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="Inductionis gradꝰ ſūmi ↄ̨̨ſideratio." file="0277" n="277"/>
                <p xml:id="N2C8A3">
                  <s xml:id="N2C8A4" xml:space="preserve">Ad quintam rationem reſpõdent con­
                    <lb/>
                  cluſiones queſtionis. </s>
                  <s xml:id="N2C8A9" xml:space="preserve">Et ſignanter ſecunda et tertia
                    <lb/>
                  et hec de queſtione.</s>
                </p>
              </div>
              <div xml:id="N2C8AE" level="4" n="5" type="chapter" type-free="capitulum">
                <head xml:id="N2C8B3" xml:space="preserve">Capitulum quintum inquirens penes quid
                  <lb/>
                gradus ſummi inductio ſit attendenda.</head>
                <p xml:id="N2C8B8">
                  <s xml:id="N2C8B9" xml:space="preserve">QUeritur quinto. </s>
                  <s xml:id="N2C8BC" xml:space="preserve">Utrum indu­
                    <lb/>
                  ctio gradus ſummi per aliquod ſubiecti
                    <lb/>
                  ſucceſſiue attendi habeat penes velocita­
                    <lb/>
                  tem progreſſionis ſiue partialis acquiſitionis: ita
                    <lb/>
                   quãto talis acquiſitio gradus ſummi fuerit per
                    <lb/>
                  maiorem partem in eodem tempore tanto motus
                    <lb/>
                  inductiõis ſiue ipſa inductio gradus ſummi (quod
                    <lb/>
                  idem eſt) eſt velocior.</s>
                </p>
                <p xml:id="N2C8CD">
                  <s xml:id="N2C8CE" xml:space="preserve">Et arguitur primo  non. </s>
                  <s xml:id="N2C8D1" xml:space="preserve">Quia tunc
                    <lb/>
                  ſequeretur /  velocitas inductiõis gradus ſummi
                    <lb/>
                  attenderetur penes maioritateꝫ ſubiecti per quod
                    <lb/>
                  in eodē tempore inducitur. </s>
                  <s xml:id="N2C8DA" xml:space="preserve">Sed cõſequens eſt falſū /
                    <lb/>
                  igitur illud ex quo ſequitur. </s>
                  <s xml:id="N2C8DF" xml:space="preserve">Sequela patꝫ quoniã
                    <lb/>
                  quanto ſubiectū eſt maius per quod in eodem tem-
                    <lb/>
                  pore inducitur gradus ſummns, tanto progreſſio
                    <lb/>
                  ſiue partialis acq̇ſitio ipſiꝰ gradꝰ ſūmi partibꝰ ſub­
                    <lb/>
                  iecti eſt maior. </s>
                  <s xml:id="N2C8EA" xml:space="preserve">Sꝫ falſitas ↄ̨ñtꝪ ꝓbr̄: q2 tūc ſeq̄ret̄̄ qḋ
                    <lb/>
                  in omne vniformiṫ difforme, ad ſummū terminatū,
                    <lb/>
                  vniformi latitudine alteratiõis per totū alteratuꝫ
                    <lb/>
                  vniformiter induceretur gradꝰ ſūmꝰ. </s>
                  <s xml:id="N2C8F3" xml:space="preserve">Sed cõſequēs
                    <lb/>
                  eſt falſū: igitur illud ex quo ſequitur. </s>
                  <s xml:id="N2C8F8" xml:space="preserve">Sequela pro-
                    <lb/>
                  batur / q2 in ea proportione qua aliquis punctꝰ eſt
                    <lb/>
                  propinquior ſūmo in ea per minorem latitudinem
                    <lb/>
                  diſtat a ſūmo. </s>
                  <s xml:id="N2C901" xml:space="preserve">vt pꝫ ex diffinitione qualitatꝪ vnifor­
                    <lb/>
                  miter difformis. </s>
                  <s xml:id="N2C906" xml:space="preserve">et oīa pūcta eq̄uelociter alterãtur
                    <lb/>
                  ↄ̨tinuo: igitur in ea proportione qua aliquis pun-
                    <lb/>
                  ctus eſt propinquior ſūmo. </s>
                  <s xml:id="N2C90D" xml:space="preserve">in ea citius ad eum ve-
                    <lb/>
