Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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                  <s xml:id="N1797D" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0077" n="77"/>
                  eadē / quod erat probandum. </s>
                  <s xml:id="N17997" xml:space="preserve">Et ſic patet concluſio
                    <lb/>
                    <note position="left" xlink:href="note-0077-01a" xlink:label="note-0077-01" xml:id="N179ED" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N179A1" xml:space="preserve">¶ Ex quo ſequitur:  ſi aliqua potentia inauriata
                    <lb/>
                  aliquod mediū inuariatū tranſeundo continuo re­
                    <lb/>
                  mittat motū ſuū vſ ad nõ gradum ſiue vniformi-
                    <lb/>
                  ter ſiue difformiter: oīs potentia maior inuariata
                    <lb/>
                  idem mediū inuariatū tranſeūdo continuo remit-
                    <lb/>
                  tendo motum ſuū ad extremū intenſius eiuſdē me-
                    <lb/>
                  dii deueniendo: in infinitū velocius remittit motuꝫ
                    <lb/>
                  ſuū quã data potentia minor. </s>
                  <s xml:id="N179B2" xml:space="preserve">Probatur / quia illa
                    <lb/>
                  potentia quecū detur in infinitū velocius moue-
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                  bitur aliquam partē illius medii tranſeūndo ſus
                    <lb/>
                  extremū intenſius deueniendo quaꝫ data potentia
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                  minor: igitur in infinitū velocius remittit motū ſuū
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                  quã illa data potētia minor. </s>
                  <s xml:id="N179BF" xml:space="preserve">Patet hec cõſequētia /
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                  qm̄ ita velociter ſicut potentia maior pertranſit a-
                    <lb/>
                  liquã partē c. medii ita velociter remittit motū de-
                    <lb/>
                  perdendum in illa: et ſimiliṫ. </s>
                  <s xml:id="N179C8" xml:space="preserve">potentia minor: igitur
                    <lb/>
                  ſi in infinitū velocius potentia maior mouetur trã-
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                  ſeūdo aliquam partē c. medii quã potentia minor
                    <lb/>
                  tranſeundo eandē: ipſa potētia maior in infinitum
                    <lb/>
                  velocius remittit motū ſuū quã potētia minor. </s>
                  <s xml:id="N179D3" xml:space="preserve">An­
                    <lb/>
                  tecedens ꝓbatur / vt ſupra qm̄ potentia maior a ꝓ-
                    <lb/>
                  portiõe quã habet ad extremū intēſius ipſiꝰ medii
                    <lb/>
                  cõtinuo mouebit̄̄ vel a maiori: et potētia minor ab
                    <lb/>
                  in infinitū minori verſus extremū intēſius deueniē-
                    <lb/>
                  do: igitur in infinitū maiori velocitate mouebitur
                    <lb/>
                  ꝑtrãſeūdo aliquã partē ipſiꝰ medii potētia maior
                    <lb/>
                  quã potētia minor ꝑtrãſeūdo eanſdē ſus extremū
                    <lb/>
                  intenſius deueniendo. </s>
                  <s xml:id="N179E6" xml:space="preserve">Et ſic patet correlarium.</s>
                </p>
                <note position="left" xml:id="N179F3" xml:space="preserve">q̄drage-
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                ſima con­
                  <lb/>
                cĺio cal-
                  <lb/>
                cĺatoris</note>
                <p xml:id="N179FD">
                  <s xml:id="N179FE" xml:space="preserve">Sexta concluſio. </s>
                  <s xml:id="N17A01" xml:space="preserve">Si aliqua potentia
                    <lb/>
                  īuariata tranſeūdo aliqḋ mediū difforme īuaria-
                    <lb/>
                  tum vniformiter remittit motū ſuū ad nõ gradū in
                    <lb/>
                  extremo intēſiori: oīs potentia minor in infinitum
                    <lb/>
                  tarde remittit motū ſuū mouēdo per idē mediū ver­
                    <lb/>
                  ſus punctū intrinſecū eiuſdem medii ad quē habet
                    <lb/>
                  ꝓportionē equalitatis deueniendo. </s>
                  <s xml:id="N17A10" xml:space="preserve">Probatur / ſit
                    <lb/>
                  b. potētia maior que īuariata c. mediū īuariatum
                    <lb/>
                  tranſeūdo vniformiter cõtinuo d. gradu velocita-
                    <lb/>
                  tis remittit motū ſuū ad nõ gradū in extremo intē­
                    <lb/>
                  ſiori c. medii: et ſit a. potentia minor que inuariata
                    <lb/>
                  ꝑtē c. medii (vt oportet) trãſeundo remittat ↄ̨tinuo
                    <lb/>
                  motū ſuū verſus e. pūctū intrinſecū ad quē hꝫ ꝓpor­
                    <lb/>
                  tionem equalitatis: q2 neceſſe eſt / ipſam habere ad
                    <lb/>
                  aliquē punctū intrinſecū illꝰ c. medii ꝓportionem
                    <lb/>
                  equalitatis / vt ptꝫ ex ſecūdo correlario quarte con-
                    <lb/>
                  cluſionis huiꝰ. </s>
                  <s xml:id="N17A27" xml:space="preserve">Tūc dico /  a. potentia verſus e. pū­
                    <lb/>
                  ctum veniendo in infinitū tarde remittit motū ſuū.
                    <lb/>
                  </s>
                  <s xml:id="N17A2D" xml:space="preserve">Quod ſic ꝓbatur / q2 a. potentia verſus e. punctū ve­
                    <lb/>
                  niendo in infinitū tardius remittit motū ſuū quam
                    <lb/>
                  b. potentia: et b. potentia certe velociter cõtinuo pu­
                    <lb/>
                  ta d. gradu velocitatis remittit motū ſuū ex hypo-
                    <lb/>
                  theſi: igitur a. potentia in infinitum tarde remittit
                    <lb/>
                  motū ſuū. </s>
                  <s xml:id="N17A3A" xml:space="preserve">Patet ↄ̨ſequentia cū minore: et arguitur
                    <lb/>
                  maior: q2 a. potentia verſus e. punctū veniendo in
                    <lb/>
                  infinitū tardius pertranſit aliquam partē ipſius c.
                    <lb/>
                  medii quam b. pertrãſeat eandē: et tam a. quam b.
                    <lb/>
                  eaſdem partes c. medii tranſeundo equalē latitu-
                    <lb/>
                  dinē motus deperdunt adequate: vt ſepe argutum
                    <lb/>
                  eſt: igitur a. potentia verſus e. punctuꝫ veniendo in
                    <lb/>
                  infinitū tardius remittit motum ſuū quam b. potē-
                    <lb/>
                  tia: quod fuit probandum. </s>
                  <s xml:id="N17A4D" xml:space="preserve">Cõſequentia probatur:
                    <lb/>
                  quoniã a. tranſeundo aliquam partem c. medii ver-
                    <lb/>
                  ſus e. punctum veniendo tantam latitudinem mo-
                    <lb/>
                  tus deperdit ſicut b. pertranſeundo eandē adequa­
                    <lb/>
                  te. </s>
                  <s xml:id="N17A58" xml:space="preserve">ergo ſi a. in infinitum tardius pertranſit aliquã
                    <lb/>
                  partem ipſius c. medii verſus e. pūctum deuenien-
                    <lb/>
                  do quam b pertranſeat eandem in infinitum tardi­
                    <lb/>
                  us remittit motum ſuum tranſeundo talem parteꝫ /
                    <cb chead="Capitulum ſeptimū."/>
                  quam b. tranſeundo eandem. </s>
                  <s xml:id="N17A64" xml:space="preserve">Sed probatur maior
                    <lb/>
                  et capio proportionem / quam habet b. ad punctum
                    <lb/>
                  e. ipſius c. medii que ſit f. / et arguo ſic / a verſus e. pū-
                    <lb/>
                  ctum deueniendo ab in infinitum minori proporti-
                    <lb/>
                  one mouetur tranſeundo aliquã partem quam ſit
                    <lb/>
                  f. proportio a qua vel maiori continuo mouetur b.
                    <lb/>
                  tranſeundo talem partem: quia ab infinite modi-
                    <lb/>
                  ca proportione mouebitur a. verſus c. punctum ve-
                    <lb/>
                  niendo: cum ſucceſſiue remittat motum ſuum conti­
                    <lb/>
                  nuo verſus idem e. punctum veniendo ad non gra-
                    <lb/>
                  dū: et b. verſus e. punctū veniendo ↄ̨tinuo mouet̄̄ ab
                    <lb/>
                  f. proportione vel a maiori: ergo ſequitur /  in in-
                    <lb/>
                  finitū tardius mouetur a. tranſeūdo aliquam par-
                    <lb/>
                  tem c. medii verſus e. punctum veniendo quam mo-
                    <lb/>
                  ueatur b. eandem partem tranſeundo: et ex conſe-
                    <lb/>
                  quenti in infinitum tardius a. potentia verſus e.
                    <lb/>
                  punctū veniendo aliquam partem c. medii pertran­
                    <lb/>
                  ſit quam b. pertranſeat eandem / quod fuit proban­
                    <lb/>
                  dum.
                    <note position="right" xlink:href="note-0077-02a" xlink:label="note-0077-02" xml:id="N17B9B" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N17A90" xml:space="preserve">¶ Ex quo ſequitur primo /  vbicun aliqua
                    <lb/>
                  potentia inuariata aliquod medium tranſeundo
                    <lb/>
                  ſucceſſiue remittit motum ſuum vſ ad non gradū
                    <lb/>
                  ſiue vniformiter continuo, ſiue difformiter, ſiue de­
                    <lb/>
                  uendo ad extremum illius medii, ſiue ad punctum
                    <lb/>
                  intrinſecum: omnis potentia minor inuariata re-
                    <lb/>
                  mittens motum ſuū ad non gradum in aliquo pun­
                    <lb/>
                  cto, in infinitum tardius ad idem punctum venien-
                    <lb/>
                  do remittit motum ſuum quam data potentia ma­
                    <lb/>
                  ior cum ad idem punctū deuenit in quo illa minor
                    <lb/>
                  habet non gradum motus. </s>
                  <s xml:id="N17AA7" xml:space="preserve">Probatur hoc correla­
                    <lb/>
                  rium: et ſit a. potentia maior que remittat inuaria-
                    <lb/>
                  ta c. medium inuariatum tranſeundo vel partē eiꝰ
                    <lb/>
                  vniformiter, vel difformiter ſucceſſiue cõtinuo, mo­
                    <lb/>
                  tum ſuum ad non gradum: et b potentia minor que
                    <lb/>
                  in puncto citeriori eiuſdem medii qui punctus ſit d.
                    <lb/>
                  remittat ad non gradum motum ſuum: ipſa b. po-
                    <lb/>
                  tentia inuariata cum ad d. punctum ipſius c. medii
                    <lb/>
                  inuariati deuenit vniformiter vel difformiter re-
                    <lb/>
                  mittente motum ſuum continuo ſucceſſiue: tunc di-
                    <lb/>
                  co /  b. potentia in infinitum tardius remittet mo-
                    <lb/>
                  tum ſuum verſus d. punctum deueniendo quam a.
                    <lb/>
                  potentia maior verſus idem d. punctum veniendo.
                    <lb/>
                  </s>
                  <s xml:id="N17AC3" xml:space="preserve">Et ſic dicendum eſt de quibuſcun duabus inequa­
                    <lb/>
                  libus potentiis: et de infinitis potentiis ſimiliter
                    <lb/>
                  quarum nulla eſt equalis alteri. </s>
                  <s xml:id="N17ACA" xml:space="preserve">Quod probatur
                    <lb/>
                  ſic: quia in infinitum tardius pertranſibit b. poten­
                    <lb/>
                  tia minor aliquam partem c. medii verſus d. pun-
                    <lb/>
                  ctum veniendo quam a. potentia maior pertranſi-
                    <lb/>
                  bit eandem: et a. et b. eaſdem partes c. medii tranſe-
                    <lb/>
                  undo equales latitudines motus deperdunt: vt ſe-
                    <lb/>
                  pe argutum eſt: igitur b. potentia minor verſus
                    <lb/>
                  d. punctum veniendo in infinitum tardius remittet
                    <lb/>
                  motum ſuum quam a. potentia verſus idem d. pun­
                    <lb/>
                  ctum veniendo. </s>
                  <s xml:id="N17ADF" xml:space="preserve">Conſequentia et maior ſuperius ar­
                    <lb/>
                  gute ſunt. </s>
                  <s xml:id="N17AE4" xml:space="preserve">Patet igitur correlarium.
                    <note position="right" xlink:href="note-0077-03a" xlink:label="note-0077-03" xml:id="N17BA1" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N17AEC" xml:space="preserve">¶ Sequitur
                    <lb/>
                  ſecundo /  vbicū aliqua potentia nõ variata me-
                    <lb/>
                  dium inuariatum tranſeundo vniformiter conti-
                    <lb/>
                  nuo remittit motum ſuum ad extremum intenſius
                    <lb/>
                  deueniendo ad gradum vel ad non gradum: ipſa
                    <lb/>
                  ſiue ei equalis idem medium tranſeundo continuo
                    <lb/>
                  ſucceſſiue procedendo ab extremo intenſiori verſus
                    <lb/>
                  extremum remiſſius continuo per eandem lineam
                    <lb/>
                  per quam antea mouebatur remittendo motum ſu­
                    <lb/>
                  um, vniformiter continuo intendit motum ſuum: et
                    <lb/>
                  omnis maior inuariata ab eodem puncto intenſio­
                    <lb/>
                  ri ꝓcedēdo per eandē lineã, per quã ꝓcedit potētia
                    <lb/>
                  intendens motū ſuū vniformiter inuariata diffor-
                    <lb/>
                  miter cõtinuo ītendit motū ſuū: et ſimiliter oīs mi-
                    <lb/>
                  nor habēs ad extremū intenſius eiuſdē medii pro-
                    <lb/>
                  portionē maioris īequalitatis. </s>
                  <s xml:id="N17B0D" xml:space="preserve">Prima pars huiꝰ </s>
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