Alvarus, Thomas, Liber de triplici motu, 1509

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          <div xml:id="N15C17" level="2" n="3" type="other" type-free="pars">
            <div xml:id="N1C8AF" level="3" n="2" type="other" type-free="tractatus">
              <div xml:id="N2063E" level="4" n="4" type="chapter" type-free="capitulum">
                <p xml:id="N20B80">
                  <s xml:id="N20CA4" xml:space="preserve">
                    <pb chead="Secundi tractatus" file="0173" n="173"/>
                  citra centrū mūdi efficit̄̄ minor et pars vltra centrū
                    <lb/>
                  mūdi maior) / igr̄ perpetuo aliqua pars aggregati
                    <lb/>
                  ex oībus partibꝰ ꝓpotiõalibꝰ ipſiꝰ d. partis deſcē-
                    <lb/>
                  det / qḋ fuit ꝓbandū. </s>
                  <s xml:id="N20CD0" xml:space="preserve">Conſequētia ꝓbat̄̄ / q2 ſi q̄libet
                    <lb/>
                  pars ꝓportionalis cõtinuo ipſius d. partis diuiſe
                    <lb/>
                  ꝓportione dupla deſcēderet ſiue moueret̄̄ a ꝓpor-
                    <lb/>
                  tione a qua ipſa īcipit deſcendere: ꝑpertuo aliqua
                    <lb/>
                  pars aggregati ex oībus partibꝰ ꝓportionalibus
                    <lb/>
                  ipſiꝰ d. partis deſcēderet / g̊ ſi q̄libet pars ꝓportio-
                    <lb/>
                  nalis ipſiꝰ d. partis cõtinuo deſcēderet et mouetur
                    <lb/>
                  a ꝓportione minori ꝙ̄ ſit illa a qua īcipit deſcēde-
                    <lb/>
                  re: ꝑpetuo aliqua pars aggregati ex oībus parti-
                    <lb/>
                  bus ꝓportionalibꝰ ipſiꝰ d. partis deſcendit / qḋ fuit
                    <lb/>
                  ꝓbandū. </s>
                  <s xml:id="N20CE7" xml:space="preserve">Cõſequētia ptꝫ cū ãtecedēte ex deductione
                    <lb/>
                  ſecūdi argumēti ſexti capitis primi tractatꝰ huius
                    <lb/>
                  partis: hoc addito /  ille partes cõtinuo ſe habent
                    <lb/>
                  in ꝓportione dupla: et in tꝑe in quo adequate deſcē­
                    <lb/>
                  dit aliqua pars ſcḋm ſe vel aliquid eiꝰ p̄tereundo
                    <lb/>
                  centrū mūdi ipſa pars deſcribit tm̄ ſpaciū quanta
                    <lb/>
                  ipſamet pars eſt / vt ptꝫ intuenti caſum. </s>
                  <s xml:id="N20CF6" xml:space="preserve">Sed iã ꝓbo
                    <lb/>
                  ſcḋam partē maioris vcꝫ  ſecūda pars ꝓportona­
                    <lb/>
                  lis ipſiꝰ d. partis īcipit deſcēdere a ꝓportione ſub­
                    <lb/>
                  dupla ad ꝓportionē f. vĺ minori: q2 cū primū ṗma
                    <lb/>
                  pars proportionalis ipſius d. partis eſt totaliter
                    <lb/>
                  vltra centrū mūdi, pars citra centrū mundi perdit
                    <lb/>
                  quartã partē exceſſus quo excedit partē vltra cen-
                    <lb/>
                  trū mūdi: et illã acquirit pars vltra centrū mūdi / vt
                    <lb/>
                  cõſtat: g̊ tūc ꝓportio f. partis citra centrū ad partē
                    <lb/>
                  vltra centrū ꝑdit pluſ̄ medietatē ſui: et pluſ̄ ad
                    <lb/>
                  ſubduplū ſui diminuit̄̄: ptꝫ ↄ̨ña ex ſecūda ſuppoſi-
                    <lb/>
                  tione huiꝰ notabilis hoc addito  pars citra cen-
                    <lb/>
                  trū eſt terminꝰ maior proportionis f. et pars vltra
                    <lb/>
                  centrū eſt terminꝰ minor. </s>
                  <s xml:id="N20D13" xml:space="preserve">Et ab illa proportione q̄
                    <lb/>
                  eſt minor quã ſubdupla ad f. īcipit ſecūda pars ꝓ-
                    <lb/>
                  portionalis ipſiꝰ d. partis deſcēdere / vt cõſtat: g̊ ꝓ-
                    <lb/>
                  poſitū. </s>
                  <s xml:id="N20D1C" xml:space="preserve">Et iſto modo ꝓbabis  tertra īcipit deſcen­
                    <lb/>
                  dere a ꝓportione ſubdupla vel mīori ſubdupla ad
                    <lb/>
                  proportionē a qua incipit deſcendere ſecūda: et ſic
                    <lb/>
                  ↄ̨ñter de aliis partibꝰ. </s>
                  <s xml:id="N20D25" xml:space="preserve">Sed iã ꝓbo maiorē vcꝫ  cū
                    <lb/>
                  primū prima pars proportionalis ipſiꝰ d. partis
                    <lb/>
                  eſt totaliter vltra centrū pars citra centrū mundi
                    <lb/>
                  perdit quartã partē exceſſus quo ipſa excedit par-
                    <lb/>
                  tem vltra centrū mūdi: q2 ipſa d. pars eſt medietas
                    <lb/>
                  exceſſus quo pars citra centrū excedit partē vltra
                    <lb/>
                  centrū / vt ptꝫ ex prima ſuppoſitione huiꝰ notabilis /
                    <lb/>
                  g̊ prima pars proportionalis proportione dupla
                    <lb/>
                  ipſiꝰ d. partis eſt quarta pars totiꝰ exceſſus: et illã
                    <lb/>
                  ꝑdit pars citra centrū mūdi primū ipſa eſt tota­
                    <lb/>
                  liter vltra centrū: g̈ propoſitū. </s>
                  <s xml:id="N20D3C" xml:space="preserve">Ptꝫ g̊ maior: et totū
                    <lb/>
                  añs / et ꝑ ↄ̨ñs cõcluſio q̄ fuerat probanda.
                    <note position="left" xlink:href="note-0173-01a" xlink:label="note-0173-01" xml:id="N20DC3" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N20D46" xml:space="preserve">¶ Ex his
                    <lb/>
                  infero aliqua correlaria. </s>
                  <s xml:id="N20D4B" xml:space="preserve">Primū in caſu huiꝰ de-
                    <lb/>
                  monſtrationis īmediate poſt inſtãs / qḋ eſt preſens
                    <lb/>
                  aſcendet aliq̇d īmediate poſt illud deſcēdet : et tñ
                    <lb/>
                  nichil īmediate poſt hoc aſcendet qḋ īmediate poſt
                    <lb/>
                  hoc deſcendet. </s>
                  <s xml:id="N20D56" xml:space="preserve">Probat̄̄ prima pars / q2 quocun
                    <lb/>
                  inſtanti dato illiꝰ tꝑis in quo deſcēdet tale quadra­
                    <lb/>
                  tū q̄libet pars illiꝰ quadrati q̄ eſt citra centrū īme-
                    <lb/>
                  diate poſt tale inſtans deſcendet / vt ſatis conſtat et
                    <lb/>
                  īmediate poſt idē inſtans aliqua talis pars aſcen-
                    <lb/>
                  det: igr̄ in caſu demonſtrationis, īmediate poſt in-
                    <lb/>
                  ſtans / qḋ eſt preſens aliq̇d aſcēdet qḋ īmediate poſt
                    <lb/>
                  idē inſtans deſcendet ſcḋa pars ptꝫ ex falſitate ſue
                    <lb/>
                  cõtradictorie. </s>
                  <s xml:id="N20D69" xml:space="preserve">Ad hoc em̄  aliquid aſcendat non
                    <lb/>
                  ſufficit aliquã partē eiꝰ aſcendere: ſed requiritur / 
                    <lb/>
                  maior pars ꝙ̄ eiꝰ medietas aſcendat. </s>
                  <s xml:id="N20D70" xml:space="preserve">Conſimiliter
                    <lb/>
                  dicat̄̄ de deſcensu.
                    <note position="left" xlink:href="note-0173-02a" xlink:label="note-0173-02" xml:id="N20DC9" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N20D7A" xml:space="preserve">¶ Scḋm correlariū. </s>
                  <s xml:id="N20D7D" xml:space="preserve">Immediate
                    <lb/>
                  poſt inſtans qḋ eſt preſens aſcendet aliq̇d qḋ p̄ſens
                    <lb/>
                  aſcendet aliq̇d qḋ īmediate poſt idē inſtans deſcen­
                    <lb/>
                  det: et tñ nõ īmediate poſt inſtãs qḋ eſt p̄ſens deſcen­
                    <cb chead="Capitulū quartū."/>
                  det aliq̇d qḋ īmediate poſt idem inſtans aſcendet.
