Alvarus, Thomas, Liber de triplici motu, 1509

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              <div xml:id="N1DD6A" level="4" n="3" type="chapter" type-free="capitulum">
                <p xml:id="N1EABE">
                  <s xml:id="N1EB1A" xml:space="preserve">
                    <pb chead="Secundi tractatus" file="0151" n="151"/>
                  ea proportione minor illorū eſt minor maiore per
                    <lb/>
                  quã maior ꝓportio excedit minorē: id eſt per quam
                    <lb/>
                  ꝓportio maioris numeri ad illud tertiū excedit ꝓ-
                    <lb/>
                  portionē minoris numeri ad idem tertiū. </s>
                  <s xml:id="N1EB2C" xml:space="preserve">Quoniã
                    <lb/>
                  ꝓportio maioris ad idē tertiū cõponit̄̄ ex ꝓportio­
                    <lb/>
                  ne illius ad numeꝝ minorem, et numeri minoris ad
                    <lb/>
                  idem tertiū. </s>
                  <s xml:id="N1EB35" xml:space="preserve">Hoc eſt primū correlariū quarte cõclu­
                    <lb/>
                  ſionis quartis capitis ſcḋe partis. </s>
                  <s xml:id="N1EB3A" xml:space="preserve">Sed ita eſt in ꝓ-
                    <lb/>
                  poſito /  ſi ꝓportio velocitatis maioris ad veloci-
                    <lb/>
                  tatē minorē eſſet equalis g. ꝓportioni tēpoꝝ: tunc
                    <lb/>
                  ipſa iam excederet ꝓportionē quã modo habet pu­
                    <lb/>
                  ta f. per h. ꝓportionē / vt ptꝫ ex caſu: ergo modo illa
                    <lb/>
                  velocitas maior eſt in h. ꝓportione minor quã tūc /
                    <lb/>
                  qḋ fuit ꝓbandū.
                    <note position="left" xlink:href="note-0151-01a" xlink:label="note-0151-01" xml:id="N1EB82" xml:space="preserve">Correĺ.</note>
                  </s>
                  <s xml:id="N1EB4E" xml:space="preserve">¶ Et vt hec theoretica non ſit expers
                    <lb/>
                  practice tale infero correlariū. </s>
                  <s xml:id="N1EB53" xml:space="preserve">Si equꝰ a. moueret̄̄
                    <lb/>
                  velocitate vt .4. in hora adequate, et equus b. velo-
                    <lb/>
                  citate vt .6. adequate in media hora, et ipſe equꝰ b.
                    <lb/>
                  6. leucas pertranſeat in illa media hora: neceſſe eſt
                    <lb/>
                  equū a. ad extremū .8. leucarum in hora deuenire.
                    <lb/>
                  </s>
                  <s xml:id="N1EB5F" xml:space="preserve">Probat̄̄ / qm̄ in p̄dicto caſu equus b. motꝰ in mino-
                    <lb/>
                  ri tēpore maiore velocitate mouet̄̄ ipſo equo a. mo­
                    <lb/>
                  to in maiore tēpore et ꝓportio dupla tēpoꝝ excedit
                    <lb/>
                  ꝓportionē velocitatū ꝑ ſexquitertiã ꝓportionē: igr̄
                    <lb/>
                  auxilio p̄cedentis ꝓpoſitiõis ꝑſpicuū euadit equū
                    <lb/>
                  a. in ſexquitertio maius ſpaciū ꝑtranſire quã equꝰ
                    <lb/>
                  b. ꝑtranſeat. </s>
                  <s xml:id="N1EB6E" xml:space="preserve">Sed equus b. ex caſu ſex leucarū ſpa-
                    <lb/>
                  ciū ꝑtranſit in illa media hora: igitur a. ſpaciū .8.
                    <lb/>
                  leucaꝝ in hora cõpleuit (quãdoquidē .8. ad .6. ſexq̇-
                    <lb/>
                  tertia eſt ꝓportio) </s>
                  <s xml:id="N1EB77" xml:space="preserve">¶ Hoc ſenario numero ꝓpoſiti-
                    <lb/>
                  onū lata illa diſtinctio velocitatum fimbrias ſuas
                    <lb/>
                  colligat, ſiquidem ſenarius perfectus eſt.</s>
                </p>
                <p xml:id="N1EB88">
                  <s xml:id="N1EB89" xml:space="preserve">Notandū eſt tertio tãgendo materiã
                    <lb/>
                  ſecūdi argumēti pricipalis ante oppoſitū /  aliud
                    <lb/>
                  eſt latitudinē motꝰ vniformiter intendi aut vnifor-
                    <lb/>
                  miter remitti: aliud vero mobile vniformiter mo-
                    <lb/>
                  ueri. </s>
                  <s xml:id="N1EB94" xml:space="preserve">Unde cum latitudo motus vniformiter inten-
                    <lb/>
                  ditur a nõ gradu vel a gradu ad certū gradū ſemꝑ
                    <lb/>
                  mobile vniformiter difformiter mouetur. </s>
                  <s xml:id="N1EB9B" xml:space="preserve">Et ſimi-
                    <lb/>
                  liter quãdo vniformiter remittitur aliquis motus
                    <lb/>
                  a gradu vſ ad nõ gradū vel certū gradū / tunc mo­
                    <lb/>
                  bile vniformiter difformiter mouetur. </s>
                  <s xml:id="N1EBA4" xml:space="preserve">Nã latitudo
                    <lb/>
                  motus ſi acquiſita aut deꝑdita coextendit̄̄ vnifor­
                    <lb/>
                  miter difformiter tēporis partibꝰ, ita  illiꝰ motꝰ
                    <lb/>
                  cuiuſlibet partis gradus mediꝰ tanto exceditur a
                    <lb/>
                  ſūmo quantū excedit infimū vel nõ gradū. </s>
                  <s xml:id="N1EBAF" xml:space="preserve">Quare
                    <lb/>
                  definitiue arguendo relinquit̄̄ oēm talē motum ſic
                    <lb/>
                  vniformiter acquiſitū vel deperditū eſſe vniformi-
                    <lb/>
                  ter difformē. </s>
                  <s xml:id="N1EBB8" xml:space="preserve">Hanc materiã latiꝰ īquiras recurren­
                    <lb/>
                  do ad hentiſberū in ſuo tractatu de motu locali ca­
                    <lb/>
                  pite primo in fine adiūctis eiuſdē hentiſberi cõmē-
                    <lb/>
                  tariis. </s>
                  <s xml:id="N1EBC1" xml:space="preserve">Inſuꝑ aduerte /  latitudo motꝰ tripliciter
                    <lb/>
                  acquiri põt vt ad ꝓpoſitū noſtrū ſufficit vel deꝑdi
                    <lb/>
                  </s>
                  <s xml:id="N1EBC7" xml:space="preserve">Quod ideo dixerim / qm̄ multis aliis modis et re-
                    <lb/>
                  mitti et intendi põt motꝰ latitudo: ſed hii tres dūta­
                    <lb/>
                  xat nr̄o quadrant ꝓpoſito. </s>
                  <s xml:id="N1EBCE" xml:space="preserve">Primo modo latitudo
                    <lb/>
                  motꝰ põt acq̇ri vel deꝑdi cõtinuo vniformiter, vt pu­
                    <lb/>
                  ta qñ mobile in partibꝰ equalibꝰ tꝑis eq̈les gradꝰ
                    <lb/>
                  velocitatis acq̇rit vel deꝑdit cõtinue. </s>
                  <s xml:id="N1EBD7" xml:space="preserve">Scḋo põt lati­
                    <lb/>
                  tudo motꝰ acq̇ri vel deꝑdi cõtinuo velociꝰ et velociꝰ
                    <lb/>
                  vt puta qñ mobile in q̈libet parte ſequēti tꝑis con-
                    <lb/>
                  tinuo maiorē latitudinē motꝰ deꝑdit quã in equali
                    <lb/>
                  p̄cedenti. </s>
                  <s xml:id="N1EBE2" xml:space="preserve">Tertio modo poteſt latitudo motus ſiue
                    <lb/>
                  velocitas acquiri vel deperdi cõtinuo tardiꝰ et tar-
                    <lb/>
                  dius: vt puta quãdo mobile ↄ̨tinuo in qualibet par­
                    <lb/>
                  te ſequēti tēporis minorē latitudinē motꝰ deperdit
                    <lb/>
                  quam in equali precedente. </s>
                  <s xml:id="N1EBED" xml:space="preserve">¶ Qua diuiſione pre-
                    <lb/>
                  miſſa pono aliquas propoſitiones.</s>
                </p>
                <p xml:id="N1EBF2">
                  <s xml:id="N1EBF3" xml:space="preserve">Prima propoſitio. </s>
                  <s xml:id="N1EBF6" xml:space="preserve">Si aliquis motus
                    <cb chead="Capitulū tertiū."/>
                  vniformiter cõtinuo intendatur vel remittat̄̄ a cer-
                    <lb/>
                  to gradu vſ ad certū gradū vel ad nõ gradū eius
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                  velocitas gradui medio correſpõdet. </s>
                  <s xml:id="N1EC00" xml:space="preserve">Probat̄̄ hec
                    <lb/>
                  ꝓpoſitio / q2 talis motꝰ ſic intenſſus aut remiſſus eſt
                    <lb/>
                  vniformiter difformis / vt ptꝫ ex principio huiꝰ nota­
                    <lb/>
                  bilis auxiliante definitione motꝰ vniformiter dif-
                    <lb/>
                  formis: igitur eiꝰ velocitas gradui ſuo medio corre­
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                  ſpondet. </s>
                  <s xml:id="N1EC0D" xml:space="preserve">Patet hec conſequentia ex notabili pri-
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                  mo huius capitis.</s>
                </p>
                <p xml:id="N1EC12">
                  <s xml:id="N1EC13" xml:space="preserve">Secūda ꝓpoſitio. </s>
                  <s xml:id="N1EC16" xml:space="preserve">Oīs motꝰ cõtinuo
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                  velocius et velocius intenſus correſpondet quantū
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                  ad velocitatē gradui remiſſiori medio gradu inter
                    <lb/>
                  extremū intēſionis eiꝰ in principio motꝰ et īter extre­
                    <lb/>
                  mū intēſionis in fine motꝰ. </s>
                  <s xml:id="N1EC21" xml:space="preserve">Exemplū / vt ſi motus vt
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                  4. cõtinuo intēdat̄̄ ꝑ horã quovſ ſit vt .8. ita  ac-
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                  quirat quatuor gradꝰ in hora et illã latitudinē .4.
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                  graduū cõtinuo velocius et velociꝰ acquirat in ipſa
                    <lb/>
                  hora: tūc tota eiꝰ velocitas correſpõdet minori gra­
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                  dui ſexto gradu qui eſt gradus mediꝰ inter .4. et .8.
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                  hoc eſt illud mobile nõ tã velociter mouetur in illa
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                  hora adequate quã velociter moueretur ſi cõtinuo
                    <lb/>
                  vniformiter moueret̄̄ gradu ſexto medio. </s>
                  <s xml:id="N1EC34" xml:space="preserve">Probat̄̄
                    <lb/>
                  hec ꝓpoſitio. </s>
                  <s xml:id="N1EC39" xml:space="preserve">Sit a. motꝰ et b. motꝰ equalis ei in prī­
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                  cipio: et volo /  a. ꝑ horã cõtinuo vniformiter inten­
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                  dat̄̄ vſ ad c. gradū acquirendo certã latitudinē, et
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                  b. cõtinuo in eadē hora adequate intendat̄̄ etiã vſ
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                  ad c. gradū acq̇rendo eandem latitudinē adequate
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                  quã acq̇rit a. ita  in fine tēporis a. et b. erūt equa-
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                  les c. gradu ſicut etiã in principio ſunt equales: ac-
                    <lb/>
                  quirat tamē b. illa in latitudinē cõtinuo velocius et
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                  velociꝰ quã a. acquirit cõtinuo vniformiter. </s>
                  <s xml:id="N1EC4C" xml:space="preserve">Et ar-
                    <lb/>
                  guit̄̄ ſic / velocitas ipſiꝰ a. correſpõdet gradui medio
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                  inter c. gradū et gradū in quo eſt a. et b. in principio /
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                  vt patꝫ ex p̄cedēte ꝓportione. </s>
                  <s xml:id="N1EC55" xml:space="preserve">et velocitas motus b.
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                  correſpondet minori gradui quam gradui medio /
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                  igr̄ oīs motus cõtinuo velocius et velociꝰ intenſus
                    <lb/>
                  correſpondet gradui remiſſiori medio gradu inter
                    <lb/>
                  extremū eiꝰ intēſius et remiſſius. </s>
                  <s xml:id="N1EC60" xml:space="preserve">Ptꝫ hec cõſeq̄ntia /
                    <lb/>
                  q2 idē eſt gradus mediꝰ vĺ equalis inter extrema a.
                    <lb/>
                  motꝰ et b. motus, vt ponit caſus. </s>
                  <s xml:id="N1EC67" xml:space="preserve">Et ſicut ꝓbatur de
                    <lb/>
                  b. in ꝓpoſito, ita arguendū eſt de quocū alio mo­
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                  tu cõtinuo velociꝰ et velociꝰ intenſo. </s>
                  <s xml:id="N1EC6E" xml:space="preserve">Sed iam reſtat
                    <lb/>
                  ꝓbare minorē / q2 motus b. in quolibet inſtãti intrī-
                    <lb/>
                  ſeco erit minor motu a. / ergo velocitas eiꝰ in toto tē­
                    <lb/>
                  pore adequate minori gradui correſpõdebit quaꝫ
                    <lb/>
                  velocitas ipſiꝰ a. </s>
                  <s xml:id="N1EC79" xml:space="preserve">Sed velocitas ipſiꝰ a. correſpon-
                    <lb/>
                  det gradui medio inter extrema ipſius b. / vt ꝓbatū
                    <lb/>
                  eſt: ergo velocitas b. correſpõdet gradui remiſſiori
                    <lb/>
                  gradu medio inter extrema eiuſdē b. / quod fuit pro­
                    <lb/>
                  bandū. </s>
                  <s xml:id="N1EC84" xml:space="preserve">Sed iã ꝓbo illud añs vcꝫ /  motus b. in quo­
                    <lb/>
                  libet inſtanti intrinſeco eſt minor et remiſſior motu
                    <lb/>
                  a. q2 ſi nõ detur aliquod inſtans in quo ſit maior vĺ
                    <lb/>
                  equalis et ſit c. tale inſtans illiꝰ hore: et argr̄ ſic / in c.
                    <lb/>
                  inſtãti b. motꝰ eſt eq̈lis a. motu cū caſu poſito: g̊ eq̈-
                    <lb/>
                  les latitudīes acq̇ſiuerūt adeq̈te in tꝑe termīato ad
                    <lb/>
                  illud inſtãs, et eq̈les reſtãt acq̇rēde vſ ad c. gradū,
                    <lb/>
                  et ↄ̨tinuo b. velocius acq̇ret latitudinē illã acq̇rendã
                    <lb/>
                  poſt illud inſtãs quã ãtea idē b. acq̇ſiuerit, et ãtea a.
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                  et b. acq̇ſiuerūt eq̈liter, et ↄ̨tinuo a. poſt illud inſtans
                    <lb/>
                  acq̇ret vniformiter: g̊ velociꝰ et citius b. acquiret c.
                    <lb/>
                  gradum quã a. / quod eſt contra caſum. </s>
                  <s xml:id="N1EC9D" xml:space="preserve">Et eodē mo-
                    <lb/>
                  do probabitur /  in illo inſtanti motus b. nõ eſt in-
                    <lb/>
                  tenſior motu a. / quia iã ſequeretur /  ante illud in-
                    <lb/>
                  ſtans velociꝰ acq̇rebat b. latitudinē motus quã a. et
                    <lb/>
                  poſt illud inſtãs velociꝰ acq̇ret ex caſu reſiduū lati-
                    <lb/>
                  tudinis acq̇rende quã antea, et ꝑ ↄ̨ñs poſt illud in-
                    <lb/>
                  ſtãs velociꝰ et citiꝰ acq̇ret reſiduū latitudinis acq̇rē-
                    <lb/>
                  de quã a. / et ſic citiꝰ habebit c. gradū quã a. / quod eſt
                    <lb/>
                  contra caſum. </s>
                  <s xml:id="N1ECB0" xml:space="preserve">Et ſic patet illa minor probata.</s>
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