Alvarus, Thomas, Liber de triplici motu, 1509

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              <div xml:id="N19642" level="4" n="10" type="chapter" type-free="capitulum">
                <p xml:id="N19669">
                  <s xml:id="N19697" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0097" n="97"/>
                  remiſſioris medietatis vt cõſtat: igitur per equaleꝫ
                    <lb/>
                  latitudinem diſtat ab vtra: et per conſequens per
                    <lb/>
                  quantum excedit extremū remiſſius medietatis re­
                    <lb/>
                  miſſioris cuius eſt extremuꝫ intenſiua, per tantum
                    <lb/>
                  exceditur ab extremo intenſiori intenſioris medie-
                    <lb/>
                  tatis cuiꝰ medietatis eſt extremū remiſſius. </s>
                  <s xml:id="N196AD" xml:space="preserve">Patet
                    <lb/>
                  hec cõſequentia ex vltima ſuppoſitione ſecūdi capi­
                    <lb/>
                  tis ſecūde partis. </s>
                  <s xml:id="N196B4" xml:space="preserve">Itē captis tribus tertiis per tan­
                    <lb/>
                  tum extremū intenſius remiſſioris tertie excedit ex­
                    <lb/>
                  tremū remiſſius eiuſdē tertie, per quantuꝫ extremū
                    <lb/>
                  intenſius tertie īmediate ſequētis excedit extremū
                    <lb/>
                  remiſſius eiuſdem tertie: et per quantum extremum
                    <lb/>
                  intenſius vltime tertie excedit extremum remiſſius
                    <lb/>
                  eiuſdem. </s>
                  <s xml:id="N196C3" xml:space="preserve">Quod probatur ſic / quia extremū intenſiꝰ
                    <lb/>
                  tertie remiſſioris eſt gradus medius inter extremū
                    <lb/>
                  intenſius tertie īmediate ſequentis et extremum re-
                    <lb/>
                  miſſius remiſſioris tertie: igitur equali latitudine
                    <lb/>
                  diſtat ab extremo intenſiori tertie īmediate ſequē-
                    <lb/>
                  tis et ab extremo remiſſiori tertie remiſſioris: et per
                    <lb/>
                  cõſequens ille gradus medius per equalem latitu-
                    <lb/>
                  dinem excedit extremū remiſſius tertie remiſſioris
                    <lb/>
                  cuiꝰ eſt extremū intenſius ſicut exceditur ab extre-
                    <lb/>
                  mo intenſiori tertie īmediate ſequentis cuiꝰ eſt ex-
                    <lb/>
                  tremū remiſſius. </s>
                  <s xml:id="N196DA" xml:space="preserve">Et iſto modo ꝓbabis /  extremuꝫ
                    <lb/>
                  intenſius ſecunde tertie per equalem latitudinem
                    <lb/>
                  excedit extremū remiſſius eiuſdem tertie: ſicut extre­
                    <lb/>
                  mū intenſius vltime tertie īmediate ſequentis exce­
                    <lb/>
                  dit ſuū extremum remiſſius. </s>
                  <s xml:id="N196E5" xml:space="preserve">Et ſic habebis /  per
                    <lb/>
                  equalem latitudinem cuiuſlibet illarum tertiarum
                    <lb/>
                  extremum intenſius excedit extremum remiſſius
                    <lb/>
                  eiuſdem. </s>
                  <s xml:id="N196EE" xml:space="preserve">Item captis duabus partibus equalibus
                    <lb/>
                  ſiue tribus, ſiue quattuor que nõ ſunt pars aut par­
                    <lb/>
                  tes aliquote: cuiuſlibet illarū extremū intēſius per
                    <lb/>
                  equalem latitudinē excedit ſuū extremū remiſſius.
                    <lb/>
                  </s>
                  <s xml:id="N196F8" xml:space="preserve">Quod ſic probatur / q2 captis duabus illarū īme-
                    <lb/>
                  diatis extremū intēſius remiſſioris partis eſt gra-
                    <lb/>
                  dus medius inter extremū intenſius intēſioris par­
                    <lb/>
                  tis et extremū remiſſius remiſſioris illarum: igitur
                    <lb/>
                  per equalem latitudinem diſtat ab extremo inten-
                    <lb/>
                  ſiori intēſioris partis et ab extremo remiſſiori par­
                    <lb/>
                  tis remiſſioris: et per conſequēs ille gradus mediꝰ
                    <lb/>
                  per equalem latitudinē excedit extremū remiſſius
                    <lb/>
                  remiſſioris partis illarum cuiꝰ eſt extremū intenſi­
                    <lb/>
                  us: et exceditur ab extremo intenſiori partis inten-
                    <lb/>
                  ſioris cuiꝰ eſt extremū remiſſius. </s>
                  <s xml:id="N1970F" xml:space="preserve">Et iſto modo pro-
                    <lb/>
                  babis ſignatis tribus /  per equalē latitudinē ex-
                    <lb/>
                  tremū intenſius tertie excedit ſuū extremū remiſſiꝰ
                    <lb/>
                  et extremū intenſius ſecunde excedit ſuū extremum
                    <lb/>
                  remiſſius. </s>
                  <s xml:id="N1971A" xml:space="preserve">Et ſic habebis /  cuiuſlibet illarū trium
                    <lb/>
                  partiū extremū intenſius per equalem latitudineꝫ
                    <lb/>
                  excedit extremū remiſſius. </s>
                  <s xml:id="N19721" xml:space="preserve">Et ſic in omnibus aliis
                    <lb/>
                  partibus equalibꝰ operaberis. </s>
                  <s xml:id="N19726" xml:space="preserve">Patet igitur ſup-
                    <lb/>
                  poſitio.
