Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Quarti Tractatus
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219
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in infinitum velociꝰ alteraret ſuū pedale ꝙ̄ a. / ſꝫ cõ-
<
lb
/>
ſequēs eſt falſum / igit̄̄ illud ex quo ſeq̇tur. </
s
>
<
s
xml:id
="
N259C4
"
xml:space
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preserve
">Sequela
<
lb
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ꝓbatur / q2 in eodē tēpore et in equali ſubiecto in in
<
lb
/>
finitū plures gradus caliditatis ꝓducit b. ꝙ̄ a. per
<
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/>
alterationē / ergo in infinitū velocius alterat b. ſuū
<
lb
/>
paſſum ꝙ̄ a. / fuit inducēdū </
s
>
<
s
xml:id
="
N259CF
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xml:space
="
preserve
">Iam ꝓbat̄̄ falſitas ↄ̨ſe
<
lb
/>
quētis / q2 equaliter oīno de forma caliditatis pro
<
lb
/>
ducit b. ſicut a. in eodē tꝑe / vt patet ex caſu / igir̄ eque
<
lb
/>
velociter oīno alterat b. ſuū paſſum ſicut a. et ꝑ ↄ̨ñs
<
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/>
non in infinitū velocius / qḋ eſt oppoſitū ↄ̨ñtis. </
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>
<
s
xml:id
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N259DA
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xml:space
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">Pa
<
lb
/>
tet ↄ̨ña / q2 velocitas motus vniuerſaliter attendi
<
lb
/>
hꝫ penes effectū ꝓductuꝫ ſaltem vbi aliquid ꝑ motuꝫ
<
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ꝓducitur. </
s
>
<
s
xml:id
="
N259E3
"
xml:space
="
preserve
">¶ Itē ſi illa ſolutio eſſet bona ſequeretur /
<
lb
/>
ab equalib3 ꝓportionibus alterantiū ad ſua al
<
lb
/>
terabilia inequales velocitates alterationis ꝓue-
<
lb
/>
nirēt: ſꝫ cõſequēs eſt manifeſte falſuꝫ / igitur illḋ ex
<
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/>
quo ſeq̇tur. </
s
>
<
s
xml:id
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N259EE
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xml:space
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preserve
">Sequela ꝓbat̄̄ et volo / a. alteret vnū
<
lb
/>
pedale in hora ad gradum vt .4. et b. equale ipſi a.
<
lb
/>
in actiuitate alteret vnū bipedale in eadē hora ad
<
lb
/>
eundem gradum vt .4. ſemper ītelligo ꝑ totū </
s
>
<
s
xml:id
="
N259F7
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xml:space
="
preserve
">Quo
<
lb
/>
poſito manifeſtum eſt ꝑ te b. in duplo velociꝰ al-
<
lb
/>
terat ſuū paſſum ꝙ̄ a. / q2 ſuum paſſum eſt in duplo
<
lb
/>
maius et ꝓportio ipſius a. ad ſuum paſſum et b. ad
<
lb
/>
ſuū paſſum ſunt equales / igitur ab equalibꝰ ꝓpor-
<
lb
/>
tionibus alterãtiū ad ſua alterabilia inequales ve
<
lb
/>
locitates alteratiõis ꝓueniūt / qḋ fuit ꝓbandū </
s
>
<
s
xml:id
="
N25A06
"
xml:space
="
preserve
">Pro
<
lb
/>
batur minor / q2 ſi ꝓportio b. ad ſuū paſſuꝫ eſſet ma
<
lb
/>
ior ꝙ̄ ꝓportio a. ad ſuū paſſuꝫ / tūc ſequeret̄̄ / intē-
<
lb
/>
ſiorē caliditatē ꝓduceret b. ī ſuū paſſum ꝙ̄ a. / ſꝫ hoc
<
lb
/>
eſt falſuꝫ / vt patet ex caſu / igit̄̄ illud ex quo ſequitur
<
lb
/>
</
s
>
<
s
xml:id
="
N25A12
"
xml:space
="
preserve
">¶ Ideo dices aliter et melius ſicut dicendū eſt ad ar
<
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/>
gumentū negando ſequelã et ad ꝓbationē dices /
<
lb
/>
velocitas motus alteratiõis nõ debet attendi ſim-
<
lb
/>
pliciter penes multitudinē graduū intēſiõis ipſiꝰ
<
lb
/>
qualitatis que mediante tali motu alterationis ꝓ-
<
lb
/>
ducitur / ſꝫ penes multitudinē graduū ipſius forme
<
lb
/>
ſiue in magno ſubiecto ꝓducat̄̄ ſiue in paruo. </
s
>
<
s
xml:id
="
N25A21
"
xml:space
="
preserve
">Ma
<
lb
/>
nifeſtum em̄ eſt / cū aliqḋ calidū vniformiter rarū
<
lb
/>
acquirit ꝑ totū vnū gradū caliditatis intenſiue in
<
lb
/>
duplo plus de forma acq̇rit illud totuꝫ calidum ̄
<
lb
/>
vna eius medietas ſicut dictū eſt ſuperiꝰ / in dēſo
<
lb
/>
finite vniforme in duplo plus eſt de materia ꝙ̄ in
<
lb
/>
ſua medietate. </
s
>
<
s
xml:id
="
N25A30
"
xml:space
="
preserve
">Uolo igitur dicere / ſicut in denſo
<
lb
/>
ſignãtur gradus entitatis materie penes quorum
<
lb
/>
multitudinē dēſitas attēdit̄̄ ita in ꝓpoſito dico ve
<
lb
/>
locitatē alteratiõis attēdi debere penes multitudi
<
lb
/>
nē qualitatis in eodē tꝑe ꝓducte nullo pacto cõſide
<
lb
/>
rando intēſionē aut ſubiectū. </
s
>
<
s
xml:id
="
N25A3D
"
xml:space
="
preserve
">Sꝫ contra hoc ſic ar
<
lb
/>
guit̄̄ / q2 tunc ſequeret̄̄ / ſi a. alterans in prīa quar
<
lb
/>
ta vnius hore ꝓducit vnū gradū caliditatis inten-
<
lb
/>
ſiue et entitatiue ꝑ totū et in ſecūda quarta tantuꝫ
<
lb
/>
et in tertia tantū et in quarta ſimiĺr tantum b. vero
<
lb
/>
in primo pedali vnius quadrupedalis ꝓduceret ſi-
<
lb
/>
militer vnū gradū caliditatis entitatiue et intenſi-
<
lb
/>
ue in prima quarta hore et in ſecūda quarta in ſecū
<
lb
/>
do pedali tantū ꝓduceret et in tertia in tertio peda
<
lb
/>
li et in quarta in quarto pedali tantū gradum ꝓdu
<
lb
/>
ceret / tunc ſeq̇retur / eque velociter in illa hora b.
<
lb
/>
alteraret quadrupedale ſicut a. pedale / ſꝫ ↄ̨ſequens
<
lb
/>
eſt falſuꝫ / igit̄̄ illud ex quo ſequit̄̄. </
s
>
<
s
xml:id
="
N25A58
"
xml:space
="
preserve
">Seq̄la patet faci-
<
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/>
le ex ſolutiõe / q2 tantū de caliditate entitatiua ꝓdu
<
lb
/>
cit b. ſicut a. adequate </
s
>
<
s
xml:id
="
N25A5F
"
xml:space
="
preserve
">Falſitas ↄ̨ſequētis arguitur /
<
lb
/>
q2 alteratio ipſius a. qua vcꝫ alterat ſuū paſſuꝫ eſt
<
lb
/>
velocior alteratiõe ipſius b. / ergo nõ eque velociter
<
lb
/>
in illa hora b. alterat quadrupedale ſicut a. pedale
<
lb
/>
</
s
>
<
s
xml:id
="
N25A69
"
xml:space
="
preserve
">Cõſequētia patet et arguitur añs / q2 intēſio qua a.
<
lb
/>
intēdit pedale eſt velocior alteratione ipſius b. et in
<
lb
/>
tenſio qua a. intendit pedale eſt alteratio qua a. al
<
cb
chead
="
Capi. primum
"/>
terat pedale: ergo alteratio qua a. alterat pedale
<
lb
/>
eſt velocior alteratiõe ipſius b. qua vcꝫ alterat qua
<
lb
/>
drupedale. </
s
>
<
s
xml:id
="
N25A77
"
xml:space
="
preserve
">Cõſequētia pꝫ cū minore </
s
>
<
s
xml:id
="
N25A7A
"
xml:space
="
preserve
">Nõ em̄, vt ſup
<
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pono, alteratio et intēſio diſtinguūtur. </
s
>
<
s
xml:id
="
N25A7F
"
xml:space
="
preserve
">et maior ꝓ
<
lb
/>
batur: q2 intēſio qua a. intendit pedale eſt velocior
<
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/>
intenſione qua b. intēdit quadrupedale et oīs intē-
<
lb
/>
ſio qua b. intendit quadrupedale eſt alteratio qua
<
lb
/>
b. alterat quadrupedale / igit̄̄ intēſio qua a. intēdit
<
lb
/>
pedale eſt velocior alteratione qua b. alterat qua-
<
lb
/>
drupedale. </
s
>
<
s
xml:id
="
N25A8E
"
xml:space
="
preserve
">Et ſic pꝫ maior.
<
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position
="
right
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xlink:href
="
note-0219-01a
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xlink:label
="
note-0219-01
"
xml:id
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N25BC9
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xml:space
="
preserve
">Dicitur.</
note
>
</
s
>
<
s
xml:id
="
N25A96
"
xml:space
="
preserve
">¶ Dices et bñ conceden-
<
lb
/>
do ſequelã et negãdo ↄ̨ñs eē falſum et ad punctū ꝓ-
<
lb
/>
bationis nego / hanc ↄ̨ñam intēſio qua a: intēdit pe
<
lb
/>
dale eſt velocior alteratiõe ipſiꝰ b. et intēſio qua a.
<
lb
/>
intēdit pedale eſt alteratio qua a. alterat pedale / g̊
<
lb
/>
alteratio qua a. alterat pedale eſt velocior altera-
<
lb
/>
tione ipſius b. </
s
>
<
s
xml:id
="
N25AA5
"
xml:space
="
preserve
">Arguit̄̄ em̄ in quatuor termīs. </
s
>
<
s
xml:id
="
N25AA8
"
xml:space
="
preserve
">debe
<
lb
/>
ret eī ſic īferri / g̊ alṫatio q̈ a. alṫat pedare ē velocior
<
lb
/>
intēſio quã alteratio ipſiꝰ b. </
s
>
<
s
xml:id
="
N25AAF
"
xml:space
="
preserve
">Uel aliter rñdēdo ad
<
lb
/>
materiã argumēti poterꝪ ſecure dicere motū ītēſio
<
lb
/>
nis nõ eē cõparabilē motui alteratiõis ī velocitate
<
lb
/>
et traditate prior tñ ſolutio magis plꝫ. </
s
>
<
s
xml:id
="
N25AB8
"
xml:space
="
preserve
">¶ Cõtra q2
<
lb
/>
tūc ſeq̇retur / velocius alteraret eandē reſiſtētiaꝫ
<
lb
/>
vnū pedale vniformiter calidū / vt q̈tuor ꝙ̄ vnū aliḋ
<
lb
/>
pedale infinite calidū vniformiter ſine aliqua con
<
lb
/>
trarii ꝑmixtiõe: ſꝫ ↄ̨ñs videt̄̄ manifeſte falſum: igit̄̄
<
lb
/>
illud ex quo ſeq̇tur </
s
>
<
s
xml:id
="
N25AC5
"
xml:space
="
preserve
">Falſitas ↄ̨ñtis relinq̇tur nota et
<
lb
/>
arguit̄̄ ſeq̄la et pono / in vno pedali qḋ ſit a. in q̄li
<
lb
/>
bet parte ꝓportionali inducãtur .4. gradus calidi-
<
lb
/>
tatis nõ tamē ꝑ totū ſꝫ in parte ꝓportionali ipſius
<
lb
/>
a. corrñdēte parti ꝓportionali tꝑis ipſo a. et tēpo-
<
lb
/>
re ꝓportione dupla diuiſis pono tamē / in ea pro
<
lb
/>
portione qua vna pars ꝓportionalis eſt minor al-
<
lb
/>
tera minus in tali parte entitatiue inducat̄̄ de cali-
<
lb
/>
ditate ſꝑ tamē vt .4. ī'tenſiue in altero vero pedali
<
lb
/>
puta b. in qualibet parte ꝓportionali tꝑis induca
<
lb
/>
tur per totū b. medietas caliditatis intēſiue et enti-
<
lb
/>
tatiue q̄ in tali parte tꝑis introducit̄̄ in aliqua par
<
lb
/>
te ꝓportionali ipſius a. </
s
>
<
s
xml:id
="
N25AE0
"
xml:space
="
preserve
">Quo poſito alterēt a. et b.
