Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Primi tractatus
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0079
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79
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uetur vniformiter cõtinuo intendēte motū ſuū. </
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conſimiliter et ex eiſdem principiis ſecundam par
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tem deduces.</
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<
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<
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xml:space
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">Si aliqua potē-
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tia nõ variata tranſeūdo mediū nõ variatu vnifor
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miter cõtinuo remittit motū ſuū: maiorē latitudi-
<
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nem motus deperdit tranſeundo partē magis re-
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ſiſtentē quã ſibi equalē minus reſiſtentē. </
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diutius inmoratur tranſeundo partē magis reſi-
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ſtentē quã ei equalē minus reſiſtentē: ergo ſi vnifor
<
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miter remittat motū ſuū maiorē latitudinē motꝰ
<
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/>
deperdit tranſeundo partē magis reſiſtentē quaꝫ
<
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ſibi equalē minꝰ reſiſtentē: igitur ſuppoſitio vera.</
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<
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quo īuariato aliqua potentia īuariata mouēs cõ
<
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tinuo vniformiter remittit motū ſuū duabus par
<
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/>
tibus īequalibus, ſignatis quarū vtrã in aliquo
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/>
tēpore adequato adequate pertranſit: et quãlibet
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partē exceſſus per quē maior pars excedit minorē
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illa potentia tranſeundo, cū maiori reſiſtentia cõ-
<
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tinuo mouetur quã quãlibet partē equalē minoris
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tranſeundo: maior eſt ꝓportio velocitatis deper-
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dite a tali potentia ſuper maiori parte mouendo
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ad velocitatē deperditã mouendo ſuper parte mi
<
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nori quã ſit taliū partiū ꝓportio: </
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potentia ſuꝑ c. mediū mouēs vniformiter remittit
<
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motū ſuū: ſignatis prima quarta c. medii et ſecun-
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da medietate eiuſdē c. medii quaꝝ vtrã in aliquo
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tēpore adequate peranſit: maior eſt ꝓportio quaꝫ
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dupla (que eſt inter partes ſignatas) velocitatis
<
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deperdite ab a. potentia mouēdo ſuꝑ ſecūda me-
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dietate ad velocitatē deperditã in prima quarta
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eiuſdē medii mouendo. </
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">Probatur / et ſit medium c.
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ſuper quo īuariato vniformiter continuo a. poten
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tia remittit motū ſuū cuius vna pars minor ſit d.
<
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et ſecūda maior ſit .ef. excedat .ef. ipſum d. per f.
<
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partē: et quamlibet partē ipſius f. minorē d. tran-
<
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ſeundo moueatur a. cū maiori reſiſtentia quã mo-
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uetur quãlibet ſibi equalē tranſeundo cū ſuper d.
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parte mouetur: et vtram illarū partiū puta d. et
<
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ef. in aliquo tēpore adequato adequate pertrãſit:
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ita in tēpore adequato in quo pertrãſit d. nichil
<
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pertrãſeat ſuꝑficiale quin ſit d. aut pars illius: et
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in tēpore in quo adequate pertrãſit .ef. nichil ſuꝑ-
<
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ficiale pertranſeat quin ſit .ef. aut pars eius (ſeclu
<
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do multas alias cauillationes que nichil ꝓpoſito
<
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/>
conducūt) et ſit inter .ef. et d. ꝓportio g. moueatur
<
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potentia a. pertranſeundo e. partē cū equali reſi-
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ſtentia adequate ſicut tranſeundo d. partē vel cum
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maiori / vt oportet / tūc dico / velocitas deperdita
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ab a. tranſeundo partē .ef. ſe habet in maiori pro-
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portione ad velocitatē deperditã ab eadē potētia
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a. tranſeundo d. partē quã ſit ꝓportio g. </
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">Quod ſic
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ꝓbatur: q2 tēporis in quo adequate ꝑtranſitur .ef.
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pars ab ipſa potētia a. ad tēpus in quo adequate
<
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pertranſitur d. pars eſt maior ꝓportio quã g. / ergo
<
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velocitatis deperdite in pertranſitione .ef. partis
<
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adequate ad velocitatē deperditã in pertranſitiõe
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d partis adequate eſt maior ꝓportio quã g. / quod
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fuit ꝓbandū. </
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<
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latitudo in aliquo tēpore cõtinuo vniformiter re-
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mittitur ſiue deperditur in qua ꝓportiõe ſe habēt
<
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tēpora in eadē ſe habent latitudines deperdite: vt
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facile ex diffinitione vniformis remiſſionis alicu-
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ius latitudinis ptꝫ. </
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velocitas qua pertranſitur adequate .ef. pars ve-
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locitate qua pertranſitur d. pars eſt minor: ergo
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Capitulum octauū.
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tēporis in quo adequate pertrãſitur .ef. pars ade
<
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quate ad tēpus in quo pertrãſitur d. pars adequa
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te eſt maior ꝓportio quã g. </
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">Conſequentia ptꝫ / q2 ſi
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velocitas qua pertranſitur .ef. pars eſſet equalis
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velocitati qua pertranſitur d. pars iam temporis
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in quo pertrãſitur .ef. ad tēpus in quo pertrãſitur
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ipſū d. eſſet g. ꝓportio que videlicet eſt inter illas
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partes .ef. et d. / igitur ſi velocitas qua pertrãſitur
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ef. pars adequate velocitate qua pertranſitur d.
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eſt minor: iam ꝓportio tēporis in quo pertrãſitur
<
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ef. pars adequate, ad tēpus in quo pertrãſitur d.
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pars adequate eſt maior ꝓportio quã g. </
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<
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">Ptꝫ hec
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cõſequeatia / q2 maius tēpus requiritur ad pertrã-
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ſeundū ſpaciū .ef. adequate minori velocitate quã
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ad pertranſeundū ipſum adequate aliqua maiori
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</
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<
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">Sed iam probatur antecedens: videlicet veloci-
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tas qua pertranſitur adequate .ef. pars velocita-
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te qua pertranſitur d. pars minor, eſt minor: quia
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velocitas qua pertranſitur e. pars ab ipſa poten-
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tia a. eſt equalis vel minor velocitate qua adequa
<
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te pertraſitur ab eadem potentia d. pars cū ex hy-
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potheſi in pertranſitione e. partis adequate mo-
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ueatur a. potentia cum equali vel maiori reſiſten-
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tia quã in pertrãſitione d. partis adequate: et ipſi
<
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velocitati qua pertranſitur e. pars adequate addi
<
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tur extenſiue adhuc minor velocitas in pertranſi-
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tione f. partis magis reſiſtentis / vt conſtat: igitur
<
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tota velocitas qua pertranſitur .ef. pars adequa-
<
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te eſt minor tota velocitate qua ꝑtranſitur d. pars
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adequate: quod fuit inferendum. </
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<
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">Ptꝫ hec cõſequē-
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tia: q2 ſi alicui latitudini intenſionis addatur ex-
<
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tenſiue aliqua latitudo minoris intenſionis (cete-
<
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ris paribꝰ) totalis illa latitudo aggregata ex ad
<
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dita et preexiſtenti efficitur minoris intenſionis: vt
<
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ſi latitudini vniformiter difformi ab octauo vſ
<
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ad quartū addatur vna latitudo minoris intēſio-
<
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nis puta a. quatuor vſ ad ſecundū: aggregatum
<
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ex eis efficitur minoris intenſionis: q2 preexiſtens
<
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erat vt .6. aggregata vero ex preexiſienti et addita
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eſt vt .5. </
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<
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ſuꝑ quo īuariato aliqua potentia īuariata mouēs
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cõtinuo vniformiter remittit motū ſuū duabꝰ par
<
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tibus inequalibus ſignatis: quarū vtram in ali
<
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/>
quo tēpore adequato adequate pertranſit: et quã-
<
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libet partē exceſſus per quē maior pars excedit mi
<
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norē illa potentia tranſeundo cū minori reſiſtētia
<
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cõtinuo mouetur, quã quãlibet partē equalē mino
<
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ris tranſeundo: velocitatis deperdite a. tali potē-
<
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tia ſuꝑ maiore parte mouēdo ad velocitatē deper
<
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ditam mouendo ſuper parte minori: nec eſt talium
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partiū ꝓportio nec maior. </
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<
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xml:space
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">Probatur: et ſit mediū
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c. ſuꝑ quo īuariato vniformiter cõtinuo a. potētia
<
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inuariata remittit motum ſuū: cuius vna pars mi
<
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/>
nor ſit d. et ſecunda maior ſit .ef. excedat .ef. ipſū
<
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d. per f. partem: et quamlibet partem ipſius f. mi-
<
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norem d. tranſeundo moueatur a. cum minori re-
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ſiſtentia quam mouetur quamlibet ſibi equalem
<
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tranſeūdo cum ſuper d. parte mouetur: et vtram
<
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illarum partium puta d. et .ef. in aliquo tempore
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adequato adequate pertranſit .etc̈. </
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<
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xml:id
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xml:space
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">Et ſit inter .ef.
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et d. proportio g. moueatur potentia a. tranſeū-
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do c. partem cum equali reſiſtentia adequate ſicut
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tranſeundo d. partem vel cum minori / vt oportet:
<
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tunc dico / velocitas deperdita ab a. tranſeundo
<
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partem .ef. nun̄ ſe habet ad velocitatem deper-
<
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ditam ab eadem potentia a. tranſeūdo d. partem
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in g. proportione: nec in maiori.</
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