Alvarus, Thomas
,
Liber de triplici motu
,
1509
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De motu locali quo ad effectū ſcḋm tempus difformi.
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ad primam partcm in proportione tripla: et totuꝫ
<
lb
/>
diuiſum proportione ſexquitertia in proportione
<
lb
/>
quadrupla: et ſic conſequenter / vt prima pars quin-
<
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to ſuo capitulo oſtendit. </
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<
s
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xml:space
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">Et ſic patet prima pars.
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</
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<
s
xml:id
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N1F610
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xml:space
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preserve
">Secunda vero patet ex quarta concluſione hoc ad
<
lb
/>
dito / in caſu concluſionis proportio ſpacii per-
<
lb
/>
tranſiti in tota hora ad ſpacium pertranſitum in
<
lb
/>
prima parte eſt dupla ad proportionem totius ve
<
lb
/>
locitatis ad velocitatem prime partis proportio-
<
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nalis temporis.</
s
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<
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xml:id
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xml:space
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">1. correĺ.</
note
>
<
p
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<
s
xml:id
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N1F622
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xml:space
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preserve
">¶ Ex hac ↄ̨cluſione ſequitur primo / diuiſa hora
<
lb
/>
per partes proportionales proportione ſuperpar
<
lb
/>
ticulari quauis libuerit: diſtributa velocitate vt
<
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/>
in caſu ſecunde concluſionis ponitur, ita videlicet /
<
lb
/>
mobile in prima parte proportiõali moueatur
<
lb
/>
aliquantulum, et in ſecunda in duplo velocius, et in
<
lb
/>
tertio in triplo velocius ꝙ̄ in prima, et in quarta in
<
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/>
quadruplo velocius ꝙ̄ in prima, et ſic conſequenter /
<
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/>
tūc tota velocitas erit equalis velocitati tertie par
<
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/>
tis proportiõalis ſi fuerit facta diuiſio ꝓportione
<
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/>
ſexquialtera: et ſi fuerit diuiſio facta ſexquitertia
<
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/>
tota velocitas erit equalis velocitati quarta par-
<
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/>
tis proportionalis: et ſi fuerit facta diuiſio propor
<
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/>
tione ſexquiquarta erit equalis velocitati quinte
<
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/>
partis proportionalis: et ſic conſequenter aſcendē
<
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/>
do per ſpecies proportionis ſuperparticularis et
<
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/>
per partes proportionales. </
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>
<
s
xml:id
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N1F645
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xml:space
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preserve
">Probatur correlariū
<
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/>
facile ex ſecunda concluſione: quoniã facta diuiſio-
<
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/>
ne hore proportione ſexquialtera: tota hora ſe ha-
<
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/>
bet ad primam partē in proportione tripla / vt con
<
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/>
ſtat: ergo tota velocitas vt dicit concluſio ſe habet
<
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/>
ad velocitatē prime partis proportionalis in pro-
<
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/>
portione tripla et in tali proportione ſe habet ve-
<
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/>
locitas tertie partis proportionalis ad velocitatē
<
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/>
prime / vt dicit caſus igr̄. </
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<
s
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xml:space
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">Itē diuiſiõe facta ꝑ partes
<
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ꝓportiõales ꝓportiõe ſexquitertia: totū ſic diuiſuꝫ
<
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/>
ſe habet ad primam partem proportionalem in ꝓ
<
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/>
portione quadrupla: ergo totalis velocitas ſe ha-
<
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/>
bet ad velocitatem prime partis proportiõalis in
<
lb
/>
proportione quadrupla / vt patet ex ſecūda conclu-
<
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/>
ſione: et tanta eſt velocitas quarte partis / igitur. </
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>
<
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xml:space
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preserve
">Et
<
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ſic probabis reſiduas partes in infinitum.</
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<
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xml:id
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xml:space
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preserve
">2. correĺ.</
note
>
<
p
xml:id
="
N1F670
">
<
s
xml:id
="
N1F671
"
xml:space
="
preserve
">¶ Sequitur ſecūdo / hora diuiſa per partes pro-
<
lb
/>
portionales proportione ſexquialtera et mobile a.
