Alvarus, Thomas, Liber de triplici motu, 1509

Page concordance

< >
Scan Original
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
< >
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="N17BB3" level="4" n="8" type="chapter" type-free="capitulum">
                <p xml:id="N17BD1">
                  <s xml:id="N17C82" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0079" n="79"/>
                  uetur vniformiter cõtinuo intendēte motū ſuū. </s>
                  <s xml:id="N17C8E" xml:space="preserve">Et
                    <lb/>
                  conſimiliter et ex eiſdem principiis ſecundam par­
                    <lb/>
                  tem deduces.</s>
                </p>
                <p xml:id="N17C95">
                  <s xml:id="N17C96" xml:space="preserve">Secūda ſuppoſitio. </s>
                  <s xml:id="N17C99" xml:space="preserve">Si aliqua potē-
                    <lb/>
                  tia nõ variata tranſeūdo mediū nõ variatu vnifor­
                    <lb/>
                  miter cõtinuo remittit motū ſuū: maiorē latitudi-
                    <lb/>
                  nem motus deperdit tranſeundo partē magis re-
                    <lb/>
                  ſiſtentē quã ſibi equalē minus reſiſtentē. </s>
                  <s xml:id="N17CA4" xml:space="preserve">Patet / q2
                    <lb/>
                  diutius inmoratur tranſeundo partē magis reſi-
                    <lb/>
                  ſtentē quã ei equalē minus reſiſtentē: ergo ſi vnifor­
                    <lb/>
                  miter remittat motū ſuū maiorē latitudinē motꝰ
                    <lb/>
                  deperdit tranſeundo partē magis reſiſtentē quaꝫ
                    <lb/>
                  ſibi equalē minꝰ reſiſtentē: igitur ſuppoſitio vera.</s>
                </p>
                <p xml:id="N17CB1">
                  <s xml:id="N17CB2" xml:space="preserve">Tertia ſuppoſitio. </s>
                  <s xml:id="N17CB5" xml:space="preserve">Alicuiꝰ medii ſuꝑ
                    <lb/>
                  quo īuariato aliqua potentia īuariata mouēs cõ­
                    <lb/>
                  tinuo vniformiter remittit motū ſuū duabus par­
                    <lb/>
                  tibus īequalibus, ſignatis quarū vtrã in aliquo
                    <lb/>
                  tēpore adequato adequate pertranſit: et quãlibet
                    <lb/>
                  partē exceſſus per quē maior pars excedit minorē
                    <lb/>
                  illa potentia tranſeundo, cū maiori reſiſtentia cõ-
                    <lb/>
                  tinuo mouetur quã quãlibet partē equalē minoris
                    <lb/>
                  tranſeundo: maior eſt ꝓportio velocitatis deper-
                    <lb/>
                  dite a tali potentia ſuper maiori parte mouendo
                    <lb/>
                  ad velocitatē deperditã mouendo ſuper parte mi­
                    <lb/>
                  nori quã ſit taliū partiū ꝓportio: </s>
                  <s xml:id="N17CCE" xml:space="preserve">Exemplū / vt ſi a.
                    <lb/>
                  potentia ſuꝑ c. mediū mouēs vniformiter remittit
                    <lb/>
                  motū ſuū: ſignatis prima quarta c. medii et ſecun-
                    <lb/>
                  da medietate eiuſdē c. medii quaꝝ vtrã in aliquo
                    <lb/>
                  tēpore adequate peranſit: maior eſt ꝓportio quaꝫ
                    <lb/>
                  dupla (que eſt inter partes ſignatas) velocitatis
                    <lb/>
                  deperdite ab a. potentia mouēdo ſuꝑ ſecūda me-
                    <lb/>
                  dietate ad velocitatē deperditã in prima quarta
                    <lb/>
                  eiuſdē medii mouendo. </s>
                  <s xml:id="N17CE1" xml:space="preserve">Probatur / et ſit medium c.
                    <lb/>
                  ſuper quo īuariato vniformiter continuo a. poten­
                    <lb/>
                  tia remittit motū ſuū cuius vna pars minor ſit d.
                    <lb/>
                  et ſecūda maior ſit .ef. excedat .ef. ipſum d. per f.
                    <lb/>
                  partē: et quamlibet partē ipſius f. minorē d. tran-
                    <lb/>
                  ſeundo moueatur a. cū maiori reſiſtentia quã mo-
                    <lb/>
                  uetur quãlibet ſibi equalē tranſeundo cū ſuper d.
                    <lb/>
                  parte mouetur: et vtram illarū partiū puta d. et
                    <lb/>
                  ef. in aliquo tēpore adequato adequate pertrãſit:
                    <lb/>
                  ita  in tēpore adequato in quo pertrãſit d. nichil
                    <lb/>
                  pertrãſeat ſuꝑficiale quin ſit d. aut pars illius: et
                    <lb/>
                  in tēpore in quo adequate pertrãſit .ef. nichil ſuꝑ-
                    <lb/>
                  ficiale pertranſeat quin ſit .ef. aut pars eius (ſeclu­
                    <lb/>
                  do multas alias cauillationes que nichil ꝓpoſito
                    <lb/>
                  conducūt) et ſit inter .ef. et d. ꝓportio g. moueatur
                    <lb/>
                  potentia a. pertranſeundo e. partē cū equali reſi-
                    <lb/>
                  ſtentia adequate ſicut tranſeundo d. partē vel cum
                    <lb/>
                  maiori / vt oportet / tūc dico /  velocitas deperdita
                    <lb/>
                  ab a. tranſeundo partē .ef. ſe habet in maiori pro-
                    <lb/>
                  portione ad velocitatē deperditã ab eadē potētia
                    <lb/>
                  a. tranſeundo d. partē quã ſit ꝓportio g. </s>
                  <s xml:id="N17D0C" xml:space="preserve">Quod ſic
                    <lb/>
                  ꝓbatur: q2 tēporis in quo adequate ꝑtranſitur .ef.
                    <lb/>
                  pars ab ipſa potētia a. ad tēpus in quo adequate
                    <lb/>
                  pertranſitur d. pars eſt maior ꝓportio quã g. / ergo
                    <lb/>
                  velocitatis deperdite in pertranſitione .ef. partis
                    <lb/>
                  adequate ad velocitatē deperditã in pertranſitiõe
                    <lb/>
                  d partis adequate eſt maior ꝓportio quã g. / quod
                    <lb/>
                  fuit ꝓbandū. </s>
                  <s xml:id="N17D1D" xml:space="preserve">Patet cõſequētia: q2 quãdo aliqua
                    <lb/>
                  latitudo in aliquo tēpore cõtinuo vniformiter re-
                    <lb/>
                  mittitur ſiue deperditur in qua ꝓportiõe ſe habēt
                    <lb/>
                  tēpora in eadē ſe habent latitudines deperdite: vt
                    <lb/>
                  facile ex diffinitione vniformis remiſſionis alicu-
                    <lb/>
                  ius latitudinis ptꝫ. </s>
                  <s xml:id="N17D2A" xml:space="preserve">Sed ꝓbatur antecedens: quia
                    <lb/>
                  velocitas qua pertranſitur adequate .ef. pars ve-
                    <lb/>
                  locitate qua pertranſitur d. pars eſt minor: ergo
                    <cb chead="Capitulum octauū."/>
                  tēporis in quo adequate pertrãſitur .ef. pars ade­
                    <lb/>
                  quate ad tēpus in quo pertrãſitur d. pars adequa­
                    <lb/>
                  te eſt maior ꝓportio quã g. </s>
                  <s xml:id="N17D38" xml:space="preserve">Conſequentia ptꝫ / q2 ſi
                    <lb/>
                  velocitas qua pertranſitur .ef. pars eſſet equalis
                    <lb/>
                  velocitati qua pertranſitur d. pars iam temporis
                    <lb/>
                  in quo pertrãſitur .ef. ad tēpus in quo pertrãſitur
                    <lb/>
                  ipſū d. eſſet g. ꝓportio que videlicet eſt inter illas
                    <lb/>
                  partes .ef. et d. / igitur ſi velocitas qua pertrãſitur
                    <lb/>
                  ef. pars adequate velocitate qua pertranſitur d.
                    <lb/>
                  eſt minor: iam ꝓportio tēporis in quo pertrãſitur
                    <lb/>
                  ef. pars adequate, ad tēpus in quo pertrãſitur d.
                    <lb/>
                  pars adequate eſt maior ꝓportio quã g. </s>
                  <s xml:id="N17D4D" xml:space="preserve">Ptꝫ hec
                    <lb/>
                  cõſequeatia / q2 maius tēpus requiritur ad pertrã-
                    <lb/>
                  ſeundū ſpaciū .ef. adequate minori velocitate quã
                    <lb/>
                  ad pertranſeundū ipſum adequate aliqua maiori
                    <lb/>
                  </s>
                  <s xml:id="N17D57" xml:space="preserve">Sed iam probatur antecedens: videlicet  veloci-
                    <lb/>
                  tas qua pertranſitur adequate .ef. pars velocita-
                    <lb/>
                  te qua pertranſitur d. pars minor, eſt minor: quia
                    <lb/>
                  velocitas qua pertranſitur e. pars ab ipſa poten-
                    <lb/>
                  tia a. eſt equalis vel minor velocitate qua adequa­
                    <lb/>
                  te pertraſitur ab eadem potentia d. pars cū ex hy-
                    <lb/>
                  potheſi in pertranſitione e. partis adequate mo-
                    <lb/>
                  ueatur a. potentia cum equali vel maiori reſiſten-
                    <lb/>
                  tia quã in pertrãſitione d. partis adequate: et ipſi
                    <lb/>
                  velocitati qua pertranſitur e. pars adequate addi­
                    <lb/>
                  tur extenſiue adhuc minor velocitas in pertranſi-
                    <lb/>
                  tione f. partis magis reſiſtentis / vt conſtat: igitur
                    <lb/>
                  tota velocitas qua pertranſitur .ef. pars adequa-
                    <lb/>
                  te eſt minor tota velocitate qua ꝑtranſitur d. pars
                    <lb/>
                  adequate: quod fuit inferendum. </s>
                  <s xml:id="N17D76" xml:space="preserve">Ptꝫ hec cõſequē-
                    <lb/>
                  tia: q2 ſi alicui latitudini intenſionis addatur ex-
                    <lb/>
                  tenſiue aliqua latitudo minoris intenſionis (cete-
                    <lb/>
                  ris paribꝰ) totalis illa latitudo aggregata ex ad­
                    <lb/>
                  dita et preexiſtenti efficitur minoris intenſionis: vt
                    <lb/>
                  ſi latitudini vniformiter difformi ab octauo vſ
                    <lb/>
                  ad quartū addatur vna latitudo minoris intēſio-
                    <lb/>
                  nis puta a. quatuor vſ ad ſecundū: aggregatum
                    <lb/>
                  ex eis efficitur minoris intenſionis: q2 preexiſtens
                    <lb/>
                  erat vt .6. aggregata vero ex preexiſienti et addita
                    <lb/>
                  eſt vt .5. </s>
                  <s xml:id="N17D8D" xml:space="preserve">Et ſic patet ſuppoſitio.</s>
                </p>
                <p xml:id="N17D90">
                  <s xml:id="N17D91" xml:space="preserve">Quarta ſuppoſitio. </s>
                  <s xml:id="N17D94" xml:space="preserve">Alicuius medii
                    <lb/>
                  ſuꝑ quo īuariato aliqua potentia īuariata mouēs
                    <lb/>
                  cõtinuo vniformiter remittit motū ſuū duabꝰ par­
                    <lb/>
                  tibus inequalibus ſignatis: quarū vtram in ali­
                    <lb/>
                  quo tēpore adequato adequate pertranſit: et quã-
                    <lb/>
                  libet partē exceſſus per quē maior pars excedit mi­
                    <lb/>
                  norē illa potentia tranſeundo cū minori reſiſtētia
                    <lb/>
                  cõtinuo mouetur, quã quãlibet partē equalē mino­
                    <lb/>
                  ris tranſeundo: velocitatis deperdite a. tali potē-
                    <lb/>
                  tia ſuꝑ maiore parte mouēdo ad velocitatē deper­
                    <lb/>
                  ditam mouendo ſuper parte minori: nec eſt talium
                    <lb/>
                  partiū ꝓportio nec maior. </s>
                  <s xml:id="N17DAD" xml:space="preserve">Probatur: et ſit mediū
                    <lb/>
                  c. ſuꝑ quo īuariato vniformiter cõtinuo a. potētia
                    <lb/>
                  inuariata remittit motum ſuū: cuius vna pars mi­
                    <lb/>
                  nor ſit d. et ſecunda maior ſit .ef. excedat .ef. ipſū
                    <lb/>
                  d. per f. partem: et quamlibet partem ipſius f. mi-
                    <lb/>
                  norem d. tranſeundo moueatur a. cum minori re-
                    <lb/>
                  ſiſtentia quam mouetur quamlibet ſibi equalem
                    <lb/>
                  tranſeūdo cum ſuper d. parte mouetur: et vtram
                    <lb/>
                  illarum partium puta d. et .ef. in aliquo tempore
                    <lb/>
                  adequato adequate pertranſit .etc̈. </s>
                  <s xml:id="N17DC2" xml:space="preserve">Et ſit inter .ef.
                    <lb/>
                  et d. proportio g. moueatur potentia a. tranſeū-
                    <lb/>
                  do c. partem cum equali reſiſtentia adequate ſicut
                    <lb/>
                  tranſeundo d. partem vel cum minori / vt oportet:
                    <lb/>
                  tunc dico /  velocitas deperdita ab a. tranſeundo
                    <lb/>
                  partem .ef. nun̄ ſe habet ad velocitatem deper-
                    <lb/>
                  ditam ab eadem potentia a. tranſeūdo d. partem
                    <lb/>
                  in g. proportione: nec in maiori.</s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum