Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N1C8AF" level="3" n="2" type="other" type-free="tractatus">
              <div xml:id="N1D065" level="4" n="2" type="chapter" type-free="capitulum">
                <p xml:id="N1D85C">
                  <s xml:id="N1D860" xml:space="preserve">
                    <pb chead="Secundi tractatus" file="0139" n="139"/>
                  miter difformis q̊ ad ſubiectū nõ d3 attendi penes
                    <lb/>
                  velocitatē pūcti exiſtētis in medio mobilis quãtū
                    <lb/>
                  ad lõgitudinē. </s>
                  <s xml:id="N1D86C" xml:space="preserve">Ptꝫ hec ↄ̨cluſio ex eodē argumēto.</s>
                </p>
                <p xml:id="N1D86F">
                  <s xml:id="N1D870" xml:space="preserve">Tertia concluſio </s>
                  <s xml:id="N1D873" xml:space="preserve">Uelocitas motꝰ vni­
                    <lb/>
                  formiter difformis quo ad ſubiectū cõmēſurari d3
                    <lb/>
                  penes gradū mediū totiꝰ latitudinis talis motus
                    <lb/>
                  vniformiter difformis vbicū fuerit talis gradus
                    <lb/>
                  ſiue in medio corꝑis ̄tū ad magnitudinē ſiue non
                    <lb/>
                  (non eſt cura) </s>
                  <s xml:id="N1D880" xml:space="preserve">Probat̄̄ hec cõcluſio / qm̄ ceteri modi
                    <lb/>
                  cognoſcēdi velocitatē motꝰ vniformiter difformis
                    <lb/>
                  quo ad ſubiectū ſuperioribꝰ argumētis īprobãtur
                    <lb/>
                  reſtat / igitur vt penes modum datum cognoſcatur</s>
                </p>
                <p xml:id="N1D889">
                  <s xml:id="N1D88A" xml:space="preserve">Quarta cõcluſio. </s>
                  <s xml:id="N1D88D" xml:space="preserve">Uelocitas motꝰ dif-
                    <lb/>
                  formiter difformis quo ad ſubiectum cognoſci põt
                    <lb/>
                  penes denoīationē partiū quantū ad longitudinē
                    <lb/>
                  </s>
                  <s xml:id="N1D895" xml:space="preserve">Intelligēdo ꝑ lõgitudinē diſtantiã a nõ gradu ta-
                    <lb/>
                  lis motꝰ vel a g̈du tardiſſimo ſus g̈dus velociores /
                    <lb/>
                  vt declaratū eſt in vltimo argumēto. </s>
                  <s xml:id="N1D89C" xml:space="preserve">Probat̄̄ hec
                    <lb/>
                  ↄ̨cluſio / q2 nõ occurrit alter modꝰ facilior ad cogno­
                    <lb/>
                  ſcendū huiuſmodi velocitatem per denominationē /
                    <lb/>
                  igr̄ tali modo īueſtiganda eſt motꝰ difformiter dif-
                    <lb/>
                  formis quo ad ſubiectū velocitas. </s>
                  <s xml:id="N1D8A7" xml:space="preserve">Nec replica fa-
                    <lb/>
                  cta de linea giratiua in vltīo argumēto huiꝰ capitꝪ
                    <lb/>
                  hãc ↄ̨cluſionē valet vllo pacto infirmare / vt patebit
                    <lb/>
                  ex ſolutione eiuſdem replice.</s>
                </p>
                <p xml:id="N1D8B0">
                  <s xml:id="N1D8B1" xml:space="preserve">Quinta concluſio. </s>
                  <s xml:id="N1D8B4" xml:space="preserve">Probabile eſt ve-
                    <lb/>
                  locitatē motꝰ difformis quo ad ſubiectū attēdi de-
                    <lb/>
                  bere penes gradū ſummū.
                    <note position="left" xlink:href="note-0139-01a" xlink:label="note-0139-01" xml:id="N1D8CB" xml:space="preserve">Opinio hentiſbe­
                      <lb/>
                    ri.</note>
                  </s>
                  <s xml:id="N1D8C0" xml:space="preserve">Ptꝫ / q2 ad illã opinionē
                    <lb/>
                  q̄ eſt hentiſberi nullū incõueniēs ſequit̄̄: īmo oīa ar­
                    <lb/>
                  gumēta q̄ in eū adducūiur facillime diſſoluūtur.</s>
                </p>
                <p xml:id="N1D8D3">
                  <s xml:id="N1D8D4" xml:space="preserve">Sexta cõcluſio. </s>
                  <s xml:id="N1D8D7" xml:space="preserve">Diſtantia punctorū
                    <lb/>
                  a cētro a q̊ ꝓcedit motꝰ difformis q̊ ad ſubiectū te-
                    <lb/>
                  net ſe ex ꝑte potētie: et auget ꝓportionē poñe ad re­
                    <lb/>
                  ſiſtentiã. </s>
                  <s xml:id="N1D8E0" xml:space="preserve">necnõ eidē potētie eſt adiumento. </s>
                  <s xml:id="N1D8E3" xml:space="preserve">et ꝑ op-
                    <lb/>
                  poſitū ꝓpinq̇tas. </s>
                  <s xml:id="N1D8E8" xml:space="preserve">nec magnitudo aut paruitans a-
                    <lb/>
                  liq̇d facit. </s>
                  <s xml:id="N1D8ED" xml:space="preserve">Probat̄̄ facile hec cõcluſio ex deductiõe
                    <lb/>
                  q̈rti argumēti huiꝰ capitis.
                    <note position="left" xlink:href="note-0139-02a" xlink:label="note-0139-02" xml:id="N1D91A" xml:space="preserve">correĺ.</note>
                  </s>
                  <s xml:id="N1D8F7" xml:space="preserve">¶ Ex q̊ ſequit̄̄ /  nõ ſtat
                    <lb/>
                  aliquã rotã q̄ mouet̄̄ a tute ſortis vt q̈tuor rare-
                    <lb/>
                  fieri et maiorari ꝑ ↄ̨tinuã elõgationē pūctoꝝ a cētro
                    <lb/>
                  et ipſã cõtinuo ab eadē ꝓportiõe moueri ceteris pa­
                    <lb/>
                  ribꝰ. </s>
                  <s xml:id="N1D902" xml:space="preserve">Ptꝫ correlariū hoc, q2 diſtãtia pūctoꝝ. </s>
                  <s xml:id="N1D905" xml:space="preserve">adau-
                    <lb/>
                  get ꝓportionē. </s>
                  <s xml:id="N1D90A" xml:space="preserve">Similiter dicendū eſt / ſi cõdenſaret̄̄
                    <lb/>
                  rota ſorte cõtinuo mouēte a tute vt q̈tuor. </s>
                  <s xml:id="N1D90F" xml:space="preserve">tunc em̄
                    <lb/>
                  totalis ꝓportio cõtinuo diminuit̄̄ ꝓpṫ deꝑditionē
                    <lb/>
                  diſtante punctorum a centro.</s>
                </p>
                <p xml:id="N1D920">
                  <s xml:id="N1D921" xml:space="preserve">Septima cõcluſio. </s>
                  <s xml:id="N1D924" xml:space="preserve">Propīquitas aut
                    <lb/>
                  diſtãtia pūctoꝝ a cētro nichil cõducit ceterꝪ paribꝰ
                    <lb/>
                  ad velocitatē circūgiratiõis ſiue circuitiõis / qḋ idē
                    <lb/>
                  eſt. </s>
                  <s xml:id="N1D92D" xml:space="preserve">Probat̄̄ / q2 eq̄ velociter oīa pūcta cõplēt circu-
                    <lb/>
                  los ſuos / vt ptꝫ ī rota in ſpera lune ſolis, et ſic ↄ̨ñter
                    <lb/>
                  ꝓcedēdo et eq̈les ãgulos faciūt circa centrū: igr̄ eq̄
                    <lb/>
                  velociter circueūt / et ꝑ ↄ̨ñs diſtãtia nichil ↄ̨fert
                    <note position="left" xlink:href="note-0139-03a" xlink:label="note-0139-03" xml:id="N1D9D4" xml:space="preserve">1. correĺ:</note>
                  </s>
                  <s xml:id="N1D93B" xml:space="preserve">¶ Ex
                    <lb/>
                  q̊ ſequit̄̄ /  nū̄ ↄ̨cēdendū eſt ab eq̈libꝰ ꝓportiõibꝰ
                    <lb/>
                  īeq̈les motꝰ circulares ꝓuenire, aut ab ineq̈libꝰ ꝓ-
                    <lb/>
                  portiõibꝰ eq̈les circuitiões / vt ſolutio q̈rti argumēti
                    <lb/>
                  oñdit.
