Alvarus, Thomas, Liber de triplici motu, 1509
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                <p xml:id="N1F1A4">
                  <s xml:id="N1F1B8" xml:space="preserve">
                    <pb chead="Secundi tractatus" file="0155" n="155"/>
                  tiõe mouet ſortes ſiue ꝓueniat illa velocitas b. et ꝓ­
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                  ponitur ſiue ſignatur proportio ſexquialtera: tunc
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                  arithmeticis principiis īueſtigare poſſumus an ꝓ­
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                  portio ſortis ad a. a qua prouenit velocitas b. ſit ꝓ­
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                  portioni ſexquialtere ꝓpoſite et ſignate cõmenſura­
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                  bilis nec ne. </s>
                  <s xml:id="N1F1CA" xml:space="preserve">Quo inueſtigatur iſto modo: capio
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                  vnum lapidem qui ſit c. ſubſexquialterum ad a. la-
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                  pidem: et moueat ſortes in eodem tempore vel equa­
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                  li ab eadem virtute a. et c. / tunc arguitur ſic / vel ſpaci­
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                  um per quod ſortes in illo tempore mouet c. eſt com­
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                  menſurabile ſpacio per quod mouet a. in eodem tē­
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                  pore, vel nõ. </s>
                  <s xml:id="N1F1D9" xml:space="preserve">Si nõ iã illa ſpacia ſe habebunt in ali­
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                  qua ꝓportione irrationali et ſic proportio ſexqui-
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                  altera erit irrationalis ꝓportioni a qua prouenit
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                  velocitas b. que eſt ſortis ad a. </s>
                  <s xml:id="N1F1E2" xml:space="preserve">Quod probatur ſic /
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                  quia ſi illa ſpacia ſint incõmenſnrabilia / conſeq̄ns
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                  eſt /  proportiones a quibus proueniunt ſint incõ-
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                  menſurabiles. </s>
                  <s xml:id="N1F1EB" xml:space="preserve">ſed proportiones a quibus proueni­
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                  unt ſunt ſortis ad a. et ſortis ad c. / igitur proportio
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                  ſortis ad c. eſt incõmenſurabilis ꝓportioni ſortis
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                  ad a. minori proportione ſortis ad c. / igitur exceſſus
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                  qua proportio ſortis ad c. excedit ꝓportionem ſor­
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                  tis ad a. eſt incõmenſurabilis proportiõi ſortis ad
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                  a. </s>
                  <s xml:id="N1F1FA" xml:space="preserve">Probatur hec conſequentia per hanc maximaꝫ.
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                  </s>
                  <s xml:id="N1F1FE" xml:space="preserve">Quandocun duo ſunt incõmenſurabilia exceſſus
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                  quo maius illorum excedit minus eſt etiam incõmē­
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                  ſurabilis minori / vt ꝓbatuꝫ eſt in prima parte hu­
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                  ius operis de exceſſu diametri ad coſtam quarto ca­
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                  pite ſuppoſitione quarta: ſaltem ex modo proban­
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                  di illius ſuppoſitiõis patet. </s>
                  <s xml:id="N1F20B" xml:space="preserve">Sed proportio ſortis
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                  ad c. eſt incõmenſurabilis proportioni ſortis ad a.
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                  et excedit proportionem ſortis ad a. per proportio­
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                  nem a. ad c. ſexquialteram: ergo ꝑ datam maximaꝫ
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                  proportio ſexquialtera eſt incõmenſurabilis ꝓpor­
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                  tioni ſortes ad a. a qua prouenit velocitas b. / quod
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                  fuit vnum inducenduꝫ. </s>
                  <s xml:id="N1F21A" xml:space="preserve">Si vero ſpacia illa videlicet
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                  ꝑ que ſortes mouet c. et mouet a. ſint commenſurabi­
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                  lia: ſequitur /  propoitio ſexquialtera ꝓpoſita eſt
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                  cõmenſurabilis proportioni ſortis ad a. a qua pro­
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                  uenit b. velocitas </s>
                  <s xml:id="N1F225" xml:space="preserve">Qḋ ſic probatur / quia ſi illa ſpa-
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                  cia ſunt cõmenſurabilia ſint illa cõmenſurabilia.</s>
                </p>
                <p xml:id="N1F22A">
                  <s xml:id="N1F22B" xml:space="preserve">argumenti gratia proportione dupla. / et ſequitur /
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                   proportio ſortis ad c. eſt dupla ad proportioneꝫ
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                  ſortis ad a. </s>
                  <s xml:id="N1F232" xml:space="preserve">Cõſequentia ſepius arguta eſt: ergo ſe­
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                  quitur /  illa ꝓportio ſortis ad a. eſt medietas eius /
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                  et per conſequens totum reſiduum / quod eſt propor­
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                  tio a. ad c. eſt alia medietas: ſed totum reſiduum eſt
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                  proportio ſexquialtera. / ergo proportio ſexquialte­
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                  ra eſt medietas illius ꝓportionis ſortis ad c. et alia
                    <lb/>
                  medietas eſt proportio ſortis ad a. a qua prouenit
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                  velocitas b. / ergo ſequitur /  illa ꝓportio ſortis ad
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                  a. a qua prouenit velocitas b. eſt equalis proportio­
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                  ni ſexquialtere: et ſic probabis ꝑticulariter in omni­
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                  bus: </s>
                  <s xml:id="N1F249" xml:space="preserve">Sed vniuerſaliter probabitur ſic / proportio
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                  ſortis ad c. eſt cõmenſurabilis ꝓportioni ſortis ad
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                  a. a qua prouenit velocitas b. et proportio ſortis ad
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                  c. excedit proportionem ſortis ad a. etc̈. per propor­
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                  tionem a. ad c. ſexquialteram adequate: igitur pro­
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                  portio illa a. ad c. ſexquialtera eſt cõmenſurabilis
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                  ꝓportioni ſortis ad a. / quod fuit inducendum. </s>
                  <s xml:id="N1F258" xml:space="preserve">Con­
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                  ſequentia patet ꝑ hanc maximam </s>
                  <s xml:id="N1F25D" xml:space="preserve">Quotienſcun
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                  duo inequalia ſunt cõmenſurabilia exceſſus maio-
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                  ris ſupra minus eſt ipſi minori cõmenſurabilis: qm̄
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                  eſt pars aliquota vel ꝑtes aliquote vtriuſ / vt pa-
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                  tet ex ſexta ſuppoſitione q̈rti capitis ſecunde par-
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                  tis. </s>
                  <s xml:id="N1F26A" xml:space="preserve">Sed in ꝓpoſito ꝓportio illa ſexquialtera a. ad
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                  c. eſt exceſſus quo proportio ſortis ad c. excedit pro­
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                  portionem ſortis ad a. a qua prouenit b. velocitas:
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                  ergo proportio ſexquialtera cõmenſurabilis eſt pro­
                    <cb chead="Capitulum tertium"/>
                  portioni ſortis ad a. a qua prouenit velocitas b. / qḋ
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                  fuit inducendum.
                    <note position="right" xlink:href="note-0155-01a" xlink:label="note-0155-01" xml:id="N1F29A" xml:space="preserve">Nicolaꝰ
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                    horem.</note>
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                  <s xml:id="N1F27D" xml:space="preserve">¶ Et hee quatuor cõcluſiones (ne
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                  alienis ſpoliis triumphare videamur) ex officina et
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                  ꝑſpicaci minerua doctiſſimi magiſtri Nicolai ho-
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                  horen deprompte ſunt et excerpte quas in ſuo trac-
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                  tatu proportionum quarto capite ſuis fulcimētis
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                  et probationibus mathematicis reperies munitas
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                  </s>
                  <s xml:id="N1F28B" xml:space="preserve">¶ Exactis notabilibus et ex conſequenti parte huiꝰ
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                  corporis noſtre queſtionis abſoluta ad ſecundaꝫ ꝑ­
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                  tem accedendum eſt in qua multe et egregie conclu-
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                  ſiones (quibus medieantibus queſtio diſſoluetur) ꝓ­
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                  babūtur: at inducentur</s>
                </p>
                <p xml:id="N1F2A2">
                  <s xml:id="N1F2A3" xml:space="preserve">Prima concluſio </s>
                  <s xml:id="N1F2A6" xml:space="preserve">Diuiſo aliquo cor-
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                  pore ſiue latitudine ꝑ partes ꝓportionales quauis
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                  libuerit ꝓportione: totum illud corpus ſiue latitu-
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                  do ſe habet ad reſiduum a prima ꝑte proportionali
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                  in ea proportione q̈ ipſum ſiue latitudo ipſa diui-
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                  ditur. </s>
                  <s xml:id="N1F2B3" xml:space="preserve">Hec eſt prima et fundamentalis concluſio cui
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                  innuitur quintum caput prime partis huius ope-
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                  ris vide eam ibi.</s>
                </p>
                <p xml:id="N1F2BA">
                  <s xml:id="N1F2BB" xml:space="preserve">Secunda concluſio </s>
                  <s xml:id="N1F2BE" xml:space="preserve">Diuiſo aliquo tē­
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                  pore per partes ꝓportionales quauis ꝓportione:
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                  et ſit aliquod mobile quod aliquãta velocitate mo-
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                  ueatur in prima parte ꝓportionali et in ſecunda in
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                  duplo maiori ꝙ̄ in prima: et in tertia in triplo ma-
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                  iori ꝙ̄ in prima: et in quarta in quadruplo maiori /
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                  et ſic conſequenter aſcendendo per omnes ſpecies
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                  proportionis multiplicis: talis velocitas totius il­
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                  lius temporis et omnium illarum partium propor­
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                  tionalium ſe habet ad velocitatem prime partis ꝓ­
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                  portionalis in ea proportione in qua ſe habet to-
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                  tum illud tempus ſic diuiſuꝫ in ordine ad primam
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                  partem proportionalem. </s>
                  <s xml:id="N1F2D9" xml:space="preserve">vt ſi illud tp̄s diuiſim fue­
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                  rit in partes proportionales ꝓportione ſexquial-
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                  tera: et velocitates illarum partium proportiona-
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                  lium diſponantur modo quo ponit concluſio: tunc
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                  dico /  totalis illa velocitas totius illius temporis
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                  adequate ſe habet ad velocitatem prime partis ꝓ-
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                  portionalis in proportione tripla. </s>
                  <s xml:id="N1F2E8" xml:space="preserve">ex eo  totū tē-
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                  pus diuiſuꝫ ꝑ partes proportionales proportione
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                  ſexquialtera ſe habet ad primam proportionalem
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                  in proportiõe tripla. </s>
                  <s xml:id="N1F2F1" xml:space="preserve">Eſt enim ṗma pars vna tertia
                    <lb/>
                  totius / vt oſtendit quarta cõcluſio quinti capituli p̄­
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                  me partis huius operis. </s>
                  <s xml:id="N1F2F8" xml:space="preserve">Probatur tamen vniuer­
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                  ſaltter hec cõcluſio. </s>
                  <s xml:id="N1F2FD" xml:space="preserve">et ſuppono /  quando velocita-
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                  tes ſe habent eo mõ q̊ textꝰ cõcluſionis pretēdit tūc
                    <lb/>
                  ꝑ totū tp̄s extendit̄̄ illa velocitas / q̄ extendit̄̄ ꝑ ṗmã
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                  partem proportionalem, et ꝑ totum reſiduū a prīa
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                  extenditur tanta adequate nõ cõicans cum prima ꝑ
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                  totum corpus extenſa, et per totum reſiduum a pri-
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                  ma et ſecunda ꝑte proportionali iterum extenditur
                    <lb/>
                  tanta velocitas adequate nõ cõmunicans cum aliq̈
                    <lb/>
                  precedeutinm: et ſic cõſequenter. </s>
                  <s xml:id="N1F310" xml:space="preserve">Hec ſuppoſitio pa­
                    <lb/>
                  tet manifeſte intuenti: qm̄ ſi velocitas ſecunde par-
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                  tis ꝓportiõalis ē dupla ad velocitatē prīe et tertie
                    <lb/>
                  tripla etc. ſcḋa ipſa ↄ̨tinet bis tã intenſã velocitatē
                    <lb/>
                  ſicut ē prīa nõ cõmunicãtē: et tertia pars cõtinet ter
                    <lb/>
                  tantam: et ſic cõſequenter. </s>
                  <s xml:id="N1F31D" xml:space="preserve">et per conſequens reſidu­
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                  um a prima continet vniformiter bis tantam velo­
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                  citatem ſicut eſt prima (quãuis nõ adequate. </s>
                  <s xml:id="N1F324" xml:space="preserve">Conti­
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                  net enim adhuc maiorem) et reſiduum a ſecunda ꝑ-
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                  te proportionaliter tantaꝫ per totum quamuis in­
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                  adequate: et ſic conſequenter ſemper ille partes ex-
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                  cedunt ſe continuo per equalem velocitatem veloci­
                    <lb/>
                  tati prime partis ꝓportionalis. </s>
                  <s xml:id="N1F331" xml:space="preserve">Hoc ſuppoſito</s>
                </p>
                <p xml:id="N1F334">
                  <s xml:id="N1F335" xml:space="preserve">Probatur cõcluſio et volo /  hora ſit diuiſa ꝑ par-
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                  tes ꝓportionales aliq̈ proportione (quauis libue-
                    <lb/>
                  rit) que ſit g. et coextēdantur ille velocitates / vt dicit </s>
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