Alvarus, Thomas, Liber de triplici motu, 1509

Table of figures

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          <div xml:id="N15C17" level="2" n="3" type="other" type-free="pars">
            <div xml:id="N1C8AF" level="3" n="2" type="other" type-free="tractatus">
              <div xml:id="N1C8BC" level="4" n="1" type="chapter" type-free="capitulum">
                <pb chead="Secūdi tractatus" file="0131" n="131"/>
                <note position="left" xml:id="N1CB60" xml:space="preserve">1. confir-
                  <lb/>
                matio.</note>
                <p xml:id="N1CB66">
                  <s xml:id="N1CB67" xml:space="preserve">¶ Et confirmatur / quia cuiuſlibet motus vniformi-
                    <lb/>
                  ter difformis gradꝰ velociſſimꝰ .i. quo mouet̄̄ pun-
                    <lb/>
                  ctus velociſſime motꝰ tm̄ excedit gradū mediū ̄tū
                    <lb/>
                  gradꝰ mediꝰ excedit gradū quo mouet̄̄ pūctus tar-
                    <lb/>
                  diſſime motꝰ vt cõcedit hec opinio et cõis ſcola: ſed
                    <lb/>
                  motꝰ talis q̈drati a.b.c.d. nõ eſt huiuſmodi, igr̄ ta-
                    <lb/>
                  lis motꝰ nõ eſt vniformiter difformis. </s>
                  <s xml:id="N1CB76" xml:space="preserve">Minor ꝓbat̄̄ /
                    <lb/>
                  q2 gradꝰ velociſſimꝰ illiꝰ partis eſt gradus octauꝰ
                    <lb/>
                  cū quadratū illud applicet̄̄ circūferētie rote: et me-
                    <lb/>
                  dius eſt vt quatuor, et motꝰ illiꝰ nõ terminat̄̄ ad nõ
                    <lb/>
                  gradū: ergo ſeq̇tur /  gradus velociſſimꝰ ꝑ maiorē
                    <lb/>
                  latitudinem excedit mediuꝫ quam medius excedat
                    <lb/>
                  infimum / quod fuit probandum.</s>
                </p>
                <note position="left" xml:id="N1CB85" xml:space="preserve">2. confir-
                  <lb/>
                matio.</note>
                <p xml:id="N1CB8B">
                  <s xml:id="N1CB8C" xml:space="preserve">¶ Confirmatur ſecundo principale argumentum /
                    <lb/>
                  q2 ſi motꝰ talis rote eſſet vniformiter difformis a
                    <lb/>
                  nõ gradū vſ ad octauū / ſeq̄ret̄̄ /  adequata velo-
                    <lb/>
                  citas illiꝰ rote eſſet vt quatuor: ſed ↄ̨ñs eſt falſū: igr̄
                    <lb/>
                  illud ex quo ſeq̇tur. </s>
                  <s xml:id="N1CB97" xml:space="preserve">Cõſequētia eſt nota, et falſitas
                    <lb/>
                  ↄ̨ñtis argr̄ / q2 velocitas totiꝰ illiꝰ partis q̄ claudit̄̄
                    <lb/>
                  circulo minori .d.e.f. eſt vt duo cuꝫ ſit a quarto vſ
                    <lb/>
                  ad nõ gradū, et velocitas totiꝰ reſidui eſt vt ſex cum
                    <lb/>
                  ſit a quarto vſ ad octauum, et ſi eſſet in medietate
                    <lb/>
                  adequate faceret ad denoīationē totiꝰ motꝰ vt tria.
                    <lb/>
                  modo eſt in ſexquialtero maiori parte medietate: g̊
                    <lb/>
                  ſeq̇tur /  motꝰ eiꝰ facit ad denoīationē totiꝰ in ſex-
                    <lb/>
                  q̇altero magis: et ꝑ ↄ̨ñs / vt quatuor cū dimidio (cum
                    <lb/>
                  quatuor cū dimidio ad tria ſit ꝓportio ſexq̇altera) /
                    <lb/>
                  g̊ ſeq̇tur /  talis motus adequate eſt velocior quã vt
                    <lb/>
                  quatuor cū dimidio, et ꝑ ↄ̨ñs velocior quã vt quatu­
                    <lb/>
                  tor / qḋ fuit ꝓbandū. </s>
                  <s xml:id="N1CBB2" xml:space="preserve">Sed iã ꝓbo /  illa pars rote q̄
                    <lb/>
                  eſt totū reſiduū a minori circulo eſt in ſexquialtero
                    <lb/>
                  maior medietate, q2 illa pars eſt tres quarte totiꝰ
                    <lb/>
                  rote: igr̄ in ſexq̇altero eſt maior medietate </s>
                  <s xml:id="N1CBBB" xml:space="preserve">Probat̄̄ /
                    <lb/>
                  q2 medietas eſt due q̈rte: mõ triū quartaꝝ ad duas
                    <lb/>
                  q̈rtas eſt ꝓportio ſexq̇altera. </s>
                  <s xml:id="N1CBC2" xml:space="preserve">Sed iã ꝓbo añs vcꝫ / 
                    <lb/>
                  reſiduū illius rote a minori circulo ſit tres quarte
                    <lb/>
                  illius rote quia totius rote ad minorem totum cir-
                    <lb/>
                  culū eſt ꝓportio quadrupla: g̊ totū reſiduū a mīori
                    <lb/>
                  circulo qui eſt vna quarta eſt tres q̈rte: ſꝫ illa ꝑs eſt
                    <lb/>
                  totū reſiduū a mīori circulo / vt notū eſt: g̊ illa ē tres
                    <lb/>
                  q̈rte totiꝰ rote / qḋ fuit ꝓbandū.
                    <note position="left" xlink:href="note-0131-01a" xlink:label="note-0131-01" xml:id="N1CC1D" xml:space="preserve">Brauar-
                      <lb/>
                    dinꝰ ī tra­
                      <lb/>
                    ctatu ꝓ-
                      <lb/>
                    portio-
                      <lb/>
                    nū capi-
                      <lb/>
                    te .4.</note>
                  </s>
                  <s xml:id="N1CBD6" xml:space="preserve">Sꝫ iã ꝓbo /  totius
                    <lb/>
                  rote ad mīorē circulū ei cõcētricū ſit ꝓportio q̈dru-
                    <lb/>
                  pla, q2 vt demõſtrat brauardinꝰ ī tractatu ꝓporti-
                    <lb/>
                  onū capite q̈rto ſēꝑ īter duos circulos īeq̈les eſt du­
                    <lb/>
                  plicata ꝓportio ad ꝓportionē q̄ eſt īter diametros
                    <lb/>
                  eorūdē circuloꝝ. </s>
                  <s xml:id="N1CBE3" xml:space="preserve">ita  ꝓportio circuloꝝ eſt ꝓportio
                    <lb/>
                  diametroꝝ duplicata / vt etiã facile poteſt intueri in
                    <lb/>
                    <figure xlink:href="fig-0131-01a" xlink:label="fig-0131-01" xml:id="N1CC2D" number="10">
                      <image file="0131-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0131-01"/>
                    </figure>
                  figura ſuppoſita
                    <lb/>
                  ſꝫ diametri totiꝰ
                    <lb/>
                  rote ad diametꝝ
                    <lb/>
                  circĺi d.e.f. ē ꝓpor­
                    <lb/>
                  tio dupla: g̊ totiꝰ
                    <lb/>
                  rote ad circulū .d
                    <lb/>
                  e.f. eſt ꝓportio q̈-
                    <lb/>
                  drupla q̄ ē dupla
                    <lb/>
                  ad duplã / qḋ fuit
                    <lb/>
                  ꝓbandū. </s>
                  <s xml:id="N1CC01" xml:space="preserve">Qḋ o
                    <lb/>
                  diametri ad dia­
                    <lb/>
                  metꝝ ſit ꝓportio
                    <lb/>
                  dupla / ptꝫ ex caſu
                    <lb/>
                  prīcipalis argu-
                    <lb/>
                  mēti. </s>
                  <s xml:id="N1CC0E" xml:space="preserve">Et ſic ex hac deductiõe ptꝫ /  totꝰ ille motꝰ eſt
                    <lb/>
                  vt quī q2 ille tres q̈rte denominã vt q̈tuor cū di-
                    <lb/>
                  midio, et alia q̈rta  eſt mīor circulꝰ denoīat vt di-
                    <lb/>
                  midiū (cū ſit vt duo) / igr̄ totꝰ motꝰ eſt vt quī et ſic nõ
                    <lb/>
                  eſt adequate vt quatuor / quod fuit probandum.</s>
                </p>
                <p xml:id="N1CC33">
                  <s xml:id="N1CC34" xml:space="preserve">Scḋo prīcipaliṫ arguit̄̄ ſic </s>
                  <s xml:id="N1CC37" xml:space="preserve">Si illa dif­
                    <lb/>
                  finitio eſſet bona ſeq̄ret̄̄ /  motꝰ celi nõ eſſet vnifor-
                    <cb chead="Capitulū primū."/>
                  miter difformis q̊ ad ſubiectū: ſꝫ ↄ̨ñs eſt falſū / et ↄ̨tra
                    <lb/>
                  cõiṫ opinãtes / ir̄ illḋ ex q̊ ſeq̇tur. </s>
                  <s xml:id="N1CC41" xml:space="preserve">Seq̄la ꝓbat̄̄ / et diuido
                    <lb/>
                  ṗmū mobile in duas medietates ꝑ coluꝝ vcꝫ ꝓcedē­
                    <lb/>
                  tē a polo artico ꝑ polū antarticū et ꝑ capita arietꝪ
                    <lb/>
                  et libre / q̊ poſito arguo ſic / nulla illaꝝ medietatū mo­
                    <lb/>
                  uet̄̄ vniformiṫ difformiṫ: igr̄ nec celū mouet̄̄ vnifor-
                    <lb/>
                  miṫ difformiṫ. </s>
                  <s xml:id="N1CC4E" xml:space="preserve">Cõſequētia ptꝫ, et argr̄ añs / qm̄ neu-
                    <lb/>
                  triꝰ illaꝝ medietatū pūctꝰ q̇ eſt ī medio tãtū excedi-
                    <lb/>
                  tur in velocitate a pūcto velociſſime moto ̄tū exce-
                    <lb/>
                  dit pūctū tardiſſime motū ſiue nõ g̈dū cū pūctꝰ exi-
                    <lb/>
                  ſtēs in medio ſit pūctꝰ exñs in circulo eq̇noctiali q̇ ē
                    <lb/>
                  pūctꝰ velociſſime motꝰ: igr̄ a nullo excedit̄̄ in veloci­
                    <lb/>
                  tate / et ꝑ ↄ̨ñs nõ tm̄ excedit a pūcto velociſſime moto
                    <lb/>
                  quantum excedit punctū tardiſſime motum vel nõ
                    <lb/>
                  gradum velocitatis / quod fuit probandum.</s>
                </p>
                <p xml:id="N1CC61">
                  <s xml:id="N1CC62" xml:space="preserve">¶ Et confirmat̄̄ / q2 ſi eſſet aliquis motus vniformi-
                    <lb/>
                  ter difformis q̊ ad ſubiectū maxīe eſſet motꝰ localis
                    <lb/>
                  q̊ ꝑ rarefactionē mouet̄̄ vnū q̈dratū qḋ rarefit vni-
                    <lb/>
                  formiter a nõ g̈du in extremo q̇eſcēte vſ ad octauū
                    <lb/>
                  in altero extremo: ſꝫ hec nõ, igr̄. </s>
                  <s xml:id="N1CC6D" xml:space="preserve">Maior eſt nota cū
                    <lb/>
                  ↄ̨ña, et ꝓbat̄̄ mīor / q2 nõ cuiuſlꝫ ꝑtis illiꝰ g̈dus mediꝰ
                    <lb/>
                  tm̄ excedit̄̄ a velociſſimo quãto excedit g̈dū tardiſſi­
                    <lb/>
                  mū illiꝰ ꝑtis vĺ nõ g̈dū: igr̄ totū illud q̈dratū nõ mo­
                    <lb/>
                  uet̄̄ vniformiṫ difformiṫ q̊ ad ſubiectū. </s>
                  <s xml:id="N1CC78" xml:space="preserve">Cõſequētia
                    <lb/>
                  ptꝫ ex definitiõe, et argr̄ añs, et ſigno vnã partē ī me­
                    <lb/>
                  dietate illiꝰ q̈drati q̄ velociꝰ rarefit: et ſit illa pars
                    <lb/>
                  figurata ꝑ modū duoꝝ lateꝝ vniꝰ triãguli faciētis
                    <lb/>
                  vnū angulū ſupra punctū mediū ex vno latere et ex
                    <lb/>
                  alio infra vt apparet in figura hic infra ſcripta.</s>
                </p>
                <figure xml:id="N1CC85" number="11">
                  <image file="0131-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0131-02"/>
                </figure>
                <p xml:id="N1CC89">
                  <s xml:id="N1CC8A" xml:space="preserve">
                    <reg norm="Tunc" type="context">Tūc</reg>
                  ſic
                    <reg norm="arguitur" type="wordlist">argr̄</reg>
                  / illa
                    <reg norm="pars" type="wordlist">ꝑs</reg>
                  eſt
                    <reg norm="pars" type="wordlist">ꝑs</reg>
                    <reg norm="illius" type="simple">illiꝰ</reg>
                  q̈dra-
                    <lb/>
                  ti: et
                    <reg norm="tamen" type="wordlist">tñ</reg>
                  ipſa
                    <reg norm="non" type="wordlist">nõ</reg>
                    <reg norm="mouetur" type="simple">mouet̄̄</reg>
                    <reg norm="vniformiter" type="simple">vniformiṫ</reg>
                    <reg norm="dif- formiter" type="simple">dif-
                      <lb/>
                    formiṫ</reg>
                  :
                    <reg norm="igitur" type="wordlist">igr̄</reg>
                    <reg norm="propoſitum" type="simple context">ꝓpoſitū</reg>
                  . </s>
                  <s xml:id="N1CC91" xml:space="preserve">
                    <reg norm="Arguitur" type="wordlist">Argr̄</reg>
                    <reg norm="antecedens" type="wordlist">añs</reg>
                  /
                    <reg norm="quia(?)" type="wordlist">q2</reg>
                    <reg norm="pun­ ctus" type="context">pū­
                      <lb/>
                    ctus</reg>
                    <reg norm="exiſtens" type="wordlist">exñs</reg>
                  in medio
                    <reg norm="illius" type="simple">illiꝰ</reg>
                    <reg norm="partis" type="wordlist">ꝑtis</reg>
                  in linea
                    <lb/>
                    <reg norm="procedente" type="simple context">ꝓcedēte</reg>
