Alvarus, Thomas, Liber de triplici motu, 1509

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                  <s xml:id="N20E7F" xml:space="preserve">
                    <pb chead="Dc motu rarefactionis  condenſationis." file="0174" n="174"/>
                  pius diſponi difformiṫ in partibꝰ ſuis  ipſū ī tꝑe
                    <lb/>
                  finito mouebit̄̄ q̊vſ cētrū eiꝰ ſit cētrū mūdi. </s>
                  <s xml:id="N20E89" xml:space="preserve">Pro-
                    <lb/>
                  bat̄̄ et pono /  ꝑs ītercepta īter centrū mūdi et cētrū
                    <lb/>
                  corporis diuidat̄̄ ꝑ partes proportionales ꝓpor-
                    <lb/>
                  tione dupla maioribꝰ ſus centrū mūdi termina-
                    <lb/>
                  tis / vt ponit̄̄ in tertio notabili q̄ pars ſit d. et poſt̄
                    <lb/>
                  prima pars proportionalis ipſiꝰ d. partis ꝑtrãſit
                    <lb/>
                  centrū q̄ (vt ſuppono) ꝑtranſit centrū ſcḋm ſe et qḋ-
                    <lb/>
                  libet ſui in hora, ſigno ꝓportionē a qua d3 tcrtia
                    <lb/>
                  pars proportionalis d. partis incipere ꝑtranſire
                    <lb/>
                  centrū mūdi q̄ ſit f. </s>
                  <s xml:id="N20E9E" xml:space="preserve">Et manifeſtū eſt /  aliqḋ ſpaciū
                    <lb/>
                  ſufficit ꝑtrãſiri ī medietate hore mediante velocita­
                    <lb/>
                  te nata prouenire a proportiõe f. pono igr̄ /  ſcḋa
                    <lb/>
                  pars proportionalis ipſiꝰ d. partis diminuat̄̄ m
                    <lb/>
                  dimenſionē ſcḋm quã ꝑtrãſit centrū mūdi, quouſ
                    <lb/>
                  ſit ſcḋm illã dimenſionē equalis ſpacio nato ꝑtrã-
                    <lb/>
                  ſiri ab .f. proportiõe in medietate hore. </s>
                  <s xml:id="N20EAD" xml:space="preserve">ipſa tñ ſemꝑ
                    <lb/>
                  manēte tanta quãta erat antea: ita  augeat̄̄ ſcḋm
                    <lb/>
                  aliã dimenſionē. </s>
                  <s xml:id="N20EB4" xml:space="preserve">Et poſt̄ ſcḋa pars proportiona­
                    <lb/>
                  lis d. ꝑtis ꝑtranſit cētrū mūdi ſcḋm ſe et qḋlꝫ ſui ſi-
                    <lb/>
                  gno ꝓportionē q̄ ſit g. a qua d3 quarta pars ꝓpor­
                    <lb/>
                  tiõalis deſcēdere q̄ eſt minor f. / vt cõſtat. </s>
                  <s xml:id="N20EBD" xml:space="preserve">Et manife-
                    <lb/>
                  ſtū eſt /  aliquod ſpaciū ſufficit ꝑtranſiri in quarta
                    <lb/>
                  parte hore mediante ꝓportiõe g̊ pono igr̄ /  tertia
                    <lb/>
                  pars ꝓportionalis d. partis dimīnuat̄̄ ſcḋm dimē­
                    <lb/>
                  ſionē ſcḋm quã ꝑtranſit centrū mūdi quovſ ſcḋ3
                    <lb/>
                  illã dimenſionē ſit eq̈lis ſpacio nato ꝑtranſiri a g.
                    <lb/>
                  ꝓportione in quarta parte hore. </s>
                  <s xml:id="N20ECC" xml:space="preserve">Et ſic fiat de qua-
                    <lb/>
                  libet ſequēte  ipſa vcꝫ diminuat̄̄ ſcḋm dimenſionē
                    <lb/>
                  ſcḋm quã ꝑtranſit centrū mūdi quovſ ſit equalis
                    <lb/>
                  ſpacio nato ꝑtranſiri a ꝓportione a qua d3 īcipere
                    <lb/>
                  ꝑtranſire centrū mūdi pars īmediate ſequēs et hoc
                    <lb/>
                  in tꝑe ſubduplo vel minori ꝙ̄ ſit tēpus in quo ade-
                    <lb/>
                  quate pars īmediate p̄cedens ꝑtranſit centrū mūdi
                    <lb/>
                  qualibet tñ cõtinuo manēte tanta quãta erat antea
                    <lb/>
                  ita  augeat̄̄ ſcḋm aliã dimenſionē. </s>
                  <s xml:id="N20EDF" xml:space="preserve">Tūc manifeſtū
                    <lb/>
                  eſt /  totū illud corpus poſt̄ prima pars d. partis
                    <lb/>
                  p̄teriuit centrū mūdi mouebit̄̄ p̄ciſe ꝑ vnã horã vĺ ꝑ
                    <lb/>
                  minꝰ tēpꝰ ante quã centrū illiꝰ corporis fiat centrū
                    <lb/>
                  mūdi. </s>
                  <s xml:id="N20EEA" xml:space="preserve">Quod ſic oſtendit̄̄ / q2 quelibet pars ꝓporti-
                    <lb/>
                  onalis ipſiꝰ d. partis ſequēs ꝑtranſibit in caſu po­
                    <lb/>
                  ſito cētrū in tꝑe ſubduplo vĺ mīori ad tēpus in quo
                    <lb/>
                  ꝑtranſibit pars īmediate p̄cedens / vt facile ptꝫ ex ca­
                    <lb/>
                  ſu: et prima ꝑtranſit centrū in vna hora vt ſupponi­
                    <lb/>
                  tur: ergo oēs alie pertranſibunt in vna hora vel in
                    <lb/>
                  minori tempore et ſic in tempore finito centrū illiꝰ
                    <lb/>
                  corporis fit centrū mūdi: põt igitur taliter diſponi
                    <lb/>
                  corpus  ipſum in tēpore finito preciſe mouebitur
                    <lb/>
                  quovſ centrum eiꝰ fiat centrum muudi / quod fuit
                    <lb/>
                  probandū.
                    <note position="left" xlink:href="note-0174-01a" xlink:label="note-0174-01" xml:id="N20F13" xml:space="preserve">Oñditur
                      <lb/>
                    Cal. de-
                      <lb/>
                    monſtra­
                      <lb/>
                    tio in effi­
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                    cax.</note>
                  </s>
                  <s xml:id="N20F06" xml:space="preserve">Et hoc ex ſequitur /  demonſtratio cal-
                    <lb/>
                  culatoris in capitulo de loco elementi non eſt effi-
                    <lb/>
                  cax non enim limitat ſiue determinat diſpoſiteonē
                    <lb/>
                  illius corporis quod tamen oportet / vt ptꝫ ex dictis</s>
                </p>
              </div>
            </div>
            <div xml:id="N20F21" level="3" n="3" type="other" type-free="tractatus">
              <p xml:id="N20F26">
                <s xml:id="N20F27" xml:space="preserve">Sequitur tractatus tertius huius
                  <lb/>
                tertie partis de motu rarefactionis
                  <lb/>
                 condenſationis.</s>
              </p>
              <div xml:id="N20F2E" level="4" n="1" type="chapter" type-free="capitulum">
                <head xml:id="N20F33" xml:space="preserve">Capitulū primū in quo diſputatiue inquiritur.
                  <lb/>
                Quid ſi raritas et dēſitas et penes q̇d raritatis et
                  <lb/>
                dēſitatis intēſio et rarefactiõis et condenſationis
                  <lb/>
                ſit velocitas attendenda.</head>
                <p xml:id="N20F3C">
                  <s xml:id="N20F3D" xml:space="preserve">Exacto tractatu de motu locali
                    <lb/>
                  inſequendo veſtigia patrū, et maioꝝ ſub-
                    <lb/>
                  iungã tractatū de motu augmeutationis
                    <lb/>
                  et rarefactionis et inquirendo ſubſtantiã raritatis
                    <lb/>
                  et denſitatis velocitatem et tarditatem rarefacti-
                    <lb/>
                  onis et condenſationis.</s>
                </p>
                <cb chead="Dc motu rarefactionis  condenſationis."/>
                <p xml:id="N20F4C">
                  <s xml:id="N20F4D" xml:space="preserve">Quero vtrum raritas  denſitas ſit
                    <lb/>
                  poſſibilis, et argr̄ primo /  nõ q2 ſi raritas et denſi­
                    <lb/>
                  tas ſit poſſibilis, vel tã raritas ꝙ̄ denſitas dicunt̄̄
                    <lb/>
                  poſitiue, et ſunt qualitates aut nõ: nullum iſtoꝝ eſt
                    <lb/>
                  dicendū: igr̄ nec raritas nec denſitas eſt poſſibilis
                    <lb/>
                  nõ primū q2 raritas ita ſe habet  equevelociter et
                    <lb/>
                  eque proportionabiliter ſicut raritas acquirit̄̄ ita
                    <lb/>
                  velociter et proportionabiliter denſitas deꝑditur:
                    <lb/>
                  ſed hoc non põt eſſe de duobꝰ poſitiuis: igr̄ raritas
                    <lb/>
                  et dēſitas nõ ſūt qualitates poſitiue. </s>
                  <s xml:id="N20F62" xml:space="preserve">Maior ꝓbat̄̄.