                    <note position="left" xlink:href="note-0139-04a" xlink:label="note-0139-04" xml:id="N1D9DA" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N1D94B" xml:space="preserve">¶ Sequit̄̄ ex hac ſolutiõe ſcḋo /  ſi in eodem
                    <lb/>
                  axe ponant̄̄ īfinite rote ↄ̨tinuo mīores et mīores ita
                    <lb/>
                   diametri prime ſit dupla ad diametrū ſecūde, et
                    <lb/>
                  ſcḋe ad diametrū tertie, et ſic ↄ̨ñter: et ſortes moue-
                    <lb/>
                  at oēs illas rotas mediãte illo axe: in īfinitū tarde
                    <lb/>
                  mouet̄̄ ibi aliqua rota: nichilominꝰ tñ q̄libet rota
                    <lb/>
                  ita velociter circuit ſicut prima. </s>
                  <s xml:id="N1D95A" xml:space="preserve">Patꝫ prima pars /
                    <lb/>
                  q2 īfinite modicū circulū deſcribit aliqua illaꝝ ro-
                    <lb/>
                  tarū in eodē tꝑe: igr̄. </s>
                  <s xml:id="N1D961" xml:space="preserve">Scḋa pars ꝓbat̄̄ / q2 eque cito
                    <lb/>
                  q̄libet circuitionē ſuã ſicut prima cõplet: igr̄ q̄libet
                    <lb/>
                  eque velociter circuit ſicut prima. </s>
                  <s xml:id="N1D968" xml:space="preserve">Ite ↄ̨tinuo cuiuſli­
                    <cb chead="Capitulū ſecundū."/>
                  bet illaꝝ ãguīus deſcriptꝰ circa cētrū eſt eq̈lis ãgu-
                    <lb/>
                  lo deſcripto a ṗma rota: igr̄ quelibet illaꝝ cõtinuo
                    <lb/>
                  equaliter circuit cū prima </s>
                  <s xml:id="N1D972" xml:space="preserve">Ex quo facile apparet 
                    <lb/>
                  magnitudo ſiue diſtãtia pūctoꝝ nihil facit ad velo­
                    <lb/>
                  citatē circuitiõis: ſed bene ad velocitatē motꝰ circu-
                    <lb/>
                  laris.
                    <note position="right" xlink:href="note-0139-05a" xlink:label="note-0139-05" xml:id="N1D9E0" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N1D980" xml:space="preserve">¶ Sequit̄̄ vlteriꝰ /  in caſu p̄dicto nõ ab eadē
                    <lb/>
                  proportiõe adequate ſortes mouet primam rotã et
                    <lb/>
                  ſcḋam: ſed a maiori primã quã ſcḋam. </s>
                  <s xml:id="N1D987" xml:space="preserve">q2 diſtantia
                    <lb/>
                  pūctoꝝ medioꝝ eſt adiumēto potētie ſortis. </s>
                  <s xml:id="N1D98C" xml:space="preserve">¶ Hic
                    <lb/>
                  tñ tu aduerte  nõ volo dicere / quãlibet illaꝝ rotaꝝ
                    <lb/>
                  moueri adeq̈te a certa ꝓportiõe: ſed bene q̄libet il-
                    <lb/>
                  larū mouet̄̄ a certa ꝓportiõe inadequate. </s>
                  <s xml:id="N1D995" xml:space="preserve">Nec volo
                    <lb/>
                  dicere / ̄libet illaꝝ circūgirare ſiue ꝓpriã circuitio­
                    <lb/>
                  nē efficere a certa ꝓportiõe adeq̊te: ſed bene īadeq̈-
                    <lb/>
                  te. </s>
                  <s xml:id="N1D99E" xml:space="preserve">Qḋ ideo dixerim / qm̄ ſi cõcedat̄̄ ſortē potētie vt
                    <lb/>
                  4. circūgirare rotã in octuplo minorē prima a cer­
                    <lb/>
                  ta ꝓportiõe adequate cū oporteat talē ꝓportionē
                    <lb/>
                  eſſe maiorē ꝓportiõe a qua ſortes circūducit primã
                    <lb/>
                  rotã (cū maior rota magis reſiſtit ſue circūgiratiõi
                    <lb/>
                  quã mīor) / tã ſeq̄ret̄̄ /  ab īeq̈libꝰ ꝓportiõibꝰ equa-
                    <lb/>
                  les circuitiões ꝓuenirēt qḋ vitare intēdit ſeptīa cõ­
                    <lb/>
                  cluſio. </s>
                  <s xml:id="N1D9AF" xml:space="preserve">Et ideo in ꝓpoſito ymaginandū eſt de illis
                    <lb/>
                  rotis ſicut de īfinitis rotis partialibꝰ cõcētricis ro­
                    <lb/>
                  te alicui cuiꝰ ſūt partes. </s>
                  <s xml:id="N1D9B6" xml:space="preserve">Manifeſtū eſt em̄ /  q̄libet
                    <lb/>
                  illaꝝ rotaꝝ eque velociter circuit cū qualꝫ aliarū: et
                    <lb/>
                  cuiuſlꝫ illaꝝ circuitio ꝓuēit ab eadē ꝓportiõe inade­
                    <lb/>
                  quate ſiue partialiter qm̄ ꝓuenit ab eadē ꝓportiõe
                    <lb/>
                  a qua circuitio totalis rote efficit̄̄ ſicut em̄ dicere-
                    <lb/>
                  mus ſortē potētie / vt .4. mouentē põdus reſiſtentie
                    <lb/>
                  vt .2. velocitate vt .4. mouere quãlibet partē illiꝰ põ­
                    <lb/>
                  deris velocitate vt q̈tuor et a ꝓportione dupla: ſed
                    <lb/>
                  hoc īadequate. </s>
                  <s xml:id="N1D9C9" xml:space="preserve">¶ Ad īducēdã octauã ↄ̨cluſionē ſolu­
                    <lb/>
                  tiuam quinti argumenti preſentis queſtiõis pono
                    <lb/>
                  aliquas ſuppoſitiones geometricas.</s>
                </p>
                <p xml:id="N1D9E6">
                  <s xml:id="N1D9E7" xml:space="preserve">Prima ſuppoſitio </s>
                  <s xml:id="N1D9EA" xml:space="preserve">Si ſūt due quãtita­
                    <lb/>
                  tes equalis ꝓfunditatis vniformiter, et eq̄ late vni-
                    <lb/>
                  formiter, et vna lõgior allera in q̈cū ꝓportiõe eſt
                    <lb/>
                  lõgior in eadē eſt maior. </s>
                  <s xml:id="N1D9F3" xml:space="preserve">Exēplū / vt ſi ſit vnū pedale
                    <lb/>
                  pedaliter latū, et pedaliter ꝓfundū, et ſit alia quã-
                    <lb/>
                  titas eq̄ ꝓfunda et eq̄ lata vniformiter, et in duplo
                    <lb/>
                  longior: manifeſtū eſt /  illa eſt in duplo maior q2
                    <lb/>
                  cõtinet duo pedalia. </s>
                  <s xml:id="N1D9FE" xml:space="preserve">Probat̄̄ hec ſuppoſitio facile /
                    <lb/>
                  qm̄ cū tales latitudines ſint vniformes in latitudī­
                    <lb/>
                  ne et ꝓfūditate illud qḋ maior plꝰ cõtinet ē eque la-
                    <lb/>
                  tū et eque ꝓfundū vniformiter ſicut mīor: ergo alia
                    <lb/>
                  quãtitas maior cõtinet totã minorē et illud vltra: et
                    <lb/>
                  illḋ ē eq̄ magnū adeq̈te ſicut tã lõga ꝑs mīoris quã­
                    <lb/>
                  tatis: igr̄ in q̈cū ꝓportiõe lõgitudo maioris ex­
                    <lb/>
                  cedit longitudinem minoris in eadeꝫ proportione
                    <lb/>
                  magnitudo maioris excedit magnitudinis mīoris</s>
                </p>
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                  <s xml:id="N1DA12" xml:space="preserve">Secūda ſuppoſitio </s>
                  <s xml:id="N1DA15" xml:space="preserve">Si due quantita­
                    <lb/>
                  tes ineq̈les ſint eq̄ profunde vniformiter et eq̄ longe
                    <lb/>
                  vniformiter et vna latior altera: in q̈cū ꝓportiõe
                    <lb/>
                  vna eſt latior in eadē eſt maior. </s>
                  <s xml:id="N1DA1E" xml:space="preserve">Exēplū / vt ſi ſit vna
                    <lb/>
                  quãtitas bipedalis ſcḋm lõgitudinē pedalis ſcḋ3 la­
                    <lb/>
                  titudinē et ꝓfūditatē vniformiter et alia vniformiṫ
                    <lb/>
                  eque lõga et eq̄ ꝓfunda et ī ſexquialtero latior: erit
                    <lb/>
                  ī ſexquialtero maior. </s>
                  <s xml:id="N1DA29" xml:space="preserve">Ptꝫ hec ſuppoſitio ſicut ṗor.</s>
                </p>
                <p xml:id="N1DA2C">
                  <s xml:id="N1DA2D" xml:space="preserve">Tertia ſuppoſitio </s>
                  <s xml:id="N1DA30" xml:space="preserve">Si ſint due quan-
                    <lb/>
                  titates eq̄ longe eque late vniformiter: et vna ſit in
                    <lb/>
                  aliq̈ ꝓqortione ꝓfundior altera: in eadē ꝓportione
                    <lb/>
                  in q̈ eſt ꝓfundior ē maior. </s>
                  <s xml:id="N1DA39" xml:space="preserve">Exemplū / vt ſi ſit vna ma-
                    <lb/>
                  gnitudo bipedaliter lõga pedaliter lata et pedali-
                    <lb/>
                  ter ꝓfunda et vna alia bipedaliter lõga et pedaliter
                    <lb/>
                  lata et ſemipedaliter profunda / tūc dico /  alia quã­
                    <lb/>
                  titas maior in ea ꝓportione in q̈ eſt ꝓfundior ī ea ē
                    <lb/>
                  maior puta in dupla. </s>
                  <s xml:id="N1DA46" xml:space="preserve">Patet etiam hec ſicut prima
                    <lb/>
                  </s>
                  <s xml:id="N1DA4A" xml:space="preserve">His ſuppoſitionibus premiſſis ſit hec.</s>
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