml:id="N22A03" xml:space="preserve">Condē-
                    <lb/>
                  ſari vero eſt effici magis denſum.
                    <note position="right" xlink:href="note-0190-04a" xlink:label="note-0190-04" xml:id="N22AA4" xml:space="preserve">qḋ rarefi­
                      <lb/>
                    eri.</note>
                  </s>
                  <s xml:id="N22A0D" xml:space="preserve">Rarefieri enim ē
                    <lb/>
                  fieri magis rarum. </s>
                  <s xml:id="N22A12" xml:space="preserve">magis autem rarum eſſe eſt ſub
                    <lb/>
                  maiori quantitate continere eandem materiam fi-
                    <lb/>
                  nitam quam antea continebat: vel ſub eadē quanti­
                    <lb/>
                  tate finita continere minus de materia: vel ſub mi-
                    <lb/>
                  nori: quantitate minus proportionale de materia
                    <lb/>
                  quam antea. </s>
                  <s xml:id="N22A1F" xml:space="preserve">Sed magis denſum eſt illud quod ſub
                    <lb/>
                  eadem quãtitate continet plus de materia: vel ſub-
                    <lb/>
                  minori quantitate eandem materiam finitã vel ma­
                    <lb/>
                  iorem vel minorem in minori tamen proportione
                    <lb/>
                  ̄ quantitas ſit minor. </s>
                  <s xml:id="N22A2A" xml:space="preserve">vel ſub maiori quantitate
                    <lb/>
                  magis proportionale de materia. </s>
                  <s xml:id="N22A2F" xml:space="preserve">Et ſi alique par­
                    <lb/>
                  ticule que non facile occurūt reſtant his diffini-
                    <lb/>
                  tionibus adiiciende eas addas cum argumenta ad
                    <lb/>
                  illud coegerint.
                    <note position="right" xlink:href="note-0190-05a" xlink:label="note-0190-05" xml:id="N22AAC" xml:space="preserve">cicero ī 4.
                      <lb/>
                    rethori.</note>
                  </s>
                  <s xml:id="N22A3D" xml:space="preserve">Definitio enim breuis debet eſſe ex
                    <lb/>
                  ſua natura teſtimonio ciceronis in ſua nona retho­
                    <lb/>
                  rica.
                    <note position="right" xlink:href="note-0190-06a" xlink:label="note-0190-06" xml:id="N22AB4" xml:space="preserve">.1. correl.</note>
                  </s>
                  <s xml:id="N22A49" xml:space="preserve">¶ Ex his diffinitiouibus ſequitur primo /  ma­
                    <lb/>
                  le deſcribitur ſic condenſari </s>
                  <s xml:id="N22A4E" xml:space="preserve">Condenſari eſt pun-
                    <lb/>
                  cta ad inuicem magis approximari quoniam ſtat
                    <lb/>
                   puncta magis approximentur: er in ea propor-
                    <lb/>
                  tione qua magis approximētur dematur de mate-
                    <lb/>
                  ria: et ſic tale corpus non condenſabitur. </s>
                  <s xml:id="N22A59" xml:space="preserve">et tamen
                    <lb/>
                  puncta magis ad inuicem approximantur. </s>
                  <s xml:id="N22A5E" xml:space="preserve">Item
                    <lb/>
                  dato pedali infinite denſo puncta illius poſſunt ma­
                    <lb/>
                  gis approximari: et tamen ipſum non condenſabi-
                    <lb/>
                  tur: quia iam eſt infinite denſum. </s>
                  <s xml:id="N22A67" xml:space="preserve">Eodem modo di-
                    <lb/>
                  cas de rarefactione ſiue de rarefieri. </s>
                  <s xml:id="N22A6C" xml:space="preserve">Non eni3 ſem­
                    <lb/>
                  per rarefieri ē puncta magis diſtare: pedale enim ī­
                    <lb/>
                  finite denſum poteſt maiorari ſtante ſua materia et
                    <lb/>
                  tamen non rarefiet.
                    <note position="right" xlink:href="note-0190-07a" xlink:label="note-0190-07" xml:id="N22ABA" xml:space="preserve">2. correl.</note>
                  </s>
                  <s xml:id="N22A7A" xml:space="preserve">¶ Sequitur ſecundo /  ſtat ali-
                    <lb/>
                  quod eſſe rarum a quo aufertur medietas ſue mate­
                    <lb/>
                  rie manente quantitate: et tamen ipſum non effici-
                    <lb/>
                  tur rarius. </s>
                  <s xml:id="N22A83" xml:space="preserve">Patet de corpore infinito habente ma-
                    <lb/>
                  teriam finitam preciſe quod eſt infinite raruꝫ a quo
                    <lb/>
                  ſi dematur medietas materie ipſum non efficietur
                    <lb/>
                  rarius cum modo ſit infinite rarum.</s>
                </p>
                <note position="right" xml:id="N22AC0" xml:space="preserve">3. correl.</note>
                <p xml:id="N22AC4">
                  <s xml:id="N22AC5" xml:space="preserve">¶ Sequitur tertio /  aliquod corpus eſt denſum et
                    <lb/>
                  finitum a quo ſi remoueatur medietas quantitatis
                    <lb/>
                  manente materia: ipſum non efficietur denſius.</s>
                </p>
                <p xml:id="N22ACC">
                  <s xml:id="N22ACD" xml:space="preserve">Patet de pedali infinite denſo poſito /  minore-
                    <lb/>
                  tur ad ſubduplum manente ſua materia.</s>
                </p>
                <note position="right" xml:id="N22AD2" xml:space="preserve">.4. corel.</note>
                <p xml:id="N22AD6">
                  <s xml:id="N22AD7" xml:space="preserve">¶ Sequitur quarto /  ſtat quantitatem alicuius fi­
                    <lb/>
                  niti diminui: et ſimiliter eius materiam. </s>
                  <s xml:id="N22ADC" xml:space="preserve">et ipſum cõ­
                    <lb/>
                  denſari. </s>
                  <s xml:id="N22AE1" xml:space="preserve">ſtat ſimiliter ipſum rarefieri. </s>
                  <s xml:id="N22AE4" xml:space="preserve">et ſtat ipſum
                    <lb/>
                  nec rafefieri nec condenſari. </s>
                  <s xml:id="N22AE9" xml:space="preserve">Probatur prima
                    <lb/>
                  pars / quia ſtat ipſum plus proportionabiliter per­
                    <lb/>
                  dere de quantitate ꝙ̄ de maieria: et tunc ipſum con­
                    <lb/>
                  denſabitur vt poſtea ex quibuſdam concluſionibus
                    <lb/>
                  patebit. </s>
                  <s xml:id="N22AF4" xml:space="preserve">et ſtat ipſum eque proportionabiliter de-
                    <lb/>
                  perdere de quantitate ſicut de materia: et ſic ipſum
                    <lb/>
                  nec rarefieri nec condenſari. </s>
                  <s xml:id="N22AFB" xml:space="preserve">et ſtat ipſum magis
                    <lb/>
                  proportionabiliter deperdere de materia ꝙ̄ de quã­
                    <lb/>
                  titate: et ſic rarefieri. </s>
                  <s xml:id="N22B02" xml:space="preserve">Et propterea poſitum eſt in de­
                    <lb/>
                  finitione vel minorem in minore tamen proportio-
                    <lb/>
                  ne ꝙ̄ quantitas ſit minor. </s>
                  <s xml:id="N22B09" xml:space="preserve">Et eodem modo poteris
                    <lb/>
                  dicere /  aliquid per acquiſitionem quantitatis et
                    <lb/>
                  materie rarefit. </s>
                  <s xml:id="N22B10" xml:space="preserve">et nõnun̄ condenſatur. </s>
                  <s xml:id="N22B13" xml:space="preserve">Si enim
                    <lb/>
                  eque proportionabiliter acquirit de materia ſi-
                    <lb/>
                  cut de quantitate nec rarefit nec condenſatur. </s>
                  <s xml:id="N22B1A" xml:space="preserve">ſi ve-
                    <lb/>
                  locius proportionabiliter acquirit de quantitate
                    <lb/>
                  ̄ de materia rarefit. </s>
                  <s xml:id="N22B21" xml:space="preserve">Omnia iſta patent mediante
                    <lb/>
                  tali fundamento. </s>
                  <s xml:id="N22B26" xml:space="preserve">Si in ea proportione in qua ali-
                    <lb/>
                  quod corpꝰ eſt maius in ea plus cõtinet de materia
                    <lb/>
                  altero corꝑe mīore illa duo ſūt eq̄ rara et eq̄ denſa:
                    <lb/>
                  et ſi in maiori ꝓportione plus cõtineret de quanti-
                    <lb/>
                  tate quã de materia ꝙ̄ alterum minus: ipſum eſt ra­
                    <lb/>
                  rius eo. </s>
                  <s xml:id="N22B33" xml:space="preserve">Si vero in maiore ꝓportione illud maiꝰ cõ­
                    <lb/>
                  tinet de materia quã de quantitate reſpectu alteri­ </s>
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