Alvarus, Thomas, Liber de triplici motu, 1509
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                  <s xml:id="N25537" xml:space="preserve">
                    <pb chead="De motu augmentationis." file="0216" n="216"/>
                  da par queſtionis noſtre reſtat ad dubia accedamꝰ</s>
                </p>
                <p xml:id="N25541">
                  <s xml:id="N25542" xml:space="preserve">Dubitatur primo. </s>
                  <s xml:id="N25545" xml:space="preserve">An ſecundū primã
                    <lb/>
                  opinionem vndecima: duodecima: et tredecima cõ-
                    <lb/>
                  cluſiones calculatoris in capitulo de augmentatio­
                    <lb/>
                  ne ſint concedēde: et an proobationes earum quas
                    <lb/>
                  ipſe calculator adduxit cõcludant et ſint efficaces.</s>
                </p>
                <p xml:id="N25550">
                  <s xml:id="N25551" xml:space="preserve">Dubitatur ſecūdo / an ille eedem ſint
                    <lb/>
                  concedende ſecundum poſteriorem opinionem.</s>
                </p>
                <p xml:id="N25556">
                  <s xml:id="N25557" xml:space="preserve">Dubitatur tertio / an iuxta ſecūdū op-
                    <lb/>
                  pinionē aliquid poſſit per totum diminui.</s>
                </p>
                <p xml:id="N2555C">
                  <s xml:id="N2555D" xml:space="preserve">¶ Ad primū accedendo probo primo /  probatio
                    <lb/>
                  calculatoris ad vndecimã concluſionem nõ valeat
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                  ſaltem in caſu ſuo: quia in illo caſu illa concluſio
                    <lb/>
                  eſt falſa: igitur non probat eam in tali caſu. </s>
                  <s xml:id="N25566" xml:space="preserve">Pro­
                    <lb/>
                  batur antecedēs: quia ipſe ponit caſum  infinita
                    <lb/>
                  incipiant augeri a non quanto: et incipiat primum
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                  in duplo velocius augeri ſecundo: et ſecundū in du-
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                  plo velocius tertio: et tertiū quarto: et ſic conſequē­
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                  ter: in caſu iſta propoſito eſt falſa: in infinitum ve­
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                  lociter incipit aliquod augeri quod iu infinitū tar­
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                  de incipit augeri. </s>
                  <s xml:id="N25577" xml:space="preserve">Probatur / quia bene ſequitur in­
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                  finite velociter incipit aliquod iſtoruꝫ augeri quod
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                  infinite tarde incipit augeri ergo poſt inſtans qḋ
                    <lb/>
                  eſt preſens infinitum velociter augebitur quod in­
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                  finitum tarde incipit augeri: et ꝑ cõſequēs poſt hoc
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                  aliqualiter velociter aliquod iſtorum augebit̄̄ qḋ
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                  infinite tarde incipit augeri: conſequens eſt falſuꝫ /
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                  igitur et antecedens. </s>
                  <s xml:id="N25588" xml:space="preserve">Conſequentie ſunt note et pro­
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                  batur falſitas conſequentis / quia nullū infinite tar­
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                  de incipit augeri / vt patet intuenti caſum: igitur.</s>
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                <p xml:id="N2558F">
                  <s xml:id="N25590" xml:space="preserve">¶ Secundo arguitur / ꝓbando inefficaciam proba­
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                  tionis qua ipſe calculator probat duodecimã con-
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                  cluſionē. </s>
                  <s xml:id="N25597" xml:space="preserve">Ad eam em̄ probandam inducit calcula-
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                  tor talem caſum ſint infinita quãta quorum primū
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                  ſit aliquantū: et ſecūdū in quadruplo maius ꝙ̄ pri­
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                  mū: et tertiū in quadruplo maius ꝙ̄ ſecundū: et ſic
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                  in infinitū: et augeatur primū aliqualiter velociter
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                  et ſecundū in duplo minus: et tertiū in duplo minꝰ
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                  ̄ ſecundū: et ſic in infinitum: tunc dicit primã par-
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                  tem concluſionis ſequi. </s>
                  <s xml:id="N255A8" xml:space="preserve">videlicet infinitum tarde
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                  incipit augeri quod infinitam quãtitatem incipit
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                  acquirere quia vt inquit: ſecundum in duplo maio­
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                  rem ̄titatē acquirit ꝙ̄ primū: et tertiuꝫ ꝙ̄ ſecundū /
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                  et ſic cõſequenter. </s>
                  <s xml:id="N255B3" xml:space="preserve">Ad quod probãdū facit hanc cõ­
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                  ſequentiã: ſi primū illorū preciſe eque velociter au-
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                  geretur ſicut ſecūdū. </s>
                  <s xml:id="N255BA" xml:space="preserve">Secundū in quadruplo velo-
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                  cius acquireret de quantitate quam primū: ſꝫ nūc
                    <lb/>
                  in duplo velocius incipit primū acquirere de quãti­
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                  tate quã tnnc: ergo in duplo velocius incipit ſcḋm
                    <lb/>
                  acquirere de quantitate ꝙ̄ primū: et ſic tertiū in du­
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                  plo velocius ſecūdo: et ſic in infinitū: et per conſe-
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                  quens ante quodcun inſtans infinita quantitas
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                  erit acquiſita alicui illorum: et ſic infinitam quan-
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                  titatem incipit aliquod illoruꝫ acquirere. </s>
                  <s xml:id="N255CD" xml:space="preserve">Sed hec
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                  ratio eſt inefficax quia conſequentia illa quã facit
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                  nichil valet videlicet hec. </s>
                  <s xml:id="N255D4" xml:space="preserve">Si primū eque velociter
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                  preciſe augeretur ſic ſecundū. </s>
                  <s xml:id="N255D9" xml:space="preserve">Secūdum in quadru­
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                  plo velocius acquireret de quantitate ꝙ̄ primū: ſed
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                  nunc puta in caſu in duplo velocius incipit primuꝫ
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                  acquirere de quantitate quã tunc: igitur in duplo
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                  velocius incipit ſecundū acquirere de quãtitate ̄
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                  primum. </s>
                  <s xml:id="N255E6" xml:space="preserve">QꝪ autem illa conſequentia nichil valet:
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                  patet / quia illius conſequentie antecedens eſt verū
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                  in caſu et conſequens falſum: igitur illa nichil va-
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                  let. </s>
                  <s xml:id="N255EF" xml:space="preserve">Probaiur antecedens: et pono /  in illo caſu
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                  primum illorum in vna hora acquirat proportio-
                    <cb chead="De motu augmentationis."/>
                  nem ſexdecuplam: et ſit illud primū vnum pedale
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                  et ſecundum in eadem hora acquirat quadruplam
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                  quod quidem ſecundum eſt quadrupedale. </s>
                  <s xml:id="N255FB" xml:space="preserve">quo po-
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                  ſito antecedens eſt verum et conſequens: igitur con­
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                  ſequentia nulla. </s>
                  <s xml:id="N25602" xml:space="preserve">QꝪ autem antecedens ſit verū pa-
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                  tet. </s>
                  <s xml:id="N25607" xml:space="preserve">quia maior eſt neceſſaria vt conſtat et minor in
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                  caſu noſtro vera. </s>
                  <s xml:id="N2560C" xml:space="preserve">quia incipit in duplo maiorē pro­
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                  portionem acquirere ꝙ̄ tunc: et continuo in duplo
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                  maiorem acquiret ꝙ̄ tunc: et ſic continuo in duplo
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                  maiorem quantitatem acquirit ꝙ̄ tunc: et per con-
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                  ſequens totum antecedens eſt verum. </s>
                  <s xml:id="N25617" xml:space="preserve">Sed iam pro­
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                  bo falſitatem falſitatē conſequentis quia in quoli­
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                  bet inſtanti illius hore: primo erit acquiſita maior
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                  quantitas ꝙ̄ ſubdupla ad quantitatem acquiſitaꝫ
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                  ipſi ſecundo: igitur in nullo tali inſtanti erit acqui­
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                  ſita ſecundo dupla quantitas ad quãtitateꝫ acqui­
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                  ſitam primo: et per cõſequens non incipit in duplo
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                  velocius acquirere de quantitate ꝙ̄ primū: ex quo­
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                  nunquam quantitas acquiſita ſecundo erit in du-
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                  plo maior quam quantitas acquiſita primo. </s>
                  <s xml:id="N2562C" xml:space="preserve">Sed
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                  iam probo /  in quolibet inſtãti illius hore primo
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                  erit acquiſita maior quautitas ꝙ̄ ſubdupla ad quã­
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                  titatem acquiſitam primo: quia quocun inſtanti
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                  dato ſi primū continuo eque velociter augeretur cū
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                  ſecundo ipſum primum in tali inſtanti haberet ac-
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                  quiſitam quantitatē ſubquadruplam ad quantita­
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                  tem acquiſitam ſecundo: ſꝫ modo ſuper illã quanti­
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                  tatem adhuc acquiſiuit tantam proportionem ſi-
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                  cut acquiſiuit tunc acquirendo illam quantitatem /
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                  ergo ſuper illam quantitatem acquiſitam adhuc
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                  acquiſiuit maioreꝫ illa acquiſita: et ꝑ ↄ̨ñs in tali
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                  inſtanti quantitas acquiſita eſt maior ꝙ̄ ſubdupla
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                  ad quantitatem acquiſitam ſecundo / quod fuit pro­
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                  bandum. </s>
                  <s xml:id="N2564B" xml:space="preserve">Patet conſequentia: quia ſi preciſe acqui­
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                  ſiuiſſet vſ ad illuod inſtans tantam proportionē
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                  ſicut ſecundū: et ſuper illam ſubquadruplã quanti-
                    <lb/>
                  tatem acquiſitam acquiſiuiſſet adhuc tantam pre-
                    <lb/>
                  ciſe: quantitas ei acquiſita manſiſſet ſubdupla ad
                    <lb/>
                  quantitatem acquiſitam ſecundo: ſed modo in illo
                    <lb/>
                  inſtanti ſuper illa quantitate ſubquadrupla ipſuꝫ
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                  primū acquirit maiorē: quia acquirit tantam pro­
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                  portionē ſicut antea et eſt maius: ergo quãtitas ſub­
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                  dupla ei acquiſita eſt maior ꝙ̄ ſubdupla ad quan-
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                  titatem acquiſitam ſecundo / qḋ fuit probandum.
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                  </s>
                  <s xml:id="N25663" xml:space="preserve">Item ad probandam ſecundam partem eiuſdē cõ-
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                  cluſionis facit calculator talem conſequētiam. </s>
                  <s xml:id="N25668" xml:space="preserve">Si
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                  primū aliquorum continuo ſe habentium in ꝓpor-
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                  tione ſubquadrupla puta quorū primū ſit vt qua-
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                  tuor et ſecundum vt vnum: tertium vt vna quarta:
                    <lb/>
                  et ſic in infinitur eque velociter diminueretur ſicut
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                  ſecundum in quadruplo velocius deꝑderet de quã-
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                  titate quam ſecūdum: ſed nunc in duplo tardius in­
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                  cipit primū deperdere de qqãtitate ꝙ̄ tunc: ergo in
                    <lb/>
                  duplo velocius incipit primum deperdere de quã-
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                  titate ꝙ̄ ſcḋm. </s>
                  <s xml:id="N2567D" xml:space="preserve">Et hec cõſequentia etiaꝫ nichil valet
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                  quia primū ſpemper deperdit maiorem quantita-
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                  tem ꝙ̄ duplã ad quãtitatem deperditam a ſecundo
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                  </s>
                  <s xml:id="N25685" xml:space="preserve">¶ Ad iſtud dubiū </s>
                  <s xml:id="N25688" xml:space="preserve">Reſpondeo ponendo aliquas ꝓ­
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                  poſitiones. </s>
                  <s xml:id="N2568D" xml:space="preserve">¶ Prīa propoſito. </s>
                  <s xml:id="N25690" xml:space="preserve">Probationes vnde­
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                  cime et duodecime concluſiõis calculatoris ſunt in
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                  efficaces. </s>
                  <s xml:id="N25697" xml:space="preserve">Patet hoc ex argumentis nuꝑrime fctīs
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                  </s>
                  <s xml:id="N2569B" xml:space="preserve">¶ Secūda ꝓpoſitio </s>
                  <s xml:id="N2569E" xml:space="preserve">Ille concluſiones vndecima vi­
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                  delicet et duodecima in caſibus ibi poſitis ſi ſumã­
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                  tur in ſenſu cathegorico ſunt falſe. </s>
                  <s xml:id="N256A5" xml:space="preserve">Probatur de
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                  vndecima ex primo argumento contra dubium: de
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                  duodecima etiam probatur /  ipſa in caſu ibi poſi­
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                  to ſit falſa: qua nullū illorum corporum infinitam
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                  quantitatem incipit acquirere: igitur non in infi­ </s>
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