Alvarus, Thomas, Liber de triplici motu, 1509

Table of contents

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                    <pb chead="Primi tractatus" file="0068" n="68"/>
                  duū. </s>
                  <s xml:id="N16A77" xml:space="preserve">igitur nõ vniformiter creſcūt. </s>
                  <s xml:id="N16A7A" xml:space="preserve">Antecedēs ptꝫ
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                  ex caſu. </s>
                  <s xml:id="N16A7F" xml:space="preserve">Sed ſecūda pars ꝓbatur: qm̄ vtra illaꝝ
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                  inequalibus tēporibus equales latitudines reſiſ­
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                  ſtentie acquirūt: vt ptꝫ ex caſu. </s>
                  <s xml:id="N16A86" xml:space="preserve">Ex hac correlariuꝫ
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                  eſt ſimile dialectico ſortes / et brunellꝰ nõ ſunt fra-
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                  tres: et tamen vter illoꝝ eſt fratrer.
                    <note position="left" xlink:href="note-0068-01a" xlink:label="note-0068-01" xml:id="N16C18" xml:space="preserve">2. correĺ.</note>
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                  <s xml:id="N16A92" xml:space="preserve">¶ Secunduꝫ
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                  correlariū ſtat /  ſubduplū in ſubduplo tempore
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                  adequate ad tēpus deꝑditionis dupli deꝑdatur:
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                  et quãdo deperdat̄̄ ſubduplū etiã duplū deperdat̄̄
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                  quãius nõ totaliter: et nichilominꝰ nõ eque velociṫ
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                  deperdat̄̄ ſubduplū cum duplo. </s>
                  <s xml:id="N16A9F" xml:space="preserve">Probat̄̄ et pono
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                  caſum /  ſint pedale a. et bipedale b. / et incipiat de-
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                  perdi taliter:  īmedietate hore future deperdat̄̄
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                  pedale a. adequate: et tūc ſit deperditū a. bipedali
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                  b. p̄ciſe ſemipedale: et totū reſiduū deperdat ī me-
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                  dietate ſeq̄nti adequate: quo poſito iam ptꝫ corre­
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                  larium.
                    <note position="left" xlink:href="note-0068-02a" xlink:label="note-0068-02" xml:id="N16C1E" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N16AB3" xml:space="preserve">¶ Ex quo ſequitur tertiū correlariū:  hec
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                  cõſequentia nichil valet. </s>
                  <s xml:id="N16AB8" xml:space="preserve">Si a. ſubduplū in ſubdu­
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                  plo tēpore adequate deperdit̄̄ ad b. duplū: a. et b.
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                  eque velociter deperdūtur. </s>
                  <s xml:id="N16ABF" xml:space="preserve">In caſu em̄ poſito an-
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                  tecedens eſt verū et cõſequēs falſum. </s>
                  <s xml:id="N16AC4" xml:space="preserve">Nec puto cal­
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                  culatorē voluiſſe illã cõcedere. </s>
                  <s xml:id="N16AC9" xml:space="preserve">Iſta tamen cõſequē­
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                  tia eſt bona: ſi ſubduplū in ſubduplo tēpore ade-
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                  quate deperdit̄̄ et vniformiter cū ſuo duplo: iam
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                  eque velociter deperdit̄̄.
                    <note position="left" xlink:href="note-0068-03a" xlink:label="note-0068-03" xml:id="N16C24" xml:space="preserve">4. correĺ.</note>
                  </s>
                  <s xml:id="N16AD7" xml:space="preserve">¶ Quartū correlarium.
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                  </s>
                  <s xml:id="N16ADB" xml:space="preserve">Iſta cõſequentia nichil valet: pluſquã in duplo ci-
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                  tius deperdit̄̄ ſubduplū quã duplū: igitur velociꝰ
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                  perditur ſubduplū quã duplū. </s>
                  <s xml:id="N16AE2" xml:space="preserve">Patet hoc correla­
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                  riū ex dictis in ſolutione argumentati.
