Alvarus, Thomas, Liber de triplici motu, 1509

Page concordance

< >
Scan Original
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
< >
page |< < of 290 > >|
    <echo version="1.0">
      <text xml:lang="la">
        <div xml:id="N10132" level="1" n="1" type="body">
          <div xml:id="N15C17" level="2" n="3" type="other" type-free="pars">
            <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
              <div xml:id="N1A8D1" level="4" n="12" type="chapter" type-free="capitulum">
                <p xml:id="N1AA6F">
                  <s xml:id="N1AA96" xml:space="preserve">
                    <pb chead="De motu penes cauſã in medio vniformiṫ difformi īuariato." file="0110" n="110"/>
                  et reſiſtentie equales) equalem ꝓportionem habe-
                    <lb/>
                  rent: et cum cõtinuo mouentur vniformiter / vt dicit
                    <lb/>
                  concluſio quam impugnamus: ſequitur /  ſemper
                    <lb/>
                  antea habebant equalem ꝓportionem qualem ha­
                    <lb/>
                  bent in termino motus: et per cõſequens ſemꝑ equa­
                    <lb/>
                  liter mouebūtur: quod eſt contra ſolutionem.</s>
                </p>
                <p xml:id="N1AAB0">
                  <s xml:id="N1AAB1" xml:space="preserve">Reſpondeo negando ſequelam et ad
                    <lb/>
                  ꝓbationem dico /  quãuis ſemper in medio mino-
                    <lb/>
                  ri ceteris paribus qualificato conſimili reſiſtentia
                    <lb/>
                  vniformiter difformi, eadem vel cõſimilis potētia
                    <lb/>
                  tardius moueatur: nõ tamen tardius in ea ꝓporti-
                    <lb/>
                  one qua eſt minus: immo in minori tardius. </s>
                  <s xml:id="N1AABE" xml:space="preserve">Ita 
                    <lb/>
                  ſemper eadem potentia citius pertranſibit minus
                    <lb/>
                  medium quam maius: dummodo talia media ſint
                    <lb/>
                  qualificata eadem vel cõſimili qualitate vniformi-
                    <lb/>
                  ter difformi. </s>
                  <s xml:id="N1AAC9" xml:space="preserve">Quod ſic ptꝫ / quia a. potentia nõ põt
                    <lb/>
                  eque cito pertranſire mediū maius ſicut b. medium
                    <lb/>
                  minus: vt nuperrime ꝓbatum eſt, nec citius: q2 tūc
                    <lb/>
                  a minori ꝓportione moueretur a. quam b. et per cõ­
                    <lb/>
                  ſequens tardius quod eſt cõtra principalē ſolutio-
                    <lb/>
                  nē. </s>
                  <s xml:id="N1AAD6" xml:space="preserve">Sequela tamen ptꝫ / quia quando a. eſſet cum re­
                    <lb/>
                  ſiſtentia vt .8. potentia b. ei equalis eſſet cum mino­
                    <lb/>
                  ri reſiſtentia cum adhuc nõ eſſet in fine per te. </s>
                  <s xml:id="N1AADD" xml:space="preserve">Qua­
                    <lb/>
                  re cõcedendum eſt /  ſemper pertranſitur citius me­
                    <lb/>
                  dium minus quã maius in caſu poſito.</s>
                </p>
                <p xml:id="N1AAE4">
                  <s xml:id="N1AAE5" xml:space="preserve">Sed contra / quia tunc ſequeretur hec
                    <lb/>
                  concluſio /  infinite potentie darentur equales po­
                    <lb/>
                  tentie a. que inciperent ſimul moueri cum potentia
                    <lb/>
                  a. per media qualificata eadē vel conſimili qualita­
                    <lb/>
                  te vniformiter difformi: et in infinitum tardius con­
                    <lb/>
                  tinuo moueretur vnū illorum quam a. et tamen que­
                    <lb/>
                  libet aliarum potentiarum citius pertranſibit me­
                    <lb/>
                  dium ſuū ꝙ̄ a. / ſed conſequens videtur impoſſibile:
                    <lb/>
                  igitur illud ex quo ſequitur. </s>
                  <s xml:id="N1AAF8" xml:space="preserve">Sequela probatur et
                    <lb/>
                  pono caſum /  ſit vnū pedale / per quod extendatur
                    <lb/>
                  latitudo reſiſtentie vniformiter difformis a nõ gra­
                    <lb/>
                  du vſ ad octauū / vt dictum eſt ſupra: et ſit aliud in
                    <lb/>
                  duplo minus, et aliud in triplo, et aliud in quadru-
                    <lb/>
                  plo, et ſic in infinitum: et per quodlibet illorum extē­
                    <lb/>
                  datur eadem vel conſimilis latitudo reſiſtentie vni­
                    <lb/>
                  formiter difformis a nõ gradu vſ ad octauū: et in
                    <lb/>
                  aliquo inſtanti incipiat a. creſcēdo a nõ gradu po-
                    <lb/>
                  tentie moueri cõtinuo a ꝓportione dupla per me-
                    <lb/>
                  dium pedale: et in quolibet aliorum mediorum inci­
                    <lb/>
                  piat in eodem inſtanti etiam conſimilis potentia
                    <lb/>
                  conſimiliter oīno creſcens moueri a nõ gradu reſi-
                    <lb/>
                  ſtentie: ita  quelibet maneat cõtinuo equalis ipſi
                    <lb/>
                  a. </s>
                  <s xml:id="N1AB17" xml:space="preserve">Quo poſito patꝫ ſecunda pars illati videlicet / 
                    <lb/>
                  quelibet aliarum potentiarū ab a. citius pertran-
                    <lb/>
                  ſibit medium ſuū quam a. </s>
                  <s xml:id="N1AB1E" xml:space="preserve">Hoc em̄ dicit ſolutio pre­
                    <lb/>
                  cedentis replice. </s>
                  <s xml:id="N1AB23" xml:space="preserve">Et arguitur prima pars videlicet /
                    <lb/>
                   in infinitum tardius continuo mouetur aliqua il­
                    <lb/>
                  larum quam a. / quia citius a. preteribit punctū me-
                    <lb/>
                  diū illiꝰ pedalis per quod mouetur hoc eſt punctuꝫ
                    <lb/>
                  vt .4. quam aliqua aliarū potentiarū pertranſibit
                    <lb/>
                  ſuū mediū per quod ipſum mouetur: et in infinituꝫ
                    <lb/>
                  minus eſt aliquod illorū mediorū per quod mouet̄̄
                    <lb/>
                  aliqua illarū potentiarū, quam eſt medietas peda­
                    <lb/>
                  lis per quod mouetur a. / vt ptꝫ ex caſu: igitur in infi­
                    <lb/>
                  nitū tardius ꝙ̄ a. mouetur aliqua illaꝝ potentiarū /
                    <lb/>
                  quod fuit ꝓbandū. </s>
                  <s xml:id="N1AB3A" xml:space="preserve">Cõſequentia ptꝫ cum minore: et
                    <lb/>
                  arguitur maior: q2 nulla aliaruꝫ potentiarū eque
                    <lb/>
                  cito deueniet ad terminū ſui medii ſicut a. deueniet
                    <lb/>
                  ad punctum mediū pedalis per quod mouetur. </s>
                  <s xml:id="N1AB43" xml:space="preserve">nec
                    <lb/>
                  citius aliqua illarum deueniet ad terminū ſui me-
                    <lb/>
                  dii ꝙ̄ a. deueniet ad punctum medium pedalis per
                    <lb/>
                  quod mouetur: igitur citius a. preteribit punctum
                    <lb/>
                  medium quam aliqua aliarum deueniet ad finem
                    <cb chead="De motu penes cauſã in medio vniformiṫ difformi īuariato."/>
                  medii / per quod mouetur / quod fuit probandū. </s>
                  <s xml:id="N1AB51" xml:space="preserve">Cõ­
                    <lb/>
                  ſequentia patet et arguitur maior. </s>
                  <s xml:id="N1AB56" xml:space="preserve">quia ſi eque cito
                    <lb/>
                  aliqua illarum deueniret ad terminū ſui medii ſi-
                    <lb/>
                  cut a. deueniet ad punctum mediū: ſignetur illa et ſit
                    <lb/>
                  b. / et arguo ſic / cum primū a. eſt in puncto medio qui
                    <lb/>
                  eſt vt .4.b. eſt in puncto terminatiuo totius latitu-
                    <lb/>
                  dinis qui eſt vt .8. / et a. mouetur a proportiõe dupla /
                    <lb/>
                  vt ponitur: igitur qualis eſt proportio ipſius a. ad
                    <lb/>
                  reſiſtentiam ipſius a. talis eſt proportio reſiſtentie
                    <lb/>
                  ipſius b. ad reſiſtentiam ipſius a. / et per conſequens
                    <lb/>
                  reſiſtentia ipſius b. et ipſa potentia a. ſunt equales
                    <lb/>
                  cum habeant eadem proportionem ad vnū tertiuꝫ:
                    <lb/>
                  et a. et b. ſunt equales ex caſu: igitur reſiſtentia ipſiꝰ
                    <lb/>
                  b. et b. ſunt equales: ſic b. mouetur a proportione
                    <lb/>
                  equalitatis / quod eſt impoſſibile. </s>
                  <s xml:id="N1AB73" xml:space="preserve">Patet igitur / 
                    <lb/>
                  nulla illarum poteſt eque cito venire ad punctū ter­
                    <lb/>
                  minatiuū ſui medii, ſicut a. ad punctum medium pe­
                    <lb/>
                  dalis per quod mouetur. </s>
                  <s xml:id="N1AB7C" xml:space="preserve">Sed iam probo minorem
                    <lb/>
                  videlicet /  nulla illarum citius deueniet ad termi-
                    <lb/>
                  nū ſui medii quam a. deueniat ad punctum medium
                    <lb/>
                  ſui pedalis per quod mouetur: quia ſi ſic ſit illa b. /
                    <lb/>
                  et arguo ſic, b. potentia equalis ipſi a. eſt in puncto
                    <lb/>
                  terminatiuo ſui medii puta in puncto vt .8. et a. eſt
                    <lb/>
                  in minori puncto quam vt .4. et mouetur a. potentia
                    <lb/>
                  a proportione dupla: igitur maior eſt proportio re­
                    <lb/>
                  ſiſtentie ipſius b. ad reſiſtentiam ipſius a. ꝙ̄ ſit pro­
                    <lb/>
                  portio ipſius a. ad reſiſtentiam ipſius a. et a. et b.
                    <lb/>
                  ſunt equales: igitur maior eſt reſiſtentia b. quam b. /
                    <lb/>
                  et per conſequens b. mouetur a. proportione mino-
                    <lb/>
                  ris inequalitatis / quod eſt impoſſibile. </s>
                  <s xml:id="N1AB97" xml:space="preserve">Patet ta-
                    <lb/>
                  men conſequentia / quia pūcti vt .8. ad punctū quod­
                    <lb/>
                  libet minus puncto vt .4. eſt maior proportio quam
                    <lb/>
                  dupla: et ipſius a. ad reſiſtentiam eiuſdē que eſt mi-
                    <lb/>
                  nor puncto vt .4. eſt proportio dupla: igitur reſiſtē­
                    <lb/>
                  tia b. maiorem proportionem habet ad reſiſtentiã
                    <lb/>
                  ipſius a. quaꝫ a. habeat ad reſiſtentiam eiuſdem a. /
                    <lb/>
                  et per conſequens maior eſt reſiſtentia ipſius b. quã
                    <lb/>
                  a. potentia / quod fuit probandum. </s>
                  <s xml:id="N1ABAA" xml:space="preserve">Patet conſequē­
                    <lb/>
                  tia per hanc maximam: id quod habet maiorē pro­
                    <lb/>
                  portionem ad vnū tertium eſt maius. </s>
                  <s xml:id="N1ABB1" xml:space="preserve">Patet igitur
                    <lb/>
                  totum illatum.</s>
                </p>
                <p xml:id="N1ABB6">
                  <s xml:id="N1ABB7" xml:space="preserve">Reſpondeo / igitur concedendo quod
                    <lb/>
                  infertur vt demonſtrat argumentum.
                    <note position="right" xlink:href="note-0110-01a" xlink:label="note-0110-01" xml:id="N1AD20" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N1ABC1" xml:space="preserve">¶ Ex hoc ar-
                    <lb/>
                  gumento et ſolutionibus replicarū eiuſdem / ſequi-
                    <lb/>
                  tur primo:  vbicun ſunt infinite potentie vt po-
                    <lb/>
                  nitur in caſu vltime replice: neceſſe eſt /  potētia que
                    <lb/>
                  mouetur in maximo illorum mediorum pretereat
                    <lb/>
                  punctum ad quod punctum intenſiſſimū illius me-
                    <lb/>
                  dii habet ſimilem proportionem illi proportioni a
                    <lb/>
                  qua mouetur illa potentia, quam aliqua aliarum
                    <lb/>
                  potentiarum equalium deueniat ad extremum ſui
                    <lb/>
                  medii. </s>
                  <s xml:id="N1ABD6" xml:space="preserve">Uolo dicere /  ſi potentia in maxima illorū
                    <lb/>
                  mediorum (loquor ſemper incipientibus a nõ gra-
                    <lb/>
                  du) moueatur a proportione quadrupla: citius de-
                    <lb/>
                  ueniat ad punctum ad quem intenſiſſimus punctus
                    <lb/>
                  puta vt .8. (ſi medium terminetur ad illum) habeat
                    <lb/>
                  proportionem quadruplam, quam aliqua aliaruꝫ
                    <lb/>
                  potentiarum pertranſeat ſuum medium. </s>
                  <s xml:id="N1ABE5" xml:space="preserve">Ita  in
                    <lb/>
                  tali caſu oportet /  prius veniat ad punctum vt .2.
                    <lb/>
                  et pretereat illum. </s>
                  <s xml:id="N1ABEC" xml:space="preserve">Alias enim vel alia potentia mo­
                    <lb/>
                  ueretur a proportione equalitatis vĺ minoris ine-
                    <lb/>
                  qualitatis vt facile eſt inducere
                    <note position="right" xlink:href="note-0110-02a" xlink:label="note-0110-02" xml:id="N1AD26" xml:space="preserve">2. correĺ</note>
                  </s>
                  <s xml:id="N1ABF8" xml:space="preserve">¶ Sequitur ſecūdo /
                    <lb/>
                   ſi ſint duo media inequalia per que extēditur ea-
                    <lb/>
                  deꝫ latitudo reſiſtentie vniformiter difformis a nõ
                    <lb/>
                  gradu vſ ad octauū: et incipiant due potentie mo­
                    <lb/>
                  ueri per illa media a nõ gradu illiꝰ reſiſtentie: et con­
                    <lb/>
                  tinuo creſcãt ille potētie vniformiter īcipiēdo a nõ
                    <lb/>
                  g̈du potētie: illa tñ que mouet̄̄ in medio mīori in ea
                    <lb/>
                  ꝓportione velociꝰ creſcat altera q̄ mouet̄̄ in medio </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum