Alvarus, Thomas, Liber de triplici motu, 1509
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            <div xml:id="N1C8AF" level="3" n="2" type="other" type-free="tractatus">
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                <pb chead="Secundi tractatus" file="0135" n="135"/>
                <note position="left" xml:id="N1D1F3" xml:space="preserve">dicitur.</note>
                <p xml:id="N1D1F7">
                  <s xml:id="N1D1F8" xml:space="preserve">¶ Dices /  iſte due concluſiones tam illate: et ab iſta
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                  opinione / et altera ſunt concedende. </s>
                  <s xml:id="N1D1FD" xml:space="preserve">Et ideo ſunt cor­
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                  relaria et non inconuenientia.</s>
                </p>
                <p xml:id="N1D202">
                  <s xml:id="N1D203" xml:space="preserve">Contra quia tunc ſequeretur /  a qua­
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                  libet parte proportionali alicuius mobilis ſecun-
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                  dum certam diuiſionem procedendo demeretur ali­
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                  qua velocitas: ita  quelibet ſecundum talem diui­
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                  ſionem moueatur minori velocitate ꝙ̄ antea mo-
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                  uebatur: et tamen totum mobile mouetur continuo
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                  vniformiṫ et eq̄ velociṫ ſicut ãtea: ſꝫ ↄ̨ſeq̄ns eſt falſū:
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                  igitur illud ex quo ſequitur: </s>
                  <s xml:id="N1D214" xml:space="preserve">Falſitas conſequentis
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                  oſtenditur / quia alias ſequeretur /  tota velocitas
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                  poteſt demi a partibus proportionalibus manen­
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                  te tamen ſemper velocitate totius equali / quod eſt
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                  mere impoſſibile. </s>
                  <s xml:id="N1D21F" xml:space="preserve">Patet hoc poſito /  in hora con-
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                  tinue cuiuſlibet partis proportionalis ſecundum /
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                  hanc diuiſionem remittatur motus quo ad vſ ve-
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                  niat ad non gradum / tunc continuo per illam horã
                    <lb/>
                  tale mobile per te mouebitur equaiiter et vniformi-
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                  ter: ergo adhuc poſt illud inſtans terminatiuum po­
                    <lb/>
                  terit ſic moueri motu partium ad non gradum re-
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                  miſſo: </s>
                  <s xml:id="N1D230" xml:space="preserve">Sed iam probo ſequelam: et pono caſum / 
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                  vna rota diuidatur per partes proportionales cir­
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                  culares concentricas minoribus terminatis verſus
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                  peripheriam rote: et a prima dematur medietas ſue
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                  velocitatis et a ſequenti eam puta a ſecunda demat̄̄
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                  medietas vnius gradus et a tertia quarta vniꝰ gra-
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                  dus: et ſic conſequenter procedendo per partes ſub­
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                  duplas quo poſito a puncto extremo nulla veloci-
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                  tas demitur: et mouetur: igitur continuo mouet̄̄ vni­
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                  formiter </s>
                  <s xml:id="N1D245" xml:space="preserve">Patet conſequentia et tamen quelibet ꝑs
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                  eius proportionalis ſecundum certam diuiſionem
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                  mouetur velocitate minori / ꝙ̄ mouebatur antea
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                  </s>
                  <s xml:id="N1D24D" xml:space="preserve">Sed ad inferendum  quelibet pars proportiona­
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                  lis ſecundum talem diuiſioneꝫ moueatur ſubdupla
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                  velocitate oportet ponere in caſu /  a qualibet illa­
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                  rum dematur medietas velocitatis qua antea mo-
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                  uebatur: et ſic habebitur propoſitum. </s>
                  <s xml:id="N1D258" xml:space="preserve">Et ſi tibi caſꝰ
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                  appareat difficilis / vt nunc michi videor facile erit
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                  verificare illum caſum in rota flexibili puta aque vĺ
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                  alterius liquoris exiſtentis intra ſperam rotundaꝫ
                    <lb/>
                  et quilibet punctus eius moueatur quieſcente cētro
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                  motu circulari: partibus eius mouentibus eodē mo­
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                  do quo ponitur in caſu:</s>
                </p>
                <p xml:id="N1D267">
                  <s xml:id="N1D268" xml:space="preserve">Tertio principaliter contra ſecundaꝫ
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                  partem queſtionis videlicet /  non debet attēdi pe-
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                  nes gradum medium arguitur ſic: quia ſi illud eſſet
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                  veruꝫ ſequeretur /  ſi vna rota moueretur difformi­
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                  ter quo ad ſubiectum a non gradu vſ ad certū gra­
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                  dum ita  pars illa que eſt a centro vſ ad medie-
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                  tatem ſemidiametri moueatur a non gradu vſ ad
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                  quartum: et reſidua pars vſ ad circunferentiã mo­
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                  ueatur a quarto vſ ad duodecimum / tunc talis ro­
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                  ta moueretur velocitate vt ſex: ſed conſequens ē fal­
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                  ſum / igitur illud ex quo ſequitur </s>
                  <s xml:id="N1D27F" xml:space="preserve">Sequela probatur /
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                  quia ille eſt gradus medius inter duodecimū et non
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                  gradum. </s>
                  <s xml:id="N1D286" xml:space="preserve">Sed iam arguitur falſitas conſequentis /
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                  quia tunc ſequeretur /  illa rota eque velociter mo­
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                  ueretur ſicut ſi motus eius eſſet vniformiter diffor-
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                  mis a non gradu vſ ad duodecimum. </s>
                  <s xml:id="N1D28F" xml:space="preserve">Sed conſe-
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                  quens eſt falſum: igitur illud ex quo ſequitur. </s>
                  <s xml:id="N1D294" xml:space="preserve">Con-
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                  ſequentia apparet: et falſitas conſequentis argui-
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                  tur / quia ſi illa rota moueretur vniformiter diffor-
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                  miter a non gradu vſ ad duodecimum: tunc pun-
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                  ctus medius ſemidiametri moueretur velocitate vt
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                  ſex / et per conſequēs maiori velocitate quam modo
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                  et quilibet punctus intrinſecꝰ maiori velocitate quã
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                  modo / vt ſatis patet intueti: ergo ſequitur /  illa ro­
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                  ta mouetur / tunc maiori velocitate quã modo. </s>
                  <s xml:id="N1D2A8" xml:space="preserve">Pro­
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                  batur hec conſequentia / quia modo videlicet quan-
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                  do vna pars eius que incipit a centro rote et termi-
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                  natur ad medium ſemidiametri mouetur a nõ gra-
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                  du vſ ad quartum et reliqua pars a quarto vſ
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                  ad duodecimum: a velocitate vel penes velocitatem
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                  alicuius puncti intrinſeci eius commēſuratur et at­
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                  tenditur motus illius rote, et ab eodem poſtea deb3
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                  attendi quando velocius mouetur: igitur propoſi-
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                  tum: quia rota manet: nec rarefacta: nec condenſa­
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                  ta: et idem continuo manet punctus eius mediꝰ quã­
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                  do mouetur ſic motu difformiter difformi et quam­
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                  do mouetur motu vniformiter difformi.</s>
                </p>
                <note position="right" xml:id="N1D2C3" xml:space="preserve">dicitur.</note>
                <p xml:id="N1D2C7">
                  <s xml:id="N1D2C8" xml:space="preserve">¶ Dices negando ſequelam: et ad probationem: di­
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                  ces /  non eſt cõtra te: quia tu vis dicere /  / debet at­
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                  tendi motus difformis quo ad ſubiectum penes gra­
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                  dum mediuꝫ quando talis motus eſt vniformiṫ dif­
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                  formis quo ad ſubiectum: ſed non quando eſt diffor­
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                  miter difformis: qnia tunc ſequenda eſt tertia pars
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                  queſtionis videlicet penes reductionem ad vnifor-
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                  mitatem.</s>
                </p>
                <p xml:id="N1D2D9">
                  <s xml:id="N1D2DA" xml:space="preserve">Sed contra / quia ſi in omni motu vni­
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                  formiter difformi quo ad ſubiectum debeat veloci-
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                  tas attendi penes gradum medium / vel igitur ꝑ gra­
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                  dum medium intelligitur gradus qui eſt medio ta-
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                  lis ſubiecti quo ad magnitudinem: vel ī medio quo
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                  ad longitudinem, vel in medio quo ad magnitudi-
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                  nem et longitudinem ſimul / ſed nullum iſtorum ē di­
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                  cendum: igitur non debet motus vniformiter diffor­
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                  mis quo ad ſubiectum velocitas penes gradum me­
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                  dium commenſurari et attendi. </s>
                  <s xml:id="N1D2EF" xml:space="preserve">Maior quo ad pri-
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                  mam partem videlicet /  non debeat attendi penes
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                  gradum medium hoc eſt exiſtentem in medio ſubie-
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                  cti / quo ad magnitudinem patet ex primo argumē-
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                  to: et ſecunda confirmatione eius in dubitatiõe for-
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                  mata in priori capite / et quo ad ſecundam partē pa­
                    <lb/>
                  tet ex confirmatione ſecundi argumenti eiuſdem du­
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                  bitationis prioris capitis. </s>
                  <s xml:id="N1D300" xml:space="preserve">Sed quantum ad tertiã
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                  partem patet manifeſte / quia quãdo rota mouetur
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                  ſic vniformiter difformiter quo ad ſubiectum a nõ
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                  gradu in centro vſ ad certum gradum in circunfe­
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                  rentia procedendo a centro vſ ad circunferentiaꝫ
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                  nullus idem punctus eſt in medio magnitudinis et
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                  longitudinis ſignanter quando  rota eſt vbi eq̈­
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                  lis craſſitudinis </s>
                  <s xml:id="N1D311" xml:space="preserve">Tamen volo efficatiori argumēto
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                  meo iudicio confirmare ſecundam partem minoris
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                  videlicet /  non debeat velocitas motus vniformi-
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                  ter difformis quo ad ſubiectum attendi penes pun­
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                  ctum exiſtentem in medio mobilis quantum ad lon-
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                  gitudinem. </s>
                  <s xml:id="N1D31E" xml:space="preserve">Et in predicta rota de qua ſepe mentio
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                  facta eſt a centro eius vſ ad circunferētiam ſigno
                    <lb/>
                  vnam colūnã ex cuius baſi in centro rote educo line­
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                  am giratiuam girantem omnes partes proportio­
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                  nales talis columne / vt ↄ̨muniter ponitur et volo / 
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                  talis rota moueat̄̄ vniformiṫ difformiter q̊ ad ſub-
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                  iectum a non gradu vſ ad octauum / quo poſito ſic
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                  argumentor illa linea giratiua mouetur vniformi­
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                  ter difformiter cum ſit pars corporis vniformiter
                    <lb/>
                  difformiter moti et tamen motus eius non correſpõ­
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                  det gradui exiſtenti in medio corporis quantuꝫ ad
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                  longitudinem cum nullum tale ſit / vt notum eſt: igi-
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                  tur aliquod mouetur vniformiter difformiter quo
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                  ad ſubiectum cuius motus velocitas non attendi-
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                  tur penes gradum motus exiſtentem in medio eius
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                  quantum ad longitudinem. </s>
                  <s xml:id="N1D33F" xml:space="preserve">Simile argumentum
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                  fierit / ſi a centro rote educeretur vna linea que circū­
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                  daret primo primam partem proportionalem cir­
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                  cularem illius rote, et ſecundam et tertiam et quartã </s>
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