Alvarus, Thomas, Liber de triplici motu, 1509

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                <p xml:id="N222B3">
                  <s xml:id="N222D5" xml:space="preserve">
                    <pb chead="De motu rarefacttonis  condenſationis." file="0186" n="186"/>
                  quantitatis ad materiã in eadē ꝓportione ſe hñt
                    <lb/>
                  raritates ab eis producte, et ꝑ ↄ̨ñs a qualibet pro-
                    <lb/>
                  portione certa raritas nata eſt ꝓuenire  fuit pro-
                    <lb/>
                  bandū. </s>
                  <s xml:id="N222ED" xml:space="preserve">Sed falſitas cõſequentis oſtenditur / q2 ſe-
                    <lb/>
                  queret̄̄ /  cū pedale in quo eſt ꝓportio quadrupla
                    <lb/>
                  quantitatis ad materiã, et tripedale in quo eſt du-
                    <lb/>
                  pla ꝓportio quãtitatis ad materiã augmētaret̄̄
                    <lb/>
                  ad duplã quantitatē, eque velociter acq̇rerēt de ra­
                    <lb/>
                  ritate: ſed hoc videtur falſum. </s>
                  <s xml:id="N222FA" xml:space="preserve">igr̄ et illud ex quo ſe­
                    <lb/>
                  quit̄̄. </s>
                  <s xml:id="N222FF" xml:space="preserve">Falſitas cõſequentis oſtenditur: q2 cū illa pu­
                    <lb/>
                  ta tripedale et pedale augmentãtur ad duplã quã-
                    <lb/>
                  titatē: etiã augmentantur ad duplã raritatē q2 ſi-
                    <lb/>
                  cut quantitas efficitur maior ita etiã raritas ma-
                    <lb/>
                  nente eadē materia: ſed tripedale minorē raritatē
                    <lb/>
                  habebat ꝙ̄ pedale. </s>
                  <s xml:id="N2230C" xml:space="preserve">et quodlibet illoꝝ acq̇ſiuit tantã
                    <lb/>
                  raritatē quantã habebat cū vtrū fuerit augmen-
                    <lb/>
                  tatū ad duplum: g̊ ſequitur /  maiorē raritatē acq̇-
                    <lb/>
                  ſiuit pedale quã tripedale: patꝫ hec ↄ̨ña: q2 qñ duo
                    <lb/>
                  inequalia efficiūtur in duplo maior a maiorē lati-
                    <lb/>
                  tudinē acquirit maiꝰ quã minꝰ: vt cõſtat. </s>
                  <s xml:id="N22319" xml:space="preserve">Sed ſeque­
                    <lb/>
                  la probatur: q2 vtrū illoꝝ acq̇rit ꝓportionem du­
                    <lb/>
                  plam: g̊ ſequitur /  vtrū illoꝝ acq̇rit raritatē na­
                    <lb/>
                  tam prouenire a proportione dupla: ſed m iſtam
                    <lb/>
                  opinionē oīs raritas nata prouenire a proportiõe
                    <lb/>
                  dupla eſt equalis cuilibet nate ꝓuenire a quacū
                    <lb/>
                  proportione dupla: igr̄ propoſitū. </s>
                  <s xml:id="N22328" xml:space="preserve">¶ Dices forte et
                    <lb/>
                  bene concedendo ſequelã et negando falſitatē con-
                    <lb/>
                  ſequentis: et ad probationē concedo ſequelã: et ne-
                    <lb/>
                  go falſitatē conſequentis et ad probationē falſita-
                    <lb/>
                  tis ↄ̨ñtis: nego hanc cõſequētiã hoc efficitur in du-
                    <lb/>
                  plo maiꝰ: g̊ in duplo rariꝰ: īmo vt m argumentuꝫ
                    <lb/>
                  ante oppoſitū prīcipalis queſtiõis oſtendit aliqñ
                    <lb/>
                  ſtat  aliqñ ad duplationē quantitatis ſequeatur
                    <lb/>
                  duplatio raritatis et aliqñ minor et aliqñ maior.</s>
                </p>
                <p xml:id="N2233B">
                  <s xml:id="N2233C" xml:space="preserve">Sꝫ ↄ̨̨tra. </s>
                  <s xml:id="N2233F" xml:space="preserve">Quia tunc ſequeret̄̄ /  qñ-
                    <lb/>
                  cun duo equalia quantitatiue, ſiue equalia, ſiue
                    <lb/>
                  inequalia in raritate equaliter acquirerēt de quã­
                    <lb/>
                  titate: ipſa equaliter rarefierent: ſed conſequens
                    <lb/>
                  eſt falſum: igr̄ et illud ex quo ſequitur. </s>
                  <s xml:id="N2234A" xml:space="preserve">Falſitas cõ-
                    <lb/>
                  ſequentis probatur: q2 ſint duo corpora equalia
                    <lb/>
                  ī eque rara q̄ equales quãtitates acq̇rant: tūc eque
                    <lb/>
                  ꝓportionabiliter ſicut acq̇runt de quantitate acq̇-
                    <lb/>
                  runt de raritate: ſed equalē ꝓportionē acq̇runt de
                    <lb/>
                  quantitate: g̊ equaliter acq̇runt de raritate: et rari­
                    <lb/>
                  tas vniꝰ eſt minor ꝙ̄ raritas alterius: g̊ raritas mi­
                    <lb/>
                  nor mīorē latitudinē raritatꝪ acq̇rit  raritas ma­
                    <lb/>
                  ior: ptꝫ hec cõſequentia ꝑ hanc maximã. </s>
                  <s xml:id="N2235D" xml:space="preserve">Qñcun
                    <lb/>
                  aliqua duo inequalia eque velociter ꝓportionabi­
                    <lb/>
                  liter maiorantur velociꝰ maiorat̄̄ maiꝰ in eodē tꝑe /
                    <lb/>
                  vt pꝫ ſi ſex et quatuor debeant ad ſexq̇alteꝝ maio­
                    <lb/>
                  rari eodem tꝑe adequate: tunc em̄ in tꝑe quo ſex ac­
                    <lb/>
                  quirit tria quatuor atq̇rit duo. / vt conſtat: ſed in ꝓ-
                    <lb/>
                  poſito. </s>
                  <s xml:id="N2236C" xml:space="preserve">vtra illarū raritatū eque ꝓportionaliter
                    <lb/>
                  maiorat̄̄: g̊ maior raritas maiorē latitudinē rari-
                    <lb/>
                  tatis acq̇rat ꝙ̄ minor in eodē tꝑe. </s>
                  <s xml:id="N22373" xml:space="preserve">Sed ſequela ꝓba­
                    <lb/>
                  tur qm̄ illa ſunt equalia, et equales quãtitates acq̇­
                    <lb/>
                  runt: igr̄ equales ꝓportiones, et vltra equales pro­
                    <lb/>
                  portiones: g̊ equales raritates ptꝫ cõſequentia: q2
                    <lb/>
                  ab equalibꝰ ꝓportionibus quãtitatis ad materiã
                    <lb/>
                  equales raritates nate ſunt prouenire: vt patet ex
                    <lb/>
                  opinione et reſponſione: igitur.</s>
                </p>
                <p xml:id="N22382">
                  <s xml:id="N22383" xml:space="preserve">Scḋo ad idē argr̄ ſic. </s>
                  <s xml:id="N22386" xml:space="preserve">Si illa poſitio
                    <lb/>
                  eſſet vera ſequeretur /  oporteret ſignare gradꝰ in
                    <lb/>
                  quantitate, et etiã in materia: ſed hoc eſt falſū: igr̄
                    <lb/>
                  illud ex quo ſeq̇tur. </s>
                  <s xml:id="N2238F" xml:space="preserve">Falſitas ↄ̨ñtis oſtēditur: qm̄ nec
                    <lb/>
                  quantitas, nec materia ſuſcipiant magis et minus /
                    <lb/>
                  igr̄ nõ habent gradus. </s>
                  <s xml:id="N22396" xml:space="preserve">Sed ſeq̄la ꝓbatur / qm̄ rari-
                    <lb/>
                  tas et raritatꝪ maioritas penes ꝓportionē quãti-
                    <cb chead="De motu rarefactionis  condenſationis."/>
                  tatis ad materiã d3 ſumi: vt dicit opinio et dēſitas
                    <lb/>
                  eocontra penes ꝓportionē materia ad quantitatē /
                    <lb/>
                  g̊ oportet quãtitatē materiã exuperare cū aliquid
                    <lb/>
                  rarū dicit̄̄: et materiã quantitatē excedere cū aliq̇d
                    <lb/>
                  denſum efficitur: ſed nun̄ quantitas exuperat ma­
                    <lb/>
                  teriam extenſiue: q2 ſunt equalis extenſionis: igit̄̄
                    <lb/>
                  oportet /  exuperet intenſiue: q2 alias nun̄ erit ꝓ-
                    <lb/>
                  portio maioris inequalitatis quantitatis ad ma-
                    <lb/>
                  teriã vel econtra.
                    <note position="right" xlink:href="note-0186-01a" xlink:label="note-0186-01" xml:id="N223E1" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N223B3" xml:space="preserve">¶ Dices et bene concedendo ſeque­
                    <lb/>
                  lam, ꝑ gradus quantitatis nõ intelligendo gradꝰ
                    <lb/>
                  intenſionis quãtitatis: ſed intelligendo certas ꝓ-
                    <lb/>
                  portiones quantitatis vt puta  vna quarta peda­
                    <lb/>
                  lis ſit vnus gradus quantitatis: et vna octaua pe-
                    <lb/>
                  dalis medietas vniꝰ gradus quantitatis etc̈. vnus
                    <lb/>
                  vero gradus materie ſit certa portio materie vtpo­
                    <lb/>
                  te tanta quãta eſt in vna octaua vniꝰ pedalis terre
                    <lb/>
                  exiſtēs in ſua naturali diſpoſitione quod (exēpli
                    <lb/>
                  gratia dico) capias em̄ ꝓ libito quãtū volueris de
                    <lb/>
                  materia ꝓ vno gradu, et etiã de quantitate ſicut di­
                    <lb/>
                  cimus de gradibꝰ qualitatis: et m hoc negetur fal­
                    <lb/>
                  ſitas conſequētis, et concedat̄̄  nec quantitas: nec
                    <lb/>
                  materia ſuſcipiūt magis et minꝰ: cū hoc tñ ſtat  et
                    <lb/>
                  ſi quantitas nõ hꝫ gradus intentionales hꝫ tñ extē­
                    <lb/>
                  ſionales. </s>
                  <s xml:id="N223D4" xml:space="preserve">et ſimiliter ̄uis materia nõ hꝫ gradus in­
                    <lb/>
                  tenſionales hꝫ tñ gradus entitatiuos qui ſunt par­
                    <lb/>
                  tes ipſius materie vt declarant cõiter hanc mate-
                    <lb/>
                  riam de raritate et denſitate tractantes.</s>
                </p>
                <p xml:id="N223E7">
                  <s xml:id="N223E8" xml:space="preserve">Sed cõtra. </s>
                  <s xml:id="N223EB" xml:space="preserve">Quia tunc ſequeretur / 
                    <lb/>
                  nullū rarū eſſet denſuꝫ: ſed hoc eſt falſum: igr̄ illud
                    <lb/>
                  ex quo ſequitur. </s>
                  <s xml:id="N223F2" xml:space="preserve">Falſitas ↄ̨ñtis oſtēditur, q2 capto
                    <lb/>
                  vno denſo finite benſo, illud eſt rarū: igr̄. </s>
                  <s xml:id="N223F7" xml:space="preserve">Probat̄̄
                    <lb/>
                  añs, q2 illud ſub magna quantitate continet parū
                    <lb/>
                  de materia: igr̄ eſt rarum, ptꝫ ex diffinitione rari.
