Alvarus, Thomas
,
Liber de triplici motu
,
1509
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Figures
Content
Thumbnails
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
>
71
72
73
74
75
76
77
78
79
80
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
>
page
|<
<
of 290
>
>|
<
echo
version
="
1.0
">
<
text
xml:lang
="
la
">
<
div
xml:id
="
N10132
"
level
="
1
"
n
="
1
"
type
="
body
">
<
div
xml:id
="
N15C17
"
level
="
2
"
n
="
3
"
type
="
other
"
type-free
="
pars
">
<
div
xml:id
="
N1C8AF
"
level
="
3
"
n
="
2
"
type
="
other
"
type-free
="
tractatus
">
<
div
xml:id
="
N1DD6A
"
level
="
4
"
n
="
3
"
type
="
chapter
"
type-free
="
capitulum
">
<
pb
chead
="
Secūdi. De motu locali quo ad effectū ſcḋm tempus difformi.
"
file
="
0160
"
n
="
160
"/>
<
p
xml:id
="
N1F907
">
<
s
xml:id
="
N1F908
"
xml:space
="
preserve
">¶ Sequitur ſecūdo / diuiſa hora ꝑ partes ꝓpor-
<
lb
/>
tionales ꝓportiõe ſuꝑtripartienti quartas cuiuſli
<
lb
/>
bet partis velocitate ſe habente ad velocitatē par-
<
lb
/>
tis maioris īmediate precedentis in ꝓportione ſex
<
lb
/>
quialtera ſpaciū pertranſitū in tota hora ſe habet
<
lb
/>
ad ſpaciū pertranſitū in prima parte proportionali
<
lb
/>
in ꝓportione ſeptupla: abſoluto pedali in prima
<
lb
/>
parte: ſeptē pedalia in tota hora abſoluētur. </
s
>
<
s
xml:id
="
N1F919
"
xml:space
="
preserve
">Pro
<
lb
/>
batur hoc correlariū ex cõcluſione īmediate precedē
<
lb
/>
ti: quia partes ꝓportionales tēporis ſe habent cõ-
<
lb
/>
tinuo in ꝓportione ſuꝑtripartienti quartas: et ve-
<
lb
/>
locitates partiū īmediatarū ſe habent in ꝓportiõe
<
lb
/>
ſexq̇altera / vt ponit caſus: et ꝓportio ſuꝑtripartiēs
<
lb
/>
q̈rtas excedit ꝓportionē ſexquialteram ꝑ .4. ꝓpor-
<
lb
/>
tionē ſexquiſextaꝫ / vt ptꝫ in his terminis .7.6.4. / igr̄
<
lb
/>
ſpaciū ꝑtranſitū in toto tēpore ſe habebit ad ſpa-
<
lb
/>
cium pertranſitū in prima parte proportionali in
<
lb
/>
ꝓportione ſeptupla / quod fuit ꝓbandū. </
s
>
<
s
xml:id
="
N1F930
"
xml:space
="
preserve
">Patet cõ-
<
lb
/>
ſequentia ex cõcluſione ſeptima: hoc adiecto / cor
<
lb
/>
pus diuiſum proportione ſexquiſexta ſe habet ad
<
lb
/>
primã ſui partē in ꝓportione ſeptupla: vt patet ex
<
lb
/>
prima parte huiꝰ operis. </
s
>
<
s
xml:id
="
N1F93B
"
xml:space
="
preserve
">Familiarius tamen ꝓba
<
lb
/>
tur ſic, et ſuppono / mobile ꝑtranſit in prima par
<
lb
/>
te proportionali vnum pedale, et arguo ſic / mobile
<
lb
/>
pertranſit in prima parte proportionali vnum pe
<
lb
/>
dale: et in ſecunda in ſexquiſexto minus, et in tertia
<
lb
/>
in ſexquiſexto minꝰ ꝙ̄ in ſecunda: et ſic conſequēter
<
lb
/>
ꝓcedendo per ꝓportiones ſexquiſextas: igitur to-
<
lb
/>
tale ſpaciū componitur ex illis infinitis continuo
<
lb
/>
ſe habentibus in ꝓportione ſexquiſexta: ergo ag-
<
lb
/>
gregatū ex omnibꝰ ſequētibus primã eſt ſextupluꝫ
<
lb
/>
ad primū / vt ptꝫ ex prima parte huiꝰ operis capite
<
lb
/>
quinto: et primū eſt vnū pedale: ergo totū reſiduum
<
lb
/>
eſt ſextupedale, et ꝑ cõſequens totū ſpaciū eſt ſeptē
<
lb
/>
pedū / quod ſe habet in proportiõe ſeptupla ad vnū
<
lb
/>
pedale ꝑtranſitū in prima parte ꝓportiõali / quod
<
lb
/>
fuit ꝓbandum. </
s
>
<
s
xml:id
="
N1F95C
"
xml:space
="
preserve
">Probatur tamen antecedens vide
<
lb
/>
licet / illud mobile in qualibet parte ſequenti per
<
lb
/>
tranſit ſubſexquiſextū ſpaciū ad ſpaciū ꝑtranſitū
<
lb
/>
in īmediate p̄cedenti, quia prime partis ꝓportio-
<
lb
/>
nalis ad ſecundã eſt ꝓportio ſuꝑtripartiens quar-
<
lb
/>
tas, et velocitatis ſecunde partis ꝓportionalis ad
<
lb
/>
velocitatē prime eſt ꝓportio ſexquialtera: ſed ꝓpor
<
lb
/>
tio ſuꝑtripartiens quartas tempoꝝ excedit ꝓpor-
<
lb
/>
tionē velocitatū ſexquialterã per ꝓportionē ſexqni
<
lb
/>
ſextam / vt notū eſt: igitur ſpaciū pertranſitū in ſe-
<
lb
/>
cunda parte ꝓportionali eſt ſubſexquiſextū ad ſpa
<
lb
/>
cium pertranſitū in prima. </
s
>
<
s
xml:id
="
N1F975
"
xml:space
="
preserve
">Patet conſequentia / ex
<
lb
/>
ſexta ꝓpoſitione ſecundi notabilis ſepius allega-
<
lb
/>
ta. </
s
>
<
s
xml:id
="
N1F97C
"
xml:space
="
preserve
">Et ſic ꝓbabis de ſpacio pertranſito in tertia ad
<
lb
/>
ſpacium ꝑtranſitum in ſecunda, et de ſpaciis ꝑtrã-
<
lb
/>
ſitis in duabus partibus īmmediatis quibuſcun
<
lb
/>
ſignatis: ergo cõtinuo ſpaciū pertranſitū in aliqua
<
lb
/>
parte ꝓportionali ſequente eſt ſubſexquiſextū ad
<
lb
/>
ſpacium ꝑtranſiium in parte īmediate precedente:
<
lb
/>
quod fuit ꝓbanduꝫ. </
s
>
<
s
xml:id
="
N1F98B
"
xml:space
="
preserve
">Inferas tuo ingenio et labore
<
lb
/>
ſimilia infinita correlaria. </
s
>
<
s
xml:id
="
N1F990
"
xml:space
="
preserve
">Iſta enim ſufficiūt pro
<
lb
/>
praxi concluſionis.</
s
>
</
p
>
<
p
xml:id
="
N1F995
">
<
s
xml:id
="
N1F996
"
xml:space
="
preserve
">Octaua cõcluſio. </
s
>
<
s
xml:id
="
N1F999
"
xml:space
="
preserve
">Partita hora ꝑ part
<
lb
/>
tes ꝓportionales quauis ꝓportione volueris, et in
<
lb
/>
certa ꝓportione continuo velocius mobile moueat̄̄
<
lb
/>
in parte p̄cedente maiore quã in īmediate ſequenti
<
lb
/>
minori: ſpaciū ꝑtranſitum in totali hora ſe habe-
<
lb
/>
bit ad ſpaciū ꝑtranſitum in prima parte ꝓportio-
<
lb
/>
nali in ꝓportione qua ſe habet aliquod totū diui-
<
lb
/>
ſum in partes ꝓportionales ꝓportione compoſi-
<
lb
/>
ta ex proportione temporis puta partis propor-
<
lb
/>
tionalis maioris ad partem immediate ſequenteꝫ
<
lb
/>
minorem, et velocitatis partis maioris ad veloci-
<
cb
chead
="
Secūdi. De motu locali quo ad effectū ſcḋm tempus difformi.
"/>
tatem partis minoris ad primam partem prpor-
<
lb
/>
tionalem talis diuiſionis. </
s
>
<
s
xml:id
="
N1F9B5
"
xml:space
="
preserve
">Hoc inuolutum theo-
<
lb
/>
rema exemplari declaratione reſoluatur: volo em̄
<
lb
/>
dicere / conſciſa hora per partes proportionales
<
lb
/>
proportione dupla, et in prima parte proportiõa-
<
lb
/>
li aliquod mobile moueatur aliquanta velocitate
<
lb
/>
q̄ in ſecunda parte proportionali in ſexquialtero
<
lb
/>
minori velocitate, et in tertia in ſexquialtero mīor
<
lb
/>
velocitate quã in ſecūda, et ſic cõſequēter </
s
>
<
s
xml:id
="
N1F9C6
"
xml:space
="
preserve
">ita cu-
<
lb
/>
iuſlꝫ ꝑtis p̄cedētis maioris velocitas ad velocitatē
<
lb
/>
mīoris īmediate ſequētꝪ ſexq̇alterã ꝓportionē ha-
<
lb
/>
beat: tūc dicit theorema poſitū. </
s
>
<
s
xml:id
="
N1F9CF
"
xml:space
="
preserve
">ſpaciū ꝑtranſitū in
<
lb
/>
totali hora ſe habere ad ſpaciū ꝑtranſitū in prima
<
lb
/>
parte proportionali in proportione ſequialtera:
<
lb
/>
qm̄ proportio compoſita ex proportione dupla tē
<
lb
/>
porum et ſexquialtera velocitatū eſt tripla: et quod
<
lb
/>
libet totū diuiſum per partes proportione tripla
<
lb
/>
ſe habet ad primã proportionalem partem eius in
<
lb
/>
proportione ſexquialtera. </
s
>
<
s
xml:id
="
N1F9E0
"
xml:space
="
preserve
">Probatur tamen vni-
<
lb
/>
uerſaliter cõcluſio: ſit hora diuiſa per partes pro-
<
lb
/>
portionales portiõe g. et moueatur mobile in ali-
<
lb
/>
qua certa proportione velocius continuo in parte
<
lb
/>
p̄cedenti maiore quam in minore ſequente ita cõ
<
lb
/>
tinuo maior velocitas ſit in parte maiori quam in
<
lb
/>
minore īmediate ſequente, ſit proportio cõtinuo
<
lb
/>
velocitatis partis maioris ad velocitatem partis
<
lb
/>
minoris f. compoſita proportio ex g. et f. ſit h. / tūc
<
lb
/>
ſpaciū ꝑtranſitum in totali hora ſe pabet ad ſpa-
<
lb
/>
cium ꝑtranſitum in prima parte proportionali in
<
lb
/>
ꝓportione in qua ſe habet aliquod totum diuiſum
<
lb
/>
in partes proportionales ꝓportione h. ad primaꝫ
<
lb
/>
partem ꝓportionalē eiuſdem diuiſionis videlicet
<
lb
/>
proportione h. </
s
>
<
s
xml:id
="
N1F9FF
"
xml:space
="
preserve
">Quod probatur ſic / quia ſpacii ꝑ-
<
lb
/>
tranſiti in prima parte proportionali ad ſpacium
<
lb
/>
ꝑtranſitū in ſecunda parte ꝓportionali eſt propor
<
lb
/>
tio h. et ſpacii ꝑtranſiti in ſecunda ad ſpaciū ꝑtran
<
lb
/>
ſiti in tertia eſt etiam proportio h. / et ſic conſequen-
