Alvarus, Thomas, Liber de triplici motu, 1509

Table of figures

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              <div xml:id="N16983" level="4" n="6" type="chapter" type-free="capitulum">
                <p xml:id="N170ED">
                  <s xml:id="N170FE" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0072" n="72"/>
                  per conſequens talis potentia agit a proportiõe
                    <lb/>
                  dupla alterius proportionis </s>
                  <s xml:id="N17110" xml:space="preserve">Nã antea agebat a
                    <lb/>
                  dupla et mõ a quadrupla. </s>
                  <s xml:id="N17115" xml:space="preserve">ſed quadrupla eſt du-
                    <lb/>
                  pla duple. </s>
                  <s xml:id="N1711A" xml:space="preserve">vt patet intelligenti ſextū capitulum ſe­
                    <lb/>
                  cunde partis: igitur agit a duplo maiori velocita­
                    <lb/>
                  te. </s>
                  <s xml:id="N17121" xml:space="preserve">quoniam velocitas ſequitur proportionem pro­
                    <lb/>
                  portionū / vt patet ex prima ſuppoſitione precedē­
                    <lb/>
                  tis capitis. </s>
                  <s xml:id="N17128" xml:space="preserve">et per conſequens corrumpit tantū re­
                    <lb/>
                  ſiſtentie in ſecunda parte proportionali propor-
                    <lb/>
                  tione dupla: et per conſequens non vniformiter /
                    <lb/>
                  quod fuit probandum.
                    <note position="left" xlink:href="note-0072-01a" xlink:label="note-0072-01" xml:id="N17146" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N17136" xml:space="preserve">¶ Dices forte concedendo
                    <lb/>
                  quod infertur. </s>
                  <s xml:id="N1713B" xml:space="preserve">videlicet  nulla reſiſtentia poteſt
                    <lb/>
                  vniformiter deperdi in aliquo tempore: ſꝫ hoc nõ
                    <lb/>
                  eſt contra concluſiones.</s>
                </p>
                <p xml:id="N1714C">
                  <s xml:id="N1714D" xml:space="preserve">Sed contra / quia manifeſtum ē hoc
                    <lb/>
                  eſſe contra viceſimã concluſionem igitur </s>
                  <s xml:id="N17152" xml:space="preserve">Item re-
                    <lb/>
                  ſiſtentia poteſt vniformiter remitti a potentia / igi­
                    <lb/>
                  tur ſolutio nulla. </s>
                  <s xml:id="N17159" xml:space="preserve">Arguitur antecedens / et pono ca­
                    <lb/>
                  ſum /  eque velociter proportionabiliter ſicut re-
                    <lb/>
                  mittitur reſiſtentia ab aliqua potentia ita ꝓpor-
                    <lb/>
                  tionabiliter potentia decreſcat: ita  potentie ad
                    <lb/>
                  reſiſtentiam maneat cõtinuo eadē proportio: quo
                    <lb/>
                  poſito motus continuo erit vniformis / igitur vni-
                    <lb/>
                  formiter deperdetur tunc reſiſtentia. </s>
                  <s xml:id="N17168" xml:space="preserve">Quod vero
                    <lb/>
                  tunc motus erit vniformis / patet ex decima octa-
                    <lb/>
                  ua concluſione precedentis capitis.</s>
                </p>
                <p xml:id="N1716F">
                  <s xml:id="N17170" xml:space="preserve">Reſpondeo / igitur ad argumentum
                    <lb/>
                  negando antecedens et ad probationem pono du­
                    <lb/>
                  as concluſiones.</s>
                </p>
                <note position="left" xml:id="N17177" xml:space="preserve">inq̇rit̄̄ an
                  <lb/>
                poſſit re­
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                ſiſtentia
                  <lb/>
                vniformi­
                  <lb/>
                ter deꝑdi</note>
                <p xml:id="N17183">
                  <s xml:id="N17184" xml:space="preserve">Prima concluſio. </s>
                  <s xml:id="N17187" xml:space="preserve">Nulla reſiſtentia
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                  poteſt vniformiter deperdi per actionem alicuius
                    <lb/>
                  potentie non variate, nec ab extrinſeco impedite.
                    <lb/>
                  </s>
                  <s xml:id="N1718F" xml:space="preserve">Patet hec concluſio ex deductione argumenti.</s>
                </p>
                <p xml:id="N17192">
                  <s xml:id="N17193" xml:space="preserve">Secunda concluſio </s>
                  <s xml:id="N17196" xml:space="preserve">Aliqua reſiſten­
                    <lb/>
                  tia poteſt vniformiter remitti ab aliqua potentia
                    <lb/>
                  continuo eque proportionabiliter variata et mi-
                    <lb/>
                  norata cum ſua reſiſtentia: vel eque proportiona­
                    <lb/>
                  biliter impedita ſicut reſiſtentia remittitur. </s>
                  <s xml:id="N171A1" xml:space="preserve">Pa-
                    <lb/>
                  tet hec concluſio ex deductione replice </s>
                  <s xml:id="N171A6" xml:space="preserve">Et dico no-
                    <lb/>
                  tanter aut eque proportionabiliter impedita etc.
                    <lb/>
                  quoniaꝫ ſi ſit aliqua reſiſtentia vt .4. que remitta­
                    <lb/>
                  tur a potentia vt .8. non variata ſed ab aliquo ex­
                    <lb/>
                  trinſeco impedita: taliter  quando reſiſtētia fue­
                    <lb/>
                  rit vt .3. impediantur duo gradus actiuitatis ipſi­
                    <lb/>
                  us potentie: et quando reſiſtentia fuerit vt duo im­
                    <lb/>
                  pediantur alii duo gradus actiuitatis ipſius po­
                    <lb/>
                  tentie: continuo fiet actio a proportione dupla.</s>
                </p>
                <note position="left" xml:id="N171B9" xml:space="preserve">correla.</note>
                <p xml:id="N171BD">
                  <s xml:id="N171BE" xml:space="preserve">¶ Sequitur ex iſtis correlarium /  vbicū aliqua
                    <lb/>
                  potentia agit in ſuam reſiſtentiam eam corrumpē­
                    <lb/>
                  do ſine reactione: neceſſe eſt reſiſtentiam difformi­
                    <lb/>
                  ter remitti ceteris aliis paribus. </s>
                  <s xml:id="N171C7" xml:space="preserve">et vbicun potē-
                    <lb/>
                  tia introducit in aliquod paſſuꝫ ſuam qualitatē:
                    <lb/>
                  difformiter eam introducit ceteris aliis paribus.</s>
                </p>
                <note position="left" xml:id="N171CE" xml:space="preserve">argumē-
                  <lb/>
                tū calcu.</note>
                <p xml:id="N171D4">
                  <s xml:id="N171D5" xml:space="preserve">Quarto contra eaſdes concluſio-
                    <lb/>
                  nes arguitur ſic / quia ſi ille eſſent vere: ſequeretur
                    <lb/>
                  hec concluſio /  omnes potentie inuariate ſiue eq̈­
                    <lb/>
                  les ſiue inequales idem mediū non variatum trã-
                    <lb/>
                  ſeuntes in quo acquiritur aut deperditur motus:
                    <lb/>
                  eandem latitudinem motus acquirerent vel deꝑ­
                    <lb/>
                  derent. </s>
                  <s xml:id="N171E4" xml:space="preserve">ſed conſequens eſt falſum: igitur illud ex
                    <lb/>
                  quo ſequitur </s>
                  <s xml:id="N171E9" xml:space="preserve">Sequela eſt nota / quia equales pro-
                    <lb/>
                  portiones acquirerent vel deperderent / igitur eq̈-
                    <lb/>
                  les latitudines motus. </s>
                  <s xml:id="N171F0" xml:space="preserve">Sed falſitas conſequētis
                    <lb/>
                  oſtenditur / et pono caſum /  ſit vnum medium vni­
                    <lb/>
                  formiter difforme a gradu vſ ad certum graduꝫ
                    <lb/>
                  intenſiorem: et volo /  ſint due potentie equa-
                    <cb chead="Capitulum ſextum"/>
                  les a. et b. quarū vna puta a. incipiat moueri a me­
                    <lb/>
                  dio gradu verſus extremum intenſius: et alia pu-
                    <lb/>
                  ta b. īcipiat moueri ab extremo remiſſiori verſus
                    <lb/>
                  medium. </s>
                  <s xml:id="N17202" xml:space="preserve">quo poſito ſic argumentor maiorem ꝓ-
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                  portioneꝫ habet b. potentia ad quodlibet punctū
                    <lb/>
                  medietatis remiſſioris quam habeat a. ad ſimile
                    <lb/>
                  punctum ſiue correſpondens medietatis intenſio­
                    <lb/>
                  ris: creſcat igitur ipſum a. quo ad vſ ad quodli-
                    <lb/>
                  bet punctum medietatis intenſioris habeat maio­
                    <lb/>
                  rem proportionem quam b. ad ſimile punctuꝫ me­
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                  dietatis remiſſioris: et capio inſtans in quo a. ha­
                    <lb/>
                  bet equalem proportionem ad quodlibet punctuꝫ
                    <lb/>
                  medietatis intenſioris ſicut b. ad ſimile punctum
                    <lb/>
                  medietatis remiſſioris: et volo /  continuo mouea­
                    <lb/>
                  tur a tali proportione. </s>
                  <s xml:id="N1721B" xml:space="preserve">quo poſito ſequitur /  a. eq̈­
                    <lb/>
                  liter mouebitur per medietatem intenſiorem ſicut
                    <lb/>
                  b. per medietatem remiſſiorem. </s>
                  <s xml:id="N17222" xml:space="preserve">et equalem latitu­
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                  dinem motus deperdet a. per intenſiorem mouen­
                    <lb/>
                  do ſicut b. ꝑ medietatē remiſſiorē: ſꝫ b. minorē la-
                    <lb/>
                  titudinem deperdet per intenſiorem medietatem
                    <lb/>
                  mouendo quam per remiſſiorem / ergo per intēſio­
                    <lb/>
                  rem medietatem minorem latitudinem motus de­
                    <lb/>
                  perdit b. quam a. / et per conſequens non equalem /
                    <lb/>
                  quod fuit probandum.</s>
                </p>
                <p xml:id="N17233">
                  <s xml:id="N17234" xml:space="preserve">Reſpondeo ad argumentum admit-
                    <lb/>
                  tendo caſum et negando illud quod aſſumitur vel
                    <lb/>
                  ſupponitur. </s>
                  <s xml:id="N1723B" xml:space="preserve">videlicet /  dabile ſit inſtãs in quo a.
