Alvarus, Thomas, Liber de triplici motu, 1509

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                  <s xml:id="N20146" xml:space="preserve">
                    <pb chead="De motu locali quo ad effectum tempore difformi." file="0166" n="166"/>
                  ſpecies proportionis ſuperparticularis: ſpaciū ꝑ-
                    <lb/>
                  tranſitum in totali tempore eſt maius quã duplum
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                  ad ſpacium pertranſitum in prima parte ꝓportio­
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                  nali, et minus ꝙ̄ quadruplum. </s>
                  <s xml:id="N20160" xml:space="preserve">Probatur prīa ꝑs /
                    <lb/>
                  quia diuiſa ſic hora per partes proportionales ꝓ-
                    <lb/>
                  portione dupla: et mobili moto continuo vniformi­
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                  ter illo motu quo mouetur in prima parte ꝓportio­
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                  nali ſpaciū pertrãſitū adequate in tota hora eſſet
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                  adequate duplum ad ſpacium pertranſitum in pri­
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                  ma parte proportionali / vt patet ex ſe: ſed mõ mo-
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                  bile velocius mouetur quam tunc in qualibet ꝑ­
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                  te proportionali dempta prima modo velociꝰ mo-
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                  uetur quã tunc / et in prima eque velociter ſicut tunc:
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                  igitur pertranſit pluſ̄ duplum ſpaciuꝫ ad ſpaciū
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                  pertranſitum in prima parte proportionali. </s>
                  <s xml:id="N20179" xml:space="preserve">Pro­
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                  batur ſecunda pars: quia ſi illud mobile mouetur ī
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                  prima parte proportionali aliquantum velociter:
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                  et in ſecunda in duplo: et in tertia in triplo velocius
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                  quã in prima: et ſic conſequenter vt ponitur in caſu
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                  quarte concluſionis: tunc adequate pertranſiret q̈­
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                  druplum ſpacium ad ſpacium pertranſitum in pri­
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                  ma parte ꝓportionali: vt patet ex quarta concluſio­
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                  ne: ſed modo mouetur in totali hora tardius quam
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                  tunc ꝑ omnes partes proportionales dempta pri-
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                  ma et ſecunda. / et in prima et ſecunda equaliter ſicut
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                  tunc: igitur modo pertranſit minus ſpacium quam
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                  tunc in totali hora: et tunc quadruplum pertranſit
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                  ad ſpacium pertranſitum in prima parte ꝓportio­
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                  nali: igitur modo minus quam quadruplū / qḋ fuit
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                  ꝓbandum. </s>
                  <s xml:id="N2019A" xml:space="preserve">Et ſic patet concluſio.
                    <note position="left" xlink:href="note-0166-01a" xlink:label="note-0166-01" xml:id="N201E6" xml:space="preserve">.1. correl.</note>
                  </s>
                  <s xml:id="N201A2" xml:space="preserve">¶ Ex cuius ꝓba-
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                  tione ſequitur primo /  ſi fuerit tempus diuiſum ꝑ
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                  partes ꝓportionales proportione ſexquialtera: et
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                  mobile moueatur eodem modo quo dictum eſt ī ca-
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                  ſu concluſionis: ſpacium pertranſitum in totali ho­
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                  ra erit maius quã triplum ad ſpacium pertranſitū
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                  in prima parte ꝓportionali: et minus quã non ocu-
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                  plum. </s>
                  <s xml:id="N201B3" xml:space="preserve">Probatur prima pars / quia ſi mobile moue­
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                  retur vniformiter per totam horam illa velocitate
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                  qua mouetur in prima parte ꝓportionali adequa-
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                  te: tunc ſpacium pertranſitū in totali hora eſſet tri­
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                  plum ad ſpacium pertranſitum in prima parte pro­
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                  portionali quia tota hora ē tripla ad primã ꝑtē ꝓ-
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                  portionalem ꝓportione ſexquialtera: ſed modo in
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                  totali hora mouetur intenſius quã tunc / vt patet: er­
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                  go ſequitur /  modo pertranſibit maius ſpacium
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                  quã tunc: et tunc pertranſit triplum ſpacium ad ſpa­
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                  cium pertranſitum in prima parte ꝓportionali: er­
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                  go modo maius quã triplum: quod fuit ꝓbandum.
                    <lb/>
                  </s>
                  <s xml:id="N201CD" xml:space="preserve">Probatur ſecunda pars / quia ſi mobile moueretur
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                  eodem modo quo ponitur in caſu quarte cõcluſiõis
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                  diuiſa ſic hora per partes ꝓportionales ꝓportio-
                    <lb/>
                  ne ſexquialtera. / tunc ꝑtranſiret nonocuplam ſpaci­
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                  um ad ſpacium pertranſitum in prima parte pro-
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                  portionali: vt patet ex quinta concluſione: et eius ſe­
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                  cundo correlario: ſed modo tardius mouetur in to-
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                  tali hora quam tunc: ergo modo tranſit minus ſpa­
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                  cium quã nonocuplū ad ſpaciū pertranſitum in pri­
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                  ma parte ꝓportionali: quod fuit ꝓbandum.</s>
                </p>
                <note position="left" xml:id="N201EC" xml:space="preserve">2. correl.</note>
                <p xml:id="N201F0">
                  <s xml:id="N201F1" xml:space="preserve">¶ Sequitur ſecundo /  hora diuiſa per partes pro­
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                  portionales ꝓportione ſuperbipartiente tertias:
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                  mobili moto in prima parte proportionali aliquã­
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                  tula velocitate: et in ſecunda in ꝓportione ſupertri-
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                  partiēte quartas velocius: et in tertia in proportio­
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                  ne ſupertripartiente octauas velocius quã in ſecū-
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                  da: et in quarta in ꝓportione ſupratripartiente de-
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                  cimas ſextas velocius ꝙ̄ in tertia: et ſic conſequēter
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                  ſpacium pertranſitum in totali hora erit maius ̄
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                  duplum ſexquialterum ad ſpacium ꝑtranſitum in
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                  prima parte ꝓportionali et minus quã ſexdecuplū
                    <cb chead="De motu locali quo ad effectum tempore difformi."/>
                  ſexquiquartum.
                    <note position="right" xlink:href="note-0166-02a" xlink:label="note-0166-02" xml:id="N20261" xml:space="preserve">.3. correl.</note>
                  </s>
                  <s xml:id="N20210" xml:space="preserve">¶ Sequitur tertio /  diuiſa hora ꝑ
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                  partes proportionales tripla proportione: et ī pri­
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                  ma parte proportionali mobile moueatur aliquã-
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                  tula velocitate. </s>
                  <s xml:id="N20219" xml:space="preserve">et in ſecunda in ſuprabipartiente ter­
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                  tias maiori velocitate: et in tertia in ſuperbipartiē­
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                  te quintas maiore velocitate ꝙ̄ in prima: et in quar­
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                  ta in ſuperbipartiente ſeptimas maiori ꝙ̄ in prīa
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                  et in quinta in ſuperbipartiente nonas maiori ꝙ̄ in
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                  prima: et ſic conſequenter procedendo ꝑ ſpecies pro­
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                  portionis ſuperbipartientis denominatas a nūe-
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                  ris īparibꝰ vĺ a ꝑtibꝰ aliq̊tis a nūeris īparibꝰ deno­
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                  minatis: ſpacium ꝑtranſitum in totali hora ē ma-
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                  ius ꝙ̄ ſexquialterum ad ſpacium pertranſitum in ṗ­
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                  ma parte proportionali: et minus quã dupluꝫ ſexq̇-
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                  quartum.
                    <note position="right" xlink:href="note-0166-03a" xlink:label="note-0166-03" xml:id="N20267" xml:space="preserve">4. correl.</note>
                  </s>
                  <s xml:id="N20237" xml:space="preserve">¶ Sequitur quarto /  diuiſa hora ꝑ par-
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                  tes ꝓportionales ꝓportione quadrupla: et in ṗma
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                  ꝑte proportionali mobile moueat̄̄ aliquantula ve­
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                  locitate: et in ſecunda in ſexquialtero velocius: et in
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                  tertia in ſuperbipartienti tertias velocius ꝙ̄ in pri­
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                  ma: et in quarta in ſupertripartiente quartas velo­
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                  cius ꝙ̄ in prima: et in quinta in ſuperbipartiente q̇n­
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                  tas velocius ꝙ̄ in prima et in ſexta in ſupertripar-
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                  tiente octauas velocius ꝙ̄ in prima: et ſic conſequen­
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                  ter in partibus imparibus procedendo per propor­
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                  tionem ſupertripartientem: et in paribus ꝑ ꝓportio­
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                  nem ſuperbipartientem: ſpacium pertranſitum in
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                  totali hora eſt pluſ̄ ſexquitertium ad ſpacium per­
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                  tranſitum in prima parte ꝓportionali: et minꝰ quã
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                  ſuperſeptipartiens nonas ad ſpacium pertranſi-
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                  tum in prima </s>
                  <s xml:id="N20258" xml:space="preserve">Iſta tria correlaria eandem cum ſu-
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                  periori correlario ſortiuntur demonſtrationem.</s>
                </p>
                <note position="right" xml:id="N2026D" xml:space="preserve">Queſtio</note>
                <p xml:id="N20271">
                  <s xml:id="N20272" xml:space="preserve">¶ Sed queret equilibris calculator ad amiſſim om­
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                  nia coniectans et numerorū quadã ſtatera appen-
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                  dens adequatam velocitatem qua in tota hora il-
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                  lud mobile mouetur: et adequatum ſpacium ꝑtran-
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                  ſitum a tali mobili in caſu duodecime concluſionis
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                  et quatuor lateralium correlariorum eam ſequenti­
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                  um. </s>
                  <s xml:id="N20281" xml:space="preserve">Hinc curioſe queſtioni (cui queſtioni querente
                    <lb/>
                  proteruo difficilis eſt reſponſio) ei ſilentium impo-
                    <lb/>
                  nens per duas ꝓpoſitiones reſpõdeo.</s>
                </p>
                <p xml:id="N20288">
                  <s xml:id="N20289" xml:space="preserve">Prima propoſitio </s>
                  <s xml:id="N2028C" xml:space="preserve">Si velocitas in in­
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                  finitum difformis aliquã coherentiam ſiue ꝓportio­
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                  nem continuo ſeruat: facile eſt totalem velocitatem
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                  cõmenſurare: et ſpacium mediante illa tranſitū mē­
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                  tiri. </s>
                  <s xml:id="N20297" xml:space="preserve">Patet hec ꝓpoſitio / quia ſi continuo velocita-
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                  tes in eadem proportione ſe habeant: et etiam ſpa­
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                  cia ſe in aliqua ꝓportione continuo ſe habebunt: et
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                  tunc cognita illa ꝓportione iam totale ſpacium ſe
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                  habebit ad ſpacium pertranſituꝫ in prima parte ꝓ­
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                  poſtionali in ea ꝓportione in qua ſe habebit totū
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                  eadem proportione diuiſum ad primam eius ꝑtem
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                  ꝓportionalem / vt dictum eſt ſupra.</s>
                </p>
                <p xml:id="N202A8">
                  <s xml:id="N202A9" xml:space="preserve">Secunda propoſitio </s>
                  <s xml:id="N202AC" xml:space="preserve">Non habentibꝰ
                    <lb/>
                  illis velocitatibus difformibus aliquam cõtinuo ī­
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                  ter ſe proportionem ſicut ſit in caſu duodecime con­
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                  cluſionis et ſequentium correlariorum: impoſſibile
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                  eſt naturaliter intellectum finite capacitatis talem
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                  velocitatem ſic difformē ad vniformitatem redige­
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                  re: et adequatum ſpacium pertranſitum infallibili­
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                  rer aſſignare. </s>
                  <s xml:id="N202BD" xml:space="preserve">Probatur hec ꝓpoſitio / quia cū ſint
                    <lb/>
                  ibi iufinite velocitates inequales ſi nullam vnifor-
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                  mitateꝫ proportionum inter ſe ſeruent ſed cõtinuo
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                  ſe habeãt in alia et alia proportione oporteret intel-
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                  lectum infinitas ꝓpoſitiones rimari, et deinde con-
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                  ſiderare quantum velocitas in vna ꝓportione mi-
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                  nor altera plus facit ad pertrãſitum ſpacii ꝙ̄ alte­
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                  ra in eadem proportione minor: ſed impoſſibile eſt /
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                   intellectus finite capacitatis iſta infinita proſpi­ </s>
                </p>
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