Alvarus, Thomas, Liber de triplici motu, 1509

Table of contents

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                    <pb chead="De motu augmentationis." file="0206" n="206"/>
                  ſi aliquod corpus diuidatur ꝑ partes proportio-
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                  nales proportiõe dupla: et in aliquo tēpore puta ī
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                  hora prīa pars proportionalis augeatur aliquã-
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                  tulū velociter: et ſecūda in duplo velocius: et tertia
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                  in triplo ꝙ̄ prima: et ſic ↄ̨ſequēter ſequeret̄̄ /  totuꝫ
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                  illud corpus in fine tēporis eſſet infinite magnū: et
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                  per cõſequēs illud corpus infinite velociter augmen-
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                  taretur: ſꝫ cõſequēs eſt falſum: igit̄̄ et añs. </s>
                  <s xml:id="N24482" xml:space="preserve">Ealſitas
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                  cõſequētis arguit̄̄: et pono caſum /  ſit vnū corpus
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                  diuiſum ꝑ partes proportionales proportiõe du-
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                  pla: et in hora prima pars proportionaiis acqui-
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                  rat proportionē ſexquialterã: et ſecūda in eodē tē-
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                  pore acquirat duas ſexquialteras: et quarta .4. / et
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                  ſic cõſequēter. </s>
                  <s xml:id="N24491" xml:space="preserve">Quo poſito arguit̄̄ ſic: prima pars
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                  proportionalis illiꝰ corporis aliqualiter auget̄̄: et
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                  ſecūda in duplo magis: et tertia in triplo: et ſic cõſe­
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                  quēter: et tamē illud corpus in fine nõ erit infinituꝫ
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                  ſed ſolū finitū / igit̄̄ in tali caſu nõ acq̇rit īfinitã pro­
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                  portionē: et ꝑ ↄ̨ſequēs illud illatū eſt falſum / q2 eſt
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                  vna cõditionalis cuius añs eſt verū / et cõſequēs fal­
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                  ſum. </s>
                  <s xml:id="N244A2" xml:space="preserve">Sed iã probo /  illud in illo caſu erit finitum
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                  in fine hore q2 ī fine hore ille partes q̄ ante augmē-
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                  tationē ſe habebãt in proportione dupla ſe habe-
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                  bunt ↄ̨tinuo in proportiõe ſexquitertia: igit̄̄ aggre­
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                  gatū ex oībꝰ ſequētibiꝰ primã eſt triplū ad primaꝫ /
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                  vt ptꝫ ītelligēti quītū caput prime partis: ſꝫ primū
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                  eſt finitū: ergo totū eſt finitū. </s>
                  <s xml:id="N244B1" xml:space="preserve">Sꝫ iã probo /  ille ꝑ-
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                  tes cõtinuo ſe habēt in ꝓportiõe ſexquitertia: qm̄
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                  prima et ſcḋa ſe habēt in ꝓportiõe ſexquitertia: et ſe­
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                  cunda et tertia: et ſic de q̇buſcū duabus immediatꝪ
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                  </s>
                  <s xml:id="N244BB" xml:space="preserve">Quod ſic ꝓbat̄̄ / quoniã ſi prima et ſcḋa equalem ꝓ-
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                  portionē acq̇ſiuiſſent puta ſexquialteram: tunc ad­
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                  huc mãſiſſent in ꝓportiõe dupla ſicut antea vt con­
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                  ſtat: ſed modo ſecūda que eſt minor acquirit adhuc
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                  ſexquialterã adequate: g̊ ꝓportio dupla que eſt in-
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                  ter primã et ſcḋam ꝑdit ſexquialterã: et ſic manet ſex­
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                  quitertia tantū inter primã et ſecundã. </s>
                  <s xml:id="N244CA" xml:space="preserve">Itē ſi tertia
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                  pars ꝓportionalis acq̇ſiuiſſet duas ſexquialteras
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                  adequate ſicut ſecūda: ſecunda et tertia manſiſſent
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                  in ꝓportõe dupla: ſꝫ modo tertia acquiſiuit adhuc
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                  vnã ſexquialterã: igit̄̄ illam ſexq̇alteram deperdit
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                  dupla q̄ eſt inter ſecundã et tertiam: et ꝑ cõſequens
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                  manet ſexquitertia / vt patet intelligenti quartū ca­
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                  put ſecunde partis cū octauo: et ſit ꝓbabis de ter-
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                  tia et quarta: et de oībus:
                    <note position="left" xlink:href="note-0206-01a" xlink:label="note-0206-01" xml:id="N2457F" xml:space="preserve">Maxīa.</note>
