Alvarus, Thomas, Liber de triplici motu, 1509

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                  <s xml:id="N1B980" xml:space="preserve">
                    <pb chead="De motu quo ad cauſam in medio non reſiſte." file="0120" n="120"/>
                  cõſequentia intelligenti modum procedendi talis
                    <lb/>
                  reſiſtentie: et vltra precedet ipſam: igitur velocius
                    <lb/>
                  mouetur ꝙ̄ potētia: et ſemper antea velocius a. mo-
                    <lb/>
                  uebatur ꝙ̄ modo cum cõtinuo remittat motum ſuū
                    <lb/>
                  ex caſu: et potētia ſemper antea mouebatur tardiꝰ
                    <lb/>
                  ̄ modo: quia cõtinuo precedebat ipſum a. mouen-
                    <lb/>
                  do cum maiori reſiſtētia quã a. non em̄ aliquando
                    <lb/>
                  ſequebatur potentia ipſum a. punctū et poſtea pre-
                    <lb/>
                  ceſſit ipſum a. patet ex quarta ſuppoſitione. </s>
                  <s xml:id="N1B9A0" xml:space="preserve">Nam
                    <lb/>
                  ſemper antea a. velocius mouetur quam potentia:
                    <lb/>
                  igitur ſemper a. precedit potentiam et ſic modo in
                    <lb/>
                  inſtanti dato nõ ſunt ſimul (incipiunt enim ab eodē
                    <lb/>
                  inſtanti et puncto) et ſunt in eodem inſtanti ſimul
                    <lb/>
                  per te: ergo cõtradictio, non eſt igitur dicendum 
                    <lb/>
                  aliquando potentia intendit motum ſuū / qudd fuit
                    <lb/>
                  probandum: patet ergo concluſio.</s>
                </p>
                <p xml:id="N1B9B1">
                  <s xml:id="N1B9B2" xml:space="preserve">Quarta concluſio. </s>
                  <s xml:id="N1B9B5" xml:space="preserve">Ubicun in me-
                    <lb/>
                  dio nõ reſiſtente fit progreſſio latitudinis reſiſten-
                    <lb/>
                  tie vniformiter difformis partibiliter quo ad ſub-
                    <lb/>
                  iectum modo expoſito quolibet puncto eius intrin­
                    <lb/>
                  ſeco cõtinuo vniformiter intendente motum ſuum
                    <lb/>
                  non gradu, aut extremo remiſſiori quieſcente: po-
                    <lb/>
                  tentia ſimul incipiens moueri in eodem inſtanti et
                    <lb/>
                  ab eodem puncto cum tali reſiſtentia continuo in-
                    <lb/>
                  tendit motum ſuum. </s>
                  <s xml:id="N1B9C8" xml:space="preserve">Et ſi pro aliquo inſtanti pro
                    <lb/>
                  quo intendit motum ſuum ad aliquod punctum
                    <lb/>
                  hoc eſt exiſtens in aliquo puncto, poneretur in
                    <lb/>
                  puncto minus reſiſtente illius reſiſtentie. </s>
                  <s xml:id="N1B9D1" xml:space="preserve">Ipſa tar­
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                  dius intenderet motum ſuum. </s>
                  <s xml:id="N1B9D6" xml:space="preserve">Prima pars huius
                    <lb/>
                  cõcluſionis patet ex immediate precedente. </s>
                  <s xml:id="N1B9DB" xml:space="preserve">Et pro-
                    <lb/>
                  batur ſecūda. </s>
                  <s xml:id="N1B9E0" xml:space="preserve">Latitudine reſiſtētie vniformiter dif-
                    <lb/>
                  formis ad nõ gradum terminate procedente / vt po-
                    <lb/>
                  nitur in caſu cõcluſionis. </s>
                  <s xml:id="N1B9E7" xml:space="preserve">Sit b. potentia in aliquo
                    <lb/>
                  inſtanti in c. puncto ſit e. punctus in g. ꝓportione
                    <lb/>
                  remiſſior c. puncto in quo e. puncto b. potentia pro
                    <lb/>
                  eodem inſtanti ponatur. </s>
                  <s xml:id="N1B9F0" xml:space="preserve">Tunc dico /  b. potentia
                    <lb/>
                  tardius intendit motum ſuum ad e. punctum ꝙ̄ ad
                    <lb/>
                  c. </s>
                  <s xml:id="N1B9F7" xml:space="preserve">Quod ſic oſtenditur: quia potentia b. poſita ad
                    <lb/>
                  punctum c. per cõtinuam acquiſitionem minoris re­
                    <lb/>
                  ſiſtentie: citius acquirit aliquam proportionem
                    <lb/>
                  ̄ ipſa poſita ad punctum e. acquirat eandem: igit̄̄
                    <lb/>
                  b. potentia tardius intendit motum ſuum ad e. pū-
                    <lb/>
                  ctum ꝙ̄ ad c. / quod fuit probandum. </s>
                  <s xml:id="N1BA04" xml:space="preserve">Cõſequētia ptꝫ
                    <lb/>
                  ex ſe / et ꝓbatur antecedens quia poſito /  pro eodeꝫ
                    <lb/>
                  inſtanti pro quo b. eſt ad c. punctū potentia ei equa­
                    <lb/>
                  lis ponatur ad punctū e. illa potentia equalis ipſi
                    <lb/>
                  b. tardius aliquam ꝓportionem acquirit ꝙ̄ ſit pro­
                    <lb/>
                  portio quam acquirit ad punctum c.b. potētia / igr̄
                    <lb/>
                  b. potentia poſita ad punctum c. per acquiſitioneꝫ
                    <lb/>
                  minoris reſiſtentie citius acquirit aliquã propor-
                    <lb/>
                  tionem quã ipſa poſita ad punctū e. acquirat ean-
                    <lb/>
                  dem. </s>
                  <s xml:id="N1BA19" xml:space="preserve">Cõſequentia patet: et ꝓbatur antecedens. </s>
                  <s xml:id="N1BA1C" xml:space="preserve">Et
                    <lb/>
                  pono /  cū b. eſt ad punctū c. potentia ei equalis a.
                    <lb/>
                  ponatur ad punctū e. et ſit d. punctus in quo b. potē­
                    <lb/>
                  tia debet acquirere ꝓportionē h. ad quem (vt opor­
                    <lb/>
                  tet) c. punctus habet ꝓportionem h. et ſit f. punctus
                    <lb/>
                  in quo a. potentia debet acquirere eandem ꝓpor-
                    <lb/>
                  tionem h. inter que puncta e. et f. eſt etiam ꝓportio
                    <lb/>
                  h. (vt oportet). </s>
                  <s xml:id="N1BA2D" xml:space="preserve">Et tunc a. potentia tardiꝰ acquirit
                    <lb/>
                  h. ꝓportionem quã b. / igitur ꝓpoſittū. </s>
                  <s xml:id="N1BA32" xml:space="preserve">Probatur.
                    <lb/>
                  </s>
                  <s xml:id="N1BA36" xml:space="preserve">autecedēs q2 f. punctꝰ tardius attinget a. ꝙ̄ d. ipſã
                    <lb/>
                  potentiã b. et in illis pūctis debent a. et b. acquirere
                    <lb/>
                  ꝓportionē h. / ergo tardius acquiret ꝓportionē h.
                    <lb/>
                  ̄ b. / qḋ fuit ꝓbandū. </s>
                  <s xml:id="N1BA3F" xml:space="preserve">Sed iam ꝓbo añs videlicet / 
                    <lb/>
                  tardius f. attinget a. etc̈. quia f. a principio motꝰ in
                    <lb/>
                  g. proportiõe minꝰ diſtat a mobili / quod inſequit̄̄ /
                    <lb/>
                  quã d. diſtet a b. et continuo f. mouetur in g. proportio­
                    <lb/>
                  tione tardius quã d. / et tamen a. nõ mouetur in g. ꝓ-
                    <lb/>
                  portione nec in maiori proportione tardius quã b. /
                    <cb chead="De motu quo ad cauſam in medio non reſiſte."/>
                  igit̄̄ nõ ita cito nec citius f. attinget a. quã d. ipſam
                    <lb/>
                  potētiam b. ſed tardius / quod erat inferendū. </s>
                  <s xml:id="N1BA51" xml:space="preserve">Ptꝫ
                    <lb/>
                  cõſequentia ex tertia ſuppoſitione huiꝰ cū ſuo cor-
                    <lb/>
                  relario (applica vtpotes). </s>
                  <s xml:id="N1BA58" xml:space="preserve">Iam ꝓbo primã parteꝫ
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                  maioris: q2 ſicut ſe habet c. ad d. ita e. ad f. ex caſu:
                    <lb/>
                  igitur permutatim ſicut ſe habet c. ad e. (puta in g.
                    <lb/>
                  proportione ex hypotheſi) ita ſe habet d. ad f. puta
                    <lb/>
                  in g. proportione. </s>
                  <s xml:id="N1BA63" xml:space="preserve">Et vltra c. ad e. eſt g. proportio et
                    <lb/>
                  latitudo eſt vniformiter difformis ad non gradum
                    <lb/>
                  terminata quieſcente nõ gradu: igitur cõtinuo di-
                    <lb/>
                  ſtantie quantitatiue ipſius c. a nõ gradu ad diſtan-
                    <lb/>
                  tiam ipſius e. ab eodem non gradu eſt g. proportio
                    <lb/>
                  </s>
                  <s xml:id="N1BA6F" xml:space="preserve">Patet conſequentia ex prima ſuppoſitione hu-
                    <lb/>
                  ius. </s>
                  <s xml:id="N1BA74" xml:space="preserve">et vltra diſtantie ipſius c. a non gradu ad diſtã­
                    <lb/>
                  tiam ipſius e. etc̈. eſt proportio g. et etiam diſtantie
                    <lb/>
                  ipſius d. ad diſtantiam ipſius f. eadem ratione eſt
                    <lb/>
                  ꝓportio g. / igitur demendo / a diſtantia c. a nõ gra-
                    <lb/>
                  du diſtantiam d. a nõ gradu, et demendo / a diſtãtia
                    <lb/>
                  c. a nõ gradu diſtãtiam f. a nõ gradu que (vt cõſtat)
                    <lb/>
                  ſunt partes aliarū diſtantiarū puta c. et e. a nõ gra­
                    <lb/>
                  du: remanentes diſtantie ſe habent in eadem g. pro­
                    <lb/>
                  proportione, et ſic reſidui diſtantie ipſius c. a non
                    <lb/>
                  gradu ad reſiduū diſtantie ipſius e. a nõ gradu eſt
                    <lb/>
                  g. proportio: ptꝫ cõſequentia ex ſeptimo correlario
                    <lb/>
                  quarte cõcluſionis octaui capitis ſecunde partis.
                    <lb/>
                  </s>
                  <s xml:id="N1BA8E" xml:space="preserve">Sed reſiduū diſtantie ipſius c. a nõ gradu eſt diſtã­
                    <lb/>
                  tia ipſius c. a d. et reſiduum diſtantie ipſius e. a non
                    <lb/>
                  gradu eſt diſtantia ipſius e. ab f. (vt conſtat) / igitur
                    <lb/>
                  diſtãtie ipſius c. a d. ad diſtantiã ipſius e. ab f. eſt g.
                    <lb/>
                  proportio. </s>
                  <s xml:id="N1BA99" xml:space="preserve">Et a principio motus a. eſt in e. et b. in c. /
                    <lb/>
                  igitur f. in g. proportione a principio motus minꝰ
                    <lb/>
                  diſtat ab a. mobili / quod īſequitur / quã d. diſtat ab
                    <lb/>
                  b. / que fuit prima pars maſoris inferenda. </s>
                  <s xml:id="N1BAA2" xml:space="preserve">Sed ꝓ-
                    <lb/>
                  batur ſecunda pars maioris: quia f. punctus in g.
                    <lb/>
                  proportione eſt remiſſior d. puncto (vt ꝓbatum eſt) /
                    <lb/>
                  igitur continuo in g. proportiõe tardius mouetur
                    <lb/>
                  ipſo puncto d. / quod fuit ꝓbandū. </s>
                  <s xml:id="N1BAAD" xml:space="preserve">Patet cõſequē-
                    <lb/>
                  tia ex prima ſuppoſitione huiꝰ / et ſic ptꝫ totū antece­
                    <lb/>
                  dens. </s>
                  <s xml:id="N1BAB4" xml:space="preserve">Et eodē modo ꝓbabis cū latitudo ad gradū
                    <lb/>
                  in vtro extremo terminat̄̄, auxiliãtibꝰ loco a ma-
                    <lb/>
                  iori: et ſecunda ſuppoſitione huius et etiam tertia.
                    <lb/>
                  </s>
                  <s xml:id="N1BABC" xml:space="preserve">Et ſic patet concluſio.</s>
                </p>
                <p xml:id="N1BABF">
                  <s xml:id="N1BAC0" xml:space="preserve">Quīta ↄ̨̨cluſio. </s>
                  <s xml:id="N1BAC3" xml:space="preserve">Data potētia intēdēte
                    <lb/>
                  motū ſuū modo dicto ad aliquē gradū reſiſtētie in
                    <lb/>
                  latitudine / vt diximus mota: oīs potentia maior q̄
                    <lb/>
                  ad eūdem punctū intederet motū ſuū, tardiꝰ intēde­
                    <lb/>
                  ret. </s>
                  <s xml:id="N1BACE" xml:space="preserve">Et oīs minor velocius.
                    <note position="right" xlink:href="note-0120-01a" xlink:label="note-0120-01" xml:id="N1BB6C" xml:space="preserve">7. cõclu.
                      <lb/>
                    Calcu.</note>
                  </s>
                  <s xml:id="N1BAD6" xml:space="preserve">Hec eſt ſeptīa cal. quã ſic
                    <lb/>
                  ꝓbo primo quo ad primã partē: q2 data aliqua po­
                    <lb/>
                  tentia q̄ ad aliquē gradū intēdit motū ſuū ꝑ acqui­
                    <lb/>
                  ſitionē minoris reſiſtētie. </s>
                  <s xml:id="N1BADF" xml:space="preserve">oīs maior ad eundē pun-
                    <lb/>
                  ctū intēdens motū ſuū tardiꝰ illã minorē reſiſtētiã
                    <lb/>
                  acquiret cõtinuo: igit̄̄ oīs maior tardiꝰ ibi intēde-
                    <lb/>
                  ret motū ſuū. </s>
                  <s xml:id="N1BAE8" xml:space="preserve">Ptꝫ ↄ̨ña / q2 nõ aliter ibi aliq̈ potētia
                    <lb/>
                  intēdit motū ſuū ꝙ̄ ꝑ cõtinuã minoris reſiſtētie ac-
                    <lb/>
                  quiſitionē: vt patet: añs tñ ꝓbatur: quia oīs maior
                    <lb/>
                  velocius mouet̄̄ recedendo a tali reſiſtētia et īcipiūt
                    <lb/>
                  ab eodē pūcto ī eodē īſtãti: igit̄̄ illa reſiſtētia tardiꝰ
                    <lb/>
                  attīget illã maiorē potentiã ꝙ̄ minorē: et ꝑ ↄ̨ñs tar-
                    <lb/>
                  dius illa potentia maior acquiret illã minorē reſi-
                    <lb/>
                  ſtentiã / qḋ fuit ꝓbandū. </s>
                  <s xml:id="N1BAF9" xml:space="preserve">Et eadē oīno eſt ꝓbatio ſe-
                    <lb/>
                  cūde partis: qm̄ minor citius acquirit minorē reſi-
                    <lb/>
                  ſtentiã quã maior acq̇rat eandē / ptꝫ ergo concluſio.
                    <lb/>
                    <note position="right" xlink:href="note-0120-02a" xlink:label="note-0120-02" xml:id="N1BB74" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N1BB07" xml:space="preserve">¶ Ex hac cõcluſiõe ſeq̇t̄̄ ṗmo /  latitudīe ſic mota / vt
                    <lb/>
                  dictū eſt: quocū gradu illiꝰ dato, dabit̄̄ vna poña
                    <lb/>
                  q̄ ita tarde ſufficit ibi intendere motū ſuū,  nulla
                    <lb/>
                  alia poteſt ita tarde intendere ſtante caſu. </s>
                  <s xml:id="N1BB10" xml:space="preserve">latitu-
                    <lb/>
                  dine ſic mota. </s>
                  <s xml:id="N1BB15" xml:space="preserve">Probatur / q2 ad oēm reſiſtentiã fini­
                    <lb/>
                  tã quãlibet ꝓportionē maioris īeq̈litatꝪ hꝫ aliqua
                    <lb/>
                  poña (vt patet ex ſe) / igr̄ nulla eſt dabilis reſiſtentia </s>
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