Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N20F21" level="3" n="3" type="other" type-free="tractatus">
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                  <s xml:id="N25068" xml:space="preserve">
                    <pb chead="Tertii tractatus" file="0213" n="213"/>
                  et tūc manifeſtū eſt /  viceſima prima efficitur eq̈-
                    <lb/>
                  lis illi viceſime vel maior qm̄ tot proportiones ac-
                    <lb/>
                  quiſiuit viceſima prima ſicut viceſima et cū hoc ac-
                    <lb/>
                  quiſiuit bis ꝓportionē diuiſionis vel maiorē ea: g̊
                    <lb/>
                  effecta eſt maior viceſima parte. </s>
                  <s xml:id="N2507C" xml:space="preserve">et ſic ꝓbabis de vi-
                    <lb/>
                  ceſima ſcḋa reſpectu viceſime prime.
                    <note position="left" xlink:href="note-0213-01a" xlink:label="note-0213-01" xml:id="N25096" xml:space="preserve">Correĺ.</note>
                  </s>
                  <s xml:id="N25086" xml:space="preserve">¶ Ex quo ſe-
                    <lb/>
                  quit̄̄ /  diuiſo corpore quauis ꝓportiõe volueris
                    <lb/>
                  vt ponit̄̄ in caſu ↄ̨cluſiõis nõ eſt poſſibile tale cor-
                    <lb/>
                  pꝰ ſucceſſiue ī tali caſu augmentari. </s>
                  <s xml:id="N2508F" xml:space="preserve">Ptꝫ ex ↄ̨cĺone</s>
                </p>
                <p xml:id="N2509C">
                  <s xml:id="N2509D" xml:space="preserve">Quarta ↄ̨̨cluſio. </s>
                  <s xml:id="N250A0" xml:space="preserve">Diuiſo corpore qua-
                    <lb/>
                  uis optata ꝓportione, et prima pars ꝓportiõalis
                    <lb/>
                  talis corporis in hora aliqualiter augeat̄̄: et ſcḋa
                    <lb/>
                  velociꝰ prima in ꝓportione in qua eſt minor ea vel
                    <lb/>
                  maiori: et tertia etiã velociꝰ prima in qua eſt minor
                    <lb/>
                  ea vel maiori, et ſic ↄ̨ñter ↄ̨tinuo totū illud corpus
                    <lb/>
                  infinite velociter auget̄̄ in illa hora et ſubito efficit̄̄
                    <lb/>
                  infinite magnū. </s>
                  <s xml:id="N250B1" xml:space="preserve">Probat̄̄ hec ↄ̨cluſio et volo /  di-
                    <lb/>
                  uidat̄̄ aliqḋ corpꝰ ꝓportione a. et incipiant partes
                    <lb/>
                  augmentari: vt ponit̄̄ in ↄ̨cluſione. </s>
                  <s xml:id="N250B8" xml:space="preserve">Tunc argr̄ ſic.
                    <lb/>
                  </s>
                  <s xml:id="N250BC" xml:space="preserve">Quocun inſtanti dato poſt hoc dabit̄̄ vna pars
                    <lb/>
                  ꝓportionalis equalis īmediate p̄cedenti vĺ maior
                    <lb/>
                  et q̄libet ſequēs equalis illi vĺ maior: ergo quocū
                    <lb/>
                  inſtanti dato poſt hoc illud corpꝰ erit infinite ma-
                    <lb/>
                  gnū. </s>
                  <s xml:id="N250C7" xml:space="preserve">Cõſequētia ptꝫ et argr̄ añs. </s>
                  <s xml:id="N250CA" xml:space="preserve">Qm̄ ſignato aliq̊
                    <lb/>
                  inſtanti poſt hoc aliqua eſt ꝓportio acq̇ſita prime
                    <lb/>
                  parte ꝓportionali q̄ ſit h. et in īfinitū maior acq̇ſi-
                    <lb/>
                  ta eſt alicui parti / vt ptꝫ ex caſu: qm̄ in īfinitū mīor
                    <lb/>
                  prima eſt aliqua pars, capio igr̄ vnã / que acq̇ſiuit
                    <lb/>
                  vnã ꝓportionē a. vel maiorē vltra ꝓportionē acq̇-
                    <lb/>
                  ſitã parti īmediate p̄cedenti: et ſequit̄̄ /  illa eſt eq̈-
                    <lb/>
                  lis vel maior īmediate p̄cedenti: qm̄ acq̇ſiuit tantã
                    <lb/>
                  ꝓportionē ſicut īmediate p̄cedens: et inſuꝑ illã per
                    <lb/>
                  quã excedebat̄̄ ab īmediate p̄cedenti vel maiorē: et
                    <lb/>
                  ꝑ ↄ̨ñs eſt equalis vel maior / vt ptꝫ ex maxīa ſcḋe cõ-
                    <lb/>
                  cluſionis. </s>
                  <s xml:id="N250E3" xml:space="preserve">et ſiĺr pars ſequēs illã eſt eq̈lis īmediate
                    <lb/>
                  p̄cedēti vel maior: qm̄ acquiſiuit tantã ꝓportionē
                    <lb/>
                  quantã īmediate p̄cedens et cū hoc vnã ꝓportionē
                    <lb/>
                  maiorē ꝙ̄ ſic proportio a. per quã excedebatur ab
                    <lb/>
                  īmediate p̄cedēti: et ſic ↄ̨ñter ꝓbabis de q̈libet alia</s>
                </p>
                <p xml:id="N250EE">
                  <s xml:id="N250EF" xml:space="preserve">Quīta ↄ̨̨cluſio. </s>
                  <s xml:id="N250F2" xml:space="preserve">Diuiſo corꝑe quacū-
                    <lb/>
                   proportione volueris: et tn aliquo tꝑe prima pars
                    <lb/>
                  ꝓportionalis acquirat aliquã ꝓportionē: et q̄libet
                    <lb/>
                  ſequēs tantã in eodē tꝑe: tūc oēs ille partes manēt
                    <lb/>
                  in eadē ꝓportione in qua antea ſe habebãt: et totū
                    <lb/>
                  acquirit illã ꝓportionē quã acquirit prima eiꝰ ꝑs
                    <lb/>
                  </s>
                  <s xml:id="N25100" xml:space="preserve">Probat̄̄ prima pars ↄ̨cluſiõis: qm̄ q̄libet due par­
                    <lb/>
                  tes īmediate ita ſe hñt  quanttã ꝓportionē acq̇ſi-
                    <lb/>
                  uit maior tantã acq̇ſiuit mīor: et ſic manent in eadē
                    <lb/>
                  ꝓportiõe in qua ſe habebãt ãtea. </s>
                  <s xml:id="N25109" xml:space="preserve">Ptꝫ ↄ̨ña ex ſcḋa
                    <lb/>
                  parte: et ꝑ ↄ̨ñs oēs ille partes ꝓportiõales ſe hñt in
                    <lb/>
                  ea ꝓportiõe in qua ſe habebant antea. </s>
                  <s xml:id="N25110" xml:space="preserve">Scḋa pars
                    <lb/>
                  ꝓbat̄̄ / et ſit h. ꝓportio acq̇ſita primi parti ꝓportio­
                    <lb/>
                  nali. </s>
                  <s xml:id="N25117" xml:space="preserve">et argr̄ ſic. </s>
                  <s xml:id="N2511A" xml:space="preserve">Quelꝫ ꝑs ꝓportionalis iſtiꝰ corꝑis
                    <lb/>
                  demõſtrato corꝑe ſic diuiſo et augmētato eſt in h.
                    <lb/>
                  ꝓportiõe maior ꝙ̄ ãtea: g̊ totū corpꝰ eſt in h. ꝓpor-
                    <lb/>
                  tiõe maiꝰ: et illa eſt ꝓportio quã acq̇ſiuit ṗma ꝑs ꝓ-
                    <lb/>
                  portiõalis: igr̄ in caſu ↄ̨cluſiõis totū corpꝰ effectuꝫ
                    <lb/>
                  ē maiꝰ in ꝓportiõe quã acq̇ſiuit ṗma ꝑs ꝓportiõa-
                    <lb/>
                  lis. </s>
                  <s xml:id="N25129" xml:space="preserve">Probat̄̄ ↄ̨ña: et ſit illud corpꝰ a. in fine augmē-
                    <lb/>
                  tatiõis: et b. in prīcipio. </s>
                  <s xml:id="N2512E" xml:space="preserve">Et argr̄ ſic / ṗme ꝑtꝪ ꝓpor-
                    <lb/>
                  tiõalis ipſiꝰ a .h. ꝓportiõe ad primã ipſiꝰ b. eſt ꝓpor­
                    <lb/>
                  tio h. </s>
                  <s xml:id="N25135" xml:space="preserve">Et ſcḋe ipſiꝰ a. ad ſcḋaꝫ ipſiꝰ b. eſt etiã ꝓportio
                    <lb/>
                  h. / Et ṫtie ipſiꝰ a. ad ṫtiã ipſiꝰ b. eſt ꝓportio h. / et ſic
                    <lb/>
                  ↄ̨ñter: igr̄ oīm partiū ꝓportionaliū ipſiꝰ a. ad oēs
                    <lb/>
                  ꝑtes ꝓportiõales ipſiꝰ b. eſt ꝓportio h. / ptꝫ hec ↄ̨ña
                    <lb/>
                  qm̄ eadē eſt ꝓpor° ↄ̨iūtoꝝ et diuiſorū / vt ptꝫ ex ſcḋo
                    <lb/>
                  capite ſecunde partis. </s>
                  <s xml:id="N25142" xml:space="preserve">Et ex conſequenti totum a.
                    <lb/>
                  eſt in h. proportione maius ipſo b.</s>
                </p>
                <cb chead="Capitulū ſecundum."/>
                <p xml:id="N25149">
                  <s xml:id="N2514A" xml:space="preserve">Sexta cõcluſio. </s>
                  <s xml:id="N2514D" xml:space="preserve">Partito corpore per
                    <lb/>
                  partes ꝓportionales quacun ꝓportione volue-
                    <lb/>
                  ris et in aliquo tēpore prima pars proportionalis
                    <lb/>
                  acquirat aliquã ꝓportionē et ſecunda acquirat in
                    <lb/>
                  aliqua certa ꝓportione in eodē tēpore ꝓportioneꝫ
                    <lb/>
                  minorē: et tertia in eadē ꝓportione minorē ſecūda:
                    <lb/>
                  et quarta in eadem ꝓportione minorē tertia: et ſic
                    <lb/>
                  ↄ̨ñter. </s>
                  <s xml:id="N2515E" xml:space="preserve">tūc ꝓportio inter primã partē et ſcḋam effi-
                    <lb/>
                  citur maior ꝑ primã partē ꝓportionalē ꝓportiõis
                    <lb/>
                  acquiſite prime diuiſe in ea ꝓportione qua ſecūda
                    <lb/>
                  tardius augmētaã prima: et tertia ꝙ̄ ſcḋa: et ſic cõ-
                    <lb/>
                  ſequēter: et ꝓportio īter ſcḋaꝫ et tertiã efficit̄̄ maior
                    <lb/>
                  ꝑ ſcḋam partē ꝓportionalē ꝓportiõis acq̇ſite ṗme
                    <lb/>
                  et ꝓportio īter tertiã et quartã efficit̄̄ maior ꝑ tertiã
                    <lb/>
                  partē ꝓportionalē ꝓportionis acq̇ſite prime: r ſic
                    <lb/>
                  ↄ̨ñter: et (vt opinor) nõ valet finita intellectꝰ capaci­
                    <lb/>
                  tas cõmenſurare ꝓportionē toti corpori acquiſitã
                    <lb/>
                  </s>
                  <s xml:id="N25174" xml:space="preserve">Exemplū / vt ſi aliqḋ corpꝰ diuidat̄̄ ꝑ partes ꝓpor-
                    <lb/>
                  tionales ꝓportiõe dupla: et prima pars ꝓportiõa­
                    <lb/>
                  lis acq̇rat ꝓportionē ſexquialterã: et ſcḋa ſubqua-
                    <lb/>
                  druplã: et tertia ſubquadruplã ad acquiſitã ſecūde
                    <lb/>
                  et quarta ſubquadruplã ad acquiſitã tertie: et ſic cõ­
                    <lb/>
                  ſequenter: tūc dico /  ꝓportio inter primã partem
                    <lb/>
                  ꝓportionalē et ſcḋam acquiſiuit primã partē ꝓpor­
                    <lb/>
                  tionis ſexq̇altere diuiſe ꝑ partes ꝓportiõales pro­
                    <lb/>
                  portione quadrupla. </s>
                  <s xml:id="N25187" xml:space="preserve">Et ꝓportio inter ſcḋaꝫ et ter-
                    <lb/>
                  tiã acq̇ſiuit ſcḋam partē ꝓportionalē ꝓportionis
                    <lb/>
                  ſexq̇altere. </s>
                  <s xml:id="N2518E" xml:space="preserve">Et ꝓportio inter tertiã et quartã tertiã
                    <lb/>
                  partē ꝓportionalē ꝓportionis ſexq̇altere. </s>
                  <s xml:id="N25193" xml:space="preserve">Et ſi cõ­
                    <lb/>
                  ſequēter. </s>
                  <s xml:id="N25198" xml:space="preserve">Probat̄̄ / ſit a. proportio acq̇ſita prime
                    <lb/>
                  parti ꝓportionali: et ſit f. ꝓportio in qua velocius
                    <lb/>
                  auget̄̄ prima ꝙ̄ ſcḋa. </s>
                  <s xml:id="N2519F" xml:space="preserve">Et argr̄ ſic. </s>
                  <s xml:id="N251A2" xml:space="preserve">Proportiões ac-
                    <lb/>
                  quiſite partibꝰ huiꝰ corporis cõtinuo ſe habent in
                    <lb/>
                  ꝓportione f. / vt ptꝫ ex caſu: ergo exceſſus quibꝰ cõti­
                    <lb/>
                  nuo ſe excedūt etiã ſe hñt ↄ̨tinuo in ꝓportione f. et
                    <lb/>
                  ꝑ primū illoꝝ exceſſuū ꝓportio inter primã et ſcḋaꝫ
                    <lb/>
                  partē efficit̄̄ maior: et ꝑ ſcḋm ꝓportio inter ſcḋaꝫ et
                    <lb/>
                  tertiaꝫ efficit̄̄ maior: et ꝑ tertiū ꝓportio inter tertiã
                    <lb/>
                  et quartã efficit̄̄ maior: et ſic ↄ̨ñter: et primꝰ illoꝝ ex-
                    <lb/>
                  ceſſuū eſt prima pars ꝓportionalis ipſiꝰ a. ꝓpor-
                    <lb/>
                  tionis diuiſe ꝓportiõe f. et ſcḋus ſcḋa: et tertiꝰ tertia /
                    <lb/>
                  et ſic ↄ̨ñter: igr̄ ꝓportio inter primã et ſcḋam partē
                    <lb/>
                  efficit̄̄ maior ꝑ primã partē ꝓportionalē ipſius a.
                    <lb/>
                  ꝓportione f. et ſcḋa ꝑ ſcḋaꝫ: et tertia per tertiã: et ſic
                    <lb/>
                  ↄ̨ñter / qḋ fuit ꝓbandū. </s>
                  <s xml:id="N251BF" xml:space="preserve">Ptꝫ tamē prima ↄ̨ña ꝑ hãc
                    <lb/>
                  regulã q̄ ſuperiꝰ demõſtrata eſt in quacun ꝓpor-
                    <lb/>
                  tione ſe hñt aliqua ↄ̨tinuo in eadē ↄ̨tinuo ſe habēt
                    <lb/>
                  exceſſus eoꝝ. </s>
                  <s xml:id="N251C8" xml:space="preserve">Sed iã ꝓbo /  ꝑ primū illorū exceſſuū
                    <lb/>
                  ꝓportio inter primã et ſcḋam efficitur maior: et per
                    <lb/>
                  ſcḋm proportio inter ſcḋam et tertiã etc̈. / et hoc ꝑ hãc
                    <lb/>
                  maximã. </s>
                  <s xml:id="N251D1" xml:space="preserve">Quãdocū due quãtitates inequales ac­
                    <lb/>
                  quirūt aliquas ꝓportiones: et maior illaꝝ acqui-
                    <lb/>
                  rit maiorē ꝓportionē ꝙ̄ minor: tunc ꝓportio inter
                    <lb/>
                  illas quantitates efficitur maior per exceſſum quo
                    <lb/>
                  ꝓportio acquiſita maiori excedit ꝓportionē acqui­
                    <lb/>
                  ſitam mīori vt in capĺo .8. ſcḋe partis oſtēſum eſt
                    <lb/>
                  ſed ſic eſt in ꝓpoſito: igr̄. </s>
                  <s xml:id="N251E0" xml:space="preserve">Sed iam ꝓbat̄̄ /  primꝰ
                    <lb/>
                  illoꝝ exceſſuū eſt prima pars ꝓportionalis ipſius
                    <lb/>
                  a. ꝓportione f. q2 a. ſe habet ad ꝓportionē acquiſi­
                    <lb/>
                  tam prime partiū ꝓportionali in ꝓportione f. / ergo
                    <lb/>
                  exceſſus quo a. excedit ꝓportionē acquiſitã ſecunde
                    <lb/>
                  parti ꝓportionali eſt prima pars proportionalis
                    <lb/>
                  ipſius a. ꝓportione f. </s>
                  <s xml:id="N251EF" xml:space="preserve">Ptꝫ ↄ̨ña per hanc regulam.
                    <lb/>
                  </s>
                  <s xml:id="N251F3" xml:space="preserve">Quandocū aliquod totū excedit aliquid in cer-
                    <lb/>
                  ta ꝓportione tūc excedit illud per primã ſui partē
                    <lb/>
                  ꝓportionalē tali ꝓportione: vt ſi vnū pedale exce-
                    <lb/>
                  dat aliam quantitatē in proportione ſexquialtera
                    <lb/>
                  illud pedale excedit aliud per primã ſui partē pro-
                    <lb/>
                  portionalē ꝓportione ſexquialtera quia per vnaꝫ </s>
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