Alvarus, Thomas, Liber de triplici motu, 1509

Page concordance

< >
Scan Original
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
< >
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="N17509" level="4" n="7" type="chapter" type-free="capitulum">
                <p xml:id="N1779F">
                  <s xml:id="N1781B" xml:space="preserve">
                    <pb chead="Primi partis" file="0076" n="76"/>
                  poris g. ſpacium pertranſit adequate et eadem ra-
                    <lb/>
                  tione h. ſpacium in ſecunda medietate eiuſdem
                    <lb/>
                  temporis pertranſit / quod fuit probandum. </s>
                  <s xml:id="N17831" xml:space="preserve">Ma-
                    <lb/>
                  ior eſt nota / et minor probatur / quia b. potentia il-
                    <lb/>
                  lam medietatem velocitatis deperdende deper-
                    <lb/>
                  dendo adequate g. ſpacium adequate pertranſit /
                    <lb/>
                  vt patet ex hypotheſi: igitur a. potentia eandem
                    <lb/>
                  medietatem deperdendo idem g. ſpacium adequa­
                    <lb/>
                  te pertranſit: quia diuerſe potentie ſiue equales
                    <lb/>
                  ſiue inequales idem medium et eaſdem partes me-
                    <lb/>
                  dii difformis in quibus acquiritur vel deperditur
                    <lb/>
                  motus tranſeundo equalem latitudinem motus
                    <lb/>
                  acquirunt vel deperdunt / vt patet ex quarto argu-
                    <lb/>
                  mento ſexti capitis huius tractatus: igitur minor
                    <lb/>
                  vera. </s>
                  <s xml:id="N1784C" xml:space="preserve">Et eodem modo probabis ſecundam par-
                    <lb/>
                  tem concluſionis videlicet /  vbi aliqua potentia
                    <lb/>
                  etc̈. nulla minor inuariata idem medium inuaria-
                    <lb/>
                  tum tranſeundo: vniformiter continuo remittit
                    <lb/>
                  motum ſuum: quia ſi ſic: ſit illa potentia minor b.
                    <lb/>
                  et potentia que inuariata ſufficit illud c. medium
                    <lb/>
                  pertranſire continuo vniformiter remittendo mo-
                    <lb/>
                  tum ſuum ſit a. / et arguo ſic / a. pertranſeundo c. me-
                    <lb/>
                  dium vniformiter continuo remittit motum ſuum
                    <lb/>
                  et b. potentia minor idem c. medium tranſeundo
                    <lb/>
                  vniformiter continuo remittit motum ſuum: igitur
                    <lb/>
                  vbi b. potentia minor tranſeundo c. medium, vni-
                    <lb/>
                  formiter continuo remittit motum ſuum a. poten-
                    <lb/>
                  tia maior idem c. medium tranſeundo vniformi-
                    <lb/>
                  ter continuo remittit motum ſuum / quod eſt contra
                    <lb/>
                  priorem partem concluſionis. </s>
                  <s xml:id="N1786D" xml:space="preserve">Patet igitur con-
                    <lb/>
                  cluſio.
                    <note position="left" xlink:href="note-0076-01a" xlink:label="note-0076-01" xml:id="N178F9" xml:space="preserve">1. correĺ.</note>
                  </s>
                  <s xml:id="N17877" xml:space="preserve">¶ Ex hac cõcluſione facile ſequitur /  nulle
                    <lb/>
                  due potentie inequales nõ variate tranſeuntes idē
                    <lb/>
                  mediū adequate poſſunt ad nõ gradū ſuos motus
                    <lb/>
                  remittere. </s>
                  <s xml:id="N17880" xml:space="preserve">Probatur correlariū / quia ſi nõ ſit verū
                    <lb/>
                  detur oppoſitū videlicet /  aliquarū duarū poten­
                    <lb/>
                  tiarum inequaliū vtra idē mediū adequate tran-
                    <lb/>
                  ſeundo remittat motū ſuū ad nõ gradū / et arguitur
                    <lb/>
                  ſic / vtra potentiarū inequaliū idem mediū ade-
                    <lb/>
                  quate tranſeundo remittit motū ſuū ad nõ gradū /
                    <lb/>
                  igitur maiorē latitudinē motus deperdit potentia
                    <lb/>
                  maior quã minor idem mediū adequatū tranſeund-
                    <lb/>
                  do / ſed conſequens eſt falſum / et contra concluſionē
                    <lb/>
                  quarti argumenti ſexti capitis preallegatã: igitur
                    <lb/>
                  et antecedens. </s>
                  <s xml:id="N17897" xml:space="preserve">Sequela tamen probatur / qm̄ ſi ille
                    <lb/>
                  potentie ſunt inequales nõ variate: maior illarum
                    <lb/>
                  intenſiori latitudine motus mouetur ſupra eãdem
                    <lb/>
                  reſiſtentiã quã minor: et tamē vtra per te remittit
                    <lb/>
                  motum ſuū ad nõ gradū: igitur maiorē latitudineꝫ
                    <lb/>
                  motus perdit maior quã minor;: etc̈. igitur.
                    <note position="left" xlink:href="note-0076-02a" xlink:label="note-0076-02" xml:id="N178FF" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N178A9" xml:space="preserve">¶ Sequi­
                    <lb/>
                  tur ſecūdo /  ſi aliqua potētia nõ variata tranſeū-
                    <lb/>
                  do aliquod mediū nõ variatū remittit motum ſuū
                    <lb/>
                  ad nõ gradum: oīs potentia maior nõ variata re-
                    <lb/>
                  mittens in eodem medio motum ſuū remittit illum
                    <lb/>
                  ad gradū. </s>
                  <s xml:id="N178B6" xml:space="preserve">et oīs minor remittit ad nõ gradū in ali-
                    <lb/>
                  quo puncto medii intrinſeco. </s>
                  <s xml:id="N178BB" xml:space="preserve">Probat̄̄ prima pars /
                    <lb/>
                  qm̄ illa potentia maior remittit ibi motum ſuū et
                    <lb/>
                  nõ remittit ad non gradum / vt patet ex antecedenti
                    <lb/>
                  correlario: igitur remittit illū ad gradum. </s>
                  <s xml:id="N178C4" xml:space="preserve">Secun-
                    <lb/>
                  da pars probatur / qm̄ oīs minor potētia in aliquo
                    <lb/>
                  puncto intrinſeco deueniet ad proportionem equa­
                    <lb/>
                  litatis: igitur in aliquo puncto intrinſeco remittet
                    <lb/>
                  motū ſuum ad nõ gradū. </s>
                  <s xml:id="N178CF" xml:space="preserve">Patet hoc etiã facile exē-
                    <lb/>
                  plo / quoniã ſi ſit aliqua potentia vt .4. et incipiat re­
                    <lb/>
                  mittere motum ſuum et remittat ad non gradū ali-
                    <lb/>
                  quod medium pertranſeundo: neceſſe eſt cum ipſa
                    <lb/>
                  ſit inuariata medium illud in ſuo extremo intenſio­
                    <cb chead="Capitulū ſeptimū."/>
                  ri reſiſtere vt .4. et in nullo puncto alio ãteriori tan­
                    <lb/>
                  tum reſiſtere quoniã alias iam in tali puncto motꝰ
                    <lb/>
                  ad non gradum deueniret et ſic non pertranſiret to­
                    <lb/>
                  tum: capiatur tunc alia potentia minor vt tria vel
                    <lb/>
                  vt duo (in idem redit) remittens in eodē medio mo-
                    <lb/>
                  tum ſuum / tunc manifeſtum eſt /  illa potētia ad nõ
                    <lb/>
                  gradum remittet motum ſuum cum deueneret ad
                    <lb/>
                  punctum reſiſtentie vt duo vel ad punctum reſiſten­
                    <lb/>
                  tie vt tria ſi ipſa fuerit vt tria: et tale punctū eſt pun­
                    <lb/>
                  ctum intrinſecum / vt ſatis patet quoniam extrinſe­
                    <lb/>
                  cum reſiſtit et .4. / igitur talis potentia minor ad nõ
                    <lb/>
                  gradum remittet motum ſuum in aliquo puncto in­
                    <lb/>
                  trinſeco / quod fuit probandum.</s>
                </p>
                <note position="right" xml:id="N17905" xml:space="preserve">Trigeſi-
                  <lb/>
                ma .9. cõ­
                  <lb/>
                cluſio cal­
                  <lb/>
                culatorꝪ</note>
                <p xml:id="N1790F">
                  <s xml:id="N17910" xml:space="preserve">Quinta concluſio. </s>
                  <s xml:id="N17913" xml:space="preserve">Si aliqua poten-
                    <lb/>
                  tia non variata in aliquo medio difformi non va-
                    <lb/>
                  riato vniformiter ad non gradum motum ſuum re­
                    <lb/>
                  mittit: omnis potentia maior inuariata idem me-
                    <lb/>
                  dium tranſeundo inuariatum in infinitum veloci-
                    <lb/>
                  ter remittit motum ſuum verſus extremum inten-
                    <lb/>
                  ſius eiuſdem medii deueniēdo. </s>
                  <s xml:id="N17922" xml:space="preserve">Probatur / ſit b. po-
                    <lb/>
                  tentia minor que inuariata c. medium inuariatum
                    <lb/>
                  tranſeundo: vniformiter remittit motum ſuum ad
                    <lb/>
                  non gradum continuo d. gradu velocitatis. </s>
                  <s xml:id="N1792B" xml:space="preserve">ſit a.
                    <lb/>
                  potentia maior que inuariata ipſum c. medium in­
                    <lb/>
                  uariatum totaliter pertranſeat remittendo motuꝫ
                    <lb/>
                  ſuuꝫ procedendo continuo per eandem lineam per
                    <lb/>
                  quam ꝓcedit b. </s>
                  <s xml:id="N17936" xml:space="preserve">(Semper enim hoc modo intelligo
                    <lb/>
                  et ſi propter breuiloquium id non explicem) / tunc di­
                    <lb/>
                  co /  a. potentia maior verſus extremum intenſius
                    <lb/>
                  c. medii deueniendo in infinitum velociter remittit
                    <lb/>
                  motum ſuum. </s>
                  <s xml:id="N17941" xml:space="preserve">Quod ſic probatur / quia a. verſus ex­
                    <lb/>
                  tremum intenſius c. medii deueniendo in infinitum
                    <lb/>
                  velocius remittit motum ſuum quam b. et b. conti-
                    <lb/>
                  nuo certe velociter remittit motum ſuum puta
                    <lb/>
                  d. gradu / ergo a. in infinitum velociori gradu re-
                    <lb/>
                  mittit motum ſuum quam ſit d. gradus / et per con-
                    <lb/>
                  ſequens in infinitum velociter remittit motum ſuū /
                    <lb/>
                  quod eſt probandū. </s>
                  <s xml:id="N17952" xml:space="preserve">Conſequentie ſunt manifeſte et
                    <lb/>
                  minor ex hypotheſi patet / et maior arguitur / quia
                    <lb/>
                  a. et b. cum ſint potentie inuariate idem medium in­
                    <lb/>
                  uariatum traſeuntes eaſdem partes eiuſdem me-
                    <lb/>
                  dii tranſeundo equales latitudines motus deper-
                    <lb/>
                  dunt adequate / vt iam ſepius argutum eſt / ſed a.
                    <lb/>
                  verſus extremū ītēſiꝰ c. medii deueniendo in infini­
                    <lb/>
                  tum velocius pertranſibit aliquam partem ipſius
                    <lb/>
                  c: medii quam b. pertranſibit eandem / ergo a. in in-
                    <lb/>
                  finitum velocius remittet motum ſuum verſus ex-
                    <lb/>
                  tremum intenſius c. medii deueniendo quã b. / quod
                    <lb/>
                  fuit probandum. </s>
                  <s xml:id="N1796B" xml:space="preserve">Patet hec conſequentia / quoniã
                    <lb/>
                  ita velociter ſicut a. pertranſit aliquam partem c.
                    <lb/>
                  medii ita velociter remittit motum ſuū deperden-
                    <lb/>
                  dum in illa parte medii et b. ſimiliter: ſed in infini-
                    <lb/>
                  tum velocius pertranſibit a. aliquam partem ipſi-
                    <lb/>
                  us c. medii quam b. pertranſibit eandem: igitur in
                    <lb/>
                  infinitum velocius a. remittet motum ſuum verſus
                    <lb/>
                  extremum intenſius c. medii deueniendo quam b.
                    <lb/>
                  </s>
                  <s xml:id="N1797D" xml:space="preserve">Sed iam probatur minor / et capio proportionem /
                    <lb/>
                  quam habet a. ad extremum intenſius c. medii que
                    <lb/>
                  ſit f. / et arguo ſic: continuo a. mouebitur a propor-
                    <lb/>
                  tione f. vĺ a. maiori: et b. ab īfinite modica propor-
                    <lb/>
                  tione mouebitur tranſeundo illud medium: ergo
                    <lb/>
                  ab in infinitū maiori proportione tranſeundo ali-
                    <lb/>
                  quam partem c. medii mouebitur a. quam b. ean-
                    <lb/>
                  dem partem tranſeundo: igitur a. verſus extremū
                    <lb/>
                  intenſiꝰ c. medii deueniēdo in īfinitū velociꝰ ꝑtrã-
                    <lb/>
                  ſibit aliquã partē eiuſdē c. medii quã b. ꝑtranſibit </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum