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
>
121
122
123
124
125
126
127
128
129
130
<
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
="
N20F21
"
level
="
3
"
n
="
3
"
type
="
other
"
type-free
="
tractatus
">
<
div
xml:id
="
N20F2E
"
level
="
4
"
n
="
1
"
type
="
chapter
"
type-free
="
capitulum
">
<
p
xml:id
="
N236A4
">
<
s
xml:id
="
N236A8
"
xml:space
="
preserve
">
<
pb
chead
="
De motu rarefactionis cõdenſationis.
"
file
="
0198
"
n
="
198
"/>
acquirit vel deperdit de quantitate.</
s
>
</
p
>
<
p
xml:id
="
N236B6
">
<
s
xml:id
="
N236B7
"
xml:space
="
preserve
">Tertium. </
s
>
<
s
xml:id
="
N236BA
"
xml:space
="
preserve
">Si ſint duo inequalia in
<
lb
/>
quantitate et denſitate et ſicut vnum eſt alio maius
<
lb
/>
ita ſit eo denſius que eque velociter acquirant vel
<
lb
/>
deperdant de denſitate: eque velocitrr acquirunt
<
lb
/>
vel deperdunt de quantitate.</
s
>
</
p
>
<
p
xml:id
="
N236C5
">
<
s
xml:id
="
N236C6
"
xml:space
="
preserve
">Quartum notabile. </
s
>
<
s
xml:id
="
N236C9
"
xml:space
="
preserve
">Si ſint duo ine-
<
lb
/>
qualia et inequaliter denſa ita tamen maior ſit
<
lb
/>
proportio quantitatis vnius ad quantitatem al-
<
lb
/>
terius ꝙ̄ denſitatis vnius ad denſitatem alterius
<
lb
/>
que eque velociter acquirant vel deperdãt de den-
<
lb
/>
ſitate: velocius acquirit vel deperdit de quantita-
<
lb
/>
te maius quam minus.</
s
>
</
p
>
<
p
xml:id
="
N236D8
">
<
s
xml:id
="
N236D9
"
xml:space
="
preserve
">Quintum. </
s
>
<
s
xml:id
="
N236DC
"
xml:space
="
preserve
">Si ſint duo inequalia in
<
lb
/>
quantitate et in denſitate, et minor ſi proportio
<
lb
/>
quãtitatis denſioris ad quantitatem alterius quã
<
lb
/>
denſitatis vnius ad denſitatem alterius que eque
<
lb
/>
velociter acquirant vel deperdãt de denſitate: den
<
lb
/>
ſius tardius acquiret vel deperdet de quantitate
<
lb
/>
quam rarius. </
s
>
<
s
xml:id
="
N236EB
"
xml:space
="
preserve
">His notabilibus poſitis pono ali-
<
lb
/>
quas propoſitiones.</
s
>
</
p
>
<
p
xml:id
="
N236F0
">
<
s
xml:id
="
N236F1
"
xml:space
="
preserve
">Prima propoſitio: ſecūdum notabile
<
lb
/>
eſt falſum
<
note
position
="
left
"
xlink:href
="
note-0198-01a
"
xlink:label
="
note-0198-01
"
xml:id
="
N23751
"
xml:space
="
preserve
">ↄ̈ calcuĺ.</
note
>
</
s
>
<
s
xml:id
="
N236FB
"
xml:space
="
preserve
">Probatur / quia eſt vna cõditionalis cu
<
lb
/>
ius eſt antecedens eſt verum et conſequens falſum: er-
<
lb
/>
go illud notabile eſt falſum. </
s
>
<
s
xml:id
="
N23702
"
xml:space
="
preserve
">Probatur antecedēs /
<
lb
/>
et volo / ſint duo pedalia quorum vnum ſit denſuꝫ
<
lb
/>
vt .8. et aliud vt .4. et vtrum illorum eque velociter
<
lb
/>
acquirat duos gradus denſitatis: tunc illud quod
<
lb
/>
eſt minus denſum deperdit vnam tertiam, et aliud
<
lb
/>
vnam quintam / vt patet. </
s
>
<
s
xml:id
="
N2370F
"
xml:space
="
preserve
">Sed vnius tertie ad vnaꝫ
<
lb
/>
quintam non eſt proportio dupla qualis eſt pro-
<
lb
/>
portio inter illorum pedalium denſitates: ergo nõ
<
lb
/>
in ea proportione qua vnuꝫ eſt minus denſum alio
<
lb
/>
in ea proportione velocius deperdit de quantita-
<
lb
/>
te: et ſic in hoc caſu anteccdens illius conditiona-
<
lb
/>
lis eſt verum, et conſequens falſum: quod fuit pro-
<
lb
/>
bandum. </
s
>
<
s
xml:id
="
N23720
"
xml:space
="
preserve
">Sed tu diceres / iſta ratio nõ impugnat
<
lb
/>
notabile quoniam in notabile habetur que eque ve
<
lb
/>
lociter acquirant vel deperdant de denſitate pro-
<
lb
/>
portionali: modo in caſu argumenti non eque pro
<
lb
/>
portionalem denſitatem deperdunt illa duo peda
<
lb
/>
lia. </
s
>
<
s
xml:id
="
N2372D
"
xml:space
="
preserve
">Sed hoc nichil eſt dicere. </
s
>
<
s
xml:id
="
N23730
"
xml:space
="
preserve
">Nam ſi eque propor-
<
lb
/>
tionalem denſitatem acquirerent vel deperderent
<
lb
/>
cum ſint equalia: ipſa equalem quantitatem oīno
<
lb
/>
acquirerunt aut deperderent quod eſt contra no-
<
lb
/>
tabile. </
s
>
<
s
xml:id
="
N2373B
"
xml:space
="
preserve
">Nec probatio qua calculator intēdit illud
<
lb
/>
notabile probare aliquid valet: quia antecedens
<
lb
/>
eius eſt falſum: videlicet hoc in qua proportione
<
lb
/>
vnum eſt minus denſum alio in ea proportione ve-
<
lb
/>
locius proportionabiliter acquirit vĺ deperdit de
<
lb
/>
denſitate. </
s
>
<
s
xml:id
="
N23748
"
xml:space
="
preserve
">Falſitas enim eius patet ex caſu argu-
<
lb
/>
menti contra illud notabile.</
s
>
</
p
>
<
p
xml:id
="
N23757
">
<
s
xml:id
="
N23758
"
xml:space
="
preserve
">Secunda propoſitio. </
s
>
<
s
xml:id
="
N2375B
"
xml:space
="
preserve
">Tertium nota
<
lb
/>
bile eſt ſimiliter falſum.
<
note
position
="
left
"
xlink:href
="
note-0198-02a
"
xlink:label
="
note-0198-02
"
xml:id
="
N23799
"
xml:space
="
preserve
">Impuḡ-
<
lb
/>
tur terti-
<
lb
/>
um nöbi-
<
lb
/>
le calcuĺ.</
note
>
</
s
>
<
s
xml:id
="
N23765
"
xml:space
="
preserve
">Probatur / quia eſt vna cõ-
<
lb
/>
ditionalis cuius antecedens eſt verū , et conſquens
<
lb
/>
falſum: ergo illud notabile eſt falſū. </
s
>
<
s
xml:id
="
N2376C
"
xml:space
="
preserve
">Arguitur an-
<
lb
/>
tecedens / quia capto quadrupedali denſo vt .4. et
<
lb
/>
pedali denſo vt vnum, et acquirat quadrupedale
<
lb
/>
4. gradus denſitatis, et pedale etiam eque veloci-
<
lb
/>
ter: tunc antecedens illius conditionalis eſt verum /
<
lb
/>
vt conſtat: et conſequens falſum : ergo propoſitum.
<
lb
/>
</
s
>
<
s
xml:id
="
N2377A
"
xml:space
="
preserve
">Iam probo falſitatem conſequentis in illo caſu
<
lb
/>
quoniã illud quadrupedale efficitur in duplo den-
<
lb
/>
ſius, et per conſequens in duplo minus: et ſic perdit
<
lb
/>
bipedale: pedale vero non perdit bipedale / vt con-
<
lb
/>
ſtat cum non ſit niſi pedale: ergo tunc illa duo non
<
lb
/>
eque velociter acquirunt vel deperdunt de denſi-
<
cb
chead
="
De motu rarefactionis cõdenſationis.
"/>
tate et ſic antecedens eſt verū: et conſequens falſum /
<
lb
/>
quod fuit probandū. </
s
>
<
s
xml:id
="
N2378C
"
xml:space
="
preserve
">Nec valet fugere ad id qḋ cal-
<
lb
/>
culator dicit in illo notabili tertio pro hoc inſtan
<
lb
/>
ti quoniam pro inſtanti nulla fit acquiſitio quan-
<
lb
/>
titatis: et ideo illud nullo modo iuuat.</
s
>
</
p
>
<
note
position
="
right
"
xml:id
="
N237A5
"
xml:space
="
preserve
">īpugnat̄̄
<
lb
/>
4. nõbile</
note
>
<
p
xml:id
="
N237AB
">
<
s
xml:id
="
N237AC
"
xml:space
="
preserve
">Tertia propoſitio. </
s
>
<
s
xml:id
="
N237AF
"
xml:space
="
preserve
">Quartum notabi
<
lb
/>
le non eſt verum.
<
note
position
="
right
"
xlink:href
="
note-0198-03a
"
xlink:label
="
note-0198-03
"
xml:id
="
N2381A
"
xml:space
="
preserve
">Calcuĺ.</
note
>
</
s
>
<
s
xml:id
="
N237B9
"
xml:space
="
preserve
">Probatur / quia eſt vna conditio-
<
lb
/>
nalis: cuius antecedens in caſu eſt verum: et conſe-
<
lb
/>
quens falſum: ergo. </
s
>
<
s
xml:id
="
N237C0
"
xml:space
="
preserve
">Probatur antecedens, et ca-
<
lb
/>
pio pedale et ſemipedale, et pedale ſit denſum vt .6
<
lb
/>
ſemipedale vero vt .4. et deperdat vtrum illorum
<
lb
/>
duos gradus denſitatis in hora eque velociter.
<
lb
/>
</
s
>
<
s
xml:id
="
N237CA
"
xml:space
="
preserve
">Quo poſito antecedens eſt verum. </
s
>
<
s
xml:id
="
N237CD
"
xml:space
="
preserve
">Nam illa ſunt
<
lb
/>
inequalia in quantitate et dēſitate maior et eſt pro-
<
lb
/>
portio quantitatis proportione denſitatis. </
s
>
<
s
xml:id
="
N237D4
"
xml:space
="
preserve
">Nam
<
lb
/>
illa eſt dupla hec vero ſexquialtera: et illa duo eque
<
lb
/>
velociter deperdunt vel acquirunt de denſitate. </
s
>
<
s
xml:id
="
N237DB
"
xml:space
="
preserve
">Et
<
lb
/>
tamen conſequens eſt falſum / quoniam maius illo
<
lb
/>
rum non velocius acquirit de quantitate quã mi-
<
lb
/>
nus: immo equaliter. </
s
>
<
s
xml:id
="
N237E4
"
xml:space
="
preserve
">Nam vtrum illorum acqui
<
lb
/>
rit ſemipedale / vt conſtat: ergo illud notabile falſū /
<
lb
/>
quod fuit probandum. </
s
>
<
s
xml:id
="
N237EB
"
xml:space
="
preserve
">Et aduerte aliquãdo da-
<
lb
/>
ta veritate antecedentis: maius illorum equaliter
<
lb
/>
acquirit vt in caſu poſito. </
s
>
<
s
xml:id
="
N237F2
"
xml:space
="
preserve
">Aliquãdo maius acqui-
<
lb
/>
rit maiorem quantitatem quam minus: vt poſito
<
lb
/>
quadrupedali denſo vt .6. et pedali denſo vt .4. et
<
lb
/>
equaliter deperdat vtrum duos gradus denſita
<
lb
/>
tis: tunc quadrupedale acquirit bipedale: pedale
<
lb
/>
vero vnū pedale preciſe. </
s
>
<
s
xml:id
="
N237FF
"
xml:space
="
preserve
">Aliquando maius deper-
<
lb
/>
dit minus de quantitate: vt videlicet poſito a. ſit
<
lb
/>
9. pedum b.4.a. denſum vt .8.b. vero vt .4. et deper
<
lb
/>
dat vtrum illorum eque velociter vnum gradum
<
lb
/>
denſitatis: tūc quadrupedale acquirit pedale cum
<
lb
/>
tertia. </
s
>
<
s
xml:id
="
N2380C
"
xml:space
="
preserve
">Aliud vero corpus maius acquirit pedale
<
lb
/>
cum duabus ſeptimis: modo plus eſt pedale cum
<
lb
/>
tertia quã cū duabus ſeptimis. </
s
>
<
s
xml:id
="
N23813
"
xml:space
="
preserve
">Ptꝫ hoc calculãti.</
s
>
</
p
>
<
note
position
="
right
"
xml:id
="
N23820
"
xml:space
="
preserve
">īpugnat̄̄
<
lb
/>
.5. nöbile</
note
>
<
p
xml:id
="
N23826
">
<
s
xml:id
="
N23827
"
xml:space
="
preserve
">Quarta propoſitio. </
s
>
<
s
xml:id
="
N2382A
"
xml:space
="
preserve
">Quiutum nota-
<
lb
/>
bile eſt falſum.
<
note
position
="
right
"
xlink:href
="
note-0198-04a
"
xlink:label
="
note-0198-04
"
xml:id
="
N2384C
"
xml:space
="
preserve
">calcuĺ.</
note
>
</
s
>
<
s
xml:id
="
N23834
"
xml:space
="
preserve
">Probatur: quoniã dato ſit vnuꝫ
<
lb
/>
ſextipedale denſum vt octo, et vnū bipedale denſū
<
lb
/>
vt .2. et vtrum illorum acquirat .4. gradus denſi-
<
lb
/>
tatis eque velociter: tunc antecedens illius conditi
<
lb
/>
onalis eſt verum, et conſequens falſum. </
s
>
<
s
xml:id
="
N2383F
"
xml:space
="
preserve
">Nam tunc
<
lb
/>
denſius deperdit duo pedalia, et minus denſum nõ
<
lb
/>
perdit tantum quia tunc efficeretur non quantum /
<
lb
/>
g̊ illud notabile quintū eſt falſū / qḋ fuit ꝓbandum.</
s
>
</
p
>
<
p
xml:id
="
N23852
">
<
s
xml:id
="
N23853
"
xml:space
="
preserve
">Sit ergo concluſio reſponſiua ad du
<
lb
/>
bium quodlibet illorum notabilium dēpto primo
<
lb
/>
eſt falſum. </
s
>
<
s
xml:id
="
N2385A
"
xml:space
="
preserve
">Patet hec concluſio per quatuor predi-
<
lb
/>
ctas concluſiones. </
s
>
<
s
xml:id
="
N2385F
"
xml:space
="
preserve
">Sed quia poſſunt poni et demõ-
<
lb
/>
ſtari .4. notabilia conformia .4. his notabilibus
<
lb
/>
falſis impugnatis que plurimum ſubtilitatis ha
<
lb
/>
bent. </
s
>
<
s
xml:id
="
N23868
"
xml:space
="
preserve
">Ideo huic loco ea interſerenduꝫ non ī merito
<
lb
/>
optaui illorum demonſtrationibus breuiitatis cau
<
lb
/>
ſa et quadaꝫ alia occulta cauſa omiſſis. </
s
>
<
s
xml:id
="
N2386F
"
xml:space
="
preserve
">Sit igitur
<
lb
/>
<
note
position
="
right
"
xlink:href
="
note-0198-05a
"
xlink:label
="
note-0198-05
"
xml:id
="
N238B4
"
xml:space
="
preserve
">1. nöbile</
note
>
</
s
>
<
s
xml:id
="
N23879
"
xml:space
="
preserve
">Primū illorum .4. notabilium. </
s
>
<
s
xml:id
="
N2387C
"
xml:space
="
preserve
">¶ Si ſint duo ine-
<
lb
/>
qualiter denſa equalia tamen in quantitate que
<
lb
/>
eque velociter acquirant vel deperdant de denſita
<
lb
/>
te: tunc in ea proportione minus denſum plus ac-
<
lb
/>
quirit vel deperdit de quantitate in qua ſe habet
<
lb
/>
denſitas denſioris ad denſitatem minus denſi in
<
lb
/>
fine depertionis vel acquiſitionis talis denſitatis.
<
lb
/>
</
s
>
<
s
xml:id
="
N2388C
"
xml:space
="
preserve
">et nolo dicere / per totum tempus in ea proporti-
<
lb
/>
one velocius acquirit: ſed in toto tempore cathego
<
lb
/>
rematice. </
s
>
<
s
xml:id
="
N23893
"
xml:space
="
preserve
">Exēplum / vt ſi duo pedalia quoꝝ vnū eſt
<
lb
/>
denſum vt .8. et aliud vt .4. perdant duos gradus
<
lb
/>
denſitatis eque velociter dico / pedale minꝰ den-
<
lb
/>
ſum in triplo maiorem quantitatem acquiſiuit
<
lb
/>
quam magis denſum quia proportio denſitatum </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>