Alvarus, Thomas, Liber de triplici motu, 1509

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          <div xml:id="N15C17" level="2" n="3" type="other" type-free="pars">
            <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="N163EE">
                  <s xml:id="N163FA" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0064" n="64"/>
                  merus ſenarius aequirit binarium et numerꝰ qui­
                    <lb/>
                  narius in eodem tempore etiam binariuꝫ: dico / 
                    <lb/>
                  eque velociter intenduntur ſed non eque ꝓportio-
                    <lb/>
                  nabiliter ſed ſi numerus ternarius acquirat vni-
                    <lb/>
                  tatem et numerus ſenarius acquirat in eodem tē-
                    <lb/>
                  pore dualitatem: dico /  tunc eque proportionabi­
                    <lb/>
                  liter acquirunt et non eque velociter. </s>
                  <s xml:id="N16410" xml:space="preserve">quoniam tã­
                    <lb/>
                  ternarius numerus quam ſenarius ꝓportionem
                    <lb/>
                  ſexquitertiaꝫ acquirit / vt facile eſt intueri. </s>
                  <s xml:id="N16417" xml:space="preserve">Hec dif­
                    <lb/>
                  finitio eſt.</s>
                </p>
                <p xml:id="N1641C">
                  <s xml:id="N1641D" xml:space="preserve">His ſuppoſitis p̄miſſis ſit prima con­
                    <lb/>
                  cluſio. </s>
                  <s xml:id="N16422" xml:space="preserve">Si aliqua potentia creſcit reſpectu reſiſtē-
                    <lb/>
                  tie non variate: tantam proportioneꝫ acquirit ſu­
                    <lb/>
                  pra ſe quantam ſupra ſuam reſiſtentiam et eocon­
                    <lb/>
                  tra: </s>
                  <s xml:id="N1642B" xml:space="preserve">Probatur hec concluſio auxiliante ſeptima
                    <lb/>
                  concluſione octaui capitis precedentis partis.</s>
                </p>
                <p xml:id="N16430">
                  <s xml:id="N16431" xml:space="preserve">Nam potentia ſe habet vt quantitas maior et re-
                    <lb/>
                  ſiſtentia vt minor ſi actiuitas ꝓdeat.</s>
                </p>
                <p xml:id="N16436">
                  <s xml:id="N16437" xml:space="preserve">Secunda concluſio </s>
                  <s xml:id="N1643A" xml:space="preserve">Si aliqua vir-
                    <lb/>
                  tus decreſcat reſpectu reſiſtentie non variate. </s>
                  <s xml:id="N1643F" xml:space="preserve">tan­
                    <lb/>
                  tam proportionem deperdit reſpectu ſue reſiſten­
                    <lb/>
                  tie quantam reſpectu ſui ipſius. </s>
                  <s xml:id="N16446" xml:space="preserve">vt capta potentia
                    <lb/>
                  vt .4. et reſiſtentia vt .2. ſi potentia / vt quatuor effi­
                    <lb/>
                  ciatur in ſexquitertio minor perdendo vnitatem
                    <lb/>
                  ſiue proportionem ſexquitertiam: eandem ꝓpor-
                    <lb/>
                  tionem ſexquitertiam perdit reſpectu ſue reſiſten­
                    <lb/>
                  tie vt duo. </s>
                  <s xml:id="N16453" xml:space="preserve">Probatur hec concluſio ex ſeptima cõ­
                    <lb/>
                  cluſione i capitis preallegata eo modo quo
                    <lb/>
                  prior.</s>
                </p>
                <p xml:id="N1645A">
                  <s xml:id="N1645B" xml:space="preserve">Tertia concluſio </s>
                  <s xml:id="N1645E" xml:space="preserve">Si aliqua reſiſtē-
                    <lb/>
                  tia creſcat vel decreſcat reſpectu potentie non va­
                    <lb/>
                  riate: tantam proportionem acquiret vel deper-
                    <lb/>
                  det reſpectu ſui ipſius quantam acquiret vel deꝑ-
                    <lb/>
                  det reſpectu talis potentie. </s>
                  <s xml:id="N16469" xml:space="preserve">Hoc eſt: tantam acqui­
                    <lb/>
                  rit vel deperdit talis potentia reſpectu eiuſdeꝫ re­
                    <lb/>
                  ſiſtentie. </s>
                  <s xml:id="N16470" xml:space="preserve">Patet hec concluſio ex octaua concluſio­
                    <lb/>
                  ne octaui capitis p̄allegati et ſuo prīo correlario</s>
                </p>
                <p xml:id="N16475">
                  <s xml:id="N16476" xml:space="preserve">Quarta concluſio </s>
                  <s xml:id="N16479" xml:space="preserve">Si potētia creſ-
                    <lb/>
                  cat vel decreſcat reſpectu potentie non variate: tã­
                    <lb/>
                  tam proportionem acquirit vel deperdit reſpectu
                    <lb/>
                  ſue reſiſtentie qnantam acquirit vel deperdit reſ­
                    <lb/>
                  pectu ſui ipſius. </s>
                  <s xml:id="N16484" xml:space="preserve">Probatur hec concluſio ex primo
                    <lb/>
                  correlario ſeptime concluſionis capitis prealle-
                    <lb/>
                  gati / et facile ex prima et ſecunda huius deducitur</s>
                </p>
                <p xml:id="N1648B">
                  <s xml:id="N1648C" xml:space="preserve">Quinta concluſio. </s>
                  <s xml:id="N1648F" xml:space="preserve">Si aliqua potē-
                    <lb/>
                  tia eque velociter creſcit vĺ decreſcit reſpectu dua­
                    <lb/>
                  rum reſiſtentiarum ſiue equalium ſiue inequaliuꝫ
                    <lb/>
                  eque velociter cum vtra illarum intendet vel re­
                    <lb/>
                  mittet motum ſuum </s>
                  <s xml:id="N1649A" xml:space="preserve">Probatur hec concluſio / quo­
                    <lb/>
                  niam illa potentia equalem ꝓportionem acquirit
                    <lb/>
                  vel deperdit reſpectu vtriuſ reſiſtentie / vt patet
                    <lb/>
                  ex prima concluſione huius / et ſecunda parte ſepti­
                    <lb/>
                  me concluſionis octaui capitis preallegati et ſuo
                    <lb/>
                  ſecundo correlario / igitur equalem velocitatē ac-
                    <lb/>
                  quirit vel deperdit reſpectu vtriuſ reſiſtentie.</s>
                </p>
                <p xml:id="N164A9">
                  <s xml:id="N164AA" xml:space="preserve">Patet conſequentia ex tertia ſuppoſitione.</s>
                </p>
                <p xml:id="N164AD">
                  <s xml:id="N164AE" xml:space="preserve">Sexta concluſio </s>
                  <s xml:id="N164B1" xml:space="preserve">Si aliqua reſiſtē-
                    <lb/>
                  tia creſcat vel decreſcat reſpectu duarum poten-
                    <lb/>
                  tiarum ſiue equalium ſiue inequaliū non variata­
                    <lb/>
                  rum: vtra potentia eque velociter cum illa reſi-
                    <lb/>
                  ſtentia intendet vel remittet motum ſuum. </s>
                  <s xml:id="N164BC" xml:space="preserve">Pro-
                    <lb/>
                  batur hec concluſio / quoniam reſpectu vtriuſ po­
                    <lb/>
                  tentie equalem ꝓportionem acquirit vel deperdit /
                    <lb/>
                  vt patet ex ſecundo correlario octaue concluſiõis
                    <lb/>
                  octaui capitis preallegati: igitur vtra potentia
                    <lb/>
                  equalem velocitatem acquirit vel deperdit.</s>
                </p>
                <cb chead="Capitulum quintum"/>
                <p xml:id="N164CB">
                  <s xml:id="N164CC" xml:space="preserve">Septima concluſio </s>
                  <s xml:id="N164CF" xml:space="preserve">Si due potētie
                    <lb/>
                  inequales eque velociter creſcant vel decreſcãt reſ­
                    <lb/>
                  pectu eiuſdem reſiſtentie non variate: potentia mi­
                    <lb/>
                  nor velocius intendet vel remittet motū ſuū </s>
                  <s xml:id="N164D8" xml:space="preserve">Pro­
                    <lb/>
                  batur hec concluſio / quoniam ſemper potentia mi­
                    <lb/>
                  nor per equale crementum vel decrementū additū
                    <lb/>
                  ſibi vel deperditum et maiori: maiorem ꝓportio-
                    <lb/>
                  nem acquiret vel deperdet quam maior. </s>
                  <s xml:id="N164E3" xml:space="preserve">vt ptꝫ ex
                    <lb/>
                  quinta ſuppoſitiõe huius capitis: igitur talis po­
                    <lb/>
                  tentia velocius intendet vel remittet motum ſuuꝫ
                    <lb/>
                  </s>
                  <s xml:id="N164EB" xml:space="preserve">Conſequentia patet ex prima ſuppoſitione. </s>
                  <s xml:id="N164EE" xml:space="preserve">Ab
                    <lb/>
                  equalibus enim ꝓportionibus acquiſitis ſiue de-
                    <lb/>
                  perditis inequales velocitates acquiruntur ſiue
                    <lb/>
                  deperduntur / et per idem ſequitur /  ad acquiſitio­
                    <lb/>
                  nem vel deperditionem maioris maior velocitas
                    <lb/>
                  acquiritur vel deperditur</s>
                </p>
                <p xml:id="N164FB">
                  <s xml:id="N164FC" xml:space="preserve">Octaua concluſio </s>
                  <s xml:id="N164FF" xml:space="preserve">Si due reſiſtētie
                    <lb/>
                  inequales eque velociter creſcant vel decreſcãt reſ­
                    <lb/>
                  pectu eiuſdem potentie non variate: illa potentia
                    <lb/>
                  velocius intendet vel remittet motum ſuum cū mi­
                    <lb/>
                  nori reſiſtentia quam cum maiori. </s>
                  <s xml:id="N1650A" xml:space="preserve">Probatur hec
                    <lb/>
                  concluſio / quoniam ſemper minor reſiſtentia ma-
                    <lb/>
                  iorem proportionem acquirit vel deperdit ꝑ equa­
                    <lb/>
                  lem deperditionē vel additionē ipſi et maiori / igi­
                    <lb/>
                  tur potentia cum ea velocius intendet vel remittet
                    <lb/>
                  motū ſuum. </s>
                  <s xml:id="N16517" xml:space="preserve">Patet conſequentia auxilio duarum
                    <lb/>
                  primarum ſuppoſitionum.</s>
                </p>
                <p xml:id="N1651C">
                  <s xml:id="N1651D" xml:space="preserve">Nona concluſio </s>
                  <s xml:id="N16520" xml:space="preserve">Si due potentie in-
                    <lb/>
                  equales eque velociter creſcant vel decreſcant reſ­
                    <lb/>
                  pectu duarum reſiſtentiarum ſiue equalium ſiue ī­
                    <lb/>
                  equalium: potentia minor ſemper velocius inten­
                    <lb/>
                  det vel remittet motum ſuum ſiue agat cum reſiſtē­
                    <lb/>
                  tia maiore ſiue minore. </s>
                  <s xml:id="N1652D" xml:space="preserve">Patet hec concluſio ex ſe-
                    <lb/>
                  ptima huius.</s>
                </p>
                <p xml:id="N16532">
                  <s xml:id="N16533" xml:space="preserve">Decima concluſio </s>
                  <s xml:id="N16536" xml:space="preserve">Si due reſiſten-
                    <lb/>
                  tie inequales creſcant vel decreſcant reſpectu dua­
                    <lb/>
                  rum potentiarum ſiue equalium ſiue inequalium:
                    <lb/>
                  potentia agens cum minore velocius intendet vel
                    <lb/>
                  remittet motum ſuum. </s>
                  <s xml:id="N16541" xml:space="preserve">Hec patet ex octaua.</s>
                </p>
                <p xml:id="N16544">
                  <s xml:id="N16545" xml:space="preserve">Undecima concluſio </s>
                  <s xml:id="N16548" xml:space="preserve">Si due potētie
                    <lb/>
                  equales vel inequales eque ꝓporrionabiliter creſ­
                    <lb/>
                  cant vel decreſcant reſpectu eiuſdem reſiſtentie nõ
                    <lb/>
                  variate: tales potentie eque velociter intendēt vel
                    <lb/>
                  remittēt motus ſuos. </s>
                  <s xml:id="N16553" xml:space="preserve">Patet hec concluſio ex ſexta
                    <lb/>
                  ſuppoſitione / que diffinit iſtum terminum eque ꝓ­
                    <lb/>
                  portionabiliter auxilio prime ſuppoſitionis.</s>
                </p>
                <p xml:id="N1655A">
                  <s xml:id="N1655B" xml:space="preserve">Duodecima concluſio </s>
                  <s xml:id="N1655E" xml:space="preserve">Si due reſi-
                    <lb/>
                  ſtentie equales ſiue inequales eque ꝓportionabi-
                    <lb/>
                  liter creſcant vel decreſcant reſpectu eiuſdem po-
                    <lb/>
                  tentie non variate. </s>
                  <s xml:id="N16567" xml:space="preserve">talis potentia cum vtra illa­
                    <lb/>
                  rum reſiſtentiarum eque velociter intendet vel re-
                    <lb/>
                  mittet motum ſuum. </s>
                  <s xml:id="N1656E" xml:space="preserve">Hec cum precedente eandem
                    <lb/>
                  ſortitur demonſtrationem.</s>
                </p>
                <p xml:id="N16573">
                  <s xml:id="N16574" xml:space="preserve">Tridecima concluſio </s>
                  <s xml:id="N16577" xml:space="preserve">Si due poten-
                    <lb/>
                  tie inequales eque ꝓportionabiliter creſcant vel
                    <lb/>
                  decreſcant reſpectu duarum reſiſtentiaruꝫ ſiue eq̄­
                    <lb/>
                  lium ſiue inequalium non variatarum: ipſe eque­
                    <lb/>
                  velociter intendent vel remittent motus ſuos. </s>
                  <s xml:id="N16582" xml:space="preserve">Pa­
                    <lb/>
                  tet hec concluſio ex prima ſuppoſitione auxiliãte
                    <lb/>
                  vltima diffiniente eque velociter et eque propor-
                    <lb/>
                  tionabiliter.</s>
                </p>
                <p xml:id="N1658B">
                  <s xml:id="N1658C" xml:space="preserve">Quartadecima concluſio </s>
                  <s xml:id="N1658F" xml:space="preserve">Si due re­
                    <lb/>
                  ſiſtentie inequales creſcant vel decreſcant eque ꝓ­
                    <lb/>
                  portionabiliter reſpectu duarum potentiarum ſi­
                    <lb/>
                  ue equalium ſiue inqualium: tales potentie eque </s>
                </p>
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