Alvarus, Thomas, Liber de triplici motu, 1509

List of thumbnails

< >
161
161 		162
162
163
163 		164
164
165
165 		166
166
167
167 		168
168
169
169 		170
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="N1FE85">
                  <s xml:id="N1FE86" xml:space="preserve">
                    <pb chead="De motu locali quo ad effectum tempore difformi." file="0164" n="164"/>
                  cium ꝑtranſitum in toto tempore eſt dupluꝫ ſexqui­
                    <lb/>
                  alterum ad ſpacium pertranſitum in prima parte
                    <lb/>
                  proportionali </s>
                  <s xml:id="N1FEA8" xml:space="preserve">Quod probatur eſto /  velocitas ṗ­
                    <lb/>
                  me partis ſit vt .4. et pertranſeatur quadrupedale
                    <lb/>
                  mediante illa per totam horam exrenſa: et ſic medi­
                    <lb/>
                  ante illa in prima ꝑte ꝓportionali bipedale / et ar-
                    <lb/>
                  guitur ſic / mediãte illa velocitate extenſa ꝑ totã ho­
                    <lb/>
                  ram mobile ꝑtranſit quadrupedale et mediantibꝰ
                    <lb/>
                  exceſſibus quibus velocitates partium proportio-
                    <lb/>
                  nalium aliarum a prima excedunt primam pertrã­
                    <lb/>
                  ſitur vuum: et ſic mediante totali illa velocitate per­
                    <lb/>
                  tranſeuntur quin pedalia in totali illa hora: et q̇n­
                    <lb/>
                  tupedalis ad bipedale pertranſitum in prima par­
                    <lb/>
                  te proportionali hore eſt proportio dupla ſexqui-
                    <lb/>
                  altera. </s>
                  <s xml:id="N1FEC3" xml:space="preserve">igitur propoſitum. </s>
                  <s xml:id="N1FEC6" xml:space="preserve">Probatur tamen /  me­
                    <lb/>
                  diantibus illis exceſſibus pertranſitur vnum peda­
                    <lb/>
                  le: quia mediante exceſſu quo velocitas ſecunde par­
                    <lb/>
                  tis excedit velocitatem prime pertranſeuntur tres
                    <lb/>
                  quarte et mediante exceſſu quo tertia excedit primã
                    <lb/>
                  pertranſitur ſubquadruplum ſpacium ad tres q̈r-
                    <lb/>
                  tas / et ſic conſequenter (quia illi exceſſus cõtinuo ſe
                    <lb/>
                  habent in proportione ſubdupla / vt facile eſt intue­
                    <lb/>
                  ri: et continuo coextenduntur tempori in duplo mi­
                    <lb/>
                  nori) / igitur aggregatum ex omnibus illis ſpaciis
                    <lb/>
                  pertranſitis mediantibus illis exceſſibus cõponi-
                    <lb/>
                  tur ex infinitis continuo ſe habentibus in propor-
                    <lb/>
                  tione ſubquadrupla et ex hoc illud habet ſe ad pri-
                    <lb/>
                  mum illoruꝫ ī proportione ſexquitertia / vt patet ex
                    <lb/>
                  prima parte capite quinto: et primum illoruꝫ ē tres
                    <lb/>
                  quarte pedalis: ergo totum eſt pedale: </s>
                  <s xml:id="N1FEE7" xml:space="preserve">Patet con-
                    <lb/>
                  ſequentia / q2 pedalis ad tres quartas eſt propor-
                    <lb/>
                  tio ſexquitertia. </s>
                  <s xml:id="N1FEEE" xml:space="preserve">Sed reſtat probare ſpacium per-
                    <lb/>
                  tranſitum ab illo exceſſu quo ſecunda pars propor­
                    <lb/>
                  tionalis excedit primam eſſe tres quartas quia ve­
                    <lb/>
                  locitas ṗme partis eſt vt .4. et velocitas ſecunde ꝑ-
                    <lb/>
                  tis habet ꝓportionē ſuꝑtripartienteꝫ q̈rtas ad ve-
                    <lb/>
                  locitatē prīe / igit̄̄ eſt vt .7. et ſic exceſſus eſt trium gra­
                    <lb/>
                  duū: ſꝫ mediãte vno gradu in prīa ꝑte ꝓportionali
                    <lb/>
                  mobile ꝑtranſibat dimidium pedale vt habetur ex
                    <lb/>
                  caſu: igitur mediante vno gradu in ſecunda parte
                    <lb/>
                  ꝓportionali que eſt in duplo minor mobile pertrã­
                    <lb/>
                  ſit vnam quartam et ſunt ibi tres gradus exceſſus:
                    <lb/>
                  igitur mediantibus illis ꝑtranſibit tres quartas /
                    <lb/>
                  quod fuit ꝓbandum.
                    <note position="left" xlink:href="note-0164-01a" xlink:label="note-0164-01" xml:id="N1FFD6" xml:space="preserve">2. correl.</note>
                  </s>
                  <s xml:id="N1FF0E" xml:space="preserve">¶ Sequitur ſecundo /  parti-
                    <lb/>
                  ta hora ꝑ partes ꝓportionales proportiõe dupla
                    <lb/>
                  et in prima illarum mobile aliquod moueatur aliq̈
                    <lb/>
                  velocitate: et in ſecunda illarum in ſexquitertio ma­
                    <lb/>
                  iori: et in tertia in ſexquiſexto maiori ꝙ̄ in prima et
                    <lb/>
                  in quarta in ſexquiduodecuplo maiori ꝙ̄ in prima /
                    <lb/>
                  et ſic conſequenter aſcendo ꝑ numeros pares conti­
                    <lb/>
                  nuo ſe habentes in ꝓportione dupla exordiendo a
                    <lb/>
                  numero ternario: hoc eſt ꝑ ſpecies ꝓportionis ſuꝑ-
                    <lb/>
                  particularis denomīatas a partibus aliquotis de­
                    <lb/>
                  nominatis ab illis numeris: ſpacium pertranſituꝫ
                    <lb/>
                  in totali hora eſt duplum ſuperbipartiens nonas
                    <lb/>
                  ad ſpacium pertranſitum in prima parte ꝓportio­
                    <lb/>
                  nali. </s>
                  <s xml:id="N1FF2B" xml:space="preserve">Probatur eſto exempli cauſa /  velocitas pri­
                    <lb/>
                  me partis ꝓportionalis ſit vt .3. et mediante illa mo­
                    <lb/>
                  bile pertranſeat in prima parte ꝓportionali tripe­
                    <lb/>
                  dale: et ꝑ conſequens mediante illa extenſa ꝑ totaꝫ
                    <lb/>
                  horam ſextipedale: et arguitur ſic mediante illa ve­
                    <lb/>
                  locitate vt .3: coextenſa toti hore mobile ꝑtranſibit
                    <lb/>
                  ſextipedale: et mediantibus excrementis quibus ve­
                    <lb/>
                  locitates parttium ꝓportionalium aliarum a pri-
                    <lb/>
                  ma excedunt primam mobile pertranſit duas ter-
                    <lb/>
                  tias pedalis: igitur in totali illa hora pertranſit
                    <lb/>
                  ſextipedale cum duabus tertius: ſed ſextipedalis cū
                    <lb/>
                  duabus tertiis ad tripedale pertranſituꝫ in prima
                    <lb/>
                  parte ꝓportionali eſt proportio dupla ſuperbipar­
                    <cb chead="De motu locali quo ad effectum tempore difformi."/>
                  tiens nonas: igitur propoſitum. </s>
                  <s xml:id="N1FF49" xml:space="preserve">Sed iam probo / 
                    <lb/>
                  mediantibus exceſſibus velocitatum quibus alie ꝑ­
                    <lb/>
                  tes proportionales excedunt velocitatem ṗme mo-
                    <lb/>
                  bile pertranſit duas tertias. </s>
                  <s xml:id="N1FF52" xml:space="preserve">quia velocitas ſecun-
                    <lb/>
                  de partis ꝓportionalis excedit velocitatem prime
                    <lb/>
                  ꝑ vnum gradum (eſt enim velocitas prime vt .3. et ſe­
                    <lb/>
                  cunde ſexquitertia ad illam) et mediante vno gradu
                    <lb/>
                  in prima parte ꝓportionali mobile pertranſit vnū
                    <lb/>
                  pedale: ergo mediante illo gradu mobile ꝑtranſit
                    <lb/>
                  vnum ſemipedale in ſecunda parte proportionali
                    <lb/>
                  ſubdupla ad primam: et mediante exceſſu quo tertia
                    <lb/>
                  pars excedit primam pertranſit ſubquadruplū ad
                    <lb/>
                  illud ſemipedale. </s>
                  <s xml:id="N1FF67" xml:space="preserve">et mediante exceſſu quo quarta ex­
                    <lb/>
                  cedit primam adhuc pertranſit ſubquadruplū ad
                    <lb/>
                  precedens / et ſic conſequenter: quia illi exceſſus con-
                    <lb/>
                  tinuo ſe habent in ꝓportione ſubpupla / vt patet ex
                    <lb/>
                  caſu: et continuo extenduntur in duplo minori par­
                    <lb/>
                  te: igitur aggregatum ex omnibus illis ſpaciis per­
                    <lb/>
                  tranſitis mediantibus illis exceſſibus componitur
                    <lb/>
                  ex infinitis continuo ſe habentibus in proportione
                    <lb/>
                  ſubquadrupla. </s>
                  <s xml:id="N1FF7A" xml:space="preserve">igitur ſe habet ad primum illorum
                    <lb/>
                  in ꝓportione ſexquitertia. </s>
                  <s xml:id="N1FF7F" xml:space="preserve">Conſequentia ſepiꝰ ar-
                    <lb/>
                  guta eſt. </s>
                  <s xml:id="N1FF84" xml:space="preserve">et cum primum illorum ſit ſemipedale: con­
                    <lb/>
                  ſequens eſt vt aggregatum ex omnibus illis ſit due
                    <lb/>
                  tertie (ſiquidem duarum tertiarum ad ſemipedale
                    <lb/>
                  ſit ſexquitertia proportio) </s>
                  <s xml:id="N1FF8D" xml:space="preserve">Et ſic patet probandum
                    <lb/>
                  et totum correlarium. </s>
                  <s xml:id="N1FF92" xml:space="preserve">¶ Innumera talia correlaria
                    <lb/>
                  poſſunt inferri diuidendo horam aliis ſpeciebus ꝓ­
                    <lb/>
                  poportionis: et faciendo exceſſus quibus alie par-
                    <lb/>
                  tes excedunt primam in certa ꝓportiõe continue ſe
                    <lb/>
                  habere: vt ſi hora diuidatur per partes proportio­
                    <lb/>
                  nales ꝓportione tripla: et in prima illaruꝫ aliquod
                    <lb/>
                  mobile moueatur aliquanta velocitate et in ſecun-
                    <lb/>
                  da in duplo ſexquialtero maiori: et in tertia in du-
                    <lb/>
                  plo ſexquiſexto: et in quarta in duplo ſexquidecimo
                    <lb/>
                  octauo maiori ꝙ̄ in prima: et in quinta in duplo ſex­
                    <lb/>
                  quiquīquageſimo quarto maiori ꝙ̄ in prima: et ſic
                    <lb/>
                  conſequenter procedendo ex parte ꝓportionis mul­
                    <lb/>
                  tiplicis ſuperparticularis per numeros ſe haben-
                    <lb/>
                  tes continuo in ꝓportione ſubtripla </s>
                  <s xml:id="N1FFAF" xml:space="preserve">Ibi enim ex-
                    <lb/>
                  ceſſus ſe habent in proportione ſubtripla </s>
                  <s xml:id="N1FFB4" xml:space="preserve">Itē ſi ho­
                    <lb/>
                  ra partiatur per partes ꝓportionales ꝓportione
                    <lb/>
                  ſuperbipartiente tertias et a. mobile in prima mo-
                    <lb/>
                  ueatur aliquanta velocitate et in ſecunda in triplo
                    <lb/>
                  ſexquiquinto velocius: et in tertia in triplo ſexqui-
                    <lb/>
                  decimo velocius ꝙ̄ in prima: et in quarta in triplo
                    <lb/>
                  ſexqui viceſimo velocius ꝙ̄ in prima: et in quinto in
                    <lb/>
                  triplo ſexquiquadrigeſimo progrediendo per ſpe­
                    <lb/>
                  cies denomīatas a numeris imparibus ſiue ab vni­
                    <lb/>
                  tate et partibus aliquotis denominatis ab illis nu­
                    <lb/>
                  meris continuo ſe habentibus in ꝓportione dupla
                    <lb/>
                  exordiendo a quinario. </s>
                  <s xml:id="N1FFCD" xml:space="preserve">Et ſic conſequenter poteris
                    <lb/>
                  infinita ſimilia ponere</s>
                </p>
                <p xml:id="N1FFDC">
                  <s xml:id="N1FFDD" xml:space="preserve">Undecima concluſio </s>
                  <s xml:id="N1FFE0" xml:space="preserve">Diuiſa hora per
                    <lb/>
                  partes proportionales quacun libuerit propor-
                    <lb/>
                  tione et in prima mobile moueatur aliquanta velo­
                    <lb/>
                  citate et in ſecunda in ſexquialtero maiori: et in ter-
                    <lb/>
                  tia in ſexquitertia maiori ꝙ̄ in ſecunda: et in quarta
                    <lb/>
                  in ſexquiquarta maiori ꝙ̄ in tertia et in quinta ī ſex­
                    <lb/>
                  quiquinto maiori ꝙ̄ in quarta / et ſic conſequenter.
                    <lb/>
                  </s>
                  <s xml:id="N1FFF0" xml:space="preserve">et ſi nõ valeat regula vniuerſalis ſignari ad reperi­
                    <lb/>
                  endum ſpacium pertranſitum in totali hora: nichi­
                    <lb/>
                  lominus tamen qualibet ſpecie diuiſionis hore ſi-
                    <lb/>
                  gnata poteſt certitudinaliter inueſtigari ſpaciuꝫ ꝑ­
                    <lb/>
                  tranſitum in tota hora: et ꝓportio eius ad ſpacium
                    <lb/>
                  pertranſitum in prima parte ꝓportionali. </s>
                  <s xml:id="N1FFFD" xml:space="preserve">Proba­
                    <lb/>
                  tur hec concluſio / et primo probatur ſecunda ꝑs eiꝰ.
                    <lb/>
                  </s>
                  <s xml:id="N20003" xml:space="preserve">quia ſit hora fuerit diuiſa per partes proportiona­ </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum