Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N20F21" level="3" n="3" type="other" type-free="tractatus">
              <div xml:id="N24010" level="4" n="2" type="chapter" type-free="capitulum">
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                  <s xml:id="N242F8" xml:space="preserve">
                    <pb chead="Tertii tractatus" file="0205" n="205"/>
                  oīno eodē modo ſicut diminuebat̄̄ acq̇rendo vnifor­
                    <lb/>
                  miter quãtitatē ſicut eam deperdebat. </s>
                  <s xml:id="N24314" xml:space="preserve">quo poſito
                    <lb/>
                  arguit̄̄ ſic .a. in inſtanti initiatiuo alterius hore ſe-
                    <lb/>
                  quentis incipit vniformiter acq̇rere quãtitatē quia
                    <lb/>
                  vniformiter deperdit in hora priori cum poſitis in
                    <lb/>
                  caſu: et tamen incipit in infinitū velociter augeri / vt
                    <lb/>
                  patet ex principio huiꝰ ſecūdi argumēti: igit̄̄ ꝓpo­
                    <lb/>
                  ſitum.
                    <note position="left" xlink:href="note-0205-01a" xlink:label="note-0205-01" xml:id="N24336" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N24328" xml:space="preserve">¶ Dices et bene cõcedēdo quod infertur: et ne­
                    <lb/>
                  gando  illud repugnet. </s>
                  <s xml:id="N2432D" xml:space="preserve">Immo in tali caſu illud
                    <lb/>
                  ſeq̇tur ex hac poſitiõe.</s>
                </p>
                <p xml:id="N2433C">
                  <s xml:id="N2433D" xml:space="preserve">Sꝫ contra q2 tūc ſequeretur /  quoti-
                    <lb/>
                  enſcun hora diuidit̄̄ ꝓportiõe dupla et aliq̇d inci­
                    <lb/>
                  pit augeri a non quãto in qualibet parte ꝓportio-
                    <lb/>
                  nali acq̇rēdo vniformiter vnam ſui partē propor-
                    <lb/>
                  tionalē ꝓportione dupla: ip̄m incipit vniformiter
                    <lb/>
                  acq̇rere quãtitatē: et cõtinuo vniformiter aquirit.
                    <lb/>
                  </s>
                  <s xml:id="N2434B" xml:space="preserve">Patet hoc / q2 in equalibꝰ partibꝰ tēporis equaleꝫ
                    <lb/>
                  quãtitatē oīno acquirit: ſꝫ cõſequēs eſt falſum: igit̄̄
                    <lb/>
                  illud ex quo ſequit̄̄. </s>
                  <s xml:id="N24352" xml:space="preserve">Falſitas ↄ̨ſequētꝪ arguitur: q2
                    <lb/>
                  tunc ſeq̄retur /  ſi duo inciperēt augeri a nõ quãto:
                    <lb/>
                  et vnū illorū in qualibet parte ꝓportionli tempo­
                    <lb/>
                  ris ꝓportõe dupla iucipiēdo a minoribus acq̇reret
                    <lb/>
                  vniformiter vnã partē ꝓportionalē ſui ꝓportione
                    <lb/>
                  dupla ita  in qualibet ꝑte ꝓportionali acq̇reret
                    <lb/>
                  proportionē duplã: et aliud in certa ꝓportione cõ-
                    <lb/>
                  tinuo velocius augeretur puta in qualibet parte ꝓ­
                    <lb/>
                  portionali talis tēporis acquirēdo ꝓportionē qua­
                    <lb/>
                  druplam vel octuplam cõtinuo: tunc illud quod in
                    <lb/>
                  certa proportiõe cõtinuo velocius augetur incipit
                    <lb/>
                  infinitū tarde acq̇rere de quãtitate: ſed ↄ̨ſequēs eſt
                    <lb/>
                  falſum: quia tūc ſequeret̄̄ /  omne qḋ a nõ quãto in­
                    <lb/>
                  cipit augeri: et in qualibet parte tēporis ꝓportio-
                    <lb/>
                  nali ꝓportione dupla maiorē ꝓportionē acquirit
                    <lb/>
                  quã dupla: ī īfinitū tarde acq̇reret de ̄titate quod
                    <lb/>
                  videt̄̄ oīno extraneū. </s>
                  <s xml:id="N24375" xml:space="preserve">Sequela tamē ꝓbat̄̄: et volo /
                    <lb/>
                   a. ſic incipiat augeri a nõ quãto: et ī qualibet ꝑte
                    <lb/>
                  ꝓportiõali tēporis ꝓportiõe dupla acq̇rat pro­
                    <lb/>
                  portionē duplã acq̇rendo vniformiter de quãtitate
                    <lb/>
                  et .b. in omni ↄ̨ſimili parte tēporis acquirat maio­
                    <lb/>
                  rem proportionē dupla puta triplã vel quadruplã
                    <lb/>
                  vel octuplã, in idē redit, quo poſito arguitur ſic .a.
                    <lb/>
                  et .b. incipiūt augeri a nõ quãto: et .b. in certa ꝓpor-
                    <lb/>
                  tione cõtinuo velocius augebitur ꝙ̄ a. / ergo ſeq̇tur /
                    <lb/>
                   a. incipit in infinitū eē maius ip̄o .b. / et ꝑ ↄ̨ſequēs
                    <lb/>
                  incipit in infinitū maiorē quãtitatē acq̇rere ipſo .b. /
                    <lb/>
                  vt patet ex vltima replica ſecundi argumēti: et vltra
                    <lb/>
                  ſequitur /  in infinitū maiorē quãtitatē acquirit .a.
                    <lb/>
                  ̄ .b. in eodē tempore: et a. cõtinuo vniformiter et eq̄
                    <lb/>
                  velociter acquirit quãtitatē: ergo .b. incipit in infi-
                    <lb/>
                  nitū tarde acq̇rere de quãtitate / quod fuit ꝓbandū.</s>
                </p>
                <note position="left" xml:id="N24396" xml:space="preserve">Cõfir° .2.</note>
                <p xml:id="N2439A">
                  <s xml:id="N2439B" xml:space="preserve">Confirmatur ſecundo / quia ſi poſitio
                    <lb/>
                  eſſet vera ſequeret̄̄ /  ſi a nõ quãto aliquid inciperet
                    <lb/>
                  augeri in qualibet parte ꝓportionali temporis ꝓ-
                    <lb/>
                  portiõe dupla diuiſi acquirēdo minorē ꝓportionē
                    <lb/>
                  ̄ duplã: ip̄m inciperet in infinitū velociter acq̇rere
                    <lb/>
                  de quãtitate: ſꝫ cõſequēs eſt falſum: igitur illud ex
                    <lb/>
                  quo ſeq̇tur. </s>
                  <s xml:id="N243AA" xml:space="preserve">Seq̄la ꝓbat̄̄ et capio .a. et .b. et volo /  .a.
                    <lb/>
                  incipiat augeri a nõ quãto in qualibet parte ꝓpor­
                    <lb/>
                  tionali tēporis ꝓportiõe dupla diuiſi acq̇rendo vni­
                    <lb/>
                  formiter ↄ̨ſimilem partē ꝓportionalē ſui ꝓportio­
                    <lb/>
                  ne dupla ita  in qualibet tali parte tēporis acq̇-
                    <lb/>
                  rat vnã ꝓportionē duplã: et .b. in qualibet conſimili
                    <lb/>
                  parte tēporis acquirat vnã partē ꝓportionalē ſui
                    <lb/>
                  ꝓportione minori dupla puta ſexquitertia vel ſex­
                    <lb/>
                  quialtera. </s>
                  <s xml:id="N243BD" xml:space="preserve">Quo poſito arguit̄̄ ſic .a. et .b. incipiunt
                    <lb/>
                  augeri a nõ quãto: et b. ī certa ꝓportiõe cõtinuo tar­
                    <lb/>
                  dius ip̄o .a. / igit̄̄ incipit eē in infinitū maius ipſio .a. /
                    <lb/>
                  et per ↄ̨ſequens incipit in infinitū velociter maiorē
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                  quãtitatē acq̇rere ꝙ̄ a. in eodem tēpore. </s>
                  <s xml:id="N243C9" xml:space="preserve">Patēt conſe-
                    <lb/>
                  quentia vt prius: et a. cõtinuo certe velociter acq̇rit
                    <lb/>
                  quãtitatē vt poſitū eſt: igit̄̄ .b. in infinitū velociter ac­
                    <lb/>
                  quirit quãtitatē / quod fuit ꝓbadū. </s>
                  <s xml:id="N243D2" xml:space="preserve">Sꝫ iam probo
                    <lb/>
                  falſitatē cõſequētis: q2 tūc ſequeretur /  ſi a. et b. in­
                    <lb/>
                  ciperet a nõ quãto augeri: et a. in qualibet parte
                    <lb/>
                  ꝓportionali tēporis proportiõe dupla acquereret
                    <lb/>
                  proportionē ſexquialterã: et b. in cõſimili parte cõ-
                    <lb/>
                  tinuo acq̇reret ꝓportiõeꝫ ſexquitertiã: tunc vtrun
                    <lb/>
                  illorū inciperet infinite velociter acquirere de quã­
                    <lb/>
                  titate: et ꝑ cõſequēs .b. nõ īciperet velocius acq̇rere
                    <lb/>
                  de quãtitate ꝙ̄ a. et ſic nõ inciperet in īfinitū eē maiꝰ
                    <lb/>
                  ipſo a. / quod eſt ↄ̨tra cõcluſionē ꝓbatã in vltima re­
                    <lb/>
                  plica ſecundi argumēti. </s>
                  <s xml:id="N243E9" xml:space="preserve">Falſitas cõſequētis patet /
                    <lb/>
                  quia nõ videt̄̄ poſſibile  vtrū illorū inciperet in­
                    <lb/>
                  finite velociter acquirere de quãtitate: et tamē vnuꝫ
                    <lb/>
                  illorum inciperet in infinitū velocius altero acqui-
                    <lb/>
                  rere. </s>
                  <s xml:id="N243F4" xml:space="preserve">Cõſequētia tamē patet / quia vtrū illorū inci­
                    <lb/>
                  pit augeri a nõ quãto continuo in qualibet parte ꝓ-
