Alvarus, Thomas, Liber de triplici motu, 1509

Table of figures

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                  <s xml:id="N24919" xml:space="preserve">
                    <pb chead="Tertii tractatus" file="0209" n="209"/>
                  Probat̄̄ antecedens / qm̄ ille proportiones acqui-
                    <lb/>
                  ſite ↄ̨tinuo ſe habent in ꝓportione dupla et prima
                    <lb/>
                  illaꝝ eſt dupla: ergo totū eſt vna ꝓportio q̈drupla /
                    <lb/>
                  vt ſepius argutū eſt. </s>
                  <s xml:id="N24926" xml:space="preserve">Q, autē continuo ſe habēt in
                    <lb/>
                  ꝓportiõe dupla. </s>
                  <s xml:id="N2492B" xml:space="preserve">Ptꝫ / q2 in prima parte ꝓportiõa-
                    <lb/>
                  bili acq̇rit illud corpꝰ ꝓportionē dupla: et in ſcḋa
                    <lb/>
                  medietatē duple: qm̄ ſi eque velociter augmētaret̄̄
                    <lb/>
                  in ſcḋa ſicut in prima acq̇reret vnã quartã duple:
                    <lb/>
                  ſed mõ in duplo velociꝰ auget̄̄ ꝙ̄ tūc: g̊ acq̇rit vnam
                    <lb/>
                  medietatē duple: et ſic ꝓbabis /  in tertia parte ac­
                    <lb/>
                  quirit vnã quartã: et ſic ↄ̨ñter: igr̄ ↄ̨tinuo acq̇rit ꝓ-
                    <lb/>
                  portiões ſe habētes in ꝓportiõe ſubdupla, et ſub-
                    <lb/>
                  dupla / qḋ fuit ꝓbandū.
                    <note position="left" xlink:href="note-0209-01a" xlink:label="note-0209-01" xml:id="N24988" xml:space="preserve">Cõfirma­
                      <lb/>
                    tio .2.</note>
                  </s>
                  <s xml:id="N24943" xml:space="preserve">¶ Cõfirmat̄̄ ſcḋo / q2 ſi poſi-
                    <lb/>
                  tio eſſet uera: ſeq̄ret̄̄ /  aliqḋ corpꝰ augmētaret̄̄, et
                    <lb/>
                  in nulla ꝓportiõe fierit maiꝰ: ↄ̨ñs eſt falſñ: igr̄ et il-
                    <lb/>
                  lud ex quo ſequit̄̄. </s>
                  <s xml:id="N2494C" xml:space="preserve">Seq̄la ꝓbat̄̄: et volo /  vnū peda-
                    <lb/>
                  le in prima parte ꝓportiõali hore ꝓportiõe dupla
                    <lb/>
                  diuiſe aliq̈liter augmētet̄̄: et in ſcḋa in ſuꝑbipartiē­
                    <lb/>
                  te tertias velociꝰ, et in tertia in ſuꝑtripartiēte quī-
                    <lb/>
                  tas, et ī quarta in ſupraq̈dripartiēte ſeptīas, ī .5. et
                    <lb/>
                  ſupraquītipartiēte vndecimas, et ſic ↄ̨ñter ꝓcedēdo
                    <lb/>
                  ꝑ nūeros īpares primos et incõpoſitos. </s>
                  <s xml:id="N2495B" xml:space="preserve">Quo poſi­
                    <lb/>
                  to ſic argr̄: tale corpꝰ augmētat̄̄ vt notū eſt: et tñ in
                    <lb/>
                  nulla ꝓportiõe ſit maiꝰ: igr̄. </s>
                  <s xml:id="N24962" xml:space="preserve">Probat̄̄ mīor: q2 nec
                    <lb/>
                  in multiplici, nec ī ſuꝑparticulari, nec in ſuprapar­
                    <lb/>
                  tiente, nec in multiplici ſupraparticulari, nec ī mul­
                    <lb/>
                  tiplici ſuprabprrtiēte, et ſi hoc negas des illã. </s>
                  <s xml:id="N2496B" xml:space="preserve">Itē
                    <lb/>
                  poſito /  in prima parte ꝓportiõali vnū pedale ac­
                    <lb/>
                  quirit ꝓportionē ſaꝑbipartientē tertias, et in ſcḋa
                    <lb/>
                  acq̇rat ꝓportionē ſuꝑbipartientē quītas, et in ter-
                    <lb/>
                  tia ſuꝑbipartientē ſeptīas, et in q̈rta ſuprabipar-
                    <lb/>
                  tiēte nonas, et ſic ↄ̨ñter ꝓcedendo ꝑ ſpecies ꝓporti-
                    <lb/>
                  onis ſuꝑbipartiētes: tale corpꝰ augmentabit̄̄: et in
                    <lb/>
                  nulla uroportione fiet maius quam erat antea igr̄</s>
                </p>
                <p xml:id="N24990">
                  <s xml:id="N24991" xml:space="preserve">Sexto principaliṫ ad idē argr̄ ſic. </s>
                  <s xml:id="N24994" xml:space="preserve">Si
                    <lb/>
                  illa poſitio eſſet a ſeq̄ret̄̄ /  ſi duo corpora equa-
                    <lb/>
                  lia augmētarent̄̄ talr̄ /  medietas vniꝰ augmētaret̄̄
                    <lb/>
                  ad duplū, et quarta alteriꝰ ad quadruplū: illa cor­
                    <lb/>
                  pora eq̄ velociter augmētarent̄̄: ſed ↄ̨ñs eſt falſum /
                    <lb/>
                  igr̄ illud ex quo ſequit̄̄. </s>
                  <s xml:id="N249A1" xml:space="preserve">Seq̄la ptꝫ. </s>
                  <s xml:id="N249A4" xml:space="preserve">qm̄ ſi eq̈lis aug-
                    <lb/>
                  mentatio aut acq̇ſitio ꝓportiõis in parte alicuiꝰ to­
                    <lb/>
                  tius aliq̇d facit ad denoīationē augmētatiõis to-
                    <lb/>
                  tius, ſequit̄̄ qḋ dupla ꝓportio acq̇ſita parti in du­
                    <lb/>
                  plo mīori tm̄ facit ſicut ſubdupla ꝓportio acq̇ſita
                    <lb/>
                  parti in duplo maiori: igr̄ in ꝓpoſito illa acq̇ſitio
                    <lb/>
                  ꝓportiõis in medietate tm̄ adequate facit ad aug-
                    <lb/>
                  mentū totiꝰ ſicut acq̇ſitio ꝓportiõis in duplo maio­
                    <lb/>
                  ris in vna quarta. </s>
                  <s xml:id="N249B7" xml:space="preserve">Ptꝫ añs a ſimili de denoīatiõe
                    <lb/>
                  q̈litatis et denſitatis. </s>
                  <s xml:id="N249BC" xml:space="preserve">Iam ꝓbo falſitatē ↄ̨ñtis qm̄
                    <lb/>
                  in tali caſu corpꝰ cuiꝰ vna medietas auget̄̄ ad du-
                    <lb/>
                  plum ſui acq̇rit ꝓportionē ſexq̇alterã, et aliud acq̇-
                    <lb/>
                  rit ꝓportionē ſuꝑtripartientē quartas q̄ maior eſt /
                    <lb/>
                  igr̄ nõ eque velociter augmentat̄̄, et ꝑ ↄ̨ñs illatum
                    <lb/>
                  falſū. </s>
                  <s xml:id="N249C9" xml:space="preserve">Probat̄̄ maior / q2 ſi medietas acq̇ſiuit ꝓpor­
                    <lb/>
                  tionē duplã ſequit̄̄  tale corpꝰ acq̇ſiut tm̄ quantū
                    <lb/>
                  eſt medietas eiꝰ, et ꝑ ↄ̨ñs ſexq̇alterã ꝓportionē. </s>
                  <s xml:id="N249D0" xml:space="preserve">Mi­
                    <lb/>
                  nor ꝓbat̄̄: q2 ſi vna quarta alteriꝰ corporis facta
                    <lb/>
                  eſt in q̈druplo maior, ſequit̄̄ qḋ acq̇ſiuit ter tm̄ ſi-
                    <lb/>
                  cut ipſa eſt, et ſic acq̇ſiuit tres quartas totiꝰ, et per
                    <lb/>
                  ↄ̨ñs in fine illud totū componitur ex ſeptem parti-
                    <lb/>
                  bus quaꝝ q̄libet eſt equalis vni quarte totiꝰ corpo­
                    <lb/>
                  ris in principio augmētatiõis, et ſic illud corpꝰ erit
                    <lb/>
                  in ſupratripartiēte quartas maiꝰ quã erat antea /
                    <lb/>
                  qḋ fuit ꝓbandū.
                    <note position="left" xlink:href="note-0209-02a" xlink:label="note-0209-02" xml:id="N24A79" xml:space="preserve">ↄ̨firma°.</note>
                  </s>
                  <s xml:id="N249E8" xml:space="preserve">¶ Cõfirmat̄̄ / q2 ſi iſta poſitio eſſet
                    <lb/>
                  vera, ſeq̄ret̄̄ /  uõ eſſet poſſibile aliq̇d īcipere auge-
                    <lb/>
                  ri a nõ quanto vniformiṫ, aut īfinite tarde ſed ↄ̨ñs
                    <lb/>
                  eſt flm̄: igr̄ illud ex q̊ ſequit̄̄. </s>
                  <s xml:id="N249F1" xml:space="preserve">Seq̄la ꝓbat̄̄ / q2 qḋlibet
                    <lb/>
                  qḋ a nõ quãto īcipit augeri īfinite velociter incipit
                    <lb/>
                  augeri: igr̄ nullū tale / qḋ a nõ quãto incipit augeri
                    <cb chead="Capitulū ſecundum."/>
                  incipit vniformiter aut infinitū tarde augeri. </s>
                  <s xml:id="N249FB" xml:space="preserve">Con­
                    <lb/>
                  ſequētia ſatis apparet, et añs ꝓbat̄̄ vcꝫ /  quodli-
                    <lb/>
                  bet tale incipit infinite velociter augeri: qm̄ quod-
                    <lb/>
                  libet tale incipit infinitã magnã ꝓportionē acqui-
                    <lb/>
                  rere: igr̄. </s>
                  <s xml:id="N24A06" xml:space="preserve">Probat̄̄ tñ falſitas ↄ̨ñtis: q2 aliq̇d incipit
                    <lb/>
                  a nõ quanto augeri īfinite tarde: et illud idē incipit
                    <lb/>
                  a nõ quãto īfinite velociter augeri, et illud idē etiã
                    <lb/>
                  a nõ quanto incipit vniformiter augeri. </s>
                  <s xml:id="N24A0F" xml:space="preserve">igr̄ poſſi-
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                  bile eſt aliq̇d incipere a nõ quãto vniformiter, et in-
                    <lb/>
                  finitū tarde augeri: et ꝑ ↄ̨ñs illud ↄ̨ñs eſt flm̄. </s>
                  <s xml:id="N24A16" xml:space="preserve">Pro-
                    <lb/>
                  bat̄̄ añs, et volo /  diuidat̄̄ hora futura in partes
                    <lb/>
                  ꝓportionales ꝓportione dupla, et capio tres ordi­
                    <lb/>
                  nes partiū ꝓportionaliū qui ordines continuo ſe
                    <lb/>
                  habēt in ꝓportione octupla puta pro primo ordīe
                    <lb/>