<
lb
/>
conſimilē reſiſtentiã et ſequit̄̄ / a. velocius altera-
<
lb
/>
bit eandē reſiſtãtiam ꝙ̄ b. et tñ b. eſt infinite caliduꝫ
<
lb
/>
vniformiter ſiue cõtrarii admixtiõe: vt ſuppono: et
<
lb
/>
a. vniformiter calidū vt .4. / igit̄̄ ꝓpoſitū. </
s
>
<
s
xml:id
="
N25AEB
"
xml:space
="
preserve
">Minor fa-
<
lb
/>
cile patet ex caſu et minor ꝓbatur / q2 a. eſt in duplo
<
lb
/>
maioris põne ꝙ̄ b. / igit̄̄ in dupla velociꝰ alterat eã-
<
lb
/>
dem reſiſtentiã ꝙ̄ b. </
s
>
<
s
xml:id
="
N25AF4
"
xml:space
="
preserve
">Cõſequētia pꝫ et arguit̄̄ añs / q2
<
lb
/>
a. hꝫ in duplo magis de forma eiuſdē ſpēi b. / igit̄̄
<
lb
/>
a. eſt in duplo maioris põne ꝙ̄ b. </
s
>
<
s
xml:id
="
N25AFB
"
xml:space
="
preserve
">¶ Scḋo ṗncipaĺr
<
lb
/>
arguit̄̄ ſic. </
s
>
<
s
xml:id
="
N25B00
"
xml:space
="
preserve
">Si pars affirmatiua q̄ſtiõis eēt vera / ſeq̇
<
lb
/>
ret̄̄ / qḋlibet alterans finitū alterans certã reſiſtē
<
lb
/>
tiã infinitã formã entitatiue in quãtulocū tꝑe ꝓ-
<
lb
/>
duceret ſꝫ ↄ̨ñs eſt manifeſte falſum / igit̄̄ illud ex quo
<
lb
/>
ſequit̄̄. </
s
>
<
s
xml:id
="
N25B0B
"
xml:space
="
preserve
">Probat̄̄ añs / qm̄ qḋlibet alterãs certã reſi-
<
lb
/>
ſtētiã infinite velociter adequate agit in quantulo-
<
lb
/>
cū tꝑe / igit̄̄ quodlibet alterãs finitū certã alterãs
<
lb
/>
reſiſtētiam infinitã formã entitatiue in quãtulocū
<
lb
/>
tꝑe ꝓducit. </
s
>
<
s
xml:id
="
N25B16
"
xml:space
="
preserve
">Probat̄̄ añs / q2 ſi nõ det̄̄ illud et ſit a. ca
<
lb
/>
lidū vniforme ꝑ totū in forma entitatiue / qḋ alterat
<
lb
/>
b. paſſuꝫ certe reſiſtētie ꝑ horam. </
s
>
<
s
xml:id
="
N25B1D
"
xml:space
="
preserve
">Et arguit̄̄ ſic / a. īfi
<
lb
/>
nite velociter agit in illa hora adequate alterando
<
lb
/>
b. paſſum / igitur propoſitum. </
s
>
<
s
xml:id
="
N25B24
"
xml:space
="
preserve
">Probatur antecedēs
<
lb
/>
et volo / a. tangat b. paſſum et diuidatur ipſum a.
<
lb
/>
per partes proportionales ꝓportione dupla mi-
<
lb
/>
noribus ſus b. paſſum terminatꝪ et arguit̄̄ ſic: pri
<
lb
/>
ma pars proportionalis ipſius a. aliquãtulū agit
<
lb
/>
in hora adequate in b. paſſum et ſecunda tantum vĺ
<
lb
/>
magis et tertia tantum vel magis ꝙ̄ ſecunda et ſic
<
lb
/>
cõſequēter et ſunt infinite: ergo ſequitur / infinita
<
lb
/>
eſt actio ī illa hora adequate. </
s
>
<
s
xml:id
="
N25B37
"
xml:space
="
preserve
">Conſequētia patet
<
gap
/>
̀
<
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/>
</
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>
<
s
xml:id
="
N25B3D
"
xml:space
="
preserve
"/>
</
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>
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>
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