Alvarus, Thomas, Liber de triplici motu, 1509

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                <p xml:id="N26575">
                  <s xml:id="N2659B" xml:space="preserve">
                    <pb chead="De motu rarefactionis quo ad cauſam." file="0226" n="226"/>
                  lem quãtitatē: et ſic ↄ̨ñter: ita  in qualꝫ parte pro-
                    <lb/>
                  portionali tꝑis ſequēti fiat in duplo minꝰ intenſa
                    <lb/>
                  caliditas ipſiꝰ a. ꝙ̄ ī īmediate p̄cedēti: et maneat. </s>
                  <s xml:id="N265B7" xml:space="preserve">ſic
                    <lb/>
                  in fine hore nõ reſtituta p̄ſtine intēſioni vel maiori:
                    <lb/>
                  </s>
                  <s xml:id="N265BD" xml:space="preserve">Quo poſito ſequit̄̄ correlarium. </s>
                  <s xml:id="N265C0" xml:space="preserve">Equalis em̄ poñe
                    <lb/>
                  manet a. ſicut ante remiſſionē: cū maneat eadē for-
                    <lb/>
                  ma.
                    <note position="left" xlink:href="note-0226-01a" xlink:label="note-0226-01" xml:id="N265FD" xml:space="preserve">7. correĺ.</note>
                  </s>
                  <s xml:id="N265CC" xml:space="preserve">¶ Sequit̄̄ ſeptimo /  a. et b. ſunt eq̈lis quãtita-
                    <lb/>
                  tis puta pedalis b. īfinite calidū, a. vero īfinite re-
                    <lb/>
                  miſſe calidū: et tñ a. eſt in īfinitū maioris poñe quã
                    <lb/>
                  b. </s>
                  <s xml:id="N265D5" xml:space="preserve">Ptꝫ ex priori: et primo.
                    <note position="left" xlink:href="note-0226-02a" xlink:label="note-0226-02" xml:id="N26603" xml:space="preserve">Calcuĺ. ḋ
                      <lb/>
                    poña rei</note>
                  </s>
                  <s xml:id="N265DD" xml:space="preserve">¶ Hanc materiã latiꝰ vi-
                    <lb/>
                  dere poteris apud calculatorē capitulo de potētia
                    <lb/>
                  rei. </s>
                  <s xml:id="N265E4" xml:space="preserve">et ſic ptꝫ quid poña rei, et penes / q̇d attendi ha-
                    <lb/>
                  beat. </s>
                  <s xml:id="N265E9" xml:space="preserve">Et cõſimiliter dicas de reſiſtētia /  ipſa attē-
                    <lb/>
                  di habet penes multitudinem forme. </s>
                  <s xml:id="N265EE" xml:space="preserve">Eadem enim
                    <lb/>
                  ratio eſt reſiſtentie et potentie.</s>
                </p>
                <p xml:id="N2660B">
                  <s xml:id="N2660C" xml:space="preserve">Notandū eſt tertio </s>
                  <s xml:id="N2660F" xml:space="preserve">Pro materia ſcḋi
                    <lb/>
                  argumēti /  oē agens ab īfinita latitudine ꝓpor-
                    <lb/>
                  tionis natū eſt agere. </s>
                  <s xml:id="N26616" xml:space="preserve">Nã agens vt .2. in reſiſtentiã
                    <lb/>
                  vt vnū agit a ꝓportiõe dupla: in ſubduplã vero re-
                    <lb/>
                  ſiſtentiã a ꝓportiõe in triplo maiori, et in ſubq̈dru­
                    <lb/>
                  plã a ꝓportione in triplo maiori: et in ſuboctuplaꝫ
                    <lb/>
                  a ꝓportiõe in q̈druplo maiori: et ſic in īfinitū. </s>
                  <s xml:id="N26621" xml:space="preserve">Ptꝫ
                    <lb/>
                  igr̄ agens vt .2. natū eſſe ab īfinita latitudine ꝓpor­
                    <lb/>
                  tionis agere: ꝑinde at qḋuis alind. </s>
                  <s xml:id="N26628" xml:space="preserve">Eadeꝫ em̄ rõ
                    <lb/>
                  cuilibet ſuffragat̄̄ agēti. </s>
                  <s xml:id="N2662D" xml:space="preserve">Nec ꝓpoſitū infringit mi­
                    <lb/>
                  nima reſiſtētia per ſe potēs naturaliter reſiſtere ſi
                    <lb/>
                  q̇ſpiã opinet̄̄ talē eſſe dandã. </s>
                  <s xml:id="N26634" xml:space="preserve">Et ſi em̄ illa ponatur
                    <lb/>
                  nichilominꝰ agens ſuapte natura ab īfinita ꝓpor-
                    <lb/>
                  tionis latitudine natū eſſe agere nequa̄ ãbigēdū
                    <lb/>
                  eſt. </s>
                  <s xml:id="N2663D" xml:space="preserve">Q, o a finita dūtaxat agat ꝓportiõe: ex īpedi­
                    <lb/>
                  mento reſiſtētie ſibi accidit.
                    <note position="left" xlink:href="note-0226-03a" xlink:label="note-0226-03" xml:id="N267A1" xml:space="preserve">q̇d ſit re-
                      <lb/>
                    ſtere.</note>
                  </s>
                  <s xml:id="N26647" xml:space="preserve">Uñ reſiſtere nihil aliud
                    <lb/>
                  eſt quã actionē agētis īpedire totaliter aut partia­
                    <lb/>
                  liter. </s>
                  <s xml:id="N2664E" xml:space="preserve">Dico totalr̄ / cū īpedit actiouē a ꝓportiõe eq̈-
                    <lb/>
                  litatis vel maioris ineq̈litatis. </s>
                  <s xml:id="N26653" xml:space="preserve">Dico partialr̄ / cnm
                    <lb/>
                  aliquã latitudinē actiõis īpedit ipſa reſiſtētia a ꝓ-
                    <lb/>
                  portione mīoris īeq̈litatis. </s>
                  <s xml:id="N2665A" xml:space="preserve">Reſiſtentia .n. vt a pḣis
                    <lb/>
                  diffinitū eſt nichil aliud eſt ꝙ̄ actionis īpedimentū
                    <lb/>
                  </s>
                  <s xml:id="N26660" xml:space="preserve">Cū o īpedimentū actiõis p̄t agenti ↄ̨tingere du-
                    <lb/>
                  pliciter ex ꝑte vcꝫ paſſi / in qḋ agit ita  paſſū reſi-
                    <lb/>
                  ſtat vel ex parte alicuiꝰ extrinſeci in qḋ nõ agit: q2
                    <lb/>
                  forte ad illud in tali diſtãtia hꝫ ꝓportionē mīoris
                    <lb/>
                  ineq̈litatꝪ vel ſi forte agit in illud: illud tñ nõ ſolū
                    <lb/>
                  īpedit actionē in ſemet ipſū ſed in aliqḋ etiã extrin­
                    <lb/>
                  ſecū: ideo duplex eſt reſiſtētia: quedã vcꝫ eſſentialis
                    <lb/>
                  q̄dã accidētalis: vt bñ oñdit Suiſeth ī capite de rea­
                    <lb/>
                  ctiõe.
                    <note position="left" xlink:href="note-0226-04a" xlink:label="note-0226-04" xml:id="N267A9">
                      <s xml:id="N267AD" xml:space="preserve">Calcula.
                        <lb/>
                      </s>
                      <s xml:id="N267B1" xml:space="preserve">Reſiſtē-
                        <lb/>
                      tia eſſen-
                        <lb/>
                      tialis.</s>
                    </note>
                  </s>
                  <s xml:id="N26678" xml:space="preserve">Reſiſtētia eſſētialis eſt reſiſtētia paſſi ī qḋ a-
                    <lb/>
                  gēs agit adeq̈te: vt ſi a. agit in b. et b. ei reſiſtat m
                    <lb/>
                  illã partē inquã agit, talis reſiſtentia illiꝰ partis
                    <lb/>
                  dr̄ eſſentialis.
                    <note position="left" xlink:href="note-0226-05a" xlink:label="note-0226-05" xml:id="N267B8" xml:space="preserve">Reſiſtē-
                      <lb/>
                    tia acci-
                      <lb/>
                    dentalis</note>
                  </s>
                  <s xml:id="N26686" xml:space="preserve">Sed reſiſtentia accidētalis eſt reſiſtē­
                    <lb/>
                  tia īpediēs actionē agētis in aliqḋ extrinſecū ei vĺ
                    <lb/>
                  ſubiecto in quo eſt: vt ſi a. agit in b. et c. actionē ſiue
                    <lb/>
                  aliquã latitudinē actiõis īpediat in ipſo b. / tūc c. re­
                    <lb/>
                  ſiſtit accidētalr̄ ipſi a.
                    <note position="left" xlink:href="note-0226-06a" xlink:label="note-0226-06" xml:id="N267C2" xml:space="preserve">.1. correĺ.</note>
                  </s>
                  <s xml:id="N26696" xml:space="preserve">¶ Ex q̊ ſequit̄̄ /  nõnū̄ eadē
                    <lb/>
                  reſiſtētia eſt eſſentialis et accidentalis vt cū a. agit
                    <lb/>
                  in b. et etiã agit in c. et .c. reſiſtit ipſi a. ue tã velociter
                    <lb/>
                  agat in b. ſicut ageret a moto ipſo c. / tūc reſiſtentia
                    <lb/>
                  ipſiꝰ c. eſt accidētalis reſpectu actiõis ipſiꝰ a. in b.
                    <lb/>
                  paſſū, et eſſentialis reſpectu actiõis ipſiꝰ a. in idē c.
                    <lb/>
                    <note position="left" xlink:href="note-0226-07a" xlink:label="note-0226-07" xml:id="N267C8" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N266AA" xml:space="preserve">¶ Sequit̄̄ ſcḋo /  cõiṫ cū aliqḋ agens agit per totū
                    <lb/>
                  aliqḋ paſſū q̄libet pars ipſiꝰ paſſi reſiſtit eſſentia-
                    <lb/>
                  liter: et q̄libet etiã reſiſtit accidētalr̄. </s>
                  <s xml:id="N266B1" xml:space="preserve">Reſiſtit em̄ eſ-
                    <lb/>
                  ſentialiṫ reſpectu actiõis in ipſam: et accidētaliter
                    <lb/>
                  reſpectu actiõis in alterã. </s>
                  <s xml:id="N266B8" xml:space="preserve">Et vĺr pars ꝓpinquior
                    <lb/>
                  agenti magis reſiſtit accidētalr̄ ipſi agenti quã re­
                    <lb/>
                  mota reſiſtens. </s>
                  <s xml:id="N266BF" xml:space="preserve">Dico reſiſtēs / q2 tm̄ p̄t elongari 
                    <lb/>
                  nõ reſiſtet. </s>
                  <s xml:id="N266C4" xml:space="preserve">Intelligas ſēꝑ ceteris paribꝰ.
                    <note position="left" xlink:href="note-0226-08a" xlink:label="note-0226-08" xml:id="N267CE" xml:space="preserve">Aduerte</note>
                  </s>
                  <s xml:id="N266CC" xml:space="preserve">¶ Nõ tñ
                    <lb/>
                  in ea ꝓportione in qua pars eſt ꝓpinquior agenti
                    <lb/>
                  ceteris paribꝰ in ea plus reſiſtit: vt bñ ꝓbari põt ex
                    <lb/>
                  deductione ↄ̨firmatiõis ſcḋi argumēti principalis
                    <cb chead="De motu rarefactionis quo ad cauſam."/>
                  antc oppoſitã. </s>
                  <s xml:id="N266D8" xml:space="preserve">Et ſiĺr dicendū eſt de actione /  cum
                    <lb/>
                  aliqḋ agens agit pars eiꝰ ꝓptnquior magis agit
                    <lb/>
                  quã pars remotior ceteris paribꝰ: nõ tñ in ea ꝓpor­
                    <lb/>
                  tione qua partes ſūt ꝓpinquiores in ea velociꝰ a-
                    <lb/>
                  gūt: vt facile deduci p̄t ex ꝓceſſu ſcḋi argumēti prī-
                    <lb/>
                  cipalis ante oppoſitū.
                    <note position="right" xlink:href="note-0226-09a" xlink:label="note-0226-09" xml:id="N267D4" xml:space="preserve">.1. correĺ.
                      <lb/>
                    ↄ̈ calcul.</note>
                  </s>
                  <s xml:id="N266EA" xml:space="preserve">¶ Ex q̊ ſequit̄̄ / q̄ ꝓbatio ſiue
                    <lb/>
                  argumentū calculatoris in capite de actiõe lumīo-
                    <lb/>
                  ſi circa principiū quo intēdit ꝓbare /  partes me-
                    <lb/>
                  dii diſtantes a lumīoſo nullo pacto īpediūt actio-
                    <lb/>
                  nē lūinoſi in partibꝰ ꝓpīquioribꝰ eſt īefficax: ̄uis
                    <lb/>
                  ↄ̨cluſio ſit a: īnititur em̄ illa ꝓbatio huic funda-
                    <lb/>
                  mēto: in ea ꝓportiõe qua partes ſūt ꝓpinquiores
                    <lb/>
                  lūinoſo ceteris paribꝰ in ea magis īpedirēt: dūmõ
                    <lb/>
                  ponant̄̄ īpedire / qḋ eſt flm̄ / et negatū ab ipſo calcu-
                    <lb/>
                  latore ī capite de reactiõe iuxta mediū vbi hãc ma­
                    <lb/>
                  teriã ad plenū ꝑ eū digeſtã īuenies.
