Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Primi tractatus
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file
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0113
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113
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gere. </
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<
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xml:space
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">opus ē ſic argumentari a. poña in certa ꝓpor
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tione adequate vel inadequate velociꝰ continuo mo
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uetur ꝙ̄ b. poña precedens / igitur a. poña tandeꝫ b.
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poñam attinget (eſto / ꝑpetuo motus eius dura-
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ret) </
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<
s
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xml:space
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">Patet hoc correlarium ex ſe. </
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<
s
xml:id
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xml:space
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">¶ Plura alia ar
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gumenta contra pleraſ duorum precedentiuꝫ ca-
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pitum concluſiones adducit calculator in ſecundo
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capite de medio non reſiſtente: ſed ea omnia intelle
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ctis his / que dicta ſunt facile diſſoluuntur. </
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>
<
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xml:space
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">Poſſet
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hic etiam plures induci concluſiones de velocitate
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motus in medio vniformiter difformi vtrī ad gra
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dum terminato et de diuerſarum poñarum motuuꝫ
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comparatione in huiuſcemodi medio: ſed ex predi-
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ctis a perpſicaciuſculo ingenio aliquali tamen la-
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bore comprehendi valent </
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>
<
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xml:space
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">Ideo ſuperſedeo et hec de
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his dixiſſe ſufficiat.</
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<
s
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xml:space
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">¶De motu penes cauſam in medio vni-
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formiter difformi non variato finis.</
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>
</
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<
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xml:space
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">¶ Sequitur de motu penes cauſam
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in medio non reſiſtente.</
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</
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<
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xml:id
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level
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type
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type-free
="
capitulum
">
<
head
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xml:space
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">Capitulum tridecimum / in quo ponū
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tur alique concluſiones velocitatē mo
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tus penes cauſam declarãtes in medio
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non reſiſtente in quo eſt progreſſio la-
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titudinis reſiſtentie vniformiter diffor
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mis: gradu intenſiori quieſcente.</
head
>
<
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<
s
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xml:space
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">QUoniam iam ſupereſt ponere
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aliquas concluſiones de velocitate et tar
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ditate motus penes cauſam in medio nõ
<
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reſiſtente in quo eſt progreſſio, generatio, ſiue extē
<
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ſio latitudinis reſiſteutie partibiliter quo ad ſubie
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ctum. </
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>
<
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xml:space
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">Ideo pro hiis concluſionibus īducendis ma
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thematico ordine aliquas ſuppoſitiones per mo-
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dum terminorum declarationis duximus premit-
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tendas.</
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>
</
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<
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xml:space
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">Prima ſuppoſitio </
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xml:space
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">Reſiſtentia in pro-
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poſito accipitur pro quadam qualitate diſtincta a
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ſuo ſubiecto cõnotando ipſam natam eſſe impedi-
<
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re velocitatem motus: ne mobile ita cito pertranſe
<
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at ſpacium in quo ipſa eſt: ſicut pertranſiret ſi ipſa
<
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non eſſet: et loquor de reſiſtentia motus localis.</
s
>
</
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>
<
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<
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">Secunda ſuppoſitio </
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<
s
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xml:space
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">Per medium nõ
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reſiſtens in propoſito intelligendum eſt ſpacium ſe
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paratum a tali qualitate id eſt carens reſiſtentia
<
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inſtar vacui quod antiqui philoſophãtes ponebãt
<
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cuius vacui philoſophus quarto de phiſico auditu
<
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tractatu ſecundo capitibus ſecundo et tertio memi
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nit.
<
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xml:id
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xml:space
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">phūs .4.
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phi.
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cal. ḋ me:
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nõ reſiſ.</
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</
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<
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xml:space
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">Quare non ī merito Calcu. in concluſionibꝰ de
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medio non reſiſtente nonnū̄ tale ſpacium vacuuꝫ
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appellat: ſepius vero medium non reſiſtens.</
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>
</
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<
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">Tertia ſuppoſitio. </
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">Qualitas que par
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tibiliter alicui ſubiecto acquiritur: tripliciter põt
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acquiri: </
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">Uno modo partibiliter quo ad intenſionē
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tantum. </
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<
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">Alio modo partibiliter quo ad intenſionē
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et extenſionem ſimul: </
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<
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xml:space
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">Et tertio modo partibiliter
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ſiue ſucceſſiue quo ad extenſionem tãtū ſiue quo ad
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ſubiectum tantum (quod idem eſt in propoſito) pri
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mi duo modi declarabuntur inferius in quarto tra
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ctatu. </
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>
<
s
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xml:space
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">Sed tertius modus nunc venit declarandus
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</
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<
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">Pro quo aduertendum eſt / tunc qualitas dicitur
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acquiri: ſiue progredi: ſiue generari: (quod idem ē)
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partibiliter quo ad ſubiectum tantum quando ip-
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ſã continuo efficitur maior: et continuo magis extē
<
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ditur per ſubiectum: et nullo pacto efficitur intēſior
<
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et talis acquiſitio quo ad partes ſubiecti ſit per ac-
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Capitulum tridecimum
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quiſitionem raritatis ipſi qualitati. </
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>
<
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xml:space
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">Hoc autem fa
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miliari exemplo poteſt ſic declarari. </
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<
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">Nam capto
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pedali albo per totum volo / pedali manente nec
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rarefacto nec condenſato. </
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>
<
s
xml:id
="
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xml:space
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">et diuiſa hora preſenti ꝑ
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partes proportionales proportione dupla maio-
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ribus terminatis verſus inſtans initiatiuum in pri
<
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ma parte proportionali illa albedo cõdenſetur ad
<
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ſubduplum relinquendo primam partem ꝓportio
<
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nalem pedalis ꝓportione dupla: et maneat preciſe
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in reſiduis partibus ꝓportionalibus: et in ſecunda
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parte temporis relinquat ſecundam partem ꝓpor
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portionalem pedalis cõdenſando adhuc ad ſubdu
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plum: </
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<
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xml:space
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">Et in tertia iterum ad ſubduplum / et ſic conſe
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quenter. </
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<
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xml:space
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">Et maneat in fine hore illa albedo nõ quã-
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ta in illo ſubiecto indiuiſibiliter in eo exiſtens: dein
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de diuiſa hora futura per partes proportionales
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ordine prepoſtero puta minoribus verſus initiati-
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uum inſtans terminatis: incipiat illa albedo exten
<
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di partibiliter per illud ſubiectum ita rarefiendo ſi
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cut condēſabatur: ita in qualibet ꝓportio
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nali ſequenti efficiatur ī duplo maior / ꝙ̄ fuit in par
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te proportionali īmediate precedenti. </
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>
<
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">Tunc in tali
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caſu illa albedo dicitur in illa ſecunda hora gene-
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rari partibiliter / quo ad ſubiectum tantuꝫ. </
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<
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xml:space
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">Et de ta
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li modo ꝓgreſſionis ſiue generationis latitudinis
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reſiſtentie loquendum eſt in propoſito. </
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<
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xml:space
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">Et hoc mo-
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do intelligit Calcu. caſum prime concluſionis in ca
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pitulo de medio non reſiſtente.</
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</
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<
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">Quarta ſuppoſitio </
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<
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">Latitudo reſiſten
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tia vniformiter difformis tripliciter valet progre-
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di ſiue extendi continuo manens vniformiter dif-
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formis ſub eadem intenſione in medio non reſiſten
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te. </
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>
<
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">Uno modo quieſcente extremo remiſſiori ſiue nõ
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gradu: ceteriſ punctis mouentibus. </
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<
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xml:space
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">Secundo mo
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do quieſcente extremo remiſſiori: ceteriſ punctis
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mouentibus. </
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<
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">Tertio modo neutro extremo totali-
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ter quieſcente: ſed latitudine reſiſtentie a latere ī la
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tus mouente: vel vna parte extremi mouente: et alte
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ra quieſcente et ſic mille aliis modis poteſt imagina
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ri talis reſiſtentie progreſſio. </
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>
<
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xml:space
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">Sed duo primi modi
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duntaxat preſenti conſiderationi deſeruiunt.</
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</
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<
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xml:space
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">Quinta ſuppoſitio </
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<
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xml:space
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">Latitudine reſiſtē
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tie manente vniformiter difformi ſic mouente vt di
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ctum eſt: neceſſe eſt puncta extremo quieſcenti ꝓpin
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quior a tardius moueri. </
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<
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">Patet / quia alias reſiſten-
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tia non maneret vniformiter difformis / vt patet ex
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diffinitione qualitatis vniformiter difformis.</
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>
</
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<
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<
s
xml:id
="
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xml:space
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">¶ His adde / cum dicimus potentiam moueri cum
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huiuſcemodi reſiſtētia progrediente: intelligimus
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ipſam per lineam breuiſſimam moueri ab extremo
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in extremum.</
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>
</
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<
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<
s
xml:id
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xml:space
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">His poſitis ſit prima concluſio </
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>
<
s
xml:id
="
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xml:space
="
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">Dato
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medio non reſiſtente a cuius vno extremo incipiat
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progredi partibiliter latitudo reſiſtentie vniformi
<
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ter difformis altero extremorum ſiue intenſiori ſi-
<
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/>
ue remiſſiori quieſcente / vt declaratum eſt in tertia
<
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ſuppoſitione: ipſa latitudine cõtinuo manēte vni
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formiter difformiter extenſa: omni gradu eius cõ
<
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tinuo vniformiter mouente: ſi aliquod mobile ali-
<
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quando cum tali reſiſtentia mouetur vniformiter
<
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ipſum in eo tempore continuo eſt ad idem punctum
<
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illius reſiſtentie dummodo mobile nõ varietur nec
<
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reſiſtentia quo ad intenſionem aut remiſſionem.</
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>
</
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>
<
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<
s
xml:id
="
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xml:space
="
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">Probatur hec concluſio / quoniaꝫ ſi tale mobile ali
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quando mouetur vniformiter cum tali reſiſtētia / ſe
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quitur / in illo tempore continuo mouetur ab ea-
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dem proportione ſed nullam eandem proportionē </
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