                    <note position="left" xlink:href="note-0068-04a" xlink:label="note-0068-04" xml:id="N16C2A" xml:space="preserve">5. correĺ.</note>
                  </s>
                  <s xml:id="N16AEC" xml:space="preserve">¶ Quintum
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                  correlariū. </s>
                  <s xml:id="N16AF1" xml:space="preserve">Stat duas ꝓportiones eque velociter
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                  deperdi per crementū ſuaꝝ reſiſtentiarū: et tamen
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                  reſiſtentias nõ eque velociter creſcere: īmo hoc ne­
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                  ceſſariū eſt vbi reſiſtētie ſūt īeq̈les .etc̈. </s>
                  <s xml:id="N16AFA" xml:space="preserve">Probat̄̄ cor­
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                  relariuū ſupponēdo  ad hoc /  aliquã ꝓportio eq̄
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                  velociṫ ↄ̨tinuo et vniformiṫ cū deꝑdat̄̄: req̇rit̄̄ /  in­
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                  eq̈libꝰ tēporibꝰ equales ꝓportiones partiales ille
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                  due deperdant: vt ſi ꝓportio quadrupla eque ve-
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                  lociter debeat deperdi cū ꝓportione dupla: requi-
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                  ritur /  quando adequate quadrupla perdit ſex-
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                  quitertiã. </s>
                  <s xml:id="N16B0B" xml:space="preserve">etiã dupla ſexquitertiã perdat adequa-
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                  te: et ſic cõſequenter. </s>
                  <s xml:id="N16B10" xml:space="preserve">Sed ad hoc /  due reſiſtentie
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                  eque velociter et vniformiter deperdãtur requirit̄̄ /
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                   inequalibꝰ tēporibꝰ equales latitudines reſiſtē-
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                  tiarū deperdant. </s>
                  <s xml:id="N16B19" xml:space="preserve">Hoc patet ex ſexta ſuppoſitione
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                  p̄cedētis capitis. </s>
                  <s xml:id="N16B1E" xml:space="preserve">Ad hoc em̄  vniformiter remit-
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                  tatur ꝓportio: requiritur /  inequalibꝰ tēporibꝰ
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                  equales latitudines ꝓportionū deperdãtur: et ad
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                  hoc /  vniformiter remittatur reſiſtentia: requirit̄̄ /
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                   inequalibꝰ tēporibꝰ equales latitudines reſiſtē­
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                  tiarū deperdãtur vt ptꝫ. </s>
                  <s xml:id="N16B2B" xml:space="preserve">Quo ſuppoſito ꝓbatur
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                  correlariū in caſu argumentati. </s>
                  <s xml:id="N16B30" xml:space="preserve">ibi em̄ reſiſtentia c. /
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                  vt .2. in duplo velocius creſcit quã reſiſtentia d. / vt
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                  vnū et tamen quãdo ꝓportio a. potentie / vt .8. ad c.
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                  reſiſtentiã / vt 2. perdit ꝓportionē duplã: etiã pro-
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                  portio ipſiꝰ b. potētie / vt 4. ad d. reſiſtentiã / vt vnū
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                  ꝑdit ꝓportionē duplã: et ſic ibi ſtat proportiões per
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                  crementū reſiſtētiaꝝ eque vĺociter deꝑdi: et tamen
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                  reſiſtētias nõ eque velociter creſcere. </s>
                  <s xml:id="N16B41" xml:space="preserve">Et  hoc ſit
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                  neceſſariū vbi reſiſtētie ſiue mīores termini ꝓpor-
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                  tionū fuerit inequales: ptꝫ / q2 īplicat duo inequa-
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                  lia eque velociter creſcere et eque ꝓportiõabiliter /
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                  vt ptꝫ ex octaua ſuppoſitione quarti capitis et ex
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                  octauo capite ſecūde partis per totū. </s>
                  <s xml:id="N16B4E" xml:space="preserve">¶ In his q̄
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                  quaſi demõſtratiue ꝓcedūt: deducas locoꝝ diuer-
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                  ſitatē: cū ceterꝪ litigioſis captiūculis ſophiſtarū
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                    <note position="left" xlink:href="note-0068-05a" xlink:label="note-0068-05" xml:id="N16C30" xml:space="preserve">Aduerte</note>
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                  <s xml:id="N16B5C" xml:space="preserve">¶ Aduerte tamen /  nõ in toto tꝑe ille ꝓportiões
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                  puta dupla et quadrupla eque velociter deperdū­
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                  tur: et loquor de ꝓportione b. potentie vt .4. ad re­
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                  ſiſtentiã c. vt duo et ꝓportione b. potentie vt .4. ad
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                  d. reſiſtentiã vt vnū. </s>
                  <s xml:id="N16B68" xml:space="preserve">Sed quãdiu ſimul remittunt̄̄
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                  eque velociter decreſcunt ſiue remittuntur.
                    <note position="right" xlink:href="note-0068-06a" xlink:label="note-0068-06" xml:id="N16C36" xml:space="preserve">Aduerte
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                    pḣs pri-
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                    mo celi.</note>
                  </s>
                  <s xml:id="N16B72" xml:space="preserve">¶ Sed
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                  q2 ex ſentētia philoſophi primo celi veritates in-
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                  quiſitores arbitros eſſe decet et nõ inimicos: ideo
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                  ſecūdo loco aduerte:
                    <note position="right" xlink:href="note-0068-07a" xlink:label="note-0068-07" xml:id="N16C40" xml:space="preserve">Eque ve-
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                    lociter ca­
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                    pitur du­
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                    pliciter.</note>
                   in cõſequētia calculatoris
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                  ly eque velociter poteſt capi dupliciter: videlicet
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                  reſolutorie / vt eq̇ualeat huic aliqua equali veloci-
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                  tate. </s>
                  <s xml:id="N16B86" xml:space="preserve">vt ſit ſenſus huiꝰ ꝓpropoſitionis ſubduplū eque­
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                  velociter remittitur cū duplo: id eſt aliqua equali
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                  velocitate ſubduplū equaliter remittitur cum du­
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                  plo. </s>
                  <s xml:id="N16B8F" xml:space="preserve">Et iſto modo cõſequentia calculatoris eſt bo­
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                  na cū his que ſupponit ex parte antecedētis. </s>
                  <s xml:id="N16B94" xml:space="preserve">Alio
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                  modo ly eque velociter poteſt capi exponibiliter /
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                  vt ſit ſenſus huiꝰ ꝓpoſitionis ſubduplū eque velo­
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                  citer remittit̄̄ cū duplo: hoc eſt ita velociṫ remittit̄̄
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                  ſubduplū ſicut duplū et ē cõtra. </s>
                  <s xml:id="N16B9F" xml:space="preserve">Et in iſto ſenſu hec
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                  conſequentia nõ valet b. ſubduplū puta pedale in
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                  ſubduplo tēpore adequate deꝑditur ad a. dupluꝫ
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                  puta bipedale: ergo eque velociter ꝑditur b. ſub-
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                  duplū ſicut a. duplū. </s>
                  <s xml:id="N16BAA" xml:space="preserve">Probatur: nam poſito  pe­
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                  dale remittatur vniformiter in hora: et bipedale
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                  in duabus horis adequate remittatur vſ ad nõ
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                  quantū: ita tamen  in tēpore in quo remittit̄̄ pe-
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                  dale remittatur aliquid de bipedali: in triplo tar­
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                  dius tamen gratia exēpli: et in aliqua parte ſecū-
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                  de hore remittatur etiã aliquid de bipedali ita ve­
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                  lociter ſicut antea remittebat̄̄ pedale: et in aliqua
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                  alia parte remittatur ipſum bipedale velociꝰ quã
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                  vti̄ remittebatur pedale ſubduplum: quo poſito
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                  antecedens eſt verum et conſequens falſum. </s>
                  <s xml:id="N16BC1" xml:space="preserve">Nam
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                  tertia exponens conſequentis eſt falſa / videlicet
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                  iſta in nullo tempore a. duplum velocius remitti-
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                  tur quam b. ſubduplū / vt patet.