<
lb
/>
in prima parte moueatur aliquantulū, et in ſecun-
<
lb
/>
da parte in duplo velocius, et in tertia in triplo ve-
<
lb
/>
locius q̈ in prima, et ſic conſequenter: vt in prima
<
lb
/>
parte proportionali pertranſit vnum pedale: in to
<
lb
/>
ta hora pcriranſit nouē. </
s
>
<
s
xml:id
="
N1F680
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xml:space
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preserve
">Probatur / quia illo caſu
<
lb
/>
poſito velocitatis totius ad velocitatē prime par-
<
lb
/>
tis eſt proportio tripla: vt patet ex precedenti: igi-
<
lb
/>
tur ſpacii pertraſiti in tota hora ad ſpaciū ꝑtran-
<
lb
/>
ſitum in prima parte eſt ꝓportio dupla ad triplam /
<
lb
/>
vt ptꝫ ex quarta huius: ſed noncupla eſt dupla ad
<
lb
/>
triplam ex ſecūda parte huius operis capite ſexto /
<
lb
/>
igitur totius ſpacii pertrãſiti in tota hora ad ſpa
<
lb
/>
cium pertranſitum in prima parte eſt ꝓportio non
<
lb
/>
cupla / quod fuit probandum.
<
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position
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left
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xlink:href
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note-0158-01
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xml:id
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xml:space
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">3. correĺ.</
note
>
</
s
>
<
s
xml:id
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N1F69A
"
xml:space
="
preserve
">¶ Sequitur tertio /
<
lb
/>
diuiſa hora vel tempore aliquo proportione qua-
<
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/>
uis ſuperparticulari / vt poſitum eſt in primo corre
<
lb
/>
lario: ſpacii pertrãſiti in tota hora ad ſpaciū per-
<
lb
/>
tranſitum in prima parte eſt proportio dupla ad
<
lb
/>
proportionem quam habet velocitas tertie partis
<
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/>
ad velocitatem prime partis ſi fuerit diuiſio facta
<
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/>
proportione ſexquialtera: ſi vero fiat proportione
<
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/>
ſexquitertia in proportione dupla ad proportio-
<
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/>
nem velocitatis quarte partis ad velocitatem pri-
<
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/>
me. </
s
>
<
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xml:space
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preserve
">ſi ſexquiquarta in proportione dupla ad pro-
<
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/>
portionem velocitatis quinte partis ad velocita-
<
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De motu locali quo ad effectū ſcḋm tempus difformi.
"/>
tem prime / et ſic conſequenter. </
s
>
<
s
xml:id
="
N1F6B9
"
xml:space
="
preserve
">Et quia hoc correla-
<
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/>
rium manifeſte ſequitur ex predictes ꝓbatione non
<
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/>
indiget.
<
note
position
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right
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xlink:href
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note-0158-02a
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xlink:label
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note-0158-02
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xml:id
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N1F6FD
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xml:space
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preserve
">4. correĺ</
note
>
</
s
>
<
s
xml:id
="
N1F6C5
"
xml:space
="
preserve
">¶ Ex quo ſequitur quarto / hora diuiſa
<
lb
/>
per partes proportionales proportione aliqua
<
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/>
ſuperparticulari quauis volueris: et aliquod mo-
<
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/>
bile moueatur in prima etc̈. / vt poſitū eſt: ſpacii per
<
lb
/>
tranſiti eſt tota hora eſt noncuplum ad ſpaciū per-
<
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/>
tranſitum in prima parte proportionali ſi fuerit
<
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/>
diuiſio facta proportione ſexquialtera: ſi vero pro
<
lb
/>
portio eſt ſequitertia: eſt ſexdecuplum: ſi autē pro
<
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/>
portione ſexquiquarta: eſt vicecuplum quintuplū.
<
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</
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<
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xml:space
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">ita in prima parte pertranſit vnum pedale in to
<
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ta hora viginti quin pedalia: et ſic conſequenter.
<
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/>
</
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>
<
s
xml:id
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N1F6DF
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xml:space
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preserve
">Patet hoc correlarium ex predictis. </
s
>
<
s
xml:id
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N1F6E2
"
xml:space
="
preserve
">¶ Innumera
<
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alia correlaria inferre poteris ſi virtutē et robur,
<
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/>
ſecunde et quarte concluſionis diligenter inſpexe-
<
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/>
ris: non ſolum in generibus proportionum multi-
<
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/>
plicis at ſuperparticularis: verū etiam pari faci
<
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/>
litate in omnibus aliis generibus puta ſuprapar-
<
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/>
tiente multiplici ſuperparticulari multiplici ſu-
<
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perpartiente.</
s
>
</
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<
p
xml:id
="
N1F703
">
<
s
xml:id
="
N1F704
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xml:space
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">Sexta cõcluſio. </
s
>
<
s
xml:id
="
N1F707
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xml:space
="
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">Diuiſa hora quauis
<
lb
/>
proportione libuerit et in quacun proportione ſe
<
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/>
habuerint due partes immediate in eadem propor
<
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/>
tione vel maiori ſe habuerit velocitas minoris par
<
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/>
tis ad velocitatem maioris: tota illa velocitas eſt
<
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/>
infinita: ſpacium pertranſitum pari ratione infi
<
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/>
nitum erit. </
s
>
<
s
xml:id
="
N1F716
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xml:space
="
preserve
">Probatur ſecnnda pars concluſionis
<
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/>
quoniam in illo caſu mobile / quod ſic mouetur tan
<
lb
/>
tum ſpacium pertranſit in ſequenti parte ſicut in
<
lb
/>
priori vel maius et ſunt infinite partes proportio-
<
lb
/>
nales: ergo in totali hora infinitum pertranſibit.
<
lb
/>
</
s
>
<
s
xml:id
="
N1F722
"
xml:space
="
preserve
">Patet cõſequentia cum minore: et arguitur maior /
<
lb
/>
qm̄ qualis eſt proportio prime partis ad ſecundaꝫ
<
lb
/>
partē proportionalē talis eſt ꝓportio velocitatis
<
lb
/>
ſecunde partis proportionalis ad velocitatem pri
<
lb
/>
me partis vel maior: igitur tantum ſpaciū pertran
<
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/>
ſit in ſecūda ſicut in prima vel maius. </
s
>
<
s
xml:id
="
N1F72F
"
xml:space
="
preserve
">Item qualis
<
lb
/>
eſt proportio ſecunde partis ad tertiam partem ta
<
lb
/>
lis eſt proportio velocitatis tertie partis ad ſecun
<
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/>
de / et ſic conſequenter de quibuſcun duabus par-
<
lb
/>
tibus proportionalibus immediatis / vt ptꝫ ex caſu
<
lb
/>
concluſionis: igitur in qualibet pate immediate ſe
<
lb
/>
quente alteram maiorem, mobile motum tali velo
<
lb
/>
citate pertranſit tantum ſpacium ſicut in īmediate
<
lb
/>
precedenti vel maius / quod fuit probãdum. </
s
>
<
s
xml:id
="
N1F742
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xml:space
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preserve
">Patet
<
lb
/>
tamen conſequentia ex quarta et quīta ꝓpoſitioni
<
lb
/>
bus ſecundi notabilis. </
s
>
<
s
xml:id
="
N1F749
"
xml:space
="
preserve
">Et ſic patet ſecunda pars et
<
lb
/>
per conſequens prima. </
s
>
<
s
xml:id
="
N1F74E
"
xml:space
="
preserve
">Si enim mediante illa velo
<
lb
/>
citate mobile pertranſit infinitum ſpacium: conſe
<
lb
/>
quens eſt illam velocitatem infinitam eſſe. </
s
>
<
s
xml:id
="
N1F755
"
xml:space
="
preserve
">(Eſt em̄
<
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/>
in tempore fiuito) </
s
>
<
s
xml:id
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N1F75A
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xml:space
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preserve
">Patet igitur concluſio.</
s
>
</
p
>
<
note
position
="
right
"
xml:id
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N1F75D
"
xml:space
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preserve
">1. correĺ.</
note
>
<
p
xml:id
="
N1F761
">
<
s
xml:id
="
N1F762
"
xml:space
="
preserve
">¶ Ex quo ſequitur primo / ſi hora diuidatur per
<
lb
/>
partes proportionales proportione dupla: vt mo
<
lb
/>
bile moueatur in prima parte aliquantulum, et in
<
lb
/>
ſecunda in duplo velocius ꝙ̄ in prima, et in tertia
<
lb
/>
in duplo velocius ꝙ̄ in ſecunda, et in quarta in du-
<
lb
/>
plo velocius ꝙ̄ in tertia, ſpacium pertranſitum erit
<
lb
/>
infinitum. </
s
>
<
s
xml:id
="
N1F771
"
xml:space
="
preserve
">Patet correlarium ex concluſione quo-
<
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/>
niam in quacun proportione ſe habent partes ꝓ
<
lb
/>
portionales īmediate continuo: in eadem propor-
<
lb
/>
tione ſe habet velocitas partis minoris ad veloci
<
lb
/>
tatem partis maioris: et per conſequens totum il-
<
lb
/>
lud mobile pertranſit in qualibet ſequenti primaꝫ
<
lb
/>
tantum quantum iu prima. </
s
>
<
s
xml:id
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N1F780
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xml:space
="
preserve
">Infinitum igitur ſpa-
<
lb
/>
cium tranſcurret / quod fuit probandū.
<
note
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="
right
"
xlink:href
="
note-0158-03a
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xlink:label
="
note-0158-03
"
xml:id
="
N1F7DB
"
xml:space
="
preserve
">2. correĺ.</
note
>
</
s
>
<
s
xml:id
="
N1F78A
"
xml:space
="
preserve
">¶ Sequitur
<
lb
/>
ſcḋo / partita hora per partes ꝓportiõales ꝓpor
<
lb
/>
tione ſexquitertia: et in prima parte proportionali </
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>
</
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