Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N25905" level="3" n="4" type="other" type-free="tractatus">
              <div xml:id="N2AEE0" level="4" n="4" type="chapter" type-free="capitulum">
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                  <s xml:id="N2B7F3" xml:space="preserve">
                    <pb chead="Quarti trctatus." file="0268" n="268"/>
                  larū partiū ſubiecti: aut proportio illarū partiū ē
                    <lb/>
                  equalis ꝓportioni qusalitatū exemplū primi: vt ſi
                    <lb/>
                  in vna medietate pedalis ponat̄̄ albedo vt .4. et in
                    <lb/>
                  vna quarta albedo vt .5. / tunc ꝓportio partiū eſt ma­
                    <lb/>
                  ior ꝓportiõe q̈litatū. </s>
                  <s xml:id="N2B807" xml:space="preserve">Nam hec ē ſexq̇quīta illa
                    <lb/>
                  vero dupla. / exēmplū ſcḋi: vt ſi in vna medietate ſubie­
                    <lb/>
                  cti ponat̄̄ albedo vt .2. et in quarta ponat̄̄ albedo vt
                    <lb/>
                  6. tunc ꝓportio q̈litatū excedit ꝓportionē ꝑtiū ſub­
                    <lb/>
                  iecti. </s>
                  <s xml:id="N2B812" xml:space="preserve">nã hec dupla illa vero tripla. </s>
                  <s xml:id="N2B815" xml:space="preserve">exēmplū tertii / vt ſi
                    <lb/>
                  in vna medietate ponat̄̄ albedo vt .8. et in vna quar­
                    <lb/>
                  ta albedo vt ſexdecim tunc eadē eſt ꝓportio illaruꝫ
                    <lb/>
                  partiū et etiã qualitatū: et tot modis poſſunt quali­
                    <lb/>
                  tates variari ſi intenſior qualitas maiori ꝑti ſubie­
                    <lb/>
                  cti inhereat remiſſior vero minori. </s>
                  <s xml:id="N2B822" xml:space="preserve">adhibeas exem-
                    <lb/>
                  pla. Cõſummata diuiſione ponende ſunt aliq̄ pro-
                    <lb/>
                  poſitiões.
                    <note position="left" xlink:href="note-0268-01a" xlink:label="note-0268-01" xml:id="N2B907" xml:space="preserve">porpõ.</note>
                  </s>
                  <s xml:id="N2B82E" xml:space="preserve">¶ Prima propõ. </s>
                  <s xml:id="N2B831" xml:space="preserve">Si qualitates eq̄ inten­
                    <lb/>
                  ſe partibꝰ extendant̄̄ equalibꝰ: ip̄e equaliter totuꝫ
                    <lb/>
                  ſubiectum denoīant: ſi vero ꝑtibus ſubiecti ineq̈li-
                    <lb/>
                  bus inhereãt: tūc illa qualitas q̄ ꝑ maiorē ꝑtē extē-
                    <lb/>
                  ditur plus denoīat totū (deducto impedimēto) ī ea
                    <lb/>
                  ꝓportiõe in q̈ ſe habēt ille ꝑtes ſubiecti ad inuicem.
                    <lb/>
                    <note position="left" xlink:href="note-0268-02a" xlink:label="note-0268-02" xml:id="N2B90D" xml:space="preserve">.propõ.</note>
                  </s>
                  <s xml:id="N2B845" xml:space="preserve">¶ Scḋa propõ. </s>
                  <s xml:id="N2B848" xml:space="preserve">Qñ inequales qualitates equalibꝰ
                    <lb/>
                  ꝑtibus ſubiecti inherent: tūc intēſior in ea ꝓportio­
                    <lb/>
                  ne plus denoīat ſubiectū in qua eſt intēſior.
                    <note position="left" xlink:href="note-0268-03a" xlink:label="note-0268-03" xml:id="N2B913" xml:space="preserve">propõ.</note>
                  </s>
                  <s xml:id="N2B854" xml:space="preserve">¶ Ter-
                    <lb/>
                  tia propõ. </s>
                  <s xml:id="N2B859" xml:space="preserve">Si inequales qualitates intēſiue exten-
                    <lb/>
                  dant̄̄ ꝑ inequales partes vnius ſubiecti: et intenſior
                    <lb/>
                  maiori parti inhereat remiſſior vero minori: tunc
                    <lb/>
                  intenſior plꝰ denoīat totale ſubiectū ꝙ̄ remiſſior in
                    <lb/>
                  ꝓportiõe ↄ̨poſita ex ꝓportioni partis maioris ad
                    <lb/>
                  partem minorem: et qualitatis intenſioris ad qua-
                    <lb/>
                  litatem remiſſiorem. </s>
                  <s xml:id="N2B868" xml:space="preserve">Exemplū / vt ſi in vna medieta­
                    <lb/>
                  te pedalis ponatur albedo vt .4. et in 4. eiuſdē po-
                    <lb/>
                  natur albedo vt .2. </s>
                  <s xml:id="N2B86F" xml:space="preserve">Dico /  albedo exiſtēs īmediate
                    <lb/>
                  in quadruplo plus denoīat illud pedale ꝙ̄ albedo
                    <lb/>
                  exiſtēs in quarta eiuſdē pedalis: q2 proportio illa-
                    <lb/>
                  rum qualitatū, et etiaꝫ partiū eſt dupla compoſita
                    <lb/>
                  vero ex duabus duplis quadrupla.
                    <note position="left" xlink:href="note-0268-04a" xlink:label="note-0268-04" xml:id="N2B919" xml:space="preserve">.propõ</note>
                  </s>
                  <s xml:id="N2B87F" xml:space="preserve">¶ Quarta pro­
                    <lb/>
                  poſitio. </s>
                  <s xml:id="N2B884" xml:space="preserve">Si intēſior qualitas parti extēdatur mīo-
                    <lb/>
                  ri: et remiſſior maiori: ſit equalis ꝓportio ꝑtium
                    <lb/>
                  ad inuicē et etiã intenſionū: tunc ille qualitates eq̈li­
                    <lb/>
                  ter ad totius denoīationē faciūt. </s>
                  <s xml:id="N2B88D" xml:space="preserve">Exemplum / vt ſi ī
                    <lb/>
                  vna medietate ponat̄̄ qualitas vt .4. et in vna quar-
                    <lb/>
                  ta vt .8. q2 tunc inter partes et etiã qualitates ē pro­
                    <lb/>
                  portio dupla tantū facit ad denoīationē totiꝰ qua­
                    <lb/>
                  litas vt .8. in vna quarta: ̄tum qualitas vt .4. ī me­
                    <lb/>
                  dietate: q2 vtra. </s>
                  <s xml:id="N2B89A" xml:space="preserve">vt .2. / vt pꝫ.
                    <note position="left" xlink:href="note-0268-05a" xlink:label="note-0268-05" xml:id="N2B91F" xml:space="preserve">.propõ.</note>
                  </s>
                  <s xml:id="N2B8A2" xml:space="preserve">¶ Quinta propõ. </s>
                  <s xml:id="N2B8A5" xml:space="preserve">Si ī­
                    <lb/>
                  tenſior qualitas parti coextēdat̄̄ mīori: et remiſſior
                    <lb/>
                  maiori: ꝓportio intenſionū illarū qualitatū par­
                    <lb/>
                  tiū proportionē exuperat: tunc qualitas exiſtens in
                    <lb/>
                  minori parte ſubiecti totale ſubiectum intēſius de­
                    <lb/>
                  noīabit ꝙ̄ qualitas exiſtēs in minori parte: in ea ꝓ­
                    <lb/>
                  portiõe ꝑ quam ꝓportio intenſionū illarū qualita­
                    <lb/>
                  tū ꝑtium ꝓportionē excedit. </s>
                  <s xml:id="N2B8B6" xml:space="preserve">Exēplū / vt ſi in vna me-
                    <lb/>
                  dietate pedalis ponatur albedo vt .2. et in quarta
                    <lb/>
                  eiuſdē albedo vt .8. q2 ꝓportio ꝑtium dupla excedit̄̄
                    <lb/>
                  a ꝓportione intenſionū illarū qualitatū quadru-
                    <lb/>
                  pla: et quadrupla excedit duplã ꝑ duplã: ideo in du-
                    <lb/>
                  plo plus denoīat qualitas vt .8. ꝙ̄ vt .2. illud totale
                    <lb/>
                  ſubiectum. </s>
                  <s xml:id="N2B8C5" xml:space="preserve">quia illa vt .2. denoīat vt vnū alia o vt
                    <lb/>
                  8. denoīat vt .2. / vt patēt.
                    <note position="left" xlink:href="note-0268-06a" xlink:label="note-0268-06" xml:id="N2B925" xml:space="preserve">6. propõ.</note>
                  </s>
                  <s xml:id="N2B8CF" xml:space="preserve">¶ Sexta ꝓpõ. </s>
                  <s xml:id="N2B8D2" xml:space="preserve">Ubicū in-
                    <lb/>
                  tenſior qualitas parti ſubiecti minori inheret: et re­
                    <lb/>
                  miſſior maiori: eſt inter partes maior ꝓportio ̄
                    <lb/>
                  inter illarū qualitatū intēſiones: et tūc qualitas re­
                    <lb/>
                  miſſior plus facit ad totius denominationē ꝙ̄ intē­
                    <lb/>
                  ſior in ea ꝓportione per quã proportio partium ꝓ­
                    <lb/>
                  portionē intenſionum antecedit. </s>
                  <s xml:id="N2B8E1" xml:space="preserve">Exemplum / vt ſi in
                    <lb/>
                  vna medietate ſit qualitas vt .4. et in vna quarta
                    <lb/>
                  ſit qualitas vt .6. quia qualitas intenſior minori
                    <cb chead="Capitulum quartum"/>
                  parti inheret: et proportio partium dupla excedit ꝓ­
                    <lb/>
                  portionē intenſionū ſexq̇alterã per ſexquitertiam:
                    <lb/>
                  ideo qualitas vt .6. exiſtens in quarta in ſexq̇tertio
                    <lb/>
                  minus denominat totale ſubiectū ꝙ̄ qualitas vt .4.
                    <lb/>
                  exiſtens in mediate. </s>
                  <s xml:id="N2B8F3" xml:space="preserve">Harum .6. ꝓpoſitionū demon-
                    <lb/>
                  ſtrationes inuenies in expõne ſcḋi capitis calcula-
                    <lb/>
                  toris: et facile ex his que dicta ſunt capite tertio ſe-
                    <lb/>
                  cundi tractatus: et primo capite tertii tractatus ꝓ-
                    <lb/>
                  bari valent mutatis mutandis. </s>
                  <s xml:id="N2B8FE" xml:space="preserve">Quibus premiſſis
                    <lb/>
                  ponūtur concluſiones.</s>
                </p>
                <p xml:id="N2B92B">
                  <s xml:id="N2B92C" xml:space="preserve">Prima concluſio </s>
                  <s xml:id="N2B92F" xml:space="preserve">Diuiſo corpore qua­
                    <lb/>
                  libuerit ꝓportione et prima pars ꝓportionalis eiꝰ
                    <lb/>
                  ſit aliqualiter intenſa et ſecunda in duplo plus et
                    <lb/>
                  tertia in triplo ꝙ̄ prima et quarta in quadruplo ̄
                    <lb/>
                  prima: et ſic ī infinitū. </s>
                  <s xml:id="N2B93A" xml:space="preserve">et hoc eadē qualitate ſiue ad­
                    <lb/>
                  mixtione ↄ̈rii: tunc totū corpus eſt intenſius prima
                    <lb/>
                  prima parte ꝓportionali in ea ꝓportiõe qua ſe hꝫ
                    <lb/>
                  totū ſic diuiſuꝫ ad ṗmã ꝑtē eius ꝓportionalē. </s>
                  <s xml:id="N2B943" xml:space="preserve">Pro­
                    <lb/>
                  batur cõcluſio vĺr. </s>
                  <s xml:id="N2B948" xml:space="preserve">et ſuppono /  diuiſo aliquo cor-
                    <lb/>
                  pore ꝑ partes ꝓportionales aliqua ꝓportõe: et pri­
                    <lb/>
                  mo ꝑ totū illud corpus extendat̄̄ aliqua qualitas:
                    <lb/>
                  et ꝑ totū reſiduū a ṗma parte ꝓportionali ſuꝑ illaꝫ
                    <lb/>
                  extendatur tanta: et ꝑ reſiduū a ṗma et a ſecūda ite­
                    <lb/>
                  rum tanta extendat̄̄ ſupra p̄exñteꝫ: et deinde ſupra
                    <lb/>
                  reſiduū a prima ſcḋa et tertia extendatur iterū tan­
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                  ta ſupra preexñteꝫ: et ſic ↄ̨ñter: tunc in fine illud cor­
                    <lb/>
                  pus ita ſe habebit  prima ꝑs eius ꝓportionalis
                    <lb/>
                  erit aliqualiter intenſa: ſecūda in duplo plus: et ter­
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                  tia in triplo plus ꝙ̄ prima: et quarta ī quadruplo /
                    <lb/>
                  et ſic conſequenter vt ponitur in caſu concluſionis.
                    <lb/>
                  </s>
                  <s xml:id="N2B962" xml:space="preserve">Patet hec ſuppoſitio: qm̄ ſi in prīa eſt aliquis gra­
                    <lb/>
                  dus puta c. per ſcḋam et totū erūt reſiduū duo gra­
                    <lb/>
                  dus puta c. per ſcḋam et totū erūt reſiduū duo gra­
                    <lb/>
                  dus c. et per tertiam et totum tres tales gradus c. et
                    <lb/>
                  per quartam et totum reſiduū .4. tales: et ſic ↄ̨ñter:
                    <lb/>
                  igitur prima eſt aliqualiter intenſa: et ſecūda ī du­
                    <lb/>
                  plo plus: et tertia in triplo plus ꝙ̄ ṗma: et ſic ↄ̨ñter
                    <lb/>
                  </s>
                  <s xml:id="N2B972" xml:space="preserve">Quo poſito ꝓbatur concluſio. </s>
                  <s xml:id="N2B975" xml:space="preserve">et ſit aliqḋ corpꝰ di­
                    <lb/>
                  uiſum ꝑ partes ꝓportionales ꝓportione f. et ſit g.
                    <lb/>
                  ꝓportio totiꝰ diuiſi ꝑ partes ꝓportionales ꝓpor-
                    <lb/>
                  tione f. ad primã eius partē ꝓportiõalē: et ṗma ꝑs
                    <lb/>
                  ꝓportionalis illius ſit aliquaĺr intēſa: et ſecūda in
                    <lb/>
                  duplo plus: et tertia in triplo plus ꝙ̄ ṗma: et ſic cõ-
                    <lb/>
                  ſequenter. </s>
                  <s xml:id="N2B984" xml:space="preserve">Tūc dico /  totum eſt intenſius ṗma ꝑte
                    <lb/>
                  ꝓportionali in ꝓportione g. q̄ eſt ꝓportio totiꝰ ad
                    <lb/>
                  primã partē ꝓportionalē. </s>
                  <s xml:id="N2B98B" xml:space="preserve">Quod ſic ꝓbatur: quia
                    <lb/>
                  per totuꝫ illud corpus extenditur aliqua qualitas
                    <lb/>
                  puta illa q̄ eſt in prima parte ꝓportionali: et per to­
                    <lb/>
                  tum reſiduum a prima parte ꝓportionali iterum
                    <lb/>
                  tanta ſupra illam: et per totum reſidnum a prima
                    <lb/>
                  et ſecunda iterum tanta: et ſic conſequenter. </s>
                  <s xml:id="N2B998" xml:space="preserve">vt patꝫ
                    <lb/>
                  ex ſuppoſitione: et illa qualitas que extenditur per
                    <lb/>
                  totum denominat aliqualiter tale corpus: et que ex­
                    <lb/>
                  tenditur ꝑ totum reſiduum a prima parte ꝓportio­
                    <lb/>
                  nali denominat in f. ꝓportione minus: et que exten­
                    <lb/>
                  ditur per totum reſiduum a ṗma parte ꝓportiona-
                    <lb/>
                  li et ſecunda iterum denoīat in f. ꝓportiõe minus ̄
                    <lb/>
                  illa que extenditur per totum reſiduum a prima: et
                    <lb/>
                  ex iſtis denominationibus totius corporis denoīa­
                    <lb/>
                  tio conſurgit: igit̄̄ illa denoīatio intēſiõis totiꝰ cor­
                    <lb/>
                  poris cõponitur ex infinitis ꝑtialibꝰ denoīatiõibꝰ
                    <lb/>
                  ↄ̨tinuo ſe habētibus in ꝓportiõe f. / igit̄̄ tota illa de­
                    <lb/>
                  noīatio cõpoſita ex illis infinitis ſe habet ad ṗmã
                    <lb/>
                  illarū in ꝓportiõe qua ſe habet aliquod totum di-
                    <lb/>
                  uiſum ꝑ partes ꝓportionales ꝓportione f. ad pri-
                    <lb/>
                  mã eius ꝑtem ꝓportionalem: qm̄ illa totalis deno­
                    <lb/>
                  minatio in tales partes proportionales ſecatur: et
                    <lb/>
                  illa eſt g. ex hypotheſi: ergo in ꝓportione g. totum
                    <lb/>
                  eſt intenſius ṗma ꝑte ꝓportionali / qḋ fuit ꝓbanduꝫ
                    <lb/>
                  </s>
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