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="N16983" level="4" n="6" type="chapter" type-free="capitulum">
                <pb chead="Primi tractatus" file="0069" n="69"/>
                <p xml:id="N16C93">
                  <s xml:id="N16C94" xml:space="preserve">Sed  illã ꝑtranſibit arguitur: q2 quãlibet par-
                    <lb/>
                  tem eius proportionalē ꝓportione dupla mino-
                    <lb/>
                  ribus terminatis verſus extremū intenſius per-
                    <lb/>
                  tranſibit: igitur totã reſiſtentiã pertranſibit. </s>
                  <s xml:id="N16C9D" xml:space="preserve">Cõ-
                    <lb/>
                  ſequentia patet: q2 oēs partes ꝓportionales pro­
                    <lb/>
                  portione dupla illius reſiſtentie totã illam reſi-
                    <lb/>
                  ſtentiã conſtituūt. </s>
                  <s xml:id="N16CA6" xml:space="preserve">Sed iam reſtat ꝓbare pro ꝓba­
                    <lb/>
                  tione alterius partis /  nun̄ ad finē deueniet: q2
                    <lb/>
                  nõ ſufficit in tēpore finito tranſire illã reſiſtentiã:
                    <lb/>
                  igitur nun̄ deueniet ad finē illius reſiſtentie. </s>
                  <s xml:id="N16CAF" xml:space="preserve">Ar-
                    <lb/>
                  guitur antecedens et capio vnã aliam reſiſtentiam
                    <lb/>
                  difformiter difformē diuiſam per partes ꝓpor-
                    <lb/>
                  tionales ꝓportione dupla: cuius prima pars pro­
                    <lb/>
                  portionales ſit vniformis vt duo et ſecūda vt tria
                    <lb/>
                  et tertia vt .3. cū dimidio et quarta vt tria cū dimi-
                    <lb/>
                  dio et dimidio dimidii / et ſic ↄ̨ſequenter aſcenden-
                    <lb/>
                  do: ita  quelibet pars ꝓportionalis tali ꝓpor-
                    <lb/>
                  tionis duple diuiſione / ſit vniformiter intenſa in
                    <lb/>
                  iſta reſiſtentia difformiter difformi ſicut punctus
                    <lb/>
                  initiatiuus conſimilis partis in reſiſtētia vnifor-
                    <lb/>
                  miter difformi: et ſint tales reſiſtentie equales ex-
                    <lb/>
                  tenſiue / quo poſito ſic argumentor iſta potētia vt
                    <lb/>
                  4. non ſufficit ꝑtranſire iſtã reſiſtentiã difformem
                    <lb/>
                  in tēpore finito / et iſta reſiſtentia minꝰ reſiſtit quã
                    <lb/>
                  alia vniformiter difformis / vt conſtat reſpiciēdo
                    <lb/>
                  ad reſiſtentiã partiū ꝓportionaliū vniꝰ et alteriꝰ:
                    <lb/>
                  igitur talis potentia vt .4. nõ ſufficit pertranſire
                    <lb/>
                  talē reſiſtentiã vniformiter difformē a ſecūdo gra­
                    <lb/>
                  du vſ ad quartū / quod fuit ꝓbandū. </s>
                  <s xml:id="N16CD8" xml:space="preserve">Cõſequētia
                    <lb/>
                  eſt nota cū minore et maior arguitur / q2 aliquantū
                    <lb/>
                  tēpus requirit illa potentia ad pertranſeundum
                    <lb/>
                  primã partē ꝓportionalē: et tantū vel maiꝰ requi­
                    <lb/>
                  rit ad ꝑtrãſeundū ſcḋam: et iterū tantū vel maius
                    <lb/>
                  ad ꝑtranſeundū tertiã: et ſic cõſequenter: et ſunt in­
                    <lb/>
                  finite partes ꝓportionales: igitur in nullo tēpo-
                    <lb/>
                  re finito ſufficit talis potentia illã reſiſtentiã dif-
                    <lb/>
                  formiter difformē ꝑtranſire. </s>
                  <s xml:id="N16CEB" xml:space="preserve">Conſequentia patet /
                    <lb/>
                  et ꝓbatur antecedēs / qm̄ tranſeundo primã partē
                    <lb/>
                  ꝓportionalē / que eſt vt duo mouetur a ꝓportione
                    <lb/>
                  dupla: et tranſeundo ſcḋam / que eſt vt .3. mouetur a
                    <lb/>
                  ꝓportione ſexquitertia: et tranſeundo tertiã / que
                    <lb/>
                  eſt vt .3. cū dimidio mouetur a ꝓportione ſexqui-
                    <lb/>
                  ſeptima / et ſic conſequenter ſemꝑ a minori ꝓpor-
                    <lb/>
                  tione quã ſubdupla ad precedentē: igitur cõtinuo
