Alvarus, Thomas, Liber de triplici motu, 1509

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          <div xml:id="N15C17" level="2" n="3" type="other" type-free="pars">
            <div xml:id="N1C8AF" level="3" n="2" type="other" type-free="tractatus">
              <div xml:id="N1C8BC" level="4" n="1" type="chapter" type-free="capitulum">
                <p xml:id="N1CE64">
                  <s xml:id="N1CE79" xml:space="preserve">
                    <pb chead="Secundi tractatus" file="0133" n="133"/>
                  uis talis replica ſit pro concluſione. </s>
                  <s xml:id="N1CE83" xml:space="preserve">Quia tamē in­
                    <lb/>
                  quirit penes quē punctum debeat ibi attendi motꝰ
                    <lb/>
                  illius quadrati / dico /  debet attendi penes punctū
                    <lb/>
                  qui mouetur gradu medio inter gradum octauum
                    <lb/>
                  quo mouetur punctus velociſſime motus illius par­
                    <lb/>
                  tis et gradum quo mouetur punctus tardiſſime mo­
                    <lb/>
                  tus eiuſdem quadrati vbicun talis punctus fue-
                    <lb/>
                  rit: de ſitu enim eius non eſt curandum. </s>
                  <s xml:id="N1CE94" xml:space="preserve">Sed ad vi-
                    <lb/>
                  dendum an tale quadratum moueatur vniformiter
                    <lb/>
                  difformiter oportet aſpicere an in quacū propor­
                    <lb/>
                  tione quilibet punctus eius magis diſtet a centro ī
                    <lb/>
                  ea velociꝰ moueatur. </s>
                  <s xml:id="N1CE9F" xml:space="preserve">Et hoc ſufficit et requiritur ad
                    <lb/>
                  motum vniformiter difformem / vt ibi dictum eſt: et
                    <lb/>
                  quia ſic eſt de illo quadrato. </s>
                  <s xml:id="N1CEA6" xml:space="preserve">Ideo dico illud moue-
                    <lb/>
                  ri vniformiter difformtter. </s>
                  <s xml:id="N1CEAB" xml:space="preserve">¶ Ad ſecundam confir-
                    <lb/>
                  mationem concedo ſequelam / et nego falſitatem cõ-
                    <lb/>
                  ſequentis: et ad probationem dico /  denominatio
                    <lb/>
                  motus non debet attendi penes denominationem
                    <lb/>
                  partium ita  quantocun motus fuerit in maiori
                    <lb/>
                  parte ſubiecti tanto plus denominat. </s>
                  <s xml:id="N1CEB8" xml:space="preserve">vt bene pro-
                    <lb/>
                  bat argumentum / quãuis hoc oporteat in qualita-
                    <lb/>
                  te / vt poſtea dicetur. </s>
                  <s xml:id="N1CEBF" xml:space="preserve">Sed quomodo debeat cogno-
                    <lb/>
                  ſci velocitas talis motus dictum eſt: et poſtea latiꝰ.
                    <lb/>
                  </s>
                  <s xml:id="N1CEC5" xml:space="preserve">dicetur.</s>
                </p>
                <p xml:id="N1CEC8">
                  <s xml:id="N1CEC9" xml:space="preserve">Ad ſecundū argumentū / cum ſua con­
                    <lb/>
                  firmatione dico /  ſunt pro concluſione reſpcnſiua
                    <lb/>
                  quia impugnant definitionem communeꝫ </s>
                  <s xml:id="N1CED0" xml:space="preserve">Dico ta­
                    <lb/>
                  men /  motus celi eſt vniformiṫ difformis / vt poſtea
                    <lb/>
                  dicetur / quia quodlibet punctum eius in ea propor­
                    <lb/>
                  tione in qua plus diſtat a polo proximiori vel eque
                    <lb/>
                  propinquo in ea velocius mouetur </s>
                  <s xml:id="N1CEDB" xml:space="preserve">Dico / eque pro­
                    <lb/>
                  pinquo ꝓpter puncta exiſtentia in equinoctiali: de
                    <lb/>
                  hoc poſtea dicetur. </s>
                  <s xml:id="N1CEE2" xml:space="preserve">¶ Quantū ad confirmationem
                    <lb/>
                  dico /  illud quadratū vniformiter difformiter mo­
                    <lb/>
                  uetur per rarefactionem et ſimiliter illa pars que ſi­
                    <lb/>
                  gnatur in eo. </s>
                  <s xml:id="N1CEEB" xml:space="preserve">Et cum probatur /  non dico /  illa ꝓ­
                    <lb/>
                  batio eſt pro me et contra definitionem quam īpug-
                    <lb/>
                  gno. </s>
                  <s xml:id="N1CEF2" xml:space="preserve">Et hec de dubitatione.
                    <note position="left" xlink:href="note-0133-01a" xlink:label="note-0133-01" xml:id="N1CF13" xml:space="preserve">penes q̇d
                      <lb/>
                    velocitaſ
                      <lb/>
                    penes ef-
                      <lb/>
                    fectū hē-
                      <lb/>
                    at attēdi</note>
                  </s>
                  <s xml:id="N1CEFA" xml:space="preserve">¶ Sed de velocitate
                    <lb/>
                  motꝰ penes effectū eſt difficultas per quid habeat
                    <lb/>
                  attendi </s>
                  <s xml:id="N1CF01" xml:space="preserve">Ideo recitãde ſunt opiniones in hac mate­
                    <lb/>
                  ria cõmuniter occurrentes. </s>
                  <s xml:id="N1CF06" xml:space="preserve">Unde duplex eſt opinio
                    <lb/>
                  cõmunis tam de motu vniformiter difformi quo ad
                    <lb/>
                  tempus quaꝫ de motu vniformiter difformi quo ad
                    <lb/>
                  ſubiecum et quo ad ſubiectum et tempus ſimul.</s>
                </p>
                <p xml:id="N1CF21">
                  <s xml:id="N1CF22" xml:space="preserve">Prima opinio eſt guillermi hentiſbe-
                    <lb/>
                  ri qui dicit /  velocitas motus vniformiter diffor-
                    <lb/>
                  mis quo ad ſubiectū d3 attēdi penes punctū velociſ­
                    <lb/>
                  ſime motuꝫ </s>
                  <s xml:id="N1CF2B" xml:space="preserve">De vniformiter autē difformi quo ad tē­
                    <lb/>
                  pus coincidit cum ſecunda opinione / que dicit /  mo­
                    <lb/>
                  tus vniformiter difformis quo ad tempus debet at­
                    <lb/>
                  tendi penes gradum medium quo ad tempus id eſt
                    <lb/>
                  penes gradum quo mouetur mobile in medio ta-
                    <lb/>
                  lis temporis: et motus vniformiter difformis quo
                    <lb/>
                  ad ſubiectum debet attendi penes gradum mediuꝫ
                    <lb/>
                  totius latitudinis vniformiter difformis. </s>
                  <s xml:id="N1CF3C" xml:space="preserve">Et hec eſt
                    <lb/>
                  communior opinio:</s>
                </p>
                <p xml:id="N1CF41">
                  <s xml:id="N1CF42" xml:space="preserve">¶ Aduertendum tamen /  quando dicimus /  velo­
                    <lb/>
                  citas motus vniformiter difformis debet attēdi pe­
                    <lb/>
                  nes gradum mediuum voluminis dicere /  tale mo­
                    <lb/>
                  bile vniformiter difformiter motum mouetur ade-
                    <lb/>
                  quate ita velociter ſicut mouetur punctus in quo eſt
                    <lb/>
                  gradus medius talis latitudinis </s>
                  <s xml:id="N1CF4F" xml:space="preserve">Et quãdo dicitur /
                    <lb/>
                   motus vniformiter difformis quo ad tempus ve-
                    <lb/>
                  locitas debet attendi penes gradum mediū qui eſt
                    <lb/>
                  in medio temporis volumus dicere /  tam veloci-
                    <lb/>
                  ter mouetur in illo tempore adequate illud mobile:
                    <lb/>
                  ac ſi per totum illud tempus moueretur illo gradu
                    <lb/>
                  quem habet in medio illius temporis.</s>
                </p>
                <cb chead="Capitulum primum"/>
                <p xml:id="N1CF60">
                  <s xml:id="N1CF61" xml:space="preserve">¶ Aduertendum eſt vlterius /  velocitas motꝰ quo
                    <lb/>
                  ad effectum debet attendi penes ſpacium pertranſi­
                    <lb/>
                  tum: ita  quanto ſpacium pertranſitum fuerit ma­
                    <lb/>
                  ius in equali tēpore tanto motus erit velocior. </s>
                  <s xml:id="N1CF6A" xml:space="preserve">Di-
                    <lb/>
                  co tamen /  non debet attendi velocitas motus lo-
                    <lb/>
                  calis penes ſpacium corporale nec penes ſpacium
                    <lb/>
                  ſuperficiale ſed penes ſpacium lineale deſcriptum
                    <lb/>
                  a certo puncto / q2 tunc ſi vnus equus traheret duas
                    <lb/>
                  trabes inequales eque velociter tamen ſequeretur /
                    <lb/>
                   maior velocius moueretur / cum deſcribat maius
                    <lb/>
                  ſpacium corporale et ſuperficiale quam minor: qḋ
                    <lb/>
                  tamen falſum / quia equaliter mouentur cū in vtra-
                    <lb/>
                   punctus medius equale ſpacium deſcribat. </s>
                  <s xml:id="N1CF7F" xml:space="preserve">Et
                    <lb/>
                  ſic etiam dicendum eſt de motu circulari vniformi-
                    <lb/>
                  ter difformi quo ad ſubiectum /  velocitas eius ha­
                    <lb/>
                  bet attendi penes lineam circularem deſcriptam a
                    <lb/>
                  puncto / in quo eſt gradus medius illius latitudinis
                    <lb/>
                  motus vniformiter difformis. </s>
                  <s xml:id="N1CF8C" xml:space="preserve">Uelocitas motꝰ vni­
                    <lb/>
                  formiter difformis quo ad tempus et quo ad ſubie-
                    <lb/>
                  ctum debet attendi penes lineaꝫ deſcriptam a pun­
                    <lb/>
                  cto / in quo eſt medius gradus talis latitudinis. </s>
                  <s xml:id="N1CF95" xml:space="preserve">Et
                    <lb/>
                  ſimiliter dicenduꝫ eſt de motu difformiter difformi
                    <lb/>
                  quo ad tempus. </s>
                  <s xml:id="N1CF9C" xml:space="preserve"> velocitas eius debet attendi penes
                    <lb/>
                  ſpacium pertranſitum in tali tempore: </s>
                  <s xml:id="N1CFA1" xml:space="preserve">Qualiter
                    <lb/>
                  autem quantitas talis ſpacii debeat cognoſci / quia
                    <lb/>
                  ibi eſt huius materie precipua inquiſitio in fequent­
                    <lb/>
                  tibus ſuo loco declarabitur.
                    <note position="right" xlink:href="note-0133-02a" xlink:label="note-0133-02" xml:id="N1D053" xml:space="preserve">.1. correl.</note>
                  </s>
                  <s xml:id="N1CFAF" xml:space="preserve">¶ Ex his tamen īfer-
                    <lb/>
                  tur iſtam conſequentiam non valere. </s>
                  <s xml:id="N1CFB4" xml:space="preserve">Iſta rota vni­
                    <lb/>
                  formiter difformiter mota quo ad ſubiectuꝫ deſcri­
                    <lb/>
                  bit maiorem lineam quam punctus in quo eſt gra-
                    <lb/>
                  dus medius totius latitudinis motus: igitur moue­
                    <lb/>
                  tur velocius quam ille punctus quia antecedens eſt
                    <lb/>
                  verum cum punctus exiſtens in circunferentia ſiue
                    <lb/>
                  peripheria ipſius rote deſcribat maiorem lineam
                    <lb/>
                  quam punctus in quo eſt gradus medius latitudi­
                    <lb/>
                  nis motus et vtra illarum linearum per motuꝫ ro­
                    <lb/>
                  te deſcribitur </s>
                  <s xml:id="N1CFC9" xml:space="preserve">Similiter arguendo de celo dabitur
                    <lb/>
                  antecedens verum et cõſequens falſum / vt aliquali-
                    <lb/>
                  ter viſum eſt et poſtea videbitur.
                    <note position="right" xlink:href="note-0133-03a" xlink:label="note-0133-03" xml:id="N1D059" xml:space="preserve">2. correl.</note>
                  </s>
                  <s xml:id="N1CFD5" xml:space="preserve">¶ Secundo ſequi-
                    <lb/>
                  tur /  iſta conſequentia non valet iſta rota vnifor-
                    <lb/>
                  miter difformiter mouetur quo ad ſubiectum / et ci-
                    <lb/>
                  tius trãſibit lineam circularem equalem linee de-
                    <lb/>
                  ſcripte a puncto / in quo eſt medius gradus latitudi­
                    <lb/>
                  nis quam talis punctus / in quo eſt gradus medius
                    <lb/>
                  latitudinis motus deſcribat ſuam lineam: ergo ro­
                    <lb/>
                  ta citius mouetur quam talis punctus </s>
                  <s xml:id="N1CFE6" xml:space="preserve">Manifeſtū
                    <lb/>
                  eſt enim /  rota ſecundum ſe totam quantocun ꝑ­
                    <lb/>
                  tio tempore moueatur deſcribit talem lineam: pun­
                    <lb/>
                  ctus vero nõ. </s>
                  <s xml:id="N1CFEF" xml:space="preserve">Et ideo dictum eſt /  debet attendi pe­
                    <lb/>
                  nes lineam ab vno puncto continuo deſcriptam de
                    <lb/>
                  quo tamen latius in ſequentibus.
                    <note position="right" xlink:href="note-0133-04a" xlink:label="note-0133-04" xml:id="N1D05F" xml:space="preserve">.3. corre.</note>
                  </s>
                  <s xml:id="N1CFFB" xml:space="preserve">¶ Tertio ſequi-
                    <lb/>
                  tur /  iſta conſequcntia non valet: iſtud lignum ma­
                    <lb/>
                  ius ſpatium pertranſibit quam illud in eodem tem­
                    <lb/>
                  pore: igitur velocius mouebitur in eodem tempore
                    <lb/>
                  </s>
                  <s xml:id="N1D005" xml:space="preserve">Probatur captis / vt iam dictum eſt duobus lignis
                    <lb/>
                  in equalis craſſitudinis et longitudinis / que ab vno
                    <lb/>
                  equo equaliter trahãtur / et manifeſtum eſt /  maius
                    <lb/>
                  ſpacium corporale ſuperficiale et etiam lineale (nõ
                    <lb/>
                  tamen ab eodem puncto continuo deſcriptum) per­
                    <lb/>
                  tranſit quam aliud lignum minus: nihilominus ta­
                    <lb/>
                  men talia ligna equaliter mouentur. </s>
                  <s xml:id="N1D014" xml:space="preserve">¶ Hiis ſuper-
                    <lb/>
                  ficie tenꝰ dictꝪ / vt intelligat̄̄ ordo ꝓcedendi ī hac ma­
                    <lb/>
                  teria. </s>
                  <s xml:id="N1D01B" xml:space="preserve">primo diſceptabo penes / quid habeat atten-
                    <lb/>
                  di velocitas motus difformis qno ab ſubiectū hoc
                    <lb/>
                  eſt tam vniformiter difformis quã difformiter dif-
                    <lb/>
                  formis quo ad ſubiectum. </s>
                  <s xml:id="N1D024" xml:space="preserve">Et ſecundo diſputabo pe­
                    <lb/>
                  nes / quid habeat attendi velocitas motꝰ difformis
                    <lb/>
                  quo ad tempus tam vniformiter difformis ꝙ̄ dif-
                    <lb/>
                  formiter difformis quãtū ingenioli nr̄i capacitas </s>
                </p>
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