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="N1FC64">
                  <s xml:id="N1FD46" xml:space="preserve">
                    <pb chead="Secundi tractatus" file="0163" n="163"/>
                  velocitates ſe habeant in ꝓportione ſexquiquarta
                    <lb/>
                  omnium vero parium in ꝓportione ſexquiquinta:
                    <lb/>
                  excedat velocitas ṗme partis paris velocitatem
                    <lb/>
                  ṗme partis imparis in proportiõe ſexquiſexta: tūc
                    <lb/>
                  inueſtiga ꝓportionem totius ſpacii ad ſpaciuꝫ per­
                    <lb/>
                  tranſitū in prima innitendo p̄cedentibus. </s>
                  <s xml:id="N1FD5C" xml:space="preserve">Itē parti­
                    <lb/>
                  ta hora in partes ꝓportionales ꝓportiõe quadru­
                    <lb/>
                  pla: mobili in omni īpari ſequente mouēte in ſex­
                    <lb/>
                  quiſexto velocius ꝙ̄ in immediate ꝓcedente impari
                    <lb/>
                  et in omni pari ſequente in ſexquiſeptimo velocius
                    <lb/>
                  quã in pari immediate precedente: ſuperet veloci­
                    <lb/>
                  tas prime partis paris velocitatem prime imparis
                    <lb/>
                  in ꝓportione ſexquioctaua: tunc cõmenſura totale
                    <lb/>
                  ſpacium ſpacio prime partis ꝓportionalis precedē­
                    <lb/>
                  tibus ſuffultus </s>
                  <s xml:id="N1FD71" xml:space="preserve">Et ſic aſcendendo per ſpecies ꝓpor-
                    <lb/>
                  tionis multiplicis in diuidenda hora velocitatibꝰ
                    <lb/>
                  ſe habentibus continuo in diuerſis ꝓportionibus
                    <lb/>
                  ſuperparticularibus infinitam multitudinem ſe ſe
                    <lb/>
                  ↄ̨ſequētiū cõcluſionum inferre valebis. </s>
                  <s xml:id="N1FD7C" xml:space="preserve">Deinde diui­
                    <lb/>
                  ſa hora aliqua multipli ſimplici vel compoſita ve-
                    <lb/>
                  locitatibus partiuꝫ imparium cõtinuo ſe habētibꝰ
                    <lb/>
                  in ꝓportione aliqua ſuprapartiente: et partium pa­
                    <lb/>
                  riū immediatarum velocitatibus continuo ſe habē­
                    <lb/>
                  tibus in aliqua alia ꝓportione ſuprapartiente: ex-
                    <lb/>
                  cedente velocitate prime partis paris velocita-
                    <lb/>
                  tem prime partis imparis in aliqua alia propor-
                    <lb/>
                  tione ſuperpartiente infinita correlaria inferre po­
                    <lb/>
                  teris. </s>
                  <s xml:id="N1FD91" xml:space="preserve">Preterea partita hora per partes pro­
                    <lb/>
                  portionales ꝓportione multipici: quarūcun dua­
                    <lb/>
                  rum ꝑtium ꝑ .4. partes ꝓportionales diſtantiū ve-
                    <lb/>
                  locitatibus ſe habentibus in aliqua ꝓportione ſu­
                    <lb/>
                  perparticulari vel ſuperpartiente ita vt ṗme diſtã­
                    <lb/>
                  tes ꝑ .4. partes ꝓportionales vt puta prima et ſex­
                    <lb/>
                  ta ſe habeant in velocitate in ꝓportione ſexquial-
                    <lb/>
                  tera: et ſeptime velocitas ad velocitatem ſecunde in
                    <lb/>
                  ꝓportione ſexquitertia: et octaue velocitas ad velo­
                    <lb/>
                  citatem tertie in ꝓportione ſexquiq̈rta: et none ve-
                    <lb/>
                  locitas ad velocitatem quarte in ꝓportione ſexqui­
                    <lb/>
                  quinta: et decime velocitas ad velocitatem quinte ī
                    <lb/>
                  ꝓportione ſexquiſexta: et vndecime velocitas ad ve­
                    <lb/>
                  locitatem ſexte in ꝓportione ſexquialtera: et ſic ite-
                    <lb/>
                  rum aſcendendo vſ ad proportionem ſexquiſextã
                    <lb/>
                  et deinde redeundo vſ ad ꝓportionem ſexquial-
                    <lb/>
                  teram / et ſic conſequenter: ita  omnes diſtantes ꝑ
                    <lb/>
                  4. incipiendo a ṗma ſe habeant in ꝓportione ſexq̇­
                    <lb/>
                  altera in velocitate: et incipiendo a ſecunda in ſexq̇­
                    <lb/>
                  tertia: et a tertia in ſexquiquarta: et a quarto in ſex­
                    <lb/>
                  quiquinta: et a quinta in ſexquiſexta: et non plus.</s>
                </p>
                <p xml:id="N1FDC6">
                  <s xml:id="N1FDC7" xml:space="preserve">Ita poteris facere de partibus inter quas cõtinuo
                    <lb/>
                  mediant octo ꝑtes aſcendendo a prima vſ ad de-
                    <lb/>
                  cimã: et ſic in infinitum poteris variare caſus reten­
                    <lb/>
                  ta ſemper aliqua vniformiter ꝓportionum </s>
                  <s xml:id="N1FDD0" xml:space="preserve">Et ſi-
                    <lb/>
                  cut inferuntur multa correlaria quando velocitas
                    <lb/>
                  maior coextenditur ꝑtibꝰ minoribus. </s>
                  <s xml:id="N1FDD7" xml:space="preserve">ita plura alia
                    <lb/>
                  poſſunt inferri quando continuo velocitas maior
                    <lb/>
                  coextenditur partibus minoribus que omnia ex ṗ-
                    <lb/>
                  oribus facile inducuntur. </s>
                  <s xml:id="N1FDE0" xml:space="preserve">Et quia nimium in iſtis
                    <lb/>
                  immorari vltra modum eis inherere, eſt a melio­
                    <lb/>
                  ribus ſublimioribuſ ꝓſtergari: </s>
                  <s xml:id="N1FDE7" xml:space="preserve">Ideo calculator
                    <lb/>
                  his dedaleis laberinthulis implicitꝰ: verbiſ mul­
                    <lb/>
                  tiplicibus multiformibuſ ꝓportionibus implica­
                    <lb/>
                  tus: inflate bucce garritum contineat.</s>
                </p>
                <p xml:id="N1FDF0">
                  <s xml:id="N1FDF1" xml:space="preserve">Decima concluſio </s>
                  <s xml:id="N1FDF4" xml:space="preserve">Diuiſa hora ꝑ par­
                    <lb/>
                  tes ꝓportionales ꝓportione dupla et a. mobile in
                    <lb/>
                  prima ꝑte ꝓportionali moueatur aliquantula ve-
                    <lb/>
                  locitate: et in ſecunda in ſexquialtero maiori veloci­
                    <lb/>
                  tate: et in tertia in ſexquiquarto maiori velocitate
                    <lb/>
                  ̄ in prima: et in quinta in ſexquiſexdecimo maiori
                    <lb/>
                  quã in prima / et ſic conſequenter aſcendendo ꝑ ſpe-
                    <cb chead="Capitulum tertium"/>
                  cies ꝓportionis ſuperparticularis denominatas
                    <lb/>
                  a numeris pariter paribus </s>
                  <s xml:id="N1FE08" xml:space="preserve">(Meliꝰ tñ diceret̄̄ deſcē­
                    <lb/>
                  dēdo: q2 ꝓportiões ſuꝑparticulares ſūt mīores quã­
                    <lb/>
                  to a maiori numero denominantur hoc eſt a parte
                    <lb/>
                  aliquota denominata a maiori numero) ſpacium ꝑ­
                    <lb/>
                  trauſitum in totali hora ſe habet ad ſpacium per-
                    <lb/>
                  tranſitum in prima ꝑte ꝓportionali in ꝓportione
                    <lb/>
                  dupla ſexquitertia. </s>
                  <s xml:id="N1FE17" xml:space="preserve">Probatur et ſit gratia exempli
                    <lb/>
                  velocitas ṗme ꝑtis ꝓportionalis vt duo, ꝑtrãſeat­
                    <lb/>
                   a. mobile mediante illa velocitate in prima ꝑte ꝓ­
                    <lb/>
                  portionali bipedale: et arguitur ſic / illa velocitas vt
                    <lb/>
                  duo coextenditur toti hore, quia in qualibet parte
                    <lb/>
                  ꝓportionali hore velocitas eſt maior quam vt duo
                    <lb/>
                  vt habetur ex caſu et tota hora eſt dupla ad primaꝫ
                    <lb/>
                  partem ꝓportionalem eius in qua mobile pertran­
                    <lb/>
                  ſit bipcdale mediante velocitate vt duo: igitur me-
                    <lb/>
                  diante illa velocitate coextenſa toti hore pertran-
                    <lb/>
                  ſit quadrupedale: et mediantibus exceſſibus parti-
                    <lb/>
                  um ꝓportionalium ſupra illam velocitatem vt duo
                    <lb/>
                  pertranſit duas tertias pedalis que faciūt vnã ter­
                    <lb/>
                  tiam duorum pedalium: igitur totuꝫ ſpacium ſe ha­
                    <lb/>
                  bebit ad ſpacium pertranſitum in prima parte ꝓ-
                    <lb/>
                  portionali in proportione dupla ſexquitertia cuiuſ­
                    <lb/>
                  modi eſt ꝓportio ipſoꝝ quatuor cum duabus ter-
                    <lb/>
                  tiis vnius ad duo </s>
                  <s xml:id="N1FE3C" xml:space="preserve">Probo tamen /  mediantibꝰ il-
                    <lb/>
                  lis exceſſibus ꝑtranſeat duas tertias pedalis: quo­
                    <lb/>
                  niam cum velocitas ſecunde ꝑtis ꝓportionalis ſit
                    <lb/>
                  ſexquialtera ad velocitatem prime que eſt vt duo ſe­
                    <lb/>
                  quitur /  exceſſus velocitatis ſecunde ad velocitatē
                    <lb/>
                  prime eſt vnus gradus et quia tertia excedit primã
                    <lb/>
                  in ꝓporeione ſexquiquarta / ſequitur /  exceſſus eius
                    <lb/>
                  eſt medietas vnius gradus quoniam duorum cū di­
                    <lb/>
                  midio ad duo eſt proportio ſexquiquarta, et veloci­
                    <lb/>
                  tas quarte partis ſe habet ad velocitatem prime ī
                    <lb/>
                  ꝓportione ſexquioctaua: igitur exceſſus eius ē vna
                    <lb/>
                  quarta: igitur in illo caſu exceſſus ſecunde ad exceſ­
                    <lb/>
                  ſum tertie eſt ꝓportio dupla et exceſſus tertie ad ex-
                    <lb/>
                  ceſſum quarte dupla ſimiliter: et ſic conſequenter re­
                    <lb/>
                  peries illos exceſſus ſe habere in ꝓportione ſubdu­
                    <lb/>
                  pla et ſubdupla. et coextenduntur partibus cõtinuo
                    <lb/>
                  ſe habentibus in ꝓportione ſubdupla et ſubdupla /
                    <lb/>
                  igitur continuo illa ſpacia mediantibus illis velo­
                    <lb/>
                  citatibus ꝑtranſita ſe habet in ꝓportione ſubqua-
                    <lb/>
                  drupla / et ꝑ conſequens aggregatum ex omnibꝰ eis
                    <lb/>
                  ſe habebit ad primum illorum in ꝓportione ſexqui­
                    <lb/>
                  tertia et ṗmum illorum eſt vnum ſemipedale: ergo
                    <lb/>
                  totum erit vnum ſemipedale cum vna ſexta peda-
                    <lb/>
                  lis: et ꝑ conſequens due tertie vnius pedalis / qḋ fuit
                    <lb/>
                  ꝓbandum. </s>
                  <s xml:id="N1FE6F" xml:space="preserve">Sed iam ꝓbo /  p̄mum illorum ſit vnum
                    <lb/>
                  ſemipedale quoniam primum illorum ꝑtranſit̄̄ me­
                    <lb/>
                  diante exceſſu ſecunde ꝑtis ꝓportionalis ſupra pri­
                    <lb/>
                  mam qui exceſſus eſt vnus gradus mediante quo ī
                    <lb/>
                  prima parte ꝓportionali pertranſitur vnum peda­
                    <lb/>
                  le: igitur mediante illo in ſecunda parte ꝓportiõa-
                    <lb/>
                  li ſubdupla ad illam pertranſitur vnum ſemipeda­
                    <lb/>
                  le / quod fuit ꝓbandum. </s>
                  <s xml:id="N1FE80" xml:space="preserve">Patet conſequentia ex ſecū­
                    <lb/>
                  da ꝑte prime ꝓpoſitionis ſecundi notabilis.</s>
                </p>
                <p xml:id="N1FE85">
                  <s xml:id="N1FE86" xml:space="preserve">¶ Ex hac concluſione ſequitur primo /  ſi fuerit ho­
                    <lb/>
                  ra diuiſa ꝓportione dupla: et in prima illarum par­
                    <lb/>
                  tium moueatur aliquod mobile aliquanta velocita­
                    <lb/>
                  te, et in ſecunda in ſupertripartiente quartas maio­
                    <lb/>
                  ri velocitate, et in tertia in ſupertripartiente octa-
                    <lb/>
                  uas maiori velocitate ꝙ̄ in prima: et in quarta in ſu­
                    <lb/>
                  ꝑtripartiente ſexdecimas maiori ꝙ̄ in prima et in
                    <lb/>
                  quinta in ſuꝑtripartiente triceſimas ſecundas ma­
                    <lb/>
                  iori velocitate ꝙ̄ in prima / et ſic conſequenter ꝓcedē­
                    <lb/>
                  do per ſpecies ꝓportionis ſupertripartientis de-
                    <lb/>
                  nominatas a numeris pariter paribus ſiue a par-
                    <lb/>
                  tibus aliquotis denominatis ab illis numeris: ſpa­ </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum