Alvarus, Thomas
,
Liber de triplici motu
,
1509
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<
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<
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="
Primi tractatus
"
file
="
0064
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n
="
64
"/>
merus ſenarius aequirit binarium et numerꝰ qui
<
lb
/>
narius in eodem tempore etiam binariuꝫ: dico /
<
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/>
eque velociter intenduntur ſed non eque ꝓportio-
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/>
nabiliter ſed ſi numerus ternarius acquirat vni-
<
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tatem et numerus ſenarius acquirat in eodem tē-
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pore dualitatem: dico / tunc eque proportionabi
<
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/>
liter acquirunt et non eque velociter. </
s
>
<
s
xml:id
="
N16410
"
xml:space
="
preserve
">quoniam tã
<
lb
/>
ternarius numerus quam ſenarius ꝓportionem
<
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/>
ſexquitertiaꝫ acquirit / vt facile eſt intueri. </
s
>
<
s
xml:id
="
N16417
"
xml:space
="
preserve
">Hec dif
<
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/>
finitio eſt.</
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>
</
p
>
<
p
xml:id
="
N1641C
">
<
s
xml:id
="
N1641D
"
xml:space
="
preserve
">His ſuppoſitis p̄miſſis ſit prima con
<
lb
/>
cluſio. </
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>
<
s
xml:id
="
N16422
"
xml:space
="
preserve
">Si aliqua potentia creſcit reſpectu reſiſtē-
<
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/>
tie non variate: tantam proportioneꝫ acquirit ſu
<
lb
/>
pra ſe quantam ſupra ſuam reſiſtentiam et eocon
<
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/>
tra: </
s
>
<
s
xml:id
="
N1642B
"
xml:space
="
preserve
">Probatur hec concluſio auxiliante ſeptima
<
lb
/>
concluſione octaui capitis precedentis partis.</
s
>
</
p
>
<
p
xml:id
="
N16430
">
<
s
xml:id
="
N16431
"
xml:space
="
preserve
">Nam potentia ſe habet vt quantitas maior et re-
<
lb
/>
ſiſtentia vt minor ſi actiuitas ꝓdeat.</
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>
</
p
>
<
p
xml:id
="
N16436
">
<
s
xml:id
="
N16437
"
xml:space
="
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">Secunda concluſio </
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>
<
s
xml:id
="
N1643A
"
xml:space
="
preserve
">Si aliqua vir-
<
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/>
tus decreſcat reſpectu reſiſtentie non variate. </
s
>
<
s
xml:id
="
N1643F
"
xml:space
="
preserve
">tan
<
lb
/>
tam proportionem deperdit reſpectu ſue reſiſten
<
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/>
tie quantam reſpectu ſui ipſius. </
s
>
<
s
xml:id
="
N16446
"
xml:space
="
preserve
">vt capta potentia
<
lb
/>
vt .4. et reſiſtentia vt .2. ſi potentia / vt quatuor effi
<
lb
/>
ciatur in ſexquitertio minor perdendo vnitatem
<
lb
/>
ſiue proportionem ſexquitertiam: eandem ꝓpor-
<
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/>
tionem ſexquitertiam perdit reſpectu ſue reſiſten
<
lb
/>
tie vt duo. </
s
>
<
s
xml:id
="
N16453
"
xml:space
="
preserve
">Probatur hec concluſio ex ſeptima cõ
<
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/>
cluſione i capitis preallegata eo modo quo
<
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/>
prior.</
s
>
</
p
>
<
p
xml:id
="
N1645A
">
<
s
xml:id
="
N1645B
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xml:space
="
preserve
">Tertia concluſio </
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>
<
s
xml:id
="
N1645E
"
xml:space
="
preserve
">Si aliqua reſiſtē-
<
lb
/>
tia creſcat vel decreſcat reſpectu potentie non va
<
lb
/>
riate: tantam proportionem acquiret vel deper-
<
lb
/>
det reſpectu ſui ipſius quantam acquiret vel deꝑ-
<
lb
/>
det reſpectu talis potentie. </
s
>
<
s
xml:id
="
N16469
"
xml:space
="
preserve
">Hoc eſt: tantam acqui
<
lb
/>
rit vel deperdit talis potentia reſpectu eiuſdeꝫ re
<
lb
/>
ſiſtentie. </
s
>
<
s
xml:id
="
N16470
"
xml:space
="
preserve
">Patet hec concluſio ex octaua concluſio
<
lb
/>
ne octaui capitis p̄allegati et ſuo prīo correlario</
s
>
</
p
>
<
p
xml:id
="
N16475
">
<
s
xml:id
="
N16476
"
xml:space
="
preserve
">Quarta concluſio </
s
>
<
s
xml:id
="
N16479
"
xml:space
="
preserve
">Si potētia creſ-
<
lb
/>
cat vel decreſcat reſpectu potentie non variate: tã
<
lb
/>
tam proportionem acquirit vel deperdit reſpectu
<
lb
/>
ſue reſiſtentie qnantam acquirit vel deperdit reſ
<
lb
/>
pectu ſui ipſius. </
s
>
<
s
xml:id
="
N16484
"
xml:space
="
preserve
">Probatur hec concluſio ex primo
<
lb
/>
correlario ſeptime concluſionis capitis prealle-
<
lb
/>
gati / et facile ex prima et ſecunda huius deducitur</
s
>
</
p
>
<
p
xml:id
="
N1648B
">
<
s
xml:id
="
N1648C
"
xml:space
="
preserve
">Quinta concluſio. </
s
>
<
s
xml:id
="
N1648F
"
xml:space
="
preserve
">Si aliqua potē-
<
lb
/>
tia eque velociter creſcit vĺ decreſcit reſpectu dua
<
lb
/>
rum reſiſtentiarum ſiue equalium ſiue inequaliuꝫ
<
lb
/>
eque velociter cum vtra illarum intendet vel re
<
lb
/>
mittet motum ſuum </
s
>
<
s
xml:id
="
N1649A
"
xml:space
="
preserve
">Probatur hec concluſio / quo
<
lb
/>
niam illa potentia equalem ꝓportionem acquirit
<
lb
/>
vel deperdit reſpectu vtriuſ reſiſtentie / vt patet
<
lb
/>
ex prima concluſione huius / et ſecunda parte ſepti
<
lb
/>
me concluſionis octaui capitis preallegati et ſuo
<
lb
/>
ſecundo correlario / igitur equalem velocitatē ac-
<
lb
/>
quirit vel deperdit reſpectu vtriuſ reſiſtentie.</
s
>
</
p
>
<
p
xml:id
="
N164A9
">
<
s
xml:id
="
N164AA
"
xml:space
="
preserve
">Patet conſequentia ex tertia ſuppoſitione.</
s
>
</
p
>
<
p
xml:id
="
N164AD
">
<
s
xml:id
="
N164AE
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xml:space
="
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">Sexta concluſio </
s
>
<
s
xml:id
="
N164B1
"
xml:space
="
preserve
">Si aliqua reſiſtē-
<
lb
/>
tia creſcat vel decreſcat reſpectu duarum poten-
<
lb
/>
tiarum ſiue equalium ſiue inequaliū non variata
<
lb
/>
rum: vtra potentia eque velociter cum illa reſi-
<
lb
/>
ſtentia intendet vel remittet motum ſuum. </
s
>
<
s
xml:id
="
N164BC
"
xml:space
="
preserve
">Pro-
<
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/>
batur hec concluſio / quoniam reſpectu vtriuſ po
<
lb
/>
tentie equalem ꝓportionem acquirit vel deperdit /
<
lb
/>
vt patet ex ſecundo correlario octaue concluſiõis
<
lb
/>
octaui capitis preallegati: igitur vtra potentia
<
lb
/>
equalem velocitatem acquirit vel deperdit.</
s
>
</
p
>
<
cb
chead
="
Capitulum quintum
"/>
<
p
xml:id
="
N164CB
">
<
s
xml:id
="
N164CC
"
xml:space
="
preserve
">Septima concluſio </
s
>
<
s
xml:id
="
N164CF
"
xml:space
="
preserve
">Si due potētie
<
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/>
inequales eque velociter creſcant vel decreſcãt reſ
<
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/>
pectu eiuſdem reſiſtentie non variate: potentia mi
<
lb
/>
nor velocius intendet vel remittet motū ſuū </
s
>
<
s
xml:id
="
N164D8
"
xml:space
="
preserve
">Pro
<
lb
/>
batur hec concluſio / quoniam ſemper potentia mi
<
lb
/>
nor per equale crementum vel decrementū additū
<
lb
/>
ſibi vel deperditum et maiori: maiorem ꝓportio-
<
lb
/>
nem acquiret vel deperdet quam maior. </
s
>
<
s
xml:id
="
N164E3
"
xml:space
="
preserve
">vt ptꝫ ex
<
lb
/>
quinta ſuppoſitiõe huius capitis: igitur talis po
<
lb
/>
tentia velocius intendet vel remittet motum ſuuꝫ
<
lb
/>
</
s
>
<
s
xml:id
="
N164EB
"
xml:space
="
preserve
">Conſequentia patet ex prima ſuppoſitione. </
s
>
<
s
xml:id
="
N164EE
"
xml:space
="
preserve
">Ab
<
lb
/>
equalibus enim ꝓportionibus acquiſitis ſiue de-
<
lb
/>
perditis inequales velocitates acquiruntur ſiue
<
lb
/>
deperduntur / et per idem ſequitur / ad acquiſitio
<
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/>
nem vel deperditionem maioris maior velocitas
<
lb
/>
acquiritur vel deperditur</
s
>
</
p
>
<
p
xml:id
="
N164FB
">
<
s
xml:id
="
N164FC
"
xml:space
="
preserve
">Octaua concluſio </
s
>
<
s
xml:id
="
N164FF
"
xml:space
="
preserve
">Si due reſiſtētie
<
lb
/>
inequales eque velociter creſcant vel decreſcãt reſ
<
lb
/>
pectu eiuſdem potentie non variate: illa potentia
<
lb
/>
velocius intendet vel remittet motum ſuum cū mi
<
lb
/>
nori reſiſtentia quam cum maiori. </
s
>
<
s
xml:id
="
N1650A
"
xml:space
="
preserve
">Probatur hec
<
lb
/>
concluſio / quoniam ſemper minor reſiſtentia ma-
<
lb
/>
iorem proportionem acquirit vel deperdit ꝑ equa
<
lb
/>
lem deperditionē vel additionē ipſi et maiori / igi
<
lb
/>
tur potentia cum ea velocius intendet vel remittet
<
lb
/>
motū ſuum. </
s
>
<
s
xml:id
="
N16517
"
xml:space
="
preserve
">Patet conſequentia auxilio duarum
<
lb
/>
primarum ſuppoſitionum.</
s
>
</
p
>
<
p
xml:id
="
N1651C
">
<
s
xml:id
="
N1651D
"
xml:space
="
preserve
">Nona concluſio </
s
>
<
s
xml:id
="
N16520
"
xml:space
="
preserve
">Si due potentie in-
<
lb
/>
equales eque velociter creſcant vel decreſcant reſ
<
lb
/>
pectu duarum reſiſtentiarum ſiue equalium ſiue ī
<
lb
/>
equalium: potentia minor ſemper velocius inten
<
lb
/>
det vel remittet motum ſuum ſiue agat cum reſiſtē
<
lb
/>
tia maiore ſiue minore. </
s
>
<
s
xml:id
="
N1652D
"
xml:space
="
preserve
">Patet hec concluſio ex ſe-
<
lb
/>
ptima huius.</
s
>
</
p
>
<
p
xml:id
="
N16532
">
<
s
xml:id
="
N16533
"
xml:space
="
preserve
">Decima concluſio </
s
>
<
s
xml:id
="
N16536
"
xml:space
="
preserve
">Si due reſiſten-
<
lb
/>
tie inequales creſcant vel decreſcant reſpectu dua
<
lb
/>
rum potentiarum ſiue equalium ſiue inequalium:
<
lb
/>
potentia agens cum minore velocius intendet vel
<
lb
/>
remittet motum ſuum. </
s
>
<
s
xml:id
="
N16541
"
xml:space
="
preserve
">Hec patet ex octaua.</
s
>
</
p
>
<
p
xml:id
="
N16544
">
<
s
xml:id
="
N16545
"
xml:space
="
preserve
">Undecima concluſio </
s
>
<
s
xml:id
="
N16548
"
xml:space
="
preserve
">Si due potētie
<
lb
/>
equales vel inequales eque ꝓporrionabiliter creſ
<
lb
/>
cant vel decreſcant reſpectu eiuſdem reſiſtentie nõ
<
lb
/>
variate: tales potentie eque velociter intendēt vel
<
lb
/>
remittēt motus ſuos. </
s
>
<
s
xml:id
="
N16553
"
xml:space
="
preserve
">Patet hec concluſio ex ſexta
<
lb
/>
ſuppoſitione / que diffinit iſtum terminum eque ꝓ
<
lb
/>
portionabiliter auxilio prime ſuppoſitionis.</
s
>
</
p
>
<
p
xml:id
="
N1655A
">
<
s
xml:id
="
N1655B
"
xml:space
="
preserve
">Duodecima concluſio </
s
>
<
s
xml:id
="
N1655E
"
xml:space
="
preserve
">Si due reſi-
<
lb
/>
ſtentie equales ſiue inequales eque ꝓportionabi-
<
lb
/>
liter creſcant vel decreſcant reſpectu eiuſdem po-
<
lb
/>
tentie non variate. </
s
>
<
s
xml:id
="
N16567
"
xml:space
="
preserve
">talis potentia cum vtra illa
<
lb
/>
rum reſiſtentiarum eque velociter intendet vel re-
<
lb
/>
mittet motum ſuum. </
s
>
<
s
xml:id
="
N1656E
"
xml:space
="
preserve
">Hec cum precedente eandem
<
lb
/>
ſortitur demonſtrationem.</
s
>
</
p
>
<
p
xml:id
="
N16573
">
<
s
xml:id
="
N16574
"
xml:space
="
preserve
">Tridecima concluſio </
s
>
<
s
xml:id
="
N16577
"
xml:space
="
preserve
">Si due poten-
<
lb
/>
tie inequales eque ꝓportionabiliter creſcant vel
<
lb
/>
decreſcant reſpectu duarum reſiſtentiaruꝫ ſiue eq̄
<
lb
/>
lium ſiue inequalium non variatarum: ipſe eque
<
lb
/>
velociter intendent vel remittent motus ſuos. </
s
>
<
s
xml:id
="
N16582
"
xml:space
="
preserve
">Pa
<
lb
/>
tet hec concluſio ex prima ſuppoſitione auxiliãte
<
lb
/>
vltima diffiniente eque velociter et eque propor-
<
lb
/>
tionabiliter.</
s
>
</
p
>
<
p
xml:id
="
N1658B
">
<
s
xml:id
="
N1658C
"
xml:space
="
preserve
">Quartadecima concluſio </
s
>
<
s
xml:id
="
N1658F
"
xml:space
="
preserve
">Si due re
<
lb
/>
ſiſtentie inequales creſcant vel decreſcant eque ꝓ
<
lb
/>
portionabiliter reſpectu duarum potentiarum ſi
<
lb
/>
ue equalium ſiue inqualium: tales potentie eque </
s
>
</
p
>
</
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>
</
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>
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