Alvarus, Thomas
,
Liber de triplici motu
,
1509
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Figures
Content
Thumbnails
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 290
>
Scan
Original
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 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
">
<
p
xml:id
="
N1E680
">
<
s
xml:id
="
N1E685
"
xml:space
="
preserve
">
<
pb
chead
="
De motu locali quo ad effectū ſcḋm tempus difformi.
"
file
="
0148
"
n
="
148
"/>
Oīs potentia mouēs vniformiter difformiter lati
<
lb
/>
tudine terminata ad nõ gradū: in triplo plus ꝑtrã
<
lb
/>
ſit ī medietate in qua mouet̄̄ intēſius ꝙ̄ ī medietate
<
lb
/>
tēporis in qua mouetur remiſſius: vt ſi in medieta-
<
lb
/>
te in qua mouetur remiſſius ꝑtranſit vnū pedale: in
<
lb
/>
alia ꝑtranſit tripedale. </
s
>
<
s
xml:id
="
N1E696
"
xml:space
="
preserve
">Probatur hec propoſitio
<
lb
/>
facile ex priori: qm̄ motꝰ fluens in medietate in qua
<
lb
/>
mouetur velocius eſt triplus ad motū factū in me-
<
lb
/>
dietate tēporis in qua mouetur remiſſiꝰ / vt dicit pre
<
lb
/>
cedens: igit̄̄ ꝑtrãſitū in medietate in qua mouetur
<
lb
/>
velocius erit triplū ad ꝑtranſitū in reliqua medie-
<
lb
/>
tate. </
s
>
<
s
xml:id
="
N1E6A5
"
xml:space
="
preserve
">Cõſequentia ptꝫ / q2 tēporibꝰ exiſtentibus equa
<
lb
/>
libus et velocitatibus in equalibus ſpacia ꝑtranſi-
<
lb
/>
ta ſe habent in ea ꝓportione in qua ſe habent velo
<
lb
/>
citates: vt facile induci poteſt ex definitione velocio
<
lb
/>
ris et tardioris data ſexto phiſicoꝝ </
s
>
<
s
xml:id
="
N1E6B0
"
xml:space
="
preserve
">¶ Ex quo ſequi
<
lb
/>
tur / ſi a. mobile moueatur ꝑ horam vniformiter
<
lb
/>
difformiter incipiendo a non gradu vſ ad certum
<
lb
/>
gradū et in prima medietate vnã leucã ꝑtranſit: in
<
lb
/>
ſecūda medietate triū leucarū ſpaciū abſoluet. </
s
>
<
s
xml:id
="
N1E6BB
"
xml:space
="
preserve
">Et
<
lb
/>
ſi ordine prepoſtero moueri incepiſſet puta ab illo
<
lb
/>
dato gradu vſ ad nõ gradū in prima medietate
<
lb
/>
hore tribus abſolutis leucis: vna dumtaxat reſta-
<
lb
/>
ret tranſeunda in ſecunda tēporis medietate.</
s
>
</
p
>
<
p
xml:id
="
N1E6C6
">
<
s
xml:id
="
N1E6C7
"
xml:space
="
preserve
">Quinta ꝓpoſitio. </
s
>
<
s
xml:id
="
N1E6CA
"
xml:space
="
preserve
">Si aliquod mobile
<
lb
/>
moueatur vniformiter difformiter a nõ gradu vſ
<
lb
/>
ad certū gradū in aliquo tēpore: ipſum adequate
<
lb
/>
ſubduplū ſpaciū ꝑtranſit ad ſpaciū natū ꝑtranſiri
<
lb
/>
illo gradu intenſiori ꝑ idem tēpus cõtinuato. </
s
>
<
s
xml:id
="
N1E6D5
"
xml:space
="
preserve
">Pro
<
lb
/>
batur / q2 totalis velocitas illius motus eſt ſubdu-
<
lb
/>
pla ad velocitatē illius gradus iutenſioris eiuſdē
<
lb
/>
latitudinis: igitur ſubduplū ſpaciū ꝑtranſibitur
<
lb
/>
mediante vna illaꝝ ad ſpaciū ꝑtranſitū ab illa que
<
lb
/>
eſt in duplo intenſior dūmodo tēpora ſint equalia
<
lb
/>
ſi ſpaciorum proportio proportionem velocitatū
<
lb
/>
eodem tempore ſequitur / vt oportet. </
s
>
<
s
xml:id
="
N1E6E6
"
xml:space
="
preserve
">Ex hac ſequit̄̄.</
s
>
</
p
>
<
p
xml:id
="
N1E6E9
">
<
s
xml:id
="
N1E6EA
"
xml:space
="
preserve
">Sexta ꝓpoſitio que talis eſt. </
s
>
<
s
xml:id
="
N1E6ED
"
xml:space
="
preserve
">Omne
<
lb
/>
mobile motū vniformiter difformiter a certo gra-
<
lb
/>
du vſ ad certū gradū in aliquo tēpore maiꝰ ſpa-
<
lb
/>
ciū quã ſubduplū ꝑtranſit in eodem tēpore ad ſpa
<
lb
/>
ciū natū ꝑtranſiri mediante extremo intenſiori il-
<
lb
/>
lius latitudinis ꝑ idem tēpus cõtinuato. </
s
>
<
s
xml:id
="
N1E6FA
"
xml:space
="
preserve
">Probat̄̄ /
<
lb
/>
quia ſi talis latitudo inctperet a gradu ſuo inten-
<
lb
/>
ſiori et terminaretur ad nõ gradū: p̄ciſe illud mobi
<
lb
/>
le ꝑtranſiret in illo tēpore ſubduplū ſpaciū ad ſpa
<
lb
/>
ciū natū ꝑtranſiri mediante extremo intenſiori il
<
lb
/>
lius latitudinis ꝑ idem tēpus cõtinuato / vt patꝫ ex
<
lb
/>
priori: ſed modo illa latitudo ab illo gradu incipi
<
lb
/>
ens et ad gradū terminata eſt intenſior / vt ptꝫ ex ſe
<
lb
/>
cunda / ergo in equali tēpore maiꝰ ſpaciū quã illud
<
lb
/>
ſubduplum pertranſibit / quod fuit probandum.</
s
>
</
p
>
<
p
xml:id
="
N1E70F
">
<
s
xml:id
="
N1E710
"
xml:space
="
preserve
">Septima ꝓpoſitio. </
s
>
<
s
xml:id
="
N1E713
"
xml:space
="
preserve
">Si aliqḋ mobile
<
lb
/>
vniformiter difformiter moueat̄̄ a certo gradu in-
<
lb
/>
tēſiori ad cetū gradū remiſſiorē ī hora: ipſū in pri
<
lb
/>
ma medietate hore minus quã triplū ſpaciū ꝑtran
<
lb
/>
ſit ad ſpaciū ꝑtranſitū in ſecunda medietate hore
<
lb
/>
in qua tardiꝰ mouetur. </
s
>
<
s
xml:id
="
N1E720
"
xml:space
="
preserve
">Probatur / quia ſi talis la-
<
lb
/>
titudo motus diuidatur ꝑ partes proportionales
<
lb
/>
ꝓportione dupla ſecundū partes tēporis: ille par-
<
lb
/>
tes nõ cõtinue ſe habebūt in ꝓportione dupla ſicut
<
lb
/>
ſe habent tales partes in latitudine terminata ad
<
lb
/>
nõ gradū: igr̄ reſiduū oīm partiū a prima non eſt
<
lb
/>
ſubtriplū ad velocitatē prime ſed maius quã ſub-
<
lb
/>
triplū: et ꝑ conſequens ſpaciū ꝑtranſitum in oībus
<
lb
/>
partibus a prima puta in ſecūda medietate eſt ma
<
lb
/>
ius quã ſubtriplum ad ſpacium pertranſitū in pri
<
cb
chead
="
De motu locali quo ad effectū ſcḋm tempus difformi.
"/>
ma. </
s
>
<
s
xml:id
="
N1E738
"
xml:space
="
preserve
">Antecedens patet intuenti et conſequentia pro
<
lb
/>
batur / quia quanto proportio aliqua in qua ſe ha
<
lb
/>
bent cõtinuo aliqua infinita eſt minor tanto aggre
<
lb
/>
gatum ex omnibus ſequentibus primū eſt maius.
<
lb
/>
</
s
>
<
s
xml:id
="
N1E742
"
xml:space
="
preserve
">Item patet predicta propoſitio exemplariter / qm̄
<
lb
/>
capta latitudine incipiente a duodecim et termina
<
lb
/>
ta ad quatuor gradus medius medietatis intenſi
<
lb
/>
oris eſt vt decem: et gradus medius medietatis re-
<
lb
/>
miſſioris eſt vt .6. modo gradus ſextus nõ eſt ſub-
<
lb
/>
triplus ad duodenarium: et ſic in omni alia lati-
<
lb
/>
tudine inuenies predicte propoſitionis certitudinē
<
lb
/>
<
note
position
="
right
"
xlink:href
="
note-0148-01a
"
xlink:label
="
note-0148-01
"
xml:id
="
N1E76B
"
xml:space
="
preserve
">Queſtio</
note
>
</
s
>
<
s
xml:id
="
N1E758
"
xml:space
="
preserve
">¶ Et ſi queras quomodo cognoſcēdum ſit in omni
<
lb
/>
latitudine motus vtrim ad graduꝫ terminata in
<
lb
/>
qua proportione ſe habeat extremuꝫ intenſius ad
<
lb
/>
gradum mediuꝫ eiuſdem latitudinis: et in qua pro-
<
lb
/>
portione plus pertrãſitur mediante medietate in-
<
lb
/>
tenſiori talis latitudinis quam mediante medieta
<
lb
/>
te remiſſiori.</
s
>
</
p
>
<
p
xml:id
="
N1E771
">
<
s
xml:id
="
N1E772
"
xml:space
="
preserve
">Rſpõdeo / in hac materia nulla põt
<
lb
/>
dari certa et vniuerſalis regula. </
s
>
<
s
xml:id
="
N1E777
"
xml:space
="
preserve
">Quoniã ſecundū /
<
lb
/>
quod extremum intenſius et remiſſius ſe habent in
<
lb
/>
alia et alia ꝓportiõe ad īuicē: ita ſe habet gxadꝰ me
<
lb
/>
dius ad extremū intenſius talis latitudinis in alia
<
lb
/>
et alia ꝓportiõe: tamen poſſent ſiguari peculiares
<
lb
/>
regule certis ſpeciebus proportionum accõmode
<
lb
/>
</
s
>
<
s
xml:id
="
N1E785
"
xml:space
="
preserve
">Si enim extrema ſe habeant in proportiõe dupla
<
lb
/>
gradus medius eſt ſubſexquitertius ad extremum
<
lb
/>
intenſius. </
s
>
<
s
xml:id
="
N1E78C
"
xml:space
="
preserve
">Si vero extrema ſe habent in proporti-
<
lb
/>
one tripla: tunc gradus medius erit ſubſexquial-
<
lb
/>
terus ad extremum intenſius. </
s
>
<
s
xml:id
="
N1E793
"
xml:space
="
preserve
">Si vero ſe habent in
<
lb
/>
proportione quadrupla: tunc gradus medius eſt
<
lb
/>
ſubſupertripartiens quintas ad extremum inten-
<
lb
/>
ſius. </
s
>
<
s
xml:id
="
N1E79C
"
xml:space
="
preserve
">Si vero ſe habeant in proportione ſextupla:
<
lb
/>
gradus medius eſt ſuperquintipartiens ſeptimas
<
lb
/>
ad gradum intenſiorem. </
s
>
<
s
xml:id
="
N1E7A3
"
xml:space
="
preserve
">et ſic diuerſis proportioni
<
lb
/>
bus diuerſe regule aſſignatur.
<
note
position
="
right
"
xlink:href
="
note-0148-02a
"
xlink:label
="
note-0148-02
"
xml:id
="
N1E7B8
"
xml:space
="
preserve
">Queſtio</
note
>
</
s
>
<
s
xml:id
="
N1E7AD
"
xml:space
="
preserve
">¶ Quereret tamē
<
lb
/>
aliquis vlterius quo tramite et menſura poſſet fa-
<
lb
/>
cile inueſtigari gradus medius in omni latitudīe.</
s
>
</
p
>
<
p
xml:id
="
N1E7BE
">
<
s
xml:id
="
N1E7BF
"
xml:space
="
preserve
">Reſpondeo / per hanc regulam quia
<
lb
/>
aut latitudo illa terminatur ad nõ gradū / tūc diui
<
lb
/>
datur extremum intenſius per medium: et vna me-
<
lb
/>
dietas eſt gradus medius. </
s
>
<
s
xml:id
="
N1E7C8
"
xml:space
="
preserve
">Si vero incipit a gradu
<
lb
/>
et terminatur ad gradum: tunc ſubduplum ad ag-
<
lb
/>
gregatum ex extremo intenſiori et remiſſiori eſt gra
<
lb
/>
dus medius inter illa extrema. </
s
>
<
s
xml:id
="
N1E7D1
"
xml:space
="
preserve
">Exemplum primi /
<
lb
/>
vt ſi aliqua latitudo incipiati ab octauo et termina
<
lb
/>
tur ad non gradum: quoniam medietas ipſorum
<
lb
/>
8. eſt .4. ideo gradus quartus eſt gradus medius.
<
lb
/>
</
s
>
<
s
xml:id
="
N1E7DB
"
xml:space
="
preserve
">Exemplum ſecundi / vt ſi aliqua latitudo incipiat
<
lb
/>
ab octauo et terminatur ad quartum. </
s
>
<
s
xml:id
="
N1E7E0
"
xml:space
="
preserve
">dico / gra-
<
lb
/>
dus ſextus eſt gradus mediꝰ qui eſt ſubduplus ad
<
lb
/>
aggregatum ex 8. et .4. </
s
>
<
s
xml:id
="
N1E7E7
"
xml:space
="
preserve
">Illud enim aggregatum eſt
<
lb
/>
vt duodecim: et ſic vniuerſaliter reperies omni ſe-
<
lb
/>
cluſa exceptione.</
s
>
</
p
>
<
p
xml:id
="
N1E7EE
">
<
s
xml:id
="
N1E7EF
"
xml:space
="
preserve
">Notandum eſt ſecundo / motum ve-
<
lb
/>
locitates quando ſunt equales quãdo inequa-
<
lb
/>
les intenſiue: et ſi equales, aut coextenſe partibus
<
lb
/>
temporis equalibus, aut inequalibus. </
s
>
<
s
xml:id
="
N1E7F8
"
xml:space
="
preserve
">Si vero in
<
lb
/>
equales idem etiam contingit, quia aut extendun-
<
lb
/>
tur per tempora equalia, aut per inequalia. </
s
>
<
s
xml:id
="
N1E7FF
"
xml:space
="
preserve
">Si
<
lb
/>
ſint inequales inequalibus coextenſe temporibus /
<
lb
/>
hoc contingit dupliciter quia aut maior velocitas
<
lb
/>
coextenditur tempori maiori aut minori. </
s
>
<
s
xml:id
="
N1E808
"
xml:space
="
preserve
">Exemplū
<
lb
/>
primi / vt ſi velocitas vt .4. coextendatur vni hore:
<
lb
/>
hoc eſt mobile moueatur vt .4. per vnam horam et
<
lb
/>
vt duo per dimidiam. </
s
>
<
s
xml:id
="
N1E811
"
xml:space
="
preserve
">Exemplum ſecundi / vt ſi
<
lb
/>
aliquod mobile moueatur velocitate vt quatuor </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>