                  primã partē et quartã: et ſeptimã et decimã / et ſic cõ-
                    <lb/>
                  ſequēter omittendo duas, et ꝓ ſecūdo ordine capio
                    <lb/>
                  ſcḋam, et quintã, et octauã, et vndecimã, et ſic ↄ̨ñter:
                    <lb/>
                  ſimiliter omittēdo duas. </s>
                  <s xml:id="N24A29" xml:space="preserve">Et ꝓ tertio ordine capio
                    <lb/>
                  tertiã, ſextã, nonã, duodecimã, et ſic cõſeqnēter etiã
                    <lb/>
                  omittendo duas: et volo /  in qualibet parte ꝓpor­
                    <lb/>
                  tionali primi ordinis vnū pedale perdat ꝓportio-
                    <lb/>
                  nē duplã: et in prima parte ſcḋi ordinis perdat etiã
                    <lb/>
                  duplã: et in ſcḋa eiuſdē ordinis ꝓportiouē in octu-
                    <lb/>
                  plo minorē quã in ſcḋa: et ſic ↄ̨ñter. </s>
                  <s xml:id="N24A38" xml:space="preserve">ita  in ſcḋo or­
                    <lb/>
                  dine in ea ꝓportione qua partes ſunt minores in
                    <lb/>
                  ea ↄ̨tinuo ꝓportionē minorē deṗerdat. </s>
                  <s xml:id="N24A3F" xml:space="preserve">In prima
                    <lb/>
                  vero parte tertii ordinis idē pedale deꝑdat ꝓpor-
                    <lb/>
                  tionē duplã, et in ſcḋa eiuſdē tertii ordinis in ſexde­
                    <lb/>
                  cuplo minorē, et in tertia eiuſdē ordinis in ſexdecu-
                    <lb/>
                  plo minorē quã in ſcḋa / et ſic ↄ̨ñter. </s>
                  <s xml:id="N24A4A" xml:space="preserve">Quo poſito ma­
                    <lb/>
                  nifeſtū eſt /  hoc corpꝰ diminuet̄̄ ad nõ quantñ vſ
                    <lb/>
                  et in īfinitū velociter diminuet̄̄ ad nõ quantū in par­
                    <lb/>
                  tibꝰ ꝓportionabilibꝰ primi ordinis, et in partibus
                    <lb/>
                  ꝓportiõalibꝰ ſcḋi ordīs ↄ̨tinuo vniformiter dimi-
                    <lb/>
                  nuet̄̄ / vt ptꝫ ex caſu et in partibꝰ ꝓportiõalibꝰ tertii
                    <lb/>
                  ordinis in īfinitū tarde diminuit̄̄ ad nõ quantum.
                    <lb/>
                  </s>
                  <s xml:id="N24A5A" xml:space="preserve">Uolo igr̄ /  cū corpꝰ fuerit ad nõ quantū redactū.
                    <lb/>
                  </s>
                  <s xml:id="N24A5E" xml:space="preserve">Iteꝝ īcipiat in hora ſeq̄nti augeri a nõ quãto oīno
                    <lb/>
                  eodē mõ ſicut diminuebat̄̄. </s>
                  <s xml:id="N24A63" xml:space="preserve">Et argr̄ ſic. </s>
                  <s xml:id="N24A66" xml:space="preserve">illud corpꝰ
                    <lb/>
                  īcipit in īfinitū velociter augeri puta in partibꝰ pri­
                    <lb/>
                  mi ordinis, et incipit etiã vniformiter puta in par-
                    <lb/>
                  bꝰ ſcḋi ordīs: et ↄ̨ſimiliter īcipit in īfinitū tarde au-
                    <lb/>
                  geri / vt īdicat diminutio fucta in partibꝰ tertii or-
                    <lb/>
                  dinis: igr̄ aliq̇d īcipit a nõ quãto in īfinitū tarde, et
                    <lb/>
                  īfinitū velociter, et vniformiṫ augeri / qḋ fuit ꝓbãdū</s>
                </p>
                <p xml:id="N24A7F">
                  <s xml:id="N24A80" xml:space="preserve">Septimo prīcipaliṫ  ↄ̨̨tra aliã partē
                    <lb/>
                  q̄ſtiõis argr̄ ſic. </s>
                  <s xml:id="N24A85" xml:space="preserve">Quia ſi velocitas augmētationis
                    <lb/>
                  deberet attēdi penes abſolutã acq̇ſitionē quãtita-
                    <lb/>
                  tia ſeq̄ret̄̄ /  aliq̇d augmētaret̄̄ / qḋ tñ nõ fierit maiꝰ
                    <lb/>
                  ↄ̨ñs eſt falſū: igr̄ illud ex quo ſequit̄̄. </s>
                  <s xml:id="N24A8E" xml:space="preserve">Seq̄la ꝓbat̄̄:
                    <lb/>
                  et capio vnū bipedale, et volo /  vna medietas eius
                    <lb/>
                  vniformiter acq̇rat vnū ſemipedale, et tm̄ cõtinuo
                    <lb/>
                  deꝑdat alia medietas ſicut altera acq̇rit, q̊ poſito
                    <lb/>
                  argr̄ ſic. </s>
                  <s xml:id="N24A99" xml:space="preserve">Illud bipedale nõ ſit maiꝰ vt conſtat: et tñ
                    <lb/>
                  augmentat̄̄: igr̄ ꝓpoſitū. </s>
                  <s xml:id="N24A9E" xml:space="preserve">argr̄ minor. </s>
                  <s xml:id="N24AA1" xml:space="preserve">Q2 acq̇rit a-
                    <lb/>
                  liquã ̄titatē cū vna medietas eiꝰ acq̇rat ſemipeda­
                    <lb/>
                  lē quãtitatē: igr̄ augmētat̄̄. </s>
                  <s xml:id="N24AA8" xml:space="preserve">Ptꝫ ↄ̨ña ꝑ poſitione q̄
                    <lb/>
                  ponit /  augmētatio d3 attēdi penes abſolutã acq̇­
                    <lb/>
                  ſitionē quãtitatis.
                    <note position="right" xlink:href="note-0209-03a" xlink:label="note-0209-03" xml:id="N24B98" xml:space="preserve">Dictur</note>
                  </s>
                  <s xml:id="N24AB4" xml:space="preserve">¶ Dices et bñ: negãdo ſequelã, et
                    <lb/>
                  ad ꝓbationē admiſſo caſu negãdo /  illud bipeda­
                    <lb/>
                  le augeat̄̄, qm̄ ſemꝑ manet pedale: et cū ꝓbat̄̄ / q2 ac­
                    <lb/>
                  q̇rit aliquã quãtitatē negando illud, ̄uis em̄ vna
                    <lb/>
                  medietas eiꝰ acq̇rit quãtitatē totū nõ. </s>
                  <s xml:id="N24ABF" xml:space="preserve">Ad hoc em̄ 
                    <lb/>
                  acq̇reret oporteret /  vltra illã quã habet. </s>
                  <s xml:id="N24AC4" xml:space="preserve">haberet
                    <lb/>
                  maiorē, hoc eſt  acq̇reret aliquē exceſſum ſuꝑ illã
                    <lb/>
                  qḋ nõ ſit in ꝓpoſito: q2 quãtū vna medietas acq̇rit
                    <lb/>
                  tm̄ alia deꝑdit. </s>
                  <s xml:id="N24ACD" xml:space="preserve">¶ Sed ↄ̈ / q2 ſi alia medietas nõ di-
                    <lb/>
                  minueret̄̄: ſequeret̄̄ /  hec medietas que auget̄̄ eque­
                    <lb/>
                  velociter augeretur cum toto: ſed conſequens eſt </s>
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