Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N20F21" level="3" n="3" type="other" type-free="tractatus">
              <div xml:id="N24010" level="4" n="2" type="chapter" type-free="capitulum">
                <p xml:id="N25149">
                  <s xml:id="N251F3" xml:space="preserve">
                    <pb chead="De motu augmentationis." file="0214" n="214"/>
                  tertiã / vt conſtat. </s>
                  <s xml:id="N25205" xml:space="preserve">Ex hoc ſequit̄̄ /  ſecundus exceſſus
                    <lb/>
                  eſt ſecūda pars proportionalis proportiõe f. et ter­
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                  tius tertia / et ſic ↄ̨ſequenter. </s>
                  <s xml:id="N2520C" xml:space="preserve">Ex eo  primus illoruꝫ
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                  eſt prima / et ſic patet prīa ꝑs ↄ̨cluſiõis. </s>
                  <s xml:id="N25211" xml:space="preserve">Et ex illa fa­
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                  cile ꝑſuadetur ſcḋa quoniam ille partes cõtinuo ſe
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                  habent in alia et alia ꝓportiõe puta minori et mi-
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                  nori: igit̄̄ impoſſibile eſt intellectui finito illaꝫ inifi­
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                  nitam ꝓportionū diuerſitatē cõmenſurare: et ꝑ con­
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                  ſequens impoſſibile eſt ip̄m metiri ꝓportionē quã
                    <lb/>
                  illud corpus adequate acq̇ſiuit: et ſic patet cõcluſio</s>
                </p>
                <p xml:id="N25220">
                  <s xml:id="N25221" xml:space="preserve">Septima concluſio diuiſa hora per
                    <lb/>
                  partes proportionales proportione ad libitū ex-
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                  optata cõſtitutiſ certis ordinibꝰ partiū propor-
                    <lb/>
                  tionaliū inter ſcalariter ſe habentiū: totum cor-
                    <lb/>
                  pus abſoluētiū iuxta tenorē primi ↄ̨cluſionis ſepti­
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                  mi capitis prime partis: et in prīo illorū aliqḋ cor­
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                  pus augmētetur acquirendo aliquã proportioneꝫ
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                  et in ſecundo eque velociter augmētetur: et ita ī quo­
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                  libet ſi plures fuerint: illud corpus minorē propor­
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                  tionem acquirit in quolibet ſequenti ꝙ̄ immediate
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                  precedēti in proportione qua hora diuidit̄̄. </s>
                  <s xml:id="N25238" xml:space="preserve">Exem-
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                  plum / vt ſi hora diuidat̄̄ proportione dupla et con-
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                  ſtituūtur tres ordines partiū proportionabilium
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                  interſcalariter ſe habentiū qui ordines totū corpꝰ
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                  abſoluant: et in primo illorū ordinum vnum pedale
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                  aliqualiter velociter augmētetur: et in ſecūdo eque
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                  velociter: et in tertio ſimiliter. </s>
                  <s xml:id="N25247" xml:space="preserve">Tūc dico /  ſi in ṗmo
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                  ordine acquiſiuit proportionē duplam: in ſecundo
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                  ordine acq̇ſiuit medietatē duple. </s>
                  <s xml:id="N2524E" xml:space="preserve">Et in tertio quar­
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                  tam duple. </s>
                  <s xml:id="N25253" xml:space="preserve">Patet / q2 illi ordines cõtinuo. </s>
                  <s xml:id="N25256" xml:space="preserve">ſe habēt
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                  in proportione dupla q̄ eſt proportio diuiſionis: et
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                  vniuerſaliter patet hec ↄ̨cluſio ex prima cõcluſione
                    <lb/>
                  ſeptimi capitis preallegata.
                    <note position="left" xlink:href="note-0214-01a" xlink:label="note-0214-01" xml:id="N2528B" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N25264" xml:space="preserve">¶ Ex quo ſequitur pri­
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                  mo /  cõſciſa hora per partes ꝓportionales q̈uis
                    <lb/>
                  proportione: ſignatiſ certis ordinibus / vt dictum
                    <lb/>
                  eſt in cõcluſione: et in quolibet ſequēti velociꝰ aug-
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                  mentetur aliquod corpus ꝙ̄ in p̄cedēte in ꝓportiõe
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                  diuiſionis hore. </s>
                  <s xml:id="N25271" xml:space="preserve">Tunc in quolibet illorum ordinū
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                  tantã proportionē acquirit ſicut in prima: et ſi fue-
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                  rint quatuor ordines: et in primo acquiſiuit ꝓpor-
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                  tionē ſexquialterã: in omnibus illis acquiſiuit qua­
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                  tuor ſexquialteras. </s>
                  <s xml:id="N2527C" xml:space="preserve">Patet hoc correlariū / quia illi
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                  ordines ſe habent in proportione diuiſionis hore
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                  et in ea proportione in qua ſunt minores corpus ve­
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                  locius augmentatur in illis: igitur tantã ꝓportio-
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                  nem acquirit in quolibet ſequēti ſicut in primo.</s>
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                <note position="left" xml:id="N25291" xml:space="preserve">2. correĺ.</note>
                <p xml:id="N25295">
                  <s xml:id="N25296" xml:space="preserve">¶ Sequitur ſecūdo /  diuiſa hora quacū propor-
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                  tionem volueris: inſtructiſ ordinibus vt in ↄ̨clu-
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                  ſione dicitur: et aliquod corpus in quolibet ſequen­
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                  ti ordine velocius augmētetur ꝙ̄ immediate p̄cedē­
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                  ti in certa maiori ꝓportiõe cõtinuo ꝙ̄ ſit ꝓportio di­
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                  uiſionis: tſtc in quolibet ſequēti maiorē proportio­
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                  nem acquirit ꝙ̄ in primo in ea ꝓportione per quaꝫ
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                  proportio velocitatū augmētatiõis illius ordinis
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                  et primi excedit proportionē primi ad ip̄m: vt ſi ho­
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                  ra diuidat̄̄ proportiõe dupla et ↄ̨ſtituant̄̄ tres ordi­
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                  nes: et in quolibēt pedale a. in quadruplo velocius
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                  augmētetur p̄cederte: et tunc dico /  in tertio ordine
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                  in quadruplo maiorē proportionē acquirit ꝙ̄ ī pri­
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                  mo q2 ꝓportio primi ad tertiū eſt quadrupla et ve-
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                  locitas augmentatiõis in tertio ad velocitatem
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                  augmentatiõis in primo eſt ſexdecupla / vt pꝫ intuē­
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                  ti, ſexdecupla em̄ excedit quadruplã, ideo in q̈dru-
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                  plo maiorē proportionē acquirit in tertio ꝙ̄ in pri­
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                  mo: et in ſecundo in duplo maiorē proportionē quã
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                  in primo: quia proportio eorū ordinū eſt dnpla: et
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                  proportio velocitatū quadrupla. </s>
                  <s xml:id="N252C1" xml:space="preserve">Modo quadru-
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                  pla excedit duplam ꝑ duplã. </s>
                  <s xml:id="N252C6" xml:space="preserve">Patet ꝓbatio huius
                    <cb chead="De motu augmentationis."/>
                  correlarii ex quinta propoſitione ſecundi notabi-
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                  lis tertii capitis ſecūdi tractatus.
                    <note position="right" xlink:href="note-0214-02a" xlink:label="note-0214-02" xml:id="N2532D" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N252D3" xml:space="preserve">¶ Sequit̄̄ tertio /
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                   partita hora per partes proportionales vna cer­
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                  ta proportione ad libitū ſignata: cõſtructiſ ordi­
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                  nibus quotcū horã ip̄am abſoluētibꝰ vt in cõclu­
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                  ſione: et pedale. </s>
                  <s xml:id="N252DE" xml:space="preserve">A. in prīo aliquãtulū velociter au-
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                  geatur: et in quolibet ſequēti ī certa proportiõe mi-
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                  nore proportiõe diuiſiõis cõtinuo velocius ꝙ̄ in im­
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                  mediate precedenti: tunc maiorem proportionē ac­
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                  quirit in precēti ꝙ̄ in ſequēti in ea proportione
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                  per quã proportio ordinis precedentis ad illum or­
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                  dinē ſequentē excedit proportionē velocitatis aug-
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                  mentationis ſequentis et precedentis vt ſi hora di-
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                  uidatur ꝓportione ſexquialtera et conſtituant̄̄ tres
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                  ordines. </s>
                  <s xml:id="N252F3" xml:space="preserve">Exempli gratia et in quolibet ſequente pe­
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                  dale. </s>
                  <s xml:id="N252F8" xml:space="preserve">A. in ſexquitertio velocius augmentetur ꝙ̄ in
