Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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                <p xml:id="N1EE5F">
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                    <pb chead="Secundi tractatus" file="0153" n="153"/>
                  quate tantam latitudinem ſicut a. ita  in fine a. et
                    <lb/>
                  b. maneant equales. </s>
                  <s xml:id="N1EE7F" xml:space="preserve">Quo poſito ſic argumentor / ve­
                    <lb/>
                  locitas ipſius motus a. correſpõdet gradui medio
                    <lb/>
                  inter extremum ipſorum a. et b. in principio et ertre­
                    <lb/>
                  mum eorundem in fine (dico eorundem / quia illi mo­
                    <lb/>
                  tus tam in principio ꝙ̄ in fine ſunt equales / vt po­
                    <lb/>
                  nit caſus) </s>
                  <s xml:id="N1EE8C" xml:space="preserve">Sed b. motus in quolibet inſtanti intrin­
                    <lb/>
                  ſeco illius temporis erit remiſſior ipſo a. motu: igi­
                    <lb/>
                  tur b. motus remiſſiori gradui correſpondet quam
                    <lb/>
                  a. motus et a. motus correſpondet gradui medio in­
                    <lb/>
                  ter extrema ipſius b. / igitur b. motus correſpondet
                    <lb/>
                  gradui remiſſiori quam ſit gradus medius inter ex­
                    <lb/>
                  trema eiuſdem b. motus. </s>
                  <s xml:id="N1EE9B" xml:space="preserve">Conſequentia patet /
                    <lb/>
                  quia extrema b. motus et a. motus ſunt equalia. </s>
                  <s xml:id="N1EEA0" xml:space="preserve">Et
                    <lb/>
                  maior patet ex prima ꝓpoſitione: et minor proba-
                    <lb/>
                  tur ſic: quia ſi non detur oppoſitum illius minoris
                    <lb/>
                  videlicet /  non in quolibet inſtanti etc. ſed in aliquo
                    <lb/>
                  equalis vel intenſior: et et ſit illud c. terminans vnaꝫ
                    <lb/>
                  ſextã gr̄a argumēti / et arguo ſic / ī illo īſtãti c. ꝑ te mo­
                    <lb/>
                  tus a. et motus b. ſunt equales: et in principio erant
                    <lb/>
                  equales et equalem latitudinem debent deperdere:
                    <lb/>
                  ergo equalem latitudinem deperdiderunt: et eq̈les
                    <lb/>
                  reſtant ab eis deperdende, et a. in qualibet ſexta ſe­
                    <lb/>
                  quente c. tantã deperdet ſicut in precedēte quia vni­
                    <lb/>
                  formiter deperdet et b. in qualibet ſequēte ſexta mi­
                    <lb/>
                  nus deperdet quã in precedente quia continuo tar-
                    <lb/>
                  dius et tardius deperdit / vt dicit caſus: et in precedē­
                    <lb/>
                  te deperdet tantum ſicut a: igitur in qualibet ſexta
                    <lb/>
                  ſequente c. inſtans b. minus deperdet quã a. ei ante
                    <lb/>
                  c. inſtans equalem latitudinem deperdit: ergo in to­
                    <lb/>
                  to tempore illius hore b. minorem latitudinem de-
                    <lb/>
                  perdit quã a. / quod eſt contra caſum. </s>
                  <s xml:id="N1EEC7" xml:space="preserve">Et eodem mo-
                    <lb/>
                  do probabitur iuuamine tamen loci a maiore  b.
                    <lb/>
                  motus in inſtanti non eſt intenſior a c. motu. </s>
                  <s xml:id="N1EECE" xml:space="preserve">Et
                    <lb/>
                  ſic patet minor: et per conſequens tota propoſitio.
                    <lb/>
                    <note position="left" xlink:href="note-0153-01a" xlink:label="note-0153-01" xml:id="N1EF0E" xml:space="preserve">53. cal. ī c.
                      <lb/>
                    de mo. lo</note>
                  </s>
                  <s xml:id="N1EEDA" xml:space="preserve">Et hec eſt quiuq̈geſima tertia ↄ̨cluſio calculatoris
                    <lb/>
                  in dicto capitulo de motu locali.
                    <note position="left" xlink:href="note-0153-02a" xlink:label="note-0153-02" xml:id="N1EF16" xml:space="preserve">correlar.</note>
                  </s>
                  <s xml:id="N1EEE4" xml:space="preserve">¶ Ex hac pro-
                    <lb/>
                  poſitione ſequitur /  ſi mobile a. moueatur vnifor-
                    <lb/>
                  miter difformiter ab octauo vſ ad quartum per-
                    <lb/>
                  dendo latitudinem motus vt 4. vniformiter conti-
                    <lb/>
                  nuo ī hora et mobile b. moueatur in eadem hora ab
                    <lb/>
                  octauo vſ ad quartum perdendo etiam latitudi-
                    <lb/>
                  nem vt .4. continuo tardius et tardius: tunc ſi a. per­
                    <lb/>
                  tranſeat .6. pedalia b. pertranſibit minus. </s>
                  <s xml:id="N1EEF5" xml:space="preserve">Proba­
                    <lb/>
                  tur / quia ſi a. tranſit .6. pedalia illa .6. pedalia. </s>
                  <s xml:id="N1EEFA" xml:space="preserve">ſunt
                    <lb/>
                  ſpacium natum tranſiri a gradu medio ipſius mo­
                    <lb/>
                  tus a. vniformiter difformis, et motus b. correſpon­
                    <lb/>
                  det remiſſiori gradui gradu medio: igitur mobile
                    <lb/>
                  b. minus pertranſit quam ſex pedalia. </s>
                  <s xml:id="N1EF05" xml:space="preserve">Minor pa-
                    <lb/>
                  tet ex precedenti propoſitione.</s>
                </p>
                <p xml:id="N1EF1C">
                  <s xml:id="N1EF1D" xml:space="preserve">Sexta ꝓpoſitio </s>
                  <s xml:id="N1EF20" xml:space="preserve">Omnis latitudo mo­
                    <lb/>
                  tus conſimiliter omnino perdita et acq̇ſita vni gra­
                    <lb/>
                  dui omnino correſpondet. </s>
                  <s xml:id="N1EF27" xml:space="preserve">Uolo dicere /  ſi ſit ali-
                    <lb/>
                  quis motus qui gratia exempli incipiat a non gra­
                    <lb/>
                  du et intendatur vſ ad octauum in hora adequate
                    <lb/>
                  vniformiter: et alter motus vel idem remittatur in
                    <lb/>
                  hora vniformiter ſicut intendebatur ab octauo vſ
                    <lb/>
                  ad non gradum: tales motus eidem gradui correſ­
                    <lb/>
                  pondet: et ſic exemplificatu in aliis. </s>
                  <s xml:id="N1EF36" xml:space="preserve">Probatio hu-
                    <lb/>
                  ius concluſionis facilis eſt quoniam tanta oīno eſt
                    <lb/>
                  latitudo motus in via intenſionis quanta in via re­
                    <lb/>
                  miſſionis quoniam omnino eodem modo intendi-
                    <lb/>
                  tur ſicut remittitur. </s>
                  <s xml:id="N1EF41" xml:space="preserve">igitur eidem gradui correſpon­
                    <lb/>
                  det. </s>
                  <s xml:id="N1EF46" xml:space="preserve">Et ſic patet iſta propoſitio / que etiam ſuperius
                    <lb/>
                  probata eſt in tractatu de motu penes cauſam.
                    <note position="left" xlink:href="note-0153-03a" xlink:label="note-0153-03" xml:id="N1EF66" xml:space="preserve">.56. cal. ī
                      <lb/>
                    c. ḋ mo. l.</note>
                  </s>
                  <s xml:id="N1EF50" xml:space="preserve">Et
                    <lb/>
                  hec eſt quinquageſima ſexta concluſio calculatoris
                    <lb/>
                  in capitulo preallegato de motu locali. </s>
                  <s xml:id="N1EF57" xml:space="preserve">In quo lo-
                    <lb/>
                  co idem calculator facit paruam obiectionem con-
                    <cb chead="Capitulum tertium"/>
                  tra hanc concluſionem </s>
                  <s xml:id="N1EF5F" xml:space="preserve">Uide eum ibi.</s>
                </p>
                <p xml:id="N1EF6E">
                  <s xml:id="N1EF6F" xml:space="preserve">Notanduꝫ eſt quarto / vt ſuperius ta-
                    <lb/>
                  ctum eſt velocitates motuum dupliciter inueſtigari
                    <lb/>
                  poſſe videlicet ex cõmenſuratione ſpaciorum ꝑtran­
                    <lb/>
                  ſitorum: et hoc ab effectu: et a poſteriori quod in p̄-
                    <lb/>
                  ſenti tractatu inquirimus. </s>
                  <s xml:id="N1EF7A" xml:space="preserve">Alio vero modo ex cõ-
                    <lb/>
                  menſuratione et proportionalitate proportionum
                    <lb/>
                  a quibus proueniunt velocitates ille: </s>
                  <s xml:id="N1EF81" xml:space="preserve">Et cuꝫ aliqua
                    <lb/>
                  ars ab huius ſcientie primoribus tradita ſit ad in­
                    <lb/>
                  ueſtigandas proportiões a quibus velocitates mo­
                    <lb/>
                  tuum proueniunt. </s>
                  <s xml:id="N1EF8A" xml:space="preserve">Ideo non abs re aliquas propo­
                    <lb/>
                  ſitiones huic famulantes inueſtigationi pñti operi
                    <lb/>
                  inſerendas cenſui.</s>
                </p>
                <note position="right" xml:id="N1EF91" xml:space="preserve">ↄ̨cluſiõſe
                  <lb/>
                horen.
                  <lb/>
                trac. pro­
                  <lb/>
                por. c. 4.</note>
                <p xml:id="N1EF9B">
                  <s xml:id="N1EF9C" xml:space="preserve">Prima propoſitio </s>
                  <s xml:id="N1EF9F" xml:space="preserve">Quauis velocita-
                    <lb/>
                  te data: et quacun proportione propoſita: cuiuſ-
                    <lb/>
                  dam artis ingenio inueſtigari poteſt. </s>
                  <s xml:id="N1EFA6" xml:space="preserve">an data ve-
                    <lb/>
                  locitas a propoſita proportione: aut a minori aut
                    <lb/>
                  maiore proueniat. </s>
                  <s xml:id="N1EFAD" xml:space="preserve">Exemplum / vt data aliqua velo-
                    <lb/>
                  citate que ſit a. cuius proportionem a qua videlicet
                    <lb/>
                  proueniat talis velocitas a. ignoramus: et propoſi­
                    <lb/>
                  ta quauis proportione videlicet dupla: vel tripla
                    <lb/>
                  vel quadrupla inueſtigare et per artem inuenire 
                    <lb/>
                  videlicet talis velocitas a. proueniat a tali propor­
                    <lb/>
                  tione dupla propoſita (exempli gratia) an a maio­
                    <lb/>
                  ri: an a minorl. </s>
                  <s xml:id="N1EFBE" xml:space="preserve">Ad cuius probationem ſit illa velo­
                    <lb/>
                  citas a. qua moueatur c. reſiſtentia a b. potētia cu-
                    <lb/>
                  ius proportionem ad c. ignoro: et ſit proportio ꝓ-
                    <lb/>
                  poſita michi nota dupla exempli gratia: tunc ad ī­
                    <lb/>
                  ueſtigandum: et inueniendum: an illa velocitas a. ꝓ­
                    <lb/>
                  ueniat a maiori proportione quã dupla: an a mino­
                    <lb/>
                  ri: an ab equali: capio vnam aliam potentiam que
                    <lb/>
                  ſit d. que ſe habet in proportione dupla ad b. potē­
                    <lb/>
                  tiam: et moueat vtra illarum potentiarum c. reſi­
                    <lb/>
                  ſtentiam: et manifeſtum eſt /  d. velocius mouet c. re­
                    <lb/>
                  ſiſtentiam quam b. </s>
                  <s xml:id="N1EFD5" xml:space="preserve">Tūc his ſic poſitis: arguitur ſic /
                    <lb/>
                  vel d. mouet c. reſiſtentiam in duplo velocius quam
                    <lb/>
                  b. moueat eãdem reſiſtētiã: vel magis quã in duplo
                    <lb/>
                  velocius: vel minus. </s>
                  <s xml:id="N1EFDE" xml:space="preserve">Si in duplo velocius ſequitur /
                    <lb/>
                   proportio d. ad c. eſt dupla ad proportionem b.
                    <lb/>
                  ad c. </s>
                  <s xml:id="N1EFE5" xml:space="preserve">Patet / quia velocitates ſunt duple et talis ꝓ-
                    <lb/>
                  portio componitur ex ꝓportione d. ad b. et b. ad c. /
                    <lb/>
                  vt patet ex quarto capite ſecunde partis: ergo pro­
                    <lb/>
                  portio b. ad c. eſt medietas proportionis d. ad c. / er­
                    <lb/>
                  go reſiduum puta ꝓportio d. ad b. eſt reliqua medi­
                    <lb/>
                  etas et eſt proportio dupla vt poſitum eū: ergo alia
                    <lb/>
                  proportio b. ad c. eſt etiam proportio dupla cum ſit
                    <lb/>
                  alia medietas. </s>
                  <s xml:id="N1EFF6" xml:space="preserve">Modo omnes medie-
                    <lb/>
                  tates ſunt equales. </s>
                  <s xml:id="N1EFFB" xml:space="preserve">Et ſic inuentum /  illa ē veloci-
                    <lb/>
                  tas a. prouenit a proportione dupla / quod fuit īue­
                    <lb/>
                  ſtigandum. </s>
                  <s xml:id="N1F002" xml:space="preserve">Si vero d. poña maior moueat c. reſi-
                    <lb/>
                  ſtentiam magis quam in duplo velocius quã b. / tūc
                    <lb/>
                  ſequitur /  ꝓportio d. ad c. eſt maior quã dupla ad
                    <lb/>
                  ꝓportionē b. ad c. quia velocitas ꝓueniens a pro-
                    <lb/>
                  portione d. ad c. eſt maior ꝙ̄ dupla ad velocitatem
                    <lb/>
                  prouenientem a proportione b. ad c. et proportio d.
                    <lb/>
                  ad c. componit̄̄ adequate ex ꝓportione d. ad b. et b.
                    <lb/>
                  ad c. / ergo proportio b. ad c. eſt minus ꝙ̄ medietas:
                    <lb/>
                  quia alias tota proportio non eſſet maior ꝙ̄ dupla
                    <lb/>
                  ad illam ſui partem: et totum reſiduum puta ꝓpor-
                    <lb/>
                  tio d. ad b. eſt ꝓportio dupla et eſt maius: igitur il-
                    <lb/>
                  la proportio b. ad c. eſt minor dupla / quod a princi­
                    <lb/>
                  pio fuit inueſtigandum. </s>
                  <s xml:id="N1F01D" xml:space="preserve">Si autē d. poña maior mo­
                    <lb/>
                  ueat c. reſiſtentiam minus ꝙ̄ in duplo velocius: tūc
                    <lb/>
                  illa proportio d. ad c. eſt minor qnã dupla ad ꝓpor­
                    <lb/>
                  tionem b. ad c. / patet / quia velocitas eſt minor quam
                    <lb/>
                  dupla: et vltra eſt minor quã dupla ad ꝓportioneꝫ
                    <lb/>
                  b. ad c. / ergo illa proportio b. ad c. eſt maior quã me­
                    <lb/>
                  dietas totius ꝓportionis d. ad c. </s>
                  <s xml:id="N1F02C" xml:space="preserve">Conſequentia pa­ </s>
                </p>
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