                    <lb/>
                  habeat talem proportionem ad quodlibet pūctū
                    <lb/>
                  medietatis intenſioris qualem habet b. ad pūctū
                    <lb/>
                  ſimile ſiue correſpondens ī medietate remiſſiori.</s>
                </p>
                <p xml:id="N17244">
                  <s xml:id="N17245" xml:space="preserve">Quãuis enim poſſibile ſit  habeat maiorem. </s>
                  <s xml:id="N17248" xml:space="preserve">et
                    <lb/>
                   habeat minorem: non tamen  habeat equaleꝫ
                    <lb/>
                    <note position="right" xlink:href="note-0072-02a" xlink:label="note-0072-02" xml:id="N172AA" xml:space="preserve">1. correl.</note>
                  </s>
                  <s xml:id="N17254" xml:space="preserve">¶ Ex quo ſequitur primo /  hec conſequentia ni-
                    <lb/>
                  chil valet a. tranſit de minori ad maiꝰ: ergo a. trã­
                    <lb/>
                  ſit per eq̈le </s>
                  <s xml:id="N1725B" xml:space="preserve">Inſtantia enim eſt in propoſito </s>
                  <s xml:id="N1725E" xml:space="preserve">Trã-
                    <lb/>
                  ſit enī a. de minori proportione reſpectu cuiuſlib3
                    <lb/>
                  puncti ad maiorem: et non equalem cuilibet pun-
                    <lb/>
                  cto: </s>
                  <s xml:id="N17267" xml:space="preserve">Analogia poteſt faciliter capi quoniaꝫ dato
                    <lb/>
                   ſint hic tres homines quorum nullus eſt ſortes:
                    <lb/>
                  et mīmus illorum ſit pedalis, alter bipedalis, et
                    <lb/>
                  maximus tripedalis, et ſit ſortes ſemipedalis: et
                    <lb/>
                  creſcat ſucceſſiue ſortes quo ad vſ ſit quadrupe-
                    <lb/>
                  dalis. </s>
                  <s xml:id="N17274" xml:space="preserve">tunc manifeſtum eſt /  ſortes tranſibit a mi­
                    <lb/>
                  nori quantitate / quam ſit quantitas alicuius iſto­
                    <lb/>
                  rum ad maiorem quantitatem quam ſit quãtitas
                    <lb/>
                  alicuius iſtorum: et tamen nunquaꝫ tranſibit per
                    <lb/>
                  quantitatem equalem cuilibet quantitati illorum
                    <lb/>
                  </s>
                  <s xml:id="N17280" xml:space="preserve">Quare iſta conſequentia nichil valet a. tranſibit
                    <lb/>
                  a minori quãtitate quantitate iſtorū. </s>
                  <s xml:id="N17285" xml:space="preserve">ad maioreꝫ
                    <lb/>
                  quantitatem quãtitate iſtorum / ergo per equalem
                    <lb/>
                  quantitatem cuilibet quantitati iſtorum. </s>
                  <s xml:id="N1728C" xml:space="preserve">Et totū
                    <lb/>
                  hoc prouenit a termino diſtributo.
                    <note position="right" xlink:href="note-0072-03a" xlink:label="note-0072-03" xml:id="N172B0" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N17296" xml:space="preserve">¶ Sequitur ſe­
                    <lb/>
                  cundo /  iſta conſequentia nihil valet iſte angulꝰ
                    <lb/>
                  tranſit a minori augulo quam ſit angulus ſemi-
                    <lb/>
                  circuli ad maiorem angulum quam ſit angulꝰ ſe-
                    <lb/>
                  micirculi / ergo tranſit per equalem. </s>
                  <s xml:id="N172A1" xml:space="preserve">Patet hoc
                    <lb/>
                  correlarium in hac figura.</s>
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                <note position="right" xml:id="N172BA" xml:space="preserve">Cãpanꝰ ī
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                ↄ̨mē. 16.
                  <lb/>
                ↄ̨clu. ter-
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                tii. ele. eu</note>
                <p xml:id="N172C4">
                  <s xml:id="N172C5" xml:space="preserve">Et eſt campani in cõmento decime ſexte concluſio­
                    <lb/>
                  nis tertii elementorum euclidis / vbi oſtendit ſimi-
                    <lb/>
                  les argumentationes non valere.
                    <note position="right" xlink:href="note-0072-04a" xlink:label="note-0072-04" xml:id="N172DA" xml:space="preserve">Brauar-
                      <lb/>
                    dinꝰ capi­
                      <lb/>
                    te .4. con­
                      <lb/>
                    cluſio .7.</note>
                  </s>
                  <s xml:id="N172D1" xml:space="preserve">Et idem ponit
                    <lb/>
                  brauardinꝰ in capitulo de circulis ↄ̨cluſiõe ſeptīa</s>
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