Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N20F21" level="3" n="3" type="other" type-free="tractatus">
              <div xml:id="N20F2E" level="4" n="1" type="chapter" type-free="capitulum">
                <p xml:id="N22470">
                  <s xml:id="N22474" xml:space="preserve">
                    <pb chead="Tertii tractatus" file="0187" n="187"/>
                  tis quantitatis ad materiã eſſet rarū: et bipedale
                    <lb/>
                  in cuiꝰ vna medietate eſſet ꝓportio dupla quãtita-
                    <lb/>
                  tis ad materiã et in alia eſſet ꝓportio dupla mate-
                    <lb/>
                  rie ad quantitatē eſſet denſum et nõ rarū et bipeda­
                    <lb/>
                  le in cuiꝰ vna medietate eſſet ꝓportio dupla quan-
                    <lb/>
                  titatis ad materiã: et in alia eſſe ꝓportio ſexq̇al-
                    <lb/>
                  ra materie ad quantitatē nec eſſet rarū nec denſuꝫ /
                    <lb/>
                  ſed cõſequēs videtur falſum: igr̄ illud ex quo ſequit̄̄
                    <lb/>
                  </s>
                  <s xml:id="N2248F" xml:space="preserve">Seq̄la ꝓbatur / qm̄ ſi in vna medietate bipedalis eſt
                    <lb/>
                  ꝓportio dupla quantitatis ad materiaꝫ: et in alia
                    <lb/>
                  ꝓportio equalitatis cū vtra medietas bipedalis
                    <lb/>
                  ex dictis habeat quatuor gradus quantitatis: ſe-
                    <lb/>
                  quitur /  vna medietas illiꝰ bipedalis hꝫ duos g̈dꝰ
                    <lb/>
                  materie, et altera .4. / et ꝑ ↄ̨ñs totum illud bipedale
                    <lb/>
                  hꝫ ſex gradus materie et hꝫ .8. quãtitatis: g̊ in eo eſt
                    <lb/>
                  ꝓportio maioris inequalitatis quãtitatis ad ma-
                    <lb/>
                  teriã / et ꝑ ↄ̨ñs ipſū eſt rarū / et ſic ptꝫ prima pars illa­
                    <lb/>
                  ti. </s>
                  <s xml:id="N224A4" xml:space="preserve">Secūda pars ꝓbatur / qm̄ ſi vna medietas bipe-
                    <lb/>
                  dalis ita ſe hꝫ  in ea eſt ꝓportio dupla quautita-
                    <lb/>
                  tis ad materiã, et in reliqua materie ad quantitatē
                    <lb/>
                  et vtra medietas bipedalis hꝫ q̈tuor gradꝰ quãti­
                    <lb/>
                  tatis / ſequit̄̄ /  vna medietas illiꝰ bipedalis habet
                    <lb/>
                  duos gradus materie et reliqua hꝫ octo: et ꝑ conſe-
                    <lb/>
                  quens materia illiꝰ bipedalis eſt vt decē, et quanti-
                    <lb/>
                  tas eſt vt octo: igr̄ in hoc bipedali eſt ꝓportio ma-
                    <lb/>
                  ioris inequalitatis materie ad quantitatē hoc igr̄
                    <lb/>
                  fidē facit illud bipedale denſum eſſe. </s>
                  <s xml:id="N224B9" xml:space="preserve">Et ꝑ hoc etiaꝫ
                    <lb/>
                  ptꝫ tertia pars: qm̄ in tali bipedali (ſi bene calcula­
                    <lb/>
                  ueris) reperies octo gradus materie gradibꝰ quã-
                    <lb/>
                  titatꝪ equari. </s>
                  <s xml:id="N224C2" xml:space="preserve">Quare illud bipedale nec rarum nec
                    <lb/>
                  denſum erit / quod fuit ꝓbãdū. </s>
                  <s xml:id="N224C7" xml:space="preserve">Sed iã ꝓbo falſita­
                    <lb/>
                  tem cõſequentis: qm̄ illud bipedale in cuiꝰ vna me-
                    <lb/>
                  dietate eſt dupla ꝓportio quantitatis ad materiã
                    <lb/>
                  et in alia eſt dupla ꝓportio materie ad quantitatē
                    <lb/>
                  hꝫ vnã medietatē rarã vt duo: et aliū denſaꝫ vt duo
                    <lb/>
                  volo em̄ /  ꝓportio dupla nata ſit ꝓducere rarita­
                    <lb/>
                  tem vt duo, et etiã denſitatē vt duo </s>
                  <s xml:id="N224D6" xml:space="preserve">Nec valet hoc ne­
                    <lb/>
                  gari: q2 aliqua ꝓportio nata eſt ꝓducere raritateꝫ
                    <lb/>
                  vt duo: et aliqua denſitatē vt duo: ponãtur igr̄ ille
                    <lb/>
                  ꝓportiones in illis medietatibꝰ et ſic ſemꝑ ꝓcedit
                    <lb/>
                  argumentū: igr̄ illud bipedale nec eſt rarū, nec dē-
                    <lb/>
                  ſum. </s>
                  <s xml:id="N224E3" xml:space="preserve">Ptꝫ hec cõſequētia a ſimili: qm̄ ſi vniꝰ bipeda­
                    <lb/>
                  lis vna medietas eſſet calida vt duo et altera frigi-
                    <lb/>
                  da vt duo: illud nec eſſet calidum nec frigidum. </s>
                  <s xml:id="N224EA" xml:space="preserve">Et
                    <lb/>
                  ſic facile eſt inferre oppoſitum aliarum partium.</s>
                </p>
                <p xml:id="N224EF">
                  <s xml:id="N224F0" xml:space="preserve">Tertio ad idē argr̄. </s>
                  <s xml:id="N224F3" xml:space="preserve">Si hec opinio eēt
                    <lb/>
                  vera ſeq̄retur /  rarum difformiter difforme cuius
                    <lb/>
                  vtra medietas eſſet vniformis nõ correſponderet
                    <lb/>
                  ſuo gradui medio: ſed cõſequēs eſt falſum: igr̄ illud
                    <lb/>
                  ex quo ſequitur. </s>
                  <s xml:id="N224FE" xml:space="preserve">Falſitas cõſequētis oſtenditur: q2
                    <lb/>
                  oē qualificatū vniformiter difforme correſpondet
                    <lb/>
                  ſuo gradui medio: et etiã difformiter difforme cuiꝰ
                    <lb/>
                  vtra medietas eſt vniformis: igr̄ a ſimili ita d3
                    <lb/>
                  eſſe ꝓpoſito. </s>
                  <s xml:id="N22509" xml:space="preserve">Seq̄la ꝓbatur. </s>
                  <s xml:id="N2250C" xml:space="preserve">et capio vnū bipedale
                    <lb/>
                  in cuiꝰ vna medietate ſit ꝓportio dupla quãtitatis
                    <lb/>
                  ad materiã, et in alia medietate ſit ꝓportio quadru­
                    <lb/>
                  pla, et volo /  ꝓportioni dupla correſpondeãt duo
                    <lb/>
                  gradus raritatis, et ex hoc quadruple quatuor: ita
                    <lb/>
                   vna medietas ſit rara vt duo, et alia vt quatuor
                    <lb/>
                  </s>
                  <s xml:id="N2251A" xml:space="preserve">Quo poſito ſic argumentor: illud bipedale eſt dif-
                    <lb/>
                  formiter difforme cuiꝰ vtra medietas eſt vnifor-
                    <lb/>
                  mis, et eiꝰ raritas nõ correſpondet ſuo gradui me-
                    <lb/>
                  dio: igr̄ ꝓpoſitū. </s>
                  <s xml:id="N22523" xml:space="preserve">Argr̄ minor / qm̄ ſi eiꝰ raritas cor-
                    <lb/>
                  reſponderet ſuo gradui medio: ipſa eſſet vt tria vt
                    <lb/>
                  ſatis ptꝫ, nã gradus vt tria eſt medius inter q̈tuor
                    <lb/>
                  et duo: ſed hoc eſt falſum: igr̄. </s>
                  <s xml:id="N2252C" xml:space="preserve">Cuiꝰ cõſequētis falſi-
                    <lb/>
                  tas oſtenditur qm̄ raritas vt tria q̄ eſt ſexquialtera
                    <lb/>
                  ad raritatē vt duo correſpondet ꝓportioni ſexq̇al­
                    <lb/>
                  tere ad ꝓportionē duplã que ꝓportio ſexquialtera
                    <cb chead="Capitulū primū."/>
                  vcꝫ ad duplã eſt ꝓportio irrationalis / vt ptꝫ ex ſecū­
                    <lb/>
                  da parte huiꝰ operis: ſed quãtitatis illiꝰ bipedalis
                    <lb/>
                  ad ſuã materiã nõ eſt ꝓportio irrationalis que eſt
                    <lb/>
                  ſexquialtera ad duplã: g̊ ſequitur /  raritas illius
                    <lb/>
                  bipedalis nõ eſt vt tria. </s>
                  <s xml:id="N22540" xml:space="preserve">Ptꝫ hoc cõſequentia / qm̄ ra­
                    <lb/>
                  ritas vt tria non eſt nata ꝓuenire niſi a ꝓportione
                    <lb/>
                  ſexquialtera ad duplã. </s>
                  <s xml:id="N22547" xml:space="preserve">Secundū / em̄ hanc opinio-
                    <lb/>
                  nē in quacū ꝓportione ſe habent raritates ad in­
                    <lb/>
                  uicē in eadē ꝓportione ſe habent ꝓportiones a qui­
                    <lb/>
                  bus ꝓueniūt. </s>
                  <s xml:id="N22550" xml:space="preserve">Sed iam ꝓbo /  quantitatis illiꝰ bi-
                    <lb/>
                  pedalis ad ſuã materiã nõ ſit ꝓportio irratiõalis
                    <lb/>
                  que ſit ſexquialtera ad duplã: qm̄ materia vniꝰ me­
                    <lb/>
                  dietatis eſt duoꝝ graduū puta illiꝰ in qua eſt ꝓpor­
                    <lb/>
                  tio dupla quantitatis ad materiã: et materia alte-
                    <lb/>
                  rius medietatis eſt vniꝰ gradus, et ſic tota materia
                    <lb/>
                  eſt vt tria quantitas vero vt octo, qm̄ vna quarta
                    <lb/>
                  pedalis eſt vnꝰ gradus quantitatis vt predictū eſt
                    <lb/>
                  modo .8. ad .3. eſt ꝓportio dupla ſuꝑbipartiens ter­
                    <lb/>
                  tias q̄ eſt minor ꝙ̄ ſexquialtera ad duplã. </s>
                  <s xml:id="N22565" xml:space="preserve">Cõtinet
                    <lb/>
                  em̄ duplã et ſexquitertiã adequate ſupra duplam et
                    <lb/>
                  ſexquitertia eſt minor ꝙ̄ medietas duple vt patꝫ ex
                    <lb/>
                  ſecūda parte huius operis: g̊ cõtinet duplã, et minꝰ
                    <lb/>
                  ̄ medietatē duple adequate: , ꝑ cõſequēs eſt mīor
                    <lb/>
                  ̄ ſexquialtera ad duplã. </s>
                  <s xml:id="N22572" xml:space="preserve">Itē ſexquialtera ad du-
                    <lb/>
                  plam eſt irrationalis / vt dictū eſt iſta vero: eſt rati-
                    <lb/>
                  onalis: g̊ nõ eſt ſexquialtera ad duplã / quod fuit ꝓ-
                    <lb/>
                  banduꝫ. </s>
                  <s xml:id="N2257B" xml:space="preserve">Nec valet dicere /  non oportet ſic ſignare
                    <lb/>
                  gradus quantitatis aut materiae q2 quocū modo
                    <lb/>
                  ſignētur ſemꝑ erit ꝓportio rationalis quãtitatis
                    <lb/>
                  ad materiã in tali caſu et iſta raritas vt tria non eſt
                    <lb/>
                  nata ꝓuenire ꝓportione aliqua rationali: eſto 
                    <lb/>
                  raritas vt duo nata ſit produci a ꝓportiõe dupla.</s>
                </p>
                <p xml:id="N22588">
                  <s xml:id="N22589" xml:space="preserve"> Quarto argr̄ ſic. </s>
                  <s xml:id="N2258C" xml:space="preserve">Si iſta opinio eſſet
                    <lb/>
                  vera ſeq̄retur /  nõ poſſet dari cui g̈dus correſpõ-
                    <lb/>
                  deat raritas vniꝰ pedalis ſic ſe habentis  prima
                    <lb/>
                  pars ꝓportionalis eiꝰ ſit aliq̈liter rara et ſcḋa in
                    <lb/>
                  duplo, tertia in triplo, quarta in quadruplo ꝙ̄ pri­
                    <lb/>
                  ma, et ſic cõſequenter: ſed conſequēs eſt falſum: igr̄.
                    <lb/>
                  </s>
                  <s xml:id="N2259A" xml:space="preserve">Itē ſeq̄retur /  nõ poſſet dari cui correſpõderet ra-
                    <lb/>
                  ritas pedalis cuiꝰ prima pars ꝓportionalis ꝓpor­
                    <lb/>
                  tiõe dupla eſſet aliqualiter rara, ſecūda in duplo,
                    <lb/>
                  tertia in quadruplo ꝙ̄ prima et quarta, in octuplo
                    <lb/>
                  et quīta in ſexdecuplo: et ſic couſequenter : proceden­
                    <lb/>
                  do per numeros pariter parer: ſed hoc videtur ab-
                    <lb/>
                  ſurdum: igr̄. </s>
                  <s xml:id="N225A9" xml:space="preserve">Seq̄la ptꝫ / qm̄ ad īueniendū in ſimili-
                    <lb/>
                  bus caſibꝰ raritatē adequatã taliū corpoꝝ oportet
                    <lb/>
                  ad īuenire materiã totalē totiꝰ corporis, et tūc vide­
                    <lb/>
                  re in qua ꝓportione ſe hꝫ quantitas illiꝰ corporis
                    <lb/>
                  ad illã materiã: et ex hoc raritatē talis corporis di­
                    <lb/>
                  iudicare: ſed nõ eſt modus īueniēdi in talibꝰ et ſimi-
                    <lb/>
                  libus caſibꝰ materiã totius corporis: etiã ad inuen­
                    <lb/>
                  ta et ſcita materia prime partis ꝓportionalis: igr̄
                    <lb/>
                  nõ põt ſciri totalis raritas illoꝝ corpoꝝ ſic diffor-
                    <lb/>
                  miū in raritate. </s>
                  <s xml:id="N225BE" xml:space="preserve">Sꝫ iam ꝓbo /  nõ põt materia illiꝰ
                    <lb/>
                  corporis īueſtigari, qm̄ cõtinue materia partis ꝓ-
                    <lb/>
                  portionalis ſequentis eſt minor materia partis ī-
                    <lb/>
                  mediate p̄cedentis. </s>
                  <s xml:id="N225C7" xml:space="preserve">Et in nulla certa ꝓportione cõ-
                    <lb/>
                  tinuo minor: ſed cõtinuo in alia et in alia: et ſunt iſte
                    <lb/>
                  materie partiales infinite: igr̄ nõ apparet modus
                    <lb/>
                  quo totalis materia menſuretur: igitur.</s>
                </p>
                <p xml:id="N225D0">
                  <s xml:id="N225D1" xml:space="preserve">Quīto argr̄. </s>
                  <s xml:id="N225D4" xml:space="preserve">Si iſta optnio eſſet vera
                    <lb/>
                  ſeq̄retur /  raritas diceretur poſitue eodeꝫ modo
                    <lb/>
                  quo denſitas cū nõ ſit maior ratio de raritate ꝙ̄ de
                    <lb/>
                  denſitate: ſed cõſequēs eſt falſum: igr̄ illud ex quo
                    <lb/>
                  ſequitur. </s>
                  <s xml:id="N225DF" xml:space="preserve">Falſitas cõſequētis oſtenditur / qm̄ ſi ra-
                    <lb/>
                  ritas diceretur poſitiue ſequeret̄̄ /  poſſet dari vnū
                    <lb/>
                  finitū īfinite rarū: ſed cõſequēs eſt falſum: igr̄ illud
                    <lb/>
                  ex quo ſequitur. </s>
                  <s xml:id="N225E8" xml:space="preserve">Falſitas huiꝰ cõſequentis oſtendit̄̄ </s>
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