Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
              <div xml:id="N16349" level="4" n="5" type="chapter" type-free="capitulum">
                <p xml:id="N168C7">
                  <s xml:id="N168DD" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0067" n="67"/>
                  tis ex vigeſimaſeptima concluſione.</s>
                </p>
                <p xml:id="N168E5">
                  <s xml:id="N168E6" xml:space="preserve">Quadrageſima concluſio </s>
                  <s xml:id="N168E9" xml:space="preserve">Si aliqua
                    <lb/>
                  potentia non variata mouetur per mediuꝫ vnifor­
                    <lb/>
                  miter difforme incipiendo ab extremo intenſiori:
                    <lb/>
                  talis potentia continuo velocius et velocius intē-
                    <lb/>
                  dit motū ſuum. </s>
                  <s xml:id="N168F4" xml:space="preserve">Patet / quia continuo velocius et
                    <lb/>
                  velocius decreſcit ſibi de reſiſtentia: igitur conti-
                    <lb/>
                  nuo velocius et velocius intendit motuꝫ ſuum </s>
                  <s xml:id="N168FB" xml:space="preserve">Pa­
                    <lb/>
                  tet conſequentia ex vigeſimaoctaua concluſione.</s>
                </p>
                <p xml:id="N16900">
                  <s xml:id="N16901" xml:space="preserve">Quadrageſimaprima ↄ̨̨cluſio </s>
                  <s xml:id="N16904" xml:space="preserve">Stat
                    <lb/>
                  duas potētias equales moueri per mediū vnifor­
                    <lb/>
                  miter difforme incipiendo ab extremo remiſſiori
                    <lb/>
                  eiuſdē medii ipſis et medio ſimplicter inuariatis
                    <lb/>
                  et tamē vnam moueri velocius altera </s>
                  <s xml:id="N1690F" xml:space="preserve">Probatur
                    <lb/>
                  hec concluſio et capio vnum mediū quadratū vni­
                    <lb/>
                  formiter difforme a non gradu vſ ad octauū vel
                    <lb/>
                  a certo gradu (in idē redit) / et volo /  a. et b. ſint due
                    <lb/>
                  potentie equales: et incipiat vna moueri ab extre­
                    <lb/>
                  mo remiſſiori per diametrū et alia per lineam re-
                    <lb/>
                  ctã ab eodem extremo: quo poſito ſic arguo a. et b.
                    <lb/>
                  mouebuntur: et a. non mouebitur tardius ipſo b.
                    <lb/>
                  nec eque velociter adequate: ergo velocius. </s>
                  <s xml:id="N16922" xml:space="preserve">Ma-
                    <lb/>
                  ior ptꝫ cum conſequentia. </s>
                  <s xml:id="N16927" xml:space="preserve">et minor probatur. </s>
                  <s xml:id="N1692A" xml:space="preserve">q2 ſi
                    <lb/>
                  mouerentur equaliter ſequeretur /  equales potē­
                    <lb/>
                  tie cum inequalibus reſiſtentiis equaliter mouerē­
                    <lb/>
                  tur / et per conſequens ab inequalibus proportio-
                    <lb/>
                  nibus equales motus proueniunt: quod eſt contra
                    <lb/>
                  primã ſuppoſitionē huius capitis et directe cõtra
                    <lb/>
                  opinionem. </s>
                  <s xml:id="N16939" xml:space="preserve">Sequela tamen probatur / quoniam
                    <lb/>
                  capto quocū pūcto diametri equaliter diſtante
                    <lb/>
                  ab angulo quadrati: hoc eſt a linea quadrati fa-
                    <lb/>
                  ciente angulum ſicut certus pūctus: eſt minoris re­
                    <lb/>
                  ſiſtentie quã pūctus exiſtens in linea recta equali-
                    <lb/>
                  ter diſtante cum ipſo. </s>
                  <s xml:id="N16946" xml:space="preserve">ergo ſequitur /  ſemꝑ a. ha-
                    <lb/>
                  bebit minorē reſiſtentiam / et per conſequens maio­
                    <lb/>
                  rem proportionem ad talem pūctū quã b. in pun-
                    <lb/>
                  cto ſibi correſpondente: et tamen per te a. et b. mo­
                    <lb/>
                  uentur equaliter: igitur ꝓpoſituꝫ. </s>
                  <s xml:id="N16951" xml:space="preserve">Q, aūt in tali
                    <lb/>
                  puncto diametri ſit ſemper reſiſtentia minor quã
                    <lb/>
                  in puncto ſibi correſpõdente ī linea directe / et per-
                    <lb/>
                  pendiculariter ꝓcedente ꝓbatur / quoniaꝫ ſemper
                    <lb/>
                  talis punctus plus diſtat a gradu ſūmo illius cor­
                    <lb/>
                  poris / quam punctus ſibi correſpondens in linea
                    <lb/>
                  directe et perpēdiculariter procedente. </s>
                  <s xml:id="N16960" xml:space="preserve">igitur ſem­
                    <lb/>
                  per in eo eſt minor reſiſtentia et per conſequens ꝓ­
                    <lb/>
                  portio maior </s>
                  <s xml:id="N16967" xml:space="preserve">Patet hec demonſtratio aſpicienti
                    <lb/>
                  figuram quadrataꝫ vniformiter difformē quo ad
                    <lb/>
                  reſiſtentiam / que ſit .a.b. et .c.d. et extremū remiſſiſ­
                    <lb/>
                  ſimū ſit .ac. et linea diametralis ꝑ quã a. mouetur
                    <lb/>
                  ſit .ad. et linea per quam mouetur b. ſit .cd.</s>
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                <figure xml:id="N16972" number="6">
                  <image file="0067-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0067-01"/>
                </figure>
                <p xml:id="N16976">
                  <s xml:id="N16977" xml:space="preserve">qua figura inſpecta patet facile ꝓpoſitum. </s>
                  <s xml:id="N1697A" xml:space="preserve">Et hec
                    <lb/>
                  de his concluſionibus in quibus ferme ſequutus
                    <lb/>
                  ſum calculatorem in capitulo de motu locali dem­
                    <lb/>
                  pta vltima quam adiunxi.</s>
                </p>
              </div>
              <div xml:id="N16983" level="4" n="6" type="chapter" type-free="capitulum">
                <head xml:id="N16988" xml:space="preserve">Sextum capitulum / in quo ponūtur
                  <lb/>
                alique obiectiones contra aliquas
                  <lb/>
                concluſiones ſuperioris capitis.</head>
                <p xml:id="N1698F">
                  <s xml:id="N16990" xml:space="preserve">COntra quintam concluſio-
                    <lb/>
                  nem arguitur ſic. </s>
                  <s xml:id="N16995" xml:space="preserve">per intenſionem et cre­
                    <lb/>
                  mētum alicuius reſiſtētie reſpectu dua­
                    <lb/>
                  rum potentiarum inequalium minor potentia ve­
                    <cb chead="Capitulum ſextum"/>
                  locius remittit motū ſuum quã maior: igitur ſex-
                    <lb/>
                  ta ↄ̨cluſio falſa. </s>
                  <s xml:id="N169A1" xml:space="preserve">Arguit̄̄ antecedēs et pono /  ſit a.
                    <lb/>
                  potētia vt .8. et b. potētia vt .4. et c. reſiſtētia vt 2.
                    <lb/>
                  et d. reſiſtētia vt vnū: et agat vtra illaꝝ potētiaꝝ
                    <lb/>
                  cū vtra illarum reſiſtentiarū: et creſcat c. reſiſten­
                    <lb/>
                  tia vt .2. vniformiter / quo ad vſ ſit vt .4. et d. reſiſtē­
                    <lb/>
                  tia itidem vniformiter creſcat / quo ad vſ ſit vt .4.
                    <lb/>
                  creſcat tamen reſiſtētia vt .2. in duplo velociꝰ quã
                    <lb/>
                  reſiſtentia vt vnū. </s>
                  <s xml:id="N169B2" xml:space="preserve">ita  quando reſiſtentia vt vnuꝫ
                    <lb/>
                  acquiſiuerit vnum gradum reſiſtentie: reſiſtentia
                    <lb/>
                  vt duo acquirat duos. </s>
                  <s xml:id="N169B9" xml:space="preserve">quo poſito ſic argumentor
                    <lb/>
                  b. potentia vt .4. velocius remittit motum ſuum
                    <lb/>
                  cū c. reſiſtentia vt .2. quã a. potentia vt .8. cum ea-
                    <lb/>
                  dem reſiſtentia vt duo. </s>
                  <s xml:id="N169C2" xml:space="preserve">igitur aſſumptum verum.</s>
                </p>
                <p xml:id="N169C5">
                  <s xml:id="N169C6" xml:space="preserve">Probatur antecedens / quoniaꝫ eque velociter po­
                    <lb/>
                  tentia a. vt .8. remittet motū ſuum cum reſiſtentia
                    <lb/>
                  c. vt .2. ſicut potentia b. vt .4. cū reſiſtentia d. / vt vnū
                    <lb/>
                  quoniam proportiones erunt equales: et eque ve-
                    <lb/>
                  lociter ꝓportionabiliter deperduntur. </s>
                  <s xml:id="N169D1" xml:space="preserve">igitur ſem­
                    <lb/>
                  per manebunt equales ad inuicem ſed b. potentia
                    <lb/>
                  vt .4. velocius remittet motū ſuum cū c. reſiſtentia
                    <lb/>
                  vt .2. quam cū d. reſiſtentia vt vnum / ergo b. poten­
                    <lb/>
                  tia vt .4. velocius remittet cum c. motū ſuum. </s>
                  <s xml:id="N169DC" xml:space="preserve">quaꝫ
                    <lb/>
                  a. potentia vt .8. cū eodē c. / quod fuit probandum.
                    <lb/>
                  </s>
                  <s xml:id="N169E2" xml:space="preserve">Conſequentia patet cū maiore: et minor probatur /
                    <lb/>
                  quoniam velocius deperditur proportio b. ad c.