                  a
                    <reg norm="puncto" type="context">pūcto</reg>
                    <reg norm="non" type="wordlist">nõ</reg>
                  moto
                    <reg norm="vſque" faithful="vſ" type="simple">vſqꝫ</reg>
                  ad
                    <reg norm="pun­ ctum" type="context context">pū­
                      <lb/>
                    ctū</reg>
                  velociſſime
                    <reg norm="motum" type="context">motū</reg>
                    <reg norm="ipſius" type="simple">ipſiꝰ</reg>
                  q̈drati eſt
                    <lb/>
                    <reg norm="punctus" type="context">pūctus</reg>
                    <reg norm="medius" type="simple">mediꝰ</reg>
                    <reg norm="totius" type="simple">totiꝰ</reg>
                  q̈drati qui
                    <reg norm="mouetur" type="simple">mouet̄̄</reg>
                  vt quatuor / vt
                    <lb/>
                    <reg norm="patet" type="wordlist">ptꝫ</reg>
                  in figura:
                    <reg norm="igitur" type="wordlist">igr̄</reg>
                  ſi talis
                    <reg norm="mouetur" type="simple">mouet̄̄</reg>
                  vniformiter diffor-
                    <lb/>
                  miter
                    <reg norm="ſequitur" type="simple">ſequit̄̄</reg>
                  /
                    <reg norm="quae" type="wordlist"></reg>
                    <reg norm="totus" type="simple">totꝰ</reg>
                    <reg norm="motus" type="simple">motꝰ</reg>
                    <reg norm="eius" type="simple">eiꝰ</reg>
                  eſt vt quatuor / ſed
                    <reg norm="conſequens" type="wordlist">ↄ̨ñs</reg>
                    <lb/>
                  eſt
                    <reg norm="falſum" type="context">falſū</reg>
                  :
                    <reg norm="igitur" type="wordlist">igr̄</reg>
                  illud ex quo
                    <reg norm="ſequitur" type="simple">ſequit̄̄</reg>
                  . </s>
                  <s xml:id="N1CCA2" xml:space="preserve">Falſitas ↄ̨ñtis
                    <reg norm="pro­ batur" type="simple">pro­
                      <lb/>
                    bat̄̄</reg>
                  /
                    <reg norm="quia(?)" type="wordlist">q2</reg>
                    <reg norm="vtraque" faithful="vtra" type="simple">vtraqꝫ</reg>
                  medietas talis partis
                    <reg norm="velocius" type="simple">velociꝰ</reg>
                    <reg norm="mouetur" type="simple">mouet̄̄</reg>
                    <lb/>
                    <reg norm="per" type="wordlist">ꝑ</reg>
                    <reg norm="rarefactionem" type="context">rarefactionē</reg>
                    <reg norm="quam" type="context">quã</reg>
                  vt quatuor
                    <reg norm="quia(?)" type="wordlist">q2</reg>
                    <reg norm="vtriuſque" faithful="vtriuſ" type="simple">vtriuſqꝫ</reg>
                    <reg norm="illarum" type="simple">illaꝝ</reg>
                    <reg norm="pun- ctus" type="context">pū-
                      <lb/>
                    ctus</reg>
                    <reg norm="medius" type="simple">mediꝰ</reg>
                  eſt
                    <reg norm="intenſior" type="context">intēſior</reg>
                    <reg norm="quam" type="wordlist">ꝙ̄</reg>
                  vt .4.
                    <reg norm="cum" type="context">cū</reg>
                    <reg norm="vtriuſque" faithful="vtriuſ" type="simple">vtriuſqꝫ</reg>
                    <reg norm="illarum" type="simple">illaꝝ</reg>
                    <reg norm="me- dietatum" type="context">me-
                      <lb/>
                    dietatū</reg>
                    <reg norm="punctus" type="context">pūctus</reg>
                    <reg norm="medius" type="simple">mediꝰ</reg>
                  ſit ſupra
                    <reg norm="punctum" type="context">punctū</reg>
                    <reg norm="exiſtentem" type="context">exiſtentē</reg>
                  in
                    <lb/>
                  medio
                    <reg norm="illius" type="simple">illiꝰ</reg>
                  q̈drati: et ſic
                    <reg norm="vtraque" faithful="vtra" type="simple">vtraqꝫ</reg>
                    <reg norm="illarum" type="simple">illaꝝ</reg>
                    <reg norm="mouetur" type="simple">mouet̄̄</reg>
                    <reg norm="velocius" type="simple">velociꝰ</reg>
                    <lb/>
                  ̄ vt quatuor:
                    <reg norm="ergo" type="wordlist">g̊</reg>
                    <reg norm="per" type="wordlist">ꝑ</reg>
                    <reg norm="conſequens" type="wordlist">ↄ̨ñs</reg>
                  tota illa pars
                    <reg norm="cuius" type="simple">cuiꝰ</reg>
                  ille
                    <reg norm="ſunt" type="context">ſūt</reg>
                  me­
                    <lb/>
                  dietates
                    <reg norm="mouetur" type="simple">mouet̄̄</reg>
                    <reg norm="velocius" type="simple">velociꝰ</reg>
                    <reg norm="quam" type="wordlist">ꝙ̄</reg>
                  vt
                    <reg norm="quatuor" type="wordlist">q̈tuor</reg>
                  /
                    <reg norm="quod" type="simple">qḋ</reg>
                  eſt
                    <reg norm="oppoſitum" type="simple">oppoſituꝫ</reg>
                    <lb/>
                  aut
                    <reg norm="ſaltem" type="context">ſaltē</reg>
                    <reg norm="infert" type="context">īfert</reg>
                    <reg norm="oppoſitum" type="context">oppoſitū</reg>
                    <reg norm="conſequentis" type="wordlist">ↄ̨ñtis</reg>
                  /
                    <reg norm="quod" type="simple">qḋ</reg>
                  erat
                    <reg norm="probandum" type="simple context context">ꝓbãdū</reg>
                    <reg norm="falſum" type="context">falſū</reg>
                  .</s>
                </p>
                <p xml:id="N1CCB5">
                  <s xml:id="N1CCB6" xml:space="preserve">In oppoſitū tñ arguit̄̄ / ꝑ cõmunē au-
                    <lb/>
                  ctoritatem recentiū pḣoꝝ hãc definitionē ponentiū</s>
                </p>
                <p xml:id="N1CCBB">
                  <s xml:id="N1CCBC" xml:space="preserve">Pro ſolutiõe  enodatiõe huiꝰ q̄ſtiõis
                    <lb/>
                  pono aliquas cõcluſiones quibꝰ mediantibꝰ adīue­
                    <lb/>
                  niatur definitio motus vniformiter difformis quo
                    <lb/>
                  ad ſubiectum.</s>
                </p>
                <p xml:id="N1CCC5">
                  <s xml:id="N1CCC6" xml:space="preserve">Prima ↄ̨̨cluſio. </s>
                  <s xml:id="N1CCC9" xml:space="preserve">Motꝰ vniformiṫ dif-
                    <lb/>
                  formis quo ad ſubiectū nõ bene definit̄̄ iſto modo.
                    <lb/>
                  </s>
                  <s xml:id="N1CCCF" xml:space="preserve">Motus vniformiter difformis quo ad ſubiectū eſt
                    <lb/>
                  cuiꝰ oēs partes īmediate ſcḋm extenſionē ſunt īme-
                    <lb/>
                  diate ſcḋm intenſionē motus ſiue velocitatū ita 
                    <lb/>
                  remiſſiſſimus gradus velocitatis qui eſt in intēſio-
                    <lb/>
                  ri ſit remiſſiſſimus qui non eſt in remiſſiori illarum
                    <lb/>
                  duarum partium ſibi immediatarum. </s>
                  <s xml:id="N1CCDC" xml:space="preserve">Probatur
                    <lb/>
                  hec concluſio: quia pono caſum /  ſit vna rota que
                    <lb/>
                  que mouetur a non gradu vſ ad certum gradum
                    <lb/>
                  ita  a centro eius q̇eſcente vſ ad mediū ſemidia­
                    <lb/>
                  metri ſit motus vniformiter difformis a nõ gradu
                    <lb/>
                  vſ ad quatuor et a pūcto medio ſemidiametri vſ-
                    <lb/>
                   ad circūferentiã ſit motus vniformiter difformis </s>
                </p>
              </div>
            </div>
          </div>
        </div>
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