                    <lb/>
                  </s>
                  <s xml:id="N20D8A" xml:space="preserve">Ptꝫ prima pars huiꝰ ex priori correlario. </s>
                  <s xml:id="N20D8D" xml:space="preserve">Et ſcḋa
                    <lb/>
                  ꝓbat̄̄ / q2 ↄ̨tradictoria illiꝰ eſt falſa / vt ptꝫ ꝑ falſitatē
                    <lb/>
                  prime exponētis q̄ eſt iſta poſt inſtans quod eſt pre­
                    <lb/>
                  ſens deſcendet aliquid quod īmediate poſt idem in­
                    <lb/>
                  ſtans aſcendet q2 nulla pars illiꝰ corporis quadra­
                    <lb/>
                  ti que poſt inſtans quod eſt preſens deſcendit īme-
                    <lb/>
                  diate poſt idem inſtans aſcendet.
                    <note position="right" xlink:href="note-0173-03a" xlink:label="note-0173-03" xml:id="N20DCF" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N20DA1" xml:space="preserve">¶ Tertiū correla­
                    <lb/>
                  riū. </s>
                  <s xml:id="N20DA6" xml:space="preserve">Immediate poſt inſtans quod eſt p̄ſens aſcen-
                    <lb/>
                  det aliq̇d qḋ īmediate poſt idē inſtans quod eſt pre­
                    <lb/>
                  ſens deſcendet: et tñ nichil ſimul aſcendet, et deſcen-
                    <lb/>
                  det adequate diuiſiue capiendo ly. </s>
                  <s xml:id="N20DAF" xml:space="preserve">et ſicut ſtat  ſor­
                    <lb/>
                  tes īmediate poſt hoc erit albus, et immediate poſt
                    <lb/>
                  hoc erit niger: et tamen nõ ſimul erit albus et niger
                    <lb/>
                  </s>
                  <s xml:id="N20DB7" xml:space="preserve">Patet correlarium. </s>
                  <s xml:id="N20DBA" xml:space="preserve">¶ Ex his tribus notabilibus
                    <lb/>
                  patet facile reſponſio ad queſtionem.</s>
                </p>
                <p xml:id="N20DD5">
                  <s xml:id="N20DD6" xml:space="preserve">Ad rationes ante oppoſitū. </s>
                  <s xml:id="N20DD9" xml:space="preserve">Ad primã
                    <lb/>
                  reſponſum eſt ibi vſ ad replicam ad quam reſpo-
                    <lb/>
                  deo negando ſequelam, et ad probationem dico / 
                    <lb/>
                  illud correlarium ibi adductum ad probationem
                    <lb/>
                  illiꝰ ſequele nõ eſt ad propoſitū, q2 ſupponit ꝓpor­
                    <lb/>
                  tionē tēpoꝝ excedere proportionē velocitatū. </s>
                  <s xml:id="N20DE6" xml:space="preserve">Cuiꝰ
                    <lb/>
                  oppoſitū ī caſu argumēti eſt verū. </s>
                  <s xml:id="N20DEB" xml:space="preserve">Cõmēſurãda em̄
                    <lb/>
                  eſt vtra velocitas, et qua illud corpus mouet̄̄ cir-
                    <lb/>
                  culariter, et qua mouetur motu rarefactiõis pūcto
                    <lb/>
                  eiꝰ a quo debet ſumi velocitas totiꝰ motus cõtinuo
                    <lb/>
                  acquirente maiorē et maiorē diſtantiam a centro / vt
                    <lb/>
                  ptꝫ ex deductione eiuſdē replice.
                    <note position="right" xlink:href="note-0173-04a" xlink:label="note-0173-04" xml:id="N20E38" xml:space="preserve">1. correĺ</note>
                  </s>
                  <s xml:id="N20DFD" xml:space="preserve">¶ Ex quo ſequitur /
                    <lb/>
                   poſſibile eſt aliquod corpꝰ circulare cõtinuo vni-
                    <lb/>
                  formiter et eque velociter moueri: et tñ ipſū ↄ̨tinuo
                    <lb/>
                  rarefieri et effici maiꝰ. </s>
                  <s xml:id="N20E06" xml:space="preserve">Probat̄̄ ponēdo /  vna rota
                    <lb/>
                  incipiat moueri circulariter pūcto medio ſemidia-
                    <lb/>
                  metri incipiēte moueri velocitate vt .4. et volo /  ſiĺ
                    <lb/>
                  incipiat rarefieri illud corpus acquirendo in hora
                    <lb/>
                  pedalē diſtantiã adequate a centro ſupra diſtan-
                    <lb/>
                  tiã p̄habitã, eo tñ modo moueat̄̄ ille punctꝰ medius
                    <lb/>
                  ſemidiametri  nun̄ ꝑtranſeat ſiue deſcribat ma­
                    <lb/>
                  iorē lineã in aliquo tꝑe ꝙ̄ nata ſit deſcribi a veloci-
                    <lb/>
                  tate vt .4. in eodē tꝑe quo poſito ſequit̄̄ correlariū.
                    <lb/>
                    <note position="right" xlink:href="note-0173-05a" xlink:label="note-0173-05" xml:id="N20E3E" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N20E20" xml:space="preserve">¶ Sequit̄̄ ſecūdo /  ſi aliqua rota in hora moueat̄̄
                    <lb/>
                  circulariter puncto medio ſemidiametri continuo
                    <lb/>
                  motu circulari mouēte vniformiter, motu vero ra-
                    <lb/>
                  refactionis cõtinuo intendente motū ſuū in q̈libet
                    <lb/>
                  parte proportionali hore ꝓportione dupla ſequē-
                    <lb/>
                  te in duplo velociꝰ rarefiente ꝙ̄ in īmediate p̄cedēti
                    <lb/>
                  tūc ſpaciū deſcriptū a tali puncto eſt infinitū. </s>
                  <s xml:id="N20E2F" xml:space="preserve">Ptꝫ
                    <lb/>
                  hoc correlariū ex ſexta concluſione ꝑcedētꝪ capitis</s>
                </p>
                <p xml:id="N20E44">
                  <s xml:id="N20E45" xml:space="preserve">Ad ſecundã rationē reſponſum eſt ibi
                    <lb/>
                  vſ ad replicã: ad quã reſpõdeo negando ſequelã
                    <lb/>
                  et ad probationē nego  nullū ſit īpedimentū. </s>
                  <s xml:id="N20E4C" xml:space="preserve">īmo
                    <lb/>
                  cõtra motio nauis eſt ſorti īpedimento. </s>
                  <s xml:id="N20E51" xml:space="preserve">Fatigat̄̄ tñ
                    <lb/>
                  ſortes nõ ꝑ motū quo deſcribat aliquod ſpacium
                    <lb/>
                  fixū: ſed q2 deſcribit aliquod ſpaciū nõ fixū ad cuiꝰ
                    <lb/>
                  deſcriptionē nõ ſequit̄̄ ſortē proprie moueri. </s>
                  <s xml:id="N20E5A" xml:space="preserve">Ma-
                    <lb/>
                  net enim ſortes in eodem loco fixo.</s>
                </p>
                <p xml:id="N20E5F">
                  <s xml:id="N20E60" xml:space="preserve">Ad ṫciã rationē rñdeo negãdo añs: et
                    <lb/>
                  ad ꝓbationē ↄ̨cedo maiorē, et nego mīorē et ad ꝓba­
                    <lb/>
                  nē diſtinguo ſeq̄lã aut ſi tale corpꝰ ſit taliter diſpo­
                    <lb/>
                  ſitū  partes eiꝰ proportionales ꝓportiõe dupla
                    <lb/>
                  ita ſe habeant  ſcḋm eã dimenſionē ſcḋm quã de-
                    <lb/>
                  ſcendūt cõtinuo ſe habet in ꝓportione dupla oībꝰ
                    <lb/>
                  aliis iuuamentis et īpedimētis deductis: et ſic cõce-
                    <lb/>
                  do ſequelã. </s>
                  <s xml:id="N20E71" xml:space="preserve">Si vero partes eiꝰ proportionales pro­
                    <lb/>
                  portione dupla ſe habuerīt in maiori proportione
                    <lb/>
                  quã ſit ꝓportio dupla et hoc quantū ad dimēſionē
                    <lb/>
                  ſcḋm quã deſcendūt, et ſic nõ oportet. </s>
                  <s xml:id="N20E7A" xml:space="preserve">Nego igitur
                    <lb/>
                  illo modo ſeq̄lã. </s>
                  <s xml:id="N20E7F" xml:space="preserve">¶ Ex q̊ ſequit̄̄ /  ita põt aliqḋ cor- </s>
                </p>
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