                    <lb/>
                  </s>
                  <s xml:id="N223FF" xml:space="preserve">Sed iam ꝓbo ſequelã, qm̄ ſi aliquid eſt rarū in eo
                    <lb/>
                  quantitas ſe hꝫ in ꝓportiõe maioris inequalitatis
                    <lb/>
                  ad materiã, et ſi ipſum eſſet denſum in eo materia
                    <lb/>
                  ſe hꝫ in ꝓportione maioris in inequalitatis ad quã-
                    <lb/>
                  titatē: ſed īpoſſibile eſt  in eodē ſaltem exiſtēte in
                    <lb/>
                  eodē loco etc̈. quantitas excedat materiam, et exce-
                    <lb/>
                  datur ab ea: igr̄ īpoſſibile eſt  aliquid ſit rarum et
                    <lb/>
                  denſum: quod fuit ꝓbandū.
                    <note position="right" xlink:href="note-0186-02a" xlink:label="note-0186-02" xml:id="N2242E" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N22415" xml:space="preserve">¶ Dices et bene conce-
                    <lb/>
                  dendo ſequelã (vt hec opinio eã concedit) et negãdo
                    <lb/>
                  falſitatē ↄ̨ñtis, et ad ꝓbattonē negando hanc con-
                    <lb/>
                  ſequentiam in hoc corpore eſt modica materia ſub
                    <lb/>
                  magna quantitate: g̊ hoc eſt rarum, nec ibi argr̄ a
                    <lb/>
                  diffinitiõe ad diffinitū: ſed oportet dicere vt poſtea
                    <lb/>
                  clarius et latius dicetur in hoc corpore quantitas
                    <lb/>
                  excedit materiam, et hꝫ ad materiam ꝓportionem
                    <lb/>
                  maioris inequalitatis: igitur illud corpus eſt rarū /
                    <lb/>
                  et ſic conſequentia eſt bona.</s>
                </p>
                <p xml:id="N22434">
                  <s xml:id="N22435" xml:space="preserve">Sed contra. </s>
                  <s xml:id="N22438" xml:space="preserve">Quia tunc ſequeret̄̄ hec
                    <lb/>
                  concluſio aliquod corpus naturale, nec eſt rarum
                    <lb/>
                  nec denſum naturaliter. </s>
                  <s xml:id="N2243F" xml:space="preserve">Seq̄la ꝓbatur / q2 capio a.
                    <lb/>
                  pedale in cuiꝰ qualibet quarta eſt vnꝰ gradus ma-
                    <lb/>
                  terie: quo poſito ibi inter materiã et quantitatē eſt
                    <lb/>
                  ꝓportio equalitatis: igr̄ ibi gradus quãtitatis nõ
                    <lb/>
                  excedūt gradus materie. </s>
                  <s xml:id="N2244A" xml:space="preserve">igr̄ tale pedale nõ eſt raꝝ
                    <lb/>
                  nec gradus materie excedūt gradus quantitatis:
                    <lb/>
                  igr̄ nõ eſt denſum: igr̄ aliquod pedale eſt  nec eſt
                    <lb/>
                  rarū nec eſt denſum / quod fuit probandū. </s>
                  <s xml:id="N22453" xml:space="preserve">Falſitas
                    <lb/>
                  ↄ̨ñtis oſtenditur / q2 tale pedale hꝫ certã materiam
                    <lb/>
                  ſub certa quantitate puta paruã materiã ſub ma-
                    <lb/>
                  gna quantitate: igr̄ illud eſt rarū.
                    <note position="right" xlink:href="note-0186-03a" xlink:label="note-0186-03" xml:id="N2246A" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N22461" xml:space="preserve">¶ Dices et bene
                    <lb/>
                  concedendo quod infertur.</s>
                </p>
                <p xml:id="N22470">
                  <s xml:id="N22471" xml:space="preserve">Sed contra. </s>
                  <s xml:id="N22474" xml:space="preserve">Quia tunc ſequeretnr /
                    <lb/>
                   bipedale ī cuiꝰ vna medietate eſt ꝓportio dupla
                    <lb/>
                  quãtitatis ad materiã et iu alia eſt ꝓportio eq̈lita- </s>
                </p>
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