Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N25905" level="3" n="4" type="other" type-free="tractatus">
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                    <pb chead="Quarti tractatus" file="0282" n="282"/>
                   illorum inducitur gra. ſū. et b. eſt in .f. proportione
                    <lb/>
                  minus ip̄o .a. / ergo equeuelociter continuo per .a. et .b.
                    <lb/>
                  inducitur gradus ſnm. </s>
                  <s xml:id="N2D2A8" xml:space="preserve">Patet conſequentia ex .4.
                    <lb/>
                  propoſitione .2. notabilis (ſemper deduco rarefactio­
                    <lb/>
                  nem et condenſationem).
                    <note position="left" xlink:href="note-0282-01a" xlink:label="note-0282-01" xml:id="N2D2E3" xml:space="preserve">Corre.</note>
                  </s>
                  <s xml:id="N2D2B4" xml:space="preserve">¶ Ex hac concluſione ſequit̄̄ /
                    <lb/>
                   ſi excedente minore in quali. ꝓportio exceſſus quo
                    <lb/>
                  gra. ſū. etc̃. fuerit maior proportione quãtitatis. </s>
                  <s xml:id="N2D2BB" xml:space="preserve">Tūc
                    <lb/>
                  velocius inducitur gra. ſū. per minꝰ ī ea ꝓportione ꝑ
                    <lb/>
                  quam ꝓportio exceſſum excedit proportionem quã­
                    <lb/>
                  titatum: ipſius equali alteratione continuo alteratis
                    <lb/>
                  </s>
                  <s xml:id="N2D2C5" xml:space="preserve">Et ſi proportio quantitatum fuerit minor proportio­
                    <lb/>
                  ne exceſſum alteratione continuo equali: </s>
                  <s xml:id="N2D2CA" xml:space="preserve">Tunc gra.
                    <lb/>
                  ſū. velocius inducitur in maius ꝙ̄ in minus in ea pro­
                    <lb/>
                  portione per quam proportio quantitatum excedit
                    <lb/>
                  proportionem exceſſuum. </s>
                  <s xml:id="N2D2D3" xml:space="preserve">Hoc facile patet ex conclu-
                    <lb/>
                  ſione. </s>
                  <s xml:id="N2D2D8" xml:space="preserve">hoc addito:  quanto diſtantia eſt minor a ſū.
                    <lb/>
                  tanto mediante cõſimili alteratione citius inducitur
                    <lb/>
                  gra. ſum.</s>
                </p>
                <p xml:id="N2D2E9">
                  <s xml:id="N2D2EA" xml:space="preserve">Undecima cõcluſio. </s>
                  <s xml:id="N2D2ED" xml:space="preserve">Si ſint duo vni
                    <lb/>
                  diff. ad ſū. terminata vtro modo inequalia. </s>
                  <s xml:id="N2D2F2" xml:space="preserve">Et ma­
                    <lb/>
                  ius alteratur maiori alteratione ꝙ̄ minus: et propor­
                    <lb/>
                  tio compoſita ex proportione quantitatum et pro-
                    <lb/>
                  portione alterationum excedit proportionē exceſſuū
                    <lb/>
                  </s>
                  <s xml:id="N2D2FC" xml:space="preserve">Tunc in maius velocius inducitur gra ſū. in ea pro-
                    <lb/>
                  portione per quam proportio compoſita ex propor-
                    <lb/>
                  tione quantita. et alterationum excedit proportionē
                    <lb/>
                  exceſſuum. </s>
                  <s xml:id="N2D305" xml:space="preserve">Et ſi eocontra. </s>
                  <s xml:id="N2D308" xml:space="preserve">velocius inducitur gradus
                    <lb/>
                  ſum. in minus ꝙ̄ in maius in proportione per quam
                    <lb/>
                  proportio exceſſuum excedit proportionem compoſi­
                    <lb/>
                  tam ex proportione quantitatum et alterationum.</s>
                </p>
                <p xml:id="N2D311">
                  <s xml:id="N2D312" xml:space="preserve">Hec cum multis aliis que poſſunt conformiter ad pre­
                    <lb/>
                  dicta induci facile oſtendi poteſt ex dictis.</s>
                </p>
                <note position="left" xml:id="N2D317" xml:space="preserve">13. cal.</note>
                <p xml:id="N2D31B">
                  <s xml:id="N2D31C" xml:space="preserve">Duodecima cõcluſio. </s>
                  <s xml:id="N2D31F" xml:space="preserve">Si aliquid ſit
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                  vni. diffor. termina. ad ſū. alteratum latitudine vni.
                    <lb/>
                  diff. extenſa per totum: in nulla proporcione velocius
                    <lb/>
                  aut tardius incipit induci gra. ſū. ꝙ̄ ſi per totum al-
                    <lb/>
                  teraretur tali gradu vniformi quod verſus extremuꝫ
                    <lb/>
                  intenſius ſubiecti procedit et hec eſt .13. cal. </s>
                  <s xml:id="N2D32C" xml:space="preserve">Et hec pa­
                    <lb/>
                  tet ex .2. argumento ante oppo.
                    <note position="left" xlink:href="note-0282-02a" xlink:label="note-0282-02" xml:id="N2D34C" xml:space="preserve">Corre.</note>
                  </s>
                  <s xml:id="N2D336" xml:space="preserve">¶ Ex quo ſequitur / 
                    <lb/>
                  ſi vni diff. terminatum ad ſū. alteretur latitudine vni.
                    <lb/>
                  diff. extremo intenſiori verſus extremuꝫ intenſius ſub­
                    <lb/>
                  iecti:
                    <note position="left" xlink:href="note-0282-03a" xlink:label="note-0282-03" xml:id="N2D352" xml:space="preserve">14. cal.</note>
                  gra. ſū. continuo tardius et tardius inducetur et
                    <lb/>
                  hoc corre. patet ex deductione .2. argumenti ante op-
                    <lb/>
                  po. et eſt .14. cal.</s>
                </p>
                <p xml:id="N2D358">
                  <s xml:id="N2D359" xml:space="preserve">Tridecima concluſio. </s>
                  <s xml:id="N2D35C" xml:space="preserve">a. et .b. ſunt vni
                    <lb/>
                  diffor. ad ſūmum terminata omnino conſimilia: et a.
                    <lb/>
                  alteratur latitudine vni. diffor. terminata in extremo
                    <lb/>
                  remiſſiori ad duo continuo extremo remiſſiori verſꝰ
                    <lb/>
                  extremum remiſſius ſubiecti: </s>
                  <s xml:id="N2D367" xml:space="preserve">Et in qualibet parte ꝓ­
                    <lb/>
                  portionali temporis certa diuiſione data extremum
                    <lb/>
                  intenſius illius alterationis augebitur ad duplum
                    <lb/>
                  deductis aliis motibus. </s>
                  <s xml:id="N2D370" xml:space="preserve">Et .b. continuo alterato per
                    <lb/>
                  totum vt duo. </s>
                  <s xml:id="N2D375" xml:space="preserve">Et tamen .a. et .b. mediantibus illis al-
                    <lb/>
                  terationibus eque cito fient ſumma. </s>
                  <s xml:id="N2D37A" xml:space="preserve">Patet facile / q2
                    <lb/>
                  ſua extrema que continuo ſunt equalia: eque cito fient
                    <lb/>
                  ſumma. </s>
                  <s xml:id="N2D381" xml:space="preserve">Et .a. et .b. non citius fient ſumma ꝙ̄ ſua extre­
                    <lb/>
                  ma remiſſiora nec tardius / igitur propoſitum.</s>
                </p>
                <p xml:id="N2D386">
                  <s xml:id="N2D387" xml:space="preserve">Quartadecima concluſio tangendo
                    <lb/>
                  4. argu. ante oppoſitum. </s>
                  <s xml:id="N2D38C" xml:space="preserve">Si aliquod vnifor. diffor.
                    <lb/>
                  terminatum ad ſummum alteretur per totum vni
                    <lb/>
                  alteratione et continuo rarefiat vniformiter quo
                    <lb/>
                  ad tempus et ſubiectum: inductio gradus ſummi
                    <lb/>
                  continuo vniformiter intenditur. </s>
                  <s xml:id="N2D397" xml:space="preserve">Probatur et ſup­
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                  pono /  cum aliquid in quod inducitur gra. ſum.
                    <lb/>
                  mediante vniformi alteratione per totum extenſa
                    <lb/>
                  rarefit. </s>
                  <s xml:id="N2D3A0" xml:space="preserve">Tunc in quolibet inſtanti ita velox eſt indu­
                    <lb/>
                  ctio gra. ſum. ſicut eſſet ſi immediate poſt illud in-
                    <cb chead="Capitulū quintū."/>
                  ſtans ceſſaret rarefactio. </s>
                  <s xml:id="N2D3A8" xml:space="preserve">Quo ſuppoſito arguitur
                    <lb/>
                  ſic / cõtinuo pars remiſſa vniformiter acquirit quã-
                    <lb/>
                  titatem et efficitur maior vniformiter ex caſu con-
                    <lb/>
                  clu. cū totū rarefiat vniformiter quo ad tēpꝰ et ſub-
                    <lb/>
                  iectum: et ſicut pars remiſſa eſt maior et maior in
                    <lb/>
                  quovis inſtanti: ita inductio gra. ſum. eſt velocior:
                    <lb/>
                  vt facile elicitur ex ſuppoſito. </s>
                  <s xml:id="N2D3B7" xml:space="preserve">Sed ex caſu queuis
                    <lb/>
                  pars continuo vniformiter maioratur: igitur con-
                    <lb/>
                  tinuo inductio gra. ſū vniformiter augetur. </s>
                  <s xml:id="N2D3BE" xml:space="preserve">qnod
                    <lb/>
                  fuit probandum.</s>
                </p>
                <p xml:id="N2D3C3">
                  <s xml:id="N2D3C4" xml:space="preserve">Quintadecima concluſio. </s>
                  <s xml:id="N2D3C7" xml:space="preserve">a. et .b. ſunt
                    <lb/>
                  omnino equalia in quantitate et vniformia eodeꝫ
                    <lb/>
                  gradu omnino per totum. </s>
                  <s xml:id="N2D3CE" xml:space="preserve">Et adequate per equale
                    <lb/>
                  tempus alterantur omnino conſimili latitudine al­
                    <lb/>
                  terationis continuo per equales partes ipſorum.
                    <lb/>
                  a.b. adequate extenſe. </s>
                  <s xml:id="N2D3D7" xml:space="preserve">Et tamen citius inducet̄̄ gra.
                    <lb/>
                  ſum. in .a. vel aliquam eius partem ꝙ̄ in b. vel ali-
                    <lb/>
                  quam eius partem. </s>
                  <s xml:id="N2D3DE" xml:space="preserve">Probatur / ſint a.b calida vt .4.
                    <lb/>
                  per totum vniformiter et inducatur latitudo alte-
                    <lb/>
                  rationis vniformiter difformiter ab .8. vſ ad .4. ī
                    <lb/>
                  a. et in b. partibiliter quo ad ſubiectum et ſit ſemꝑ
                    <lb/>
                  illa latitudo extenſa per equales partes omnino
                    <lb/>
                  ipſorum a.b. quieſcat tamen in ea in vno extremo
                    <lb/>
                  a quo incipit induci illa latitudo punctus vt .8. et
                    <lb/>
                  moueat̄̄ punctus vt .4. econtra vero fiat in .b. </s>
                  <s xml:id="N2D3EF" xml:space="preserve">Quo
                    <lb/>
                  poſito manifeſtum eſt /  ad punctum in quo quieſ-
                    <lb/>
                  cit gra. vt .8. in a. citius deueniet gradus ſum. ̄
                    <lb/>
                  ad aliquod punctum .b. cum nullum punctum ipſiꝰ
                    <lb/>
                  b. continuo alteretur tanto gradu ſicut extremum
                    <lb/>
                  ipſius a. / vt patet ex caſu. </s>
                  <s xml:id="N2D3FC" xml:space="preserve">Nam per nullum tempus
                    <lb/>
                  manet gradus .8. in aliquo puncto ipſius b. quan-
                    <lb/>
                  diu illa alteratio progreditur: ergo citius inducet̄̄
                    <lb/>
                  gra. ſum. in a. vel aliquã partem eius ꝙ̄ in b. vel ali­
                    <lb/>
                  quam partem eius. </s>
                  <s xml:id="N2D407" xml:space="preserve">patet igitur cõcluſio </s>
                  <s xml:id="N2D40A" xml:space="preserve">Plura in
                    <lb/>
                  hac materia ſcriberem niſi vrgeret bibliopola.</s>
                </p>
                <p xml:id="N2D40F">
                  <s xml:id="N2D410" xml:space="preserve">Concluſio reſponſiua ad queſtionem
                    <lb/>
                  patet ex ſecundo notabili</s>
                </p>
                <p xml:id="N2D415">
                  <s xml:id="N2D416" xml:space="preserve">Ad rationem ante oppo. </s>
                  <s xml:id="N2D419" xml:space="preserve">Ad primam
                    <lb/>
                  patet reſponſio ex concluſionibus queſtionis: </s>
                  <s xml:id="N2D41E" xml:space="preserve">Et ſi­
                    <lb/>
                  militer ad confirmationem.</s>
                </p>
                <p xml:id="N2D423">
                  <s xml:id="N2D424" xml:space="preserve">Ad ſecundã rationem reſponſum eſt
                    <lb/>
                  ibi vſ ad replicam ad quam reſpondeno con-
                    <lb/>
                  cedo quod infertur: et nego  illud ſit falſum.</s>
                </p>
                <p xml:id="N2D42B">
                  <s xml:id="N2D42C" xml:space="preserve">Ad tertiam rationem reſponſum eſt
                    <lb/>
                  ibi vſ ad replicam. </s>
                  <s xml:id="N2D431" xml:space="preserve">ad quam reſpõdeo cõcedēdo
                    <lb/>
                  illatum nec illud eſt inconueniens.</s>
                </p>
                <p xml:id="N2D436">
                  <s xml:id="N2D437" xml:space="preserve">Ad quartã rationem ſufficienter re-
                    <lb/>
                  ſpondet .2. notabile. </s>
                  <s xml:id="N2D43C" xml:space="preserve">Ad confirmationem reſpon-
                    <lb/>
                  deo concedendo illatum et ratio eſt quia talis al-
                    <lb/>
                  teratio non extenditur per equalem partem ſubie­
                    <lb/>
                  cti </s>
                  <s xml:id="N2D445" xml:space="preserve">De qua partibili progreſſione alteratiõis vide­
                    <lb/>
                  as cal. in ſcḋo capitulo de inductione gra. ſum. cir­
                    <lb/>
                  ca finem. </s>
                  <s xml:id="N2D44C" xml:space="preserve">Et hec breuiter de inductione gradus ſū-
                    <lb/>
                  mi ad laudem et gloriam dei ſummi </s>
                  <s xml:id="N2D451" xml:space="preserve">Poſt hac aūt
                    <lb/>
                  reliquū erit dicere de alteratione anime ad quali­
                    <lb/>
                  tates ſpirituales quibus ipſa anima intelligit et
                    <lb/>
                  diligit. </s>
                  <s xml:id="N2D45A" xml:space="preserve">demeretur penam et meretur gloriam il-
                    <lb/>
                  lam immarceſſibilem quã nec oculus vidit nec au-
                    <lb/>
                  ris audiuit </s>
                  <s xml:id="N2D461" xml:space="preserve">Ad quam nos perducat ille qui cū pa­
                    <lb/>
                  tre et ſpritu ſancto viuit et regnat per omnia ſecu­
                    <lb/>
                  la ſeculorum </s>
                  <s xml:id="N2D468" xml:space="preserve">Amen.</s>
                </p>
                <p xml:id="N2D46B">
                  <s xml:id="N2D46C" xml:space="preserve">¶ Explicit liber de triplici motu cõpoſitꝰ per Ma­
                    <lb/>
                  giſtrū Aluarū Thomam vlix bonenſem Regentem
                    <lb/>
                  Parrhiſius in Collegio Coquereti. </s>
                  <s xml:id="N2D473" xml:space="preserve">Anno domi-
                    <lb/>
                  ni. 1509. Die Februarii .11.</s>
                </p>
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