Alvarus, Thomas, Liber de triplici motu, 1509

Table of contents

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            <div xml:id="N1C8AF" level="3" n="2" type="other" type-free="tractatus">
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                  <s xml:id="N1D024" xml:space="preserve">
                    <pb chead="De motu locali quo ad effectum ſubiecto difformi." file="0134" n="134"/>
                  ſe extendit </s>
                  <s xml:id="N1D032" xml:space="preserve">In ea em̄ parte eſt abyſſus multa et huiꝰ
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                  materie laborynthus a capacitate intellectus fini-
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                  ta in extricabilis et incomprehenſibilis: vt ibi vide-
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                  bitur in poſitione variorum caſuum varia mõſtra
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                  et difformitates motuum difformiter difformiū ad
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                  tempus ponentium. </s>
                  <s xml:id="N1D03F" xml:space="preserve">Et poſtremo aliquid quam bre­
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                  uiſſime potero de velocitate motus difformis quo
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                  ad tp̄s et quo ad ſubiectū ſimul et ēt motꝰ mixti deter­
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                  minabo </s>
                  <s xml:id="N1D048" xml:space="preserve">Et ſic trimembris dūtaxat erit huius mate­
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                  rie diſceptatio, et inquiſitio quibus determinatis
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                  abſoluta fere erit.</s>
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              <div xml:id="N1D065" level="4" n="2" type="chapter" type-free="capitulum">
                <head xml:id="N1D06A" xml:space="preserve">Capitulum ſecundum / in quo inueſtiga­
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                tur diſputatiue et per modum queſtionis
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                penes quid attendi habeat motus loca-
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                lis difformis quo ad ſubiectum velocitas</head>
                <p xml:id="N1D073">
                  <s xml:id="N1D074" xml:space="preserve">COnſequenter ad primi puncti
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                  expeditionem accedens </s>
                  <s xml:id="N1D079" xml:space="preserve">Queritur penes
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                  quid tam̄ penes effectum motus diffor-
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                  mis quod ad ſubiectum velocitas attendi habeat:
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                  an videlicet penes lineam deſcriptam a puncto ve­
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                  lociſſime moto: an penes lineam deſcriptam a pun­
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                  cto in quo eſt gradus medius: an penes reductionē
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                  ad vniformitatem.</s>
                </p>
                <note position="left" xml:id="N1D088" xml:space="preserve">opinio
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                hētiſberi</note>
                <p xml:id="N1D08E">
                  <s xml:id="N1D08F" xml:space="preserve">Et arguitur primo /  non debeat attē­
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                  di penes primum / vt opinatur hentiſber in tracta-
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                  tu de motu locali capite primo: quia ſi ſic ſequeret̄̄
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                  pari ratione /  deberet attendi penes punctum tar­
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                  diſſime motum: ſed hoc eſt falſum cum aliquãdo nõ
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                  detur: igitur. </s>
                  <s xml:id="N1D09C" xml:space="preserve">Patet conſequentia / quia non vide-
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                  tur maior ratio de vno ꝙ̄ de altero. </s>
                  <s xml:id="N1D0A1" xml:space="preserve">¶ Dices /  ar-
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                  guens dat rationem dicens /  plerum non datur
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                  punctus tardiſſime motus: et ideo non poterit con-
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                  tinuo velocitas motus penes talem punctū attēdi.</s>
                </p>
                <p xml:id="N1D0AA">
                  <s xml:id="N1D0AB" xml:space="preserve">Sꝫ ↄ̨̨tra q2 etiã vt inferiꝰ videbit̄̄ da-
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                  tur aliquis motus difformis quo ad ſubiectum cu-
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                  ius non datur punctus continuo velociſſime motus /
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                  vt patebit in rota rarefiente: igitur etiam non po-
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                  teſt continuo attendi penes talem punctum: et ſi ta-
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                  lis punctus continuo maneat non tamen linea quã
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                  diſcribit adequate.
                    <note position="left" xlink:href="note-0134-01a" xlink:label="note-0134-01" xml:id="N1D0FE" xml:space="preserve">cõfirma-
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                    tio.</note>
                  </s>
                  <s xml:id="N1D0BF" xml:space="preserve">¶ Et confirmatur / quia tunc ſe­
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                  queretur /  rota vniformiter difformiter mota mo­
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                  ueretur continuo ita velociter ſicut medietas eius
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                  que velocius mouetur: ſed hoc eſt falſum: igitur </s>
                  <s xml:id="N1D0C8" xml:space="preserve">Cõ­
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                  ſequentia patet et falſitas conſequentis oſtenditur /
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                  quoniam cum vtra medietas ſit equalis non va-
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                  let ratio ſufficiens aſſignari quare potius ita velo­
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                  citer mouetur tota rota ſicut medietas vna et non ſi­
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                  cut altera (et volo /  ly ita et ſicut diſtribuat): igitur
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                  ſi ita velociter ſicut vna etiam ſicut et altera vel ſi-
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                  cut neutra. </s>
                  <s xml:id="N1D0D9" xml:space="preserve">¶ Dices /  ideo dicitur moueri ita velo-
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                  citer ſicut medietas eius que velociꝰ mouetur: et nõ
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                  ſicut illa que tardius mouetur:
                    <note position="left" xlink:href="note-0134-02a" xlink:label="note-0134-02" xml:id="N1D106" xml:space="preserve">phūs .2.
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                    de aīa.</note>
                  quia iuxta dictū phi­
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                  loſophi ſecundo de anima dignum eſt vnumquod-
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                   a digniori denominari. </s>
                  <s xml:id="N1D0E9" xml:space="preserve">Tum etiam quia illd qḋ
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                  deſcribitur a medietate / que velocius mouetur de-
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                  ſcribitur a tota rota cathegorematice: et nullū ma-
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                  ius ſpacium a tota rota deſcribitur: ſed quodlibet
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                  minus vſ ad non gradum vel ad certum gradum
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                  </s>
                  <s xml:id="N1D0F5" xml:space="preserve">Non autem ſic eſt de ſpacio deſcripto a medietate
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                  tardius mota.</s>
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                  <s xml:id="N1D10F" xml:space="preserve">Sed contra / quia plerum nõ datur
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                  punctus extremus: vt poſito /  deus corrumpat in
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                  rota omnia puncta extrema. </s>
                  <s xml:id="N1D116" xml:space="preserve">Item etiam nominali­
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                  ſando non datur punctum extremum / quia termini­
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                  ſta omnia talia indiuiſibilia negat: et ſigmentum re­
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                  putat: igitur ſaltem ſecundum viam nominaliū nõ
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                  poteſt ſumi velocitas motus difformis / quo ad ſub­
                    <cb chead="De motu locali quo ad effectum ſubiecto difformi."/>
                  iectum penes lineam a puncto velociſſime moto de­
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                  ſcriptam.
                    <note position="right" xlink:href="note-0134-03a" xlink:label="note-0134-03" xml:id="N1D13C" xml:space="preserve">Dicitur</note>
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                  <s xml:id="N1D12B" xml:space="preserve">¶ Dices /  in tali caſu velocitas illiꝰ mo-
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                  tus debet attendi penes lineam deſcriptam a pun-
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                  cto imaginario poſito in peripheria / hoc eſt tota ro­
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                  ta tantam lineam deſcribit et tam velociter moue-
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                  tur / quam velociter mouetur vnus punctum qui eſſet
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                  in peripheria talis rote.</s>
                </p>
                <p xml:id="N1D142">
                  <s xml:id="N1D143" xml:space="preserve">Sed contra capio vnam rotam / q̄ dif-
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                  formiter mouetur quo ad ſubiectum / et cum incipit
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                  moueri incipiat maiorari per rarefactionem ita 
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                  punctus eius extremus continuo magis ac mgis di­
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                  ſtat a centro ita  in principio totius rote diame-
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                  ter ſit pedalis et in fine bipedalis. </s>
                  <s xml:id="N1D150" xml:space="preserve">quo poſito ſic ar­
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                  guitur velocitas talis motus non poteſt attendi pe­
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                  nes lineam deſcriptam a puncto velociſſime moto:
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                  igitur propoſitum. </s>
                  <s xml:id="N1D159" xml:space="preserve">Arguitur antecedens / quia ta-
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                  lis punctus nullam lineam deſcribit: quod proba-
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                  tur ſic / quia nullam circularem vt notum eſt cū non
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                  redeat ad idem punctum / a quo receſſit ſed ad pun-
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                  ctum in duplo magis diſtans a centro. </s>
                  <s xml:id="N1D164" xml:space="preserve">nec etiam li­
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                  neam rectam aliquam deſcribit: et non videtur quã
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                  aliam lineam deſcribat: igitur non datur ibi linea
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                  deſcripta a tali pnncto penes / quam poſſit veloci-
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                  tas motus illius rote commenſurari
                    <note position="right" xlink:href="note-0134-04a" xlink:label="note-0134-04" xml:id="N1D196" xml:space="preserve">2. confir.</note>
                  </s>
                  <s xml:id="N1D174" xml:space="preserve">¶ Et confirma­
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                  tur / qua illa rota non mouetur ita velociter ſicut pū­
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                  ctus eius extremus mouetur in principio motus / vt
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                  notum eſt / cum maiorem lineam deſcribat per totū
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                  tempus / quam ſi rota maneret īuariata quo ad ma­
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                  gnitudinem, nec tanta velocitate quanta mouetur
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                  in fine motus nec in medio inſtanti motus / quia tūc
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                  hoc eſſet coincidere cum alia opinione que commen­
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                  ſurat penes gradum medium: igitur non videt̄̄ pe-
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                  nes / quid attendi habeat velocitas talis motus. </s>
                  <s xml:id="N1D189" xml:space="preserve">Et
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                  ſic habetur /  non omnis velocitas motus diffor-
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                  mis quo ad ſubiectum attendi habeat penes veloci­
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                  tatem puncti velociſſime moti.</s>
                </p>
                <p xml:id="N1D19C">
                  <s xml:id="N1D19D" xml:space="preserve">Secundo principaliter contra eandē
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                  partem arguitur: quia ſi illud eſſet verum ſequere-
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                  tur hec concluſio /  aliquod mobile continuo vnifor­
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                  miter moueretur et tamen quilibet punctus eius in­
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                  trinſecus continuo intenderet motum ſuuꝫ / ſed hoc
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                  videtur impoſſibile / igitur illud ex quo ſequitur.</s>
                </p>
                <p xml:id="N1D1AA">
                  <s xml:id="N1D1AB" xml:space="preserve">Sequela tamen probatur: et capio vnam rotã quaꝫ
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                  diuido in duas medietates circulares concentricas /
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                  vt patet ſupra in figura et rarefiat continuo vnifor­
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                  miter dum talis rota mouetur circulariṫ medietas
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                  interior verſus circunferentiam condenſando me-
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                  dietatem ſuperiorem verſus circunferentiam quieſ­
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                  centibus continuo punctis circunferentialibus: ita
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                   continuo equaliter diſtant a centro. </s>
                  <s xml:id="N1D1BC" xml:space="preserve">quo poſito il­
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                  la rota continuo vniformiter mouetur / vt notum eſt
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                  ex opinione et tamen quilibet punctus eius intrin-
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                  ſecus continuo intendit motum ſuum (cum con-
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                  tinuo magis ac magis diſtet a centro et ↄ̨tinuo ma­
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                  iorem lineam deſcribat) igitur. </s>
                  <s xml:id="N1D1C9" xml:space="preserve">Poteſt vniuerſali-
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                  ter inferri talis concluſio ſi in tali rota corrumpan­
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                  tur extrema puucta. </s>
                  <s xml:id="N1D1D0" xml:space="preserve">¶ Dices /  hoc non eſt inconue­
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                  niens / vt beue probat argumentum: </s>
                  <s xml:id="N1D1D5" xml:space="preserve">Imo etiã alia
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                  opinio idem tenetur concedere.</s>
                </p>
                <p xml:id="N1D1DA">
                  <s xml:id="N1D1DB" xml:space="preserve">Contra quia tunc pari pacto ſequere-
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                  tur /  aliquod mobile continuo vniformiter moue-
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                  retur: et tamen quilibet punctus eius intrinſecus cõ­
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                  tinuo remitteret motum ſuum: ſed hoc videtur incõ­
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                  ueniēs: igitur </s>
                  <s xml:id="N1D1E6" xml:space="preserve">Sequela probatur caſu poſito /  me­
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                  dietas rote ſuperior rarefiat verſus medietatē in-
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                  tenſiorem eam condenſando punctis extremis q̇e-
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                  ſcentibus / quo poſito facile apparet propoſitum.</s>
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