                    <lb/>
                  tranſeundo partē ꝓportionalē ſequentē, requirit
                    <lb/>
                  maiꝰ tēpus quã trãſeūdo partē precedentē. </s>
                  <s xml:id="N16D00" xml:space="preserve">Patet
                    <lb/>
                  cõſequentia / qm̄ ſi cotinuo moueretur a ſubdupla
                    <lb/>
                  ꝓportione in parte ꝓportionali ſequenti ad pro-
                    <lb/>
                  portionē qua mouebatur in parte īmediate pre-
                    <lb/>
                  cedenti: ſemꝑ adequate tantū tēpus requireret ad
                    <lb/>
                  tranſeundū partē ſequentē ſicut īmediate prece-
                    <lb/>
                  dentē: q2 partes continuo ſe habent in ꝓportione
                    <lb/>
                  dupla et ſimiliter ꝓportiones ſe tunc haberent in
                    <lb/>
                  ꝓportione dupla: ſed modo cõtinuo in parte ſe-
                    <lb/>
                  quenti mouetur a minori ꝓportione quã ſubdu-
                    <lb/>
                  pla ad ꝓportionē / qua mouetur in parte īmediate
                    <lb/>
                  precedenti: igitur continuo maius tēpus requirit
                    <lb/>
                  ad pertranſeundū partē ſequentē quã precedentē
                    <lb/>
                  </s>
                  <s xml:id="N16D1C" xml:space="preserve">Sed  cõtinuo moueatur a minori ꝓportiõe quã
                    <lb/>
                  ſubdupla in parte ſequenti quã in parte īmediate
                    <lb/>
                  precedenti patet / q2 in prima mouetur a ꝓportiõe
                    <lb/>
                  dupla / et in ſecūda a ꝓportiõe ſexquitertia modo
                    <lb/>
                  ſexquitertia minor eſt quã ſubdupla duple / vt ptꝫ
                    <lb/>
                  ex ꝓbatione tertie cõcluſiõis quarti capitis ſcḋe
                    <lb/>
                  partis et ſexta ſuppoſitione capitis eiuſdē. </s>
                  <s xml:id="N16D2B" xml:space="preserve">Itē in
                    <lb/>
                  tertia mouet̄̄ a ꝓportiõe ſexquiſeptīa: modo ſexq̇­
                    <lb/>
                  ſeptīa minor eſt quã ſubdupla ſexq̇tertie / et ſic cõ-
                    <lb/>
                  ſequenter / vt patet ex ſexta ſuppoſitione quarti ca­
                    <lb/>
                  pitis preallegati: igitur.</s>
                </p>
                <cb chead="Capitulum ſextū."/>
                <p xml:id="N16D38">
                  <s xml:id="N16D39" xml:space="preserve">Reſpõdeo ad argumentum breuiter /
                    <lb/>
                  negando ſequelã: et ad ꝓbationē dico /  illa ↄ̨ña
                    <lb/>
                  nichil valet: quãlibet partē ꝓportionalē ſecundū
                    <lb/>
                  hanc diuiſionē hoc mobile ꝑtranſibit: ergo totuꝫ
                    <lb/>
                  ſpaciū ſiue reſiſtentiã ꝑtranſibit: īmo ſicut ꝓbat
                    <lb/>
                  argumentū ſi mobile et illa reſiſtentia ſimul ma-
                    <lb/>
                  nerent ꝑ infinitū tēpus: ꝑ īfinitū tēpus mobile mo­
                    <lb/>
                  ueret̄̄ ſupra reſiſtentiã / et nū̄ veniret ad terminū.</s>
                </p>
                <p xml:id="N16D4A">
                  <s xml:id="N16D4B" xml:space="preserve">Sed ↄ̨̨tra q2 poſſibile eſt /  potētia vt
                    <lb/>
                  4. ꝑtranſeat reſiſtentiã difformē in tꝑe finito, cuiꝰ
                    <lb/>
                  ṗma pars ꝓportiõalis eſt vniformiter difformis
                    <lb/>
                  a duobꝰ vſ ad tertiū, et ſecūda etiã vniformiter
                    <lb/>
                  difformis a tertio vſ ad tertiū cū dimidio, et ſic
                    <lb/>
                  cõſequenter vſ ad quartū excluſiue: igit̄̄ poſſibi-
                    <lb/>
                  le eſt potentiã vt .4. ꝑtranſire reſiſtentiã vniformi-
                    <lb/>
                  ter difformē a duobꝰ vſ ad quartū: et per conſe-
                    <lb/>
                  quens male negatū eſt hoc. </s>
                  <s xml:id="N16D5E" xml:space="preserve">Arguit̄̄ antecedens: et
                    <lb/>
                  pono /  ſit vna reſiſtentia pedalis diuiſa per par­
                    <lb/>
                  tes ꝓportionales ꝓportione quadrupla: cuiꝰ pri-
                    <lb/>
                  ma pars ꝓportionalis ſit vniformiter difformis
                    <lb/>
                  a ſecūdo vſ ad tertiū, et ſecunda a tertio vſ ad