                    <note position="right" xlink:href="note-0226-10a" xlink:label="note-0226-10" xml:id="N267DC" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N26706" xml:space="preserve">¶ Sequit̄̄ ſcḋo /
                    <lb/>
                   hec ↄ̨ña nichil valet a. et b. ſūt eq̈les p ↄ̨ñe actiue,
                    <lb/>
                  et a. agit in c. paſſū, et a. eſt in duplo ꝓpīquiꝰ c. paſ-
                    <lb/>
                  ſo quã b. / ergo a. in duplo velocius agit in c. quã b.
                    <lb/>
                  agat in c. </s>
                  <s xml:id="N26711" xml:space="preserve">Probat̄̄ quia poſſibile eſt /  c. ſit extra
                    <lb/>
                  ſpherã actiuitatis ipſius b. / et tūc añs eſt veꝝ et ↄ̨ñs
                    <lb/>
                  flm̄: g̊ ↄ̨ña nulla.
                    <note position="right" xlink:href="note-0226-11a" xlink:label="note-0226-11" xml:id="N267E2" xml:space="preserve">.3. correĺ.</note>
                  </s>
                  <s xml:id="N2671D" xml:space="preserve">¶ Sequit̄̄ tertio /  hec ↄ̨ña nichil
                    <lb/>
                  valet, a. et b. ſūt eq̈lis poñe actiue, et c. eſt īfra. ſphe-
                    <lb/>
                  ram actiuitatꝪ vtriuſ, et a. eſt in q̈druplo ꝓpīquiꝰ
                    <lb/>
                  ipſe c. ꝙ̄ ip̄m b. / igr̄ a. in q̈druplo velociꝰ agit in c. ̄
                    <lb/>
                  ip̄m b. </s>
                  <s xml:id="N26728" xml:space="preserve">Probat̄̄ / q2 ſi illa ↄ̨ña valeret pari rõne hec
                    <lb/>
                  valeret a. et b. ſūt eq̈lis poñe actiue, et c. eſt ītra ſphe­
                    <lb/>
                  ram actiuitatis vtriuſ, et in īfinitū magis appro­
                    <lb/>
                  ximat̄̄ a. ipſi c. ꝙ̄ īpſū b. approximat̄̄ eidē c. / igr̄ in īfi­
                    <lb/>
                  nitū velociꝰ aget a. in c. quã ipſū b. ſed hec nichil va­
                    <lb/>
                  let: g̊ nec alia. </s>
                  <s xml:id="N26735" xml:space="preserve">Seq̄la ſatis ptꝫ, et ꝓbat̄̄ minor: et po­
                    <lb/>
                  no /  a. ſit actiuitatꝪ vt .8. et c. reſiſtētie vt .4. hoc eſt
                    <lb/>
                   maxima ꝓportio a. qua a. põt agere in c. qñ eſt ei
                    <lb/>
                  optīe approxīatū ſicut ei põt approxīari ſit dupla
                    <lb/>
                  (ſemꝑ loquor de optīa approxīatiõe ſimplr̄ poſſi-
                    <lb/>
                  bili) et diſtet a: ab ipſo c. ꝑ pedalē diſtantiã, et in pri­
                    <lb/>
                  ma parte ꝓportiõali hore ꝓportiõe dupla appro-
                    <lb/>
                  ximet̄̄ a. ipſi c. ſcḋm qḋlibet eiꝰ punctū in duplo plꝰ
                    <lb/>
                  ꝑ ↄ̨dēſationē ſiue deꝑditione materie aut forme, et
                    <lb/>
                  in ſcḋa parte ꝓportionali approximetur in duplo
                    <lb/>
                  pluſ̄ in ṗma, et in tertia in duplo pluſ̄ in ſcḋa, et
                    <lb/>
                  ſic ↄ̨ñter: quo poſito añs eſt verū et ↄ̨ñs flm̄ / vt ptꝫ ex
                    <lb/>
                  caſu. </s>
                  <s xml:id="N26750" xml:space="preserve">Nã in caſu poſitū eſt /  maxīa ꝓportio a. q̈ a.
                    <lb/>
                  põt agere ſit dupla.
                    <note position="right" xlink:href="note-0226-12a" xlink:label="note-0226-12" xml:id="N267E8" xml:space="preserve">4. correĺ.</note>
                  </s>
                  <s xml:id="N2675A" xml:space="preserve">¶ Sequit̄̄ quarto /  hec ↄ̨ña ni­
                    <lb/>
                  chil valet a. agit in c. et b. eſt in duplo mīoris poñe
                    <lb/>
                  quã a. et in duplo ꝓpinquiꝰ ipſi c. quã a. / g̊ b. tm̄ agi
                    <lb/>
                  in c. ſicut a. </s>
                  <s xml:id="N26763" xml:space="preserve">Probat̄̄ eſto /  c. ſit reſiſtētie vt .4. et a.
                    <lb/>
                  poñe vt .8: cū ceterꝪ poſitis in caſu correlarii: tunc
                    <lb/>
                  añs eſt verū et ↄ̨ñs flm̄. </s>
                  <s xml:id="N2676A" xml:space="preserve">Nã tūc b. hꝫ ꝓportionē eq̈li­
                    <lb/>
                  tatis ad c. / et ꝑ ↄ̨ñs nõ agit in c.
                    <note position="right" xlink:href="note-0226-13a" xlink:label="note-0226-13" xml:id="N267EE" xml:space="preserve">.5. correĺ.</note>
                  </s>
                  <s xml:id="N26774" xml:space="preserve">¶ Sequit̄̄ quinto / 
                    <lb/>
                  paſſū ſimplex vniforme ſcḋm punctū eiꝰ mediū ma­
                    <lb/>
                  xime reſiſtit. </s>
                  <s xml:id="N2677B" xml:space="preserve">¶ Hoc eſt  paſſū magis reſiſtit agēti
                    <lb/>
                  ei approxīato ad punctū mediū quã quis alio mõ
                    <lb/>
                  approxīato ceteris paribꝰ.
                    <note position="right" xlink:href="note-0226-14a" xlink:label="note-0226-14" xml:id="N267F4" xml:space="preserve">Correla.
                      <lb/>
                    calcula.</note>
                  </s>
                  <s xml:id="N26787" xml:space="preserve">Illud correlariū eſt cal­
                    <lb/>
                  culatoris in capite de reactione circa mediū. </s>
                  <s xml:id="N2678C" xml:space="preserve">Uide­
                    <lb/>
                  as ibi eiꝰ ꝓbationē q̄ pulchra eſt et ſubtilis. </s>
                  <s xml:id="N26791" xml:space="preserve">Eam tñ
                    <lb/>
                  nõ pono / q2 nõ apparet michi vĺis. </s>
                  <s xml:id="N26796" xml:space="preserve">Et ideo intelli-
                    <lb/>
                  gas eã et ſiĺr correlariū de corꝑe vniformis reſiſtē­
                    <lb/>
                  tie: et omnium dimenſionum vniformium.</s>
                </p>
                <p xml:id="N267FC">
                  <s xml:id="N267FD" xml:space="preserve">Expeditis notabilibꝰ  ex hoc primo
                    <lb/>
                  mēbro q̄ſtiõis: reſtat ſcḋm mēbrū abſoluere in quo
                    <lb/>
                  ↄ̨cluſiones materiã quarti, quīti, et ſexti argumen­
                    <lb/>
                  toꝝ principaliū ante oppoſitū reſoluētes inducunt̄̄
                    <lb/>
                    <note position="right" xlink:href="note-0226-15a" xlink:label="note-0226-15" xml:id="N2681B" xml:space="preserve">.2. articu­
                      <lb/>
                    lꝰ quõuis</note>
                  </s>
                  <s xml:id="N2680D" xml:space="preserve">Et ṗmo inducã ↄ̨cluſiões tangētes materiã quarti
                    <lb/>
                  et quīti argumenti puta de velocitate motus alte-
                    <lb/>
                  rationis penes cauſam. </s>
                  <s xml:id="N26814" xml:space="preserve">Sit igitur.</s>
                </p>
                <p xml:id="N26823">
                  <s xml:id="N26824" xml:space="preserve">Prima ↄ̨̨cluſio. </s>
                  <s xml:id="N26827" xml:space="preserve">Ubicun aliqḋ alte-
                    <lb/>
                  rans vuiformiṫ ↄ̨tinuo corrūpit aliquã reſiſtentiã </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum