Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Primi tractatus
"
file
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0119
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119
"/>
li et a d. mobili: igitur ſpacii pertranſiti a c. mobili
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ad ſpacium pertrãſitū a d. mobili eſt f. ꝓportio: et
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per conſequens d. mouetur tardiꝰ c. in f. ꝓportione /
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qḋ fuit ꝓbandū: ptꝫ ergo ſuppoſito.
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xml:space
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">1. correĺ.</
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<
s
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xml:space
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">¶ Ex hac ſup-
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poſitiõe ſequitur / ſi mobile quod debet attingi a
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potentia tardius mota moueatur in maiori ꝓpor-
<
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tione tardius alio ꝙ̄ ſit proportio diſtantiaꝝ: tunc
<
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/>
citius attingetur a ſua potētia. </
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>
<
s
xml:id
="
N1B820
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xml:space
="
preserve
">Et ſi velociꝰ tardiꝰ
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attingetur: patet facile.</
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</
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>
<
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="
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<
s
xml:id
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N1B830
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xml:space
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preserve
">Quarta ſuppoſitio / latitudine reſiſtē-
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/>
tie vniformiter difformis mouente modo dicto per
<
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/>
mediū nõ reſiſtens: potentia que cū tali reſiſtentia
<
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/>
mouetur nun̄ preterit partē vel punctū illius re-
<
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/>
ſiſtentie qui velocius mouetur quã potentia ſufficit
<
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moueri cum illo. </
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>
<
s
xml:id
="
N1B83D
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xml:space
="
preserve
">Nec vn̄ punctus qui tardius mo
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uetur quã potentia ſufficit moueri cū illo preterit
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potentiã. </
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<
s
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N1B844
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xml:space
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">Nec etiã punctus qui ita velociter mouet̄̄
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ſicut potentia ſufficit moueri cū illo preterit poten
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tiã aut preteritur ab ea. </
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>
<
s
xml:id
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N1B84B
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xml:space
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preserve
">Patet hec ſuppoſitio faci
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le intelligenti modum ſe habendi illius latitudinis
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ſic progredientis in illo medio non reſiſtente.</
s
>
</
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>
<
p
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<
s
xml:id
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xml:space
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">His ſuppoſitis. </
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>
<
s
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xml:space
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">Sit prima concluſio
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</
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<
s
xml:id
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N1B85A
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xml:space
="
preserve
">Progrediente in medio nõ reſiſtente latitudine re
<
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/>
ſiſtentie vniformiter difformis a nõ gradu vſ ad
<
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/>
certū gradū: quieſcente nõ gradu: et quolibet pun-
<
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/>
cto eius continuo vniformiter moto: potentia in-
<
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/>
cipiens ſimul moueri cū tali reſiſtētia continuo vni
<
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/>
formiter mouebitur: dūmodo extremū intenſiꝰ ta-
<
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/>
lis reſiſtentie velocius cõtinuo moueatur quã talis
<
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/>
potentia ſufficit mouere cum illo aut equaliter. </
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>
<
s
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="
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xml:space
="
preserve
">Et
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intelligo in oībus cõcluſionibus ipſa latitudo cõ
<
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tinuo maneat vniformiter difformis. </
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>
<
s
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N1B872
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xml:space
="
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">Probatur
<
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hec cõcluſio. </
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>
<
s
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xml:space
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preserve
">Et ſit illa potentia in caſu cõcluſionis
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b. </
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>
<
s
xml:id
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N1B87C
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xml:space
="
preserve
">Et arguo ſic / b. potentia nun̄ intendit: nec vn̄
<
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/>
remittit motū ſuū cõtinuo mouendo cū tali reſiſtē-
<
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/>
tia in caſu dicto: et mouebitur cum tali reſiſtētia in
<
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/>
caſu cõcluſionis / igitur b. continuo vniformiter mo
<
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/>
uebitur / quod fuit ꝓbandū. </
s
>
<
s
xml:id
="
N1B887
"
xml:space
="
preserve
">Patet cõſequētia ex ſe
<
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</
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>
<
s
xml:id
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N1B88B
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xml:space
="
preserve
">Et probatur maior / q2 ſi per aliquod tēpus b. potē
<
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/>
tia intēdit motū ſuū ſignetur pūctus / in q̊ eſt in in-
<
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/>
ſtanti medio talis tēporis qui ſit a. / et arguo ſic / vel
<
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/>
ipſe punctus a. mouetur ita velociter ſicut potentia
<
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/>
ſufficit mouere cū illo: vel velociꝰ vel tardiꝰ. </
s
>
<
s
xml:id
="
N1B896
"
xml:space
="
preserve
">Si ita
<
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/>
velociter iam ſequitur / nõ intēdit motum ſuū per
<
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/>
illud tēpus: ſed vniformiter poſt illud inſtans con-
<
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/>
tinuo mouebitur (cū ſemꝑ erit ī illo pūcto / vt ptꝫ ex
<
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/>
quarta ſuppoſitione huiꝰ). </
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>
<
s
xml:id
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xml:space
="
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">Et ſi tardius ſequitur /
<
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/>
iã potentia remittit motū ſuū: q2 mouebitur ver-
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ſus puncta intēſiora. </
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>
<
s
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xml:space
="
preserve
">Si vero velocius ipſe punctꝰ
<
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a. moueatur quã ipſa potentia b. / ſequit̄̄ (cū ſemper
<
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/>
a. moueat̄̄ vniformiter) / potētia b. nun̄ p̄teriuit
<
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/>
a. punctū. </
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>
<
s
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xml:space
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preserve
">Ptꝫ cõſequētia eſt quarta ſuppoſitione:
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et vltra b. potentia nū̄ preteriuit a. punctū et īme-
<
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diate ante inſtans in quo eſt in illo pūcto a. p̄cede-
<
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/>
bat illud: igr̄ ſemꝑ ante illud inſtans p̄ceſſit illud: et
<
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/>
per cõſequens ſemꝑ ante illud inſtans mouebat̄̄ cū
<
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maiori reſiſtētia quã modo et tardius, et modo mo-
<
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uetur a. punctus velocius quam b. potentia / ergo
<
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/>
ſemꝑ ante illud inſtans a. pūctus mouebat̄̄ velociꝰ
<
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/>
quã b. potētia, et inceperūt b. potētia et a. punctꝰ in
<
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/>
eodē inſtãti et ab eodē pūcto ſus eandē differentiã
<
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/>
moueri. </
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>
<
s
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xml:space
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">ergo modo a. p̄cedit b. et ꝑ ↄ̨ñs nõ ſūt ſimĺ /
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qḋ eſt oppoſitū dati. </
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>
<
s
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xml:space
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">Sed iam ꝓbat̄̄ minor vcꝫ / per
<
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nullū tēpus remittit motum ſuū ſtante caſu: ſi ſic
<
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/>
detur punctꝰ in quo talis poña eſt in īſtanti medio
<
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talis tꝑis qui ſit a. </
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>
<
s
xml:id
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xml:space
="
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">Et arguo ſic / ipſa poña b. remit
<
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tit motū ſuū ꝑ te: ergo ipſa modo continuo ꝓcedit
<
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/>
ſus pūcta intēſiora veniēdo ad a. punctū quomo
<
cb
chead
="
Capitulū quartūdecimū.
"/>
do velociꝰ mouet̄̄ ꝑ te: ergo ſemꝑ ãtea poña b. ſeque
<
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/>
batur a. punctū mouēs cõtiuuo cū minori reſiſtētia
<
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/>
quã modo: ptꝫ ↄ̨ña / q2 nõ poteſt cū caſu priꝰ p̄cedere
<
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/>
et poſtea ſequi (vt facile deducit̄̄ ex quarta ſuppoſi-
<
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/>
tioue) / et ex cõſequēti ſequit̄̄ / cõtinuo antea moue-
<
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bat̄̄ velociꝰ quã modo cū a. pūcto, et modo etiã velo
<
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/>
cius quã a. punctꝰ motꝰ cõtinuo vniformiter: ergo
<
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/>
ſemꝑ p̄ceſſit b. poña a. punctū, et modo etiã p̄cedit: et
<
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/>
ꝑ ↄ̨ñs ſunt ſimĺ et ꝑ te ſunt ſimĺ / ergo cõtradictio /
<
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et ſic ptꝫ totū antecedens: et per cõſequēs concluſio.</
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>
</
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>
<
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<
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xml:space
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preserve
">Secunda concluſio / latitudine vni-
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formiter difformi ſic ꝓgrediente (vt dictū eſt) ꝑ me-
<
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/>
diū nõ reſiſtens quolibet puncto intrīſeco cõtinuo
<
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/>
intēdente motū ſuū: quieſcēte nõ gradu vĺ extremo
<
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/>
remiſſiori, extremo intēſiori velociꝰ cõtinuo mouē
<
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/>
te quã poña q̄ mouet̄̄ cū tali reſiſtētia ſufficiat mo-
<
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/>
ueri cū illo: talis poña incipiens moueri ab eodem
<
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/>
pūcto, et in eodē inſtãti cū tali reſiſtētia cõtinuo in-
<
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/>
tēdit motū ſuū quãdiu cū tali reſiſtētia mouet̄̄ ſtan-
<
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/>
te caſu. </
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>
<
s
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="
N1B908
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xml:space
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">Probat̄̄ / q2 talis poña ꝑ nullū tēpus moue
<
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tur vniformiter: nec ꝑ aliqḋ tēpus remittit motum
<
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/>
ſuū cū tali reſiſtētia ſtante caſu: et mouet̄̄ (vt pono) /
<
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/>
igr̄ cõtinuo intēdit motū ſuū: ↄ̨ña eſt nota / et maior
<
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/>
ptꝫ manifeſte ex ſcḋo correlario prime cõcluſionis
<
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/>
p̄cedentis capitis. </
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>
<
s
xml:id
="
N1B915
"
xml:space
="
preserve
">Sed minor ꝓbat̄̄ videlicet / per
<
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/>
nullū tēpus remittit motū ſuū ſtante caſu: q2 ſi ſic
<
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/>
detur aliqḋ tēpus per qḋ cõtinuo remittit motum
<
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/>
ſuū, et ſigno punctū in quo poña eſt in īſtãti medio
<
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/>
illiꝰ tēporis: et ſit a. </
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>
<
s
xml:id
="
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xml:space
="
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">Et arguit̄̄ ſic / in illo inſtãti po-
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tētia eſt in a. pūcto: et remittit motū ſuū ꝑ te / igr̄ ve
<
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/>
locius mouet̄̄ ipſo a. ꝓcedēdo cõtinuo ſus pūcta
<
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intēſiora. </
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>
<
s
xml:id
="
N1B929
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xml:space
="
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">Et vltra velociꝰ mouet̄̄ ipſo a. pūcto ꝓce
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dendo ↄ̨tinuo ſus pūcta intēſiora: et ipſe a. pūctꝰ
<
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/>
ſemꝑ ãte tardiꝰ mouebat̄̄ quã modo: cū cõtinuo ex
<
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/>
caſu intēdat motū ſuū: et poña ſemꝑ antea velociꝰ
<
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/>
mouebat̄̄ ꝙ̄ modo cū ↄ̨tinuo ãtea eſſet in remiſſiori
<
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/>
reſiſtētia ſiue pūcto quã eſt a. ī quomodo eſt (nõ em̄
<
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/>
priꝰ p̄ceſſit ipſa poña a. punctū, et deinde ipſe a. pū
<
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/>
ctus p̄teriuit ipſã potētiã / vt ptꝫ ex q̈rta ſuppoſiti-
<
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/>
one) / igr̄ ſemꝑ ãtea velociꝰ mouebat̄̄ poña ꝙ̄ a. pū-
<
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/>
ctꝰ: et ꝑ ↄ̨ñs modo p̄cedit ipſa ponã a. pūctū cū īci-
<
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/>
piūt ab eodē pūcto in eodē inſtãti moueri et ſic non
<
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/>
eſt modo in ipſo a. pūcto: et nūc eſt in illo ꝑ te: igit̄̄
<
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/>
ↄ̨tradictio: et ſic ptꝫ / nõ eſt dicendū illã potentiaꝫ
<
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/>
per aliquod tempus remittere motum ſuum: quod
<
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/>
fuit probandum. </
s
>
<
s
xml:id
="
N1B948
"
xml:space
="
preserve
">Patet ergo concluſio.</
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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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">Tertia concluſio. </
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>
<
s
xml:id
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xml:space
="
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">Progrediēte latitu
<
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/>
dine vniformiter difformis reſiſtētie etc̈. / vt dictū eſt
<
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/>
quieſcēte nõ g̈du, aut extremo remiſſiori, quolibet
<
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/>
pūcto ītrīſeco ↄ̨tinuo remittēte motū ſuū, intēſiori
<
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/>
extremo īcipiēte velociꝰ moueri ꝙ̄ poña q̄ mouet̄̄ cū
<
lb
/>
tali reſiſtentia ſufficiat moueri ad illo: talis poña
<
lb
/>
īcipiēs moueri cū tali reſiſtētia in eodē inſtanti ab
<
lb
/>
eodē pūcto ↄ̨tinuo ̄diu ſic mouet̄̄ cū tali reſiſtētia
<
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/>
ſtãte caſu remittit motū ſuū. </
s
>
<
s
xml:id
="
N1B962
"
xml:space
="
preserve
">Probat̄̄: qm̄ talis po
<
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/>
tētia mouet̄̄ cū tali reſiſtētia / vt ptꝫ. </
s
>
<
s
xml:id
="
N1B967
"
xml:space
="
preserve
">Et ꝑ nullū tēpꝰ
<
lb
/>
vniformiṫ mouet̄̄ ſtate caſu (vt ptꝫ ex ſcḋo correla-
<
lb
/>
rio ṗme ↄ̨cluſiõis p̄cedētis capitis. </
s
>
<
s
xml:id
="
N1B96E
"
xml:space
="
preserve
">Nec ꝑ aliqḋ tē-
<
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/>
pus intēdit motū ſuū mouēdo cū tali reſiſtētia: igr̄
<
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/>
ↄ̨tinuo remittit motū ſuū mouēdo cū tali reſiſtētia
<
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/>
ſtãte caſu / qḋ fuit ꝓbandū </
s
>
<
s
xml:id
="
N1B977
"
xml:space
="
preserve
">Ptꝫ ↄ̨ña, et ꝓbat̄̄ ſcḋa ꝑs
<
lb
/>
maioris vcꝫ / ꝑ nullū tēpꝰ intendit motū ſuū: q2 ſi
<
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/>
ſic detur punctꝰ in quo potētia eſt in inſtãti medio
<
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/>
talis temporis, et ſit a. </
s
>
<
s
xml:id
="
N1B980
"
xml:space
="
preserve
">Et arguitur ſic / per illud tem
<
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/>
pus potentia intendit motum ſuū per te, et in inſtã-
<
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/>
ti medio illius eſt in a. puncto: igitur ille pūctus a.
<
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/>
precedet ipſam potentiam immediate poſt illud in
<
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/>
ſtans, et potentia erit cum remiſſiori puncto: patet </
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>
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