                    <lb/>
                  </s>
                  <s xml:id="N20F66" xml:space="preserve">Quia quantū aliquid de raritate acq̇rit tm̄ deper­
                    <lb/>
                  dit de denſitate cū acq̇ſitio raritatis nõ ſit niſi dē,
                    <lb/>
                  perditio denſitatis et eque ꝓportionabiliter ſicut
                    <lb/>
                  aliq̇d rarefit ſiue efficit̄̄ magis rarum ita ꝓportiõa­
                    <lb/>
                  biliter efficit̄̄ minꝰ diuiſum q2 ſi in duplo magis ra­
                    <lb/>
                  riū efficit̄̄ aliq̇d illud in duplo minꝰ denſum efficit̄̄
                    <lb/>
                  et ecõtra: igr̄ equevelociter et eque ꝓportionabiliter
                    <lb/>
                  ſicut raritas acq̇rit̄̄: ita denſitas deꝑdit̄̄, et ſic patet
                    <lb/>
                  maior. </s>
                  <s xml:id="N20F79" xml:space="preserve">Probatur minor / q2 ſi aliqua duo poſitiua
                    <lb/>
                  poſſunt ita ſe habere  equevelociter et eque ꝓpor­
                    <lb/>
                  tionabiliter ſicut vnū deꝑdit̄̄ ita aliud augeat̄̄ ſeu
                    <lb/>
                  intēdat̄̄ ſint illa a. et b. et augeat̄̄ a. et deꝑdatur b. </s>
                  <s xml:id="N20F82" xml:space="preserve">Et
                    <lb/>
                  argr̄ ſic / vĺ a. et b. ſūt eq̈lia vt īeq̈lia ſi eq̈lia et argr̄ ſic
                    <lb/>
                  </s>
                  <s xml:id="N20F88" xml:space="preserve">Eq̄velociṫ auget̄̄ a. ſicut diminuit̄̄ b. / g̊ ↄ̨tinuo a . erit
                    <lb/>
                  maiꝰ b. et cõtinuo tm̄ a aēq̇;ret quãtū b. deꝑdet. </s>
                  <s xml:id="N20F8D" xml:space="preserve">Cõ-
                    <lb/>
                  ſequentia ptꝫ de ſe / q2 equevelociter auget̄̄ vnū ſi-
                    <lb/>
                  cut aliud diminuit̄̄. </s>
                  <s xml:id="N20F94" xml:space="preserve">Et vltra cõtinuo a. erit maiꝰ b.
                    <lb/>
                  et ↄ̨tinuo tm̄ acq̇rit a. ̄tū deꝑdit b. / igr̄ ↄ̨tinuo b. ma­
                    <lb/>
                  iorē ꝓportionē deꝑdit ꝙ̄ a. acq̇rit et ꝑ ↄ̨ñs non eque­
                    <lb/>
                  velociter et eque ꝓportionabiliter auget̄̄ a. ſicut di­
                    <lb/>
                  minuit̄̄ b. / ptꝫ hec ↄ̨ña ꝑ hanc maximã geometricam
                    <lb/>
                  </s>
                  <s xml:id="N20FA0" xml:space="preserve">Qñcun certa latitudo ſiue quantitas demitur a.