                    <lb/>
                  tertiū cū dimidio, et ſic cõſequēter vſ ad quarū
                    <lb/>
                  excluſiue: deinde capio vnã aliã reſiſtentiã ſimili-
                    <lb/>
                  ter pedalē: diuiſam per partes ꝓportionales ꝓ-
                    <lb/>
                  portione quadrupla: cuiꝰ prima pars ꝓportiona­
                    <lb/>
                  lis ſit vniformis vt .3. et ſecūda vt .3. cū dimidio, et
                    <lb/>
                  tertia vt .3. cū dimidio et dimidio dimidii, et ſic cõ-
                    <lb/>
                  ſequēter: ita  quelibet pars ꝓportiõalis in tali
                    <lb/>
                  reſiſtentia ſit vniformiter intēſa ſicut gradus in-
                    <lb/>
                  ſiſſimꝰ in parte cõſimili ſiue correſpondēte in alia
                    <lb/>
                  reſiſtentia pedali cuiꝰ partes ꝓportionales ſunt
                    <lb/>
                  vniformiter difformes: quo poſito ſic argumētor
                    <lb/>
                  iſta ſecūda reſiſtentia cuiꝰ partes ꝓportiõales ſūt
                    <lb/>
                  vniformes eſt maioris reſiſtentie quã altera: vt ſa­
                    <lb/>
                  tis facile ptꝫ intelligenti reſiſtentiã partiū ꝓpor-
                    <lb/>
                  tionabiliū in vna et in altera: et tamen potentia vt
                    <lb/>
                  4. ſufficit in tēpore finito ꝑtranſire iſtã ſecundam
                    <lb/>
                  reſiſtentiã: igit̄̄ et alterã cuiꝰ partes ꝓportionales
                    <lb/>
                  ſunt vniformiter difformes. </s>
                  <s xml:id="N16D8D" xml:space="preserve">Cõſequētia ptꝫ ꝑ locū
                    <lb/>
                  a maiori et maior ſimiliter: et minor ꝓbat̄̄: ſuppo-
                    <lb/>
                  nendo /  oīs ꝓportio ſuꝑparticularis diuidit̄̄ in
                    <lb/>
                  duas ꝓportiones / quaꝝ vna eſt medii numeri ad
                    <lb/>
                  minimū et alia maximi ad mediū: et illa que eſt ma­
                    <lb/>
                  ximi ad mediuꝫ, eſt maior quã tertia pars totius
                    <lb/>
                  ꝓportionis ſuꝑparticularis: vt ptꝫ ex decimo cor­
                    <lb/>
                  relario tertie cõcluſionis quarti capitis ſecunde
                    <lb/>
                  partis. </s>
                  <s xml:id="N16DA0" xml:space="preserve">Hoc ſuppoſito ſic arguo potentia / vt .4. in
                    <lb/>
                  aliquo tēpore ꝑtranſit prima partē ꝓportionalē
                    <lb/>
                  talis reſiſtentie: et in ſubſexquitertio tēpore ꝑtran­
                    <lb/>
                  ſit ſcḋam: et ſic cõſequēter ita  quãlibet ſequentē
                    <lb/>
                  ꝑtranſit in ſubſexq̇tertio tēpore ad tēpus in quo
                    <lb/>
                  ꝑtrãſit īmediate p̄cedentē: igit̄̄ totū tēpus in quo
                    <lb/>
                  pertranſit oēs partes alias a prima eſt triplū ad
                    <lb/>
                  tempus in quo pertranſit primã: vt patet intelli-
                    <lb/>
                  genti quintum caput prime partis: et tempus in
                    <lb/>
                  quo pertrãſit primam eſt finitū: igitur totū tēpus
                    <lb/>
                  aggregatū eſt finituꝫ. </s>
                  <s xml:id="N16DB7" xml:space="preserve">Sed iam probo antecedens /
                    <lb/>
                  quoniam in aliquo tempore pertranſit primam:
                    <lb/>
                  ſignetur igitur illud tempus et ſit vna hora gra-
                    <lb/>
                  tia exempli: et in illa hora per illam partem con-
                    <lb/>
                  tinuo mouetur a proportione ſexquitertia: quia
                    <lb/>
                  reſiſtentia eſt vt .3. et potentia vt .4. et tranſeundo
                    <lb/>
                  ſecundam partem proportionalem / que eſt vt .3. cū
                    <lb/>
                  dimidio mouetur a proportione ſexquiſeptima:
                    <lb/>
                  que vt patet ex ſuppoſitione non eſt ſubtripla ad
                    <lb/>
                  ſexquitertiam ſed maior quam ſubtripla: ſed ſi
                    <lb/>
                  illa eſſet ſubtripla tranſiret ſecundam partem
                    <lb/>
                  ꝓportiõalē in ſubſexquitertio tēpore / ergo modo </s>
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