Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N1C8AF" level="3" n="2" type="other" type-free="tractatus">
              <div xml:id="N1DD6A" level="4" n="3" type="chapter" type-free="capitulum">
                <p xml:id="N1DEDF">
                  <s xml:id="N1DEED" xml:space="preserve">
                    <pb chead="Secundi tractatus" file="0143" n="143"/>
                  in eodem tempore. </s>
                  <s xml:id="N1DF05" xml:space="preserve">Modo non ſit ſic in propoſito:</s>
                </p>
                <p xml:id="N1DF08">
                  <s xml:id="N1DF09" xml:space="preserve">Sed contra / quia tunc ſequeretur /  ſi
                    <lb/>
                  motus vt .4. vel aliquis alter intendatur ad ſuum
                    <lb/>
                  duplum vniformiter / et alter motus ei equalis remi­
                    <lb/>
                  tatur in eadem hora ad non gradum ſiue ad quietē /
                    <lb/>
                  tunc ille qui remittitur in infinitum velocius remit­
                    <lb/>
                  titur quam alter qui intenditur intendatur </s>
                  <s xml:id="N1DF16" xml:space="preserve">Quod
                    <lb/>
                  tamen eſt falſum cum tantam latitudinem vnus ac­
                    <lb/>
                  quirat ſicut alter deperdat.</s>
                </p>
                <note position="left" xml:id="N1DF1D" xml:space="preserve">dicitur.</note>
                <p xml:id="N1DF21">
                  <s xml:id="N1DF22" xml:space="preserve">¶ Dices et bene diſtinguendo illatum aut  ī infini­
                    <lb/>
                  tum velocius remittatur in eodem tempore veloci-
                    <lb/>
                  tate geometrica: et ſic conceditur aut arithmetica: et
                    <lb/>
                  ſic negatur.</s>
                </p>
                <p xml:id="N1DF2B">
                  <s xml:id="N1DF2C" xml:space="preserve">Sed cõtra quia tunc ſequeretur /  nõ
                    <lb/>
                  eſſet poſſibile /  ita velociter geometrice intendere­
                    <lb/>
                  tur vnus motus in tempore finito vniformiter ſicut
                    <lb/>
                  motus ei eq̈lis remitteretur vniformiter ad nõ gra­
                    <lb/>
                  dū in eodē tꝑe: ſed conſequens videtur falſum (cum
                    <lb/>
                  equalem latitudineꝫ vnus motus deperdat ſicut al­
                    <lb/>
                  ter acquirit) / igitur illud ex quo ſequitur. </s>
                  <s xml:id="N1DF3B" xml:space="preserve">Sequela
                    <lb/>
                  tamen probatur quoniam / vt patet ex reſponſione
                    <lb/>
                  motus qui remittitur ad non gradum infinitam ꝓ-
                    <lb/>
                  portionem deperdit, et motus qui intenditur ſoluꝫ
                    <lb/>
                  finitam: igitur non eque velociter geometrice vnus
                    <lb/>
                  motus intenditur ſicut alter ei equalis remittitur ī
                    <lb/>
                  eodem tempore.
                    <note position="left" xlink:href="note-0143-01a" xlink:label="note-0143-01" xml:id="N1DFF6" xml:space="preserve">2. confir.</note>
                  </s>
                  <s xml:id="N1DF4F" xml:space="preserve">¶ Confirmatur ſecundo / quo­
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                  niam ſi motus vniformiter difformis correſponde­
                    <lb/>
                  ret ſuo gradui medio ſequeretur / quando duo mo-
                    <lb/>
                  tus equales vniformiter difformes remitterentur ī
                    <lb/>
                  hora vnus ī duplo velocius altero ille qui tardiꝰ re­
                    <lb/>
                  mittitur / quando eſt remiſſus ad ſubduplum: alter
                    <lb/>
                  eſſet remiſſus ad ſubquadruplum et non ad quieteꝫ
                    <lb/>
                  ſiue ad non gradum: ſed conſequens falſum / vt pa-
                    <lb/>
                  tet intuenti: igitur illud ex quo ſequitur: </s>
                  <s xml:id="N1DF62" xml:space="preserve">Sequela
                    <lb/>
                  tamen probatur quoniam / ſi in eodem tempore vnꝰ
                    <lb/>
                  continuo in duplo velocius altero remittitur ſeq̄re­
                    <lb/>
                  tur / quando vnus deperdit proportionem duplam
                    <lb/>
                  alter deperdit proportionem quadruplam / et in tē-
                    <lb/>
                  pore quo vnus quadruplam alter ſexdecuplaꝫ que
                    <lb/>
                  eſt dupla ad quadruplam. </s>
                  <s xml:id="N1DF71" xml:space="preserve">vt patet ex ſecunda par­
                    <lb/>
                  te capite ſexto.
                    <note position="left" xlink:href="note-0143-02a" xlink:label="note-0143-02" xml:id="N1DFFC" xml:space="preserve">.3. confir.</note>
                  </s>
                  <s xml:id="N1DF7B" xml:space="preserve">¶ Confirmatur tertio / qm̄ ſi mo-
                    <lb/>
                  tus vniformiter difformis correſponderet gradui
                    <lb/>
                  medio ſequeretur /  ſi eſſent duo motus vniformi-
                    <lb/>
                  ter difformes equales incipientes ab eodem gra-
                    <lb/>
                  du terminati ad eundem vel ad non gradum et vnꝰ
                    <lb/>
                  illorum puta a. in duplo velocius continuo intende­
                    <lb/>
                  retur quam alter puta b. / et talis intenſio duraret ī
                    <lb/>
                  infinitum /  aliquando a. eſſet motus duplus ad b. /
                    <lb/>
                  ſed conſequens eſt falſuꝫ: igitur illud ex quo ſequit̄̄
                    <lb/>
                  </s>
                  <s xml:id="N1DF8F" xml:space="preserve">Seq̄la probatur / q2 qñcū b. acq̇rit aliquã latitudi­
                    <lb/>
                  nē a. acq̇rit duplã: et ſꝑ in duplo velociꝰ a. acq̇ret ali­
                    <lb/>
                  quem gradum / quam eundem acquirit b. / et hec inten­
                    <lb/>
                  ſio procedit in infinitum: igitur aliquãdo a. erit mo­
                    <lb/>
                  tus duplus ad b. </s>
                  <s xml:id="N1DF9A" xml:space="preserve">Probatur hec conſequentia / quo­
                    <lb/>
                  niam per infinitam latitudinem excedet latitudo ac­
                    <lb/>
                  quiſita ipſi a. latitudinem acquiſitam ipſi b. / igitur
                    <lb/>
                  aliquando totus motus a. erit duplus ad totuꝫ mo­
                    <lb/>
                  tuꝫ b. </s>
                  <s xml:id="N1DFA5" xml:space="preserve">Cõſequētia apparet nota et arguit̄̄ añs / q2 ī in­
                    <lb/>
                  finitum maior erit latitudo acquiſita ipſi a. quã la-
                    <lb/>
                  titudo acquiſita ipſi b. / quia per infinitos gradꝰ la-
                    <lb/>
                  titudo acquiſita ipſi a. excedet latitudinem ipſiꝰ b. /
                    <lb/>
                  igitur ꝑ infinitã latitudinē excedit latitudo acquiſi­
                    <lb/>
                  ta ipſi a. latitudinē acquiſitã ipſi b. </s>
                  <s xml:id="N1DFB2" xml:space="preserve">Probat̄̄ ante­
                    <lb/>
                  cedens / quoniam latitudo acquiſita ipſi a. cum ſem­
                    <lb/>
                  per erit dupla ad latitudinem acquiſitam ipſi b. / qñ
                    <lb/>
                  erit vt .4. excedit latitudineꝫ ipſius b, per duos gra­
                    <lb/>
                  dus et quando vt .8. per .4. et quando vt centum per
                    <lb/>
                  50. et quando vt .1000. per .500. / et ſic in infinitum: igi­
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                  tur per infinitos gradus latitudo acquiſita ipſi a.
                    <lb/>
                  excedet latitudinem acquiſitam ipſi b. / quod fuit ꝓ­
                    <lb/>
                  bandum. </s>
                  <s xml:id="N1DFC6" xml:space="preserve">Sed iam probatur falſitas conſequentis
                    <lb/>
                  quoniam / ſi aliquando totus motus a. ad totuꝫ mo­
                    <lb/>
                  tum b. erit duplus. </s>
                  <s xml:id="N1DFCD" xml:space="preserve">ſignetur illud inſtans / in quo ita
                    <lb/>
                  erit / et arguitur ſic / totus motus a. ad totum motum
                    <lb/>
                  b. eſt duplus / ergo ſi vna pars ipſius a. eſt dupla ad
                    <lb/>
                  vnam partem b. totum reſiduum de a. eſt dupluꝫ ad
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                  reſiduum de b. / ſed conſequens eſt falſum: igitur illḋ
                    <lb/>
                  ex quo ſequitur. </s>
                  <s xml:id="N1DFDA" xml:space="preserve">Falſitas conſequētis probatur / q2
                    <lb/>
                  in illo inſtanti totum acquiſitum a. eſt duplū ad to­
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                  tum acquiſitum b. / et tamen reſidua pars de a. non
                    <lb/>
                  eſt dupla ad reſiduam partem de b. / ſed ille partes
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                  ſunt equales ſicut erant in principio: et ſic ſequitur /
                    <lb/>
                   quando vna pars a. eſt dupla ad vnam partem
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                  b. totum reſiduum a. non eſt duplum ad totum reſi-
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                  duum b. / et ſic a. non eſt duplum ad b. </s>
                  <s xml:id="N1DFEB" xml:space="preserve">Patet hec con­
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                  ſequentia ex ſeptimo correlario q̈rte concluſionis
                    <lb/>
                  octaui capitis ſecunde partis.</s>
                </p>
                <p xml:id="N1E002">
                  <s xml:id="N1E003" xml:space="preserve">¶ Et confirmatur quarto et vltimo / quia ſi oīs mo-
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                  tus vniformiter difformis commenſurari hꝫ gradu
                    <lb/>
                  medio: vel igitur in quolibet tali motu ille gradus
                    <lb/>
                  medius eſt ſubduplus adequate ad intenſius extre­
                    <lb/>
                  mum talis motus vel maior ſubduplo: vel minor:
                    <lb/>
                  nullum iſtorum eſt dicendum igitur. </s>
                  <s xml:id="N1E010" xml:space="preserve">Probatur mi­
                    <lb/>
                  nor / quia capto motu vniformiter difformi ab octa­
                    <lb/>
                  uo vſ ad quartum gradus medius eius eſt vt .6. /
                    <lb/>
                  et talis eſt dumtaxat ſubſexquitertius ad gradum ī­
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                  tenſiorem: et non ſubduplus: igitur non in omni mo­
                    <lb/>
                  tu vniformiter difformi gradus medius eſt ſubdu-
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                  plus ad gradum intenſiorem. </s>
                  <s xml:id="N1E01F" xml:space="preserve">Item capto motu
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                  vniformiter difformi ab octauo vſ ad non gradū
                    <lb/>
                  medius gradus eius eſt ſubduplus ad extremū in-
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                  tenſius: igitur non in omni motu vniformiter dif-
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                  formi gradus medius eſt maior quam ſubduplus.
                    <lb/>
                  </s>
                  <s xml:id="N1E02B" xml:space="preserve">Item nullus gradus medius alicuius motꝰ vnifor-
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                  miter difformis eſt minor quam ſubduplus ad ex-
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                  tremum intenſius / vt facile eſt intueri: igitur illa mi­
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                  nor vera.
                    <note position="right" xlink:href="note-0143-03a" xlink:label="note-0143-03" xml:id="N1E056" xml:space="preserve">dicitur.</note>
                  </s>
                  <s xml:id="N1E039" xml:space="preserve">¶ Dices ſicut dicendum eſt negando illaꝫ
                    <lb/>
                  minorem: immo in aliquibus motibus vniformiter
                    <lb/>
                  difformibus gradus medius eſt preciſe ſubduplus
                    <lb/>
                  ad gradum ſummū eiuſdem motus / vt patet in om­
                    <lb/>
                  ni motu vniformiter difformi terminato ad nõ gra­
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                  dum. </s>
                  <s xml:id="N1E046" xml:space="preserve">In omni motu vero vniformiter difformi ter-
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                  minato vtrim ad gradum. </s>
                  <s xml:id="N1E04B" xml:space="preserve">gradus medius eſt ma­
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                  ior quam ſubduplus ad extremum intenſius / vt po­
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                  ſtea oſtenditur.</s>
                </p>
                <p xml:id="N1E05C">
                  <s xml:id="N1E05D" xml:space="preserve">Sed contra / quia tunc ſequeretur / 
                    <lb/>
                  aliquando gradus medius alicuius motus vnifor­
                    <lb/>
                  miter difformis vtrim terminati ad gradum eēt
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                  ſubſexquitertius ad gradum ſummum: aliquando
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                  ſubſexquialterius: aliquando ſubſexquiquartus:
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                  et ſic in infinitum. </s>
                  <s xml:id="N1E06A" xml:space="preserve">Quod ſi concedis ſicut conceden­
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                  dum eſt ſequitur /  nulla poteſt inueniri certa regu­
                    <lb/>
                  la et vniuerſalis ad ſciendum in quolibet motu vni­
                    <lb/>
                  formiter difformi quanto plus pertranſitur per to­
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                  tum motum in medietate intenſiori quam in medie­
                    <lb/>
                  tate remiſſiori: quod videtur ſatis inconueniens.</s>
                </p>
                <p xml:id="N1E077">
                  <s xml:id="N1E078" xml:space="preserve">Secundo principaliter tangendo ve­
                    <lb/>
                  locitatem, motus difformiṫ difformis cuius nulla
                    <lb/>
                  pars eſt vniformis comparando ipſum ad vnifor­
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                  miter difformem: arguitur ſic. </s>
                  <s xml:id="N1E081" xml:space="preserve">quia ſi prima pars et
                    <lb/>
                  ſecunda queſtionis eſſent vere: ſequeretur /  aliqui
                    <lb/>
                  duo motus ſunt modo equales: et in tempore equa-
                    <lb/>
                  li equales latitudines deperdent ſucceſſiue ita  in
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                  fine illius temporis erunt equales: et tamen ꝑ vnuꝫ
                    <lb/>
                  illorum motuum maius ſpacium continuo pertrã-
                    <lb/>
                  ſitur quã per alium: hoc videtur īpoſſibile: igitur </s>
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