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                  immediate precedēte. </s>
                  <s xml:id="N252FD" xml:space="preserve">Tunc dico /  in primo maio­
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                  rem proportionem acquirit quam in tertio ordine
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                  in ea proportione ꝑ quam proportio dupla ſexqui­
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                  quarta qualis eſt inter primū ex tertiū excedit pro­
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                  portionem ſuper ſeptipartientē nouas qualis eſt
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                  inter velocitatem augmentationis tertii ordinis et
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                  velocitatem primi: et quia proportio dupla ſexqui­
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                  quarta excedit proportionē ſupra ſeptipartieutem
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                  nouas per ꝓportionē ſupra decēſeptipartientem
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                  ſexageſimas quartas. </s>
                  <s xml:id="N25312" xml:space="preserve">Ideo in tali ꝓportione ma­
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                  iorem latitudinē proportionis acquirit tale corpꝰ
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                  in primo ordine ꝙ̄ in tertio. </s>
                  <s xml:id="N25319" xml:space="preserve">Patet probatio huiꝰ
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                  correlarii ex ſexta ꝓpoſitiõe ſecundi notabilis ter-
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                  tii capitis ſecundi tractatꝰ preallegati. </s>
                  <s xml:id="N25320" xml:space="preserve">Et ſic pote­
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                  ris inferre infinita alia correlaria ex hac ſeptima
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                  cõcluſione auxiliãtibus propoſitionibꝰ poſitis in
                    <lb/>
                  notabili preallegato.</s>
                </p>
                <p xml:id="N25333">
                  <s xml:id="N25334" xml:space="preserve">Octaua concluſio diuiſo corpore per
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                  partes proportionales qua volueris proportiõe
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                  aſſumptiſ certis ordinibus partium proportio-
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                  nabilium interſcalariter ſe habentium qui totum
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                  corpus abſoluant: et quieſcentibus ceteris ordini-
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                  bus vnꝰ illorū augeatur taliter  quelibet eiꝰ pars
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                  acquirat tantam proportionem ſicut prima. </s>
                  <s xml:id="N25343" xml:space="preserve">Tunc
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                  ille ordo acquirat eam proportionem quam acqui­
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                  rat prima pars eius: et totum corpus minorem pro­
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                  portionē acquirit </s>
                  <s xml:id="N2534C" xml:space="preserve">Quã adinuenies documētis po­
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                  ſitis in prima parte huius operis capite ſeptimo.
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                  </s>
                  <s xml:id="N25352" xml:space="preserve">Prima pars huius concluſionis. </s>
                  <s xml:id="N25355" xml:space="preserve">patet ex quinta
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                  concluſione huius / et ſecunda patet ex tertia cõclu-
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                  ſione capitis in ea allegati. </s>
                  <s xml:id="N2535C" xml:space="preserve">Applica ſi potes.</s>
                </p>
                <p xml:id="N2535F">
                  <s xml:id="N25360" xml:space="preserve">Nona concluſio </s>
                  <s xml:id="N25363" xml:space="preserve">Diuiſa hora per par­
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                  tes proportionales qua volueris proportione: et
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                  in prima a. pedale aliquantulum velociter augea-
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                  tur: et in ſecunda in duplo velocius: et in tertia in
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                  triplo ꝙ̄ in prima: et in quarta in quadruplo ꝙ̄ in
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                  prima: et ſic conſequenter: tunc illud pedale in illa
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                  hora acquirit maiorem proportionem ꝙ̄ in prima
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                  parte probortionali hore in proportione duplica­
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                  ta ad ꝓportionē in qua ſe habet tota illa hora ſic
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                  diuiſa ad primam partem eius proportionalē. </s>
                  <s xml:id="N25378" xml:space="preserve">vt
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                  diuiſa hora per partes proportionales proportio­
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                  ne ſexquialtera: et augmentato pedali vt ponitur ī
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                  concluſione. </s>
                  <s xml:id="N25381" xml:space="preserve">Dico /  in tota illa hora illud pedale
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                  acquirit maiorē proportionē ī nouocuplo ꝙ̄ in pri­
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                  ma parte proportionali. </s>
                  <s xml:id="N25388" xml:space="preserve">Quoniam hora diuiſa
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                  per partes proportiones proportione ſexquialte-
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                  ra ſe habet ad primã partē proportionalem pro-
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                  portionē triplã: et proportio dupla ad triplam eſt
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                  nouocupla. </s>
                  <s xml:id="N25393" xml:space="preserve">Probatur hec concluſio. </s>
                  <s xml:id="N25396" xml:space="preserve">¶ Supponē-
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                  do primo /  ſi in hora diuiſa quauis proportione </s>
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