Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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                <p xml:id="N1978C">
                  <s xml:id="N1981C" xml:space="preserve">
                    <pb chead="De motu penes cauſã ī medio vniformiṫ difformi īuariato." file="0098" n="98"/>
                  patet ex ſecundo correlario ſuppoſitionis: igitur
                    <lb/>
                  a. potentia continuo in equalibus partibus tēpo-
                    <lb/>
                  ris equalem latitudinem reſiſtentie deperdit: et per
                    <lb/>
                  conſequens reſiſtentia ipſius a. potentie continuo
                    <lb/>
                  vniformiter decreſcit ſiue diminuitur / qḋ fuit pro-
                    <lb/>
                  bandum. </s>
                  <s xml:id="N1983C" xml:space="preserve">Patet igitur correlarium.</s>
                </p>
                <note position="left" xml:id="N19849" xml:space="preserve">Prima
                  <lb/>
                cõcluſio
                  <lb/>
                calcula.</note>
                <p xml:id="N19851">
                  <s xml:id="N19852" xml:space="preserve">Secunda concluſio. </s>
                  <s xml:id="N19855" xml:space="preserve">Oīs potentia a
                    <lb/>
                  non gradu potentie creſcens continuo vniformiter
                    <lb/>
                  tranſeundo medium vniformiter difforme īuaria-
                    <lb/>
                  tum ad non gradū terminatum, incipiendo ab ex-
                    <lb/>
                  tremo remiſſiori: continuo vniformiter mouetur.
                    <lb/>
                  </s>
                  <s xml:id="N19861" xml:space="preserve">Probatur / ſit c. medium vniformiter difforme ad
                    <lb/>
                  non gradum terminatum vt in caſu concluſionis:
                    <lb/>
                  ſit a. potentia que a nõ gradu potentie continuo
                    <lb/>
                  vniformiter creſcens c. medium in d. tempore ade-
                    <lb/>
                  quate pertranſit, ab extremo remiſſiori incipiēdo
                    <lb/>
                  moueatur continuo ſecundum proportionem po­
                    <lb/>
                  tentie ad reſiſtentiam ſibi īmediatam ceteris dedu­
                    <lb/>
                  ctis: ſit etiam b. potentia que in eodem d. tēpore
                    <lb/>
                  adequate continuo vniformiter mouendo per ſui
                    <lb/>
                  variationem pertranſeat idem c. medium ab extre­
                    <lb/>
                  mo remiſſiori incipiendo: et manifeſtum eſt ex con-
                    <lb/>
                  cluſione precedenti b. potentiam a non gradu po-
                    <lb/>
                  tentie continuo vniformiter intendere potentiã ſuã
                    <lb/>
                  </s>
                  <s xml:id="N1987D" xml:space="preserve">Dico igitur tunc /  a. potentia continuo vniformi-
                    <lb/>
                  ter mouetur c. medium tranſeundo. </s>
                  <s xml:id="N19882" xml:space="preserve">Quod ſic oſten­
                    <lb/>
                  ditur / quia a. et b. continuo eque velociter mouētur
                    <lb/>
                  oīno: et b. cõtinuo vniformiter mouetur tranſeundo
                    <lb/>
                  c. mediū / quod etiam pertranſit a. / vt patet ex hypo-
                    <lb/>
                  theſi: igitur a. potentia continuo vniformiter mo-
                    <lb/>
                  uetur c. medium tranſeundo / quod fuit probandum
                    <lb/>
                  </s>
                  <s xml:id="N19890" xml:space="preserve">Cõſequentia ptꝫ cum minore: et arguitur maior / q2
                    <lb/>
                  a. et b. potentie cõtinuo ſunt in eodem puncto c. me­
                    <lb/>
                  dii: igitur cõtinuo eque velociter mouētur omnino
                    <lb/>
                  </s>
                  <s xml:id="N19898" xml:space="preserve">Cõſequentia ptꝫ: et probatur antecedens / quia ſi nõ
                    <lb/>
                  detur inſtans in quo a. ſit in pūcto citeriori, aut vl-
                    <lb/>
                  teriori: et ſit e. / et arguitur ſic / in e. inſtanti d. tēporis
                    <lb/>
                  a. eſt in puncto citeriori vel vlteriori ipſius c. medii
                    <lb/>
                  quam b. et a. et b. cõtinuo ſunt equalis potentie: igit̄̄
                    <lb/>
                  nõ eque cito pertranſibūt c. medium / quod eſt cõtra
                    <lb/>
                  hypotheſim. </s>
                  <s xml:id="N198A7" xml:space="preserve">Patet cõſequentia / q2 ſi a. eſt in pūcto
                    <lb/>
                  vlteriori: et cõtinuo eſt equalis b. / ſequitur /  citius
                    <lb/>
                  deueniet ad terminum c. medii quam b. et ſi in cite-
                    <lb/>
                  riori et cõtinuo eſt equalis ipſi b. / ſequitur /  tardiꝰ
                    <lb/>
                  deueniet ad terminū c. medii. </s>
                  <s xml:id="N198B2" xml:space="preserve">Alias eadem potētia
                    <lb/>
                  vel equalis eque cito abſolueret totam reſiſtētiam
                    <lb/>
                  et partem eius adequate / quod eſt impoſſibile dedu­
                    <lb/>
                  ctis litigioſis captiūculis. </s>
                  <s xml:id="N198BB" xml:space="preserve">Sed tã probo illas po-
                    <lb/>
                  tentias continuo eſſe equales / q2 detur oppoſitum
                    <lb/>
                  videlicet /  aliquãdo altera illarum ſit altera ma-
                    <lb/>
                  ior: et ſequitur cum cõtinuo vniformiter creſcant in
                    <lb/>
                  eodem tempore a nõ gradu potētie /  ipſa cõtinuo
                    <lb/>
                  erit maior: et per cõſequēs citius abſoluet c. mediū
                    <lb/>
                  quam altera / quod eſt contra hypotheſim. </s>
                  <s xml:id="N198CA" xml:space="preserve">Patet
                    <lb/>
                  cõſequentia / quia potentia continuo maior maius
                    <lb/>
                  ſpacium pertranſit in eodem tēpore quam poten-
                    <lb/>
                  tia in eodē tēpore continuo minor ea.
