Alvarus, Thomas, Liber de triplici motu, 1509

Table of figures

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                  <s xml:id="N1D6A4" xml:space="preserve">
                    <pb chead="De motu locali quo ad effectū ſcḋm ſubiectū difformi." file="0138" n="138"/>
                  quã certam velocitatē et ponere ī equali parte ſicut
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                  fit in reductione qualitatis vniformiter difformis
                    <lb/>
                  vel capiendo ab aliq̈ parte et ponēdo in minori vel
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                  a mīori et ponēdo in maiori. </s>
                  <s xml:id="N1D6B8" xml:space="preserve">Nõ tertiū / q2 tūc facile
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                  reducēdo ad vniformitatē ꝓbaret̄̄ /  velocitas illiꝰ
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                  rote ſit īfinita q2 caperet̄̄ a prima parte ꝓportiõali
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                  vnꝰ g̈dus, et a ſcḋa tm̄, et a tertia tm̄: et poneret̄̄ per
                    <lb/>
                  totã rotã: et ſic eſſet īfinita velocitas. </s>
                  <s xml:id="N1D6C3" xml:space="preserve">Nec ſcḋm / quia
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                  tūc ſeq̄ret̄̄ /  tota velocitas eſſet minor quã vt q̈tu-
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                  or vt ſi velocitas totiꝰ rote poneret̄̄ īmedietate eiꝰ
                    <lb/>
                  et ibi eſſet vniformis vt quatuor: deinde accipiendo
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                  medietatē illiꝰ latitudinis motꝰ reducta ad vnifor-
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                  mitatē puta duos g̈dus. </s>
                  <s xml:id="N1D6D0" xml:space="preserve">et ponēdo eos in alia me-
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                  dietate et ſic tota velocitas maneret vt duo: </s>
                  <s xml:id="N1D6D5" xml:space="preserve">Nec eſt
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                  dicendū primū / q2 diuiſa illa rota in duas partes
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                  cõcentricas quaꝝ vna ſit quarta pars totiꝰ rote, et
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                  reſidua ſus circūferentiã ſit tres quarte / vt pone-
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                  batur in p̄cedēti capite in ſcḋa cõfirmatiõe puta vl­
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                  tima primi argumēti. </s>
                  <s xml:id="N1D6E2" xml:space="preserve">Deinde volo /  ille tres q̈rte
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                  reducant̄̄ ad vniformitatē / et ptꝫ /  erūt vniformis
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                  in motu g̈du ſexto cū totalis motꝰ illiꝰ partis q̄ cõ-
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                  ponit̄̄ ex illis tribꝰ quartis ſit vniformiter diffor-
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                  mis a quarto vſ ad octauū: et volo etiã /  reducat̄̄
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                  alia pars ꝓpe centū ad vniformitatē: et manifeſtū
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                  eſt /  erit vt duo motꝰ eiꝰ: cū ſit vniformiter diffor-
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                  mis a non gtadū vſ ad quartū. </s>
                  <s xml:id="N1D6F3" xml:space="preserve">Deinde volo /  a
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                  q̄libet triū quartaꝝ magis intēſaꝝ remoueat̄̄ vnꝰ
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                  g̈dusꝰ / et ponat̄̄ in quarta minꝰ intēſēſa / q̄ eſt vt duo /
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                  et manifeſtū eſt /  oēs quarte manebūt vt quī vni-
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                  formes: et ꝑ ↄ̨ñs tota illa velocitas talis motꝰ vni-
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                  formiter difformis reducendo ad vniformitatē re-
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                  mouēdo a parte equali et ponēdo ſibi in equali erit
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                  vt quin / quod eſt falſum: quia eſt vt quatuor cum
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                  eſt a non gradu vſ ad octauū: igr̄ velocitas mo-
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                  tus vniformiter difformis quo ad ſubiectū nõ de-
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                  bet cõmenſari penes reductionē ad vniformitatē.
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                    <note position="left" xlink:href="note-0138-01a" xlink:label="note-0138-01" xml:id="N1D745" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N1D711" xml:space="preserve">¶ Dices forte cõcedēdo /  motꝰ circularis nõ poteſt
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                  reduci ad vniformitatē ipſo manēte in ſubiecto cir­
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                  culariter moto q2 hoc repugnat et ītellige ſicut ītel­
                    <lb/>
                  ligendum eſt: ſed bene talis velocitas reduceret̄̄ ad
                    <lb/>
                  vniformitatē qua tale mobile moueat̄̄ vniformiter
                    <lb/>
                  motu recto quolibet pūcto deſcribente tantã lineã
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                  quantã deſcribit pūctꝰ mediꝰ. </s>
                  <s xml:id="N1D720" xml:space="preserve">Et hoc loquendo de
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                  motu circulari / vt loquūtur terminiſte. </s>
                  <s xml:id="N1D725" xml:space="preserve">Si autē lo-
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                  quimur / vt reales credo /  dicendū eſſet ſcḋm eoruꝫ
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                  viã /  motꝰ circularis eſſentialiter eſſet circularis
                    <lb/>
                  ita  talis motꝰ nõ põt eſſe quin ſit motꝰ circularis
                    <lb/>
                  q2 differt ſpecie eſſentiali a motu recto. </s>
                  <s xml:id="N1D730" xml:space="preserve">Et ideo / vt
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                  modꝰ reſpõdendi huic argumēto et etiã cognoſcē-
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                  di velocitatem motus difformis quo ad ſubiectum
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                  ſit vtri vie communis.</s>
                </p>
                <p xml:id="N1D74B">
                  <s xml:id="N1D74C" xml:space="preserve">Reſpõdeo alter  de facto motꝰ diffor­
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                  mis quo ad ſubiectū velocitas nequa̄ cõmēſura-
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                  ri debet ꝑ reductionē ad vniformitatē: ſed cõmēſu-
                    <lb/>
                  randa eſt penes denoīationē partiū nõ ̄tū ad ma­
                    <lb/>
                  gnitudinē: ſed ̄tū ad lõgitudinē </s>
                  <s xml:id="N1D757" xml:space="preserve">Uolo dicere /  nõ
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                  in ea ꝓportionē qua pars eſt maior altera in ea ꝓ-
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                  porõe velocitas motꝰ exiſtēs in ea plus facit ad de-
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                  noīationē totiꝰ velocitatis. </s>
                  <s xml:id="N1D760" xml:space="preserve">Sꝫ volo dicere /  in ea
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                  ꝓportiõe in qua eſt lõgior ceteris paribꝰ in ea plus
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                  facit ad denoīationē totiꝰ ita  tm̄ adequate mo-
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                  uet̄̄ vna rota ̄tū vna linea ꝓcedēs a cētro illiꝰ ro-
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                  te vſ ad circūferentiã. </s>
                  <s xml:id="N1D76B" xml:space="preserve">Et ſi talis linea moueat̄̄ a
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                  nõ g̈du vſ ad octauū etiã tota rota. </s>
                  <s xml:id="N1D770" xml:space="preserve">Et põt vena-
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                  ri velocitas motꝰ illiꝰ linee penes denoīationē iſto
                    <lb/>
                  mõ medietas huiꝰ linee q̄ velociua mouet̄̄, mouet̄̄ vt
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                  ſex: igr̄ denoīat totū moueri vt tria: et alia medietas
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                  totius vt vnū: et ſic tota linea mouetur vt quatuor.</s>
                </p>
                <cb chead="De motu locali quo ad effectū ſcḋm ſubiectū difformi."/>
                <p xml:id="N1D77D">
                  <s xml:id="N1D77E" xml:space="preserve">Sed ↄ̨̨tra. </s>
                  <s xml:id="N1D781" xml:space="preserve">Q2 ſi talis modꝰ cognoſcē-
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                  di velocitatē motꝰ difformis q̊ ab ſubiectū eſſet vĺr
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                  validꝰ ſeq̄ret̄̄ /  dabilis eēt vna ꝑs rote vniformiter
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                  difformiṫ mote q̄ nõ vniformiṫ difformiṫ moueret̄̄
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                  īmo nõ eēt dabilis g̈dꝰ q̊ adeq̈te moueret̄̄: ſꝫ q̊libet
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                  īadeq̈te citra ſūmū / et ↄ̨ñs oī opiniõi aduerſat̄̄: igr̄
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                  illud ex q̊ ſequit̄̄. </s>
                  <s xml:id="N1D790" xml:space="preserve">Seq̄la ꝓbat̄̄ / et capio vnã rotã que
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                  moueat̄̄ vniformiṫ difformiṫ a nõ g̈du vſ ad octa-
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                  uū, et ſigno in ea vnã colūnã cuiꝰ vnū extremū tãgat
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                  cētrū et aliud circūferētiã. </s>
                  <s xml:id="N1D799" xml:space="preserve">Deīde educo lineã girati­
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                  uã ꝓcedentē a cētro talis rote et girantē oēs partes
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                  ꝓportiõales taĺ colūne (et loquor de linea giratiua
                    <lb/>
                  ſicut loquūtur noīales ̄uis idē eſſet ſi loq̄rer ſcḋm
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                  reales) / q̊ poſito ſic arguitur talis linea eſt. ꝑs illius
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                  colūne: et hꝫ īfinitas ꝑtes eq̈les quaꝝ q̄libet mouet̄̄
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                  maiori et velociori g̈du quã q̈tuor, et hꝫ īfinitas eq̈-
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                  les quaꝝ q̄libet mouet̄̄ velociꝰ quã quī, et ſic ↄ̨ñter
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                  vſ ad octauū g̈dū excluſiue: et reſidue partes ſolū
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                  ſūt finite vt facile eſt ītueri: igr̄ talis linea mouetur
                    <lb/>
                  maiori vtlocitate quã vt quatuor quã vt quī ꝙ̄ vt
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                  ſex etc̈. vſ ad octauū g̈dū excluſiue / qḋ fuit ꝓbãdū</s>
                </p>
                <p xml:id="N1D7B2">
                  <s xml:id="N1D7B3" xml:space="preserve">In oppoſitū tamē eſt coīs ſchola aſſe­
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                  rens velocitatē motꝰ difformis quo ad ſubiectū ali­
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                  quo illorū modorū attendi debere ſiue cõmēſurari</s>
                </p>
                <p xml:id="N1D7BA">
                  <s xml:id="N1D7BB" xml:space="preserve">Pro deſciſioue huiꝰ q̄ſtionis ſupponē­
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                  da eſt diffinitio motus vniformiter difformis quo
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                  ad ſubiectū. </s>
                  <s xml:id="N1D7C2" xml:space="preserve">Et etiã diffinitio motꝰ difformiter dif-
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                  formis quo ad ſubiectū q̄ ſuꝑiori capite poſite ſunt
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                  </s>
                  <s xml:id="N1D7C8" xml:space="preserve">¶ Item aduertendū eſt /  in motu circulari duo cõ-
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                  ſiderãda ſunt: puta ipſa circuitio: et ipſe motus cir-
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                  cularis: quãuis eī idē ſit motꝰ circularis et circuitio
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                  penes aliud tñ cõmenſurari habet velocitas circui­
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                  tionis: et velocitas motus circularis: ſicut idē eſt al­
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                  bedo et ſiĺitudo: et penes aliḋ cognoſci hꝫ intēſio al­
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                  bedinis: et ītenſio ſiĺitudinls qḋ facile ex dialecticis
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                  ꝑcipi põt. </s>
                  <s xml:id="N1D7D9" xml:space="preserve">In iſtis eī aſpicienda eſt appellatio ne in
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                  ea fallamur: </s>
                  <s xml:id="N1D7DE" xml:space="preserve">Uelocitas em̄ motꝰ circularis attendi­
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                  tur penes lineam deſcriptam a certo puncto vt infe­
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                  riꝰ declarabit̄̄.
                    <note position="right" xlink:href="note-0138-02a" xlink:label="note-0138-02" xml:id="N1D833" xml:space="preserve">Penes
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                    q̇d hꝫ at-
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                    tēdi velo­
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                    citas cir­
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                    caitiõis.</note>
                  </s>
                  <s xml:id="N1D7EA" xml:space="preserve">Sed velocitas circuitionis attēdi hꝫ
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                  penes angulū deſcriptū in tãto vel tanto tp̄e circa
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                  centrū: ita  ſi in eq̈li tp̄e duo mobilia ſiue eq̈lia ſi-
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                  ue ineq̈lia circulariter mota eq̈les angulos circa cē­
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                  trū deſcribūt ipſa eq̈liter circueūt et circūgyrãt: </s>
                  <s xml:id="N1D7F5" xml:space="preserve">Si
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                  vero in eodē tp̄e ineq̈les deſcribãt circa cētrū angu­
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                  los: notū euadet eorū circuitiones ineq̈les eē.
                    <note position="right" xlink:href="note-0138-03a" xlink:label="note-0138-03" xml:id="N1D841" xml:space="preserve">paulꝰ ve­
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                    netꝰ ī ſū.
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                    phiſi. ca.
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                    35.</note>
                  </s>
                  <s xml:id="N1D801" xml:space="preserve">Et hec
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                  opinio eſt cõiter loq̄ntiū: et ſignãter Pauli veneti ī
                    <lb/>
                  ſua ſūma in libro phiſicoꝝ capitulo .35. vide eū ibi.
                    <lb/>
                  </s>
                  <s xml:id="N1D809" xml:space="preserve">Poſſet tñ facile attēdi velocitas circuitiõis penes
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                  velocitatē motꝰ alicuiꝰ pūcti equaliter diſtãtis a cē­
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                  tro: hoc eſt dicere /  ſi in duobus mobilibꝰ circulari­
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                  ter ſiue eq̈lia ſint ſiue īequalia duo pūcta eq̈liter di­
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                  ſtãtia a cētro equaliter moueant̄̄: talia mobilia eq̈­
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                  liter circueūt. </s>
                  <s xml:id="N1D816" xml:space="preserve">Nõ tñ arbitreris  quãto pūctū ē pro­
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                  pinquiꝰ cētro tãto velociꝰ circuit: qm̄ qḋlibet eq̄ve-
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                  lociter circuit cū altero dūmõ corꝑis motꝰ ſit vnifor­
                    <lb/>
                  miter difformis quo ad ſubiectū </s>
                  <s xml:id="N1D81F" xml:space="preserve">Quare ꝑſpicuū ē
                    <lb/>
                  videre diſtãtiã pūctorū nullo pacto conferre ad ve­
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                  locitatē circuitiõis (loquor de diſtãtia a cētro) quã­
                    <lb/>
                  uis plurimū ad velocitatē motꝰ circularis vt ſupe-
                    <lb/>
                  rius tactū eſt in quodã argumēto: et inferius tange­
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                  tur. </s>
                  <s xml:id="N1D82C" xml:space="preserve">His ſuppoſitis ſit.</s>
                </p>
                <p xml:id="N1D84D">
                  <s xml:id="N1D84E" xml:space="preserve">Prīa ↄ̨̨cluſio. </s>
                  <s xml:id="N1D851" xml:space="preserve">Uelocitas motꝰ vnifor-
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                  miṫ difformis quo ad ſubiectū nõ d3 attēdi aut cõ-
                    <lb/>
                  menſurari penes velocitatē pūcti exiſtētis in medio
                    <lb/>
                  corporis quãtū ad magnitudinē vt bene probat ter­
                    <lb/>
                  tium argumentum huius capitis</s>
                </p>
                <p xml:id="N1D85C">
                  <s xml:id="N1D85D" xml:space="preserve">Scḋa ↄ̨̨cluſio. </s>
                  <s xml:id="N1D860" xml:space="preserve">Uelocitas motus vni- </s>
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