                  igit̄̄ ille partes cõtinuo ꝓ­
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                  portionãtur ꝓportiõe ſexquitertia / qḋ fuit ꝓbandū
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                  tenet hec deductio ꝑ hanc maximã biꝑtitã. </s>
                  <s xml:id="N244E6" xml:space="preserve">Quãdo­
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                  cū aliqui duo numeri vel ̄titates ſe habēt ī ali-
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                  qua ꝓportione et equales ꝓportiões acq̇runt ſem-
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                  per manēt in eadē proportiõe et ſi numerus mīor
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                  ſiue ̄titas minor acq̇rat aliquã ꝓportionē vltra
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                  numerū ſiue ̄titatē maiorē ita tamē  ſemꝑ ma-
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                  neat minor illã ꝓportionē deperdit ꝓportio que a
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                  principio erat inter numerū maiorē et minorē. </s>
                  <s xml:id="N244F7" xml:space="preserve">Hec
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                  maxīa claret ex quarta cõcluſiõe et ſecundo correla-
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                  rio ſexte ↄ̨̨cluſiõis octaui capitis ſecūde partꝪ. </s>
                  <s xml:id="N244FE" xml:space="preserve">Sꝫ
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                  iam probo ſeq̄lam prīcipalē argumēti: q2 ſi prima
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                  pars ꝓportionalis talis corporis diuiſi ꝑ partes
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                  ꝓportionales ꝓportiõe dupla acquireret duplã
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                  et ſecūda duas duplas: et tertia tres duplas: et q̈rta
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                  quatuor: et ſic ↄ̨ſequēter: tūc ī fine hore illud corpꝰ
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                  manebit īfinite magnū: igit̄̄ īfinitã ꝓportionē ac-
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                  quiſiuit in illo tꝑe et ſic infinite velociter augmēta-
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                  bit̄̄: igit̄̄ ſi talis corporis diuiſi ꝑ partes ꝓportio-
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                  nales ꝓportiõe dupla prīa pars ꝓportionalis ac-
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                  quirat aliquã proportionē: et ſecūda duas tales: et
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                  tertia tres: et quarta .4. / et ſic ↄ̨ſequēter: tūc tale cor­
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                  pus in illa hora infinitã proportionē acq̇rit: et ſic ī­
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                  finite velociter augmētat̄̄: quod fuit ꝓbãdū </s>
                  <s xml:id="N2451B" xml:space="preserve">Ptꝫ
                    <cb chead="De motu augmentationis."/>
                  hec cõſequētia ab inferiori ad ſuꝑius. </s>
                  <s xml:id="N24521" xml:space="preserve">Sꝫ iam ꝓbo
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                  añs / q2 in fine hore quelibet illarū partiū propor-
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                  tionaliū erit equalis prime: et ſunt infinite / igit̄̄ illḋ
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                  corpus erit infinitū: </s>
                  <s xml:id="N2452A" xml:space="preserve">Probat̄̄ maior / q2 prīa et ſcḋa
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                  erūt equales in fiue: et ſecunda et tertia: et tertia et
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                  quarta: et ſic de q̇buſcū aliis immediatis: quoni-
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                  am ſi ſcḋa acq̇reret adequate vnam duplã ſicut pri­
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                  ma: tunc ṗma et ſcḋa adhuc manerēt in ꝓportione
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                  dupla / vt pꝫ ex maxīa nuperrime poſita: ſꝫ modo ſe­
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                  cunda acq̇rit adhuc vnã duplã: et illã deꝑdit ꝓpor-
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                  portio inter ṗmã et ſcḋam: igitur totalis ꝓportio
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                  inter primã et ſcḋaꝫ deꝑditur q2 nõ erat niſi dupla
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                  et ſic prima et ſcḋa manēt equales. </s>
                  <s xml:id="N2453F" xml:space="preserve">Itē ſi tertia p̄ciſe
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                  acquireret duas duplas ſicut ſecūda adhuc inter
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                  ſecūdam et tertiam maneret proportio dupla: ſed
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                  modo illam duplã acquirit tertia: igit̄̄ ſecunda et
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                  tertia manent equales. </s>
                  <s xml:id="N2454A" xml:space="preserve">Patet / q2 quando ſubdu-
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                  plū auget̄̄ ad duplū efficit̄̄ duplo equale. </s>
                  <s xml:id="N2454F" xml:space="preserve">et iſto mõ
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                  ꝓbabis de q̇buſcū aliis duabꝰ immediatis: igit̄̄
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                  oēs ille partes in fine manebūt equales: et ꝑ conſe-
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                  quens illud corpus erit in fine infiuitū / qḋ fuit pro­
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                  bandū.
                    <note position="right" xlink:href="note-0206-02a" xlink:label="note-0206-02" xml:id="N24585" xml:space="preserve">Maxīa
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                    ſiue poſi­
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                    tio.</note>
                  </s>
                  <s xml:id="N2455F" xml:space="preserve">hec inductio gñaliter pꝫ ꝑ hanc maximam.
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                  </s>
                  <s xml:id="N24563" xml:space="preserve">Quãdocū alique due ̄titates ſe habēt in aliq̈ ꝓ­
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                  portiõe maioris inequalitatis et minor acq̇rit totã
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                  illam proportionē que eſt inter ip̄am et maiorem q̄
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                  maior etiã auget̄̄: et cū hoc illa minor acq̇rit etiam
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                  illam ꝓportionē quã acq̇rit maior: tūc in fine mane­
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                  bunt equales. </s>
                  <s xml:id="N24570" xml:space="preserve">Patet / q2 minor acq̇ſiuit totū quod
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                  deficiebat ei vt eſſet equalis alteri et cū hoc illḋ qḋ
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                  illa maior acq̇ſiuit: ſꝫ ſic eſt in propoſito de his ꝑti­
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                  bus īmeditatis vt cõſtat: igitur in fine ille ꝑtes ma-
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                  nent equales.</s>
                </p>
                <note position="right" xml:id="N2458F" xml:space="preserve">Confir°.</note>
                <p xml:id="N24593">
                  <s xml:id="N24594" xml:space="preserve">Et confirmatur / quia ſi illa poſitio eēt
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                  vera ſequeret̄̄ /  ſi aliquod corpus diuideret̄̄ ī par-
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                  tes ꝓportionales ꝓportione dupla: et prima pars
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                  proportionalis in hora acq̇rat aliquã proportio-
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                  ne ita  augeat̄̄ aliquantulū velociter: et ſecūda ī
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                  duplo velocius in eodē tꝑe: et tertia in duplo veloci­
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                  us ꝙ̄ ſecūda: et quarta in duplo velocius ꝙ̄ tertia
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                  in eodē tēpore / et ſic ↄ̨ſeq̄nter tunc in fine illud cor-
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                  pus manebit infinite magnū: et ſic in illo tēpore in­
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                  finite velociter augmētabitur: ſꝫ ↄ̨ſequēs eſt falſuꝫ /
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                  igitur et añs. </s>
                  <s xml:id="N245AB" xml:space="preserve">Falſitas cõſequētis probat̄̄: et capio
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                  vnū pedale diuiſum in partes proportionales pro­
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                  portione dupla: et volo /  in vna hora prima pars
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                  proportionalis acq̇rat vnã ſexquioctauã: et in eodē
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                  tēpore ſecunda acquirat duas ſexquioctauas: et ter­
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                  tia. quatuor: et quarta .8. et q̇nta .16. / et ſic ↄ̨ſequen-
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                  ter duplando. Quo poſito ſic arguo prima pars
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                  illius corporis proportione dupla in hora aliquã­
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                  tulū auget̄̄: et ſecūda in duplo velocius: et tertia in
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                  duplo velocius ꝙ̄ ſecūda: et ſic ↄ̨ſequēter / et tñ in fine
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                  illud corpus nõ erit infinite magnū nec tale corpꝰ
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                  infinite velociter augetur: igit̄̄ illud ↄ̨ſequens fal-
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                  ſum. </s>
                  <s xml:id="N245C6" xml:space="preserve">Probat̄̄ añs / q2 ille partes proportionales q̄
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                  ſunt minores cõtinuo manebūt minores: nec vni̄
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                  aliqua ſequēs erit equalis immediate precedēti in
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                  tali caſu: igit̄̄ illud corpus in fine nõ erit infinitum
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                  </s>
                  <s xml:id="N245D0" xml:space="preserve">Probatur añs / q2 ſecunda pars non erit equalis
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                  prime: nec tertia ſecunde: nec quarta tertia: et ſic cõ-
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                  ſequenter vt apparet: igitur non dabunt̄̄ in tali ca­
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                  ſu due partes quarum vna ſit equalis immediate
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                  precedēti. </s>
                  <s xml:id="N245DB" xml:space="preserve">Sed iam probo ſeq̄lam principaleꝫ: qm̄
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                  ſi quelibet pars proportionalis ſequens acquire­
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                  ret adequate tot proportiões ſicut īmediate prece­
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                  dens: tunc ille partes cõtinuo ſe haberēt in propor­
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                  tione dupla ſicut ſe habent in ṗncipio: ſed mõ aliq̈
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                  pars ſequēs acquiret decē proportiones pluſ̄ im­ </s>
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