Alvarus, Thomas, Liber de triplici motu, 1509

List of thumbnails

< >
161
161 		162
162
163
163 		164
164
165
165 		166
166
167
167 		168
168
169
169 		170
170
< >
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="N1C8AF" level="3" n="2" type="other" type-free="tractatus">
              <div xml:id="N2063E" level="4" n="4" type="chapter" type-free="capitulum">
                <p xml:id="N20650">
                  <s xml:id="N20651" xml:space="preserve">
                    <pb chead="Secundi tractatus" file="0169" n="169"/>
                  tempus velocius: iã nūc reſtat velocitateꝫ motus
                    <lb/>
                  difformis quo ad tempus et quo ad ſubiectū ſimul
                    <lb/>
                  itidē motus mixti inquiramus ſolito per more diſ­
                    <lb/>
                  putatiue ꝓcedētes. </s>
                  <s xml:id="N20663" xml:space="preserve">¶ Queritur ergo penes qḋ tan-
                    <lb/>
                  ̄ penes effectum motus difformis quo ad tempus
                    <lb/>
                  et ſubiectū ſimul necnõ motus mixti velocitas atten­
                    <lb/>
                  di habeat. </s>
                  <s xml:id="N2066C" xml:space="preserve">an vcꝫ motꝰ difformis quo ad tp̄s et ſub-
                    <lb/>
                  iectū ſimul velocitas menſurari debeat penes lineã
                    <lb/>
                  deſcriptam mediante velocitate vniformi ad quaꝫ
                    <lb/>
                  talis velocitas difformis reduci habet: et an motus
                    <lb/>
                  mixti velocitas attendi habeat penes ſpacium com­
                    <lb/>
                  poſitum ex ſpaciis ꝑtranſitis mediantibus pluri-
                    <lb/>
                  bus motibus quibus ſimul moueatur mobile motū
                    <lb/>
                  motu mixti.</s>
                </p>
                <p xml:id="N2067D">
                  <s xml:id="N2067E" xml:space="preserve">Et arguitur primo /  velocitas motꝰ
                    <lb/>
                  difformis quo ad tempus et ſubiectum ſimul nõ at­
                    <lb/>
                  tendi habeat penes lineam deſcriptam etc. </s>
                  <s xml:id="N20685" xml:space="preserve">Quia ſi
                    <lb/>
                  ſic ſequeretur /  adequata velocitas talis motꝰ mē­
                    <lb/>
                  ſuranda eēt penes reductionē ad vniformitatē: ſed
                    <lb/>
                  ↄ̨ñs eſt falſum / igitur illud ex quo ſequitur /. </s>
                  <s xml:id="N2068E" xml:space="preserve">Seque-
                    <lb/>
                  la patet et arguitur falſitas conſequentis. </s>
                  <s xml:id="N20693" xml:space="preserve">quia tūc
                    <lb/>
                  ſequeretur /  ſi vna rota inciperet moueri circulari­
                    <lb/>
                  ter cõtinuo vniformiter intendo motū ſuū a gradu
                    <lb/>
                  quarto vſ ad octauū in hora adequate: tunc talis
                    <lb/>
                  rota in tota illa hora moueretur adequate veloci-
                    <lb/>
                  tate vt ſex tranſeundo ſpaciū natū abſolui a veloci­
                    <lb/>
                  tate vt .6. in hora adeq̈te: ſed ↄ̨ñs eſt falſū / igitur il-
                    <lb/>
                  lud ex quo ſequitur /. </s>
                  <s xml:id="N206A4" xml:space="preserve">Sequela ptꝫ / q2 tota illa veloci­
                    <lb/>
                  tas q̄ (vt conſtat) eſt vniformiter difformis a quar-
                    <lb/>
                  to vſ ad octauum correſpondet motui vniformi vt
                    <lb/>
                  6. ex ſupradictis </s>
                  <s xml:id="N206AD" xml:space="preserve">Falſitas conſequentis probatur:
                    <lb/>
                  q2 tunc ſequeretur /  ſi illa rota ſic incipiens moue­
                    <lb/>
                  ri vniformiter difformiter cõtinuo vniformiter in-
                    <lb/>
                  tendendo motum ſuum a quarto vſ ad octauū cõ­
                    <lb/>
                  tinuo etiã rarefieret per illam horam: ipſa adeq̈te
                    <lb/>
                  moueretur etiã velocitate vt .6. / ſed conſequens ē fal­
                    <lb/>
                  ſum / igitur illud ex quo ſequitur /. </s>
                  <s xml:id="N206BC" xml:space="preserve">Sequela patet / q2
                    <lb/>
                  ille motus vt ponitur eſt vniformiter difformis a q̈r­
                    <lb/>
                  to vſ ad octauū: et velocitas vniformis cui correſ­
                    <lb/>
                  pondet eſt vt .6. / ergo ſi illa rota mouetur vniformi­
                    <lb/>
                  ter difformiter continuo ī illa hora: a quarto vſ
                    <lb/>
                  ad octauum: ipſa adequate in illa hora mouetur ve­
                    <lb/>
                  locitate vt .6. </s>
                  <s xml:id="N206CB" xml:space="preserve">Sed iam ꝓbo falſitatem conſequētis /
                    <lb/>
                  q2 ſi illa rota nõ rarefieret ſed ſoluꝫ moueretur mo­
                    <lb/>
                  tu circulari vniformiter difformi in illa hora a q̈r-
                    <lb/>
                  to vſ ad octauū ſine rarefactione: tūc ipſa moue-
                    <lb/>
                  ret̄̄ ī illa hora adeq̈te velocitate vt .6.: ſed addita il-
                    <lb/>
                  la rarefactiõe ipſa mouet̄̄ velociꝰ ꝙ̄ tūc: igr̄ ī illo ca­
                    <lb/>
                  ſu quo rarefit ipſa mouet̄̄ maiori velocitate ꝙ̄ ſit ve­
                    <lb/>
                  locitas vt .6. </s>
                  <s xml:id="N206DC" xml:space="preserve">Cõſequentia patet ex ſe et arguitur mi­
                    <lb/>
                  nor / q2 ex ſuperius dictis velocitas totiꝰ illius rote
                    <lb/>
                  attendi hꝫ cõtinuo penes pūctū mediū vel ſūmū. </s>
                  <s xml:id="N206E3" xml:space="preserve">ſꝫ
                    <lb/>
                  pūtus medius et ſūmꝰ in tota hora adequate ꝑ mo-
                    <lb/>
                  tū circularē quo mouet̄̄ a q̈rto vſ ad octauum per­
                    <lb/>
                  tranſit tm̄ ſpaciū ac ſi nõ rarefieret: et in ſuꝑ ꝑ motū
                    <lb/>
                  rarefactionis pertranſiuit illud ſpaciū ꝑ qḋ plꝰ di­
                    <lb/>
                  ſtat a centro illiꝰ rote ꝙ̄ diſtabat a prīcipio illiꝰ mo­
                    <lb/>
                  tus: igr̄ maius ſpaciū ꝑtrãſit qñ rarefit ꝙ̄ qñ nõ ra­
                    <lb/>
                  refit / quod fuit probandum.
                    <note position="left" xlink:href="note-0169-01a" xlink:label="note-0169-01" xml:id="N20732" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N206F9" xml:space="preserve">¶ Dices et bene ad ar-
                    <lb/>
                  gumentum concedendo ſequelam et negando falſi-
                    <lb/>
                  tatem conſequentis. </s>
                  <s xml:id="N20700" xml:space="preserve">et ad ꝓbationem concedo ſeq̄-
                    <lb/>
                  lam et nego iterum falſitatem conſequentis: et cū ꝓ-
                    <lb/>
                  batur nego ſequelam:  vlꝫ ſi illa rota ſic incipiēs
                    <lb/>
                  moueri vniformiter difformiter continuo vniformi­
                    <lb/>
                  ter intendendo motum ſuum et ipſa adequate mo-
                    <lb/>
                  ueretur etiam velocitate vt ſex. </s>
                  <s xml:id="N2070D" xml:space="preserve">Et ratio eſt / quia il-
                    <lb/>
                  la rota mouetur duplici motu per vtrū deſcriben­
                    <lb/>
                  do ſpacium: puta motu circulari vel quodammodo
                    <cb chead="Capitulum quartum"/>
                  habente naturam motus circularis (quia continuo
                    <lb/>
                  mouetur ſuper eodem axe quamuis non proprie li­
                    <lb/>
                  neam circularem deſcribat / vt ſuperius dictum eſt)
                    <lb/>
                  et inſuper mouetur punctus a cuius velocitate deb3
                    <lb/>
                  ſumi totalis velocitas ipſius rote motu rarefactio­
                    <lb/>
                  nis continuo recedendo a centro </s>
                  <s xml:id="N20721" xml:space="preserve">Quare velocitas
                    <lb/>
                  illius puncti et ex conſequenti ipſius rote debet cõ-
                    <lb/>
                  menſurari penes lineam aggregatam ex linea quã
                    <lb/>
                  deſcriberet ille punctus ſecluſa rarefactione: et pe-
                    <lb/>
                  nes lineam breuiſſimam per quam plus diſtat a cē­
                    <lb/>
                  tro ꝙ̄ ante rarefactionem diſtabat.</s>
                </p>
                <p xml:id="N20738">
                  <s xml:id="N20739" xml:space="preserve">Sed contra / quia tunc ſequeretur / 
                    <lb/>
                  ſi rota b. inciperet moueri circulariter puncto eius
                    <lb/>
                  medio a cuius velocitate (vt ſuppono) debet com-
                    <lb/>
                  menſurari totalis rote velocitas mouēte in prima
                    <lb/>
                  parte proportionali hore proportiune quadrupla
                    <lb/>
                  diuiſe velocitate vt quatuor et in ſecunda in duplo
                    <lb/>
                  velocius: et in tertia in duplo velocius ꝙ̄ in ſecun-
                    <lb/>
                  da: et ſic conſequenter: et cum hoc in qualibet parte
                    <lb/>
                  proportionali illa rota vniformiter rarefieret tali­
                    <lb/>
                  ter  ille punctus medius in qualibet parte ꝓpor-
                    <lb/>
                  tionali acquireret pedalem diſtanttam a centro ſu­
                    <lb/>
                  pra diſtantiam habitam: tunc ipſa rota in illa ho-
                    <lb/>
                  ra adequate finite deſcriberet ad lineam deſcriptam
                    <lb/>
                  in prima parte proportionali: ſecundum conſequens eſt
                    <lb/>
                  falſum / igitur illud ex quo ſequitur: </s>
                  <s xml:id="N20758" xml:space="preserve">Sequela patet
                    <lb/>
                  ex primo correlario ſeptime concluſionis preceden­
                    <lb/>
                  tis capitis: et falſitas conſeqnentis probatur quia
                    <lb/>
                  punctus ille a cuius velocitate debet ſumi veloci-
                    <lb/>
                  tas totius rote infinitam lineam deſcribit in illa
                    <lb/>
                  hora. </s>
                  <s xml:id="N20765" xml:space="preserve">ergo ſequitur /  non pertranſit in totali ho-
                    <lb/>
                  ra duplum ſpacium adequate ad ſpacium ꝑirã-
                    <lb/>
                  ſitum in prima parte proportionali: </s>
                  <s xml:id="N2076C" xml:space="preserve">Antecedens
                    <lb/>
                  probatur / quia ille punctus deſcribit lineam in illa
                    <lb/>
                  hora qua magis diſtat a centro per pedale ꝙ̄ an-
                    <lb/>
                  tea: et per bipedale ꝙ̄ antea: et per quadrupedale:
                    <lb/>
                  et ſic in infinitum: cum ex caſu in qualibet parte pro­
                    <lb/>
                  portionali deſcribit pedalem diſtantiam per rare­
                    <lb/>
                  factionem recedendo a centro. </s>
                  <s xml:id="N2077B" xml:space="preserve">igitur ille punctus ī-
                    <lb/>
                  finitam lineam deſcribit in illa hora / quod fuit pro­
                    <lb/>
                  bandum.</s>
                </p>
                <p xml:id="N20782">
                  <s xml:id="N20783" xml:space="preserve">Secundo principaliter contra ſecun­
                    <lb/>
                  dam partem queſtionis arguitur ſic. </s>
                  <s xml:id="N20788" xml:space="preserve">quia ſi illa
                    <lb/>
                  pars eſſet vera ſequeretur /  aliquod mobile in ali­
                    <lb/>
                  quo tempore continuo remitteret motum ſuum pro­
                    <lb/>
                  prium vſ ad non gradum: et tamen continuo in eo­
                    <lb/>
                  dem tempore velocius et velocius ſpacium pertran­
                    <lb/>
                  ſiret: ſed hoc videtur implicare / igitur illud ex quo
                    <lb/>
                  ſequitur. </s>
                  <s xml:id="N20797" xml:space="preserve">Sequela probatur. </s>
                  <s xml:id="N2079A" xml:space="preserve">et pono /  ſortes mo-
                    <lb/>
                  ueatur in aliqua naui verſus eandem differentiam
                    <lb/>
                  verſus quam mouetur nauis ab aliquo gradu: con­
                    <lb/>
                  tiuuo remittendo motum ſuum vſ ad non gradū
                    <lb/>
                  ipſa naue continuo intendente motum ſuum ab eo­
                    <lb/>
                  deꝫ gradu velocius ꝙ̄ ſortes remittat. </s>
                  <s xml:id="N207A7" xml:space="preserve">Quo poſito
                    <lb/>
                  ſortes continuo remittit motuꝫ ſuum et hoc vſ ad
                    <lb/>
                  non gradum: et tamen continuo in eodem tempore
                    <lb/>
                  velocius et velocius ſpacium pertranſit: quod fuit
                    <lb/>
                  probandum: igitur propoſitum. </s>
                  <s xml:id="N207B2" xml:space="preserve">Maior patet ex ca­
                    <lb/>
                  ſu et minor probatur. </s>
                  <s xml:id="N207B7" xml:space="preserve">quia continuo velocitas mix-
                    <lb/>
                  ta ſiue compoſita ex velocitate propria qua moue-
                    <lb/>
                  tur ſortes et ex velocitate ipſins nauis eſt maior et
                    <lb/>
                  maior cum continuo maiorem velocitatem acqui-
                    <lb/>
                  rit ꝙ̄ deperdit ex caſu: igitur continuo ſortes velo-
                    <lb/>
                  cius et velocius ſpacium pertranſit / quod fuit pro-
                    <lb/>
                  bandum.
                    <note position="right" xlink:href="note-0169-02a" xlink:label="note-0169-02" xml:id="N207D2" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N207CB" xml:space="preserve">¶ Dices et bene concedendo ſequelam.</s>
                </p>
                <p xml:id="N207D8">
                  <s xml:id="N207D9" xml:space="preserve">Nec hoc eſt inconueniens quando mobile mouetur
                    <lb/>
                  motu mixto ex motu proprio et motu lationis.</s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum