Alvarus, Thomas
,
Liber de triplici motu
,
1509
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De motu quo ad cauſã in medio non reſiſtente.
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<
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xml:space
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">quod etiam probare intēdimus. </
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<
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xml:space
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">Iam probatur pri
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ma pars minoris: videlicet / non per aliquod tem
<
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pus mouetur eque velociter: quia ſi ſic capio inſtãs
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initiatiuum talis temporis: in quo (vt oportet ꝑ te)
<
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a. et b. ſunt inequalibus reſiſtentiis: </
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<
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xml:space
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">Et arguo ſic / ꝑ
<
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aliqḋ tempus poſt tale inſtans b. poña ↄ̨tinuo mo
<
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/>
uetur eque velociter ſicut a. per te: ergo cõtinuo ꝑ il
<
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/>
lud tempus b. poña eſt in puncto equaliter diſtante
<
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a pūcto in quo ipſa eſt in principio talis temporis
<
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/>
ſicut a. potentia ab eque reſiſtēte puncto in ſuo ma
<
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/>
iori medio ſiue reſiſtentia magis extenſa: et quilib3
<
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/>
punctus eq̈liter diſtans a pūcto ↄ̨ſimilis intēſiõis
<
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/>
in minori medio et in maiori: ī mīori ſiue ī reſiſtētia
<
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/>
minus extenſa eſt intenſior puncto ſibi correſꝑõdē
<
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/>
te in reſiſtentia magis extenſa / vt patet: ergo per il
<
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/>
lud tempus continuo b. eſt in maiori reſiſtentia: et ꝑ
<
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conſequens continuo mouetur tardius: et non eque
<
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velociter / quod probare intendimus. </
s
>
<
s
xml:id
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xml:space
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">Pro-
<
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batur ſecunda pars minoris: videlicet / non per
<
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/>
aliquod tempus mouetur velocius: et īmediate poſt
<
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/>
etc. / quia ſi ſic ſignetur inſtans / in quo b. incipit mo-
<
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/>
ueri per aliquod tempus velocius ante quod īmedi
<
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ate continuo per aliquod tempus tardius moueba
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tur. </
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>
<
s
xml:id
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xml:space
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">Et ſequitur / in tali inſtanti a. et b. habēt equa
<
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les proportiones ad puncta in quibus ſunt quia ſi
<
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/>
b. habeat maiorem ſequitur / īmediate antea ha-
<
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/>
bebat maiorem, et ſic non īmediate antea mouebat̄̄
<
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/>
tardius ꝙ̄ a. / et ſi minorem ſequitur / īmediate poſt
<
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/>
illud inſtans datum mouetur tardius et ſic non tūc
<
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incipit velocius moueri ꝙ̄ a. </
s
>
<
s
xml:id
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xml:space
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">Tunc igitur ſic arguo /
<
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a. et b. in inſtanti dato ſunt ad puncta eque intenſa
<
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/>
et b. incipit continuo velocius moueri recedendo a
<
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/>
ſuo puncto ꝙ̄ a. / ergo b. incipit continuo magis di-
<
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/>
ſtare ab illo puncto ꝙ̄ a. a conſimili: et per conſeq̄ns
<
lb
/>
īcipit continuo eſſe in maiori reſiſtentia quã a. / et ex
<
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/>
hoc ſeq̇tur incipit continuo tardius moueri et non
<
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velocius / quod eſt oppoſitum dati. </
s
>
<
s
xml:id
="
N1C344
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xml:space
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">Sed probatur
<
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tertia pars minoris videlicet / non per aliquod
<
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/>
tempus b. potentia velocius mouetur et immediate
<
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/>
poſt continuo per aliquod tempus tardius moue-
<
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/>
tur: quia ſi ſic. </
s
>
<
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xml:id
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xml:space
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">Capio inſtans / in quo b. incipit mo-
<
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ueri tardius quã a. per aliquod tempꝰ īmediate an
<
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/>
te quod per aliquod tempus continuo velociꝰ mo-
<
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/>
uebatur quã a. </
s
>
<
s
xml:id
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xml:space
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">Et arguo ſic / vel continuo ante illud
<
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/>
inſtans b. mouetur velocius quã a. vel aliquando
<
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/>
tardius et īmediate poſt velocius: </
s
>
<
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xml:space
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">Sed neutrū iſtoꝝ
<
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/>
eſt dicendum: ergo non per aliquod tempus b. potē
<
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/>
tia velocius mouetur et īmediate poſt per aliquod
<
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tewpus continuo tardius mouetur. </
s
>
<
s
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xml:space
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">Patet conſeq̄n
<
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tia / quia b. nū̄ eque velociter mouetur ſicut a. ex ṗ-
<
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ma parte minoris </
s
>
<
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xml:id
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xml:space
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">Sed probatur minor / quia nõ ē
<
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/>
dicendum primum / vt patet ex maiore: nec ſecunduꝫ /
<
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vt patet ex ſecunda parte minoris: ergo propoſitū
<
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</
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<
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xml:space
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">Et ſic patet tota minor et per conſequens correla-
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rium / quod fuit ꝓbandum.
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xml:space
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">3. correl.</
note
>
</
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<
s
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xml:space
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">¶ Sequitur tertio / vbi
<
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cun in latitudinibus ſic vniformiter difformibus
<
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equalibus intenſiue et inequalibus extenſiue / vt po-
<
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nitur in caſu precedentis correlarii alique potentie
<
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incipiunt moueri procedendo ab extremis remiſſio
<
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ribus: poña que mouetur in reſiſtentia minus exten
<
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/>
ſa ſemper citius deueniet ad finem ſue reſiſtentie</
s
>
</
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<
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xml:space
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">Hoc eſt citius pertranſibit totam ſuam reſiſtentiaꝫ
<
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quam altera pertranſeat ſuam reſiſtentiam magis
<
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/>
extenſam ̄uis ipſa tardius continuo moueant̄̄ eã
<
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/>
adequate pertranſeundo. </
s
>
<
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xml:space
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">Probatur correlarium /
<
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qui potentia que mouetur cum reſiſtentia minꝰ ex
<
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tenſa continuo mouetur tardius ex precedenti cor-
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relario. </
s
>
<
s
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xml:space
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">igitur continuo eſt in intenſiori reſiſtentia:
<
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et continuo citius deueniet ad aliquem punctum re
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De motu quo ad cauſã in medio non reſiſtente.
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ſiſtentie quam poña que mouetur in reſiſtentia ma
<
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gis extenſa deueniat ad conſimile punctum. </
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<
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">Conſe
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quentia patet ex probatione precedentis correlarii /
<
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et per conſequens citius deueniet ad punctum extre
<
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mum reſiſtentie minus extenſe ꝙ̄ poña ei equalis de
<
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/>
ueniat ad idem punctum in reſiſtentia magis exten
<
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ſa et ex hoc citius pertranſibit illam / quod fuit pro-
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bandum.
<
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right
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xml:id
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xml:space
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">4. correl.</
note
>
</
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<
s
xml:id
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xml:space
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">¶ Sequitur quarto / datis duabus lati
<
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/>
tudinibus reſiſtentie vniformiter difformis equali
<
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bus intenſiue: et inequalibus extenſiue: et captis dua
<
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/>
bus potentiis equalibus quarum vna incipit mo-
<
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/>
ueri per minus extenſam: et altera per magis exten
<
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/>
ſam ab extremo intenſiori quieſcentibus continuo
<
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latitudinibus et potentiis non variatis: poña que
<
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mouetur cuꝫ reſiſtentia minus extenſa continuo ve
<
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/>
locius mouetur quã altera que mouetur cum reſiſtē
<
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tia magis extenſa: </
s
>
<
s
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xml:space
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">Hoc correlariuꝫ facile ex proba
<
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tione precedentis demonſtratur: hoc premiſſo / oī
<
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/>
um punctorum equaliter diſtantium in illis latitu-
<
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/>
dinibus ab extremo intenſiori punctus in latitudi
<
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/>
ne minus extenſa minus reſiſtit ꝙ̄ punctus ſibi cor
<
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reſpondens in latitudine magis extenſa </
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<
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">Quod pa
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tet intuenti.
<
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xml:id
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xml:space
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">5. correl.</
note
>
</
s
>
<
s
xml:id
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xml:space
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">¶ Sequitur quinto / latitudine reſiſtē
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tie vniformiter difformi ſic ſe condenſante / vt po-
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nitur in caſu argumenti: quolibet eius puncto ītrin
<
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ſeco continuo vniformiter mouente, quieſcente gra
<
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du remiſſiori: et intenſiori tardius mouente quã po
<
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tentia que incipit moueri cum illo mouetur cum eo
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dem, potentia et omni pūcto verſus intenſius extre
<
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mum quieſcens mouentibus: omnis talis poña que
<
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ſic mouetur continuo intendit motum ſuum. </
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>
<
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N1C40A
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">Pro-
<
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batur / quia talis poña continuo velocius mouetur
<
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quã punctus in quo pro tunc eſt: et continuo moue-
<
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tur verſus minorem reſiſtentiam: igitur propoſitū
<
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</
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>
<
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xml:id
="
N1C414
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xml:space
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">Conſequentia patet cum minori ex caſu: et maior ꝓ
<
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batur / quia talis potentia velocius mouetur quam
<
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/>
punctus velociſſime motus / vt patet ex caſu: ergo ̄
<
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/>
quicun alter eiuſdem latitudinis </
s
>
<
s
xml:id
="
N1C41D
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xml:space
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">Patet con-
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ſequentia / quia quilibet aliorum qui mouetur tar-
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dius mouetur: et ad ipſum habet potentia maioreꝫ
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proportionem / igitur etc.
<
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xlink:href
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xml:id
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xml:space
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">6. correl.</
note
>
</
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<
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xml:id
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xml:space
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">¶ Sequitur ſexto / ſi q̇li
<
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bet punctus intrinſecus talis reſiſtentie ↄ̨tinuo mo
<
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/>
ueretur verſus extremum remiſſius quieſcens: conti
<
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/>
nuo remittendo motum ſuum: potentia etiam con-
<
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/>
tinuo intenderet motum ſuuꝫ: dūmodo incipiat po
<
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/>
tentia velocius moueri ꝙ̄ punctus qui velociſſime
<
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mouetur. </
s
>
<
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xml:space
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">Patet hoc correlarium ex precedenti iun
<
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cto loco a fortiori.
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xml:id
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xml:space
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preserve
">7. correl.</
note
>
</
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<
s
xml:id
="
N1C444
"
xml:space
="
preserve
">¶ Sequitur ſeptimo / latitudi-
<
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/>
ne reſiſtentie vniformiter difformis ſic ſe condenſã
<
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/>
te: vt poſitum eſt quolibet puncto eius intrinſeco cõ
<
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/>
tinuo ſucceſſiue intendente motum ſuum, et potētia
<
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/>
velocius incipiat moueri a puncto velociſſime mo-
<
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/>
to quã talis punctus incipit moueri: ipſis mouen-
<
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/>
tibus verſus extremum remiſſius / non oportet /
<
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/>
talis potentia continuo intendat motum ſuum: nec
<
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/>
oportet / continuo remittat motū ſuum / nec opor
<
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/>
tet / aliquando intendat et aliquando remittat: ſꝫ
<
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/>
poteſt aliquando intendere, et aliquando remitte-
<
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/>
rē: oportet tamen / incipiat intendere. </
s
>
<
s
xml:id
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N1C45D
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xml:space
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preserve
">Probatur
<
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/>
quia caſu poſito / ſit vna latitudo r̄ſiſtētie ab octa
<
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/>
uo vſ ad non gradum: et incipiat poña vt .12. mo-
<
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/>
ueri cum illa ſe condenſante / vt poſitum eſt: quoli-
<
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/>
bet puncto intrinſeco continuo intendente motum
<
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/>
ſuum taliter quando poña deuenerit ad punctuꝫ
<
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/>
vt ſex / tunc primo punctum vt ſex incipiat moueri a
<
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/>
proportione dupla. / et iam ſequitur (cum ille pūctus
<
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/>
continuo intendat motum ſum) / poña non ſufficit
<
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/>
ipſum precedere: ſed ipſe precedet potentiam: et ſic
<
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/>
poña manebit cum intenſiori reſiſtentia et remittit </
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>
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