                    <note position="left" xlink:href="note-0097-01a" xlink:label="note-0097-01" xml:id="N19780" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N19730" xml:space="preserve">¶ Ex quo ſequitur /  oīs potentia latitudi­
                    <lb/>
                  nem vniformiter difformē īuariatam pertranſiēs:
                    <lb/>
                  equales partes tranſeundo incipiēdo ab extremo
                    <lb/>
                  remiſſiori equalem latitudinē reſiſtentie adequate
                    <lb/>
                  acquirit. </s>
                  <s xml:id="N1973B" xml:space="preserve">Probatur / q2 talis potentia tranſeundo
                    <lb/>
                  aliquam partē adequate, acquirendo reſiſtentiam
                    <lb/>
                  illã reſiſtentiã adequate acquirit per quã extremū
                    <lb/>
                  intenſius illius partis excedit extremum remiſſius
                    <lb/>
                  eiuſdem partis / vt ſatis conſtat: et cuiuſlibet partis
                    <lb/>
                  equalis (ex precedenti ſuppoſitione) extremū inten­
                    <lb/>
                  ſius per equalem latitudinem excedit extremum re­
                    <lb/>
                  miſſius: igitur talis potentia latitudinem reſiſten­
                    <lb/>
                  tie vniformiter difformem inuariatam pertranſi-
                    <lb/>
                  ens: equalem latitudinem reſiſtentie adequate ac-
                    <lb/>
                  quirit. </s>
                  <s xml:id="N19752" xml:space="preserve">Et ſic ptꝫ correlarium.
                    <note position="left" xlink:href="note-0097-02a" xlink:label="note-0097-02" xml:id="N19786" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N1975A" xml:space="preserve">¶ Sequitur ſecundo /
                    <lb/>
                   omnis potentia latitudinem reſiſteutie vniformi­
                    <lb/>
                  ter difformē īuariatã pertranſiens incipiendo ab
                    <cb chead="Capitulū decimū."/>
                  extremo intēſiori, equales partes tranſeūdo, equa­
                    <lb/>
                  lem latitudinē reſiſtentie adequate deperdit. </s>
                  <s xml:id="N19766" xml:space="preserve">Ptꝫ /
                    <lb/>
                  quia incipiēdo ab extremo remiſſiori, equales par­
                    <lb/>
                  tes tranſeundo equalem latitudinē reſiſtentie ade-
                    <lb/>
                  quate acquirit / vt ptꝫ ex precedenti correlario: igit̄̄
                    <lb/>
                  incipiendo ab extremo intenſiori, equales partes
                    <lb/>
                  tranſeundo equalem latitudinē reſiſteutie adequa­
                    <lb/>
                  te deperdit: quia in eiſdem partibus eandem lati-
                    <lb/>
                  tudinem reſiſtentie adequate deperdit quaꝫ antea
                    <lb/>
                  in eiſdem acquirebat. </s>
                  <s xml:id="N19779" xml:space="preserve">Et ſic patet correlarium.</s>
                </p>
                <p xml:id="N1978C">
                  <s xml:id="N1978D" xml:space="preserve">Hoc iacto fundamento ſit prima con-
                    <lb/>
                  cluſio. </s>
                  <s xml:id="N19792" xml:space="preserve">Omnis potentia mouens continuo vnifor-
                    <lb/>
                  miter mediū vniformiter difforme īuariatum tran­
                    <lb/>
                  ſeundo incipiendo ab extremo remiſſiori: continuo
                    <lb/>
                  vniformiter intendit potentiam ſuam, ceteris iuua­
                    <lb/>
                  mentis ac impedimētis deductis. </s>
                  <s xml:id="N1979D" xml:space="preserve">Probatur: ſit c.
                    <lb/>
                  mediū vniformiter difforme quod inuariatū a. po-
                    <lb/>
                  tentia vniformiter continuo mouendo ab f. propor­
                    <lb/>
                  tione pertranſeat ab extremo remiſſiori incipiēdo
                    <lb/>
                  moueatur continuo a. potentia ſecundū propor-
                    <lb/>
                  tionem quam habet ad īmediatem reſiſtentiam, ce­
                    <lb/>
                  teris aliis iuuaminibus et obſtaculis deductis: tūc
                    <lb/>
                  dico /  a. potentia cõtinuo vniformiter intendit po­
                    <lb/>
                  tentiam ſuam. </s>
                  <s xml:id="N197B0" xml:space="preserve">Quod ſic oſtenditur / quia a. poten-
                    <lb/>
                  tia continuo ſe habet in f. proportione ad ſuam re-
                    <lb/>
                  ſiſtentiam. </s>
                  <s xml:id="N197B7" xml:space="preserve">Nam a. potentia continuo ab f. propor­
                    <lb/>
                  tione mouetur ex hypotheſi: et ſua reſiſtentia conti-
                    <lb/>
                  nuo vniformiter creſcit: igitur a. potentia cõtinuo
                    <lb/>
                  vniformiter creſcit: et per conſequens a. potentia cõ­
                    <lb/>
                  tinuo vniformiter intendit potentiam ſuam / quod
                    <lb/>
                  fuit probandum. </s>
                  <s xml:id="N197C4" xml:space="preserve">Patet hec cõſequentia ex proba-
                    <lb/>
                  tione prime ſuppoſitionis octaui capitis huiꝰ tra-
                    <lb/>
                  ctatus / hoc addito /  reſiſtentia eſt terminus minor
                    <lb/>
                  continuo proportionis f. et potentia a. terminꝰ ma-
                    <lb/>
                  ior. </s>
                  <s xml:id="N197CF" xml:space="preserve">Probatur minor / quia a. potentia continuo in
                    <lb/>
                  equalibus partibus temporis equales partes illiꝰ
                    <lb/>
                  reſiſtentie vniformiter difformis pertranſit conti-
                    <lb/>
                  nuo acquirendo reſiſtentiam, quia mouetur conti-
                    <lb/>
                  nuo vniformiter verſus extremū intenſius: et conti-
                    <lb/>
                  nuo equales partes tranſeundo equalem latitudi-
                    <lb/>
                  nem reſiſtentie acquirit / vt ptꝫ ex primo correlario
                    <lb/>
                  ſuppoſitionis: igitur continuo in equalibus parti­
                    <lb/>
                  bus temporis equalem latitudinem reſiſtentie ac-
                    <lb/>
                  quirit: et per conſequens reſiſtentia ipſius a. poten­
                    <lb/>
                  tie vniformiter continuo creſcit / quod fuit proban-
                    <lb/>
                  dum. </s>
                  <s xml:id="N197E8" xml:space="preserve">Et ſic patꝫ concluſio.
                    <note position="right" xlink:href="note-0097-03a" xlink:label="note-0097-03" xml:id="N19843" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N197F0" xml:space="preserve">¶ Ex quo ſequitur /  oīs
                    <lb/>
                  potentia continuo mouens vniformiter, mediū vni­
                    <lb/>
                  formiter difforme inuariatum tranſeundo, incipi-
                    <lb/>
                  endo ab extremo intenſiori: continuo vniformiter
                    <lb/>
                  remittit potentiã ſuã: ceteris aliis deductis. </s>
                  <s xml:id="N197FB" xml:space="preserve">Pro-
                    <lb/>
                  batur: ſit c. medium vt ſupra quod inuariatū a. po-
                    <lb/>
                  tentia vniformiter continuo mouendo ab f. propor­
                    <lb/>
                  tione pertranſeat ab extremo intenſiori incipiēdo /
                    <lb/>
                  tunc dico /  a. potentia continuo vniformiter remit­
                    <lb/>
                  tit potentiam ſuam. </s>
                  <s xml:id="N19808" xml:space="preserve">Quod ſic oſtēditur / quia a. po­
                    <lb/>
                  tentia continuo ſe habet in f. proportione ad ſuam
                    <lb/>
                  reſiſtentiam (cum continuo moueatur ab f. propor-
                    <lb/>
                  tione ex hypotheſi) et ſua reſiſtentia vniformiter cõ­
                    <lb/>
                  tinuo decreſcit ſiue diminuitur: igitur a. potentia
                    <lb/>
                  continuo vniformiter remittit potentiam ſuã. </s>
                  <s xml:id="N19815" xml:space="preserve">Pa­
                    <lb/>
                  tet cõſequentia ex probatione prime ſuppoſitionis
                    <lb/>
                  octaui capitis preallegati. </s>
                  <s xml:id="N1981C" xml:space="preserve">Minor probatur / quia
                    <lb/>
                  a. potentia continuo in equalibus partibus tēpo-
                    <lb/>
                  ris equales partes illius reſiſtētie vniformiter dif-
                    <lb/>
                  formis pertranſit continuo deperdendo reſiſten-
                    <lb/>
                  tiam (cum continuo vniformiter moueatur verſus
                    <lb/>
                  extremū remiſſius ex hypotheſi) et continuo verſus
                    <lb/>
                  extremū remiſſius mouēdo, equales partes tran-
                    <lb/>
                  ſeūdo, equalē latitudinē oīno reſiſtētie deperdit / vt </s>
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