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="N1D065" level="4" n="2" type="chapter" type-free="capitulum">
                <p xml:id="N1D420">
                  <s xml:id="N1D4D1" xml:space="preserve">
                    <pb chead="Secundi tractatus" file="0137" n="137"/>
                  laris eſt ita velox circulatio ſicut antea vt conclu-
                    <lb/>
                  datur maior extremitas de minori. </s>
                  <s xml:id="N1D4E5" xml:space="preserve">Quãuis enim
                    <lb/>
                  idē ſit circulatio et motus circularis nõ tamen pe-
                    <lb/>
                  nes idem iudicari debet velocitas circuitiõis et ve-
                    <lb/>
                  locitas motus localis circularis / vt poſtea dicetur.</s>
                </p>
                <p xml:id="N1D500">
                  <s xml:id="N1D501" xml:space="preserve">Sed ↄ̨̨tra. </s>
                  <s xml:id="N1D504" xml:space="preserve">Q2 ſi illa ſolutio eſſet bona
                    <lb/>
                  ſeq̄ret̄̄ /  ab eadē ꝓportione potētie ad ſuã reſiſtē-
                    <lb/>
                  tiã ꝓuenirēt īequales motꝰ, et equales circuitiones /
                    <lb/>
                  qḋ eſt falſū. </s>
                  <s xml:id="N1D50D" xml:space="preserve">Seq̄la ptꝫ facile ex ſolutiõe. </s>
                  <s xml:id="N1D510" xml:space="preserve">Poſitum
                    <lb/>
                  eſt em̄ /  poña moueret ab eodē conamine rotã cõti­
                    <lb/>
                  nuo equaliter reſiſtentē / et dictū eſt /  a tali ꝓporti-
                    <lb/>
                  one ꝓueniebãt īequales motꝰ. </s>
                  <s xml:id="N1D519" xml:space="preserve">eq̈les aūt circuitiões
                    <lb/>
                    <note position="left" xlink:href="note-0137-01a" xlink:label="note-0137-01" xml:id="N1D545" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N1D523" xml:space="preserve">¶ Dices forte /  iã / tūc nõ eſt eadē ꝓportio īter mo-
                    <lb/>
                  uēs et mobile ſed eſt mīor. </s>
                  <s xml:id="N1D528" xml:space="preserve">Sed hoc nõ põt dici qm̄
                    <lb/>
                  volo /  poña ſit naturalis: et maneat in rota tanta
                    <lb/>
                  reſiſtētia ſicut ãtea erat vt poſitū eſt. </s>
                  <s xml:id="N1D52F" xml:space="preserve">Et ſi hoc non
                    <lb/>
                  admittas equa lance currit ↄ̨tra te argumentū de
                    <lb/>
                  circuitiõibꝰ q2 tūc ex īequalibꝰ ꝓportiõibꝰ ꝓuenirēt
                    <lb/>
                  equales circuitiões et īequales motꝰ / qḋ tã incõueni­
                    <lb/>
                  ens videt̄̄ ſicut reliquū. </s>
                  <s xml:id="N1D53A" xml:space="preserve">¶ Et ideo dices forte / vt di-
                    <lb/>
                  cūt alii  nõ eſt incõueniēs ab eq̈li ꝓportiõe eq̈les
                    <lb/>
                  circuitiões īequales autē motꝰ ꝓuenire / vt dictū eſt.</s>
                </p>
                <p xml:id="N1D54B">
                  <s xml:id="N1D54C" xml:space="preserve">Sed ↄ̨̨tra. </s>
                  <s xml:id="N1D54F" xml:space="preserve">Q2 hoc dato iã deſtruit̄̄ fū­
                    <lb/>
                  damentū totiꝰ materie: et iã pari facilitate ꝓteruus
                    <lb/>
                  phiſicꝰ cõcederet  a ꝓportiõe dupla, et a ꝓportio-
                    <lb/>
                  ne quadrupla equales velocitates nate ſunt ꝓueni­
                    <lb/>
                  re. </s>
                  <s xml:id="N1D55A" xml:space="preserve">et multa ſimilia q̄ ſunt abſona calculatori pḣo
                    <lb/>
                    <note position="left" xlink:href="note-0137-02a" xlink:label="note-0137-02" xml:id="N1D595" xml:space="preserve">Reſpon­
                      <lb/>
                    ſio cõis.</note>
                  </s>
                  <s xml:id="N1D564" xml:space="preserve">¶ Qua ꝓpter dicūt alii ad argumētū concedendo
                    <lb/>
                  conſequentiã, et negãdo falſitatē ↄ̨ñtis: et ad pun-
                    <lb/>
                  ctū ꝓbationis negant /  talis rota ãtea et poſt mo­
                    <lb/>
                  uebat̄̄ ab equali ꝓportione / q2 vt dicūt magnitudo
                    <lb/>
                  rote tenet ſe ex ꝑte poñe. </s>
                  <s xml:id="N1D56F" xml:space="preserve">Mõ manēte eodē conamīe
                    <lb/>
                  poñe rota tardiꝰ mouet̄̄ et a minore ꝓportione quia
                    <lb/>
                  ãtea magnitudo iṗiꝰ rote iuuabat poñaꝫ ad deſcri­
                    <lb/>
                  bendã lineã. </s>
                  <s xml:id="N1D578" xml:space="preserve">Mõ vero cū ipſa rota cõtinuo efficiat̄̄
                    <lb/>
                  minor nõ ita iuuat poñam ſicut añ </s>
                  <s xml:id="N1D57D" xml:space="preserve">Qḋ facile exem­
                    <lb/>
                  plo declarart põt. </s>
                  <s xml:id="N1D582" xml:space="preserve">Manifeſtū eſt em̄ /  ſi in ſuꝑficie
                    <lb/>
                  alicuiꝰ rote addat̄̄ aliq̇d eiuſdē ſpeciei cõtinuatū cū
                    <lb/>
                  rota nulliꝰ grauitatis: et ſortes giret totū illud ab
                    <lb/>
                  eodē conamine illa totalis rota velociꝰ mouet̄̄ quã
                    <lb/>
                  mouebat̄̄ ãtea pars eiꝰ et tñ poña manet eq̈lis et re-
                    <lb/>
                  ſiſtentia rote: ſed totalis proportio eſt maior quia
                    <lb/>
                  iuuatur ibi poña ſortis a magnitudine rote.</s>
                </p>
                <p xml:id="N1D59D">
                  <s xml:id="N1D59E" xml:space="preserve">Sed ↄ̨̨tra. </s>
                  <s xml:id="N1D5A1" xml:space="preserve">Q2 magnitudo tenet ſe ex
                    <lb/>
                  parte reſiſtētie: g̊ nõ ex parte potētie etiã manente
                    <lb/>
                  eq̈li g̈uitate oīno. </s>
                  <s xml:id="N1D5A8" xml:space="preserve">Probat̄̄ añs de orbe / qui maio-
                    <lb/>
                  ratur ꝑ rarefactionē quovſ fiat ſpera ſolida qui
                    <lb/>
                  tūc tardiꝰ mouet̄̄ quã qñ erat minor / vt patꝫ ex ſcḋa
                    <lb/>
                  replica huiꝰ quarti argumēti.
                    <note position="left" xlink:href="note-0137-03a" xlink:label="note-0137-03" xml:id="N1D5DB" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N1D5B6" xml:space="preserve">¶ Dices ſicut dicēdū
                    <lb/>
                  eſt /  nec magnitudo, nec paruitas in talibꝰ tenet
                    <lb/>
                  ſe ex parte poñe vt ſatis ꝓbat replica: ſed diſtãtia
                    <lb/>
                  pūcti a cētro penes cuiꝰ motū d3 attēdi velocitas to­
                    <lb/>
                  tiꝰ mobilis puta ipſiꝰ pūcti ī q̊ eſt g̈dꝰ mediꝰ totiꝰ la-
                    <lb/>
                  titudīs motꝰ tenet ſe ex ꝑte poñe. </s>
                  <s xml:id="N1D5C3" xml:space="preserve">CeterꝪ em̄ paribꝰ
                    <lb/>
                  iuuat poñaꝫ ad velociꝰ deſcribēdū lineã / ꝙ̄ deſcribit
                    <lb/>
                  qñ recedit a cētro: et ꝑ contrariū iuuat ad deſcribē-
                    <lb/>
                  dam tardiꝰ qñ magis accedit ad centrū a quo exori­
                    <lb/>
                  tur motus. </s>
                  <s xml:id="N1D5CE" xml:space="preserve">Et ſic dico /  qñ rota rarefit verſus cir-
                    <lb/>
                  cunferentiam mouente circūferentia: tota ꝓportio
                    <lb/>
                  efficitur maior, et quando condenſatur ordine con-
                    <lb/>
                  uerſo tota ꝓportio efficitur minor.</s>
                </p>
                <p xml:id="N1D5E1">
                  <s xml:id="N1D5E2" xml:space="preserve">Sed ↄ̨̨tra </s>
                  <s xml:id="N1D5E5" xml:space="preserve">Q2 iſta ſolutio nõ ſatiſfacit
                    <lb/>
                  adhuc em̄ ſequit̄̄ /  ab īeq̈libꝰ ꝓportiõibꝰ eq̈les cir-
                    <lb/>
                  cuitiões ꝓueniūt / qḋ eſt īpoſſibile. </s>
                  <s xml:id="N1D5EC" xml:space="preserve">Ptꝫ ↄ̨ña / q2 ſorte
                    <lb/>
                  cū eq̈li cõamīe ↄ̨tinuo girante ſiue rota rarefiat ſi-
                    <lb/>
                  ue ↄ̨dēſet̄̄ ipſe eque velociter ↄ̨tinuo circuit et tñ ꝑ te
                    <lb/>
                  ꝓportio eſt continuo maior vel minor: igr̄ ꝓpoſitū.</s>
                </p>
                <cb chead="Capitulū ſecundū."/>
                <p xml:id="N1D5F7">
                  <s xml:id="N1D5F8" xml:space="preserve">Quīto ↄ̨̨tra eandē partē arguit̄̄ ſic / ali­
                    <lb/>
                  q̇s motꝰ eſt vniformiṫ difformis q̊ ad ſubiectū: et tñ
                    <lb/>
                  eiꝰ velocitas nõ corrñdet g̈dui medio: igr̄. </s>
                  <s xml:id="N1D5FF" xml:space="preserve">Añs ꝓba­
                    <lb/>
                  tur et ſuppono /  rarefactio ſit motꝰ localis diffor-
                    <lb/>
                  mis q̊ ad ſubiectū. </s>
                  <s xml:id="N1D606" xml:space="preserve">q̊ ſuppoſito pono /  ſint duo pe-
                    <lb/>
                  dalia ſcḋm oēm dimēſionē puta a.b. / et volo /  a ra-
                    <lb/>
                  refiat vniformiṫ quovſ efficiat̄̄ in duplo longiꝰ et
                    <lb/>
                  in duplo latiꝰ vniformiṫ, et b. rarefiat vniformiter
                    <lb/>
                  q̊vſ efficiat̄̄ in ſexq̇altero lõgiꝰ, et in ſexq̇altero la­
                    <lb/>
                  tius vniformiṫ ita  a. in fine ſit vnū q̈dratū cuiꝰ co­
                    <lb/>
                  ſta ſit dupla ad coſtã eiuſdē in prīcipio rarefactõis
                    <lb/>
                  et b. ſit aliud q̈dratū cuiꝰ coſta in fine rarefactionis
                    <lb/>
                  ſit ſexq̇altera ad coſtã eiꝰ in prīcipio rarefactiõis / q̊
                    <lb/>
                  poſito ſic argr̄: ſi ille motꝰ q̊ mouet̄̄ a. et etiã q̊ mouet̄̄
                    <lb/>
                  b. debeãt ↄ̨mēſurari penes pūctū mediū / ſequit̄̄ /  a
                    <lb/>
                  adeq̈te in duplo velociꝰ moueret̄̄ quã b. / ſed ↄ̨ñs eſt
                    <lb/>
                  falſum: igitur illud ex quo ſequitur. </s>
                  <s xml:id="N1D621" xml:space="preserve">Seq̄la ꝓbatur /
                    <lb/>
                  quia pūctus medius ipſius a. in toto illo tempore
                    <lb/>
                  rarefactionis pertrãſibit vnū ſemipedale q2 pūctꝰ
                    <lb/>
                  extremius mouet̄̄ ꝑ pedale: et pūctus medius ipſius
                    <lb/>
                  b. mouet̄̄ ꝑ quartã pedalis cū pūctꝰ extremꝰ eiuſdeꝫ
                    <lb/>
                  b. moueat̄̄ ꝑ ſemipedale: ſed ſemipedalis ad quar-
                    <lb/>
                  tã pedalis eſt ꝓportio dupla / vt ptꝫ: igitur in duplo
                    <lb/>
                  velociꝰ mouet̄̄ a. quã b. / qḋ fuit ꝓbãdū. </s>
                  <s xml:id="N1D632" xml:space="preserve">Sed falſitas
                    <lb/>
                  ↄ̨ñtis arguitur ſuppoſita illa concluſione geome-
                    <lb/>
                  trica vcꝫ  ſemꝑ quadrata ꝑfecta equalis craſſitu-
                    <lb/>
                  dinis ſe habent in proportione duplicata ad ꝓpor­
                    <lb/>
                  tionē ſuarū cõſtarū / vt poſtea dicetur ī capitulo de
                    <lb/>
                  augmentatione. </s>
                  <s xml:id="N1D63F" xml:space="preserve">ſi vero ſint vndiqua quadrata
                    <lb/>
                  ꝑfecta tunc ſe habēt in ꝓportione triplicata ad pro­
                    <lb/>
                  portionē ſuarū coſtarū. </s>
                  <s xml:id="N1D646" xml:space="preserve">Quo ſuppoſito ſic arguit̄̄ /
                    <lb/>
                  pedale a. in duplo ſuprabipartiente quintas velo­
                    <lb/>
                  cius rarefit quã pedale b. et ipſa rarefactio eſt motꝰ
                    <lb/>
                  localis vt ſuppoſitū eſt: ergo in duplo ſuprabipar­
                    <lb/>
                  tiente quintas velocius mouetur a. quã b. / et per cõ-
                    <lb/>
                  ſequēs nõ in duplo adequate / quod fuit probandū.
                    <lb/>
                  </s>
                  <s xml:id="N1D654" xml:space="preserve">Conſequentia apparet, et arguitur maior / quia pe­
                    <lb/>
                  dale a. efficitur quadruplū in fine rarefactionis ad
                    <lb/>
                  ipſum in principio quia in principio rarefactionis
                    <lb/>
                  coſte ipſius a. ad coſtam eius in fine rarefactionis
                    <lb/>
                  eſt proportio dupla cū ceteris poſitis in caſu: ergo
                    <lb/>
                  ipſius quadrati a. in fine ad ipſum in principio eſt
                    <lb/>
                  proportio quadrupla que eſt duplicata proportio
                    <lb/>
                  coſtarū, et antea erat illud pedale adequate: ergo
                    <lb/>
                  acquiſiuit tria pedalia: et aliud puta b. acquiſiuit
                    <lb/>
                  pedale cum quarta preciſe: igitur quantitatis ac-
                    <lb/>
                  acquiſite ipſi a. ad quãtitatē acquiſitã ipſi b. eſt pro­
                    <lb/>
                  portio dupla ſuꝑbipartiēs q̇ntas: et tãta ē ꝓportio
                    <lb/>
                  rarefactionis ipſius a. ad rarefactionē ipſiꝰ b. igit̄̄
                    <lb/>
                  </s>
                  <s xml:id="N1D670" xml:space="preserve">Sed iã ꝓbo /  b. acq̇ſiuit pedale cū quarta q2 coſte
                    <lb/>
                  ipſiꝰ b. in fine ad coſtã eiuſdē in prīcipio rarefactio­
                    <lb/>
                  nis eſt ꝓportio ſexq̇altera. </s>
                  <s xml:id="N1D677" xml:space="preserve">g̊ totiꝰ quadrati b. in fi-
                    <lb/>
                  ne ad ipſū in prīcipio eſt ꝓportio dupla ſexquiq̈rta
                    <lb/>
                  q̄ eſt dupla ad ſexq̇alterã. </s>
                  <s xml:id="N1D67E" xml:space="preserve">Ptꝫ ↄ̨ña ex ſuppoſitione
                    <lb/>
                  et antea b. erat pedale: g̊ acq̇ſiuit pedale cū quarta /
                    <lb/>
                  qḋ fuit ꝓbandū. </s>
                  <s xml:id="N1D685" xml:space="preserve">Simile argumētū poſſet fieri de ra­
                    <lb/>
                  refactione duarū ſperarū ſolidarū equaliū in ṗnci­
                    <lb/>
                  pio rarefactiõis: et in fine ita ſe habētiū  diametri
                    <lb/>
                  vnius ad diameirum alterius eſſet ꝓportio dupla.</s>
                </p>
                <p xml:id="N1D68E">
                  <s xml:id="N1D68F" xml:space="preserve">Sexto prīcipaliṫ arguit̄̄  hoc ↄ̨̨tra ter­
                    <lb/>
                  tiã ꝑtē q̄ſtionis vcꝫ /  debet attēdi motꝰ localis dif-
                    <lb/>
                  formis velocitas quo ad ſubiectū penes reductiõeꝫ
                    <lb/>
                  ad vniformitatē. </s>
                  <s xml:id="N1D698" xml:space="preserve">q2 motus circularis in ſubiecto cir­
                    <lb/>
                  culari nõ p̄t reduci ad vniformitatē: igitur nõ debet
                    <lb/>
                  attendi penes reductionē ad vniformitatē.
                    <note position="right" xlink:href="note-0137-04a" xlink:label="note-0137-04" xml:id="N1D73D" xml:space="preserve">Confir-
                      <lb/>
                    matio.</note>
                  </s>
                  <s xml:id="N1D6A4" xml:space="preserve">¶ Et cõ-
                    <lb/>
                  firmatur / q2 ſi reduceretur ad vniformitateꝫ motus
                    <lb/>
                  circularis alicuiꝰ rote a non gradu vſ ad octauū
                    <lb/>
                  vel oporteret reducēdo ab aliqua parte capere ali­ </s>
                </p>
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