Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N1C8AF" level="3" n="2" type="other" type-free="tractatus">
              <div xml:id="N1DD6A" level="4" n="3" type="chapter" type-free="capitulum">
                <p xml:id="N202A8">
                  <s xml:id="N202BD" xml:space="preserve">
                    <pb chead="Secundi tractatus" file="0167" n="167"/>
                  ciat et ſine tali preſpectione et preſcrutatione nõ po­
                    <lb/>
                  terit ſpacium pertranſitum in totali tempore meti­
                    <lb/>
                  ri: conſequens igitur erit /  in tali caſu nequit certi­
                    <lb/>
                  tudinaliter reſponſionem ferre </s>
                  <s xml:id="N202DB" xml:space="preserve">Et ſic patet ꝓpoſi-
                    <lb/>
                  tio. </s>
                  <s xml:id="N202E0" xml:space="preserve">Credo tamen animas ſeparatas a corpore et in­
                    <lb/>
                  telligentias in imꝑſpecto tempore omīa iſta cogno­
                    <lb/>
                  ſcere </s>
                  <s xml:id="N202E7" xml:space="preserve">Ceſſet / igitur dolor querulantium et non putat
                    <lb/>
                  homo ſua terminus clauſa intelligentia et finita ca­
                    <lb/>
                  pacitate vniuerſalem rerum naturalium amplitu-
                    <lb/>
                  dineꝫ difformes monſtruoſaſ motiones amplecti
                    <lb/>
                  at comprehendere. </s>
                  <s xml:id="N202F2" xml:space="preserve">Hoc enim valde difficile eſt ꝑ-
                    <lb/>
                  inde at infinitam magnitudinem finito loco ꝑſtrī­
                    <lb/>
                  gere
                    <note position="left" xlink:href="note-0167-01a" xlink:label="note-0167-01" xml:id="N203E1" xml:space="preserve">cccleſia-
                      <lb/>
                    ſtes .1. ca.</note>
                  </s>
                  <s xml:id="N202FE" xml:space="preserve">Quare non abs re ſapientiſſimus ille ſalomõ
                    <lb/>
                  rerum naturalium difformes motus animo reuol-
                    <lb/>
                  ueus res naturales quo ad ſui motiones cognitu
                    <lb/>
                  difficiles cenſuit ecclaſiaſtes primo capite inquiēs
                    <lb/>
                  </s>
                  <s xml:id="N20308" xml:space="preserve">Cunte res difficiles: non poteſt eas homo explica­
                    <lb/>
                  re ſermone quare non ſatiatur oculus viſu nec au­
                    <lb/>
                  ris auditu
                    <note position="left" xlink:href="note-0167-02a" xlink:label="note-0167-02" xml:id="N203E9" xml:space="preserve">hugo car­
                      <lb/>
                    di.</note>
                  </s>
                  <s xml:id="N20314" xml:space="preserve">Quam ſententiã pertractans hugo car­
                    <lb/>
                  dinalis inquit explicat ecclaſiaſtes quam in explica­
                    <lb/>
                  bilis ſit rerum naturalium mitabilitas dicēs cun-
                    <lb/>
                  ctas res naturales difficiles eſſe tū ad ītelligendū
                    <lb/>
                  tū ēt ad explicãdū </s>
                  <s xml:id="N2031F" xml:space="preserve">Nec eī nūerari poſſūt mĺtitudīe
                    <lb/>
                  nec ↄ̨p̄hendi quãtitate: nec inueſtigari queunt ꝓfun­
                    <lb/>
                  ditate </s>
                  <s xml:id="N20326" xml:space="preserve">Et ſubdit infirmitati noſtri intellectus cõdo­
                    <lb/>
                  lens. </s>
                  <s xml:id="N2032B" xml:space="preserve">Quantis ergo tenebris homo inuoluit̄̄: quan­
                    <lb/>
                  ta ignorantie cecitate humanus ſenſus coartatur /
                    <lb/>
                  vt vix pauca etiam ſecundum ſuperficiem attinge-
                    <lb/>
                  re poteſt qui ſi ſingula ſecundū exteriorē ſpē3 cerne­
                    <lb/>
                  ret: vim lateutem, naturam inuiſibilem rerū nul-
                    <lb/>
                  latenus penetraret. </s>
                  <s xml:id="N20338" xml:space="preserve">Uniuerſitas igitur rerum om-
                    <lb/>
                  nino hoī incõp̄hēſibilis et m exteriorē ſpē3 ē et m ī­
                    <lb/>
                  terioreꝫ qualitatē </s>
                  <s xml:id="N2033F" xml:space="preserve">Hec ille </s>
                  <s xml:id="N20342" xml:space="preserve">Quare non ſolum in p̄-
                    <lb/>
                  dictis caſibus non valet infallibiliter adequatum
                    <lb/>
                  ſpacium tali velocite difformi pertranſitum inue-
                    <lb/>
                  niri (quãuis de facto ſit aliquod adequatum ſpaci­
                    <lb/>
                  um / quod adequate pertranſitur) verumetiam ī no­
                    <lb/>
                  tioribus aliis caſibus talis ſpacii certitudo cecutiē­
                    <lb/>
                  tibus nobis in hoc ſeculo non valet reperiri: et certi­
                    <lb/>
                  tudinaliter metiri: vt ſi quiſpiam ponat /  partita
                    <lb/>
                  hora per partes ꝓportionales proportione dupla
                    <lb/>
                  mobile in prima parte ꝓportionali aliquantū ve-
                    <lb/>
                  lociter mouatur, et in ſecunda in ſexquialtero velo­
                    <lb/>
                  cius et in tertia in ſexquiquinto et in quarta in ſexq̇­
                    <lb/>
                  octauo ꝙ̄ in prima. / et ſic conſequenter procedendo
                    <lb/>
                  per ſpecies proportionis ſuperparticularis inter
                    <lb/>
                  ſcalariter continuo duos omittendo. </s>
                  <s xml:id="N20361" xml:space="preserve">Item ſi diui-
                    <lb/>
                  ſa hora per partes ꝓportionales ꝓportione tripla
                    <lb/>
                  a. mobile in prima parte proportionali moueatur
                    <lb/>
                  aliquãtulum: et in ſecunda in ſexquiquinto velocius
                    <lb/>
                  et in tertia in ſexquinono velocius ꝙ̄ in prima, et in
                    <lb/>
                  quarta in ſexquitridecimo velocius ꝙ̄ ī prima et in
                    <lb/>
                  quinta in ſexdecimo ſeptimo velocius ꝙ̄ in prima /
                    <lb/>
                  et ſic conſequenter procedendo per ſpecies propor-
                    <lb/>
                  tionis ſuperparticularis continuo omittendo tres
                    <lb/>
                  </s>
                  <s xml:id="N20375" xml:space="preserve">Item ſic procedendo continuo omittendo quatuor
                    <lb/>
                  </s>
                  <s xml:id="N20379" xml:space="preserve">Item omittendo continuo quin et .6. et .7. / et ſic cõ­
                    <lb/>
                  ſequenter: infinite dabuntur velocitates difformes
                    <lb/>
                  quarum vniformitas a nobis nequa̄ naturaliter
                    <lb/>
                  reperiri poteſt. </s>
                  <s xml:id="N20382" xml:space="preserve">Deinde diuiſa hora per partes ꝓ-
                    <lb/>
                  portionales ꝓportione quadrupla. </s>
                  <s xml:id="N20387" xml:space="preserve">et in prima par­
                    <lb/>
                  te ꝓportionali moueatur a. mobile aliquantū velo­
                    <lb/>
                  citer: et in ſecunda in duplo ſexquialtero velocius: et
                    <lb/>
                  in tertia in ſupertripartiente quartas velocius ꝙ̄ ī
                    <lb/>
                  prima: et in quarta in ſexquialtero velocius ꝙ̄ in ṗ­
                    <lb/>
                  ma et in quinta in triplo velocius ꝙ̄ in prima: et ī ſex­
                    <lb/>
                  ta in dupla ſexquiſexto velocius ꝙ̄ in prima / et ſic cõ­
                    <lb/>
                  ſequenter ꝑmiſcendo ſeriatim ſpecies diuerſorum
                    <lb/>
                  generum proportionis. </s>
                  <s xml:id="N2039A" xml:space="preserve">¶ Ex his ſatis facile appa­
                    <cb chead="Capitulum tertium"/>
                  ret multa talia nobis incomprehenſibilia eſſe. </s>
                  <s xml:id="N203A0" xml:space="preserve">Nec
                    <lb/>
                  tamen propterea hec ars reiicienda eſt: quoniã et ſi
                    <lb/>
                  infinita ſint nobis incomprehēſibilia: infinita etiã
                    <lb/>
                  mathematica demonſtratione valent a nobis infal­
                    <lb/>
                  libiliter demonſtrari. </s>
                  <s xml:id="N203AB" xml:space="preserve">puta ea que continuum ordi-
                    <lb/>
                  nem alicuius ꝓportionis obſeruant vt ſuperius di­
                    <lb/>
                  ctum eſt </s>
                  <s xml:id="N203B2" xml:space="preserve">Cetera vero ſicut nullum ordinem ſeruant
                    <lb/>
                  ita nullis regulis ſcientie aſtringi valent
                    <note position="right" xlink:href="note-0167-03a" xlink:label="note-0167-03" xml:id="N203F1" xml:space="preserve">nota.</note>
                  </s>
                  <s xml:id="N203BC" xml:space="preserve">¶Hic ta-
                    <lb/>
                  men vnum aduertendum eſt /  plerun homo arbi­
                    <lb/>
                  trabitur nullam eſſe ſeriem aut ordinem proportio­
                    <lb/>
                  num in aliquo caſu ſibi propoſito: nihilominꝰ ma­
                    <lb/>
                  turius et diutius conſideranti occurret talis ordo.
                    <lb/>
                  </s>
                  <s xml:id="N203C8" xml:space="preserve">ſicut in caſu quarte concluſionis non apparet ali-
                    <lb/>
                  quis ordo alicuius ꝓportionis continue: nihilomi­
                    <lb/>
                  nus ibi reperitur continuo equalitas velocitatū in
                    <lb/>
                  partibus inequalibus.
                    <note position="right" xlink:href="note-0167-04a" xlink:label="note-0167-04" xml:id="N203F7" xml:space="preserve">Queſtio</note>
                  </s>
                  <s xml:id="N203D6" xml:space="preserve">¶ Sed petes / q̇d igitur calcu­
                    <lb/>
                  latori proponenti tales caſus in publica et celebri
                    <lb/>
                  litteraria paleſtra reſpondendum ſit.</s>
                </p>
                <note position="right" xml:id="N203FD" xml:space="preserve">horen.</note>
                <p xml:id="N20401">
                  <s xml:id="N20402" xml:space="preserve">Reſpondeo ponendo / quandam ꝓpo-
                    <lb/>
                  ſitionem quã ponit doctiſſimus ꝓportionū indaga­
                    <lb/>
                  tor magiſter nicholaus horen. </s>
                  <s xml:id="N20409" xml:space="preserve">¶ Ubicun occurrit
                    <lb/>
                  multiplicitas ꝓportionum inṫ quas facile nõ repe­
                    <lb/>
                  ritur proportio cenſendum eſt multas earum irra-
                    <lb/>
                  tionales eſſe ad inuicem, quare et ſpacia pertranſi­
                    <lb/>
                  ta irrationalia eſſe </s>
                  <s xml:id="N20414" xml:space="preserve">Qua propter cuꝫ talis caſus ꝓ­
                    <lb/>
                  ponitur reſpondendum eſt ſpacium pertranſitū in
                    <lb/>
                  tota hora incõmenſurabile eſſe ſpacio pertranſito
                    <lb/>
                  in prima parte ꝓportionali. </s>
                  <s xml:id="N2041D" xml:space="preserve">¶ Sed dices īſtabit ta­
                    <lb/>
                  men totis viribus illiberalis at acerrimus calcu­
                    <lb/>
                  lator: grandia verba trutinando inflata bucca:
                    <lb/>
                  ſupercilio eleuato: rugata fronte: at ore tragi-
                    <lb/>
                  co: rationem ſuam inſolubilem perſonabit, multiſ­
                    <lb/>
                   clamoribus reſpondentem vulgo ſuperatum at­
                    <lb/>
                   deuictum nitetur oſtendere.</s>
                </p>
                <p xml:id="N2042C">
                  <s xml:id="N2042D" xml:space="preserve">Reſpondeo /  in ſimili negocio dupli-
                    <lb/>
                  ci cautela vtendum cenſeo </s>
                  <s xml:id="N20432" xml:space="preserve">¶ Prima pro delubrio et
                    <lb/>
                  ridiculo habeatur argumentum eius tan̄ inutile
                    <lb/>
                  et intelligibile petatur calamus et atramentariū /
                    <lb/>
                  vt ſpecie multiplicationis ceteriſ algoriſmi ſpe-
                    <lb/>
                  ciebꝰ calculari valeat velocitatis ītēſio in caſu ꝑ eū
                    <lb/>
                  poſito. </s>
                  <s xml:id="N2043F" xml:space="preserve">¶ Secunda cautela </s>
                  <s xml:id="N20442" xml:space="preserve">Dicatur breuiter arguē­
                    <lb/>
                  ti /  talis velocitas non poteſt infallibiliter et certi­
                    <lb/>
                  tudinaliter calculari perinde at multe alie diffor­
                    <lb/>
                  mes velocitates non valent naturaliter ad vnifor-
                    <lb/>
                  mitatem reduci. </s>
                  <s xml:id="N2044D" xml:space="preserve">Et ſi clamoribus velit reſponden-
                    <lb/>
                  tem expugnare oppoſitum aſſeuerendo: proponat
                    <lb/>
                  ei reſpondens ſimilem caſum et dicat ei vt certificet
                    <lb/>
                  illi de ſpacio pertranſito adequato mediante tali
                    <lb/>
                  velocitate difformi. </s>
                  <s xml:id="N20458" xml:space="preserve">Et ſi dixerit /  non eſt poſſibile
                    <lb/>
                  naturaliter inuenire velocitatem adequatam in ta­
                    <lb/>
                  li caſu: ſubiungat reſpondens /  nec in ſuo ſimiliter
                    <lb/>
                  pari ratione. </s>
                  <s xml:id="N20461" xml:space="preserve">Si autem dicat opponens ſe nolle ta­
                    <lb/>
                  le ſpacium aſſignare quauis aſſignabile ſit natura­
                    <lb/>
                  liter: hoc idem dicat ei reſpondens.
                    <note position="right" xlink:href="note-0167-05a" xlink:label="note-0167-05" xml:id="N2049F" xml:space="preserve">luce .20.</note>
                  </s>
                  <s xml:id="N2046D" xml:space="preserve">
                    <note position="right" xlink:href="note-0167-06a" xlink:label="note-0167-06" xml:id="N204A5" xml:space="preserve">hebre. 4.</note>
                  </s>
                  <s xml:id="N20475" xml:space="preserve">Et hac cautela
                    <lb/>
                  reſpondendi (ſi fas eſt etiam eam cautelam in ꝓpo­
                    <lb/>
                  ſito appellare) vſus eſt redemptor noſter luce .20.
                    <lb/>
                  cuius oculis omnia nuda et aperta ſūt ad hebreos
                    <lb/>
                  quarto cum interrogantibus principibus ſacerdo­
                    <lb/>
                  tum in qua poteſtate hoc facis: dixit: interrogabo
                    <lb/>
                  vus et ego vnum aliud verbum. </s>
                  <s xml:id="N20484" xml:space="preserve">Reſpondente michi
                    <lb/>
                  baptiſmus iohannis de celo erat an ex hominibus
                    <lb/>
                  qui perplexi in reſponſione ne videlicet in igno-
                    <lb/>
                  miniam aut iram populi inciderent: reſpondebant
                    <lb/>
                  ſe neſcire. </s>
                  <s xml:id="N2048F" xml:space="preserve">Et rurſum ſubiunxit dominus nec ego di­
                    <lb/>
                  cam vobis in qua poteſtate hec facio </s>
                  <s xml:id="N20494" xml:space="preserve">¶ His exactis
                    <lb/>
                  ſecundum noſtri ingenioli capacitatē ſit concluſio
                    <lb/>
                  reſponſiua ad queſtionem.</s>
                </p>
                <p xml:id="N204AB">
                  <s xml:id="N204AC" xml:space="preserve">Oīs motꝰ vniformiter difformis quo </s>
                </p>
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