Alvarus, Thomas, Liber de triplici motu, 1509

Page concordance

< >
Scan Original
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
< >
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="N1DD6A" level="4" n="3" type="chapter" type-free="capitulum">
                <p xml:id="N1EF9B">
                  <s xml:id="N1F02C" xml:space="preserve">
                    <pb chead="De motu locali quo ad effectum tempore difformi." file="0154" n="154"/>
                  tet de ſe: et vltra eſt magis quã medietas: ergo totū
                    <lb/>
                  reſiduuꝫ (quod eſt ꝓportio d. ad b) eſt minus illa ꝓ­
                    <lb/>
                  portione b. ad c. : et illud reſiduum eſt proportio du­
                    <lb/>
                  pla: ergo illa proportio b. ad c. eſt maior ꝓportio
                    <lb/>
                  quã dupla a qua prouenit illa velocitas a. </s>
                  <s xml:id="N1F03C" xml:space="preserve">Et ſic ha­
                    <lb/>
                  betur /  velocitas a. prouenit a maiore ꝓportione
                    <lb/>
                  quã dupla / quod a principio fuerat inueſtigandum
                    <lb/>
                  </s>
                  <s xml:id="N1F044" xml:space="preserve">Et ſic vniuerſaliter probabis propoſita proportio­
                    <lb/>
                  ne vel tripla vel ſexq̇altera vel quauis mutatis mu-
                    <lb/>
                  tandis.</s>
                </p>
                <p xml:id="N1F04B">
                  <s xml:id="N1F04C" xml:space="preserve">Secunda propoſitio. </s>
                  <s xml:id="N1F04F" xml:space="preserve">Captis duabus
                    <lb/>
                  potentiis inequalibus mouentibus eandem reſiſtē­
                    <lb/>
                  tiam: et ſcita ꝓportione inter illas potentias: ſcita
                    <lb/>
                  etiam proportione in qua maior potentia velocius
                    <lb/>
                  mouet reſiſtentiam quã minor moueat eandem: ar-
                    <lb/>
                  tificio quodam reperitur quanta eſt ꝓportio maio­
                    <lb/>
                  ris potentie ad reſiſtentiam: et etiam minoris potē­
                    <lb/>
                  tie ad eandem reſiſtentiam: </s>
                  <s xml:id="N1F060" xml:space="preserve">Exemplum / vt poſito 
                    <lb/>
                  ſortes ſit duple poñe ad platonē: et moueat tam ſor­
                    <lb/>
                  tes quã plato a. mobile: et moueat ſortes illḋ a. mo­
                    <lb/>
                  bile in ſexquialtero velocius platone / tunc volo in-
                    <lb/>
                  ueſtigare / que ꝓportio ſit ſortis ad illam reſiſtētiã
                    <lb/>
                  a. et platonis ad eandem reſiſtentiam. </s>
                  <s xml:id="N1F06D" xml:space="preserve">Quod ſic oñ­
                    <lb/>
                  ditur. </s>
                  <s xml:id="N1F072" xml:space="preserve">ſortes mouet ī ſexquialtero velocius a. reſiſtē­
                    <lb/>
                  tiam quã plato: ergo ꝓportio ſortis ad a. eſt ſexq̇-
                    <lb/>
                  altera ad ꝓportionem platonis ad idem a. et vltra
                    <lb/>
                  eſt ſexquialtera ad ꝓportionem platonis ad a. / er-
                    <lb/>
                  go ꝓportio platonis ad a. eſt due tertie ꝓportiõis
                    <lb/>
                  ſortis ad a. quia ſemper ſubſexquialterum ad ali-
                    <lb/>
                  quid eſt due tertie illius: et vltra illa ꝓportio plato­
                    <lb/>
                  nis ad a. eſt due tertie ꝓportiones ſortis ad a. / ergo
                    <lb/>
                  totum reſiduum eſt vna tertia totius ꝓportiõis ſor­
                    <lb/>
                  tis ad a. / vt patet de ſe: et totum reſiduum eſt ꝓpor-
                    <lb/>
                  tio ſortis ad platonem dupla nota / vt poſitum eſt /
                    <lb/>
                  quia totalis ꝓportio ſortis ad a. componitur ex ꝓ­
                    <lb/>
                  portiõe ſortis ad platonem: et platonis ad a. / vt pa­
                    <lb/>
                  tet ex quarto capite ſecunde partis: ergo dupla ꝓ-
                    <lb/>
                  portio eſt vna tertia ꝓportionis ſortis ad a. / et ꝑ cõ­
                    <lb/>
                  ſequens tota ꝓportio ſortis ad a. eſt tripla a ꝓpor­
                    <lb/>
                  tionem duplam que eſt vna tertia eius: et ſic eſt pro-
                    <lb/>
                  portio octupla: cum octupla ſit tripla ad duplam /
                    <lb/>
                  vt patet ex ſecunda parte octaua concluſione ſexti
                    <lb/>
                  capitis </s>
                  <s xml:id="N1F09B" xml:space="preserve">Iuter termīos em̄ ꝓportionis octuple re-
                    <lb/>
                  periuntur .4. termini cõputatis extremis ↄ̨tinuo ꝓ­
                    <lb/>
                  portionabiles ꝓportioe dupla. </s>
                  <s xml:id="N1F0A2" xml:space="preserve">Et ſic habetur / q̄ ꝓ-
                    <lb/>
                  portio ſit ſortis ad a. reſiſtentiam / quod fuit inueſti­
                    <lb/>
                  gandum: et quia ꝓportio platonis ad a. eſt due ter­
                    <lb/>
                  tie ꝓportionis ſortis ad a. que eſt octupla / cõſequēs
                    <lb/>
                  eſt  ſit quadrupla: qm̄ q̈drupla ē due tertie ꝓpor­
                    <lb/>
                  tionis octuple: et ſic habetur que ꝓportio ſit plato-
                    <lb/>
                  nis ad a. / quod a principio extitit ꝑſcrutandum</s>
                </p>
                <p xml:id="N1F0B1">
                  <s xml:id="N1F0B2" xml:space="preserve">Tertia proportio </s>
                  <s xml:id="N1F0B5" xml:space="preserve">Data quauis potē-
                    <lb/>
                  tia mouente duas reſiſtentias inequales inter quas
                    <lb/>
                  reſiſtentias eſt proportio nota: notū eſt in qua ꝓ­
                    <lb/>
                  portione velocius data potentia moueat minorem
                    <lb/>
                  ̄ maiorem: mathematica induſtria ꝓportiões po­
                    <lb/>
                  tentie ad vtram reſiſtentiam quales videlicet exi­
                    <lb/>
                  ſtant inueſtigare licebit vt ſi ſortes proiiciat in ali­
                    <lb/>
                  quo tempore lapidem a. et in eodem vel equali lapi­
                    <lb/>
                  dem b. minorem inter quos lapides eſt ꝓportio no­
                    <lb/>
                  ta gratia argumenti dupla: moueat ſortes illos
                    <lb/>
                  lapides ab eadem virtute: ſit ſcitū /  moueat ſor­
                    <lb/>
                  tes b. lapidem in triplo velocius quã a. lapidē gra­
                    <lb/>
                  tia exempli </s>
                  <s xml:id="N1F0D0" xml:space="preserve">Iam inueſtigare intendimus ingenio
                    <lb/>
                  artis mathematice / que eſt illa proportio a qua ſor­
                    <lb/>
                  tes mouet b. lapideꝫ, et que ſit illa a qua moueat a.
                    <lb/>
                  lapidem vtrum videlicet dupla: an tripla: aut aliq̈
                    <lb/>
                  alia: quia hoc ignotum eſt. </s>
                  <s xml:id="N1F0DB" xml:space="preserve">Non enim ſequtiur mo-
                    <cb chead="De motu locali quo ad effectum tempore difformi."/>
                  uet in triplo velocius b. quã a. / ergo a ꝓportione tri­
                    <lb/>
                  pla mouet b. </s>
                  <s xml:id="N1F0E3" xml:space="preserve">Quando enim aliquid mouet aliud a
                    <lb/>
                  ꝓportione dupla adhuc dabitur aliquid quod ī tri­
                    <lb/>
                  plo tardius in eodem tempore ab eodem mouetur:
                    <lb/>
                  vt ſuperius dictum eſt. </s>
                  <s xml:id="N1F0EC" xml:space="preserve">His ſuppoſitis volo inueſti­
                    <lb/>
                  gare a qua ꝓportione ſortes mouet a. lapidem: et
                    <lb/>
                  a qua b. lapidē: et arguo ſic / ſortes in triplo velociꝰ
                    <lb/>
                  mouet b. quã a. / ergo ſequitur /  ꝓpoſtio ſortis ad
                    <lb/>
                  b. lapidem eſt tripla ad ꝓportionem ſortis ad a. la­
                    <lb/>
                  pidē (ſiq̇dē ꝓportio velocitatū ꝓportionē ꝓportio-
                    <lb/>
                  nū inſequatur: et econtra) et vltra ꝓportio ſortis ad
                    <lb/>
                  b. eſt tripla ad ꝓportionem ſortis ad a. / igitur pro-
                    <lb/>
                  portio ſortis ad a. eſt vna tertia totius ꝓportionis
                    <lb/>
                  ſortis ad b. et ꝓportio ſortis ad b. componitur ex ꝓ­
                    <lb/>
                  portione ſortis ad a. et a. ad b. adequate / vt patet in­
                    <lb/>
                  telligenti quartum caput ſecunde partis: et ꝓpor-
                    <lb/>
                  tio ſortis ad a. eſt vna tertia / vt dictum eſt: ergo reſi­
                    <lb/>
                  duum puta ꝓportio a. ad b. ſunt due tertie: et illa ꝓ-
                    <lb/>
                  portio a. ad b. eſt dupla nota / vt poſitum eſt. </s>
                  <s xml:id="N1F10B" xml:space="preserve">ergo ꝓ­
                    <lb/>
                  portio dupla eſt dupla ad ꝓportionem ſortis ad a.
                    <lb/>
                  que eſt vna tertia. et dupla due tertie proportionis
                    <lb/>
                  ſortis ad b. </s>
                  <s xml:id="N1F114" xml:space="preserve">Modo duarū tertiarum ad vnam ter-
                    <lb/>
                  tiam eſt ꝓportio dupla: </s>
                  <s xml:id="N1F119" xml:space="preserve">Et ſic habetur /  illa ꝓpor­
                    <lb/>
                  tio ſortis ad a. qua ſortes mouet a. lapidem eſt ſub­
                    <lb/>
                  dupla ad duplam. </s>
                  <s xml:id="N1F120" xml:space="preserve">Eſt enim medietas duple / quod
                    <lb/>
                  erat inquirendum. </s>
                  <s xml:id="N1F125" xml:space="preserve">Et ſic ſimiliter habetur /  illa ꝓ­
                    <lb/>
                  portio ſortis ad b. id eſt qua ſortes mouet b. lapidē
                    <lb/>
                  eſt ſexquialtera ad duplam. </s>
                  <s xml:id="N1F12C" xml:space="preserve">componitur ex dupla
                    <lb/>
                  a. ad b. et medietate duple ſortis ad a. / quod fuit al-
                    <lb/>
                  terum inueſtigandum.
                    <note position="right" xlink:href="note-0154-01a" xlink:label="note-0154-01" xml:id="N1F198" xml:space="preserve">.1. correl.</note>
                  </s>
                  <s xml:id="N1F138" xml:space="preserve">¶ Ex hac ꝓpoſitione ſequi-
                    <lb/>
                  tur /  ſi ſortes moueat b. lapidem per tantum ſpa-
                    <lb/>
                  cium quantus eſt diameter quadrati: et a. lapidem
                    <lb/>
                  per tantum ſpacium quanta eſt coſta eiuſdem qua-
                    <lb/>
                  drati: tunc ꝓportio ſortis ad a. lapidem id eſt a qua
                    <lb/>
                  mouet a. lapidem eſt pluſ̄ dupla ad ꝓportionem
                    <lb/>
                  duplam: et proportio qua ſortes mouet b. lapidem
                    <lb/>
                  eſt pluſ̄ tripla ad duplam. </s>
                  <s xml:id="N1F149" xml:space="preserve">Quod ſic ꝓbatur: q2
                    <lb/>
                  tota ꝓportio ſortis ad b. ſe habet ad ꝓportionem
                    <lb/>
                  ſortis ad a. ſicut diameter ſe habet ad coſtam: ergo
                    <lb/>
                  ꝓportio ſortis ad a. eſt ſicut coſta. </s>
                  <s xml:id="N1F152" xml:space="preserve">et ꝓportio ſortis
                    <lb/>
                  ad b. eſt ſicut diameter et ſic ꝓportio a. ad b. eſt ſicut
                    <lb/>
                  exceſſus diametri ad coſtam: ſed ille exceſſus eſt mi­
                    <lb/>
                  nor quã ſubduplus ad coſtam: quia coſta cõtinet il-
                    <lb/>
                  lum exceſſum pluſ̄ bis / vt patet ex ſecunda cõcluſio­
                    <lb/>
                  ne et eiuſdem ꝓbatione quarti capitis prime ꝑtis:
                    <lb/>
                  et illa ꝓportio a. ad b. que eſt ſicut exceſſus diame-
                    <lb/>
                  tri ad coſtam eſt ꝓportio dupla / vt poſitum eſt: et eſt
                    <lb/>
                  minus quã ſubdupla ad proportioneꝫ ſortis ad a. /
                    <lb/>
                  vt dictum eſt: igitur ꝓportio ſortis ad a. eſt maior
                    <lb/>
                  quam dupla / quod fuit vnum ꝓbandum. </s>
                  <s xml:id="N1F169" xml:space="preserve">Sed  ꝓ-
                    <lb/>
                  portio ſortis ad b. ſit maior quã tripla ad duplam /
                    <lb/>
                  iam pene argutum eſt. </s>
                  <s xml:id="N1F170" xml:space="preserve">Componitur enim illa ex ꝓ-
                    <lb/>
                  portione ſortis ad a. que eſt pluſ̄ due duple vt ꝓ-
                    <lb/>
                  batum eſt: et ex ꝓportione a. ad b. dupla: ergo cõpo­
                    <lb/>
                  nitur ex vna dupla: et duabus maioribus dupla a­
                    <lb/>
                  dequate: et ſic cõtinet pluſ̄ tres duplas: conſeq̄ns
                    <lb/>
                  eſt igitur vt ſit illa proportio ſortis ad b. maior ̄
                    <lb/>
                  tripla ad duplam: qnod fuit alterum inducendum.
                    <lb/>
                    <note position="right" xlink:href="note-0154-02a" xlink:label="note-0154-02" xml:id="N1F19E" xml:space="preserve">2. correl.</note>
                  </s>
                  <s xml:id="N1F186" xml:space="preserve">¶ Ex quo ſequitur /  illa ꝓportio ſortis ad b. ē pluſ­
                    <lb/>
                  ̄ octupla. </s>
                  <s xml:id="N1F18B" xml:space="preserve">Eſt enim octupla adequate tripla ad du­
                    <lb/>
                  plam / vt patet ex octaua concluſione ſexti capitis ſe­
                    <lb/>
                  cunde partis: et illa ſortis ad b. maior quam tripla
                    <lb/>
                  ad duplam / vt ꝓbatum eſt: igitur ꝓpoſitum.</s>
                </p>
                <p xml:id="N1F1A4">
                  <s xml:id="N1F1A5" xml:space="preserve">Quarta propoſitio </s>
                  <s xml:id="N1F1A8" xml:space="preserve">Data quauis velo­
                    <lb/>
                  citate: quauiſ ſignata ꝓportione: arithmetico ap­
                    <lb/>
                  paratu an ꝓportio a qua ꝓuenit illa velocitas pro­
                    <lb/>
                  portioni ſignate cõmenſurabilis exiſtat an nõ ope­
                    <lb/>
                  re preciū erit īueſtigare. </s>
                  <s xml:id="N1F1B3" xml:space="preserve">vt eſto /  ſortes moueat a.
                    <lb/>
                  lapidem velocitate b. </s>
                  <s xml:id="N1F1B8" xml:space="preserve">et ignotum ſit a qua propor- </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum