Alvarus, Thomas, Liber de triplici motu, 1509

Page concordance

< >
Scan Original
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
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="N1DD6A" level="4" n="3" type="chapter" type-free="capitulum">
                <p xml:id="N1F417">
                  <s xml:id="N1F493" xml:space="preserve">
                    <pb chead="Secundi tractatus" file="0157" n="157"/>
                  huius capitis. </s>
                  <s xml:id="N1F49D" xml:space="preserve">Et minor ex ſecunda parte prime
                    <lb/>
                  propoſitionis eiuſdem notabilis.</s>
                </p>
                <p xml:id="N1F4A2">
                  <s xml:id="N1F4A3" xml:space="preserve">¶ Alio modo et breuiꝰ demonſtratur concluſio ſic:
                    <lb/>
                  velocitatis totius hore ad velocitatem prime par-
                    <lb/>
                  tis proportionalis eſt proportio f. et temporis to-
                    <lb/>
                  tius hore quod eſt maius ad tempus prime partis
                    <lb/>
                  proportionalis eſt etiam f. proportio: ergo ſpacii
                    <lb/>
                  pertranſiti in tota hora ad ſpacium pertranſitum
                    <lb/>
                  in prima parte proportionali eſt proportio com-
                    <lb/>
                  poſita ex duplici proportione f. / et per conſequens
                    <lb/>
                  ſpacium pertranſitum in tota hora ad ſpaciū per­
                    <lb/>
                  tranſitū in prima parte proportionali eſt propor-
                    <lb/>
                  tio dupla ad proportionem velocitatum que eſt f.
                    <lb/>
                  </s>
                  <s xml:id="N1F4BB" xml:space="preserve">Patet tamen conſequentia ex tertia propoſitione
                    <lb/>
                  ſecundi notabilis huius capitis.</s>
                </p>
                <note position="left" xml:id="N1F4C0" xml:space="preserve">1. correĺ.</note>
                <p xml:id="N1F4C4">
                  <s xml:id="N1F4C5" xml:space="preserve">¶ Ex his concluſionibus ſequitur primo:  diuiſa
                    <lb/>
                  hora per partes proportionales proportione mul­
                    <lb/>
                  tiplici, ſiue dupla, ſiue tripla, ſiue quadrupla, ſiue
                    <lb/>
                  quauis alia multiplici: et in prima parte proporti-
                    <lb/>
                  onali aliquod mobile moueatur aliquantulum, et
                    <lb/>
                  ī ſcḋa in duplo maiori velocitate ꝙ̄ in ṗma: et ī ṫcia
                    <lb/>
                  in triplo ꝙ̄ in prima / vt precedentis theorematis
                    <lb/>
                  caſus oſtendit: totius illius velocitatis ad velo-
                    <lb/>
                  citatem prime partis proportionalis erit propor-
                    <lb/>
                  tio dupla, ſi diuiſio facta fuerit proportiõe dupla:
                    <lb/>
                  et ſexquialtera ſi tripla: et ſexquitertia ſi quadru-
                    <lb/>
                  pla: et ſic in infinitum aſcendendo ſeriatim per ſpe-
                    <lb/>
                  cies proportiõis ſuperparticularis et multiplicis.
                    <lb/>
                  </s>
                  <s xml:id="N1F4E1" xml:space="preserve">et ſpacli pertranſiti in tota hora ad ſpacium per-
                    <lb/>
                  tranſituꝫ in prima parte eſt proportio quadrupla
                    <lb/>
                  que eſt dupla ad duplam et hoc ſi fiat diuiſio par-
                    <lb/>
                  tium proportionalium proportione dupla: ſi vero
                    <lb/>
                  fiat proportione tripla: ſpacii pertranſiti in tota
                    <lb/>
                  hora ad ſpacium pertranſitum in prima parte erit
                    <lb/>
                  proportio dupla ad ſexquialteram que eſt dupla
                    <lb/>
                  ſexquiquarta: ſi vero fiat diuiſio proportione qua­
                    <lb/>
                  drupla: tunc ſpacii pertranſiti in tota hora ad ſpa­
                    <lb/>
                  cium pertranſitum in prima parte proportionali
                    <lb/>
                  erit proportio dupla ad ſexquitertiam que eſt ſu-
                    <lb/>
                  pra ſeptipartiens nonas: et ſi fiat diuiſio proporti-
                    <lb/>
                  one quintupla: tunc totius ſpacii ad ſpacium per-
                    <lb/>
                  tranſitū in prima parte proportionali eſt propor-
                    <lb/>
                  tio dupla ad proportioneꝫ ſexquiquartam que eſt
                    <lb/>
                  proportio ſupra nonipartiens ſexdecimas: et ſic in
                    <lb/>
                  infinitum duplicando proportionem velocitatum.
                    <lb/>
                  </s>
                  <s xml:id="N1F505" xml:space="preserve">Prima pars huius correlarii patet ex ſecūda con­
                    <lb/>
                  cluſione manifeſte et ſecunda pars eiuſdem ex quar­
                    <lb/>
                  ta: et applica ſi potes
                    <note position="left" xlink:href="note-0157-01a" xlink:label="note-0157-01" xml:id="N1F5AD" xml:space="preserve">2. correĺ.</note>
                  </s>
                  <s xml:id="N1F511" xml:space="preserve">¶ Sequitur ſecundo particu-
                    <lb/>
                  lariter /  diuiſa hora per partes proportionales
                    <lb/>
                  proportione ſextupla: et in prima illarū moueatur
                    <lb/>
                  aliquod mobile aliquanta velocitate, et in ſecunda
                    <lb/>
                  in duplo maiori, et in tertia in triplo, modo ſepi-
                    <lb/>
                  us recitato: tunc totius velocitatis ad velocitatem
                    <lb/>
                  prime partis proportionalis eſt proportio ſexqui­
                    <lb/>
                  quinta: et ſpacii pertranſiti in tota hora ad ſpaciū
                    <lb/>
                  pertranſitū in prima parte proportionali eſt pro-
                    <lb/>
                  portio ſupra vndecimpartiens viceſimas quintas
                    <lb/>
                  </s>
                  <s xml:id="N1F527" xml:space="preserve">Probatur prima pars huius correlarii: quia velo­
                    <lb/>
                  citate ita ſe habente vt ponitur: totalis velocitas
                    <lb/>
                  ex omniū partium velocitatibus conſurgens ſe ha­
                    <lb/>
                  bet ad velocitateꝫ prime partis proportionalis in
                    <lb/>
                  proportione in qua ſe habet totum tempus ad pri­
                    <lb/>
                  mam partem proportionalem / vt patet ex ſecunda
                    <lb/>
                  concluſione: ſed hora diuiſa per partes proporti-
                    <lb/>
                  onales proportione ſextupla ſe habet ad primam
                    <lb/>
                  partem proportionalē in proportione ſexquiquin­
                    <lb/>
                  ta / vt docet quītum capitulum prime partis huius
                    <lb/>
                  operis: igitur tota illa velocitas ſe habet ad velo-
                    <cb chead="Capitulū tertiū."/>
                  citatē prime patis proportionalis in proportione
                    <lb/>
                  ſexquiquinta / quod fuit probandum. </s>
                  <s xml:id="N1F543" xml:space="preserve">Sed iam pro­
                    <lb/>
                  batur ſecunda pars: quia proportio ſupra vndecī-
                    <lb/>
                  patiēs viceſimas quintas eſt dupla ad proportio-
                    <lb/>
                  nem ſexquiquītam / vt patet in his terminis .36.30.
                    <lb/>
                  25. iuuamine ſexti capitis ſecunde partis huiꝰ ope-
                    <lb/>
                  ris: igitur ſpacium pertranſitum in tota hora ad
                    <lb/>
                  ſpacium pertranſitum in parte ꝓportionali ſe ha-
                    <lb/>
                  bet in proportione ſupra vndecimpartiente viceſi-
                    <lb/>
                  maſquintas. </s>
                  <s xml:id="N1F556" xml:space="preserve">Patet hec conſequentia ex quarta cõ­
                    <lb/>
                  cluſione.
                    <note position="right" xlink:href="note-0157-02a" xlink:label="note-0157-02" xml:id="N1F5B3" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N1F560" xml:space="preserve">¶ Sequitur tertio /  diuiſa hora per par­
                    <lb/>
                  tes proportionales proportione octupla: et in eiſdē
                    <lb/>
                  moueatur aliquod mobile modo pluries reſūpto
                    <lb/>
                  totius velocitatis ad velocitatē prime partis pro-
                    <lb/>
                  portionalis eſt ꝓportio ſexquiſeptima: et ſpacii ꝑ-
                    <lb/>
                  tranſiti in tota hora ad ſpacium pertranſitum in
                    <lb/>
                  prima parte proportionnali erit proportio dupla
                    <lb/>
                  ad ſexquiſeptima que eſt ſuper quindecimpartiens
                    <lb/>
                  quadrageſimas: cuiuſmodi eſt .9. cū ſeptima ad .7.
                    <lb/>
                  et .64. ad .49. </s>
                  <s xml:id="N1F575" xml:space="preserve">Probatur prima pars correlarii:
                    <lb/>
                  quia hora ſic diuiſa per partes proportiõales pro­
                    <lb/>
                  portione octupla ſe habet ad primaꝫ partem pro-
                    <lb/>
                  portionalem in proportione ſexquiſeptima / vt ptꝫ
                    <lb/>
                  ex quīto capite prime partis huiꝰ operis: et in eadē
                    <lb/>
                  proportione ſe debet habere velocitas totiꝰ ad ve-
                    <lb/>
                  locitatem prime partis / vt dicit ſecunda concluſio:
                    <lb/>
                  igitur propoſitum. </s>
                  <s xml:id="N1F586" xml:space="preserve">Secunda pars probatur: quia
                    <lb/>
                  proportio ſupra quindecimpartiens quadrageſi-
                    <lb/>
                  maſnonas eſt dupla ad proportionem ſexquiſepti­
                    <lb/>
                  mam / vt patet in his terminis .64.56. et .49. patro­
                    <lb/>
                  cinio ſexti capitis ſecunde partis: igitur in ſupra-
                    <lb/>
                  quīdecimpartiens quadrageſimaſnonas ſe habet
                    <lb/>
                  ſpacium pertranſitū in tota hora ad ſpacium per-
                    <lb/>
                  tranſitum in prima parte proportiõali / quod fuit
                    <lb/>
                  probandum. </s>
                  <s xml:id="N1F599" xml:space="preserve">Patet tamen conſequentia: ex quar-
                    <lb/>
                  ta concluſione. </s>
                  <s xml:id="N1F59E" xml:space="preserve">¶ Ex hoc modo poteris inferre in-
                    <lb/>
                  nita correlaria ſimilia retento caſu velocitatis et
                    <lb/>
                  variando continuo diuiſionē hore, que omnia cor-
                    <lb/>
                  relaria ſuffragantibus ſeēunda et quarta conclu-
                    <lb/>
                  ſionibus facilem ſortiuntur demonſtrationem.</s>
                </p>
                <p xml:id="N1F5B9">
                  <s xml:id="N1F5BA" xml:space="preserve">Quinta concluſio generi proportiõis
                    <lb/>
                  ſuperparticularis ſpeciebuſ eius deſeruiens. </s>
                  <s xml:id="N1F5BF" xml:space="preserve">Di­
                    <lb/>
                  uiſa hora per partes proportionales proportiõe
                    <lb/>
                  ſuperparticulari ſexquialtera, ſexquiquarta, ſeu
                    <lb/>
                  quauis alia ſuperparticulari: diſtributa veloci-
                    <lb/>
                  tate partibus illis proportionalibus ita vt mobi-
                    <lb/>
                  le in prima illarum moueatur aliqnantulum, et in
                    <lb/>
                  ſecunda in duplo velocius, et in tertia in triplo ve-
                    <lb/>
                  locius ꝙ̄ in prima, et ſic conſequenter in caſu ſepiꝰ
                    <lb/>
                  repetito: tunc tota velocitas ſe habet ad velocita-
                    <lb/>
                  tem prime partis proportionalis in proportione
                    <lb/>
                  tripla ſi fuerit hora diuiſa in proportione ſexqui-
                    <lb/>
                  altera. </s>
                  <s xml:id="N1F5D8" xml:space="preserve">ſi vero fuerit diuiſa in proportione ſexqui-
                    <lb/>
                  tertia: in proportione quadrupla: ſi in proportio-
                    <lb/>
                  ne ſexquiquarta: in proportione quintupla. </s>
                  <s xml:id="N1F5DF" xml:space="preserve">et ſic cõ­
                    <lb/>
                  ſequenter aſcendendo ſeriatim per ſpecies propor­
                    <lb/>
                  tionis ſuperparticularis et multiplicis. </s>
                  <s xml:id="N1F5E6" xml:space="preserve">Et ſpacia
                    <lb/>
                  pertranſita in totali tempore ad ſpacia prime par­
                    <lb/>
                  tis proportionalis ſe habent in proportione du-
                    <lb/>
                  plicata (duplicata inquam ad triplam ſiue dupla
                    <lb/>
                  ad triplam: ſi fuerit diuiſio facta in proportione
                    <lb/>
                  ſexquialtera: et quadrupla ſi fuerit facta diuiſio
                    <lb/>
                  in proportione ſexquitertia: et ſic conſequenter).</s>
                </p>
                <p xml:id="N1F5F5">
                  <s xml:id="N1F5F6" xml:space="preserve">Probatur hec concluſio / que infinitas habet par-
                    <lb/>
                  tes in termino illo / et ſic cõſequenter incluſas et pri­
                    <lb/>
                  mo probatur eius prima pars que eſt de ꝓportiõe
                    <lb/>
                  velocitatum ex ſecunda concluſione: hoc addito / 
                    <lb/>
                  totum diuiſum proportione ſexquialtera ſe habet </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum