Alvarus, Thomas, Liber de triplici motu, 1509

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                  <s xml:id="N20B6A" xml:space="preserve">
                    <pb chead="De motu locali mixto  difformi tꝑe  ſubiecto quo ad effectū" file="0172" n="172"/>
                  Patet ↄ̨ña cū minore et ꝓbatur maior: q2 tota ꝑs
                    <lb/>
                  citra centrum mundi continet b. partem equalem
                    <lb/>
                  parti citra centrū mūdi ex hypotheſi: et inſuꝑ cõti-
                    <lb/>
                  net d. et c. / igr̄ ꝑ d. et c. pars citra centrū mūdi exce-
                    <lb/>
                  dit partē vltra centrū mundi / qḋ fuit ꝓbandū. </s>
                  <s xml:id="N20B79" xml:space="preserve">Ptꝫ
                    <lb/>
                  ↄ̨ña intelligenti / quid ſit vnū excedere alterum per
                    <lb/>
                  aliquid: et ſic patet ſuppoſitio .</s>
                </p>
                <p xml:id="N20B80">
                  <s xml:id="N20B81" xml:space="preserve">Scḋa ſuppoſitio. </s>
                  <s xml:id="N20B84" xml:space="preserve">Qñ inter aliquos
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                  terminos eſt ꝓportio maioris īequalitatis et ma-
                    <lb/>
                  iore quartã exceſſus quo minorē excedit deꝑdente
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                  adequate: minore eandē dūtaxat quartã acq̇ren-
                    <lb/>
                  te que a minori deperdit̄̄: ꝓportio inter datos ter-
                    <lb/>
                  minos pluſ̄ ad ſubduplum ſui diminuit̄̄ et ex ↄ̨ñti
                    <lb/>
                  data ꝓportio vltra ſuã medietatē deꝑdit. </s>
                  <s xml:id="N20B93" xml:space="preserve">Probat̄̄
                    <lb/>
                  ſit ꝓportio f. īter a. terminū maiorem et e. terminū
                    <lb/>
                  minorē: diuidat̄̄ exceſſus quo a. excedit e: in q̈tuor
                    <lb/>
                  partes equales adequate hoc eſt in quatuor q̈rtas
                    <lb/>
                  et ſignētur ibi īter a. et e. ãnumeratis extremis q̇n
                    <lb/>
                  termini cõtinuo arithmetice ꝓportionabiles quoꝝ
                    <lb/>
                  primꝰ ſit a. ſecūdus b. qui excedit̄̄ ab a. ꝑ vnã quar-
                    <lb/>
                  tã illiꝰ exceſſus quo a. excedit e. adequate, et tertius
                    <lb/>
                  ſit c. qui excedat̄̄ a b. ꝑ aliã quartã illius exceſſus, et
                    <lb/>
                  quartꝰ ſit d. que excedat̄̄ a c. ꝑ vnã aliã quartã ex-
                    <lb/>
                  ceſſus, et quītus ſit e. terminꝰ minor ꝓportiõis date
                    <lb/>
                  qui excedit̄̄ ab ipſo d. ꝑ vltimam quartã exceſſus: et
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                  manifeſtū eſt illos quī termīos cõtinuo eſſe arith­
                    <lb/>
                  metice ꝓportionabiles cū equali exceſſu exupe­
                    <lb/>
                  rent. </s>
                  <s xml:id="N20BB2" xml:space="preserve">deꝑdat igr̄ a. terminꝰ maior vnã quartã exceſ-
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                  ſus illã vcꝫ ꝑ quã b. terminū excedit: et illã adequate
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                  acq̇rat e. terminꝰ minor. </s>
                  <s xml:id="N20BB9" xml:space="preserve">Tūc dico /  data ꝓportio
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                  diminuit̄̄ et plus quã ſuã medietatē deꝑdit et ex hoc
                    <lb/>
                  plus quã ad ſubduplū diminuit̄̄. </s>
                  <s xml:id="N20BC0" xml:space="preserve">Quod ſic oſtendi­
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                  tur / q2 ꝓportio f. diminuit̄̄ et plus quã ſui medieta-
                    <lb/>
                  tem deꝑdit ꝓpoſitū. </s>
                  <s xml:id="N20BC7" xml:space="preserve">Maior ptꝫ manifeſte ex ſe­
                    <lb/>
                  cūdo correlario tertie concluſionis octaui capitis
                    <lb/>
                  ſecūde partis auxiliãte hypotheſi: et minor ꝓbatur /
                    <lb/>
                  q2 illa ꝓportio f. q̄ eſt inter a. et e. cõponit̄̄ adequate
                    <lb/>
                  ex quatuor proportionibꝰ puta ex ꝓportiõe d. ad e.
                    <lb/>
                  et ex ꝓportiõe c. ad d. et ex ꝓportiõe b. ad c. et ex q̈rta
                    <lb/>
                  ꝓportione ipſiꝰ a. ad b. / vt cõſtat cõſideranti hypo-
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                  theſim: et ille ꝓportiones ſunt cõtinuo minores et
                    <lb/>
                  minores et minori exceſſu continuo ſeſe excedunt:
                    <lb/>
                  igitur aggregatum ex duabus extremis proporti-
                    <lb/>
                  onibus puta ex ꝓportione d. ad e. et ex ꝓportione a.
                    <lb/>
                  ad b. eſt maiꝰ quã medietas aggregati ex illis qua­
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                  tuor ꝓportionibꝰ: et ꝑ ↄ̨ñs eſt maius quã medietas
                    <lb/>
                  ipſiꝰ f. ꝓportionis adequate ex illis quatuor ꝓpor­
                    <lb/>
                  tionibꝰ cõpoſite. </s>
                  <s xml:id="N20BE6" xml:space="preserve">Ptꝫ hec ↄ̨ña ex quarto correlario
                    <lb/>
                  ſecūde cõcluſionis ſecūdi capitis ſecunde partis: et
                    <lb/>
                  aggregatū ex illis extremis ꝓportiõibꝰ ꝑdit ꝓpor­
                    <lb/>
                  tio f. / vt ptꝫ ex hypotheſi auxiliãte primo correlario
                    <lb/>
                  ſexte concluſiõis octaui capitis ſecūde partis. </s>
                  <s xml:id="N20BF1" xml:space="preserve">(Ter-
                    <lb/>
                  minꝰ em̄ maior puta a. cū deꝑdit exceſſum quo exce­
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                  dit b. deꝑdit ꝓportionē q̄ eſt ipſiꝰ a. ad b. et terminꝰ
                    <lb/>
                  minor puta e. cū acq̇rit illū exceſſum quo excedit̄̄ a
                    <lb/>
                  d. acq̇rit illã ꝓportionē adequate q̄ eſt ipſiꝰ d. ad e.) /
                    <lb/>
                  igr̄ ꝓportio f. plus quã ſui medietatē deꝑdit / qḋ fuit
                    <lb/>
                  ꝓbandū. </s>
                  <s xml:id="N20C00" xml:space="preserve">Prima pars mīoris vcꝫ  ille ꝓportiões
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                  ſunt cõtinuo minores et mīoris ꝓbat̄̄ / q2 qñ īter ali-
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                  quos termīos eſt aliqua ꝓportio maioris inequa-
                    <lb/>
                  litatis: et maiores equali exceſſu excedūt ſuos mīo-
                    <lb/>
                  res ſemꝑ inter maiores eſt minor ꝓportio quã inter
                    <lb/>
                  mīores / vt ptꝫ ex octaua ſuppoſitiõe quarti capitis
                    <lb/>
                  ſecūde partis: ſed oēs illi termini .a. b.c.d. excedūt
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                  ſuos minores eq̈li exceſſu et d. et e. ſunt minores quã
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                  d. et c. et d. et c. mīores quã c. et b. et c. et b. minores quã
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                  b. et a. / igr̄ ꝓportio ipſiꝰ d. ad e. eſt maior ꝓportiõe
                    <lb/>
                  c. ad d. et ꝓportio c. ad d. maior eſt ꝓportionē b. ad
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                  c. et ꝓportio b. ad c. maior ꝓportiõe a. ad b. et ſic ille
                    <cb chead="De motu locali mixto  difformi tꝑe  ſubiecto quo ad effectū"/>
                  ꝓportiones ſunt ↄ̨tinuo minores et mīores / qḋ fuit
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                  ꝓbandū. </s>
                  <s xml:id="N20C1E" xml:space="preserve">Sed iã ꝓbo aliã partē minoris vcꝫ  cõti­
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                  nuo minori exceſſu ſe excedant: q2 ꝓportio ipſiꝰ d.
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                  ad e. ꝑ maiorē ꝓportionē excedit ꝓportionē ipſiꝰ c.
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                  ad d. quã ꝓportio ipſius c. ad d. excedit ꝓportionē
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                  ipſiꝰ b. ad c. et ꝓportio ipſiꝰ c. ad d. ꝑ maiorē ꝓpor-
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                  tionē excedit ꝓportionē b. ad. c. quã ꝓportio b. ad c.
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                  excedat ꝓportionē a. ad b. / igr̄ ille ꝓportiões conti-
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                  nuo minori exceſſu ſe excedūt. </s>
                  <s xml:id="N20C2F" xml:space="preserve">Maior ptꝫ ex quinto
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                  correlario quīte cõcluſionis octaui capitis ſecūde
                    <lb/>
                  partis qm̄ .b.c.d.e. ſunt quatuor termini continuo
                    <lb/>
                  arithmetice ꝓportionabiles ex hypotheſi: igr̄ pro­
                    <lb/>
                  portio q̄ eſt inter duos termīos mīores puta inter
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                  d. et e. ꝑ plus excedit ſecūdã ꝓportionē q̄ eſt inter c.
                    <lb/>
                  et d. quã illa ſcḋa excedat tertia q̄ eſt ipſiꝰ b. ad c. / vt
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                  ptꝫ ex correlario allegato. </s>
                  <s xml:id="N20C40" xml:space="preserve">Et ſic ꝓbabis minorem
                    <lb/>
                  capiendo iſtos quatuor terminos cõtinuo arithme­
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                  tice ꝓportionabiles puta .a. b.c.d. </s>
                  <s xml:id="N20C47" xml:space="preserve">Et ſic ptꝫ corre-
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                  larium. </s>
                  <s xml:id="N20C4C" xml:space="preserve">¶ Cõſimiliter ꝓbares /  diuiſo exceſſu quo
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                  maior terminꝰ excedit minorē in qñ partes eq̈les
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                  maiore termino deꝑdente vnã illaꝝ quītaꝝ minore
                    <lb/>
                  acq̇rente eandē  tūc ꝓportio inter datos termīos
                    <lb/>
                  perdit plus quã duas quītas ſui et ſi exceſſus diui-
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                  datur in ſex partes equales maiore deꝑdente vnã
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                  illaꝝ et minore acq̇rente eandē: ꝓportio īter datos
                    <lb/>
                  terminos perdit plus quam vnã tertiã: et ſi diuidat̄̄
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                  exceſſus in ſeptē maiore deꝑdente vnã illaꝝ et mīore
                    <lb/>
                  acq̇rente eandē: ꝓportio inter datos termīos ꝑdit
                    <lb/>
                  plus quã duas ſeptimas / et ſic ↄ̨ñter. </s>
                  <s xml:id="N20C63" xml:space="preserve">Oīa iſta patēt
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                  ex deductionibꝰ quīti correlarii prime cõcluſionis
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                  et quīti correlarii ſecūde cõcluſionis ſecūdi capitis
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                  ſecūde partis. </s>
                  <s xml:id="N20C6C" xml:space="preserve">¶ Ex his inducit̄̄ et demõſtratur ꝓpo­
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                  ſitū vcꝫ  illud quadratū terreū ꝑpetuo moueret̄̄
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                  in tali caſu. </s>
                  <s xml:id="N20C73" xml:space="preserve">Sit vna pars illiꝰ q̈drati vltra centruꝫ
                    <lb/>
                  mūdi minor medietate: et diuidat̄̄ pars intercepta
                    <lb/>
                  inter centrū illiꝰ quadrati et centrū mūdi q̄ eſt me-
                    <lb/>
                  dietas totiꝰ exceſſus partis citra centrū mundi ad
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                  partē vltra centrū mūdi ex prima ſuppoſitione et
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                  hoc ꝑ partes ꝓportionales ꝓportione dupla ma-
                    <lb/>
                  ioribꝰ ſus centrū mundi terminatis: q̄ pars ſit d.
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                  ſit totū illud quadratū vniforme in grauitate: ſit
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                  etiã ꝓportio totiꝰ partis citra centrū mūdi ad par­
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                  tē vltra centrū mūdi f. </s>
                  <s xml:id="N20C88" xml:space="preserve">Quo poſito ſic argr̄ q̈dratū
                    <lb/>
                  illud tamdiu mouebit̄̄ quãdiu aliqua pars ipſius
                    <lb/>
                  d. partis intercepte inter centrū q̈drati et centrum
                    <lb/>
                  mundi fuerit citra centrū mūdi qm̄ tamdiu excedet
                    <lb/>
                  pars citra centrū partē vltra centrū q2 tūc cõtinuo
                    <lb/>
                  erit maior: ſed ꝑpetuo aliqua pars ipſiꝰ d. partis
                    <lb/>
                  erit citra centrū mūdi: g̊ ꝑpetuo tale q̈dratū moue­
                    <lb/>
                  bitur / qḋ fuit ꝓbandū. </s>
                  <s xml:id="N20C99" xml:space="preserve">Cõſequētia ptꝫ cū maiore et
                    <lb/>
                  ꝓbat̄̄ minor / q2 ꝑpetuo aliqua pars aggregati ex
                    <lb/>
                  oībus partibꝰ ꝓportionalibꝰ ipſiꝰ d. partis deſcē­
                    <lb/>
                  det: g̊ ꝑpetuo aliqua pars ipſiꝰ d. partis erit citra
                    <lb/>
                  centrū mūdi / qḋ fuit ꝓbandū, </s>
                  <s xml:id="N20CA4" xml:space="preserve">Cõſequētia ptꝫ et pro­
                    <lb/>
                  batur añs / q2 prima pars ꝓportionalis ipſius d.
                    <lb/>
                  partis incipit deſcēdere a ꝓportiõe f. vt habet̄̄ hy-
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                  potheſi: et ſecūda pars ꝓportiõalis ipſiꝰ d. partis
                    <lb/>
                  incipit deſcēdere a ꝓportiõe ſubdupla ad ꝓportio­
                    <lb/>
                  nē f. vel a minori: et tertia īcipit deſcēdere a ſubdu-
                    <lb/>
                  pla vel minori ſubdupla ad ꝓportionē a q̈ incipit
                    <lb/>
                  deſcēdere ſcḋa / et ſic ↄ̨ñter q̄libet pars ꝓportiõalis
                    <lb/>
                  ipſiꝰ d. ſequēs īcipiet deſcēdere a ꝓportione ſubdu­
                    <lb/>
                  pla vel minori ad ꝓportionē a qua īcipit deſcēde-
                    <lb/>
                  re pars īmediate p̄cedēſupra: et q̄libet pars quãdiu ali-
                    <lb/>
                  q̇d eiꝰ deſcēdit cõtinuo deſcēdit ſiue mouet̄̄ a mīori
                    <lb/>
                  ꝓportione ꝙ̄ ſit illa a qua incipit illa eadem pars
                    <lb/>
                  deſcēdere (cū cõtinuo partis citra centrū mūdi ad
                    <lb/>
                  partē vltra centrū mūdi ꝓportio a qua partes ille
                    <lb/>
                  deſcendūt cõtinuo diminuatur: continuo em̄ pars </s>
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