Alvarus, Thomas, Liber de triplici motu, 1509

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                    <pb chead="Primi tractatus" file="0070" n="70"/>
                  ꝑtranſit illã in ſubſexquitertio tēpore vel minori.
                    <lb/>
                  </s>
                  <s xml:id="N16DD6" xml:space="preserve">Cõſequentia eſt nota et minor ꝓbatur: q2 ſi tran-
                    <lb/>
                  ſeundo ſecundã moueretur a ſubtripla ꝓportiõe
                    <lb/>
                  et ſecūda eſſet equalis prime extēſiue / tūc in triplo
                    <lb/>
                  tēpore ꝑtranſiret illã ad tēpus in quo pertranſit
                    <lb/>
                  primã puta in tribus horis qm̄ ꝑtranſit primã in
                    <lb/>
                  hora / vt poſitū eſt: ſed modo illa ſecunda pars eſt
                    <lb/>
                  ſubquadrupla ad primaꝫ / ergo in ſubquadruplo
                    <lb/>
                  tēpore ꝑtranſibit eam: ſed ſubquadruplū ad tres
                    <lb/>
                  horas ſunt .3. quarte: et tres quarte ſūt ſubſexqui­
                    <lb/>
                  tertiū ad vnã horã in qua ꝑtranſit primã partem /
                    <lb/>
                  igitur ſecundã trãſit in ſubſexquitertio tēpore ad
                    <lb/>
                  primã. </s>
                  <s xml:id="N16DEF" xml:space="preserve">Et ſic ꝓbabis /  tertiã in ſubſexquitertio
                    <lb/>
                  tēpore ꝑtranſit ad ſecundã: et de oībus aliis con-
                    <lb/>
                  ſequenter. </s>
                  <s xml:id="N16DF6" xml:space="preserve">adiutorio ſecūdi correlarii quarte con­
                    <lb/>
                  cluſionis quarti capitis ſecunde partis.</s>
                </p>
                <p xml:id="N16DFB">
                  <s xml:id="N16DFC" xml:space="preserve">Reſpondeo ad replicã cõcedendo an­
                    <lb/>
                  tecedens: dūmodo ille partes ꝓportiõales illius
                    <lb/>
                  reſiſtentie nõ ſe habeant in ꝓportione dupla nec
                    <lb/>
                  in aliqua minori: et nego cõſequentiã. </s>
                  <s xml:id="N16E05" xml:space="preserve">Et ratio eſt /
                    <lb/>
                  q2 talis reſiſtentia de qua cõceditur nõ eſt vnifor-
                    <lb/>
                  miter difformis: nec talis potētia requirit tantū
                    <lb/>
                  tēpus ad ꝑtranſeundū ſecundã partē ꝓportiõa-
                    <lb/>
                  lem quantū ad ꝑtrãſeundū primã: vt iam ꝓbatuꝫ
                    <lb/>
                  eſt.
                    <note position="left" xlink:href="note-0070-01a" xlink:label="note-0070-01" xml:id="N16F71" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N16E17" xml:space="preserve">¶ Ex deductione et ſolutione huiꝰ argumenti
                    <lb/>
                  ſequitur primo:  ſi potentia vt quatuor cõtinuo
                    <lb/>
                  moueretur per mediū vniformiter difforme a non
                    <lb/>
                  gradu reſiſtentie vſ ad quartū: et perpetuo du-
                    <lb/>
                  raret potentia et mediū taliter diſpoſitū: ꝑpetuo
                    <lb/>
                  ipſa moueretur: et nun̄ ipſuꝫ ꝑtranſiret. </s>
                  <s xml:id="N16E24" xml:space="preserve">Patet
                    <lb/>
                  hoc correlariū ex deductiõe et ſolutiõe argumenti
                    <lb/>
                    <note position="left" xlink:href="note-0070-02a" xlink:label="note-0070-02" xml:id="N16F77" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N16E30" xml:space="preserve">¶ Sequitur ſecūdo:  reſiſtentia vniformiter dif-
                    <lb/>
                  formis nõ correſpõdet gradui medio reſiſtentie:
                    <lb/>
                  ita  tantū reſiſtat ſicut gradus medius. </s>
                  <s xml:id="N16E37" xml:space="preserve">Proba­
                    <lb/>
                  tur hoc ex p̄cedenti correlario / q2 alias ſequeretur
                    <lb/>
                   potentia vt .4. poſſet in tēpore finito ꝑtranſire
                    <lb/>
                  reſiſtentiã vniformiter difformē a nõ gradu vel a
                    <lb/>
                  gradu certo minori vſ ad quartū / q2 moueretur
                    <lb/>
                  in ea a ꝓportiõe dupla vel aliqua alia certa eq̇ua­
                    <lb/>
                  lenter per totã illã reſiſtentiam. </s>
                  <s xml:id="N16E46" xml:space="preserve">¶ Sed q2 aliquis
                    <lb/>
                  poſſet dicere /  correſpõdet gradui medio: dūmo­
                    <lb/>
                  do g̈dus ſūmꝰ talis teſiſtētie nõ ſit eq̈lis potentie
                    <lb/>
                  mouēti in ea vel minor.
                    <note position="left" xlink:href="note-0070-03a" xlink:label="note-0070-03" xml:id="N16F7D" xml:space="preserve">Gaytha-
                      <lb/>
                    uus de
                      <lb/>
                    thebis.</note>
                  </s>
                  <s xml:id="N16E54" xml:space="preserve">Ideo aliter ꝓbo p̄dictum
                    <lb/>
                  correlariū ratiõe Gaythani de thebis ſi memini:
                    <lb/>
                  q2 ſi correſpõderet gradui medio ſeq̄ret̄̄ /  poten­
                    <lb/>
                  tia vt .9. in equali tēpore adequate ꝑtranſiret re-
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                  ſiſtentiã vniformiter difformē a nõ gradu vſ ad
                    <lb/>
                  octauū: in quo adequate ꝑtranſiret ſcḋaꝫ medie-
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                  tatē eiꝰ: ita  ita cito ꝑtranſiret totū ſicut eiꝰ me-
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                  dietatē adequate: ſed ↄ̨ñs eſt manifeſte falſū: igit̄̄
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                  illud ex quo ſequit̄̄. </s>
                  <s xml:id="N16E67" xml:space="preserve">Sequela ꝓbatur / q2 talis po-
                    <lb/>
                  tentia vt .9. haberet ad totã illã reſiſtentiã ꝓpor-
                    <lb/>
                  tionē duplã ſexquiquartã: cū tota illa reſiſtentia
                    <lb/>
                  ſit per te vt .4. qui eſt gradus mediꝰ. </s>
                  <s xml:id="N16E70" xml:space="preserve">Modo .9. ad
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                  4. eſt ꝓportio dupla ſexquiquarta: et ad ſecundaꝫ
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                  medietatē haberet ꝓportionē ſexquialterã: cum
                    <lb/>
                  gradus eiꝰ medius ſit vt .6. </s>
                  <s xml:id="N16E79" xml:space="preserve">Modo .9. ad .6. eſt ꝓ-
                    <lb/>
                  portio ſexquialtera: ſed ꝓportio ſexquialtera eſt
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                  ſubdupla ad duplã ſexquiquartã / vt patꝫ ex ſexto
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                  capite ſcḋe partis et ſpaciū trãſeundū ab illa pro­
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                  portiõe puta ſcḋa medietas eſt ſubduplū ad totã
                    <lb/>
                  illã reſiſtentiã: ergo ſequit̄̄ /  ī equali tēpore ꝑtrã­
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                  ſit illã ſcḋam medietatē et totã illã reſiſtentiã: qḋ
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                  fuit ꝓbandū.
                    <note position="left" xlink:href="note-0070-04a" xlink:label="note-0070-04" xml:id="N16F87" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N16E8F" xml:space="preserve">¶ Sequit̄̄ tertio /  quãuis potentia
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                  vt .4. nõ ſufficit ꝑtrãſire reſiſtentiam vniformiter
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                  difformē a ſcḋo g̈du vſ ad quartū: cuiꝰ videlicet
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                  prima pars ꝓportiõalis ꝓportiõe dupla incipit
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                  a ſcḋo vſ ad tertiū et ſcḋa īcipit a tertio vſ ad
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                  tertiū cū dimidio / et ſic cõſequēter: nichilominꝰ tñ
                    <cb chead="Capitulū ſextū."/>
                  talis potētia vt .4. ſufficit ꝑtrãſire tantã reſiſten-
                    <lb/>
                  tiã extenſiue: cuiꝰ videlicet prima pars ꝓportiõa-
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                  lis ꝓportione quadrupla eſt oīno cõſimilis reſi-
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                  ſtētie cū prima parte ꝓportiõali ꝓportiõe dupla
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                  alterius reſiſtentie vniformiter difformis, et ſcḋa
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                  cū ſecūda, et tertia cū tertia, et ſic cõſequēter. </s>
                  <s xml:id="N16EA9" xml:space="preserve">Pri­
                    <lb/>
                  ma pars ptꝫ ex deductione et ſolutione argumēti
                    <lb/>
                  et ſecūda ex deductione et ſolutione replice.
                    <note position="right" xlink:href="note-0070-05a" xlink:label="note-0070-05" xml:id="N16F8D" xml:space="preserve">4. correĺ.</note>
                  </s>
                  <s xml:id="N16EB5" xml:space="preserve">¶ Se-
                    <lb/>
                  quitur quarto /  quãuis potētia vt .4. nõ ſufficit
                    <lb/>
                  ꝑtranſire in aliquo tēpore finito reſiſtentiã peda­
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                  lem vniformiter difformē terminatã ad quartū:
                    <lb/>
                  cuiꝰ videlicet prima pars ꝓportiõalis ꝓportione
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                  dupla incipiat a ſcḋo et terminet̄̄ ad tertiū .etc̈. vt
                    <lb/>
                  poſitū eſt in priori ꝑte p̄cedētꝪ correlarii: nichilo­
                    <lb/>
                  minus vbi talis reſiſtētia pedalis efficeretur qua­
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                  drupedalis per rarefactionē aut augmentationē
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                  (nõ eſt cura) ita tamen  ille partes reſiſtētie que
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                  cõtinuo ſe habebant in ꝓportione dupla cõtinuo
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                  ſe habeant in ꝓportione quadrupla quo ad extē-
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                  ſionē: ipſis tamē manētibꝰ ſemꝑ in eodē ſtatu quo
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                  ad ītēſionē: potētia vt .4. ſufficit tūc illã reſiſtentiã
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                  in tꝑe finito ꝑtrãſire. </s>
                  <s xml:id="N16ED4" xml:space="preserve">Patet ṗma pars correlarii
                    <lb/>
                  ex ṗori correlaro et ſcḋa ex deductiõe replice.
                    <note position="right" xlink:href="note-0070-06a" xlink:label="note-0070-06" xml:id="N16F93" xml:space="preserve">5. correĺ.</note>
                  </s>
                  <s xml:id="N16EDE" xml:space="preserve">¶ Ex
                    <lb/>
                  q̊ correlario ſequitur facile quītū /  quãuis talis
                    <lb/>
                  reſiſtentia ſic ad quadruplū augeat̄̄ extenſiue: ni­
                    <lb/>
                  chilominus tamē infinite partes eiꝰ ꝓportiõales
                    <lb/>
                  diminuūtur, et efficiūtur minores extenſiue. </s>
                  <s xml:id="N16EE9" xml:space="preserve">Pri-
                    <lb/>
                  ma pars ponit̄̄ / et ſcḋa ꝓbatur / q2 ſi infinite mane­
                    <lb/>
                  rent tante quãte erant antea: cū maneãt eque in-
                    <lb/>
                  tenſe et eque reſiſtētes: eo modo reſiſterēt quo reſi­
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                  ſtebant antea quãdo cõtinuo ſe habebãt in ꝓpor­
                    <lb/>
                  tione dupla: ſed antea requirebat̄̄ tēpus infinitū
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                  ad ꝑtranſeundū illas a tali potentia: cū tantū tē­
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                  pus requirebat̄̄ ad ꝑtranſeundū aliquã partē vel
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                  maiꝰ quantū ad quãlibet p̄cedentē: vt ptꝫ ex dedu­
                    <lb/>
                  ctione argumēti: igitur modo etiã requireret̄̄ tē-
                    <lb/>
                  pus infinitū: ſed hoc eſt falſum / vt patꝫ ex p̄cedenti
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                  correlario / igitur illud ex quo ſequitur: et ꝑ conſe­
                    <lb/>
                  quēs dicendū eſt /  īfinite efficiūtur minores extē-
                    <lb/>
                  ſiue: cū nec etiã dicendū ſit /  efficiant̄̄ maiores vt
                    <lb/>
                  facile eſſet ꝓbare ꝑ locū a maiori. </s>
                  <s xml:id="N16F08" xml:space="preserve">Et hoc etiã faci­
                    <lb/>
                  le ptꝫ experimēto: nã capto tali pedali ſic diuiſo
                    <lb/>
                  ꝑ partes ꝓportiõales ꝓportiõe dupla vt poſituꝫ
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                  eſt: et augeatur prima pars ꝓportiõalis eius ad
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                  quadruplū: ita  efficiat̄̄ bipedalis: tūc ad hoc / 
                    <lb/>
                  ſecūda efficiatur ſubquadrupla ad ipſaꝫ oportet
                    <lb/>
                  ipſam ſimiliter augeri ad duplū: ita  efficiatur
                    <lb/>
                  ſemipedalis: et oportet tertiam manere nec auctã
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                  nec diminutã: q2 eſt vna octaua: ſed oportet iam
                    <lb/>
                  quartam minui ad ſubduplū: q2 erat vna decima
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                  ſexta et oportet  efficiatur vna triceſimaſecūda:
                    <lb/>
                  vt ſit ſubquadrupla ad octauã que eſt tertia pars /
                    <lb/>
                  et tunc manebit equalis cū quīta parte et ſic opor-
                    <lb/>
                  tebit quintã ad ſubquadruplum minui: et ſextam
                    <lb/>
                  ad ſuboctuplum: et ſic in infinitū / vt patet intuenti
                    <lb/>
                  igitur.
                    <note position="right" xlink:href="note-0070-07a" xlink:label="note-0070-07" xml:id="N16F99" xml:space="preserve">Calcu. in
                      <lb/>
                    capite de
                      <lb/>
                    augmen.</note>
                  </s>
                  <s xml:id="N16F2E" xml:space="preserve">Et ferme hoc modo intendit calculator ꝓ-
                    <lb/>
                  bare in capitulo de augmentatione concluſione
                    <lb/>
                  quindecima probatione ſecunda:  quantūcun
                    <lb/>
                  modicum ſit aliquod ſubiectum diuiſum per par­
                    <lb/>
                  tes proportionales certa proportione: et ſit aliud
                    <lb/>
                  quantūcun magnum diuiſum in partes propor­
                    <lb/>
                  tionales proportione maiori: aliqua erit pars
                    <lb/>
                  proportionalis minoris, maior parte proporti-
                    <lb/>
                  onali correſpondente maioris.
                    <note position="right" xlink:href="note-0070-08a" xlink:label="note-0070-08" xml:id="N16FA3" xml:space="preserve">6. correĺ</note>
                  </s>
                  <s xml:id="N16F46" xml:space="preserve">¶ Sequitur ſexto /
                    <lb/>
                   quãuis talis reſiſtentia aucta in quantitate ad
                    <lb/>
                  quadruplum vel octuplum quocun modo pla-
                    <lb/>
                  cuerit: dummodo partes reſiſtentie que antea ſe
                    <lb/>
                  habebant in proportione dupla quo ad extenſio­
                    <lb/>
                  nem ſe habeãt quo ad extenſionē in proportione </s>
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