                    <lb/>
                  minori: et addat̄̄ maiori maiorē ꝓportionē deꝑdit
                    <lb/>
                  minꝰ ꝙ̄ acq̇rat maiꝰ (qm̄ ꝑ additionē equalis quãti­
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                  tatis maiori et minori: maiorē ꝓportionē acq̇rit mi­
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                  nus ꝙ̄ maiꝰ / vt dictū eſt in ſcḋa parte) / igr̄ ꝑ ſubſtra­
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                  ctionē cuiuſdē a minori et appoſitionē maiori ma-
                    <lb/>
                  iorē ꝓportionē deꝑdit minꝰ ꝙ̄ acq̇rat maius: et ſic
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                  ptꝫ /  ſi ſint equalia nõ põt vnū illoꝝ equevelociter
                    <lb/>
                  et eque ꝓportiõabiliter augeri ſiue aliud diminui.
                    <lb/>
                  </s>
                  <s xml:id="N20FB4" xml:space="preserve">Si vero ſint inequalia et minꝰ illoꝝ diminuatur et
                    <lb/>
                  maiꝰ illoꝝ auget̄̄ equevelociter iã ſequeret̄̄ /  minꝰ
                    <lb/>
                  illoꝝ maiorē ꝓportionē deꝑdit ꝙ̄ maius acq̇rat / vt
                    <lb/>
                  ptꝫ ex ſuperiori deductione. </s>
                  <s xml:id="N20FBD" xml:space="preserve">Si vero maiꝰ diminuit̄̄
                    <lb/>
                  ita velociter ſicut minꝰ auget̄̄: ſequit̄̄ /  cõtinuo ma­
                    <lb/>
                  iorē ꝓportionē acq̇rit minꝰ ꝙ̄ deꝑdat maius: q2 qñ
                    <lb/>
                  aliqua latitudo demitur a maiori et addit̄̄ minori:
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                  maiorē ꝓportionē acq̇rit minꝰ ꝙ̄ deꝑdat maiꝰ: igr̄
                    <lb/>
                  et ſic ptꝫ /  nõ eſt dicendū raritatem et denſitatē eſſe
                    <lb/>
                  qualitates poſitiuas. </s>
                  <s xml:id="N20FCC" xml:space="preserve">Sed nec diceuumū eſt ipſas
                    <lb/>
                  nõ eſſe qualitates q2 hoc eſt contra cõmentatorem
                    <lb/>
                  in ſeptīo phiſicoꝝ quē inſequit̄̄ ibi Burleꝰ et in tra­
                    <lb/>
                  ctatu ſuo de intenſione formarū.
                    <note position="right" xlink:href="note-0174-02a" xlink:label="note-0174-02" xml:id="N20FFD" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N20FDA" xml:space="preserve">¶ Dices forte ad
                    <lb/>
                  punctū argumēti negando  ſit īpoſſibile vnū po-
                    <lb/>
                  ſituū equevelociter et eque ꝓportiõabiliter augeri
                    <lb/>
                  ſicut diminuit̄̄. </s>
                  <s xml:id="N20FE3" xml:space="preserve">Et ad ꝓbationē dices /  argumen-
                    <lb/>
                  tū illud nõ ꝓbat qñ maiꝰ diminuit̄̄ et minꝰ auget̄̄: vt
                    <lb/>
                  in diminutione ſextipedalis et augmentatione qua­
                    <lb/>
                  drupedalis. </s>
                  <s xml:id="N20FEC" xml:space="preserve">Cū em̄ ſextipedale deperdit duo peda­
                    <lb/>
                  lia, et illa acq̇rat q̈drupedale in eodē tꝑe, manifeſtū
                    <lb/>
                  eſt /  ita velociter diminuitur ſextipedale ſicut au-
                    <lb/>
                  getur quadrupedale et eque ꝓportiõabiliter: quia
                    <lb/>
                  ſextipedale deꝑdit ꝓportionē ſexquialterã et qua­
                    <lb/>
                  drupedale acquirit tantam vt notum eſt.</s>
                </p>
                <p xml:id="N21003">
                  <s xml:id="N21004" xml:space="preserve">Sed cõtra / q2 ſaltē habeo /  duo poſi-
                    <lb/>
                  tiua nõ poſſunt ita ſe hēre. </s>
                  <s xml:id="N21009" xml:space="preserve"> cõtinuo equevelociter
                    <lb/>
                  et eque ꝓportionabiliter ſicut vnū auget̄̄ ita alteꝝ
                    <lb/>
                  diminuatur. </s>
                  <s xml:id="N21010" xml:space="preserve">Sed cõtinuo equevelociter et eq̄ ꝓpor­ </s>
                </p>
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