Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
              <div xml:id="N16349" level="4" n="5" type="chapter" type-free="capitulum">
                <p xml:id="N1658B">
                  <s xml:id="N1658F" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0065" n="65"/>
                  velociter intendent vel remittent motus ſuos. </s>
                  <s xml:id="N1659D" xml:space="preserve">Ex
                    <lb/>
                  probatione prioris hec probata euadit.</s>
                </p>
                <p xml:id="N165A2">
                  <s xml:id="N165A3" xml:space="preserve">Quindemica concluſio </s>
                  <s xml:id="N165A6" xml:space="preserve">Si due po-
                    <lb/>
                  tentie per earum intenſionem eque velociter inten­
                    <lb/>
                  dunt motus ſuos cum eadem vel diuerſis reſiſten­
                    <lb/>
                  tiis non variatis: ipſe eque proportionabiliṫ creſ­
                    <lb/>
                  cunt: et ſi per earum remiſſionem etc. eque velociter
                    <lb/>
                  remittunt motus ſuos. </s>
                  <s xml:id="N165B3" xml:space="preserve">ipſe eque proportionabili­
                    <lb/>
                  ter decreſcunt. </s>
                  <s xml:id="N165B8" xml:space="preserve">Hec patet ex vndecima. </s>
                  <s xml:id="N165BB" xml:space="preserve">Et dicit cal­
                    <lb/>
                  culator /  eſt eius ↄ̨uerſa. </s>
                  <s xml:id="N165C0" xml:space="preserve">Intellige ad ſenſuꝫ ma­
                    <lb/>
                  thematicum.</s>
                </p>
                <p xml:id="N165C5">
                  <s xml:id="N165C6" xml:space="preserve">Decimaſexta concluſio </s>
                  <s xml:id="N165C9" xml:space="preserve">Si ꝑ cremē­
                    <lb/>
                  ta aliquarum reſiſtentiarum vel decrementa, po-
                    <lb/>
                  tentia vel potentie cum illis reſiſtentiis mouentes
                    <lb/>
                  vniformiter moueantur: tales potentie eque pro-
                    <lb/>
                  portionabiliter creſcunt vel decreſcunt cuꝫ ſuis re­
                    <lb/>
                  ſiſtentiis. </s>
                  <s xml:id="N165D6" xml:space="preserve">Patet concluſio quia ad hoc /  propor­
                    <lb/>
                  tio maneat ſemper equalis et numeri eius creſcūt
                    <lb/>
                  vel decreſcunt. </s>
                  <s xml:id="N165DD" xml:space="preserve">neceſſe ē /  quãtãcu ꝓportionē nu­
                    <lb/>
                  merus maior acquirat vel deperdat tantam pro-
                    <lb/>
                  portioneꝫ acquirat vel deperdat numerus minor /
                    <lb/>
                  vt patet ex primo correlario quarte concluſionis
                    <lb/>
                  octaui capitis ſecunde partis igitur.</s>
                </p>
                <p xml:id="N165E8">
                  <s xml:id="N165E9" xml:space="preserve">Decimaſeptima concluſio </s>
                  <s xml:id="N165EC" xml:space="preserve">Si potē-
                    <lb/>
                  tia creſcens vel decreſcens vniformiter mouetur et
                    <lb/>
                  eque velociter: neceſſe eſt reſiſtentiam eque ꝓpor-
                    <lb/>
                  tionabiliter creſcere vel decreſcere et eocõtra </s>
                  <s xml:id="N165F5" xml:space="preserve">Hec
                    <lb/>
                  ex primo correlario quarte concluſionis prealle-
                    <lb/>
                  gato patrocinio prime ſuppoſitionis huius ma-
                    <lb/>
                  nifeſta euadit.</s>
                </p>
                <p xml:id="N165FE">
                  <s xml:id="N165FF" xml:space="preserve">Decimaoctaua cõcluſio </s>
                  <s xml:id="N16602" xml:space="preserve">Si reſiſten­
                    <lb/>
                  tia creſcat vel decreſcat et potentia eque velociter
                    <lb/>
                  mouetur ipſa potentia eque proportionabiliter
                    <lb/>
                  creſcit vel deſcreſcit cum ſua reſiſtentia et eocontra
                    <lb/>
                  </s>
                  <s xml:id="N1660C" xml:space="preserve">Hec precedentis probationem aſſumit.</s>
                </p>
                <p xml:id="N1660F">
                  <s xml:id="N16610" xml:space="preserve">Decimanona concluſio </s>
                  <s xml:id="N16613" xml:space="preserve">Si potētia
                    <lb/>
                  eque velociter moueatur et ipſa difformiter creſ-
                    <lb/>
                  cit vel decreſcit: neceſſe eſt ſuam reſiſtentiam dif-
                    <lb/>
                  formiter creſcere vel decreſcere. </s>
                  <s xml:id="N1661C" xml:space="preserve">Patet hoc ex pro­
                    <lb/>
                  batione aliarum.</s>
                </p>
                <p xml:id="N16621">
                  <s xml:id="N16622" xml:space="preserve">Uigeſima concluſio </s>
                  <s xml:id="N16625" xml:space="preserve">Si aliqua reſi-
                    <lb/>
                  ſtentia vniformiter creſcat vel decreſcat potētia
                    <lb/>
                  eque velociter mouente: neceſſe eandem potentiaꝫ
                    <lb/>
                  creſcere vel decreſcere vniformiter. </s>
                  <s xml:id="N1662E" xml:space="preserve">Patet conclu­
                    <lb/>
                  ſio / quia alias non maneret eadeꝫ proportio / vt pa­
                    <lb/>
                  tet ex correlario preallegato et per conſequēs nec
                    <lb/>
                  eandem velocitas.</s>
                </p>
                <p xml:id="N16637">
                  <s xml:id="N16638" xml:space="preserve">Uigeſimaprima cõcluſio </s>
                  <s xml:id="N1663B" xml:space="preserve">Si aliqua
                    <lb/>
                  potentia vniformiter creſcat reſpectu reſiſtentie
                    <lb/>
                  non variate: talis potentia tardius et tardius in­
                    <lb/>
                  tendit motum ſuum </s>
                  <s xml:id="N16644" xml:space="preserve">Probatur hec concluſio ex
                    <lb/>
                  ſexta ſuppoſitione. </s>
                  <s xml:id="N16649" xml:space="preserve">Continuo enim eadem latitu-
                    <lb/>
                  do addetur maiori et maiori numero: igitur con-
                    <lb/>
                  tinuo acquiretur minor ꝓportio et ſic cõtinuo mo­
                    <lb/>
                  tus tardius et tardius intendetur.</s>
                </p>
                <p xml:id="N16652">
                  <s xml:id="N16653" xml:space="preserve">Uigeſimaſecūda concluſio </s>
                  <s xml:id="N16656" xml:space="preserve">Si ali-
                    <lb/>
                  qua potentia vniformiter decreſcat reſiſtentia nõ
                    <lb/>
                  variata: ipſa continuo velocius et velocius remit­
                    <lb/>
                  tet motum ſuum. </s>
                  <s xml:id="N1665F" xml:space="preserve">Hec itidem patet ex ſexta ſuppo­
                    <lb/>
                  ſitione.</s>
                </p>
                <p xml:id="N16664">
                  <s xml:id="N16665" xml:space="preserve">Uigeſimatertia cõcluſio </s>
                  <s xml:id="N16668" xml:space="preserve">Si aliqua
                    <lb/>
                  reſiſtentia vniformiter creſcat reſpectu potētie nõ
                    <lb/>
                  variate: talis potentia tardius et tardius remit-
                    <lb/>
                  tet motum ſuum. </s>
                  <s xml:id="N16671" xml:space="preserve">Hec modo quo precedens ꝓbat̄̄.</s>
                </p>
                <cb chead="Capitulum quintum"/>
                <p xml:id="N16676">
                  <s xml:id="N16677" xml:space="preserve">Uigeſimaquarta ↄ̨̨cluſio </s>
                  <s xml:id="N1667A" xml:space="preserve">Si aliqua
                    <lb/>
                  reſiſtentia vniformiter decreſcat potentia nõ va-
                    <lb/>
                  riata: talis potentia velocius et velocius intendet
                    <lb/>
                  motum ſuum. </s>
                  <s xml:id="N16683" xml:space="preserve">Patet / quoniam continuo maioreꝫ
                    <lb/>
                  proportionem acquirit. </s>
                  <s xml:id="N16688" xml:space="preserve">vt patet ex ſexta ſuppo-
                    <lb/>
                  ſitione.</s>
                </p>
                <p xml:id="N1668D">
                  <s xml:id="N1668E" xml:space="preserve">Uigeſimaquinta concluſio </s>
                  <s xml:id="N16691" xml:space="preserve">Si ali-
                    <lb/>
                  qua potentia tardius et tardius creſcat reſpectu
                    <lb/>
                  reſiſtentie non variate. </s>
                  <s xml:id="N16698" xml:space="preserve">ipſa tardius cõtinuo et tar­
                    <lb/>
                  dius intendet motum ſuum. </s>
                  <s xml:id="N1669D" xml:space="preserve">Patet hec concluſio
                    <lb/>
                  ex vigeſimaprima per locum a maiori: quoniaꝫ ſi
                    <lb/>
                  ſemper vniformiter creſceret: tardius continuo et
                    <lb/>
                  tardius intenderet motum ſuum. </s>
                  <s xml:id="N166A6" xml:space="preserve">igitur ſi cõtinuo
                    <lb/>
                  tardius creſcat: a fortiori tardius et tardius iutē­
                    <lb/>
                  det motum ſuum.</s>
                </p>
                <p xml:id="N166AD">
                  <s xml:id="N166AE" xml:space="preserve">Uigeſimaſexta concluſio </s>
                  <s xml:id="N166B1" xml:space="preserve">Si aliqua
                    <lb/>
                  potentia velocius continuo decreſcat reſpectu re­
                    <lb/>
                  ſiſtentie non variate: ipſa contiuuo velocius remit­
                    <lb/>
                  tet motum ſuum. </s>
                  <s xml:id="N166BA" xml:space="preserve">Patet ex vigeſimaſecunda ſuf-
                    <lb/>
                  fragante loco a maiori.</s>
                </p>
                <p xml:id="N166BF">
                  <s xml:id="N166C0" xml:space="preserve">Uigeſimaſeptima concluſio </s>
                  <s xml:id="N166C3" xml:space="preserve">Si ali-
                    <lb/>
                  qua reſiſtentia tardius continuo creſcat reſpectu
                    <lb/>
                  potentie non variate: ipſa potentia continuo tar­
                    <lb/>
                  dius remittet motum ſuum. </s>
                  <s xml:id="N166CC" xml:space="preserve">Patet ex vigeſimater­
                    <lb/>
                  tia auxilio loci a fortiori.</s>
                </p>
                <p xml:id="N166D1">
                  <s xml:id="N166D2" xml:space="preserve">Uigeſimaoctaua concluſio </s>
                  <s xml:id="N166D5" xml:space="preserve">Si ali-
                    <lb/>
                  qua reſiſtentia continuo velocius decreſcat reſpe­
                    <lb/>
                  ctu potentie non variate: talis potentia continuo
                    <lb/>
                  velocius intendet motum ſuum </s>
                  <s xml:id="N166DE" xml:space="preserve">Patet ex vigeſi-
                    <lb/>
                  ma quarta.</s>
                </p>
                <p xml:id="N166E3">
                  <s xml:id="N166E4" xml:space="preserve">Uigeſimanona cõcluſio </s>
                  <s xml:id="N166E7" xml:space="preserve">Si due vel
                    <lb/>
                  tres, vel quatuor, aut quotlibet potentie inequa-
                    <lb/>
                  les, eque velociter creſcant vel decreſcant reſpectu
                    <lb/>
                  eiuſdem reſiſtentie non variate: minima illarum
                    <lb/>
                  velocius intendet vel remittet motum ſuum. </s>
                  <s xml:id="N166F2" xml:space="preserve">Pa-
                    <lb/>
                  tet hec concluſio ex ſexta ſuppoſitione. </s>
                  <s xml:id="N166F7" xml:space="preserve">quoniaꝫ il­
                    <lb/>
                  li minori potentie per additionem vel remotionē
                    <lb/>
                  equalis latitudinis, ſemper accreſcit vel decreſcit
                    <lb/>
                  maior proportio.</s>
                </p>
                <p xml:id="N16700">
                  <s xml:id="N16701" xml:space="preserve">Triceſima cõcluſio </s>
                  <s xml:id="N16704" xml:space="preserve">Si due aut tres
                    <lb/>
                  aut quatuor: aut quotlibet reſiſtentie: eque veloci-
                    <lb/>
                  ter creſcant vel decreſcant reſpectu eiuſdem potē-
                    <lb/>
                  tie non variate: ſemper talis potentia cum mini-
                    <lb/>
                  ma illarum velocius intendet vel remittet motum
                    <lb/>
                  ſuum. </s>
                  <s xml:id="N16711" xml:space="preserve">Hec et precedens equaleꝫ ſubeunt demõſtra­
                    <lb/>
                  tionem. </s>
                  <s xml:id="N16716" xml:space="preserve">¶ Nunc modicum a ſerie diſcedentes ope­
                    <lb/>
                  re precium eſt aliquas concluſiones his aducere.</s>
                </p>
                <p xml:id="N1671B">
                  <s xml:id="N1671C" xml:space="preserve">Triceſimaprima concluſio. </s>
                  <s xml:id="N1671F" xml:space="preserve">Si du-
                    <lb/>
                  plum et ſubduplum eque velociter ad non graduꝫ
                    <lb/>
                  remittantur: in maiori tempore remittitur duplū
                    <lb/>
                  quam ſubduplum. </s>
                  <s xml:id="N16728" xml:space="preserve">Probatur hec concluſio. </s>
                  <s xml:id="N1672B" xml:space="preserve">quo-
                    <lb/>
                  niam capto quaternario et binario ſi eque veloci­
                    <lb/>
                  ter et vniformiter remittantur quando due vnita­
                    <lb/>
                  tes quaternarii remiſſe ſunt: reſtant due: et bina-
                    <lb/>
                  rius eſt complete remiſſus. </s>
                  <s xml:id="N16736" xml:space="preserve">igitur oportet /  in tē-
                    <lb/>
                  pore ſequenti remittantur alie due vnitates qua-
                    <lb/>
                  teruarii: poſt̄ binarius eſt ad non gradum dedu­
                    <lb/>
                  ctus et per conſequens concluſio vera.</s>
                </p>
                <p xml:id="N1673F">
                  <s xml:id="N16740" xml:space="preserve">Triceſimaſecunda concluſio </s>
                  <s xml:id="N16743" xml:space="preserve">Si du­
                    <lb/>
                  plum et ſubduplum vniformiter remittant̄̄ et con­
                    <lb/>
                  tinuo eque velociter: tempus remiſſionis dupli eſt
                    <lb/>
                  duplum ad tempus remiſſionis ſubdupli. </s>
                  <s xml:id="N1674C" xml:space="preserve">Et conſi­
                    <lb/>
                  militer dicatur de triplo, quadruplo, ſexqualte-
                    <lb/>
                  ro, et ſic in infinitum. </s>
                  <s xml:id="N16753" xml:space="preserve">quoniam tempus tripli erit </s>
                </p>
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