                    <note position="right" xlink:href="note-0068-08a" xlink:label="note-0068-08" xml:id="N16C4C" xml:space="preserve">Expoſi-
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                    tio ipſiꝰ
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                    ita et ſi-
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                    cut.</note>
                  </s>
                  <s xml:id="N16BCF" xml:space="preserve">Et ita debet dari
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                  tertia exponens in talibus addendo ly tēpore / qm̄
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                  alias oporteret vti circulatione in exponendo: ꝑ-
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                  inde at alti concedunt quod michi non placet.
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                  </s>
                  <s xml:id="N16BD9" xml:space="preserve">Hac diſtinctione vtendo pariter et expoſitione: fa­
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                  cile hec dicta in predictis correlariis dictis calcu-
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                  latoris conciliabis: eſto  calculator de facto nõ
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                  aduerſetur dictis. </s>
                  <s xml:id="N16BE2" xml:space="preserve">¶ Hec ex ſcriniis dialectice non
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                  abs re nec inconſulte huic argumento interſeren-
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                  da decreui: quoniam defeſſam mathemathicis et
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                  ſcientia demonſtratiua mentem dialectice at ſo­
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                  phiſtice argumētiones plurimū oblectant. </s>
                  <s xml:id="N16BED" xml:space="preserve">
                    <note position="right" xlink:href="note-0068-09a" xlink:label="note-0068-09" xml:id="N16C58" xml:space="preserve">pḣs deci­
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                    ma octa­
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                    ua partꝪ
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                    ꝓble.</note>
                  Nam
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                  teſte philoſopho decima octaua particula pro-
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                  blematum ſecundo problemate. </s>
                  <s xml:id="N16BF9" xml:space="preserve">Agoniſtice, ligi-
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                  tioſe, at ſophiſtice argumentatioues, et pluri-
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                  mum ſunt exercitatiue: et vltra alias diſputatio-
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                  nes: lõge plus iuuant at delectant.
                    <note position="right" xlink:href="note-0068-10a" xlink:label="note-0068-10" xml:id="N16C64" xml:space="preserve">Citiꝰ ca-
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                    pit̄̄ du-
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                    pliciter</note>
                  </s>
                  <s xml:id="N16C07" xml:space="preserve">His adde /
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                   iſte terminus citius dupliciter poteſt capi: pri-
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                  mo modo / vt dicit temporis propinquitatem: ſe-
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                  cundo vero modo / vt dicit tēporis breuitatem: et
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                  hoc poſteriori modo accommodatius propoſito
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                  deſeruit.</s>
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                  <s xml:id="N16C6F" xml:space="preserve">Secundo contra primam ſuppoſi-
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                  tionem: et vniuerſaliter contra fundamentum to-
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                  tius opinionis arguitur ſic: quia ſi illa ſuppoſi-
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                  tio eſſet vera: ſequeretur /  aliqua potētia poſſet
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                  pertranſire aliquam reſiſtentiam: et tamen non
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                  poſſet illam pertranſire: hoc manifeſte implicat:
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                  igitur illud ex quo ſequitur. </s>
                  <s xml:id="N16C7E" xml:space="preserve">Sequela probatur / et
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                  pono caſum /  ſit vna reſiſtentia vniformiter dif-
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                  formis a gradu / vt duo vſ̄ ad quartum et ſit vna
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                  potentia vt .4. / que inuariata incipiat pertranſi-
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                  re talem reſiſtentiam ſiue incipiat moueri in tali
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                  reſiſtentia: ab extremo remiſſiori: quo poſito ar-
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                  guitur ſic / illa potentia nun̄ perueniet ad finem
                    <lb/>
                  illius reſiſtentie: igitur non pertranſibit illam.</s>
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