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="N1FB1C">
                  <s xml:id="N1FBCF" xml:space="preserve">
                    <pb chead="De motu locali quo ad effectum tempore difformi." file="0162" n="162"/>
                  batur correlarium et in prima parte proportiona-
                    <lb/>
                  li ꝑtranſeat illud mobile vnum pedale et arguitur
                    <lb/>
                  ſic </s>
                  <s xml:id="N1FBDB" xml:space="preserve">In omnibus partibus tam paribus quam īpa-
                    <lb/>
                  ribus ꝑtranſit illud mobile tria pedalia cum dimi­
                    <lb/>
                  dio: ſed triū pedaliū cum dimidio ad vnum pedale
                    <lb/>
                  eſt ꝓportio tripla ſexquialtera: igitur correlarium
                    <lb/>
                  verum. </s>
                  <s xml:id="N1FBE6" xml:space="preserve">Arguitur maior / quia in prima ꝑte impari
                    <lb/>
                  ꝑtranſit vnum pedale et ſpacia pertranſita in om-
                    <lb/>
                  nibus partibus imparibus continuo ſe habent ī ꝓ­
                    <lb/>
                  portione dupla quoniam velocitates cõtinuo ſe ha­
                    <lb/>
                  bent in ꝓportione dupla et tempora in quadrupla:
                    <lb/>
                  et ſic totale ſpacium ꝑtranſitum in omnibus parti­
                    <lb/>
                  bus imparibus erit duplum ad ſpacium ꝑtranſitū
                    <lb/>
                  in prima illarum / vt patet ex ſeptima concluſione.
                    <lb/>
                  </s>
                  <s xml:id="N1FBF8" xml:space="preserve">ergo ꝑ cõſequens totale ſpacium pertranſitū in om­
                    <lb/>
                  nibus erit bipedale. </s>
                  <s xml:id="N1FBFD" xml:space="preserve">Et ſpacium pertranſitum in om­
                    <lb/>
                  nibus paribus eſt pedale cum dimidio. </s>
                  <s xml:id="N1FC02" xml:space="preserve">Quod pro­
                    <lb/>
                  batur ſic / quia cõtinuo velocitatis partis paris ad
                    <lb/>
                  velocitatem ꝑtis imparis immediate precedentis
                    <lb/>
                  eſt ꝓportio ſexquialtera: (cum velocitas illius par­
                    <lb/>
                  tis paris correſpondeat gradui medio inter gradū
                    <lb/>
                  velocitatis illius partis imparis immediate prece­
                    <lb/>
                  dentis et gradum duplum) et ſemper gradus mediꝰ
                    <lb/>
                  inter duplum et ſubdupluꝫ eſt ſexquialterus ad ſub­
                    <lb/>
                  duplum / vt conſtat. </s>
                  <s xml:id="N1FC15" xml:space="preserve">igitur talis gradus medius erit
                    <lb/>
                  ſexquialterus ad graduꝫ partis imparis immedia­
                    <lb/>
                  te precedentis: igitur ſpacium pertranſitum in pri­
                    <lb/>
                  ma parte ꝓportionali impari ſe habet ad ſpacium
                    <lb/>
                  pertranſituꝫ in prima parte proportionali pari in
                    <lb/>
                  ꝓportiõe ſexquitertia / vt patet ex ſexta propoſitio­
                    <lb/>
                  ne ſecundi notabilis ſed ſubſexquitertium ad peda­
                    <lb/>
                  le ſunt tres quarte et in omnibus ſequentibus pari­
                    <lb/>
                  bus pertranſibit tantum: igitur in omnibus ſimul
                    <lb/>
                  pertranſibit ſex quartas que faciunt pedale cum di­
                    <lb/>
                  midio. </s>
                  <s xml:id="N1FC2C" xml:space="preserve">et in imparibus pertrãſibit bipedale: igitur
                    <lb/>
                  in omnibus partibus ſimul paribus et imparibus
                    <lb/>
                  pertranſibit tria pedalia cum dimidio / quod fuit ꝓ­
                    <lb/>
                  bandum. </s>
                  <s xml:id="N1FC35" xml:space="preserve">Reſtat tamen probare /  in omnibus par­
                    <lb/>
                  tibus paribus ſequentibus ṗmã tm̄ pertranſit ſicut
                    <lb/>
                  in prima. </s>
                  <s xml:id="N1FC3C" xml:space="preserve">Nam ille partes pares cõtinuo ſe habēt
                    <lb/>
                  in proportione quadrupla et velocitates continuo
                    <lb/>
                  ſe habent in proportione dupla aſcendendo / vt pa-
                    <lb/>
                  tet ex caſu correlarii: ergo totale ſpacium pertran-
                    <lb/>
                  ſitum in omnibus paribus eſt duplum ad ſpaci-
                    <lb/>
                  um pertranſitum in prima illarum et ſic illud ſpaci­
                    <lb/>
                  um eſt .6. quarte. </s>
                  <s xml:id="N1FC4B" xml:space="preserve">Conſequentia patet ex ſeptima cõ­
                    <lb/>
                  cluſione: hoc addito /  proportio temporis excedit
                    <lb/>
                  ꝓportionem velocitatum ꝑ ꝓportionem duplam:
                    <lb/>
                  et totum diuiſum per partes ꝓportionales propor­
                    <lb/>
                  tione dupla eſt duplum ad primam illarum.</s>
                </p>
                <note position="left" xml:id="N1FC60" xml:space="preserve">2. correl.</note>
                <p xml:id="N1FC64">
                  <s xml:id="N1FC65" xml:space="preserve">¶ Secundo ſequitur /  diuiſa hora per partes ꝓ-
                    <lb/>
                  portionales proportione quadrupla: et in prima ꝑ­
                    <lb/>
                  te moueatur mobile aliquanta velocitate vniformi­
                    <lb/>
                  ter, et in ſecunda intendat motum ſum vniformiter
                    <lb/>
                  ab illo gradu quo mouetur in prima vſ ad triplū
                    <lb/>
                  et in tertia moueatur vniformiṫ illo triplo gradu et
                    <lb/>
                  in quarta moueatur vniformiter intendendo motū
                    <lb/>
                  ſuum a gradu quo mouebatur in tertia vſ ad tri­
                    <lb/>
                  plum illius: et ſic conſequenter ſemper in qualibet
                    <lb/>
                  pari intendendo gradum īmediate precedentis im­
                    <lb/>
                  paris vſ ad triplum eiuſdem gradus vniformiter
                    <lb/>
                  ſpacium pertranſitum in totali hora ſe habebit ad
                    <lb/>
                  ſpacium pertranſitum in prima parte proportio-
                    <lb/>
                  nali impari in proportione ſupra vndecīpartiente
                    <lb/>
                  tridecimas. </s>
                  <s xml:id="N1FC84" xml:space="preserve">Probatur ſupponendo /  medium in­
                    <lb/>
                  ter triplum et ſubtriplum eſt duplum ad ſubtriplū
                    <lb/>
                  vt medium inter vnum et .3. eſt .2. / quod eſt duplū ad
                    <lb/>
                  vnum. </s>
                  <s xml:id="N1FC8D" xml:space="preserve">Supponitur ſecūdo /  velocitas ꝑtium īpa-
                    <lb/>
                  rium immediatarum continuo ſe habent in propor­
                    <cb chead="De motu locali quo ad effectum tempore difformi."/>
                  tione tripla et etiam partium parium / vt patet aſpi­
                    <lb/>
                  ciēti caſū correlarii </s>
                  <s xml:id="N1FC97" xml:space="preserve">His ſuppoſitis eſto /  mobile ī
                    <lb/>
                  prima parte proportionali pertranſit tridecim pe­
                    <lb/>
                  dalia: arguitur ſic in omnibus partibus imparibꝰ
                    <lb/>
                  illud mobile pertranſit ſexdecim pedalia: et in om-
                    <lb/>
                  nibus paribus pertranſit octo: igitur in tota hora
                    <lb/>
                  ꝑtranſibit viginti q̈tuor: et .24. ad .13. pedalia ꝑtrã­
                    <lb/>
                  ſita in prima parte proportionali eſt proportio ſu­
                    <lb/>
                  pra vndecīpartiens tridecimas: igitur propoſituꝫ
                    <lb/>
                  </s>
                  <s xml:id="N1FCA9" xml:space="preserve">Maior ꝓbatur / quia ꝓportio temporum ꝑtum im-
                    <lb/>
                  parium que eſt ſexdecupla / vt conſtat: excedit ꝓpor­
                    <lb/>
                  tionem velocitatis triplam ꝑ ꝓportionalem quītu­
                    <lb/>
                  plam ſexquitertiam, qualis eſt .16. ad .3. et quodli-
                    <lb/>
                  bet totum diuiſum ꝓportione quintupla ſexquiter­
                    <lb/>
                  tia ſe habet ad primam ꝑtem eius ꝓportionaleꝫ in
                    <lb/>
                  ꝓportione ſupertripartiente tridecimas / vt patet
                    <lb/>
                  ex prima parte capite quinto: igitur in omnibus ꝑ­
                    <lb/>
                  tibus ꝓportionalibus imparibus illud mobile per­
                    <lb/>
                  tranſit .16. pedalia: </s>
                  <s xml:id="N1FCBE" xml:space="preserve">Patet conſequentia ex ſeptīa
                    <lb/>
                  concluſione huius: hoc addito /  in prima parte im­
                    <lb/>
                  pari pertranſit .13. pedalia: et .16. ad .13. eſt ꝓportio
                    <lb/>
                  ſupertripartiens tridecimas. </s>
                  <s xml:id="N1FCC7" xml:space="preserve">Et ſic patet maior
                    <lb/>
                  </s>
                  <s xml:id="N1FCCB" xml:space="preserve">Minor ꝓbatur / quia ꝓportio temporum partium
                    <lb/>
                  parium ſexdecupla / vt conſtat excedit proportionē
                    <lb/>
                  velocitatum triplam per ꝓportionem quintuplam
                    <lb/>
                  ſexquitertiam / vt patet ex probatione maioris: et
                    <lb/>
                  quodlibet totum diuiſum ꝓportione quintupla ſex­
                    <lb/>
                  quitertia ſe habet ad primam partem eius propor­
                    <lb/>
                  portionalem in proportione ſupertripartiente tri­
                    <lb/>
                  decimas: vt patet ex prima parte capite quinto: igi­
                    <lb/>
                  tur in omnibus partibus paribus pertranſit illud
                    <lb/>
                  mobile ſpacium ſe habens ad ſpacium pertranſitū
                    <lb/>
                  in prima illarum pariuꝫ in ꝓportione ſupertripar­
                    <lb/>
                  tiente tridecimas: et ſpacium pertranſitum in pri-
                    <lb/>
                  ma parium eſt ſpacium. </s>
                  <s xml:id="N1FCE6" xml:space="preserve">ſex pedalium cum dimidio /
                    <lb/>
                  igitur ſpacium pertranſituꝫ in omnibus partibus
                    <lb/>
                  paribus eſt .8. pedum </s>
                  <s xml:id="N1FCED" xml:space="preserve">Patet conſequen-
                    <lb/>
                  tia: q2 .8. ad .6. cum dimidio eſt proportio ſupertri­
                    <lb/>
                  partiens tridecimas. </s>
                  <s xml:id="N1FCF4" xml:space="preserve">Probatur tamen /  in pri-
                    <lb/>
                  ma parte ꝓportionali illud mobile pertrãſit .6. pe­
                    <lb/>
                  dalia cum dimidio: quia illa pars eſt ſubquadru-
                    <lb/>
                  pla ad primã imparem: et velocitas illius eſt dupla
                    <lb/>
                  ad velocitatem ṗme imparis / vt patet facile ex ṗmo
                    <lb/>
                  ſuppoſito: igitur in illa ꝑte mobile pertranſit .6. pe­
                    <lb/>
                  dalia cum dimidio. </s>
                  <s xml:id="N1FD03" xml:space="preserve">Patet conſequentia ex ſexta ꝓ­
                    <lb/>
                  poſitione ſecundi notabilis, addito /  in prima ꝑ-
                    <lb/>
                  te ꝓportionali impari ꝑtranſit .13. pedalia: et ſic pa­
                    <lb/>
                  tet minor: et ꝑ conſequens totum correlarium
                    <lb/>
                    <note position="right" xlink:href="note-0162-01a" xlink:label="note-0162-01" xml:id="N1FDC0" xml:space="preserve">.3. correl.</note>
                  </s>
                  <s xml:id="N1FD13" xml:space="preserve">¶ Sequitur tertio /  partita hora ꝑ ꝑtes ꝓportio-
                    <lb/>
                  nales ꝓportione quadrupla: et mobile in qualibet
                    <lb/>
                  parte ſequente impari in quadruplo velocius mo-
                    <lb/>
                  ueatur ꝙ̄ ī immediate p̄cedēti impari: et in qualibet
                    <lb/>
                  ſequenti pari etiam in quadruplo velocius mouea­
                    <lb/>
                  tur ꝙ̄ in immediate p̄cedenti pari: et in duplo velo-
                    <lb/>
                  cius in prima ꝑte pari ꝙ̄ in ṗma impari: tunc tota-
                    <lb/>
                  le ſpacium ꝑtranſitum in hora ſe habet ad ſpaciuꝫ
                    <lb/>
                  ꝑtranſitum in ṗma parte ꝓportionali impari ī ꝓ­
                    <lb/>
                  portione dupla </s>
                  <s xml:id="N1FD28" xml:space="preserve">Hoc correlarium ex p̄dictis facile ꝓ­
                    <lb/>
                  bari p̄t </s>
                  <s xml:id="N1FD2D" xml:space="preserve">¶ Inferat quilibet ſuopte ingenio ꝓpriiſ
                    <lb/>
                  viribus nõnulla ſimilia correlaria </s>
                  <s xml:id="N1FD32" xml:space="preserve">Poſſunt enim
                    <lb/>
                  īfinita inferri. </s>
                  <s xml:id="N1FD37" xml:space="preserve">vt puta ſi hora diuidatur ꝓportione
                    <lb/>
                  dupla: et omnium partium parium velocitates con­
                    <lb/>
                  tinuo ſe habeãt in ꝓportione ſexquialtera: omniū-
                    <lb/>
                   imparium ꝓportio velocitatum ſit ſexquitertia
                    <lb/>
                  ſit velocitatis ṗme paris ad velocitatem ṗme im­
                    <lb/>
                  paris ꝓportio ſexquiquarta: tunc calcula totale
                    <lb/>
                  ſpcium ad ſpacium ꝑtranſitum in ṗma parte. </s>
                  <s xml:id="N1FD46" xml:space="preserve">Item
                    <lb/>
                  conſciſa hora in partes ꝓportionales ꝓportiõe tri­
                    <lb/>
                  pla: et omnium partium imparium immediatarum </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum