Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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              <div xml:id="N20F2E" level="4" n="1" type="chapter" type-free="capitulum">
                <p xml:id="N23C0C">
                  <s xml:id="N23C26" xml:space="preserve">
                    <pb chead="Tertii tractatus" file="0201" n="201"/>
                  immediate poſt hoc erit rarum: et continet infini-
                    <lb/>
                  tam materiam. </s>
                  <s xml:id="N23C32" xml:space="preserve">igitur immediate poſt hoc habe-
                    <lb/>
                  bit infinitam quantitatem. </s>
                  <s xml:id="N23C37" xml:space="preserve">Patet conſequentia
                    <lb/>
                  qnia ſi haberet finitam quantitatem et infinitam
                    <lb/>
                  materiam nullo pacto eſſet rarū / et per conſequens
                    <lb/>
                  ſubito efficietur īfinite quãtitatis / qḋ fuit ꝓbandū
                    <lb/>
                    <note position="left" xlink:href="note-0201-01a" xlink:label="note-0201-01" xml:id="N23C67" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N23C47" xml:space="preserve">¶ Ex hac concluſione ſequitur /  nullū finitum nec
                    <lb/>
                  etiam infinitū vniformiter denſum: ita  quelibet
                    <lb/>
                  pars eius ſit infinite denſa poteſt rarefieri ſine de-
                    <lb/>
                  perditione materie a ſe toto et a parte: ita  nulla
                    <lb/>
                  pars eiꝰ deperdat materiã. </s>
                  <s xml:id="N23C52" xml:space="preserve">Patet hoc correlariū
                    <lb/>
                  facile / q2 tunc quelibet pars eius manebit infinite
                    <lb/>
                  denſa ſicut antea: quia vt ponitur nulla eius pars
                    <lb/>
                  debet deꝑdere aliquã materiã, nec aliquis pūctus,
                    <lb/>
                  et ſic ad quēlibet punctū manebit infinita denſitas
                    <lb/>
                  et imagineris eodē modo in iſto correlario ſicut ſi
                    <lb/>
                  vnum vniforme infinite calidum rarefieret nullo
                    <lb/>
                  puncto eius aut parte perdente caliditatem.</s>
                </p>
                <note position="left" xml:id="N23C6D" xml:space="preserve">2. correĺ.</note>
                <p xml:id="N23C71">
                  <s xml:id="N23C72" xml:space="preserve">¶ Sequitur ſcḋo /  vnū vniformiter infinite denſuꝫ
                    <lb/>
                  per totū poteſt rarefieri: id eſt effici rarū. </s>
                  <s xml:id="N23C77" xml:space="preserve">Probat̄̄
                    <lb/>
                  et capio vnū infinitū infinite denſum vniformiter:
                    <lb/>
                  ita  ad quēlibet punctū eius ſit infinita materia.
                    <lb/>
                  </s>
                  <s xml:id="N23C7F" xml:space="preserve">et volo /  oēs gradus materie qui ſunt in ſcḋo peda­
                    <lb/>
                  li illius ponant̄̄ in primo pedali dempto vno et ſic
                    <lb/>
                  fiet de quolibet pedali ſequenti: ita  in quolibet
                    <lb/>
                  pedali ſequēte primū nõ maneat niſi vnus gradus
                    <lb/>
                  materie: quo poſito illud eſt rarū q2 nõ eſt niſi den-
                    <lb/>
                  ſum vt vnū: vt patebit ex dubio ſequenti / q2 infinita
                    <lb/>
                  denſitas in parte finita infiniti nullo modo deno-
                    <lb/>
                  minat infinitū. </s>
                  <s xml:id="N23C90" xml:space="preserve">Et hec etiã eſt opinio calculatoris.
                    <lb/>
                    <note position="left" xlink:href="note-0201-02a" xlink:label="note-0201-02" xml:id="N23CEF" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N23C9A" xml:space="preserve">¶ Ex quo ſequitur tertio /  nõ poſſunt dari duo eq̄
                    <lb/>
                  denſa quorum vnū poſſet rarefieri et nõ aliud.
                    <note position="left" xlink:href="note-0201-03a" xlink:label="note-0201-03" xml:id="N23CF5" xml:space="preserve">ↄ̈ calcuĺ.</note>
                  </s>
                  <s xml:id="N23CA4" xml:space="preserve">¶ Et
                    <lb/>
                  hoc correlariñ eſt cõtra calculatorē ponentē oppo-
                    <lb/>
                  ſitū in propria forma. </s>
                  <s xml:id="N23CAB" xml:space="preserve">Probat̄̄ tamen / q2 nõ eſt da-
                    <lb/>
                  bile aliquod corpꝰ finitū infinite denſum vniformi-
                    <lb/>
                  ter quī ipſum poſſet effici īfinite, et deinde poſſunt
                    <lb/>
                  a quolꝫ pedali eiꝰ dēpto primo oēs gradus materi
                    <lb/>
                  vno dēpto remoueri et poni in primo pedali / vt po-
                    <lb/>
                  nitur in p̄cedenti correlario: quo poſito iam ptꝫ / 
                    <lb/>
                  ſcḋm eundē calculatorē manebit dēſum vt vnū et ra­
                    <lb/>
                  rum nullū eſt / igitur denſum qm̄ poſſit effici rarū et
                    <lb/>
                  per ↄ̨ñs correlariū veꝝ. </s>
                  <s xml:id="N23CBE" xml:space="preserve">Sed tu dices /  dictū corre-
                    <lb/>
                  lariū nõ ſequit̄̄ niſi addicta calculatoris: et dices /
                    <lb/>
                   illa denſitas īfinita in primo pedali adhuc ſuffi­
                    <lb/>
                  cit infinite denoīare totū. </s>
                  <s xml:id="N23CC7" xml:space="preserve">Quapropter alio modo
                    <lb/>
                  ꝓbo tale corpus poſſe effici finite denſum vniforme /
                    <lb/>
                  et volo /  poſt̄ primū pedale habet infinitos gra­
                    <lb/>
                  dus materie, et quodlibet ſequens habet preciſe
                    <lb/>
                  vnū:  dimiſſis duobus in primo pedali in prima
                    <lb/>
                  parte ꝓportionali ponat̄̄ vnꝰ gradus de reſiduis
                    <lb/>
                  in ſecūdo pedali, et in ſcḋa parte ꝓportionali po-
                    <lb/>
                  natur vnus alter in tertio, et ſic cõſequēter: quo po­
                    <lb/>
                  ſito in fine hore quodlibet pedale habebit preciſe
                    <lb/>
                  duos gradus denſitatis et materie: et ſic totū illud
                    <lb/>
                  corpus erit vniformiter rarū per totū vt duo: igit̄̄
                    <lb/>
                  poteſt rarefieri / quod fuit probandū. </s>
                  <s xml:id="N23CE0" xml:space="preserve">Si tamen ve-
                    <lb/>
                  lis dicere /  quodlibet infinitū quãtitatiue, habēs
                    <lb/>
                  infinitam materiam eſſet infinite denſum oīa iſta
                    <lb/>
                  locū non haberent: ſed hoc non videtur rationabi­
                    <lb/>
                  liter dictum / vt in ſequenti dubio declarabitur.</s>
                </p>
                <note position="left" xml:id="N23CFB" xml:space="preserve">ſoluit̄̄ .9.
                  <lb/>
                dubium.</note>
                <p xml:id="N23D01">
                  <s xml:id="N23D02" xml:space="preserve">¶ Pro ſolutione none dubitationis pono duas
                    <lb/>
                  concluſiones.</s>
                </p>
                <p xml:id="N23D07">
                  <s xml:id="N23D08" xml:space="preserve">Prima ↄ̨̨cluſio </s>
                  <s xml:id="N23D0B" xml:space="preserve">Probabile eſt qḋlibet
                    <lb/>
                  habens infinitam materiam eſſe infinite denſum.
                    <lb/>
                  </s>
                  <s xml:id="N23D11" xml:space="preserve">Probatur / q2 quodlibet finitū habēs infinitã ma-
                    <lb/>
                  teriam eſt infinite denſum, et aliquod infinitū ha-
                    <lb/>
                  bens infinitã materiam eſt infinite denſum, et non
                    <lb/>
                  eſt maior ratio de vno habente infinitã materiam
                    <lb/>
                  ̄ de altero: igitur qnodlibet tam finitū ꝙ̄ infinitã
                    <cb chead="Capitulū primum."/>
                  habens infinitam materiam eſt infinite denſum.
                    <lb/>
                    <note position="right" xlink:href="note-0201-04a" xlink:label="note-0201-04" xml:id="N23D3F" xml:space="preserve">.1. correĺ</note>
                  </s>
                  <s xml:id="N23D26" xml:space="preserve">¶ Ex quo ſequitur /  ſi ſit vnū corpus infinitū cuiꝰ
                    <lb/>
                  quodlibet pedale habet vnū gradum materie pre-
                    <lb/>
                  ciſe: illud tale eſt infinite denſum.
                    <note position="right" xlink:href="note-0201-05a" xlink:label="note-0201-05" xml:id="N23D45" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N23D32" xml:space="preserve">¶ Sequitur ſcḋo /
                    <lb/>
                   ſi ſit vnū infinitum cuius primum pedale habet
                    <lb/>
                  infinitum de materia et totum reſiduū non denſum
                    <lb/>
                  ſed infinite rarum: illud tale eſt infinite denſum.</s>
                </p>
                <note position="right" xml:id="N23D4B" xml:space="preserve">.3. correĺ.</note>
                <p xml:id="N23D4F">
                  <s xml:id="N23D50" xml:space="preserve">¶ Sequitur tertio /  infinite denſum debet ſic de-
                    <lb/>
                  finiri: infinite denſum eſt quantum habens infini-
                    <lb/>
                  tum de materia. </s>
                  <s xml:id="N23D57" xml:space="preserve">Non enim proprie non quantum
                    <lb/>
                  eſt denſum: vt patet ex definitionibus rari et denſi.</s>
                </p>
                <p xml:id="N23D5C">
                  <s xml:id="N23D5D" xml:space="preserve">Secūda ↄ̨̨cluſio. </s>
                  <s xml:id="N23D60" xml:space="preserve">Probabilius eſt nõ
                    <lb/>
                  quodlibet habens infinitum de materia eſſe infi-
                    <lb/>
                  nite denſum. </s>
                  <s xml:id="N23D67" xml:space="preserve">Probatur / quia tunc ſequeretur /  a-
                    <lb/>
                  liquod infinitum eſſet infinite denſum, et a moto
                    <lb/>
                  vno pedali eius preciſe manebit infinite rarum.
                    <lb/>
                  </s>
                  <s xml:id="N23D6F" xml:space="preserve">Patet dato /  ſit vnum infinitum in cuius primo
                    <lb/>
                  pedali ſit infinitum de materia et in toto reſiduo
                    <lb/>
                  finite tantuꝫ: quo poſito a moto primo pedali iam
                    <lb/>
                  illud manebit infinite rarum, et modo eſt infinite
                    <lb/>
                  denſum per te: igitur propoſitum.</s>
                </p>
                <p xml:id="N23D7A">
                  <s xml:id="N23D7B" xml:space="preserve">Et confirmat̄̄. </s>
                  <s xml:id="N23D7E" xml:space="preserve">Q2 nõ qḋlibet habens
                    <lb/>
                  infinitam albedinem intenſiue eſt infinite album:
                    <lb/>
                  ergo non quodlibet habens infinitam materiam
                    <lb/>
                  eſt infinite denſum. </s>
                  <s xml:id="N23D87" xml:space="preserve">Conſequentia tenet a ſimili: et
                    <lb/>
                  antecedens patet / quia dato vno infinito cuiꝰ pri-
                    <lb/>
                  mum pedale ſit infinite album, et totum reſiduum
                    <lb/>
                  non ſit album vel finite album: illud tale nõ eſt in-
                    <lb/>
                  finite album: igitur aſſumptum verum.</s>
                </p>
                <note position="right" xml:id="N23D92" xml:space="preserve">.1. correĺ.
                  <lb/>
                q̇d īfinite
                  <lb/>
                denſum.</note>
                <p xml:id="N23D9A">
                  <s xml:id="N23D9B" xml:space="preserve">¶ Ex hac concluſione ſequit̄̄ primo /  infinite den-
                    <lb/>
                  ſum debet ſic definiri: vt prius dictum eſt. </s>
                  <s xml:id="N23DA0" xml:space="preserve">Infinite
                    <lb/>
                  denſum eſt illud / quod ſub finita quantitate habet
                    <lb/>
                  infinitã materiam, vel ſub infinita quantitate ha-
                    <lb/>
                  bet infinitam materiam per totum formaliter vel
                    <lb/>
                  reductiue. </s>
                  <s xml:id="N23DAB" xml:space="preserve">Et in tali reductiõe quelibet materia po­
                    <lb/>
                  natur in tanto ſubiecto in quanto erat antea ade-
                    <lb/>
                  quate ſicut ſit in reductione qualitatis.
                    <note position="right" xlink:href="note-0201-06a" xlink:label="note-0201-06" xml:id="N23E12" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N23DB7" xml:space="preserve">¶ Ex quo
                    <lb/>
                  ſequitur ſecūdo /  ſi alicuius corporis infiniti pri­
                    <lb/>
                  mum pedale habuerit vnum gradum materie et ſe-
                    <lb/>
                  cundum duplam ad illam et tertium quadruplam
                    <lb/>
                  et quartum octuplam, et quintum ſexdecuplam, et
                    <lb/>
                  ſic in īfinitum: tale corpus eſt infinite denſum quia
                    <lb/>
                  habet per totum infinitam materiam reductiue.
                    <lb/>
                  </s>
                  <s xml:id="N23DC7" xml:space="preserve">Utendo em̄ debita reductione illa materia mane-
                    <lb/>
                  bit per totuꝫ infinita.
                    <note position="right" xlink:href="note-0201-07a" xlink:label="note-0201-07" xml:id="N23E18" xml:space="preserve">.3. correĺ.</note>
                  </s>
                  <s xml:id="N23DD1" xml:space="preserve">¶ Sequitur tertio /  quãuis
                    <lb/>
                  vnum infinitum cuius primum pedale habet infi-
                    <lb/>
                  nitos gradus materie et quodlibet aliorum vnum
                    <lb/>
                  preciſe poſſet mediante eadem materia effici infi-
                    <lb/>
                  nite denſum per totum: nichilominus tamen quã-
                    <lb/>
                  do ſic primum pedale habet infinitos gradus ma­
                    <lb/>
                  terie et quodlibet aliorum vnum dumtaxat: illud
                    <lb/>
                  corpus eſt ſolum denſum vt vnum. </s>
                  <s xml:id="N23DE2" xml:space="preserve">Probatur pri-
                    <lb/>
                  ma pars / quia vbi ſunt infiniti gradus materie ibi
                    <lb/>
                  ſunt infinities infiniti / vt patet intelligenti mate-
                    <lb/>
                  riam de infinito. </s>
                  <s xml:id="N23DEB" xml:space="preserve">Ponantur igitur in ſecundo pe-
                    <lb/>
                  dali infiniti, et in tertio infiniti, et in quarto infi-
                    <lb/>
                  niti, et ſic conſequenter: et maneant in primo etiaꝫ
                    <lb/>
                  infiniti vt eſt ſatis poſſibile. </s>
                  <s xml:id="N23DF4" xml:space="preserve">et patet /  in fine illud
                    <lb/>
                  corpus erit infinite denſum per totum per illam
                    <lb/>
                  materiam quam habebat antea preciſe: et ſic pa-
                    <lb/>
                  tet prima pars correlarii. </s>
                  <s xml:id="N23DFD" xml:space="preserve">Secunda pars proba-
                    <lb/>
                  tur / quia ſecundum hanc opinionem denſitas infi-
                    <lb/>
                  nita exiſtens in parte finita corporis infiniti nihil
                    <lb/>
                  conducit nec aliquid confert ad denſitatem corpo­
                    <lb/>
                  ris infiniti: igitur non plus denominat denſitas
                    <lb/>
                  exiſtens in illo primo pedali quam ſi eſſet ſemota
                    <lb/>
                  ſed ſi illa eſſet ſemota manentibus aliis vt modo
                    <lb/>
                  ſunt: totum eſſet denſum preciſe vt vnum.</s>
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