                  niet gradus ſummus: et ſic vniformiter inducetur:
                    <lb/>
                  vt patet / quod fuit ꝓbãdū. </s>
                  <s xml:id="N2C914" xml:space="preserve">Sed falſitas conſequen-
                    <lb/>
                  tis probat̄̄: quia tunc ſequeretur /  ſi duo inequa-
                    <lb/>
                  lia quantitatiue vniformiter difformia eadem la-
                    <lb/>
                  titudine omnino ad ſummū terminata eadem lati-
                    <lb/>
                  tudine alterationis vniformi per totum alterentur
                    <lb/>
                  quouſ per totum ſint ſumma: in ea proportione
                    <lb/>
                  qua vnum eſt minus alio quantitatiue in ea tardiꝰ
                    <lb/>
                  in eum inducitur gradus ſummus. </s>
                  <s xml:id="N2C925" xml:space="preserve">Sed conſequēs
                    <lb/>
                  eſt falſu: igitur illud ex quo ſequitur. </s>
                  <s xml:id="N2C92A" xml:space="preserve">Sequela pro­
                    <lb/>
                  batur: et ſit proportio quantitatis maioris ad quã­
                    <lb/>
                  titatē minoreꝫ f. </s>
                  <s xml:id="N2C931" xml:space="preserve">Et arguitur ſic: eque cito illa erūt
                    <lb/>
                  ſumma per totum: quia extrema remiſſiora eque ci­
                    <lb/>
                  to erunt ſumma, cum equaliter diſtent a ſummo, et
                    <lb/>
                  equeuelociter continuo alterentur. </s>
                  <s xml:id="N2C93A" xml:space="preserve">Et nõ citius de-
                    <lb/>
                  ueniet in aliquo illorū gradus ſummꝰ ad extremuꝫ
                    <lb/>
                  remiſſius ꝙ̄ ad oīa puncta intrinſeca: quia vnifor-
                    <lb/>
                  miter inducetur in vtro illorum / vt arguitum eſt:
                    <lb/>
                  igr̄ in f. proportiõe tardius in eodem tempore pro­
                    <lb/>
                  greditur per minus ſubiectū ꝙ̄ per maius: et ꝑ con­
                    <lb/>
                  ſeq̄ns in f. ꝓportiõe tardius inducit̄̄ gradꝰ ſūmꝰ in
                    <lb/>
                  minus ꝙ̄ in maius / quod fuit probandū. </s>
                  <s xml:id="N2C94B" xml:space="preserve">Iã proba­
                    <lb/>
                  tur falſitas ↄ̨ñtis: quia tunc ſequeretur /  ſi ſint
                    <lb/>
                  duo vni. diffor. inequalia quantitatiue ad ſummū
                    <lb/>
                  terminata: et in ea proportione qua vnū eſt minus
                    <lb/>
                  reliquo in eadem extremū eius remiſſius ſit minus
                    <lb/>
                  intenſum: et alterentur per totū equali alteratione
                    <lb/>
                  vniformi. </s>
                  <s xml:id="N2C95A" xml:space="preserve">Tunc gradus ſūmus inducetur in minus
                    <lb/>
                  tardius ꝙ̄ in maius in proportione compoſita ex
                    <lb/>
                  proportione quantitatis maioris ad quãtitatem
                    <lb/>
                  minoris: et intenſionis extremi remiſſioris maioris
                    <lb/>
                  ad intenſionē extremi remiſſioris minoris. </s>
                  <s xml:id="N2C965" xml:space="preserve">ſꝫ conſe­
                    <lb/>
                  quens eſt falſum: igr̄ illud ex quo ſequitur. </s>
                  <s xml:id="N2C96A" xml:space="preserve">Seque-
                    <lb/>
                  la probatur et ſit a. maius et b. minus et proportio
                    <lb/>
                  quãtitatis a. ad quãtitatē b. ſit f. et ſimiliter extremi
                    <lb/>
                  remiſſioris etc̈. </s>
                  <s xml:id="N2C973" xml:space="preserve">Et arguitur ſic / eque cito erit vtrū
                    <cb chead="Inductionis gradꝰ ſūmi ↄ̨̨ſideratio."/>
                  illorū ſummū cū extremo ſuo remiſſiori / vt argutū
                    <lb/>
                  eſt. </s>
                  <s xml:id="N2C97B" xml:space="preserve">Et ſi vtriuſ illorum extrema remiſſiora eſſent
                    <lb/>
                  eque intenſa in f. proportione tardius induceretur
                    <lb/>
                  gradus ſummꝰ in b. ꝙ̄ in a. / vt iam argutuꝫ eſt. </s>
                  <s xml:id="N2C982" xml:space="preserve">Sed
                    <lb/>
                  modo inducetur in b. adhuc in f. proportiõe tardiꝰ
                    <lb/>
                  ̄ tūc qm̄ extremū remiſſiꝰ in f. proportione magis
                    <lb/>
                  diſtat ꝙ̄ a ſūmo tunc ex caſu: igr̄ mõ in f. ꝓportione
                    <lb/>
                  tardius inducitur gradus ſummꝰ in b. ꝙ̄ tunc. </s>
                  <s xml:id="N2C98D" xml:space="preserve">Et iã
                    <lb/>
                  tunc inducebatur in b. in f. proportione tardius ̄
                    <lb/>
                  in a. </s>
                  <s xml:id="N2C994" xml:space="preserve">Ergo modo in duplici proportione f. tardius
                    <lb/>
                  inducitur gradus ſūmꝰ in b. ꝙ̄ in a. </s>
                  <s xml:id="N2C999" xml:space="preserve">Sed falſitas cõ­
                    <lb/>
                  ſequentis. </s>
                  <s xml:id="N2C99E" xml:space="preserve">Patet / quia cõtinuo equales partes in-
                    <lb/>
                  tenſiue ipſius gradus ſummꝰ inducuntur per totū
                    <lb/>
                  b. ſicut per totum a. / vt patet ex caſu: igitur equeue-
                    <lb/>
                  lociter inducitur gra. ſū. in a. ſicut in b. et nõ tardiꝰ.
                    <lb/>
                  </s>
                  <s xml:id="N2C9A8" xml:space="preserve">¶ Et ↄ̨firmat̄̄ / q2 ſi queſtio eſſet vera ſequeret̄̄ /  ſint
                    <lb/>
                  duo inequalia quãtitatīe vni. diffor. ad ſum. termi.
                    <lb/>
                  </s>
                  <s xml:id="N2C9AE" xml:space="preserve">Et qualis eſt proportio quãtitatis vnius ad quan-
                    <lb/>
                  titatē alterius: talis eſt inter exceſſum quo gra. ſū.
                    <lb/>
                  excedit extremū remiſſius maioris ad exceſſuꝫ quo
                    <lb/>
                  excedit extremū remiſſius minorꝪ: alterētur equali
                    <lb/>
                  altera. vniformi per totū. </s>
                  <s xml:id="N2C9B9" xml:space="preserve">In vtrū illorū eque ve-
                    <lb/>
                  lociter inducetur gradus ſūmus. </s>
                  <s xml:id="N2C9BE" xml:space="preserve">quod eſt falſum.
                    <lb/>
                  </s>
                  <s xml:id="N2C9C2" xml:space="preserve">Probatur. </s>
                  <s xml:id="N2C9C5" xml:space="preserve">Et ſit a. maius et b. minus in f. ꝓportio­
                    <lb/>
                  ne: in eadem ꝓportione ꝑ minꝰ diſtet a ſum. </s>
                  <s xml:id="N2C9CA" xml:space="preserve">Et ar­
                    <lb/>
                  guitur ſic. </s>
                  <s xml:id="N2C9CF" xml:space="preserve">Eque cito in vtrun illorū inducetur gra­
                    <lb/>
                  dus ſicut in extrema eorum remiſſiora et etiam vni-
                    <lb/>
                  formiter / vt argutū eſt: ſꝫ in f. ꝓportione citiꝰ īducet̄̄
                    <lb/>
                  ī extremū remiſſi. ipſius b. ꝙ̄ ipſiꝰ a. quia equaliter
                    <lb/>
                  alterantur: et in f. proportione per minus diſtat a
                    <lb/>
                  ſum. extremū b. ꝙ̄ a. / igitur in f. proportione citius
                    <lb/>
                  inducetur gra. ſum. in b. ꝙ̄ a. et b. eſt in f. ꝓportione
                    <lb/>
                  minus ꝙ̄ a: ergo eque velociter īduci. gra. ſum. in b.
                    <lb/>
                  ſicut in a. / qḋ fuit probanduꝫ. </s>
                  <s xml:id="N2C9E2" xml:space="preserve">Sed falſitas cõſequē­
                    <lb/>
                  tis probatur / quia alteratio ad gra. ſū. nõ eſt alud
                    <lb/>
                  ̄ inductio gra. ſum. </s>
                  <s xml:id="N2C9E9" xml:space="preserve">Sed alteratio a. non eſt equa-
                    <lb/>
                  lis alterationi ipſius b. / vt patet ex primo capite
                    <lb/>
                  huius tractatꝰ. </s>
                  <s xml:id="N2C9F0" xml:space="preserve">igit̄̄ inductio gra. ſum. in b. non eſt
                    <lb/>
                  equalis indnctioni gra. ſū. in a. / qḋ eſt oppoſi. ↄ̨ñtis</s>
                </p>
                <p xml:id="N2C9F5">
                  <s xml:id="N2C9F6" xml:space="preserve">Secundo principaliter arguitur ſic.
                    <lb/>
                  </s>
                  <s xml:id="N2C9FA" xml:space="preserve">Si queſtio eſſet vera ſeq̄ret̄̄ /  aliqḋ vni. dif. ad ſū.
                    <lb/>
                  termina. alteretur latitudine vni. dif. extremo intē­
                    <lb/>
                  ſiori ſus extremū intenſius ſubiecti. </s>
                  <s xml:id="N2CA01" xml:space="preserve">Nõ tardius
                    <lb/>
                  incipit induci gradus ſū. ꝙ̄ ſi extremo intenſiori il-
                    <lb/>
                  lius latitudinis vniformiter per totum alteraretur /
                    <lb/>
                  ſꝫ ↄ̨ſequens eſt falſum: igitur illud ex quo ſequitur.
                    <lb/>
                  </s>
                  <s xml:id="N2CA0B" xml:space="preserve">ſeq̄la ꝓbatur. </s>
                  <s xml:id="N2CA0E" xml:space="preserve">Et ſit extremū intenſius alteratiõis
                    <lb/>
                  a. </s>
                  <s xml:id="N2CA13" xml:space="preserve">Et arguit̄̄ ſic / gra. ſū. mediante illa alteratiõe inci­
                    <lb/>
                  pit velocius induci ꝙ̄ ſi quouis alio remiſſiori inci-
                    <lb/>
                  peret induci / igitur non tardius incipit induci ꝙ̄ ſi
                    <lb/>
                  gradu intenſiori illius altera. vnifor. ꝑ totū incipe­
                    <lb/>
                  peret īduci. </s>
                  <s xml:id="N2CA1E" xml:space="preserve">Probat̄̄ añs: quia nullus eſt remiſſior
                    <lb/>
                  gradus ipſo a. quī aliqua pars illius altera. termi­
                    <lb/>
                  nata minor ad ipſum a. ſit illo vt conſtat: igitur me­
                    <lb/>
                  diante illa parte incipit gra. ſum. velociꝰ induci ̄
                    <lb/>
                  ſi quouis gradu remiſſiori ipſo a. inciperet induci.
                    <lb/>
                  </s>
                  <s xml:id="N2CA2A" xml:space="preserve">quod fuit ꝓbandum. </s>
                  <s xml:id="N2CA2D" xml:space="preserve">Sed iam ꝓbat̄̄ falſitas ↄ̨ñtis /
                    <lb/>
                  q2 tūc ſequeretur /  tardius induceretur gra. ſum.
                    <lb/>
                  mediante lati. illa vni. difformi in tale corpus vni.
                    <lb/>
                  diffor. ꝙ̄ ſi induceretur mediante extremo illius re­
                    <lb/>
                  miſſiori vnifor. per totū extenſo. </s>
                  <s xml:id="N2CA38" xml:space="preserve">Sed ↄ̨ñs eſt falſuꝫ /
                    <lb/>
                  quia continuo tale corpus alteratur per totaꝫ par­
                    <lb/>
                  tem remiſſam intenſiori latitudine ꝙ̄ ſi remiſſiori
                    <lb/>
                  gradu illius latitudinis ꝑ totum alteraretur: igit̄̄
                    <lb/>
                  velo. continuo inducetur gra. ſum. mediante illa la­
                    <lb/>
                  ti. ꝙ̄ mediante extremo eius remiſſiori. </s>
                  <s xml:id="N2CA45" xml:space="preserve">quod eſt op­
                    <lb/>
                  poſitum ↄ̨ſequentis. </s>
                  <s xml:id="N2CA4A" xml:space="preserve">Iam ꝓbatur ſequela / quia ſit
                    <lb/>
                  a. tale vni. diffor. alteratū lati. c. vni. diffor. / vt poni­
                    <lb/>
                  tur in caſu argumenti: et ſit b. oīno et cõſimile ꝑ to- </s>
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