Alvarus, Thomas, Liber de triplici motu, 1509

Table of figures

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                  <s xml:id="N1ABF8" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0111" n="111"/>
                  maiori in qua proportione maius medium excedit
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                  minꝰ: tūc cõtinuo vniformiter et eque velociter oīno
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                  ille potentie mouētur. </s>
                  <s xml:id="N1AC12" xml:space="preserve">Uolo dicere /  ſi ſint duo me­
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                  dia ſe habentia in proportione dupla, per que ex-
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                  tenditur cõſimilis latitudo reſiſtentie vniformiter
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                  difformis terminata ad non gradum: et moueatur
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                  vna potentia in minori medio incipiendo a nõ gra­
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                  du medii, et a nõ gradu potentie, continuo creſcen-
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                  do vniformiter: et in medio maiori moueatur vna
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                  alia potentia incipiēdo ſimiliter creſcere a nõ gra­
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                  du potentie, et a non gradu reſiſtentie: quia inter
                    <lb/>
                  illa media eſt proportio dupla creſcat cõtinuo po-
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                  tentia que mouetur in medio minori in duplo velo-
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                  cius altera que mouetur in medio maiori: tunc di-
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                  co  ille potentie mouentur equaliter. </s>
                  <s xml:id="N1AC2D" xml:space="preserve">Probatur
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                  correlariū vniuerſaliter. </s>
                  <s xml:id="N1AC32" xml:space="preserve">Et ſuppono /  in quacū
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                  proportione ſe habent talia media per que extendi­
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                  tur latitudo eadem vel cõſimilis reſiſtentie vnifor-
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                  miter difformis terminate ad nõ gradū: in ea pro-
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                  portione ſe habēt puncta equi diſtantia a nõ gradu
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                  in illis mediis. </s>
                  <s xml:id="N1AC3F" xml:space="preserve">Quod ptꝫ facile ex diffinitione qua­
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                  litatis vniformiter difformis quarto tractatu. </s>
                  <s xml:id="N1AC44" xml:space="preserve">Hoc
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                  ſuppoſito probatur correlarium. </s>
                  <s xml:id="N1AC49" xml:space="preserve">Et ſint duo me-
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                  dia ſe habentia in f. proportione et moueatur a. po­
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                  tentia in maiori continuo vniformiter: et b. in mino­
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                  ri: et creſcat b. cõtinuo in f. proportione velocius a.
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                  </s>
                  <s xml:id="N1AC53" xml:space="preserve">Quo poſito ſic argumentor / potentia b. que moue-
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                  tur in medio minori nõ mouetur velocius a. nec tar­
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                  dius: igitur cõtinuo equaliter. </s>
                  <s xml:id="N1AC5A" xml:space="preserve">Patet conſequētia /
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                  et probatur maior: quia ſi b. mouetur velocius quã
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                  a. / ſequitur /  b. eſt in puncto magis diſtante a non
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                  gradu ſui medii ꝙ̄ a. / igitur mouetur a. minori pro-
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                  portione ꝙ̄ a. / et per conſequēs tardius. </s>
                  <s xml:id="N1AC65" xml:space="preserve">Patet hec
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                  conſequentia / quia ſi eſſent in punctis equidiſtanti­
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                  bus mouerentur ab eadem proportione: quoniam
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                  tunc f. proportio eſſet inter illa puncta / vt patet ex
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                  ſuppoſitione: et inter potentias etiam eſſet f. pro-
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                  portio: ergo ſequitur /  ille potentie haberent e-
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                  quales proportiones ad ſuas reſiſtentias. </s>
                  <s xml:id="N1AC74" xml:space="preserve">Patet
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                  conſequentia / quia ſi inter b. et a. eſt f. proportio: et
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                  inter reſiſtentiam ipſius b. et reſiſtentiam ipſius a.
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                  eſt f. proportio: igitur qualis eſt proportio ipſiꝰ b.
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                  ad a. talis eſt reſiſtentie ipſius b. ad reſiſtentiam
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                  ipſius a. et ſi talis eſt proportio ipſius b. ad a. qua-
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                  lis eſt reſiſtentie ipſius b. ad reſiſtentiam ipſius a. /
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                  ſequitur permutatim ex ſecunda concluſione tertii
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                  capitis ſecunde partis /  talis eſt proportio ipſius
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                  b. ad reſiſtentiam ipſius b. qualis eſt ipſiꝰ a. ad re-
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                  ſiſtentiam ipſius a. / et ſic ptꝫ conſequentia. </s>
                  <s xml:id="N1AC8B" xml:space="preserve">Et vltra
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                  ex ↄ̨ſequēti ille potentie a. et b. / tunc haberent equa-
                    <lb/>
                  les proportiones ad ſuas reſiſtentias: ergo modo
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                  proportio ipſius b. ad ſuam reſiſtentiam eſt minor
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                  quam proportio ipſius a. ad ſuam reſiſtentiam: et
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                  per conſequens mouetur tardius. </s>
                  <s xml:id="N1AC98" xml:space="preserve">Patet conſequē­
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                  tia / quia b. eſt in maiori reſiſtentia quam tunc eſſet.
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                  </s>
                  <s xml:id="N1AC9E" xml:space="preserve">Et per hoc ptꝫ minor / quia ſi b. mouetur tardiꝰ quã
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                  a. / ſequitur /  eſt in minori reſiſtentia quam eſſet ſi
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                  moueretur equaliter ſicut a. ſed ſi moueret̄̄ equali-
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                  ter ſicut a. moueretur ab eadem proportione: et mo­
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                  do mouetur in minori reſiſtentia quam tunc: ergo
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                  a. maiori proportione/ et per conſequens velocius et
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                  nõ tardius / quod eſt oppoſitum conceſſi. </s>
                  <s xml:id="N1ACAD" xml:space="preserve">Et ſic patꝫ
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                  antecedens et per conſequens totum correlarium.
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                    <note position="left" xlink:href="note-0111-01a" xlink:label="note-0111-01" xml:id="N1AD2C" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N1ACB9" xml:space="preserve">¶ Sequitur tertio /  ſi ſint duo media ineq̈lia qua­
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                  lificata eadem vel conſimili reſiſtentia vniformiter
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                  difformi terminata ad nõ gradum: et incipiant due
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                  potentie non variate in eodem inſtanti moueri per
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                  illa media: et talis ſit proportio potentie mouentis
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                  in medio minori ad reliquam potentiaꝫ qualis eſt
                    <cb chead="Capitulū duodecimū."/>
                  proportio medii maioris ad medium minus: tunc
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                  tales potētie cõtinuo eque velociter mouētur. </s>
                  <s xml:id="N1ACCB" xml:space="preserve">Pro­
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                  batur: et ſint duo media īter que eſt ꝓportio f. et ſint
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                  due potentie a. et b. et b. ad a. ſit f. proportio: et in-
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                  cipiat b. moueri in minori medio ad non gradu et
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                  a. in maiori. </s>
                  <s xml:id="N1ACD6" xml:space="preserve">Quo poſito arguo ſic / a. et b. continuo
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                  ſunt in punctis equidiſtantibus a nõ gradu ſui me-
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                  dii: ergo continuo eque velociter mouentur. </s>
                  <s xml:id="N1ACDD" xml:space="preserve">Patet
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                  conſequentia / quia pūcta equaliter diſtantia ſe ha­
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                  bent in f. proportione: vt patet ex ſuppoſitione ſu-
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                  perioris correlarii: ergo ſequitur /  ſi potētie ſunt
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                  in punctis eque diſtantibus  ipſe mouentur ab e-
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                  quali proportione. </s>
                  <s xml:id="N1ACEA" xml:space="preserve">Patet conſequentia vt in ſupe­
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                  riori correlario. </s>
                  <s xml:id="N1ACEF" xml:space="preserve">Et ex conſequenti ſequitur:  ſi b.
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                  eſt in puncto magis propinquo non gradui ꝙ̄ a. 
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                  iã mouetur a. maiori ꝓportione ꝙ̄ a. q2 eſt in remiſ­
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                  ſiori puncto quã eſſet ſi eſſet in puncto equidiſtanti
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                  ſicut a. / et per cõſequens moueretur velocius ꝙ̄ a. </s>
                  <s xml:id="N1ACFA" xml:space="preserve">Et
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                  ſi eſſet in puncto magis diſtanti a nõ gradu ꝙ̄ a. / iã
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                  ſequitur /  tunc moueretur cū reſiſtentia intenſiori
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                  quã ſi eſſet in puncto equidiſtãti ſicut pūctus in quo
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                  eſt a. / et per ↄ̨ſequēs moueret̄̄ tardiꝰ quã a. et ſic nõ ve­
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                  lociꝰ. </s>
                  <s xml:id="N1AD07" xml:space="preserve">Patet cõſequētia / q2 ſi eſſet in puncto equidi-
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                  ſtanti ſicut a. moueretur ab equali ꝓportione: ergo
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                  quãdo eſt in intēſiori mouetur a minori. </s>
                  <s xml:id="N1AD0E" xml:space="preserve">Et ſic patꝫ
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                  veritas correlarii / qm̄ ad b. moueri velociꝰ a. / ſequit̄̄
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                  ipſum moueri tardius: et ad b. moueri tardius, ſe-
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                  quitur ipſum moueri velocius. </s>
                  <s xml:id="N1AD17" xml:space="preserve">Opus eſt dicere igi­
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                  tur /  continuo mouetur equaliter cum ipſo a.</s>
                </p>
                <note position="right" xml:id="N1AD32" xml:space="preserve">4. correĺ.</note>
                <p xml:id="N1AD36">
                  <s xml:id="N1AD37" xml:space="preserve">¶ Sequitur quarto:  dabile eſt medium vniformi­
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                  ter difforme in reſiſtentia ad nõ gradum termina-
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                  tum: quod potentia a non gradu potentie creſcens
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                  vniformiter continuo, nõ valet vniformiter conti-
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                  nuo mouendo ſuo motu abſoluere ab extremo re-
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                  miſſiori inchoando. </s>
                  <s xml:id="N1AD44" xml:space="preserve">Probatur / et capio vnū mediū
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                  difforme in quantitate vniformiter difforme in re-
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                  ſiſtentia terminata ad non gradū: cuius medii pri-
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                  ma medietas puta remiſſior ſit longior quam ſecū­
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                  da in ſexquialtero / vt patet in figura.</s>
                </p>
                <figure xml:id="N1AD4F" number="8">
                  <image file="0111-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0111-01"/>
                </figure>
                <p xml:id="N1AD53">
                  <s xml:id="N1AD54" xml:space="preserve">Et incipiat b. potentia ab extremo remiſſiori talis
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                  medii moueri creſcendo a nõ gradu potentie conti-
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                  nuo vniformiter inchoando ab extremo remiſſiori
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                  vt ſepius poſitū eſt: et moueatur quo ad vſ ad ex-
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                  tremū intenſius deueniat per lineã rectam: tunc di­
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                  co /  ipſa potentia b. nõ cõtinuo vniformiter moue­
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                  tur illud medium tranſeundo. </s>
                  <s xml:id="N1AD63" xml:space="preserve">Quod ſic probatur /
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                  q2 ſi b. potentia cõtinuo vniformiter moueretur pu­
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                  ta a. proportione f. exempli gratia in ſexquialtero
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                  minori tēpore totam ſecundã medietatē magis re-
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                  ſiſtentē abſolueret quaꝫ primã quia ipſa eſt in ſex-
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                  quialtero breuior ex hypotheſi: et ex cõſequenti ſe-
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                  quitur /  b. potentia tranſeundo ſecundã medieta-
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                  tem in ſexquialtero minorē potētiam acquirit quã
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                  tranſeundo primam medietatem: cum vniformiter
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                  continuo intendatur: et tranſeundo eandē ſecundã
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                  medietatē ſue reſiſtentie, tantam latitudinē acqui-
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                  rit adequate ſicut tranſeūdo primã q2 reſiduã me-
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                  dietatē latitudinis: igitur tranſeundo ſecundã me-
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                  dietatem inter acquiſitū potentie et acquiſitū reſi-
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                  ſtentie nõ eſt tanta proportio ſicut tranſeundo pri-
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                  mam: et tranſeundo primam eſt proportio f. / vt pa-
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                  tet / quia continuo ab f. proportiõe mouetur per te: </s>
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