Alvarus, Thomas, Liber de triplici motu, 1509

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            <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="N1E1E4">
                  <s xml:id="N1E201" xml:space="preserve">
                    <pb chead="Secundi tractatus" file="0145" n="145"/>
                  ram in proportione irrationali / et volo /  in maio­
                    <lb/>
                  ri illarum moueatur a. mobile gradu octauo et in
                    <lb/>
                  minori illarū moueatur idem mobile gradu quar­
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                  to </s>
                  <s xml:id="N1E213" xml:space="preserve">(Semper in iſtis argumentis ſuppono /  vni gra­
                    <lb/>
                  dui velocitatis in hora correſpondeat pedanea per­
                    <lb/>
                  tranſitio) quo poſito ſic argumentor talis motus
                    <lb/>
                  eſt difformiter difformis: et tamen non poteſt redu-
                    <lb/>
                  ci ad vniformitatem: </s>
                  <s xml:id="N1E21E" xml:space="preserve">Nec eius valet dari ſiue aſſi-
                    <lb/>
                  gnari determinata intenſio: igitur. </s>
                  <s xml:id="N1E223" xml:space="preserve">Maior eſt nota /
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                  et minor probatur ſupponēdo /  quanto aliq̈ pars
                    <lb/>
                  motus totalis eſt tn minori parte temporis tãto mi­
                    <lb/>
                  nus facit ad denominationem intenſionis totiꝰ mo­
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                  tus ceteris aliis paribus: et tanto minus de ſpacio
                    <lb/>
                  per talem motum tranſitur: vt motus vt vnum par-
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                  tialis in vna quarta hore facit ad intenſionem to-
                    <lb/>
                  tius motus vt vna quarta, et per illum in illa quar-
                    <lb/>
                  ta pertranſitur quarta pars pedalis. </s>
                  <s xml:id="N1E236" xml:space="preserve">Et generali-
                    <lb/>
                  ter obſeruandum eſt /  in quacun proportione ſe
                    <lb/>
                  habet pars temporis ad totuꝫ tempus in eadem ſe
                    <lb/>
                  habet velocitas motus in llla parte ad velocitateꝫ
                    <lb/>
                  totalis motus in toto tempore. </s>
                  <s xml:id="N1E241" xml:space="preserve">Quo poſito argui-
                    <lb/>
                  tur aſſumptum / quia motus vt .8. in illa parte tem-
                    <lb/>
                  poris non ſe habet in aliqua proportione rationa­
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                  li ad totalem motum, nec etiam vt quatuor: et penes
                    <lb/>
                  tales proportiones debet inueſtigari eius intenſio
                    <lb/>
                  et reductio ad vniformitatem: igttur non poteſt da­
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                  ri eius determinata intenſio aut reductio ad vnifor­
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                  mitatem. </s>
                  <s xml:id="N1E252" xml:space="preserve">Conſequentia patet cum minore: et argui­
                    <lb/>
                  tur maior / quia partes temporis in quibus ſunt illi
                    <lb/>
                  motus ſe habent ad totum tempus in proportione
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                  irrationali / vt poſitum eſt: igitur etiam motus illa­
                    <lb/>
                  rum partium ad totalem motum. </s>
                  <s xml:id="N1E25D" xml:space="preserve">Conſequentiã de­
                    <lb/>
                  clarat ſuppoſitio.
                    <note position="left" xlink:href="note-0145-01a" xlink:label="note-0145-01" xml:id="N1E285" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N1E267" xml:space="preserve">¶ Dices forte et bene concedendo /
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                   talis motus non poteſt dari determinata inten-
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                  ſio et rationalis reductio ad vniformitatem: ita  ī­
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                  tenſio illius motus ſe habeat ad motum alicuius il­
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                  larum partium in proportione aliqua rationali:
                    <lb/>
                  nec hoc eſt inconueniens, nec contra tituluꝫ queſtio­
                    <lb/>
                  nis: quia intelligitur titulus queſtionis dūmodo ꝑ­
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                  tes in quibus tales motus ponūtur ſe habeãt in ꝓ-
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                  portione rationali. </s>
                  <s xml:id="N1E27A" xml:space="preserve">Unum tamen eſt / quod poſtea
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                  oſtendetur /  talis motus totalis eſt intenſior quã
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                  motus vt ſex.</s>
                </p>
                <p xml:id="N1E28B">
                  <s xml:id="N1E28C" xml:space="preserve">Sed contra ſolutionem arguitur ſic /
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                  quia aliquis eſt motus difformis cuius partes ſūt
                    <lb/>
                  in partibus temporis rationalē ꝓportionē haben­
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                  tibus ad totū tempus: et tamē talis motꝰ nõ valet
                    <lb/>
                  reduci ad vniformitatē, nec valet inueniri certa eiꝰ
                    <lb/>
                  intenſio: igit̄̄ ſolutio nulla. </s>
                  <s xml:id="N1E299" xml:space="preserve">Arguitur antecedēs et
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                  pono caſum /  diuidatur hora per partes ꝓportio­
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                  nales proportione dupla: et in prima a. mobile mo­
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                  ueatur aliquatulū velociter exempli gratia vt .2. et
                    <lb/>
                  in ſecunda in duplo velocius quã in prima. et in ter­
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                  tia in triplo: et ſic conſequenter aſcendendo per om­
                    <lb/>
                  nes numeros. </s>
                  <s xml:id="N1E2A8" xml:space="preserve">quo poſito ſic arguitur / talis mo-
                    <lb/>
                  tus eſt difformiter difformis cuius partes ſunt in
                    <lb/>
                  partibus temporis habentibꝰ proportionē ratio-
                    <lb/>
                  nalem in ordine ad totum: et tamē non inuenit̄̄ nec
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                  dabilis eſt certa intenſio eiꝰ nec reductio ad vnifor­
                    <lb/>
                  mitatem: igitur propoſitū: tota ratio patet dem-
                    <lb/>
                  pta minore / que ſic arguit̄̄ / q2 ille motus videtur eſſe
                    <lb/>
                  infinitus: igitur nõ valet dari determinata eiꝰ intē­
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                  tio ſaltem finita de qua loquimur. </s>
                  <s xml:id="N1E2BB" xml:space="preserve">Probatur añs /
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                  quia in infinitū intēſus eſt ille motus in illa hora:
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                  igitur apparet /  ſit īfinitus.
                    <note position="left" xlink:href="note-0145-02a" xlink:label="note-0145-02" xml:id="N1E30D" xml:space="preserve">Dicitur.</note>
                  </s>
                  <s xml:id="N1E2C7" xml:space="preserve">¶ Dices forte /  tota-
                    <lb/>
                  lis ille motus eſt ita intenſus ſicut motus qui fit in
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                  ſecunda parte ꝓportionali temporis: ita  talis
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                  motus eſt ī duplo ītenſior motu facto ī prima par­
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                  te ꝓportionali tēporis: et reduciter ad vniformita­
                    <cb chead="Capitulum tertium"/>
                  tem ſupponendo /  per quamlibet partē illius ho­
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                  re eſt motus vt duo et per totū reſiduū a prima par­
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                  te ꝓportionali eſt motꝰ vt .4. et per totū reſiduum
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                  a ſecunda eſt motꝰ vt .6. et per totū reſiduū a tertia
                    <lb/>
                  eſt motus vt .8. / vt facile patet ex caſu: ita  queli-
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                  bet pars ſequens alterã cū oībus ſequētibus eam
                    <lb/>
                  excedit immediate precedentem per duos gradus.
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                  </s>
                  <s xml:id="N1E2E2" xml:space="preserve">Quo ſuppoſito arguitur reductio vniformitatis
                    <lb/>
                  talis motus: et volo /  capiãtur duo gradus extēſi
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                  per totū reſiduū a. prīa ꝑte ꝓportionali: et ponan­
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                  tur in prima ſibi equali. </s>
                  <s xml:id="N1E2EB" xml:space="preserve">Diuidendo em̄ proportio­
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                  ne dupla totū aggregatū ex oībus immediate ſe-
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                  quentibus aliquã eſt equalis illi / vt patet ex quinto
                    <lb/>
                  capite prime partis) / deinde capiantur duo gradꝰ
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                  a toto a ſecunda / et ponãtur in ſecunda: et nichil po­
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                  natur vlterius in prima: aut ſecunda: deinde a ſe-
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                  quentibus tertiam capiantur duo gradus / qui po­
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                  nantur in tertia: et ſic cõſequenter. </s>
                  <s xml:id="N1E2FC" xml:space="preserve">quo poſito in fi­
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                  ne totus ille motus erit vniformis vt .4. / igit̄̄ dabi-
                    <lb/>
                  lis eſt eius intēſio et ad vniformitateꝫ reductio ha­
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                  betur em̄ /  velocitas totalis motus eſt dupla ad
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                  velocitatem eiꝰ que eſt in prima parte proportio-
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                  nali hore.</s>
                </p>
                <p xml:id="N1E313">
                  <s xml:id="N1E314" xml:space="preserve">Sed contra / quia tunc ſequeretur / 
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                  ſi hora diuidatur per partes ꝓportionales ꝓpor-
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                  tione tripla et per primã illarū moueat̄̄ aliquod
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                  mobile aliquantula velocitate: et ꝑ ſecundam du­
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                  pla velocitate: et per tertiam tripla: et ſic in infini­
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                  tuꝫ vt in priori caſu. </s>
                  <s xml:id="N1E321" xml:space="preserve">tale mobile etiã moueret̄̄ in to­
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                  tali hora adequate dupla velocitate ad velocitatē
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                  qua mouetur in prima parte proportionali hore /
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                  ſed cõſequens eſt falſum / igitur illud ex quo ſequit̄̄
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                  </s>
                  <s xml:id="N1E32B" xml:space="preserve">Sequela probatur / quia non videtur maior ratio­
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                  ni iſto caſu quam in p̄cedenti: falſitas tamē conſe­
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                  quentis arguitur / quia talis motus eſt dūtaxat in
                    <lb/>
                  ſexquialtero velocior motu prime partis propor-
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                  tionalis temporis: igitur non eſt ī duplo velocior.
                    <lb/>
                  </s>
                  <s xml:id="N1E337" xml:space="preserve">Conſequentia patet: et arguitur añs: et volo gra-
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                  tia argumēti /  motus prime partis proportiona­
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                  lis ſit vt .2. / quo poſito ſic argumētor motus vt duo
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                  eſt per totam horã. </s>
                  <s xml:id="N1E340" xml:space="preserve">ergo talis motus denominat
                    <lb/>
                  totū moueri vt duo in tota hora motꝰ vero vt duo
                    <lb/>
                  ſuperadditus in ſecunda parte ꝓportionali et in
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                  oībus ſequentibus eſt in ſubtriplo tempore: et eſt
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                  equalis intenſionis cñ aliis duobꝰ gradibꝰ per to­
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                  tum: igitur in triplo minus denominat. </s>
                  <s xml:id="N1E34D" xml:space="preserve">Duo vero
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                  gradus extenſi per tertiã partē ꝓpottionalē et to­
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                  tum reſiduū ſunt in triplo minori ſubiecto / ergo ad­
                    <lb/>
                  huc in triplo minꝰ denominãt: et ſic conſequenter
                    <lb/>
                  ꝓcedendo per ſubtriplam proportionē: ergo tota­
                    <lb/>
                  lis denominatio talis motꝰ facti in illa hora con-
                    <lb/>
                  flatur ex infinitis cõtinuo ſe habentibꝰ in ꝓportio­
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                  ne ſubtripla: igitur reſiduū a prima eſt ſubdupluꝫ
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                  ad primū / vt patet ex correlario prīe ↄ̨cluſionis q̇nti
                    <lb/>
                  capitis prime partis et primū illoꝝ erat vt duo hoc
                    <lb/>
                  eſt prima denomīatio erat vt .2. / igitur oēs alie de­
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                  nominatiões ſunt vt vnū: modo duo et vnū ſūt tria /
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                  igit̄̄ totalis motꝰ velocitas eſt vt .3. et velocitas in
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                  prima parte ꝓportionali eſt vt .2. / ergo velocitas to­
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                  talis motus ſe habet in ꝓportiõe ſexquialtera ad
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                  velocitatem eiuſdē motꝰ in prima parte ꝓportio-
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                  nali temporis / quod fuit ꝓbandū: patet tamen con­
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                  ſequentia / q2 triū ad duo eſt ꝓportio ſexquialtera.</s>
                </p>
                <p xml:id="N1E372">
                  <s xml:id="N1E373" xml:space="preserve">Quarto principaliter tangēdo motꝰ
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                  difformiter difformis quorū partes diuerſis con-
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                  tinuo ꝓportionibus ſe habent: arguitur ſic: q2 ali­
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                  quis eſt motus difformiter difformis cuius nõ eſt
                    <lb/>
                  dabilis vniformitas nec denoīationis intēſio: igit̄̄ </s>
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