Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
              <div xml:id="N16349" level="4" n="5" type="chapter" type-free="capitulum">
                <p xml:id="N1673F">
                  <s xml:id="N16753" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0066" n="66"/>
                  triplum: et quadrupli quadruplum: et ſexquialte­
                    <lb/>
                  ri ſexquialterum, et ſic deīceps. </s>
                  <s xml:id="N1675D" xml:space="preserve">Probatur hec cõ­
                    <lb/>
                  cluſio / quoniam duplum continet bis ſubduplum
                    <lb/>
                  et triplum ter ſubtriplum et ſic in infinitum / ergo
                    <lb/>
                  ſi remittantur vniformiter et eque velociter conti­
                    <lb/>
                  nuo neceſſe eſt cum ſubduplum fuerit remiſſum: re­
                    <lb/>
                  ſtat tantum de duplo remittendum quantuꝫ erat
                    <lb/>
                  ſubduplum: et cum ſubtriplum fuerit remiſſum re­
                    <lb/>
                  ſtet bis tantum remittendum etc.</s>
                </p>
                <p xml:id="N1676E">
                  <s xml:id="N1676F" xml:space="preserve">Triceſimatertia cõcluſio </s>
                  <s xml:id="N16772" xml:space="preserve">Si dupluꝫ
                    <lb/>
                  et ſubduplum vniformiter et eque velociter remit­
                    <lb/>
                  tantur ad non gradum: et quodlibet illorum cõti-
                    <lb/>
                  nuo tardius et tardius ſubduplum in minori tem­
                    <lb/>
                  pore quam ſubduplum remittetur. </s>
                  <s xml:id="N1677D" xml:space="preserve">ita  ſi duo re­
                    <lb/>
                  mittantur in vna hora .4. remittentur in maiori tē­
                    <lb/>
                  pore quam ſit tempus duarum horaruꝫ. </s>
                  <s xml:id="N16784" xml:space="preserve">Probat̄̄
                    <lb/>
                  hec concluſio et capio .4. et .8. et volo /  vniformi-
                    <lb/>
                  ter et eque velociter remittantur: ſed continuo ta-
                    <lb/>
                  men quodlibet illorum tardius et tardius. </s>
                  <s xml:id="N1678D" xml:space="preserve">Uolo
                    <lb/>
                  dicere /  ſemper quando remittitur vnitas vnius
                    <lb/>
                  puta ſubdupli remittatur vnitas alterius ſed con­
                    <lb/>
                  tinuo tardius et tardius / hoc eſt  ſi vtriuſ vni­
                    <lb/>
                  tas prima fuerit remiſſa in media hora alia vni-
                    <lb/>
                  tas ī maiori tempore adequate remittatur. </s>
                  <s xml:id="N1679A" xml:space="preserve">Quo
                    <lb/>
                  poſito manifeſtum eſt:  ſi in vna hora fuerit re-
                    <lb/>
                  miſſus quaternarius etiam in eadem hora remiſ-
                    <lb/>
                  ſus eſt quaternarius ab octonario et ab ip̄o octo­
                    <lb/>
                  nario reſtat remittendus quaternarius et conti-
                    <lb/>
                  nuo tardius remittetur. </s>
                  <s xml:id="N167A7" xml:space="preserve">igitur in maiori tempore
                    <lb/>
                  quam alter quaternarius / igitur totum tempus in
                    <lb/>
                  quo duplum remittitur adequate eſt maius quaꝫ
                    <lb/>
                  duplum ad tempus in quo remittitur ſubduplum</s>
                </p>
                <p xml:id="N167B0">
                  <s xml:id="N167B1" xml:space="preserve">Triceſimaquarta concluſio. </s>
                  <s xml:id="N167B4" xml:space="preserve">Si du-
                    <lb/>
                  plum et ſubduplum remittantur eque velociter et
                    <lb/>
                  continuo velocius et velocius: totale tempus re-
                    <lb/>
                  miſſionis dupli eſt minus quam duplum ad tem-
                    <lb/>
                  pus totalis remiſſiõis ſubdupli. </s>
                  <s xml:id="N167BF" xml:space="preserve">Et volo dicere / 
                    <lb/>
                  ſi duo et quatuor remittant̄̄: ita  quando remit-
                    <lb/>
                  titur vnitas binarii / tunc adequate remittatur vni­
                    <lb/>
                  as quaternarii ſed tamen velocius: ſic  ſi prima
                    <lb/>
                  vnitas binarii et quaternarii remittatur in hora:
                    <lb/>
                  ſecunda vnitas in minori tempore remittatur. </s>
                  <s xml:id="N167CC" xml:space="preserve">di­
                    <lb/>
                  co /  tempus totale in quo remittūtur ipſa .4. eſt
                    <lb/>
                  minus quam duplum ad tempus totalis remiſſio­
                    <lb/>
                  nis ipſorum .2. </s>
                  <s xml:id="N167D5" xml:space="preserve">Probatur hec concluſio / q2 ſi eque­
                    <lb/>
                  velociter et vniformiter remittentur quo ad tem-
                    <lb/>
                  pus: tunc tempus remiſſionis dupli eſſet adequa-
                    <lb/>
                  te duplum ad tempus remiſſionis ſubdupli / vt di-
                    <lb/>
                  cit triceſimaſecunda concluſio / ſed modo cõtinuo
                    <lb/>
                  velocius remittuntur duplum et ſubduplum: igi-
                    <lb/>
                  tur duplum in minori tempore quam duplum ad
                    <lb/>
                  tempus remiſſionis ipſius ſubdupli totaliter re-
                    <lb/>
                  mittetur. </s>
                  <s xml:id="N167E8" xml:space="preserve">¶ Et confirmatur / quia quãdo .2. et .4. re­
                    <lb/>
                  mittuntur eque velociter. </s>
                  <s xml:id="N167ED" xml:space="preserve">et continuo velocius et ve­
                    <lb/>
                  locius: tempus in quo remittetur prima medietas
                    <lb/>
                  ipſorum .4. erit equale tempore in quo remittun-
                    <lb/>
                  tur .2. et tempus remiſſionis alterius medietatis
                    <lb/>
                  ipſorum .4. eſt minus tempori remiſſionis prime
                    <lb/>
                  medietatis: ergo totum tempus remiſſionis ipſo-
                    <lb/>
                  rum .4. eſt minus quam ſubduplū ad tēpus remiſ-
                    <lb/>
                  ſionis ipſius dualitatis.</s>
                </p>
                <p xml:id="N167FE">
                  <s xml:id="N167FF" xml:space="preserve">Triceſimaquinta concluſio </s>
                  <s xml:id="N16802" xml:space="preserve">Aliquid
                    <lb/>
                  alio pluſ̄ in duplo citius remittitur: et tamē quã­
                    <lb/>
                  diu manent ambo eque velociter continuo remit-
                    <lb/>
                  tuntur. </s>
                  <s xml:id="N1680B" xml:space="preserve">Probatur hec concluſio. </s>
                  <s xml:id="N1680E" xml:space="preserve">et capio pedale et
                    <lb/>
                  bipedale: ſiue albedinem vnius gradus et albedi­
                    <lb/>
                  nem duorum graduum: et volo /  incipiant remit­
                    <lb/>
                  ti / et ↄ̨tinuo taliter remittant̄̄:  in eq̈libus tꝑibus
                    <cb chead="Capitulum quintum"/>
                  equales partes deperdant: continuo tamen tardi­
                    <lb/>
                  us et tardius quo poſito ſic arguo. </s>
                  <s xml:id="N1681C" xml:space="preserve">vnus gradus
                    <lb/>
                  pluſquã in duplo citius remittetur quam duo gra­
                    <lb/>
                  dus. </s>
                  <s xml:id="N16823" xml:space="preserve">vt patet ex triceſimatertia concluſione. </s>
                  <s xml:id="N16826" xml:space="preserve">et ta-
                    <lb/>
                  men continuo eque velociter quamdiu ſimul ma-
                    <lb/>
                  ment remittuntur. </s>
                  <s xml:id="N1682D" xml:space="preserve">vt patet ex caſu / igitur conclu-
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                  ſio vera.</s>
                </p>
                <p xml:id="N16832">
                  <s xml:id="N16833" xml:space="preserve">Triceſimaſexta concluſio /  iſta con­
                    <lb/>
                  ſequentia nihil valet a. eſt duplum et b. ſubduplū
                    <lb/>
                  et pluſquã in duplo citius deperditur b. / ſubduplū
                    <lb/>
                  quam a. / duplum igitur velocius deperditur b. ſub­
                    <lb/>
                  duplum quã. duplū </s>
                  <s xml:id="N1683E" xml:space="preserve">Stat em̄ cū añte /  a. duplum
                    <lb/>
                  in aliquo tēpore ita velociter mouetur ſicut b. ſub­
                    <lb/>
                  duplū ex anteriori concluſione / quod eſt oppoſitū
                    <lb/>
                  tertie exponentis ipſius conſequentis. </s>
                  <s xml:id="N16847" xml:space="preserve">Sed hec cõ­
                    <lb/>
                  ſequentia eſt bona b. eſt ſubduplū et a. duplū eius
                    <lb/>
                  et pluſquã in duplo velociꝰ deperditur ſiue remit­
                    <lb/>
                  titur quã b. / et vtrum illorum ſemper remittitur
                    <lb/>
                  vniformiter: ergo a. velocius remittetur quã b. / ſꝫ
                    <lb/>
                  antecedens talis conſequentie eſt impoſſibile: vt
                    <lb/>
                  patet ex triceſimaſecunda concluſione. </s>
                  <s xml:id="N16856" xml:space="preserve">Partes eī
                    <lb/>
                  antecedentis repugnant.</s>
                </p>
                <p xml:id="N1685B">
                  <s xml:id="N1685C" xml:space="preserve">Triceſimaſeptima concluſio </s>
                  <s xml:id="N1685F" xml:space="preserve">Si ali­
                    <lb/>
                  qua potentia inuariata mouetur per mediū vni-
                    <lb/>
                  formiter difforme inuariatum a remiſſiori extre-
                    <lb/>
                  mo incipiendo: talis potentia continuo tardius et
                    <lb/>
                  tardius acquirit ſibi reſiſtentiam. </s>
                  <s xml:id="N1686A" xml:space="preserve">Probatur hec
                    <lb/>
                  concluſio ſupponendo /  oīm duarū partiū equa­
                    <lb/>
                  lium corporis vniformiter difformis extremum ī­
                    <lb/>
                  tenſius per equalem latitudinem excedit extremū
                    <lb/>
                  remiſſius. </s>
                  <s xml:id="N16875" xml:space="preserve">vt capta latitudīe vniformiter difformi
                    <lb/>
                  a quarto vſ ad octauum: prime quarte extremū
                    <lb/>
                  intenſius puta vt .5. excedit remiſſius per vnū gra­
                    <lb/>
                  dum: et ſecunde quarte extremum intenſius / puta
                    <lb/>
                  vt ſex excedit extremum remiſſius eiuſdem quarte /
                    <lb/>
                  vt .5. etiam per vnum gradum: et ſic conſequenter
                    <lb/>
                  </s>
                  <s xml:id="N16883" xml:space="preserve">Et hoc non ſolum habet verum de partibus equa­
                    <lb/>
                  libus immediatis verumetiam de mediatis / vt
                    <lb/>
                  facile eſt intueri et etiam hoc in capite decimo hu­
                    <lb/>
                  ius tractatus probabitur. </s>
                  <s xml:id="N1688C" xml:space="preserve">Iſto ſuppoſito proba-
                    <lb/>
                  tur concluſio quoniam continuo pertranſitioneꝫ
                    <lb/>
                  duarum partium equalium equaliter acquiret de
                    <lb/>
                  reſiſtentia </s>
                  <s xml:id="N16895" xml:space="preserve">Quando enim pertranſibit ſecundam
                    <lb/>
                  quartã: tantã reſiſtentiã acquiret ſuper reſiſtentiã
                    <lb/>
                  habitã quantã tranſeundo primã quartam ade-
                    <lb/>
                  quate: et tantã reſiſtentiã acquiret adequate tran­
                    <lb/>
                  ſeundo primã octauã ſicut ſecundã: et ſicut tertiaꝫ
                    <lb/>
                  et ſicut quartam. </s>
                  <s xml:id="N168A2" xml:space="preserve">et ſic de quibuſcun partibꝰ eq̈-
                    <lb/>
                  libus: et continuo tardius et tardius talis poten­
                    <lb/>
                  tia mouetur: quia ſemper ſibi accreſcet reſiſtentia
                    <lb/>
                  ipſa inuariata: igitur tardius continue acquiret
                    <lb/>
                  ſibi reſiſtentiam.</s>
                </p>
                <p xml:id="N168AD">
                  <s xml:id="N168AE" xml:space="preserve">Triceſimaoctaua concluſio </s>
                  <s xml:id="N168B1" xml:space="preserve">Si ali-
                    <lb/>
                  qua potentia non variata continuo moueatur ꝑ
                    <lb/>
                  medium vniformiter difforme implendo ab extre­
                    <lb/>
                  mo intenſiori continuo velocius et velocius decreſ­
                    <lb/>
                  cet ſibi de reſiſtentia. </s>
                  <s xml:id="N168BC" xml:space="preserve">Patet / quia continuo veloci­
                    <lb/>
                  us et velocius mouetur et continuo equalem par-
                    <lb/>
                  tem tranſeundo equalem reſiſtentiaꝫ deperdit / igi­
                    <lb/>
                  tur continuo velocius et velocius decreſcit ſibi de
                    <lb/>
                  reſiſtentia.</s>
                </p>
                <p xml:id="N168C7">
                  <s xml:id="N168C8" xml:space="preserve">Triceſimanona cõcluſio </s>
                  <s xml:id="N168CB" xml:space="preserve">Si aliqua
                    <lb/>
                  potentia non variata mouetur per mediū vnifor­
                    <lb/>
                  miter difforme ab extremo remiſſiori incipiendo:
                    <lb/>
                  talis potentia continuo tardius et tardius remit­
                    <lb/>
                  tit motum ſuum. </s>
                  <s xml:id="N168D6" xml:space="preserve">Patet / quia tardius et tardiꝰ ac-
                    <lb/>
                  creſcet ſibi de reſiſtentia: igitur continuo tardius
                    <lb/>
                  et tardius remittit motum ſuum. </s>
                  <s xml:id="N168DD" xml:space="preserve">Patet conſequē­ </s>
                </p>
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