Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Secundi tractatus
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0173
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173
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citra centrū mūdi efficit̄̄ minor et pars vltra centrū
<
lb
/>
mūdi maior) / igr̄ perpetuo aliqua pars aggregati
<
lb
/>
ex oībus partibꝰ ꝓpotiõalibꝰ ipſiꝰ d. partis deſcē-
<
lb
/>
det / qḋ fuit ꝓbandū. </
s
>
<
s
xml:id
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N20CD0
"
xml:space
="
preserve
">Conſequētia ꝓbat̄̄ / q2 ſi q̄libet
<
lb
/>
pars ꝓportionalis cõtinuo ipſius d. partis diuiſe
<
lb
/>
ꝓportione dupla deſcēderet ſiue moueret̄̄ a ꝓpor-
<
lb
/>
tione a qua ipſa īcipit deſcendere: ꝑpertuo aliqua
<
lb
/>
pars aggregati ex oībus partibꝰ ꝓportionalibus
<
lb
/>
ipſiꝰ d. partis deſcēderet / g̊ ſi q̄libet pars ꝓportio-
<
lb
/>
nalis ipſiꝰ d. partis cõtinuo deſcēderet et mouetur
<
lb
/>
a ꝓportione minori ꝙ̄ ſit illa a qua īcipit deſcēde-
<
lb
/>
re: ꝑpetuo aliqua pars aggregati ex oībus parti-
<
lb
/>
bus ꝓportionalibꝰ ipſiꝰ d. partis deſcendit / qḋ fuit
<
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/>
ꝓbandū. </
s
>
<
s
xml:id
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N20CE7
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xml:space
="
preserve
">Cõſequētia ptꝫ cū ãtecedēte ex deductione
<
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/>
ſecūdi argumēti ſexti capitis primi tractatꝰ huius
<
lb
/>
partis: hoc addito / ille partes cõtinuo ſe habent
<
lb
/>
in ꝓportione dupla: et in tꝑe in quo adequate deſcē
<
lb
/>
dit aliqua pars ſcḋm ſe vel aliquid eiꝰ p̄tereundo
<
lb
/>
centrū mūdi ipſa pars deſcribit tm̄ ſpaciū quanta
<
lb
/>
ipſamet pars eſt / vt ptꝫ intuenti caſum. </
s
>
<
s
xml:id
="
N20CF6
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xml:space
="
preserve
">Sed iã ꝓbo
<
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/>
ſcḋam partē maioris vcꝫ ſecūda pars ꝓportona
<
lb
/>
lis ipſiꝰ d. partis īcipit deſcēdere a ꝓportione ſub
<
lb
/>
dupla ad ꝓportionē f. vĺ minori: q2 cū primū ṗma
<
lb
/>
pars proportionalis ipſius d. partis eſt totaliter
<
lb
/>
vltra centrū mūdi, pars citra centrū mundi perdit
<
lb
/>
quartã partē exceſſus quo excedit partē vltra cen-
<
lb
/>
trū mūdi: et illã acquirit pars vltra centrū mūdi / vt
<
lb
/>
cõſtat: g̊ tūc ꝓportio f. partis citra centrū ad partē
<
lb
/>
vltra centrū ꝑdit pluſ̄ medietatē ſui: et pluſ̄ ad
<
lb
/>
ſubduplū ſui diminuit̄̄: ptꝫ ↄ̨ña ex ſecūda ſuppoſi-
<
lb
/>
tione huiꝰ notabilis hoc addito pars citra cen-
<
lb
/>
trū eſt terminꝰ maior proportionis f. et pars vltra
<
lb
/>
centrū eſt terminꝰ minor. </
s
>
<
s
xml:id
="
N20D13
"
xml:space
="
preserve
">Et ab illa proportione q̄
<
lb
/>
eſt minor quã ſubdupla ad f. īcipit ſecūda pars ꝓ-
<
lb
/>
portionalis ipſiꝰ d. partis deſcēdere / vt cõſtat: g̊ ꝓ-
<
lb
/>
poſitū. </
s
>
<
s
xml:id
="
N20D1C
"
xml:space
="
preserve
">Et iſto modo ꝓbabis tertra īcipit deſcen
<
lb
/>
dere a ꝓportione ſubdupla vel mīori ſubdupla ad
<
lb
/>
proportionē a qua incipit deſcendere ſecūda: et ſic
<
lb
/>
ↄ̨ñter de aliis partibꝰ. </
s
>
<
s
xml:id
="
N20D25
"
xml:space
="
preserve
">Sed iã ꝓbo maiorē vcꝫ cū
<
lb
/>
primū prima pars proportionalis ipſiꝰ d. partis
<
lb
/>
eſt totaliter vltra centrū pars citra centrū mundi
<
lb
/>
perdit quartã partē exceſſus quo ipſa excedit par-
<
lb
/>
tem vltra centrū mūdi: q2 ipſa d. pars eſt medietas
<
lb
/>
exceſſus quo pars citra centrū excedit partē vltra
<
lb
/>
centrū / vt ptꝫ ex prima ſuppoſitione huiꝰ notabilis /
<
lb
/>
g̊ prima pars proportionalis proportione dupla
<
lb
/>
ipſiꝰ d. partis eſt quarta pars totiꝰ exceſſus: et illã
<
lb
/>
ꝑdit pars citra centrū mūdi primū ipſa eſt tota
<
lb
/>
liter vltra centrū: g̈ propoſitū. </
s
>
<
s
xml:id
="
N20D3C
"
xml:space
="
preserve
">Ptꝫ g̊ maior: et totū
<
lb
/>
añs / et ꝑ ↄ̨ñs cõcluſio q̄ fuerat probanda.
<
note
position
="
left
"
xlink:href
="
note-0173-01a
"
xlink:label
="
note-0173-01
"
xml:id
="
N20DC3
"
xml:space
="
preserve
">1. correĺ.</
note
>
</
s
>
<
s
xml:id
="
N20D46
"
xml:space
="
preserve
">¶ Ex his
<
lb
/>
infero aliqua correlaria. </
s
>
<
s
xml:id
="
N20D4B
"
xml:space
="
preserve
">Primū in caſu huiꝰ de-
<
lb
/>
monſtrationis īmediate poſt inſtãs / qḋ eſt preſens
<
lb
/>
aſcendet aliq̇d īmediate poſt illud deſcēdet : et tñ
<
lb
/>
nichil īmediate poſt hoc aſcendet qḋ īmediate poſt
<
lb
/>
hoc deſcendet. </
s
>
<
s
xml:id
="
N20D56
"
xml:space
="
preserve
">Probat̄̄ prima pars / q2 quocun
<
lb
/>
inſtanti dato illiꝰ tꝑis in quo deſcēdet tale quadra
<
lb
/>
tū q̄libet pars illiꝰ quadrati q̄ eſt citra centrū īme-
<
lb
/>
diate poſt tale inſtans deſcendet / vt ſatis conſtat et
<
lb
/>
īmediate poſt idē inſtans aliqua talis pars aſcen-
<
lb
/>
det: igr̄ in caſu demonſtrationis, īmediate poſt in-
<
lb
/>
ſtans / qḋ eſt preſens aliq̇d aſcēdet qḋ īmediate poſt
<
lb
/>
idē inſtans deſcendet ſcḋa pars ptꝫ ex falſitate ſue
<
lb
/>
cõtradictorie. </
s
>
<
s
xml:id
="
N20D69
"
xml:space
="
preserve
">Ad hoc em̄ aliquid aſcendat non
<
lb
/>
ſufficit aliquã partē eiꝰ aſcendere: ſed requiritur /
<
lb
/>
maior pars ꝙ̄ eiꝰ medietas aſcendat. </
s
>
<
s
xml:id
="
N20D70
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xml:space
="
preserve
">Conſimiliter
<
lb
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dicat̄̄ de deſcensu.
<
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position
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left
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xlink:href
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note-0173-02a
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xlink:label
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note-0173-02
"
xml:id
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N20DC9
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xml:space
="
preserve
">2. correĺ.</
note
>
</
s
>
<
s
xml:id
="
N20D7A
"
xml:space
="
preserve
">¶ Scḋm correlariū. </
s
>
<
s
xml:id
="
N20D7D
"
xml:space
="
preserve
">Immediate
<
lb
/>
poſt inſtans qḋ eſt preſens aſcendet aliq̇d qḋ p̄ſens
<
lb
/>
aſcendet aliq̇d qḋ īmediate poſt idē inſtans deſcen
<
lb
/>
det: et tñ nõ īmediate poſt inſtãs qḋ eſt p̄ſens deſcen
<
cb
chead
="
Capitulū quartū.
"/>
det aliq̇d qḋ īmediate poſt idem inſtans aſcendet.
<
lb
/>
</
s
>
<
s
xml:id
="
N20D8A
"
xml:space
="
preserve
">Ptꝫ prima pars huiꝰ ex priori correlario. </
s
>
<
s
xml:id
="
N20D8D
"
xml:space
="
preserve
">Et ſcḋa
<
lb
/>
ꝓbat̄̄ / q2 ↄ̨tradictoria illiꝰ eſt falſa / vt ptꝫ ꝑ falſitatē
<
lb
/>
prime exponētis q̄ eſt iſta poſt inſtans quod eſt pre
<
lb
/>
ſens deſcendet aliquid quod īmediate poſt idem in
<
lb
/>
ſtans aſcendet q2 nulla pars illiꝰ corporis quadra
<
lb
/>
ti que poſt inſtans quod eſt preſens deſcendit īme-
<
lb
/>
diate poſt idem inſtans aſcendet.
<
note
position
="
right
"
xlink:href
="
note-0173-03a
"
xlink:label
="
note-0173-03
"
xml:id
="
N20DCF
"
xml:space
="
preserve
">3. correĺ.</
note
>
</
s
>
<
s
xml:id
="
N20DA1
"
xml:space
="
preserve
">¶ Tertiū correla
<
lb
/>
riū. </
s
>
<
s
xml:id
="
N20DA6
"
xml:space
="
preserve
">Immediate poſt inſtans quod eſt p̄ſens aſcen-
<
lb
/>
det aliq̇d qḋ īmediate poſt idē inſtans quod eſt pre
<
lb
/>
ſens deſcendet: et tñ nichil ſimul aſcendet, et deſcen-
<
lb
/>
det adequate diuiſiue capiendo ly. </
s
>
<
s
xml:id
="
N20DAF
"
xml:space
="
preserve
">et ſicut ſtat ſor
<
lb
/>
tes īmediate poſt hoc erit albus, et immediate poſt
<
lb
/>
hoc erit niger: et tamen nõ ſimul erit albus et niger
<
lb
/>
</
s
>
<
s
xml:id
="
N20DB7
"
xml:space
="
preserve
">Patet correlarium. </
s
>
<
s
xml:id
="
N20DBA
"
xml:space
="
preserve
">¶ Ex his tribus notabilibus
<
lb
/>
patet facile reſponſio ad queſtionem.</
s
>
</
p
>
<
p
xml:id
="
N20DD5
">
<
s
xml:id
="
N20DD6
"
xml:space
="
preserve
">Ad rationes ante oppoſitū. </
s
>
<
s
xml:id
="
N20DD9
"
xml:space
="
preserve
">Ad primã
<
lb
/>
reſponſum eſt ibi vſ ad replicam ad quam reſpo-
<
lb
/>
deo negando ſequelam, et ad probationem dico /
<
lb
/>
illud correlarium ibi adductum ad probationem
<
lb
/>
illiꝰ ſequele nõ eſt ad propoſitū, q2 ſupponit ꝓpor
<
lb
/>
tionē tēpoꝝ excedere proportionē velocitatū. </
s
>
<
s
xml:id
="
N20DE6
"
xml:space
="
preserve
">Cuiꝰ
<
lb
/>
oppoſitū ī caſu argumēti eſt verū. </
s
>
<
s
xml:id
="
N20DEB
"
xml:space
="
preserve
">Cõmēſurãda em̄
<
lb
/>
eſt vtra velocitas, et qua illud corpus mouet̄̄ cir-
<
lb
/>
culariter, et qua mouetur motu rarefactiõis pūcto
<
lb
/>
eiꝰ a quo debet ſumi velocitas totiꝰ motus cõtinuo
<
lb
/>
acquirente maiorē et maiorē diſtantiam a centro / vt
<
lb
/>
ptꝫ ex deductione eiuſdē replice.
<
note
position
="
right
"
xlink:href
="
note-0173-04a
"
xlink:label
="
note-0173-04
"
xml:id
="
N20E38
"
xml:space
="
preserve
">1. correĺ</
note
>
</
s
>
<
s
xml:id
="
N20DFD
"
xml:space
="
preserve
">¶ Ex quo ſequitur /
<
lb
/>
poſſibile eſt aliquod corpꝰ circulare cõtinuo vni-
<
lb
/>
formiter et eque velociter moueri: et tñ ipſū ↄ̨tinuo
<
lb
/>
rarefieri et effici maiꝰ. </
s
>
<
s
xml:id
="
N20E06
"
xml:space
="
preserve
">Probat̄̄ ponēdo / vna rota
<
lb
/>
incipiat moueri circulariter pūcto medio ſemidia-
<
lb
/>
metri incipiēte moueri velocitate vt .4. et volo / ſiĺ
<
lb
/>
incipiat rarefieri illud corpus acquirendo in hora
<
lb
/>
pedalē diſtantiã adequate a centro ſupra diſtan-
<
lb
/>
tiã p̄habitã, eo tñ modo moueat̄̄ ille punctꝰ medius
<
lb
/>
ſemidiametri nun̄ ꝑtranſeat ſiue deſcribat ma
<
lb
/>
iorē lineã in aliquo tꝑe ꝙ̄ nata ſit deſcribi a veloci-
<
lb
/>
tate vt .4. in eodē tꝑe quo poſito ſequit̄̄ correlariū.
<
lb
/>
<
note
position
="
right
"
xlink:href
="
note-0173-05a
"
xlink:label
="
note-0173-05
"
xml:id
="
N20E3E
"
xml:space
="
preserve
">2. correĺ.</
note
>
</
s
>
<
s
xml:id
="
N20E20
"
xml:space
="
preserve
">¶ Sequit̄̄ ſecūdo / ſi aliqua rota in hora moueat̄̄
<
lb
/>
circulariter puncto medio ſemidiametri continuo
<
lb
/>
motu circulari mouēte vniformiter, motu vero ra-
<
lb
/>
refactionis cõtinuo intendente motū ſuū in q̈libet
<
lb
/>
parte proportionali hore ꝓportione dupla ſequē-
<
lb
/>
te in duplo velociꝰ rarefiente ꝙ̄ in īmediate p̄cedēti
<
lb
/>
tūc ſpaciū deſcriptū a tali puncto eſt infinitū. </
s
>
<
s
xml:id
="
N20E2F
"
xml:space
="
preserve
">Ptꝫ
<
lb
/>
hoc correlariū ex ſexta concluſione ꝑcedētꝪ capitis</
s
>
</
p
>
<
p
xml:id
="
N20E44
">
<
s
xml:id
="
N20E45
"
xml:space
="
preserve
">Ad ſecundã rationē reſponſum eſt ibi
<
lb
/>
vſ ad replicã: ad quã reſpõdeo negando ſequelã
<
lb
/>
et ad probationē nego nullū ſit īpedimentū. </
s
>
<
s
xml:id
="
N20E4C
"
xml:space
="
preserve
">īmo
<
lb
/>
cõtra motio nauis eſt ſorti īpedimento. </
s
>
<
s
xml:id
="
N20E51
"
xml:space
="
preserve
">Fatigat̄̄ tñ
<
lb
/>
ſortes nõ ꝑ motū quo deſcribat aliquod ſpacium
<
lb
/>
fixū: ſed q2 deſcribit aliquod ſpaciū nõ fixū ad cuiꝰ
<
lb
/>
deſcriptionē nõ ſequit̄̄ ſortē proprie moueri. </
s
>
<
s
xml:id
="
N20E5A
"
xml:space
="
preserve
">Ma-
<
lb
/>
net enim ſortes in eodem loco fixo.</
s
>
</
p
>
<
p
xml:id
="
N20E5F
">
<
s
xml:id
="
N20E60
"
xml:space
="
preserve
">Ad ṫciã rationē rñdeo negãdo añs: et
<
lb
/>
ad ꝓbationē ↄ̨cedo maiorē, et nego mīorē et ad ꝓba
<
lb
/>
nē diſtinguo ſeq̄lã aut ſi tale corpꝰ ſit taliter diſpo
<
lb
/>
ſitū partes eiꝰ proportionales ꝓportiõe dupla
<
lb
/>
ita ſe habeant ſcḋm eã dimenſionē ſcḋm quã de-
<
lb
/>
ſcendūt cõtinuo ſe habet in ꝓportione dupla oībꝰ
<
lb
/>
aliis iuuamentis et īpedimētis deductis: et ſic cõce-
<
lb
/>
do ſequelã. </
s
>
<
s
xml:id
="
N20E71
"
xml:space
="
preserve
">Si vero partes eiꝰ proportionales pro
<
lb
/>
portione dupla ſe habuerīt in maiori proportione
<
lb
/>
quã ſit ꝓportio dupla et hoc quantū ad dimēſionē
<
lb
/>
ſcḋm quã deſcendūt, et ſic nõ oportet. </
s
>
<
s
xml:id
="
N20E7A
"
xml:space
="
preserve
">Nego igitur
<
lb
/>
illo modo ſeq̄lã. </
s
>
<
s
xml:id
="
N20E7F
"
xml:space
="
preserve
">¶ Ex q̊ ſequit̄̄ / ita põt aliqḋ cor- </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
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>
</
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>
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