                    <lb/>
                  quam proportio b. ad d. / ergo velocius remittitur
                    <lb/>
                  motus proueniens a proportione b. ad c. / quã mo­
                    <lb/>
                  tus proueniens a proportione b. ad d. </s>
                  <s xml:id="N169ED" xml:space="preserve">Conſequen­
                    <lb/>
                  tia eſt nota et arguitur antecedens. </s>
                  <s xml:id="N169F2" xml:space="preserve">quoniam pro­
                    <lb/>
                  portio b. potētie vt 4. ad c. reſiſtētiã vt .2. ē ī duplo
                    <lb/>
                  minor ꝓportione b. potētie vt .4. ad d. reſiſtentiã vt
                    <lb/>
                  vnum: quoniam vna dupla et alia quadrupla. </s>
                  <s xml:id="N169FB" xml:space="preserve">et
                    <lb/>
                  plꝰquã ī duplo citiꝰ remittet̄̄ ꝓportio b. ad c. quã
                    <lb/>
                  ꝓportio b. ad d. / igr̄ velociꝰ remittet̄̄ ꝓportio b. ad
                    <lb/>
                  c. quã b. ad .d. / quod fuit probandū. </s>
                  <s xml:id="N16A04" xml:space="preserve">Conſequentia
                    <lb/>
                  eſt nota / vt apparet cum maiore: et minor ꝓbatur /
                    <lb/>
                  quoniam quando reſiſtentia c. acquiſiuerit duos
                    <lb/>
                  gradus reſiſtentie / tunc proportio b. ad c. erit omī­
                    <lb/>
                  no deperdita. </s>
                  <s xml:id="N16A0F" xml:space="preserve">et in eodem tempore adequate ꝑde­
                    <lb/>
                  tur proportio dupla ipſi quadruple, et acquiretur
                    <lb/>
                  vnus gradus dūtaxat ipſi reſiſtentie d. / et reſtabūt
                    <lb/>
                  acquirendi duo qui debēt acquiri vniformiter: er­
                    <lb/>
                  go illi acquirentur adequate ī duplo tempore ad
                    <lb/>
                  acquiſitionem primi: et ſic ſequitur /  tempus de-
                    <lb/>
                  perditionis proportionis b. ad c. eſt ſubtriplū, ad
                    <lb/>
                  tempus deperditionis proportionis b. ad d. / et per
                    <lb/>
                  conſequens pluſquã in duplo citius deperditur ꝓ­
                    <lb/>
                  portio b. ad c. quã b. ad d. / quod fuit probanduꝫ.</s>
                </p>
                <p xml:id="N16A24">
                  <s xml:id="N16A25" xml:space="preserve">Reſpondeo negando antecedens: et
                    <lb/>
                  ad probationē admiſſo caſu negat̄̄ añs: et ad pro-
                    <lb/>
                  bationē negatur hec minor b. velociꝰ remittet mo­
                    <lb/>
                  tū ſuū cū c. quã cum d. / et ad ꝓbationē negatur an-
                    <lb/>
                  tecedens et ad probationē antecedētis negat̄̄ hec
                    <lb/>
                  ↄ̨ña in qua eſt virtus argumenti: proportio b. ad
                    <lb/>
                  c. ē in duplo minor ꝓportione b. ad d. / et pluſquaꝫ
                    <lb/>
                  in duplo citius deperdetur proportio b. ad c. quã
                    <lb/>
                  ꝓportio b. ad .d. / ergo velocius deperdetur propor­
                    <lb/>
                  portio b. ad .c. / quã deperdetur proportio b. ad d. / ſi­
                    <lb/>
                  cut eam eſſe negandam docet triceſimaſexta con-
                    <lb/>
                  cluſio
                    <note position="right" xlink:href="note-0067-01a" xlink:label="note-0067-01" xml:id="N16A56" xml:space="preserve">inq̇rit̄̄ bo­
                      <lb/>
                    uitaſ ↄ̨ña­
                      <lb/>
                    rū calcu.</note>
                  </s>
                  <s xml:id="N16A43" xml:space="preserve">In probatione tamē ↄ̨ñe negate adducit
                    <lb/>
                  calculator duas conditionales: quarū neutra eſt
                    <lb/>
                  bona ↄ̨ña. </s>
                  <s xml:id="N16A4A" xml:space="preserve">Ipſe tamē nihil ad eas reſpondet </s>
                  <s xml:id="N16A4D" xml:space="preserve">Pro
                    <lb/>
                  quarū impugnatione pono aliqua correlaria.</s>
                </p>
                <note position="right" xml:id="N16A60" xml:space="preserve">1. correl.</note>
                <p xml:id="N16A64">
                  <s xml:id="N16A65" xml:space="preserve">¶ Primū correlariū in caſu argumenti d. reſiſtē-
                    <lb/>
                  tia vt vnum et .c. reſiſtentia vt .2. / non vniformiter
                    <lb/>
                  creſcūt / et tamē vtra illarum vniformiter creſcit.
                    <lb/>
                  </s>
                  <s xml:id="N16A6D" xml:space="preserve">Probatur / quia quando reſiſtentia vt vnum acq̇-
                    <lb/>
                  rit vnitatem: reſiſtentia vt .2. acquirit dualitē gra­ </s>
                </p>
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