Alvarus, Thomas, Liber de triplici motu, 1509

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                <p xml:id="N2BCA2">
                  <s xml:id="N2BCFA" xml:space="preserve">
                    <pb chead="De intenſione difformium" file="0271" n="271"/>
                  duplo minor ꝙ̄ in ſecūda: et ſic cõſequenter: totius
                    <lb/>
                  intēſionis ad intēſionē ſiue denoīationē qua totuꝫ
                    <lb/>
                  denoīabit̄̄ ab albedine prīe et ſcḋe partis ꝓportio­
                    <lb/>
                  nalis eſt illa ꝓportio qua ſe hꝫ totum diuiſuꝫ in ꝓ-
                    <lb/>
                  portiõe duodecupla ad primã cuiꝰ partē ꝓportio-
                    <lb/>
                  nalē. </s>
                  <s xml:id="N2BD12" xml:space="preserve">Ptꝫ hoc correlariū habito /  diuidēdo corpꝰ
                    <lb/>
                  ꝓportiõe irrõnali que eſt medietas triple: oēs ꝑtes
                    <lb/>
                  pares et oēs impares immediate ſe habent in ꝓpor­
                    <lb/>
                  tione tripla: quod pꝫ ex .4. correlario ſcḋe ↄ̨cluſio-
                    <lb/>
                  nis ſextis capitis ſcḋe partis. </s>
                  <s xml:id="N2BD1D" xml:space="preserve">et  in caſu correlarii
                    <lb/>
                  continuo intenſiõis partis paris ad intētionē pa-
                    <lb/>
                  ris īmediate ſequētis eſt ꝓportio quadrupla et ſiĺr
                    <lb/>
                  intenſionis partis īparis ad ītēſionem īparis īme­
                    <lb/>
                  diate ſequētis. </s>
                  <s xml:id="N2BD28" xml:space="preserve">Quod pꝫ intuēti caſum. </s>
                  <s xml:id="N2BD2B" xml:space="preserve">¶ Inferas
                    <lb/>
                  ꝓpria induſtria quot volueris correlaria.</s>
                </p>
                <p xml:id="N2BD40">
                  <s xml:id="N2BD41" xml:space="preserve">Sexta concluſio </s>
                  <s xml:id="N2BD44" xml:space="preserve">A. nunc eſt ſolum fi­
                    <lb/>
                  nite intēſum: et ꝑ rarefactionē finitã ſolū fiet ſubito
                    <lb/>
                  infinite intenſum. </s>
                  <s xml:id="N2BD4B" xml:space="preserve">Probat̄̄ / ſit a. tale corpus quale
                    <lb/>
                  eſt illud de quo fit mentio in caſu ṗme concluſionis
                    <lb/>
                  cuiꝰ vcꝫ prima pars ꝓportionalis eſt eq̈liter intēſa
                    <lb/>
                  ſcḋa in duplo intēſior et .3. in triplo intēſior ꝙ̄ prīa
                    <lb/>
                  etc. incipiat a. rarefieri iſto mõ vcꝫ  prīa pars ꝓ­
                    <lb/>
                  portionalis acq̇rat vniformiter in hora ̄titatē pe­
                    <lb/>
                  dalē: et in quocū tꝑe ipſa acq̇rit aliquã ̄titatem
                    <lb/>
                  pars ꝓportionalis duple ītenſionis ad illam acq̇-
                    <lb/>
                  rat ſubduplã ̄titatē ad acq̇ſitam ipſi prime parti
                    <lb/>
                  et pars quadruple ītenſionis ad primã acq̇rat ī eo-
                    <lb/>
                  dem tempore ſubquadruplã ̄titatē ad acq̇ſitã pri­
                    <lb/>
                  me: et ꝑs octuple intēſionis ad primã acq̇rat in eo-
                    <lb/>
                  dē tēpore ſuboctuplã ̄titatē ad acquiſitam prime /
                    <lb/>
                  et ſic ↄ̨ñter ꝓcedēdo ꝑ partes ꝓportionales ↄ̨tinuo
                    <lb/>
                  ſe hñtes in ꝓportiõe dupla quo ad intēſionē: ita 
                    <lb/>
                  q̄libet ſequēs in duplo minꝰ acq̇rat ↄ̨tinuo de quã-
