Alvarus, Thomas, Liber de triplici motu, 1509

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                  <s xml:id="N25B3D" xml:space="preserve">
                    <pb chead="De motu alterationis quo ad cauſam" file="0220" n="220"/>
                  Probat̄̄ maior et diuido ṗmã ꝑtē ꝓportionalē ipſiꝰ
                    <lb/>
                  a. in duas medietates / et arguo ſic / ſcḋa pars ꝓpor-
                    <lb/>
                  tionalis ipſiꝰ a. eſt eq̈lis in ponã medietati ṗme re­
                    <lb/>
                  motiori a b. paſſo et eſt pluſ̄ ī duplo meliꝰ appli­
                    <lb/>
                  cata ip̄i b. paſſo ꝙ̄ medietas ṗme remotior a b. paſ­
                    <lb/>
                  ſo et ip̄a ſcḋa ꝑs ꝓportionalis ē eq̈lis ī pone medie­
                    <lb/>
                  tati ṗme ꝓpinquiori ip̄i b. paſſo et eſt ī duplo meliꝰ
                    <lb/>
                  applicata ip̄i b. paſſo ꝙ̄ ip̄a medietas prīe ꝓpinq̇or
                    <lb/>
                  agenti et totalis actio ṗme ꝑtis ꝓportionalis ↄ̨po-
                    <lb/>
                  nitur ex actiõibꝰ ſuaꝝ medietatū: igr̄ ſcḋa ꝑs ꝓpor­
                    <lb/>
                  tionalis plus agit in b. paſſū in eodē tꝑe ꝙ̄ ṗma / qḋ
                    <lb/>
                  fuit probãdū. </s>
                  <s xml:id="N25B5A" xml:space="preserve">qm̄ eodē argumēto ꝓbabis tertiã plꝰ
                    <lb/>
                  agere in b. paſſū in eodē tꝑe ꝙ̄ ſcḋa et q̈rtã ꝙ̄ tertia /
                    <lb/>
                  et ſic ↄ̨ñter </s>
                  <s xml:id="N25B61" xml:space="preserve">Probat̄̄ tñ ↄ̨ña ꝑ hoc /  ī ea ꝓportiõe q̄
                    <lb/>
                  aliqḋ agēs ē propīquiꝰ eidē paſſo in ea velociꝰ aget
                    <lb/>
                  ceteris paribꝰ.
                    <note position="left" xlink:href="note-0220-01a" xlink:label="note-0220-01" xml:id="N25BCF" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N25B6D" xml:space="preserve">¶ Dices et bñ negãdo ſequelã et ad
                    <lb/>
                  probationē negãdo añs et cū probat̄̄ admittit̄̄ caſꝰ
                    <lb/>
                  de ip̄o a. et negat̄̄ añs. </s>
                  <s xml:id="N25B74" xml:space="preserve">et ad probationē dico ṗmo /
                    <lb/>
                   mīor eſt dubia qm̄ poſſibile eſt /  b. paſſū ſit vltra
                    <lb/>
                  ſpheram actiuitatꝪ medietatꝪ remotioris ṗme par­
                    <lb/>
                  tis proportiõalis a. </s>
                  <s xml:id="N25B7D" xml:space="preserve">Stat eī  b. paſſū ſit ītra am-
                    <lb/>
                  bitū actiuitatꝪ totiꝰ a. agētis et tñ ſit vltra ſpherã
                    <lb/>
                  actiuitatꝪ certe partis ipſius a. ita  talis pars nõ
                    <lb/>
                  hēat ibi actionē ꝑ ſe. </s>
                  <s xml:id="N25B86" xml:space="preserve">Dico ſcḋo /  eſto  vtra me-
                    <lb/>
                  dietas ṗme partis proportionalis ipſiꝰ a. ſufficiat
                    <lb/>
                  agere ꝑ ſe in ip̄m b. adhuc. </s>
                  <s xml:id="N25B8D" xml:space="preserve">tñ negat̄̄ ↄ̨ña et ad proba­
                    <lb/>
                  tionē negat̄̄ propõ / q̄ ibi aſſumit vcꝫ /  in ea propor­
                    <lb/>
                  tione q̈ aliqḋ agēs ē propīquiꝰ eiḋ paſſo / in qḋ ſuffi­
                    <lb/>
                  cit agere in ea velociꝰ agit ceteris ꝑibꝰ / q2 tūc ſeq̄re­
                    <lb/>
                  tur /  in īfinitū velociꝰ in eodē tꝑe ageret agēs īme­
                    <lb/>
                  diatū paſſo ꝙ̄ diſtãs a paſſo cū in īfinitū ſit ei pro-
                    <lb/>
                  pinquiꝰ / qḋ eſt manifeſte falſuꝫ: q2 tūc ſeq̄ret̄̄ ignem
                    <lb/>
                  ſubito calefacere aquã ſibi proximã īducēdo in eaꝫ
                    <lb/>
                  totã caliditatē natã induci ab ip̄o igne. </s>
                  <s xml:id="N25BA0" xml:space="preserve">Nec iuuat
                    <lb/>
                  dicere /  cū aliqḋ agēs diſtãs ab aliq̊ paſſo appro­
                    <lb/>
                  ximat̄̄ ei nõ in infinitū meliꝰ applicat̄̄ ei ſcḋm quēli­
                    <lb/>
                  bet eiꝰ pūctū: ſꝫ preciſe ſcḋm vnū pūctū </s>
                  <s xml:id="N25BA9" xml:space="preserve">Q2 volo / 
                    <lb/>
                  cõdenſet̄̄ vnū agēs ita  in q̈libet ꝑte proportiona­
                    <lb/>
                  li tꝑis efficiat̄̄ ī duplo propinq̇us ſcḋm ſe et qḋlibet
                    <lb/>
                  eiꝰ punctū ip̄i paſſo ꝙ̄ in parte īmediate p̄cedēti / et
                    <lb/>
                  tūc ſi illa propõ eēt vera ageret illud agens in illo
                    <lb/>
                  tꝑe infinita velocitate / qḋ eſt falſuꝫ / q2 ē agēs finitū
                    <lb/>
                  agēs ī reſiſtētiã. </s>
                  <s xml:id="N25BB8" xml:space="preserve">Itē ſi ſic approxīatū reſiſtētie age­
                    <lb/>
                  ret īfinite velociṫ: ageret ī ſibi eq̈lē reſiſtētiã et in īfi-
                    <lb/>
                  nite magnã / quod eſt impoſſibile.</s>
                </p>
                <p xml:id="N25BD5">
                  <s xml:id="N25BD6" xml:space="preserve">Sed ↄ̨̨tra q2 aliquod alterãs finitum
                    <lb/>
                  ſufficit agere īfinita velocitate adeq̈te ī hora q̈libet
                    <lb/>
                  ꝑte eiꝰ ꝓportionali tm̄ agēte ̄tū ṗma rõe ꝓpīqui-
                    <lb/>
                  tatis: igr̄ ſolutio nulla. </s>
                  <s xml:id="N25BDF" xml:space="preserve">Probat̄̄ añs et ſigno a. alte­
                    <lb/>
                  rans et b. paſſuꝫ ſicut ī priori caſu et mãifeſtū eſt ex
                    <lb/>
                  ſolutiõe /  ſcḋa pars ꝓportiõalis minꝰ agit ꝙ̄ ṗma
                    <lb/>
                  vel aliq̈ ſequēs ꝙ̄ īmediate p̄cedēs eã et hoc ꝓpṫ de-
                    <lb/>
                  fectū forme: volo igr̄ /  tm̄ de forma addat̄̄ ſcḋe ꝑti
                    <lb/>
                  ꝓportionali quovſ tm̄ ſufficiat agere in b. paſſū
                    <lb/>
                  ſicut prīa adeq̈te in hora ī eadē diſtãtia in q̄ ſe hñt
                    <lb/>
                  ad b. paſſū. </s>
                  <s xml:id="N25BF0" xml:space="preserve">et mãifeſtū eſt /  ſcḋa ꝑs ꝓportiõalis nõ
                    <lb/>
                  hꝫ tm̄ de forma ſicut ṗma ſi eī tm̄ hēret (cū ſit in du-
                    <lb/>
                  plo propīquior) plus ageret / qḋ eſt ↄ̈ caſuꝫ. </s>
                  <s xml:id="N25BF7" xml:space="preserve">Habeat
                    <lb/>
                  igit̄̄ prima ī f. ꝓportiõe plus de forma ꝙ̄ .2. et pono /
                    <lb/>
                   tertie tm̄ addat̄̄ de forma quouſ ſcḋa hēat pre-
                    <lb/>
                  ciſe in f. proportiõe plus de forma ꝙ̄ ip̄a tertia et ſic
                    <lb/>
                  addatur cuilibet ſequenti de forma taliter  in f. ꝓ­
                    <lb/>
                  portione minus habeat de forma ꝙ̄ immediate pre­
                    <lb/>
                  cedens. </s>
                  <s xml:id="N25C06" xml:space="preserve">Quo poſito a. agit infinita velocitate ī ho-
                    <lb/>
                  ra in b. paſſum et eſt finitum finite habēs de forma /
                    <lb/>
                  igitur aliquod alterans finitum ſufficit agere infi-
                    <lb/>
                  nita velocitate in hora adequate etc. / quod fuit pro-
                    <lb/>
                  bandum. </s>
                  <s xml:id="N25C11" xml:space="preserve">Patet cõſequētia cū minore / quia forma
                    <cb chead="De motu alterationis quo ad cauſam"/>
                  ipſius a. agentis componitur ex infinitis continuo
                    <lb/>
                  ſe habentibus in ꝓportione f. finita deſcēdendo / vt
                    <lb/>
                  patet ex caſu. </s>
                  <s xml:id="N25C1B" xml:space="preserve">Et maior probatur / quia ſcḋa pars ꝓ­
                    <lb/>
                  portionalis agit tantū adequate in b. paſſum quã-
                    <lb/>
                  tum prima / q2 in f. proportiõe habet minus de for-
                    <lb/>
                  ma et eſt in duplo propinquior ipſi b. paſſo / igitur
                    <lb/>
                  tertia pars ꝓportionalis tãtū agit adequate quã­
                    <lb/>
                  tum ſecunda et quarta quãtū tertia / et ſic cõſequēter /
                    <lb/>
                  et ꝑ ↄ̨ſequēs a. agit infinita velocitate in hora in b.
                    <lb/>
                  paſſum / quod fuit ꝓbandum. </s>
                  <s xml:id="N25C2C" xml:space="preserve">Añs patet ex caſu et cõ­
                    <lb/>
                  ſequentia probat̄̄ / quia ſi ſecūda pars proportio-
                    <lb/>
                  nalis tantū agit in b. paſſum ſicut prima eo  in f.
                    <lb/>
                  proportione minꝰ habet de forma ꝙ̄ prima et eſt
                    <lb/>
                  in duplo propinquior b. paſſo: ſequit̄̄ eadē ratione
                    <lb/>
                  cum tertia habeat in f. proportiõe minus de forma
                    <lb/>
                  ̄ ſecūda et ſit in duplo propinquior b. paſſo  ſe-
                    <lb/>
                  cunda  ipſa tantū adequate aget ī hora in b. paſ-
                    <lb/>
                  ſum ſicut ſecunda. </s>
                  <s xml:id="N25C3F" xml:space="preserve">Et ſic in ꝓbabis de quibuſcun
                    <lb/>
                  duabus immediatis.
                    <note position="right" xlink:href="note-0220-02a" xlink:label="note-0220-02" xml:id="N25C89" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N25C49" xml:space="preserve">¶ Dices et bene negando añs
                    <lb/>
                  et ad probationē admiſſo caſu negando iteruꝫ añs
                    <lb/>
                  et ad probationē negatur maior et cū ꝓbatur nega­
                    <lb/>
                  tur añs vcꝫ /  iõ ſecūda tantū agit quantum prima /
                    <lb/>
                  quia habet in f. minus de forma ꝙ̄ prima et eſt ī du­
                    <lb/>
                  plo propinquior b. paſſo. </s>
                  <s xml:id="N25C56" xml:space="preserve">Nõ em̄ illa eſt cauſa qua­
                    <lb/>
                  re ſecūda tantū agit in b. paſſuꝫ quãtū prima ſꝫ / q2
                    <lb/>
                  in tali diſtantia tantã proportionē habet ſecunda
                    <lb/>
                  ad b. paſſum quantū habet prima ad idē b. paſſum.
                    <lb/>
                  </s>
                  <s xml:id="N25C60" xml:space="preserve">Nã illa cauſalis eſt falſa. </s>
                  <s xml:id="N25C63" xml:space="preserve">Tu primo ꝓpter cauſaꝫ
                    <lb/>
                  dictã </s>
                  <s xml:id="N25C68" xml:space="preserve">Tū ſecūdo / q2 illa nõ eſt bona ↄ̨ña. </s>
                  <s xml:id="N25C6B" xml:space="preserve">nam cū in
                    <lb/>
                  infinitū modicū de forma habet aliqua pars ꝓpor­
                    <lb/>
                  tionalis: deueniēdū eſt ad aliquã partē proportio-
                    <lb/>
                  nalē ipſius a. agentis / que non agit in b. cū ad ip̄m
                    <lb/>
                  habeat proportionē equalitatis vel minoris ineq̈-
                    <lb/>
                  litatis / et tñ illa pars eſt in duplo ꝓpinquior ipſi b.
                    <lb/>
                  paſſo ꝙ̄ pars īmediate precedēs et hꝫ in f. ꝓportiõe
                    <lb/>
                  minus de forma. </s>
                  <s xml:id="N25C7C" xml:space="preserve">Et in hoc ↄ̨ſiſtit ſolutio replice / 
                    <lb/>
                  vcꝫ deueniendū eſt ad aliquã partem proportiona­
                    <lb/>
                  lem / q̄ nullo mõ ſufficit ꝑ ſe agere in b. paſſuꝫ ſꝫ ha-
                    <lb/>
                  bet ad illud proportiõeꝫ mīoris inequalitatis.</s>
                </p>
                <p xml:id="N25C8F">
                  <s xml:id="N25C90" xml:space="preserve">Sed cõtra et pono /  ſecunde parti ꝓ­
                    <lb/>
                  portionali ipſiꝰ a. alterãtis addatur de forma quo
                    <lb/>
                  vſ agat tm̄ ī b. paſſū ſicut ṗma adeq̈te: et ſiĺr tm̄
                    <lb/>
                  addat̄̄ tertie de forma /  tantum agat in b. paſſū
                    <lb/>
                  ſicut prima et quarte. / et q̇nte: et ſic ↄ̨ñter ita  queli-
                    <lb/>
                  bet ſequens agat tm̄ ſicut p̄cedens. </s>
                  <s xml:id="N25C9D" xml:space="preserve">Quo poſito ſic
                    <lb/>
                  arguit̄̄ a. agit infinite velociter in b. paſſum / vt patꝫ
                    <lb/>
                  ex caſu et a. eſt finitum alterans hoc eſt habēs finitū
                    <lb/>
                  de forma adequate / igit̄̄ aliqḋ alterãs finitū hñs fi­
                    <lb/>
                  nite de forma adeq̈te alterat īfinite velociter certaꝫ
                    <lb/>
                  reſiſtentiã / qḋ eſt negatū. </s>
                  <s xml:id="N25CAA" xml:space="preserve">Probat̄̄ minor / q2 ſecūda
                    <lb/>
                  pars proportionalis habet minus de forma ꝙ̄ pri­
                    <lb/>
                  ma adequate et tertia minus ꝙ̄ ſecūda et quarta ̄
                    <lb/>
                  tertia / et ſic ↄ̨ſequēter: igitur totalis forma ipſius a.
                    <lb/>
                  alterantis eſt finita. </s>
                  <s xml:id="N25CB5" xml:space="preserve">Patet iſta ↄ̨ſequētia: q2 for-
                    <lb/>
                  ma totalis ipſius a. vni certe parti date nõ habet
                    <lb/>
                  infinitas equales non cõicantes. </s>
                  <s xml:id="N25CBC" xml:space="preserve">Probo tamē an-
                    <lb/>
                  tecedens. </s>
                  <s xml:id="N25CC1" xml:space="preserve">quia ſi ſecunda habent tantum ſicut pri-
                    <lb/>
                  ma vel plus cum ſit propinquior ſequeretur /  plꝰ
                    <lb/>
                  ageret ꝙ̄ prima / ſed conſequens eſt falſum et contra
                    <lb/>
                  caſum / igitur et antecedēs </s>
                  <s xml:id="N25CCA" xml:space="preserve">Et ſic probabis de qui-
                    <lb/>
                  buſcun immediatis.
                    <note position="right" xlink:href="note-0220-03a" xlink:label="note-0220-03" xml:id="N25D12" xml:space="preserve">Confir°.</note>
                  </s>
                  <s xml:id="N25CD4" xml:space="preserve">¶ Et confirmatur / quia ſi q̄-
                    <lb/>
                  ſtio eſſet vera / ſequeretur /  quodlibet alterans fi-
                    <lb/>
                  nitum alteraret certam reſiſtentiam infinita tar-
                    <lb/>
                  ditate / ſꝫ ↄ̨ñs eſt fĺm: igr̄ illud ex q̇ ſeq̇tur. </s>
                  <s xml:id="N25CDD" xml:space="preserve">Sequela
                    <lb/>
                  ꝓbat̄̄ / q2 ſi nõ ſignet̄̄ illud et ſit a. / et arguo ſic / a. agit ī­
                    <lb/>
                  finita tarditate: igr̄ propoſitū. </s>
                  <s xml:id="N25CE4" xml:space="preserve">Argr̄ añs et volo / 
                    <lb/>
                  in caſu ſuꝑiꝰ poſito b. paſſū diuidat̄̄ ꝑ partes ꝓpor­ </s>
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