Alvarus, Thomas, Liber de triplici motu, 1509

List of thumbnails

< >
101
101 		102
102
103
103 		104
104
105
105 		106
106
107
107 		108
108
109
109 		110
110
< >
page |< < of 290 > >|
    <echo version="1.0">
      <text xml:lang="la">
        <div xml:id="N10132" level="1" n="1" type="body">
          <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="N1A8D1" level="4" n="12" type="chapter" type-free="capitulum">
                <p xml:id="N1A8E9">
                  <s xml:id="N1A8EA" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0109" n="109"/>
                  pitis obiicitur ſic. </s>
                  <s xml:id="N1A8F2" xml:space="preserve">Si illa cõcluſio eſſet vera: ſeque-
                    <lb/>
                  retur /  due potentie equales continuo manentes
                    <lb/>
                  equales idem medium vel equale tranſeuntes vna
                    <lb/>
                  altera continuo velocius moueretur cõſequens eſt
                    <lb/>
                  falſum: igitur illud ex quo ſequitur. </s>
                  <s xml:id="N1A8FD" xml:space="preserve">Falſitas conſe­
                    <lb/>
                  quentis ptꝫ: quia reſiſtentiis equalibus potētiiſ
                    <lb/>
                  equalibus, neceſſe eſt motus eſſe equales / vt ſatis cõ­
                    <lb/>
                  ſtat: quia tunc proportiones equales erūt ex quibꝰ
                    <lb/>
                  equales motus conſurgunt. </s>
                  <s xml:id="N1A908" xml:space="preserve">Sed iam ſequela dedu­
                    <lb/>
                  citur / et capio vnū pedale et vnū ſemipedale: et per
                    <lb/>
                  vtrū illorum ſit extenſa latitudo reſiſtētie vnifor-
                    <lb/>
                  miter difformis a nõ gradu vſ ad octauū: et inci-
                    <lb/>
                  piat a. potentia moueri a nõ gradu reſiſtentie in pe­
                    <lb/>
                  dali vniformiter continuo, creſcens vniformiter a
                    <lb/>
                  nõ gradu potentie / vt ſepius dictum eſt: et b. poten-
                    <lb/>
                  tia incipiat moueri a non gradu reſiſtentie in ſemi­
                    <lb/>
                  pedali, continuo vniformiter et eque velociter cre-
                    <lb/>
                  ſcens ſicut a. potentia. </s>
                  <s xml:id="N1A91D" xml:space="preserve">Quo poſito ſic argumentor
                    <lb/>
                  illa duo media ſunt equaliter reſiſtentia cum habe­
                    <lb/>
                  ant equalem reſiſtentiam oīno: puta a non gradu
                    <lb/>
                  vſ ad octauum: et a. et b. continuo manentes equa­
                    <lb/>
                  les vniformiter mouentur / vt dicit ſecunda cõcluſio
                    <lb/>
                  quam impugnamus: et a. velocius mouetur quã b. /
                    <lb/>
                  igitur propoſitum. </s>
                  <s xml:id="N1A92C" xml:space="preserve">Maior eſt nota et minor proba­
                    <lb/>
                  tur: et ſuppono /  quãdo in duobus mediis inequa­
                    <lb/>
                  libus extenditur eadem latitudo reſiſtentie vnifor-
                    <lb/>
                  miter difformis a non gradu vſ ad certum gradū
                    <lb/>
                  in ea proportione in qua ſe habent media ad inuicē
                    <lb/>
                  quantitatiue, in eadē proportione plus diſtat qui-
                    <lb/>
                  libet punctus a non gradu in medio maiori quam
                    <lb/>
                  conſimilis punctus in medio minori: ita  ſi vnum
                    <lb/>
                  mediū ſit duplum ad alterum: gradus medius per
                    <lb/>
                  duplum maius ſpacium diſtat a non gradu in me-
                    <lb/>
                  dio maiori ꝙ̄ in medio minori. </s>
                  <s xml:id="N1A943" xml:space="preserve">Et ſic de quocū a-
                    <lb/>
                  lio puncto. </s>
                  <s xml:id="N1A948" xml:space="preserve">Hoc ptꝫ ex diffiniitõe qualitatis vnifor-
                    <lb/>
                  miter difformis quarto tractatu. </s>
                  <s xml:id="N1A94D" xml:space="preserve">Quo ſuppoſito
                    <lb/>
                  arguitur ſic minor: quia a. et b. mouentur vniformi­
                    <lb/>
                  ter continuo / vt dicit illa ſecunda concluſio quã im­
                    <lb/>
                  pugnamus: et a. non mouetur ita velociter ſicut b.
                    <lb/>
                  adequate: nec tardius: igitur a. cõtinuo velociꝰ mo-
                    <lb/>
                  uetur quã b. / quod fuit probandū. </s>
                  <s xml:id="N1A95A" xml:space="preserve">Cõſequentia ptꝫ
                    <lb/>
                  et arguitur maior: q2 ſi a. mouetur ita velociter ade­
                    <lb/>
                  quate ſicut b. / ſequitur (cū cõtinuo a. et b. ſunt equa-
                    <lb/>
                  les) /  cõtinuo in quocū puncto eſt a. in medio pe-
                    <lb/>
                  dali in conſimili puncto eſt b. in medio ſemipedali.
                    <lb/>
                  </s>
                  <s xml:id="N1A966" xml:space="preserve">Patet cõſequētia ex ſe et vltra: in quocū puncto
                    <lb/>
                  eſt a. in pedali in ↄ̨ſimili eſt b. in ſemipedali: et quod­
                    <lb/>
                  libet punctū ī pedali in duplo plus diſtat a nõ g̈du
                    <lb/>
                  ̄ cõſimile punctū in ſemipedali: igit̄̄ cõtinuo in du­
                    <lb/>
                  plo plus diſtat a. a puncto a quo īcepit moueri ꝙ̄ b.
                    <lb/>
                  cū tam a. quã b. inceperūt moueri a nõ gradu illius
                    <lb/>
                  reſiſtentie: et ꝑ cõſequēs a. ↄ̨tinuo in duplo velocius
                    <lb/>
                  mouetur ꝙ̄ b. et ex hoc nõ ita velociter adequate / qḋ
                    <lb/>
                  eſt ꝓbandū. </s>
                  <s xml:id="N1A979" xml:space="preserve">Sed tã probo minorē videlicet /  a. nõ
                    <lb/>
                  mouet̄̄ tardius ꝙ̄ b. q2 ſi mouetur tardiꝰ: ſequit̄̄ / 
                    <lb/>
                  cõtinuo eſt in puncto magis reſiſtente ꝙ̄ b. et ſi cõti-
                    <lb/>
                  nuo eſt in pūcto magis reſiſtente ꝙ̄ b. / ſequit̄̄ /  con-
                    <lb/>
                  tinuo pluſ̄ in duplo velociꝰ mouetur ꝙ̄ b. / et ꝑ ↄ̨ñs
                    <lb/>
                  nõ tardius / qḋ fuit ꝓbandū. </s>
                  <s xml:id="N1A986" xml:space="preserve">Patet ↄ̨ña / q2 ſi ↄ̨tinuo
                    <lb/>
                  a. eſſet in pūcto ↄ̨ſimili ſiue equali illi pūcto in quo
                    <lb/>
                  eſt b. cõtinuo a. in duplo velociꝰ moueret̄̄ ipſo b. / vt
                    <lb/>
                  ꝓbatū eſt: igit̄̄ ſi cõtinuo ſit in pūcto adhuc magis
                    <lb/>
                  reſiſtente / ſequitur /  continuo velocius mouetur ̄
                    <lb/>
                  b. </s>
                  <s xml:id="N1A993" xml:space="preserve">Patet conſequentia per locum a maiori.</s>
                </p>
                <p xml:id="N1A996">
                  <s xml:id="N1A997" xml:space="preserve">Reſpõdeo cõcedendo quod īfertur / q2
                    <lb/>
                  illud ſufficienter demõſtrat argumentū: et nego fal­
                    <lb/>
                  ſitatē cõſequētis: et cū ꝓbatur nego /  ille reſiſtētie
                    <lb/>
                  ſint ſimpliciter equales. </s>
                  <s xml:id="N1A9A0" xml:space="preserve">Ad equalitatem enim reſi­
                    <cb chead="Capitulū duodecimū."/>
                    <note position="right" xlink:href="note-0109-01a" xlink:label="note-0109-01" xml:id="N1A9B5" xml:space="preserve">Quid re­
                      <lb/>
                    q̇rit̄̄ ad e­
                      <lb/>
                    q̈litatem
                      <lb/>
                    reſiſtētia­
                      <lb/>
                    rum.</note>
                  ſtentiarum (quod nota) ſaltem vniformiter diffor-
                    <lb/>
                  mium non ſufficit equalitas intenſionis, ſed etiam
                    <lb/>
                  extenſionum equalitas requiritur / vt probat argu-
                    <lb/>
                  mentum.</s>
                </p>
                <p xml:id="N1A9C3">
                  <s xml:id="N1A9C4" xml:space="preserve">Sed ↄ̨̨tra: q2 ſi ſolutio eſſet vera vide­
                    <lb/>
                  licet /  quãto eadē reſiſtētia vniformiter difformis
                    <lb/>
                  eſt in minori medio tantū plus reſiſtit ſed nõ adeq̈-
                    <lb/>
                  te: ſequeret̄̄ /  hoc ꝓueniret ratiõe dēſitatꝪ: ſed hoc
                    <lb/>
                  eſt falſum: igit̄̄ ſolutio nulla. </s>
                  <s xml:id="N1A9CF" xml:space="preserve">Sequela ptꝫ / q2 nõ vi­
                    <lb/>
                  detur alia ratio. </s>
                  <s xml:id="N1A9D4" xml:space="preserve">Sed falſitas cõſequētis arguitur /
                    <lb/>
                  q2 volo /  pedale et ſemipedale ſint eq̈liter dēſa ſi-
                    <lb/>
                  cut facile ſit / vt ptꝫ ex primo capite tertii tractatꝰ: et
                    <lb/>
                  eadē latitudo reſiſtētie vniformiter difformis extē-
                    <lb/>
                  datur ꝑ pedale et ſemipedale. </s>
                  <s xml:id="N1A9DF" xml:space="preserve">Quo poſito ptꝫ /  il-
                    <lb/>
                  le q̈litates ſūt eque rare: q2 ſūt in ſubiectis eq̈liter
                    <lb/>
                  raris.
                    <note position="right" xlink:href="note-0109-02a" xlink:label="note-0109-02" xml:id="N1A9FA" xml:space="preserve">Raritas
                      <lb/>
                    q̈litatis
                      <lb/>
                    vnde ſu-
                      <lb/>
                    matur.</note>
                  </s>
                  <s xml:id="N1A9EB" xml:space="preserve">(Raritas em̄ vel dēſitas accidētis penes ra-
                    <lb/>
                  ritatē vel dēſitatē ſubiecti cõmenſurari hꝫ) et tamē
                    <lb/>
                  eadē poña velociꝰ mouet̄̄ in reſiſtētia pedali ꝙ̄ in ſe­
                    <lb/>
                  mipedali / vt probatū eſt: igit̄̄ illud non prouenit ex
                    <lb/>
                  parte raritatis aut denſitatis / quod fuit ꝓbandū.</s>
                </p>
                <p xml:id="N1AA06">
                  <s xml:id="N1AA07" xml:space="preserve">Reſpondeo vt michi apparet pro nūc
                    <lb/>
                  concedendo ſequelam: et negando falſitatem conſe­
                    <lb/>
                  quentis: et ab probatione admiſſo caſu nego /  ille
                    <lb/>
                  qualitates ſint eque rare in maiori ſubiecto et in mi­
                    <lb/>
                  nori: et cum probatur / quia ſubiecta ſunt eque rara
                    <lb/>
                  concedo illud: et cum infertur ergo et accidentia: ne­
                    <lb/>
                  go conſequentiam: et ad probationem nego /  ex ra­
                    <lb/>
                  ritate ſubiecti debeat ſumi raritas accidētis in or-
                    <lb/>
                  dine ad aliud accidens: ſed debet ſumi ex multitu-
                    <lb/>
                  dine forme accidentalis ſub proportionali quanti­
                    <lb/>
                  tate. </s>
                  <s xml:id="N1AA1E" xml:space="preserve">Credo tamen /  naturaliter loquendo in den-
                    <lb/>
                  ſiori ſubiecto eſt denſius accidens ceteris paribus
                    <lb/>
                  </s>
                  <s xml:id="N1AA24" xml:space="preserve">Et ſi hec ſolutio tibi non placeat: dicas /  maior re­
                    <lb/>
                  ſiſtentia in medio minori quam in maiori prouenit
                    <lb/>
                  ex minoritate medii: hoc eſt  continuo ibi fiet mo-
                    <lb/>
                  tus minoris velocitatis, prouenit ex parte minoris
                    <lb/>
                  extenſionis conſimilis reſiſtentie illi que eſt in me-
                    <lb/>
                  dio maiori.
                    <note position="right" xlink:href="note-0109-03a" xlink:label="note-0109-03" xml:id="N1AA5D" xml:space="preserve">Calcula.
                      <lb/>
                    de react.</note>
                  </s>
                  <s xml:id="N1AA36" xml:space="preserve">Quoniam vt placet calculatori in ca-
                    <lb/>
                  pitulo de reactione in primo notabili quod ponit,
                    <lb/>
                  denſitas nõ ſimpliciter auget rei potentiam. </s>
                  <s xml:id="N1AA3D" xml:space="preserve">Et cū
                    <lb/>
                  querit̄̄ quare / igitur dēſius fortius agit aut reſiſtit.
                    <lb/>
                    <note position="right" xlink:href="note-0109-04a" xlink:label="note-0109-04" xml:id="N1AA65" xml:space="preserve">q̈rto ce. et
                      <lb/>
                    mū. tex.
                      <lb/>
                    cõ. 42.</note>
                  </s>
                  <s xml:id="N1AA49" xml:space="preserve">Reſpõdet /  hoc eſt ratiõe melioris applicationis:
                    <lb/>
                  quēadmoduꝫ diuerſitas figure eſt cauſa velocioris
                    <lb/>
                  motus teſtimonio philoſophi .4. ce. et mūdi tex. cõ.
                    <lb/>
                  42. </s>
                  <s xml:id="N1AA52" xml:space="preserve">Et ſi hec ſolutio tibi non placeat: quere aliam.
                    <lb/>
                  </s>
                  <s xml:id="N1AA56" xml:space="preserve">Argumentum em̄ conuīcit concedere illatum.</s>
                </p>
                <p xml:id="N1AA6F">
                  <s xml:id="N1AA70" xml:space="preserve">Sed cõtra vtrã ſolutionem arguit̄̄
                    <lb/>
                  ſic: quia ſi hoc eſſet verum videlicet /  in caſu poſito
                    <lb/>
                  eadem potentia vel equalis continuo velocius mo­
                    <lb/>
                  uetur per reſiſtentiã conſimilis intenſionis in me-
                    <lb/>
                  dio maiori quam in minori: ſequeretur /  poſſibile
                    <lb/>
                  eſſet  eadem potentia eque cito pertranſiret me-
                    <lb/>
                  dium duplum ſicut medium ſubduplum per quod
                    <lb/>
                  tardius mouetur: dūmodo illa media eſſent oīno
                    <lb/>
                  eodem modo qualificata per eandem reſiſtentiam
                    <lb/>
                  vniformiter difformem: ſed conſequens eſt falſum:
                    <lb/>
                  igitur illud ex quo ſequitur. </s>
                  <s xml:id="N1AA87" xml:space="preserve">Sequela patet quoniã
                    <lb/>
                  ſi ex eo /  medium eſt minus potentia equalis in eo
                    <lb/>
                  tardius mouetur per conſimilem reſiſtentiam vni-
                    <lb/>
                  formiter difformē: ſequitur /  in quacun propor-
                    <lb/>
                  tione medium eſt minus in eadem proportione ea-
                    <lb/>
                  dem potentia tardius illud pertranſit reſiſtentia
                    <lb/>
                  exiſtente eadem vel conſimili. </s>
                  <s xml:id="N1AA96" xml:space="preserve">Sed falſitas conſe-
                    <lb/>
                  quentis oſtenditur / quia ſi eque cito potetia a. eſſet
                    <lb/>
                  in fine pedalis ſicut potentia b. in fine medii ſemipe­
                    <lb/>
                  dalis: (cū vtrū illoꝝ medioꝝ terminet̄̄ ad gradum
                    <lb/>
                  octauū) / ſequit̄̄ /  in illo īſtãti (cū ille poñe ſint eq̈les </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum