Alvarus, Thomas, Liber de triplici motu, 1509

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          <div xml:id="N15C17" level="2" n="3" type="other" type-free="pars">
            <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">
                <p xml:id="N2B003">
                  <s xml:id="N2B01E" xml:space="preserve">
                    <pb chead="Quarti tractatus." file="0264" n="264"/>
                  Et tamē nõ cuiuſlbet partis gradus q̇ eſt ī medio tã­
                    <lb/>
                  tū exceditur a ſūmo ̄tum etc̃. / igr̄ aſſumptū verum
                    <lb/>
                  </s>
                  <s xml:id="N2B028" xml:space="preserve">Probatur minor / q2 illa linea nõ hꝫ mediū cū ſit in­
                    <lb/>
                  finita. </s>
                  <s xml:id="N2B02D" xml:space="preserve">nec tota pars eiꝰ depto prīo giro hꝫ medium
                    <lb/>
                  ꝓpter eãdem cãm: ergo nõ cuiuſlꝫ partis eiꝰ gradus
                    <lb/>
                  qui eſt in medio tm̄ excedit̄̄ etc̃.
                    <note position="left" xlink:href="note-0264-01a" xlink:label="note-0264-01" xml:id="N2B05F" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N2B039" xml:space="preserve">¶ Dices forte ad pū­
                    <lb/>
                  ctū argumēti diſtinguendo /  in illa lignea non ſit
                    <lb/>
                  medium aut mediū longitudinis: et ſic ↄ̨ceditur /  ī
                    <lb/>
                  illa nõ ſit mediū. </s>
                  <s xml:id="N2B042" xml:space="preserve">Nec de tali medio intelligit̄̄ diffi-
                    <lb/>
                  nitio: aut mediū magnitudines et ſic negat̄̄. </s>
                  <s xml:id="N2B047" xml:space="preserve">Illa eī
                    <lb/>
                  linea ̄uis ſit infinite longa nõ tñ eſt corpus infini-
                    <lb/>
                  tū ſiue quãtitas īfinita. </s>
                  <s xml:id="N2B04E" xml:space="preserve">Sed finita: et per ↄ̨ñs habet
                    <lb/>
                  duas medietates: illud em̄ de ratione quãti finiti-
                    <lb/>
                  eſt habere videlicet duas medietates: quare facile
                    <lb/>
                  dici põt /  ī medio magnitudinis illius eſt gradus
                    <lb/>
                  mediꝰ: cū tale mediū ſit dabile et de tali medio in-
                    <lb/>
                  telligitur dicta diffinitio.</s>
                </p>
                <p xml:id="N2B065">
                  <s xml:id="N2B066" xml:space="preserve">Sed cõtra q2 aliqua eſt qualitas vni-
                    <lb/>
                  formiter difformis: et tñ nõ cuiuſlꝫ partis eiꝰ gra-
                    <lb/>
                  dus / qui eſt in medio magnitudinis tantū exceditur
                    <lb/>
                  a ſūmo ̄tum excedit īfinitū / igr̄ ſolutio nulla. </s>
                  <s xml:id="N2B06F" xml:space="preserve">Pro­
                    <lb/>
                  batur añs: et ſigno vnū quadratū vniformiṫ diffor­
                    <lb/>
                  miter albū ab .8. vſ ad nõ gradū: et diuido illḋ in
                    <lb/>
                  duas medietates triangulares ꝑ diametrū ꝓcedē-
                    <lb/>
                  tē ab vno angulo in relinquū: vt pꝫ in figura ī mar­
                    <lb/>
                  gine. </s>
                  <s xml:id="N2B07C" xml:space="preserve">Et manifeſtū eſt /  altera pars ſiue medietas
                    <lb/>
                  triangularis illiꝰ quadrati hꝫ maiorē partē ſui ̄
                    <lb/>
                  medietatē qualificatã maiori gradu ꝙ̄ vt .4. habet
                    <lb/>
                  enim .3. quartas incipientes a .4. et terminatas ad
                    <lb/>
                  nõ gradū: et vnã dūtaxat incipientē a .4. et termina­
                    <lb/>
                  tã ad .8. / ergo ſequit̄̄ /  gradus medius nõ eſt in me-
                    <lb/>
                  dio magnitudinis illius partis triangularis. </s>
                  <s xml:id="N2B08B" xml:space="preserve">Sed
                    <lb/>
                  in fine ṗme .4. / ergo aliqua eſt qualitas vniformiter
                    <lb/>
                  difformis: et tamē nõ cuiuſlibet partis eius gradꝰ
                    <lb/>
                  qui eſt in medio talis partis tantū exceditur a ſum-
                    <lb/>
                  mo ̄tū excedit infiniū eiuſdē partis puta illꝰ par­
                    <lb/>
                  tis triangularis: quod fuit probandum.</s>
                </p>
                <p xml:id="N2B098">
                  <s xml:id="N2B099" xml:space="preserve">Tertio prīcipaliter arguitur ſic. </s>
                  <s xml:id="N2B09C" xml:space="preserve">Q2
                    <lb/>
                  ſi qualitatis vniformiter difformis et difformiṫ dif­
                    <lb/>
                  formis intentio attendēda eſt penes reductionē ad
                    <lb/>
                  vniformitatē: ſeq̄retur /  qualitas difformis cuius
                    <lb/>
                  vtra medietas eſt vniofrmis correſpõderet gra-
                    <lb/>
                  dui medio. </s>
                  <s xml:id="N2B0A9" xml:space="preserve">ſꝫ ↄ̨ñs eſt fĺm: igitur illud ex quo ſeq̇tur
                    <lb/>
                  ſequela pꝫ. </s>
                  <s xml:id="N2B0AE" xml:space="preserve">Et ꝓbatur falſitas cõſequētis. </s>
                  <s xml:id="N2B0B1" xml:space="preserve">Et ſigno
                    <lb/>
                  vnū bipedale cuiꝰ vna medietas ſit calida vt .8. et
                    <lb/>
                  alia vt .4. </s>
                  <s xml:id="N2B0B8" xml:space="preserve">Et volo /  pars calida vt .8. perdat duos
                    <lb/>
                  gradus caliditatis: et illos acq̇rat pars calida vt
                    <lb/>
                  4. </s>
                  <s xml:id="N2B0BF" xml:space="preserve">Et cõtinuo cū pars intēſior remittit̄̄ cõdēſetur ꝑ­
                    <lb/>
                  dendo ̄titatē ad ſubduplū et eque velociter pars
                    <lb/>
                  remiſſior rarefiat acq̇rēdo quãtitatē: ita  illḋ cor­
                    <lb/>
                  pus ſꝑ maneat bipedale: quo poſito ſic argumen-
                    <lb/>
                  tor: iſtud corpus cõtinuo intēdet̄̄: et in fine manebit
                    <lb/>
                  vniforme ſub gradu medio puta vt .6. / igit̄̄ modo ē
                    <lb/>
                  remiſſius gradu medo. </s>
                  <s xml:id="N2B0CE" xml:space="preserve">Coña pꝫ et ꝓbatur maior: q2
                    <lb/>
                  cõtinuo ꝑ maiorē partē illis corporis fiet intēſio ̄
                    <lb/>
                  remiſſio eodē gradu: igit̄̄ cõtinuo illud corpus intē­
                    <lb/>
                  detur: ↄ̨ña probat̄̄ a ſimili / q2 ſi ꝑ maiorē partē ali-
                    <lb/>
                  cuius corporis eſſet albedo ꝙ̄ nigredo cõtinuo tale
                    <lb/>
                  corpus denominaret̄̄ albū: igit̄̄ aſimili ſi cõtinuo ꝑ
                    <lb/>
                  maiorē partē illius ſubiecti eſt intenſio ꝙ̄ remiſſio
                    <lb/>
                  eodē gradu: continuo illud corpus denominabitur
                    <lb/>
                  remitti. </s>
                  <s xml:id="N2B0E1" xml:space="preserve">añs ꝓbat̄̄ videlicet /  ꝑ maiorē partē conti­
                    <lb/>
                  nuo fiet intēſio ꝙ̄ remiſſio et eodē gradu: q2 ↄ̨tinuo
                    <lb/>
                  pars q̄ intendit̄̄ erit maior parte que remittit̄̄ ꝑ to­
                    <lb/>
                  tū: cū modo ſit equalis: et continuo rarefiat: et alia
                    <lb/>
                  cõdēſetur. </s>
                  <s xml:id="N2B0EC" xml:space="preserve">igr̄ cõtinuo ꝑ maiorē partem fiet intēſio
                    <lb/>
                  ̄ remiſſio eodē gradu: qḋ fuit ꝓbandū. </s>
                  <s xml:id="N2B0F1" xml:space="preserve">iam ꝓbat̄̄
                    <cb chead="Capitulum tertium"/>
                  minor videlicet /  in fine illud corpus manebit vni­
                    <lb/>
                  forme ſub gradu medio: quia manebit vniforme vt
                    <lb/>
                  ſex: q̇ ē medietas vt .8. perdet duos gradus: et me­
                    <lb/>
                  dietas vt .4. acq̇ret illos duos: igit̄̄ totū manebit vt
                    <lb/>
                  ſex: et gradus medius inter .8. et .4. cū equaliter di-
                    <lb/>
                  ſtet ab extremis: igit̄̄ illud corpus in fine manebit
                    <lb/>
                  vniforme ſub gradu medio.</s>
                </p>
                <p xml:id="N2B103">
                  <s xml:id="N2B104" xml:space="preserve">Quarto principaliter arguitur ſic. </s>
                  <s xml:id="N2B107" xml:space="preserve">ſi
                    <lb/>
                  intenſio q̈litatis vni difformis attendēda eſt penes
                    <lb/>
                  reductionē ad vniformitatē: ſeq̄retur /  etiam intē­
                    <lb/>
                  ſio corporis difformiter difformis attēdenda eſſet
                    <lb/>
                  penes reductionē ad vniformitatē: ſꝫ ↄ̨ñs eſt falſum /
                    <lb/>
                  igitur illud ex quo ſeq̄tur. </s>
                  <s xml:id="N2B114" xml:space="preserve">ſequela eſt nota: et ꝓbat̄̄
                    <lb/>
                  falſitas ↄ̨ñtis. </s>
                  <s xml:id="N2B119" xml:space="preserve">Et capio vnū corpus finitū cuiꝰ prīa
                    <lb/>
                  pars ꝓportionalis ſic calida vt .4. et .2. vt .3. et ſimi­
                    <lb/>
                  liter quelibet ſequens ſit calida vt .3. </s>
                  <s xml:id="N2B120" xml:space="preserve">Quo poſito
                    <lb/>
                  ſic argumētor. </s>
                  <s xml:id="N2B125" xml:space="preserve">Iſtud corpus eſt difformimter cali-
                    <lb/>
                  dū. </s>
                  <s xml:id="N2B12A" xml:space="preserve">Et tamen eius intēſio nõ debet attēdi penes re-
                    <lb/>
                  ductionē ad vniformitatē: igr̄ ꝓpoſitū. </s>
                  <s xml:id="N2B12F" xml:space="preserve">Minor pro­
                    <lb/>
                  batur: q2 tunc ſeq̄retur ip̄m eſſe infinite caliduꝫ. </s>
                  <s xml:id="N2B134" xml:space="preserve">Sꝫ
                    <lb/>
                  ↄ̨ñs eſt falſum vt cõſtat: igr̄ illḋ ex quo ſequit̄̄. </s>
                  <s xml:id="N2B139" xml:space="preserve">Pro­
                    <lb/>
                  batur ſequela: q2 ip̄m corpus poteſt reduci ad vni-
                    <lb/>
                  formē caliditateꝫ infinitã: igr̄ ſeq̇tur ip̄m eē infinite
                    <lb/>
                  calidū ꝓbatur añs: et pono /  vnꝰ gradus q̇ eſt in .2.
                    <lb/>
                  parte ꝓportionali extēdat̄̄ ꝑ totū et vnꝰ q̇ eſt in .3. ex­
                    <lb/>
                  tendat̄̄ etiã per totū, et ſic cõſequēter et hoc penetra­
                    <lb/>
                  tiue et vnitiue, quo poſito illa caliditas manet infi­
                    <lb/>
                  nita et vniformis / igit̄̄ illud corpus poteſt reduci ad
                    <lb/>
                  vniformē caliditatē infinitã / quod fuit probandum
                    <lb/>
                  </s>
                  <s xml:id="N2B14D" xml:space="preserve">¶ Dices forte ad argumentū cõcedēdo ſequelam et
                    <lb/>
                  negando falſitatē ↄ̨ñtis et ad punctū ꝓbatiõis ne-
                    <lb/>
                  go /  ſequeret̄̄ illud corpus eē infinite calidū. </s>
                  <s xml:id="N2B154" xml:space="preserve">Et ad
                    <lb/>
                  ꝓbationē diſtinguo añs videlicet /  tale corpus p̄t
                    <lb/>
                  reduci ad caliditatē infinitã aut debita reductione
                    <lb/>
                  et ſic nego, aut indebita et ſic cõcedo. </s>
                  <s xml:id="N2B15D" xml:space="preserve">vnde vt dicis
                    <lb/>
                  ad hoc /  aliqua qualitas debite reducatur ad vni­
                    <lb/>
                  formitatē oportet /  nulla fiat rarefactio aut ↄ̨dē-
                    <lb/>
                  ſatio in qnalitate q̄ reducitur etc̃. </s>
                  <s xml:id="N2B166" xml:space="preserve">Sꝫ in ꝓpoſito q̄lꝫ
                    <lb/>
                  caliditas exiſtens ī aliqua parte ꝓportionali alia
                    <lb/>
                  a prima rarefit ad ̄titatē totiꝰ corporis. </s>
                  <s xml:id="N2B16D" xml:space="preserve">Non igr̄
                    <lb/>
                  fit debita reductio.</s>
                </p>
                <p xml:id="N2B172">
                  <s xml:id="N2B173" xml:space="preserve">Sed cõtra quia tunc ſequeretur /  ſi
                    <lb/>
                  eſſet vnum corpus infinitū cuius primū pedale eſſet
                    <lb/>
                  calidū vt .4. et quodlibet aliud: corpus eſſet infinite
                    <lb/>
                  calidū. </s>
                  <s xml:id="N2B17C" xml:space="preserve">Sꝫ ↄ̨ñs eſt falſum (cū nõ ſit calidius corpo-
                    <lb/>
                  re calido vt .4. vniformiter ꝑ totū) / igr̄ illud ex quo
                    <lb/>
                  ſequitur. </s>
                  <s xml:id="N2B183" xml:space="preserve">Probatur ſequela / q2 fine rarefactiõe et
                    <lb/>
                  cõdēſatiõe põt illud corpus effici infinite calidū / igr̄
                    <lb/>
                  eſt infinite calidū probatur añs, et pono /  a quolꝫ
                    <lb/>
                  pedali ſequēte primū dematur vnus gradus et po-
                    <lb/>
                  natur in prīo et hoc ſiue aliqua rarefactione aut cõ­
                    <lb/>
                  dēſatione. </s>
                  <s xml:id="N2B190" xml:space="preserve">Et manifeſtum eſt /  in fine ī primo peda­
                    <lb/>
                  li ſunt īfiniti gradus caliditatis, et ꝑ ↄ̨ñs infinities
                    <lb/>
                  infiniti volo igr̄ /  capiantur infiniti ex illis et po-
                    <lb/>
                  nantur in .2. pedali: et iterū alii infiniti et ponãtur
                    <lb/>
                  in .3. </s>
                  <s xml:id="N2B19B" xml:space="preserve">Et ſic cõſequēter fine rarefactione et cõdēpſa-
                    <lb/>
                  tione. </s>
                  <s xml:id="N2B1A0" xml:space="preserve">quo poſito in fine totū illud corpus manebit
                    <lb/>
                  vniformiter infinite calidū: igitur iam modo eſt in­
                    <lb/>
                  finite calidū patet hec conſequētia / q2 per te eius in­
                    <lb/>
                  tenſio debet attendi penes reductionē ad vniformi­
                    <lb/>
                  tatē debite factam, quēadmodū ſit in propoſito.</s>
                </p>
                <p xml:id="N2B1AB">
                  <s xml:id="N2B1AC" xml:space="preserve">Quinto principaĺr arguitur ſic </s>
                  <s xml:id="N2B1AF" xml:space="preserve">Si
                    <lb/>
                  corporis difformis intenſio deberet cognoſci pe-
                    <lb/>
                  pes reductionem ad vniformitatē ſeq̄retur /  ſi vnū
                    <lb/>
                  pedale diuidatur ꝑ partes ꝓportionales ꝓportio­
                    <lb/>
                  ne quadrupla et prima ſit aliqualiter alba et .2. in </s>
                </p>
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