Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
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                  <s xml:id="N16A6D" xml:space="preserve">
                    <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
                    <lb/>
                  ex caſu. </s>
                  <s xml:id="N16A7F" xml:space="preserve">Sed ſecūda pars ꝓbatur: qm̄ vtra illaꝝ
                    <lb/>
                  inequalibus tēporibus equales latitudines reſiſ­
                    <lb/>
                  ſtentie acquirūt: vt ptꝫ ex caſu. </s>
                  <s xml:id="N16A86" xml:space="preserve">Ex hac correlariuꝫ
                    <lb/>
                  eſt ſimile dialectico ſortes / et brunellꝰ nõ ſunt fra-
                    <lb/>
                  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>
                  </s>
                  <s xml:id="N16A92" xml:space="preserve">¶ Secunduꝫ
                    <lb/>
                  correlariū ſtat /  ſubduplū in ſubduplo tempore
                    <lb/>
                  adequate ad tēpus deꝑditionis dupli deꝑdatur:
                    <lb/>
                  et quãdo deperdat̄̄ ſubduplū etiã duplū deperdat̄̄
                    <lb/>
                  quãius nõ totaliter: et nichilominꝰ nõ eque velociṫ
                    <lb/>
                  deperdat̄̄ ſubduplū cum duplo. </s>
                  <s xml:id="N16A9F" xml:space="preserve">Probat̄̄ et pono
                    <lb/>
                  caſum /  ſint pedale a. et bipedale b. / et incipiat de-
                    <lb/>
                  perdi taliter:  īmedietate hore future deperdat̄̄
                    <lb/>
                  pedale a. adequate: et tūc ſit deperditū a. bipedali
                    <lb/>
                  b. p̄ciſe ſemipedale: et totū reſiduū deperdat ī me-
                    <lb/>
                  dietate ſeq̄nti adequate: quo poſito iam ptꝫ corre­
                    <lb/>
                  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
                    <lb/>
                  cõſequentia nichil valet. </s>
                  <s xml:id="N16AB8" xml:space="preserve">Si a. ſubduplū in ſubdu­
                    <lb/>
                  plo tēpore adequate deperdit̄̄ ad b. duplū: a. et b.
                    <lb/>
                  eque velociter deperdūtur. </s>
                  <s xml:id="N16ABF" xml:space="preserve">In caſu em̄ poſito an-
                    <lb/>
                  tecedens eſt verū et cõſequēs falſum. </s>
                  <s xml:id="N16AC4" xml:space="preserve">Nec puto cal­
                    <lb/>
                  culatorē voluiſſe illã cõcedere. </s>
                  <s xml:id="N16AC9" xml:space="preserve">Iſta tamen cõſequē­
                    <lb/>
                  tia eſt bona: ſi ſubduplū in ſubduplo tēpore ade-
                    <lb/>
                  quate deperdit̄̄ et vniformiter cū ſuo duplo: iam
                    <lb/>
                  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.
                    <lb/>
                  </s>
                  <s xml:id="N16ADB" xml:space="preserve">Iſta cõſequentia nichil valet: pluſquã in duplo ci-
                    <lb/>
                  tius deperdit̄̄ ſubduplū quã duplū: igitur velociꝰ
                    <lb/>
                  perditur ſubduplū quã duplū. </s>
                  <s xml:id="N16AE2" xml:space="preserve">Patet hoc correla­
                    <lb/>
                  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
                    <lb/>
                  correlariū. </s>
                  <s xml:id="N16AF1" xml:space="preserve">Stat duas ꝓportiones eque velociter
                    <lb/>
                  deperdi per crementū ſuaꝝ reſiſtentiarū: et tamen
                    <lb/>
                  reſiſtentias nõ eque velociter creſcere: īmo hoc ne­
                    <lb/>
                  ceſſariū eſt vbi reſiſtētie ſūt īeq̈les .etc̈. </s>
                  <s xml:id="N16AFA" xml:space="preserve">Probat̄̄ cor­
                    <lb/>
                  relariuū ſupponēdo  ad hoc /  aliquã ꝓportio eq̄
                    <lb/>
                  velociṫ ↄ̨tinuo et vniformiṫ cū deꝑdat̄̄: req̇rit̄̄ /  in­
                    <lb/>
                  eq̈libꝰ tēporibꝰ equales ꝓportiones partiales ille
                    <lb/>
                  due deperdant: vt ſi ꝓportio quadrupla eque ve-
                    <lb/>
                  lociter debeat deperdi cū ꝓportione dupla: requi-
                    <lb/>
                  ritur /  quando adequate quadrupla perdit ſex-
                    <lb/>
                  quitertiã. </s>
                  <s xml:id="N16B0B" xml:space="preserve">etiã dupla ſexquitertiã perdat adequa-
                    <lb/>
                  te: et ſic cõſequenter. </s>
                  <s xml:id="N16B10" xml:space="preserve">Sed ad hoc /  due reſiſtentie
                    <lb/>
                  eque velociter et vniformiter deperdãtur requirit̄̄ /
                    <lb/>
                   inequalibꝰ tēporibꝰ equales latitudines reſiſtē-
                    <lb/>
                  tiarū deperdant. </s>
                  <s xml:id="N16B19" xml:space="preserve">Hoc patet ex ſexta ſuppoſitione
                    <lb/>
                  p̄cedētis capitis. </s>
                  <s xml:id="N16B1E" xml:space="preserve">Ad hoc em̄  vniformiter remit-
                    <lb/>
                  tatur ꝓportio: requiritur /  inequalibꝰ tēporibꝰ
                    <lb/>
                  equales latitudines ꝓportionū deperdãtur: et ad
                    <lb/>
                  hoc /  vniformiter remittatur reſiſtentia: requirit̄̄ /
                    <lb/>
                   inequalibꝰ tēporibꝰ equales latitudines reſiſtē­
                    <lb/>
                  tiarū deperdãtur vt ptꝫ. </s>
                  <s xml:id="N16B2B" xml:space="preserve">Quo ſuppoſito ꝓbatur
                    <lb/>
                  correlariū in caſu argumentati. </s>
                  <s xml:id="N16B30" xml:space="preserve">ibi em̄ reſiſtentia c. /
                    <lb/>
                  vt .2. in duplo velocius creſcit quã reſiſtentia d. / vt
                    <lb/>
                  vnū et tamen quãdo ꝓportio a. potentie / vt .8. ad c.
                    <lb/>
                  reſiſtentiã / vt 2. perdit ꝓportionē duplã: etiã pro-
                    <lb/>
                  portio ipſiꝰ b. potētie / vt 4. ad d. reſiſtentiã / vt vnū
                    <lb/>
                  ꝑdit ꝓportionē duplã: et ſic ibi ſtat proportiões per
                    <lb/>
                  crementū reſiſtētiaꝝ eque vĺociter deꝑdi: et tamen
                    <lb/>
                  reſiſtētias nõ eque velociter creſcere. </s>
                  <s xml:id="N16B41" xml:space="preserve">Et  hoc ſit
                    <lb/>
                  neceſſariū vbi reſiſtētie ſiue mīores termini ꝓpor-
                    <lb/>
                  tionū fuerit inequales: ptꝫ / q2 īplicat duo inequa-
                    <lb/>
                  lia eque velociter creſcere et eque ꝓportiõabiliter /
                    <lb/>
                  vt ptꝫ ex octaua ſuppoſitione quarti capitis et ex
                    <lb/>
                  octauo capite ſecūde partis per totū. </s>
                  <s xml:id="N16B4E" xml:space="preserve">¶ In his q̄
                    <lb/>
                  quaſi demõſtratiue ꝓcedūt: deducas locoꝝ diuer-
                    <lb/>
                  ſitatē: cū ceterꝪ litigioſis captiūculis ſophiſtarū
                    <lb/>
                    <note position="left" xlink:href="note-0068-05a" xlink:label="note-0068-05" xml:id="N16C30" xml:space="preserve">Aduerte</note>
                  </s>
                  <s xml:id="N16B5C" xml:space="preserve">¶ Aduerte tamen /  nõ in toto tꝑe ille ꝓportiões
                    <lb/>
                  puta dupla et quadrupla eque velociter deperdū­
                    <lb/>
                  tur: et loquor de ꝓportione b. potentie vt .4. ad re­
                    <lb/>
                  ſiſtentiã c. vt duo et ꝓportione b. potentie vt .4. ad
                    <cb chead="Capitulū ſextū."/>
                  d. reſiſtentiã vt vnū. </s>
                  <s xml:id="N16B68" xml:space="preserve">Sed quãdiu ſimul remittunt̄̄
                    <lb/>
                  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
                      <lb/>
                    pḣs pri-
                      <lb/>
                    mo celi.</note>
                  </s>
                  <s xml:id="N16B72" xml:space="preserve">¶ Sed
                    <lb/>
                  q2 ex ſentētia philoſophi primo celi veritates in-
                    <lb/>
                  quiſitores arbitros eſſe decet et nõ inimicos: ideo
                    <lb/>
                  ſecūdo loco aduerte:
                    <note position="right" xlink:href="note-0068-07a" xlink:label="note-0068-07" xml:id="N16C40" xml:space="preserve">Eque ve-
                      <lb/>
                    lociter ca­
                      <lb/>
                    pitur du­
                      <lb/>
                    pliciter.</note>
                   in cõſequētia calculatoris
                    <lb/>
                  ly eque velociter poteſt capi dupliciter: videlicet
                    <lb/>
                  reſolutorie / vt eq̇ualeat huic aliqua equali veloci-
                    <lb/>
                  tate. </s>
                  <s xml:id="N16B86" xml:space="preserve">vt ſit ſenſus huiꝰ ꝓpropoſitionis ſubduplū eque­
                    <lb/>
                  velociter remittitur cū duplo: id eſt aliqua equali
                    <lb/>
                  velocitate ſubduplū equaliter remittitur cum du­
                    <lb/>
                  plo. </s>
                  <s xml:id="N16B8F" xml:space="preserve">Et iſto modo cõſequentia calculatoris eſt bo­
                    <lb/>
                  na cū his que ſupponit ex parte antecedētis. </s>
                  <s xml:id="N16B94" xml:space="preserve">Alio
                    <lb/>
                  modo ly eque velociter poteſt capi exponibiliter /
                    <lb/>
                  vt ſit ſenſus huiꝰ ꝓpoſitionis ſubduplū eque velo­
                    <lb/>
                  citer remittit̄̄ cū duplo: hoc eſt ita velociṫ remittit̄̄
                    <lb/>
                  ſubduplū ſicut duplū et ē cõtra. </s>
                  <s xml:id="N16B9F" xml:space="preserve">Et in iſto ſenſu hec
                    <lb/>
                  conſequentia nõ valet b. ſubduplū puta pedale in
                    <lb/>
                  ſubduplo tēpore adequate deꝑditur ad a. dupluꝫ
                    <lb/>
                  puta bipedale: ergo eque velociter ꝑditur b. ſub-
                    <lb/>
                  duplū ſicut a. duplū. </s>
                  <s xml:id="N16BAA" xml:space="preserve">Probatur: nam poſito  pe­
                    <lb/>
                  dale remittatur vniformiter in hora: et bipedale
                    <lb/>
                  in duabus horis adequate remittatur vſ ad nõ
                    <lb/>
                  quantū: ita tamen  in tēpore in quo remittit̄̄ pe-
                    <lb/>
                  dale remittatur aliquid de bipedali: in triplo tar­
                    <lb/>
                  dius tamen gratia exēpli: et in aliqua parte ſecū-
                    <lb/>
                  de hore remittatur etiã aliquid de bipedali ita ve­
                    <lb/>
                  lociter ſicut antea remittebat̄̄ pedale: et in aliqua
                    <lb/>
                  alia parte remittatur ipſum bipedale velociꝰ quã
                    <lb/>
                  vti̄ remittebatur pedale ſubduplum: quo poſito
                    <lb/>
                  antecedens eſt verum et conſequens falſum. </s>
                  <s xml:id="N16BC1" xml:space="preserve">Nam
                    <lb/>
                  tertia exponens conſequentis eſt falſa / videlicet
                    <lb/>
                  iſta in nullo tempore a. duplum velocius remitti-
                    <lb/>
                  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-
                      <lb/>
                    tio ipſiꝰ
                      <lb/>
                    ita et ſi-
                      <lb/>
                    cut.</note>
                  </s>
                  <s xml:id="N16BCF" xml:space="preserve">Et ita debet dari
                    <lb/>
                  tertia exponens in talibus addendo ly tēpore / qm̄
                    <lb/>
                  alias oporteret vti circulatione in exponendo: ꝑ-
                    <lb/>
                  inde at alti concedunt quod michi non placet.
                    <lb/>
                  </s>
                  <s xml:id="N16BD9" xml:space="preserve">Hac diſtinctione vtendo pariter et expoſitione: fa­
                    <lb/>
                  cile hec dicta in predictis correlariis dictis calcu-
                    <lb/>
                  latoris conciliabis: eſto  calculator de facto nõ
                    <lb/>
                  aduerſetur dictis. </s>
                  <s xml:id="N16BE2" xml:space="preserve">¶ Hec ex ſcriniis dialectice non
                    <lb/>
                  abs re nec inconſulte huic argumento interſeren-
                    <lb/>
                  da decreui: quoniam defeſſam mathemathicis et
                    <lb/>
                  ſcientia demonſtratiua mentem dialectice at ſo­
                    <lb/>
                  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
                      <lb/>
                    ma octa­
                      <lb/>
                    ua partꝪ
                      <lb/>
                    ꝓble.</note>
                  Nam
                    <lb/>
                  teſte philoſopho decima octaua particula pro-
                    <lb/>
                  blematum ſecundo problemate. </s>
                  <s xml:id="N16BF9" xml:space="preserve">Agoniſtice, ligi-
                    <lb/>
                  tioſe, at ſophiſtice argumentatioues, et pluri-
                    <lb/>
                  mum ſunt exercitatiue: et vltra alias diſputatio-
                    <lb/>
                  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-
                      <lb/>
                    pit̄̄ du-
                      <lb/>
                    pliciter</note>
                  </s>
                  <s xml:id="N16C07" xml:space="preserve">His adde /
                    <lb/>
                   iſte terminus citius dupliciter poteſt capi: pri-
                    <lb/>
                  mo modo / vt dicit temporis propinquitatem: ſe-
                    <lb/>
                  cundo vero modo / vt dicit tēporis breuitatem: et
                    <lb/>
                  hoc poſteriori modo accommodatius propoſito
                    <lb/>
                  deſeruit.</s>
                </p>
                <p xml:id="N16C6E">
                  <s xml:id="N16C6F" xml:space="preserve">Secundo contra primam ſuppoſi-
                    <lb/>
                  tionem: et vniuerſaliter contra fundamentum to-
                    <lb/>
                  tius opinionis arguitur ſic: quia ſi illa ſuppoſi-
                    <lb/>
                  tio eſſet vera: ſequeretur /  aliqua potētia poſſet
                    <lb/>
                  pertranſire aliquam reſiſtentiam: et tamen non
                    <lb/>
                  poſſet illam pertranſire: hoc manifeſte implicat:
                    <lb/>
                  igitur illud ex quo ſequitur. </s>
                  <s xml:id="N16C7E" xml:space="preserve">Sequela probatur / et
                    <lb/>
                  pono caſum /  ſit vna reſiſtentia vniformiter dif-
                    <lb/>
                  formis a gradu / vt duo vſ̄ ad quartum et ſit vna
                    <lb/>
                  potentia vt .4. / que inuariata incipiat pertranſi-
                    <lb/>
                  re talem reſiſtentiam ſiue incipiat moueri in tali
                    <lb/>
                  reſiſtentia: ab extremo remiſſiori: quo poſito ar-
                    <lb/>
                  guitur ſic / illa potentia nun̄ perueniet ad finem
                    <lb/>
                  illius reſiſtentie: igitur non pertranſibit illam.</s>
                </p>
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