Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Primi tractatus
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0069
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69
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<
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xml:space
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">Sed illã ꝑtranſibit arguitur: q2 quãlibet par-
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tem eius proportionalē ꝓportione dupla mino-
<
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ribus terminatis verſus extremū intenſius per-
<
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/>
tranſibit: igitur totã reſiſtentiã pertranſibit. </
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<
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xml:space
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ſequentia patet: q2 oēs partes ꝓportionales pro
<
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portione dupla illius reſiſtentie totã illam reſi-
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ſtentiã conſtituūt. </
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<
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xml:space
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">Sed iam reſtat ꝓbare pro ꝓba
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tione alterius partis / nun̄ ad finē deueniet: q2
<
lb
/>
nõ ſufficit in tēpore finito tranſire illã reſiſtentiã:
<
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/>
igitur nun̄ deueniet ad finē illius reſiſtentie. </
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>
<
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xml:space
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guitur antecedens et capio vnã aliam reſiſtentiam
<
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/>
difformiter difformē diuiſam per partes ꝓpor-
<
lb
/>
tionales ꝓportione dupla: cuius prima pars pro
<
lb
/>
portionales ſit vniformis vt duo et ſecūda vt tria
<
lb
/>
et tertia vt .3. cū dimidio et quarta vt tria cū dimi-
<
lb
/>
dio et dimidio dimidii / et ſic ↄ̨ſequenter aſcenden-
<
lb
/>
do: ita quelibet pars ꝓportionalis tali ꝓpor-
<
lb
/>
tionis duple diuiſione / ſit vniformiter intenſa in
<
lb
/>
iſta reſiſtentia difformiter difformi ſicut punctus
<
lb
/>
initiatiuus conſimilis partis in reſiſtētia vnifor-
<
lb
/>
miter difformi: et ſint tales reſiſtentie equales ex-
<
lb
/>
tenſiue / quo poſito ſic argumentor iſta potētia vt
<
lb
/>
4. non ſufficit ꝑtranſire iſtã reſiſtentiã difformem
<
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/>
in tēpore finito / et iſta reſiſtentia minꝰ reſiſtit quã
<
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/>
alia vniformiter difformis / vt conſtat reſpiciēdo
<
lb
/>
ad reſiſtentiã partiū ꝓportionaliū vniꝰ et alteriꝰ:
<
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/>
igitur talis potentia vt .4. nõ ſufficit pertranſire
<
lb
/>
talē reſiſtentiã vniformiter difformē a ſecūdo gra
<
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/>
du vſ ad quartū / quod fuit ꝓbandū. </
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eſt nota cū minore et maior arguitur / q2 aliquantū
<
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/>
tēpus requirit illa potentia ad pertranſeundum
<
lb
/>
primã partē ꝓportionalē: et tantū vel maiꝰ requi
<
lb
/>
rit ad ꝑtrãſeundū ſcḋam: et iterū tantū vel maius
<
lb
/>
ad ꝑtranſeundū tertiã: et ſic cõſequenter: et ſunt in
<
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/>
finite partes ꝓportionales: igitur in nullo tēpo-
<
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re finito ſufficit talis potentia illã reſiſtentiã dif-
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formiter difformē ꝑtranſire. </
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">Conſequentia patet /
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et ꝓbatur antecedēs / qm̄ tranſeundo primã partē
<
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ꝓportionalē / que eſt vt duo mouetur a ꝓportione
<
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/>
dupla: et tranſeundo ſcḋam / que eſt vt .3. mouetur a
<
lb
/>
ꝓportione ſexquitertia: et tranſeundo tertiã / que
<
lb
/>
eſt vt .3. cū dimidio mouetur a ꝓportione ſexqui-
<
lb
/>
ſeptima / et ſic conſequenter ſemꝑ a minori ꝓpor-
<
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/>
tione quã ſubdupla ad precedentē: igitur cõtinuo
<
lb
/>
tranſeundo partē ꝓportionalē ſequentē, requirit
<
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/>
maiꝰ tēpus quã trãſeūdo partē precedentē. </
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">Patet
<
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cõſequentia / qm̄ ſi cotinuo moueretur a ſubdupla
<
lb
/>
ꝓportione in parte ꝓportionali ſequenti ad pro-
<
lb
/>
portionē qua mouebatur in parte īmediate pre-
<
lb
/>
cedenti: ſemꝑ adequate tantū tēpus requireret ad
<
lb
/>
tranſeundū partē ſequentē ſicut īmediate prece-
<
lb
/>
dentē: q2 partes continuo ſe habent in ꝓportione
<
lb
/>
dupla et ſimiliter ꝓportiones ſe tunc haberent in
<
lb
/>
ꝓportione dupla: ſed modo cõtinuo in parte ſe-
<
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/>
quenti mouetur a minori ꝓportione quã ſubdu-
<
lb
/>
pla ad ꝓportionē / qua mouetur in parte īmediate
<
lb
/>
precedenti: igitur continuo maius tēpus requirit
<
lb
/>
ad pertranſeundū partē ſequentē quã precedentē
<
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/>
</
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<
s
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xml:space
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">Sed cõtinuo moueatur a minori ꝓportiõe quã
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ſubdupla in parte ſequenti quã in parte īmediate
<
lb
/>
precedenti patet / q2 in prima mouetur a ꝓportiõe
<
lb
/>
dupla / et in ſecūda a ꝓportiõe ſexquitertia modo
<
lb
/>
ſexquitertia minor eſt quã ſubdupla duple / vt ptꝫ
<
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/>
ex ꝓbatione tertie cõcluſiõis quarti capitis ſcḋe
<
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partis et ſexta ſuppoſitione capitis eiuſdē. </
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<
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">Itē in
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tertia mouet̄̄ a ꝓportiõe ſexquiſeptīa: modo ſexq̇
<
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ſeptīa minor eſt quã ſubdupla ſexq̇tertie / et ſic cõ-
<
lb
/>
ſequenter / vt patet ex ſexta ſuppoſitione quarti ca
<
lb
/>
pitis preallegati: igitur.</
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Capitulum ſextū.
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<
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xml:space
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">Reſpõdeo ad argumentum breuiter /
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negando ſequelã: et ad ꝓbationē dico / illa ↄ̨ña
<
lb
/>
nichil valet: quãlibet partē ꝓportionalē ſecundū
<
lb
/>
hanc diuiſionē hoc mobile ꝑtranſibit: ergo totuꝫ
<
lb
/>
ſpaciū ſiue reſiſtentiã ꝑtranſibit: īmo ſicut ꝓbat
<
lb
/>
argumentū ſi mobile et illa reſiſtentia ſimul ma-
<
lb
/>
nerent ꝑ infinitū tēpus: ꝑ īfinitū tēpus mobile mo
<
lb
/>
ueret̄̄ ſupra reſiſtentiã / et nū̄ veniret ad terminū.</
s
>
</
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<
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">Sed ↄ̨̨tra q2 poſſibile eſt / potētia vt
<
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4. ꝑtranſeat reſiſtentiã difformē in tꝑe finito, cuiꝰ
<
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/>
ṗma pars ꝓportiõalis eſt vniformiter difformis
<
lb
/>
a duobꝰ vſ ad tertiū, et ſecūda etiã vniformiter
<
lb
/>
difformis a tertio vſ ad tertiū cū dimidio, et ſic
<
lb
/>
cõſequenter vſ ad quartū excluſiue: igit̄̄ poſſibi-
<
lb
/>
le eſt potentiã vt .4. ꝑtranſire reſiſtentiã vniformi-
<
lb
/>
ter difformē a duobꝰ vſ ad quartū: et per conſe-
<
lb
/>
quens male negatū eſt hoc. </
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<
s
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">Arguit̄̄ antecedens: et
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pono / ſit vna reſiſtentia pedalis diuiſa per par
<
lb
/>
tes ꝓportionales ꝓportione quadrupla: cuiꝰ pri-
<
lb
/>
ma pars ꝓportionalis ſit vniformiter difformis
<
lb
/>
a ſecūdo vſ ad tertiū, et ſecunda a tertio vſ ad
<
lb
/>
tertiū cū dimidio, et ſic cõſequēter vſ ad quarū
<
lb
/>
excluſiue: deinde capio vnã aliã reſiſtentiã ſimili-
<
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/>
ter pedalē: diuiſam per partes ꝓportionales ꝓ-
<
lb
/>
portione quadrupla: cuiꝰ prima pars ꝓportiona
<
lb
/>
lis ſit vniformis vt .3. et ſecūda vt .3. cū dimidio, et
<
lb
/>
tertia vt .3. cū dimidio et dimidio dimidii, et ſic cõ-
<
lb
/>
ſequēter: ita quelibet pars ꝓportiõalis in tali
<
lb
/>
reſiſtentia ſit vniformiter intēſa ſicut gradus in-
<
lb
/>
ſiſſimꝰ in parte cõſimili ſiue correſpondēte in alia
<
lb
/>
reſiſtentia pedali cuiꝰ partes ꝓportionales ſunt
<
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/>
vniformiter difformes: quo poſito ſic argumētor
<
lb
/>
iſta ſecūda reſiſtentia cuiꝰ partes ꝓportiõales ſūt
<
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/>
vniformes eſt maioris reſiſtentie quã altera: vt ſa
<
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/>
tis facile ptꝫ intelligenti reſiſtentiã partiū ꝓpor-
<
lb
/>
tionabiliū in vna et in altera: et tamen potentia vt
<
lb
/>
4. ſufficit in tēpore finito ꝑtranſire iſtã ſecundam
<
lb
/>
reſiſtentiã: igit̄̄ et alterã cuiꝰ partes ꝓportionales
<
lb
/>
ſunt vniformiter difformes. </
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>
<
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xml:space
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preserve
">Cõſequētia ptꝫ ꝑ locū
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a maiori et maior ſimiliter: et minor ꝓbat̄̄: ſuppo-
<
lb
/>
nendo / oīs ꝓportio ſuꝑparticularis diuidit̄̄ in
<
lb
/>
duas ꝓportiones / quaꝝ vna eſt medii numeri ad
<
lb
/>
minimū et alia maximi ad mediū: et illa que eſt ma
<
lb
/>
ximi ad mediuꝫ, eſt maior quã tertia pars totius
<
lb
/>
ꝓportionis ſuꝑparticularis: vt ptꝫ ex decimo cor
<
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/>
relario tertie cõcluſionis quarti capitis ſecunde
<
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/>
partis. </
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<
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xml:space
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">Hoc ſuppoſito ſic arguo potentia / vt .4. in
<
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/>
aliquo tēpore ꝑtranſit prima partē ꝓportionalē
<
lb
/>
talis reſiſtentie: et in ſubſexquitertio tēpore ꝑtran
<
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/>
ſit ſcḋam: et ſic cõſequēter ita quãlibet ſequentē
<
lb
/>
ꝑtranſit in ſubſexq̇tertio tēpore ad tēpus in quo
<
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ꝑtrãſit īmediate p̄cedentē: igit̄̄ totū tēpus in quo
<
lb
/>
pertranſit oēs partes alias a prima eſt triplū ad
<
lb
/>
tempus in quo pertranſit primã: vt patet intelli-
<
lb
/>
genti quintum caput prime partis: et tempus in
<
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/>
quo pertrãſit primam eſt finitū: igitur totū tēpus
<
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aggregatū eſt finituꝫ. </
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>
<
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xml:space
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preserve
">Sed iam probo antecedens /
<
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quoniam in aliquo tempore pertranſit primam:
<
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ſignetur igitur illud tempus et ſit vna hora gra-
<
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tia exempli: et in illa hora per illam partem con-
<
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/>
tinuo mouetur a proportione ſexquitertia: quia
<
lb
/>
reſiſtentia eſt vt .3. et potentia vt .4. et tranſeundo
<
lb
/>
ſecundam partem proportionalem / que eſt vt .3. cū
<
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/>
dimidio mouetur a proportione ſexquiſeptima:
<
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/>
que vt patet ex ſuppoſitione non eſt ſubtripla ad
<
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/>
ſexquitertiam ſed maior quam ſubtripla: ſed ſi
<
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illa eſſet ſubtripla tranſiret ſecundam partem
<
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ꝓportiõalē in ſubſexquitertio tēpore / ergo modo </
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