<
lb
/>
ter de ſpaciis ꝑtranſitis in duabus partibus pro-
<
lb
/>
portionalibus īmediatis quibuſuis demonſtratis /
<
lb
/>
ergo totale ſpaciū ꝑtrãſitū in tota hora componit̄̄
<
lb
/>
ex infinitis continuo ſe habentibus in proportione
<
lb
/>
h. / igitur totale ſpaciū ſe habet ad primū illoꝝ ſpa
<
lb
/>
ciorum / quod eſt ꝑtranſitū in prima parte propor-
<
lb
/>
tionali in proportiõe in qua ſe habet aliquod totū
<
lb
/>
diuiſum ꝑ partes ꝓportionales proportione h. ad
<
lb
/>
primã eius partē / quod fuit probandū. </
s
>
<
s
xml:id
="
N1FA1C
"
xml:space
="
preserve
">Patet con-
<
lb
/>
ſequentia / quia eodem modo ſe habent illa ſpacia
<
lb
/>
continuo ſe habentia in proportione h. ſicut ſe ha-
<
lb
/>
bent partes proportionales alicuiꝰ continui pro-
<
lb
/>
portiõe h. </
s
>
<
s
xml:id
="
N1FA27
"
xml:space
="
preserve
">Probatur tamen añs videlicet / ſpacii
<
lb
/>
ꝑtranſiti in prima parte ꝓportionali ad ſpaciū ꝑ-
<
lb
/>
tranſitū in ſecūda eſt ꝓpertio h. et ſpacii ꝑtrãſiti in
<
lb
/>
ſcḋa ad ſpaciū ꝑtranſitum in tertia etc̈. quia prima
<
lb
/>
pars proportionalis eſt maius tempus quã ſecun-
<
lb
/>
da in g. proportione, et ei coextenditur velocitas in
<
lb
/>
tenſior quam ſeēunde in f. proportione / vt dici hipo
<
lb
/>
teſis: et h. proportio eſt proportio cõpoſita ex g. et f.
<
lb
/>
proportionibus ex hypoteſi: igitur ſpaciū ꝑtranſi
<
lb
/>
tum in prima parte ꝓportiõali ſe habet ad ſpaciū
<
lb
/>
ꝑtrãſitū in ſecūda in h. ꝓportiõe. </
s
>
<
s
xml:id
="
N1FA3E
"
xml:space
="
preserve
">Cõſimili argumē
<
lb
/>
to ꝓbabis de quibuſcū ſpaciis ꝑtranſitis in qui
<
lb
/>
buſcū duabus partibus immediatis: quod erat
<
lb
/>
inferendum. </
s
>
<
s
xml:id
="
N1FA47
"
xml:space
="
preserve
">Patet tamen conſequentia ꝑ tertiam
<
lb
/>
propoſitionem ſecundi notabilis huius queſtiõis.
<
lb
/>
<
note
position
="
right
"
xlink:href
="
note-0160-01a
"
xlink:label
="
note-0160-01
"
xml:id
="
N1FB10
"
xml:space
="
preserve
">Correĺ.</
note
>
</
s
>
<
s
xml:id
="
N1FA53
"
xml:space
="
preserve
">¶ Ex hac ſolutione ſequitur primo / partitiõe ho
<
lb
/>
re facta ꝑ partes proportionales proportione ſu-
<
lb
/>
prabipartiēte tertias, et in prima parte ꝓporõali
<
lb
/>
moueatur aliquod mobile aliquãta velocitate, et ī
<
lb
/>
ſecunda in ſuprabipartiente quintas minore et in
<
lb
/>
tertia in eadē proportiõe ſuprabipartiēte quintas </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>