                    <note position="left" xlink:href="note-0098-01a" xlink:label="note-0098-01" xml:id="N19952" xml:space="preserve">Contra
                      <lb/>
                    calcula-
                      <lb/>
                    torē.</note>
                  </s>
                  <s xml:id="N198D8" xml:space="preserve">¶ Et ſic patet
                    <lb/>
                  concluſio / que eſt prima calculatoris in ſecūdo eius
                    <lb/>
                  capite de medio non reſiſtente quam aliter nititur
                    <lb/>
                  demonſtrare: ſed ſaluo meliori iudicio demonſtra­
                    <lb/>
                  tio eſt inefficax. </s>
                  <s xml:id="N198E3" xml:space="preserve">Innititur em̄ huic cõſequentie per
                    <lb/>
                  nullū tēpus terminatū ad principiū a. intendit mo­
                    <lb/>
                  tum ſuū nec remittit: ergo a. nun̄ intendit motum
                    <lb/>
                  ſuū aut remittit. </s>
                  <s xml:id="N198EC" xml:space="preserve">Modo illa cõſequētia nõ eſt bona
                    <lb/>
                  </s>
                  <s xml:id="N198F0" xml:space="preserve">Stat em̄ /  a. potentia per nullū tēpus terminatuꝫ
                    <lb/>
                  ad inſtans initiatiuū intendat aut remittat motuꝫ
                    <lb/>
                  ſuū: et tamen per aliquod tēpus nõ terminatum ad
                    <lb/>
                  principium tēporis intēdat aut remittat motū ſuū
                    <cb chead="De motu penes cauſã ī medio vniformiṫ difformi īuariato."/>
                  </s>
                  <s xml:id="N198FC" xml:space="preserve">Diuiſa em̄ hora per partes proportionales mino­
                    <lb/>
                  ribus verſus inſtans initiatiuū motus terminatis
                    <lb/>
                  a. potentia in qualibet impari intendente motum:
                    <lb/>
                  et in qualibet pari remittente: tunc per nullū tēpus
                    <lb/>
                  terminatum ad principium intendit motum ſuum:
                    <lb/>
                  nec per aliquod tale remittit: et tamen intendit mo­
                    <lb/>
                  tuꝫ ſuū: et remittit per aliquod tēpus nõ terminatū
                    <lb/>
                  ad principium temporis. </s>
                  <s xml:id="N1990D" xml:space="preserve">Et hoc forte nare ſagaci­
                    <lb/>
                  ol faciens calculator adiecit ſecundam probationē
                    <lb/>
                  aſſumens /  a. potentia per nullum tempus inten-
                    <lb/>
                  dit motum ſuū nec remittit: ita arguens: quia ſi ſic
                    <lb/>
                  ſit illud inſtans c. in quo incipit iutendere motum
                    <lb/>
                  ſuū aut remittere: et ſit f. proportio ex qua cõtinuo
                    <lb/>
                  vniformiter mouebitur ante c. / et ſequitur /  conti-
                    <lb/>
                  nuo ante in f. proportione tardius creſcit reſiſtētia
                    <lb/>
                  ̄ eius potentia .etc̈. </s>
                  <s xml:id="N19920" xml:space="preserve">In qua probatione calculator
                    <lb/>
                  duo aſſumit dubia et probãda que aduerſarius de­
                    <lb/>
                  monſtrationem vndiqua certam et inuiolabilem
                    <lb/>
                  efflagitans negaret. </s>
                  <s xml:id="N19929" xml:space="preserve">Aſſumit em̄ primo pro certo et
                    <lb/>
                  manifeſto /  aliquod eſt inſtans intrinſecum tēpo-
                    <lb/>
                  ris in quo primo incipit intendere motum ſuū aut
                    <lb/>
                  in quo primo incipit remittere motum ſuum ita 
                    <lb/>
                  nun̄ antea remittit nec intendit motum ſuum. </s>
                  <s xml:id="N19934" xml:space="preserve">Ad
                    <lb/>
                  amuſſim vero omnia dubitabilia ſibi demonſtrari
                    <lb/>
                  expetens diceret nullum tale eſſe inſtans: ſicut con-
                    <lb/>
                  tingeret cum in qualibet parte pari intenderet in
                    <lb/>
                  qualibet vero impari remitteret / vt dictum eſt. </s>
                  <s xml:id="N1993F" xml:space="preserve">Se-
                    <lb/>
                  cundo aſſumit /  ante illud c. inſtans intrinſecū a.
                    <lb/>
                  potentia mouetur vniformiter / quod eſt probandū
                    <lb/>
                  </s>
                  <s xml:id="N19947" xml:space="preserve">Et ſic ptꝫ modum illum probandi predictam con-
                    <lb/>
                  cluſionem inefficacem eſſe qui et ſi ſcientiam nõ ge-
                    <lb/>
                  neret magnam tamen fidem facit.</s>
                </p>
                <p xml:id="N1995C">
                  <s xml:id="N1995D" xml:space="preserve">Tertia cõcluſio. </s>
                  <s xml:id="N19960" xml:space="preserve">Si potentia que mo­
                    <lb/>
                  uetur vniformiter cõtinuo medium vniformiter
                    <lb/>
                  difforme īuariatum et ad nõ gradum terminatum
                    <lb/>
                  incipiendo ab extremo remiſſiori: et cõtinuo creſcē-
                    <lb/>
                  do vniformiter quouſ deueniat ad extremū intē-
                    <lb/>
                  ſius: et deīde retrograde moueatur verſus extremū
                    <lb/>
                  remiſſius cõtinuo vniformiter et eque velociter de-
                    <lb/>
                  creſcendo ſicut antea creuit: ipſa continuo vnifor-
                    <lb/>
                  miter mouebitur. </s>
                  <s xml:id="N19973" xml:space="preserve">Probatur / ſit a. potentia que ab
                    <lb/>
                  extremo remiſſiori c. medii vniformiter difformis
                    <lb/>
                  nõ variati et ad nõ gradum terminati incipiendo,
                    <lb/>
                  continuo vniformiter mouetur per continuum ſue
                    <lb/>
                  potentie vniforme crementum, quo ad vſ ad extre­
                    <lb/>
                  mū intenſius ipſius c. medii deueniat / ad quod ha-
                    <lb/>
                  beat proportionē f. a qua antea continuo moueba­
                    <lb/>
                  tur: ſit b. potētia ei equalis que (vt oportet) ad idē
                    <lb/>
                  extremum intenſius habet f. proportionem. </s>
                  <s xml:id="N19986" xml:space="preserve">Uarie-
                    <lb/>
                  tur igitur / ipſa b. potentia taliter continuo ab eodē
                    <lb/>
                  extremo intenſiori verſus remiſſius,  cõtinuo mo­
                    <lb/>
                  ueatur ab f. proportione: et a. ſimul in eodem inſtãti
                    <lb/>
                  incipiat moueri cum b. potentia verſus extremū re­
                    <lb/>
                  miſſius cõtinuo vniformiter et eque velociter remit-
                    <lb/>
                  tendo potentiam ſuam ſicut antea intendebat: ſit
                    <lb/>
                  g. tempus in quo a. antea vniformiter potentiã ſuã
                    <lb/>
                  intendebat totum c. medium adequate tranſeundo
                    <lb/>
                  et h. ſit tempus in quo adequate b. potentia pertrã­
                    <lb/>
                  ſit c. medium. </s>
                  <s xml:id="N1999D" xml:space="preserve">Tunc dico /  a. ſic mouendo continuo
                    <lb/>
                  vniformiter mouetur. </s>
                  <s xml:id="N199A2" xml:space="preserve">Quod ſic oſtēditur / q2 a. et b.
                    <lb/>
                  continuo eque velociter mouētur: et b continuo vni-
                    <lb/>
                  formiter mouet̄̄ ex hypotheſi: ergo a. vniformiṫ mo­
                    <lb/>
                  uetur cõtinuo / qḋ fuit ꝓbandū. </s>
                  <s xml:id="N199AB" xml:space="preserve">Conſequentia ptꝫ cū
                    <lb/>
                  minore: et arguit̄̄ maior / q2 a. et b. poñe cõtinuo ſunt
                    <lb/>
                  in eodē pūcto c. medii: igr̄ a. et b. ↄ̨tinuo eque velociṫ
                    <lb/>
                  mouentur. </s>
                  <s xml:id="N199B4" xml:space="preserve">Conſequentia patet: et probatur antece­
                    <lb/>
                  dens / quia ſi non: detur inſtans in quo a. ſit in pun-
                    <lb/>
                  cto vlteriori vel citeriori quam b. et ſit illud inſtans
                    <lb/>
                  e. / et argr̄ ſic in e. inſtãti a. potētia eſt in puncto vlte- </s>
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