                    <lb/>
                  portionali tēporis ꝓportiõe dupla acquirēdo mi-
                    <lb/>
                  norē ꝓportionem dupla: igitur.</s>
                </p>
                <note position="right" xml:id="N243FD" xml:space="preserve">Cõfir° .3.</note>
                <p xml:id="N24401">
                  <s xml:id="N24402" xml:space="preserve">Confirmatur tertio / quia ſi poſitio eēt
                    <lb/>
                  vera ſeq̄retur /  quãtuncun magnū corpus ſit di­
                    <lb/>
                  uiſum per partes ꝓportionales aliquã proportio­
                    <lb/>
                  ne: et aliud quãtuncū parū diuiſum per partes
                    <lb/>
                  ꝓportionales aliqua proportione minori: in infini­
                    <lb/>
                  tū maior eſt aliqua pars proportionalis minoris
                    <lb/>
                  parte proportionali correſpõdente maioris: ſꝫ cõ-
                    <lb/>
                  ſequens apparet falſum: igitur illud ex quo ſequit̄̄
                    <lb/>
                  </s>
                  <s xml:id="N24414" xml:space="preserve">Sequela probatur / q2 ſi non detur vnū cētupedale
                    <lb/>
                  diuiſum ꝑ partes proportionales proportiõe qua­
                    <lb/>
                  durupla: et vnū ſemipedale vel quãtūcū paruum
                    <lb/>
                  volueris diuiſum ꝑ partes portionales proportio­
                    <lb/>
                  ne ſexquitertia ſeu quauis alia proportiõe minori
                    <lb/>
                  quadrupla: et diminuãtur illa duo vſ ad nõ ̄tuꝫ
                    <lb/>
                  ita  maius cõtinuo in qualibet parte proportio-
                    <lb/>
                  nali tēporis proportiõe dupla vnã ſui partiē pro-
                    <lb/>
                  portionalē perdat ꝑdēdo proportionē quadruplã
                    <lb/>
                  et ſemipedale in qualibet parte cõſimili perdat ꝓ-
                    <lb/>
                  portionē ſexquitertiã ꝑdendo vnam partē propor-
                    <lb/>
                  tionalē ſui proportiõe ſextertia quouſ veniãt ad
                    <lb/>
                  nõ quãtū: tūc volo /  īcipiãt oīno eodē modo acqui­
                    <lb/>
                  rere quãtitates deperditas et oīno eodē modo au-
                    <lb/>
                  geri ſicut diminuebant̄̄. </s>
                  <s xml:id="N24433" xml:space="preserve">Quo poſito arguitur ſic
                    <lb/>
                  illud / qḋ fuit cētupedale: et illḋ quod fuit ſemipe­
                    <lb/>
                  dale incipit in certa portiõe tardius cõtinuo auge-
                    <lb/>
                  ri ꝙ̄ centupedale: igit̄̄ illud qḋ fuit ſemipedale inci­
                    <lb/>
                  pit in infinitū eē maius illo altero quod fuit centi-
                    <lb/>
                  pedale: et illud qḋ fuit centipedale incipit acquire-
                    <lb/>
                  re partes proportionales proportiõe quadrupla
                    <lb/>
                  quas antea ṗdidit: et illḋ qḋ fuit ſemipedale īcipit
                    <lb/>
                  acq̇rere partes proportionales proportione ſexq̇-
                    <lb/>
                  tertia quas antea deꝑdit: igit̄̄ incipit in infinitum
                    <lb/>
                  maiores partes acquirere illud quod fuit ſemipe-
                    <lb/>
                  dale ꝙ̄ illud qḋ fuit centipedale. </s>
                  <s xml:id="N2444C" xml:space="preserve">Patet cõſequētia /
                    <lb/>
                  q2 immediate poſt illud qḋ fuit ſemipedale in infi-
                    <lb/>
                  nitū erit maius illo qḋ fuit centipedale. </s>
                  <s xml:id="N24453" xml:space="preserve">igit̄̄ imme-
                    <lb/>
                  diate poſt hoc in infinitū maiores erunt partes pro­
                    <lb/>
                  portiõales illius proportiõe ſexquitertia partibꝰ
                    <lb/>
                  proportionalibꝰ alterius proportiõe quadrupla:
                    <lb/>
                  et tales partes īcipit acq̇rere: et ſemꝑ acq̇runt par-
                    <lb/>
                  tes correſpõdētes ſicut deperdebãt: igit̄̄ in infinitū
                    <lb/>
                  maior eſt aliqua pars proportionalis minoris ꝑ-
                    <lb/>
                  te proportionali correſpõdente maioris quod fuit
                    <lb/>
                  probandum.</s>
                </p>
                <p xml:id="N24466">
                  <s xml:id="N24467" xml:space="preserve">Tertio prīcipaliter ad idem arguitur
                    <lb/>
                  ſic. </s>
                  <s xml:id="N2446C" xml:space="preserve">Si illa poſitio eſſet vera ſeq̄retur hec cõcluſio  </s>
                </p>
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