                    <lb/>
                  titate ꝙ̄ īmediate p̄cedēs. </s>
                  <s xml:id="N2BD6E" xml:space="preserve">Quo poſito argr̄ ſic / īme­
                    <lb/>
                  diate poſt inſtãs īitiatiuū talis rarefactiõis illud
                    <lb/>
                  corpus erit infinite intenſum: et hoc ꝑ rarefactionē
                    <lb/>
                  finitã ſolū: et in illo inſtanti eſt ſolū finite intenſum:
                    <lb/>
                  igitur ꝓpoſitum. </s>
                  <s xml:id="N2BD79" xml:space="preserve">Coña patet: et argr̄ maior / q2 īme­
                    <lb/>
                  diate poſt illud inſtãs erūt ibi īfinite partes quarū
                    <lb/>
                  q̄lꝫ denoīabit tm̄ ſicut prima illaꝝ: g̊ īmediate poſt
                    <lb/>
                  illud inſtãs totū erit īfinite ītenſum. </s>
                  <s xml:id="N2BD82" xml:space="preserve">pꝫ ↄ̨ña et ꝓba­
                    <lb/>
                  tur añs / qm̄ īmediate poſt illud inſtãs illud qḋ acq̇-
                    <lb/>
                  ſitū erit prīe parti ꝓportionali aliquãtulū denoīa­
                    <lb/>
                  bit: et illḋ qḋ tunc acq̇ſitū erit parti duple ītēſiõis
                    <lb/>
                  ad primã tm̄: q2 eſt ſubduple ̄titatꝪ et in duplo ītēſi­
                    <lb/>
                  us: et ſiĺr tm̄ denoīabit illḋ qḋ tūc acq̄ſitū erit par­
                    <lb/>
                  ti quadruple intēſiõis ad ṗmã: et ſic ↄ̨ñter: igr̄ īme-
                    <lb/>
                  diate poſt illḋ inſtãs erūt ibi īfinite ꝑtes quaꝝ que-
                    <lb/>
                  libet denoīabit totum tm̄ ſicut ṗma illarū / qḋ erat
                    <lb/>
                  ꝓbandū. </s>
                  <s xml:id="N2BD97" xml:space="preserve">QꝪ vero illa rarefactio ſit finita pꝫ: q2 in
                    <lb/>
                  tꝑe finito finitã quãtitatē adequate a. acq̇rit puta
                    <lb/>
                  bipedalem / vt pꝫ. </s>
                  <s xml:id="N2BD9E" xml:space="preserve">Nã acq̇rit infinita ↄ̨tinuo ſe habē­
                    <lb/>
                  tia in ꝓportiõe dupla et primū illorū eſt pedale ex
                    <lb/>
                  hypotheſi. </s>
                  <s xml:id="N2BDA5" xml:space="preserve">Et ſic ptꝫ cõcluſio.
                    <note position="left" xlink:href="note-0271-01a" xlink:label="note-0271-01" xml:id="N2BDE6" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N2BDAD" xml:space="preserve">¶ Ex quo ſeq̇tur prīo /
                    <lb/>
                   aliqḋ corpus eſt nūc infinite albū et ꝑ ſolã ↄ̨dēſa­
                    <lb/>
                  tionē finitã efficiet̄̄ remiſſe albū hoc eſt ſine deperdi­
                    <lb/>
                  tione aut acq̇ſitiõe alicuiꝰ qualitatis.
                    <note position="left" xlink:href="note-0271-02a" xlink:label="note-0271-02" xml:id="N2BDEC" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N2BDBB" xml:space="preserve">¶ Seq̇t̄̄ ſcḋo /
                    <lb/>
                   aliquid ē mõ īfinite albū: et ꝑ ſolã rarefactionem
                    <lb/>
                  finitã efficiet̄̄ nõ albū nulla qualitate acquiſita aut
                    <lb/>
                  deꝑdita.
                    <note position="left" xlink:href="note-0271-03a" xlink:label="note-0271-03" xml:id="N2BDF2" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N2BDC9" xml:space="preserve">¶ Seq̇tur tertio /  aliqḋ corpus ē nõ albuꝫ
                    <lb/>
                  et per ſolã finitã condēſationē efficiet̄̄ infinite albū
                    <lb/>
                  nõ acq̇rēdo aut deperdēdo aliquã qualitatē.
                    <note position="left" xlink:href="note-0271-04a" xlink:label="note-0271-04" xml:id="N2BDF8" xml:space="preserve">4. correĺ</note>
                  </s>
                  <s xml:id="N2BDD5" xml:space="preserve">¶ Se­
                    <lb/>
                  quit̄̄ .4. /  aliqḋ corpus eſt p̄ciſe albū vt .4. et nõ eſt
                    <lb/>
                  in eo aliqua impediētis qualitatis aut cõtrarie ad­
                    <lb/>
                  mixtio: et illḋ nõ acq̇ret aliquã qualitatē nec deper­
                    <lb/>
                  det nec m ſe nec m aliq̇d eiꝰ: nec rarefiet aut cõdē­
                    <lb/>
                  ſabitur et tamen ſubito efficietur infinite album.</s>
                </p>
                <cb chead="De intenſione difformium"/>
                <note position="right" xml:id="N2BE00" xml:space="preserve">5. correĺ.</note>
                <p xml:id="N2BE04">
                  <s xml:id="N2BE05" xml:space="preserve">¶ Seq̇tur .5. /  infinite album nec rarefiet: nec cõdē-
                    <lb/>
                  ſabitur: nec aliquã qualitatē acq̇ret aut deperdet,
                    <lb/>
                  qualitatibꝰ cõtrariis aut ſe impediētibus excluſis
                    <lb/>
                  et tamē efficietur finite albū.
                    <note position="right" xlink:href="note-0271-05a" xlink:label="note-0271-05" xml:id="N2BE1E" xml:space="preserve">Calcula.
                      <lb/>
                    de diffor.</note>
                  </s>
                  <s xml:id="N2BE13" xml:space="preserve">Patēt oīa iſta corre-
                    <lb/>
                  laria ex expoſitiõe ſcḋe cõcluſiouis calculatoris in
                    <lb/>
                  capitulo de difformibus.</s>
                </p>
                <note position="right" xml:id="N2BE26" xml:space="preserve">Decīa cõ­
                  <lb/>
                cluſio cal­
                  <lb/>
                cu. in c. de
                  <lb/>
                diffor.</note>
                <p xml:id="N2BE30">
                  <s xml:id="N2BE31" xml:space="preserve">Septima concluſio </s>
                  <s xml:id="N2BE34" xml:space="preserve">A. eſt infinite in-
                    <lb/>
                  tenſum et b. ſolū finite intenſuꝫ et a. cõtinuo tm̄ deꝑ-
                    <lb/>
                  dit preciſe ſicut b. et per tantū ſubiectū et a. remitte­
                    <lb/>
                  tur ad nõ gradū et nõ b. </s>
                  <s xml:id="N2BE3D" xml:space="preserve">Probat̄̄ / ſit a. vnū infinituꝫ
                    <lb/>
                  quãtitatiue cuiꝰ primū pedale habeat infinitas calidi­
                    <lb/>
                  tates vt .4. et ſcḋm infinitas in duplo mīores et ter-
                    <lb/>
                  tium infinitas in quadruplo minores, et quartū in­
                    <lb/>
                  fiuitas in octuplo mīores: et ſic in īfinitū: ita  qḋ­
                    <lb/>
                  libet pedale ſequens ſit infinite intēſum hñs īfini-
                    <lb/>
                  tas caliditates quarū quelꝫ ſit ſubdupla ad quãlꝫ
                    <lb/>
                  infinitarū pedalis īmediate p̄cedētꝪ .b. vero habeat
                    <lb/>
                  duas per totū equalis intēſionis cū duabꝰ ṗmi pe­
                    <lb/>
                  dalis ipſiꝰ a. puta duas vt .4. et inſuꝑ vnã vt .4. ita
                    <lb/>
                   ſit vniforme vt .12. et in qualꝫ parte ꝓportionali
                    <lb/>
                  vnius hore primū pedale ipſius a. ꝑdat vnã illaruꝫ
                    <lb/>
                  infinitaꝝ qualitatū ↄ̨tinuo ꝑ ordinē nullã omitten-
                    <lb/>
                  do et in qualꝫ parte ꝓportionali dempta prīa m
                    <lb/>
                  pedale ipſius a. perdat vnã illarū ſuarū infinitaꝝ
                    <lb/>
                  qualitatū per ordinē ↄ̨ñter nullã omittēdo et ī qua­
                    <lb/>
                  libet parte ꝓportionali dēpta ṗma et ſcḋa: m peda­
                    <lb/>
                  le ipſiꝰ a. ꝑdat vnã ſuaꝝ īfinitaꝝ qualitatū: et ī qua-
                    <lb/>
                  libet ſequēte tertiã quartū pedale perdat vnã ſuaꝝ /
                    <lb/>
                  et ſic ↄ̨ñter: ita  ṗmū perdat per oēs, m per oēs
                    <lb/>
                  excepta prīa ṫtiū per oēs excepta .1. et .2. et ſic ī īfini-
                    <lb/>
                  tū: ita  ī fine nichil maneat in ip̄o a. nec ī eiꝰ aliq̄
                    <lb/>
                  pedali. </s>
                  <s xml:id="N2BE6C" xml:space="preserve">Et ī ṗma parte ꝓportionali ṗmū pedale ip­
                    <lb/>
                  ſius b. perdat vnã illaꝝ qualitatū vt .4. quas hꝫ, et
                    <lb/>
                  in ſcḋa qñ primū pedale ipſiꝰ a. perdit vnã qualita­
                    <lb/>
                  tē vt .4. et m perdit vnã vt .2. m pedale ipſiꝰ b. per-
                    <lb/>
                  dat vnã vt .4. et ṗmū eiuſdē perdat vnã vt .2. et in ṫtia
                    <lb/>
                  parte ꝓportionali qñ primū pedale ipſiꝰ a. perdit
                    <lb/>
                  4. gradus: et m duos: et tertiū vnū: ṗmū ipſiꝰ b. per­
                    <lb/>
                  dat vnū: et m .2. et ṫtiū .4. et ſic in īfinitū ita  qua-
                    <lb/>
                  cun parte hore ꝓportionali data in illa perdat
                    <lb/>
                  ṗmū pedale ipſiꝰ a. vnã ſuarū qualitatū corrñdētē
                    <lb/>
                  in nūero tali parti ꝓportionali: et ī quacū parte
                    <lb/>
                  ꝓportionali dēpta ṗma m pedale perdat vnã ſua­
                    <lb/>
                  rū corrñdētē ī nūero parti ꝓportionali īmediate p̄-
                    <lb/>
                  cedēti / et ſic ↄ̨ñter: et ī eadē parte ꝓportiõali pedale
                    <lb/>
                  ipſius b. corrñdēs in nūero tali parti proportiona­
                    <lb/>
                  li deperdat tantã qualitatē ſicut primū ipſius a. et
                    <lb/>
                  pedale immediate precedens in b. perdat tãtum ſi-
                    <lb/>
                  cut ſecundum pedale ipſius a. / et ſic conſequenter.</s>
                </p>
                <p xml:id="N2BE91">
                  <s xml:id="N2BE92" xml:space="preserve">Exemplū / vt data ſexta parte proportionali hore:
                    <lb/>
                  tunc primū pedale ipſius a. deperdit ſextã illarum
                    <lb/>
                  ſuarū qualitatū vt .4. et ſecūdum quintã que eſt vt
                    <lb/>
                  2. et tertiū quartã q̄ eſt vt vnū: et quartū tertiã q̄ eſt
                    <lb/>
                  vt dimidiū et q̇ntū ſcḋaꝫ vt vna quarta: et ſextū prīaꝫ
                    <lb/>
                  vt vna octaua: et in eadē parte ſextū ipſiꝰ b. perdit
                    <lb/>
                  4. gradus et q̇ntū .2. et quartū vnū: et ṫtiū dimidiuꝫ,
                    <lb/>
                  et m vnã quartã: et primū vnã octauã. </s>
                  <s xml:id="N2BEA3" xml:space="preserve">Quo poſito
                    <lb/>
                  pꝫ /  ipſum a. in fine erit nõ intēſum: et b. per totum
                    <lb/>
                  erit intēſum vt .4. / igr̄ ↄ̨° vera. </s>
                  <s xml:id="N2BEAA" xml:space="preserve">Probationē huiꝰ vi-
                    <lb/>
                  deas latiꝰ in expõe calculatoris cuius hec ↄ̨° eſt de­
                    <lb/>
                  cima.
                    <note position="right" xlink:href="note-0271-06a" xlink:label="note-0271-06" xml:id="N2BEBF" xml:space="preserve">3. articu.</note>
                  </s>
                  <s xml:id="N2BEB6" xml:space="preserve">¶ Expedito primo articulo et ſecundo iam re­
                    <lb/>
                  ſtat dubia mouere.</s>
                </p>
                <p xml:id="N2BEC5">
                  <s xml:id="N2BEC6" xml:space="preserve">Dubitat̄̄ primo vtrū cuiuſlibet quali­
                    <lb/>
                  tatis difformis ſiue qualificati intenſio correſpon­
                    <lb/>
                  deat qualitati vniformi ad cuius intenſionem po-
                    <lb/>
                  teſt reduci.</s>
                </p>
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