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
>
171
172
173
174
175
176
177
178
179
180
<
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
">
<
pb
chead
="
Tertii tractatus
"
file
="
0203
"
n
="
203
"/>
</
div
>
<
div
xml:id
="
N24010
"
level
="
4
"
n
="
2
"
type
="
chapter
"
type-free
="
capitulum
">
<
head
xml:id
="
N24015
"
xml:space
="
preserve
">Secundū capitulū huiꝰ tractatus / in quo ſolito
<
lb
/>
pro more diſputatiue inquirimus penes quid velo
<
lb
/>
citas augmētationis attendi habeat.</
head
>
<
p
xml:id
="
N2401C
">
<
s
xml:id
="
N2401D
"
xml:space
="
preserve
">NUnc cõſequēter q̄ritur vtrū
<
lb
/>
velocitas motus augmētatiõis penes ꝓ
<
lb
/>
portionalē acquiſitionē ̄titatis attēdi
<
lb
/>
habeat: an penes abſolutã acq̇ſitione ̄titatis.</
s
>
</
p
>
<
p
xml:id
="
N24026
">
<
s
xml:id
="
N24027
"
xml:space
="
preserve
">Arguitur primo / non penes propor
<
lb
/>
tionabilē acquiſitionē ̄titatis ita non ſemꝑ illḋ
<
lb
/>
quod in eodē tꝑe maiorem ꝓportionē acquirit ̄
<
lb
/>
aliud velocius augmētetur ꝙ̄ aliud in eodē tēpore
<
lb
/>
quia ſi ſic tūc ſequeretur / a. et b. ſunt equalia: et a
<
lb
/>
continuo velocius augmētabit̄̄ ꝙ̄ b. et tamen ſemꝑ
<
lb
/>
a. manebit minus .b. / ſꝫ conſequēs eſt manifeſte fal-
<
lb
/>
ſum: igitur illud ex quo ſequit̄̄. </
s
>
<
s
xml:id
="
N24038
"
xml:space
="
preserve
">Sequela ꝓbat̄̄: et
<
lb
/>
volo / .a. et .b. ſint duo pedalia: et acquirat vnifor-
<
lb
/>
miter .b. in hora vnū pedale: et nichil deperdat de
<
lb
/>
qnantitate prehabita .a vero acquirat vnū pedale
<
lb
/>
vniformiter ꝑ horã: et deꝑdat vnū ſemipedale ̄ti-
<
lb
/>
tatis prehabite vniformiter in illa hora. </
s
>
<
s
xml:id
="
N24045
"
xml:space
="
preserve
">quo poſi-
<
lb
/>
to arguitur ſic / .a. et .b. ſunt modo equalia: et ſemꝑ .a
<
lb
/>
poſt hoc manebit minꝰ .b. / vt cõſtat qm̄ ſi nichil de
<
lb
/>
perderet maneret equale: ſꝫ modo cõtinuo perdet.
<
lb
/>
</
s
>
<
s
xml:id
="
N2404F
"
xml:space
="
preserve
">ergo cõtinuo manet minus: et tamē .a. cõtinuo velo
<
lb
/>
cius augmētabitur ꝙ̄ .b. / igitur intentū. </
s
>
<
s
xml:id
="
N24054
"
xml:space
="
preserve
">Probatur
<
lb
/>
minor / q2 .a. cõtinuo erit minus .b. et cõtinuo equa-
<
lb
/>
lem ̄titatē acquiret cū .b. / igit̄̄ .a. cõtinuo maiorem
<
lb
/>
ꝓportionē acquiret ꝙ̄ .b. et penes acq̇ſitionē maio
<
lb
/>
ioris ꝓportiõis in eodē tēpore attēdit̄̄ maior veloci
<
lb
/>
tas augmētatõis: igit̄̄ .a. ↄ̨tinuo velociꝰ augmētabi
<
lb
/>
tur ꝙ̄ .b. / quod fuit ꝓbandū. </
s
>
<
s
xml:id
="
N24063
"
xml:space
="
preserve
">Hec ↄ̨ſequētia patꝫ de
<
lb
/>
ſe: et prior ex octaua ſuppoſitiõe quarti capitis ſe-
<
lb
/>
cunde partis: et in aliis pleriſ locis libri arguta
<
lb
/>
eſt.
<
note
position
="
left
"
xlink:href
="
note-0203-01a
"
xlink:label
="
note-0203-01
"
xml:id
="
N240AF
"
xml:space
="
preserve
">Dicitur</
note
>
</
s
>
<
s
xml:id
="
N24071
"
xml:space
="
preserve
">¶ Dices et bene negando ſequelam: et ad ꝓbatio
<
lb
/>
nē admiſſo caſu ad bonū ſenſum poſſet em̄ negari /
<
lb
/>
vt poſtea dicemus: reſpõdeo negando minorē vi-
<
lb
/>
delicet / .a. cõtinuo poſt hoc velocius augmentabi
<
lb
/>
tur ꝙ̄ .b. et ad ꝓbationē concedo / .a. cõtinuo mane
<
lb
/>
bit minus et nego / ↄ̨tinuo equalē quãtitatem acq̇
<
lb
/>
ret cū .b. ſicut de facto eſt negandū qm̄ ſi nichil de-
<
lb
/>
perderet ſemꝑ acquireret equalē ̄titatē: ſꝫ modo
<
lb
/>
cõtinuo deꝑdit: ergo cõtinuo acquirit minorē: quo
<
lb
/>
niã in tota hora nõ acquirit .a. niſi ſemipedale. </
s
>
<
s
xml:id
="
N24086
"
xml:space
="
preserve
">Ma
<
lb
/>
nebit em̄ in fine pedale cū dimidio quoniã mãſiſſet
<
lb
/>
bipedale niſi perdidiſſet dimidiū. </
s
>
<
s
xml:id
="
N2408D
"
xml:space
="
preserve
">¶ Item in inſtã-
<
lb
/>
ti medio hore acquiſiuit .a. vnã quartã pedalis .b.
<
lb
/>
vero vnã medietatē: et ſic in illa prīa medietate ma
<
lb
/>
iorē quãtitatē acquiſiuit .b. ꝙ̄ .a. cuius oppoſitum
<
lb
/>
aſſumit argumētum.
<
note
position
="
left
"
xlink:href
="
note-0203-02a
"
xlink:label
="
note-0203-02
"
xml:id
="
N240B5
"
xml:space
="
preserve
">Coutra
<
lb
/>
ca'lcna.</
note
>
</
s
>
<
s
xml:id
="
N2409D
"
xml:space
="
preserve
">¶ Ex quo a ꝑte infertur cal-
<
lb
/>
latorē male induxiſſe illud cõſequēs tan̄ ſequens
<
lb
/>
ex opinione quam impugnamus: qm̄ illa cõcluſio
<
lb
/>
nullo pacto ſequit̄̄ expoſitione. </
s
>
<
s
xml:id
="
N240A6
"
xml:space
="
preserve
">Teneat̄̄ igit̄̄ poſi-
<
lb
/>
tio vniuerſaliter.</
s
>
</
p
>
<
p
xml:id
="
N240BD
">
<
s
xml:id
="
N240BE
"
xml:space
="
preserve
">Sed contra hanc reſponſionē argui
<
lb
/>
tur ſic / quia ſi illa poſitio eſſet vniuerſaliter vera / ſe
<
lb
/>
queretur hec concluſio. </
s
>
<
s
xml:id
="
N240C5
"
xml:space
="
preserve
"> ſi ſint duo ſiue equalia ſiue
<
lb
/>
inequalia q̄ cõtinuo eque velociter diminuãtur per
<
lb
/>
dendo cõtinuo equales ꝓportiones eque cito veni-
<
lb
/>
ent ad non quãtum: ſed ↄ̨ſequens eſt falſum: igitur
<
lb
/>
illud ex quo ſequit̄̄: falſitas ↄ̨ſequētis ꝓbat̄̄: q2 ſtat
<
lb
/>
aliqua duo in aliquo tepore eque velociter dimi
<
lb
/>
nuatur ꝑdendo in illo tꝑe p̄ciſe .4. duplas: igit̄̄ tūc
<
lb
/>
ↄ̨tinuo eque velociter diminuētur: et tamē nõ eque
<
lb
/>
cito deueniēt ad nõ ̄tū: et ꝑ ↄ̨ſequēs illḋ illatuꝫ eſt
<
lb
/>
vna conditionalis q̄ eſt falſa: igitur illud cõſequēs
<
lb
/>
eſt falſum. </
s
>
<
s
xml:id
="
N240DC
"
xml:space
="
preserve
">¶ Dices et bñ / de rigore illud ↄ̨ſequēs
<
lb
/>
eſt falſum ̄uis ſub illa forma ponatur a calcula-
<
lb
/>
tore: ſed oportet addere in antecedende illius con-
<
cb
chead
="
Capi. ſecundum
"/>
ditionalis q̄ eque velociter diminuūtur vſ ad nõ
<
lb
/>
quãtū: et tūc illa ↄ̨cluſio eſt ↄ̨cedenda ſecundū opi-
<
lb
/>
nionē. </
s
>
<
s
xml:id
="
N240EA
"
xml:space
="
preserve
">Quod ſic oſtēditur / quoniã ſi aliquod corpꝰ
<
lb
/>
puta .a. in hora diminuat̄̄ ad nõ quãtū: illud corpꝰ
<
lb
/>
infinitã latitudinē ꝓportionū deperdet: et .b. aliud
<
lb
/>
corpus maius in tota illa hora eque velociter di-
<
lb
/>
minuitur cū .a. / ergo ſequit̄̄ / infinitã latitudinē ꝓ-
<
lb
/>
portionis etiã deperdit .b. in illa hora: et vltra infi
<
lb
/>
nitã latitudinē ꝓportionis deperdit .b. in illa hora
<
lb
/>
et nõ reſtituit̄̄ in inſtanti terminatiuo priſtine quã
<
lb
/>
titati vt volo: igit̄̄ in inſtãti termīatiuo hore .b. erit
<
lb
/>
nõ ̄tum: et tunc .a. erit nõ ̄tum: igitur eq̄ cito .a. et .b.
<
lb
/>
deuenient ad nõ ̄tū in tali caſu: qḋ fuit ꝓbandum
<
lb
/>
</
s
>
<
s
xml:id
="
N24102
"
xml:space
="
preserve
">Sꝫ tã probo hanc cõſequētiã .b. inifinitã latitudinē
<
lb
/>
ꝓportiõis deꝑdit ī hora et ñ reſtituit̄̄ in inſtanti ter
<
lb
/>
minatiuo priſtine ̄titati: ergo in illo inſtanti non
<
lb
/>
quãtū manet </
s
>
<
s
xml:id
="
N2410B
"
xml:space
="
preserve
">Quia ſi in illo inſtãti maneret alicuiꝰ
<
lb
/>
quãtitatis: ſit illa quãtitas vna milleſima exempli
<
lb
/>
gratia: et tã ſequit̄̄ / in illa hora nõ deꝑdit niſi mil
<
lb
/>
lecuplã ꝓportionē: et per ↄ̨ſequēs nõ infinitã / quod
<
lb
/>
eſt oppoſitū ↄ̨ſequētis. </
s
>
<
s
xml:id
="
N24116
"
xml:space
="
preserve
">Et iſto modo ꝓbat̄̄ hec ↄ̨ſe-
<
lb
/>
quētia prius facta deuenit .a. ad nõ ̄tum / ergo infi
<
lb
/>
nitam ꝓportionē deperdit: quia ſi ſolū finita puta
<
lb
/>
millecuplã iam illud in fine maneret vt vna milleſi
<
lb
/>
ma et ſic non maneret nõ quãtum.</
s
>
</
p
>
<
p
xml:id
="
N24121
">
<
s
xml:id
="
N24122
"
xml:space
="
preserve
">Sed contra hoc arguitur ſic / quia ſi
<
lb
/>
hoc eſſet verū ſeq̇retur eodē mõ / ſi in aliqua duo
<
lb
/>
ſiue equalia ſiue inequalia in certa ꝓportione cõti
<
lb
/>
nuo inequaliter diminuãtur vſ ad non quãtum ta
<
lb
/>
lia eque cito deueniunt ad nõ quãtū: ſed conſequēs
<
lb
/>
videtur falſum: igitur illud ex quo ſequitur. </
s
>
<
s
xml:id
="
N2412F
"
xml:space
="
preserve
">Seq̄la
<
lb
/>
ꝓbatur et volo / ſint .a. et .b. pedale: et ꝑdat .a. in
<
lb
/>
qualibet parte ꝓportionali ꝓportionē quadruplã
<
lb
/>
b. vero ſemꝑ in duplo minorē proportionē in qua
<
lb
/>
libet parte ꝓportionali puta ꝓportionē duplam.
<
lb
/>
</
s
>
<
s
xml:id
="
N2413B
"
xml:space
="
preserve
">Et arguitur ſic / cū primū .a. ꝑdiderit infinitas ꝓpor
<
lb
/>
tiones quadruplas ip̄m deuenerit ad non quantū:
<
lb
/>
et tunc .b. ꝑdidit īfinitas duplas / vt patet ex caſu: er
<
lb
/>
go tunc .b. deuenit ad nõ quãtū. </
s
>
<
s
xml:id
="
N24144
"
xml:space
="
preserve
">Nõ em̄ poteſt infini
<
lb
/>
tas duplas perdere quī infinitã latitudinē ꝓportio
<
lb
/>
nis deperdat: et ꝑ conſequens eque cito .a et .b. de-
<
lb
/>
uenient ad nõ quãtū: quod fuit probandū. </
s
>
<
s
xml:id
="
N2414D
"
xml:space
="
preserve
">Et iſto
<
lb
/>
modo probabis de q̇buſcū aliis corporibus ſiue
<
lb
/>
equalibus ſiue inequalibus: dūmodo vnum altero
<
lb
/>
in certa ꝓportione continuo velocius diminuatur
<
lb
/>
ad non quantum.</
s
>
</
p
>
<
p
xml:id
="
N24158
">
<
s
xml:id
="
N24159
"
xml:space
="
preserve
">Secūdo prīcipaliter ad idem arguit̄̄
<
lb
/>
ſic. </
s
>
<
s
xml:id
="
N2415E
"
xml:space
="
preserve
">Si velocitas augmētatiõis attenderet̄̄ penes ꝓ
<
lb
/>
portionalē acquiſitionē quãtitatis: ſequeretur hec
<
lb
/>
concluſio / ſi aliquid inciperet ſucceſſiue augeri
<
lb
/>
a non quãto: ipſum infinite velociter inciperet au-
<
lb
/>
geri: ſꝫ conſequens eſt falſum: igitur illud ex quo ſe
<
lb
/>
quitur. </
s
>
<
s
xml:id
="
N2416B
"
xml:space
="
preserve
">Falſitas cõſequēs arguit̄̄ ſic: q2 tunc ſeq̇re
<
lb
/>
tur / quodlibet tale infinite velociter inciperet ac-
<
lb
/>
quirere de quãtitate: ſꝫ ↄ̨ſequens eſt falſum: igitur
<
lb
/>
illud ex quo ſequitur. </
s
>
<
s
xml:id
="
N24174
"
xml:space
="
preserve
">Sed tã probo ſequelam / quia
<
lb
/>
ſi .a. incipit augeri a nõ quãto poſt inſtans inceptio
<
lb
/>
nis talis augmentationis ipſum eſt aliquãtum: et
<
lb
/>
ante illud inſtans fuit in duplo minus: et in triplo
<
lb
/>
et in quadruplo et ſic infinitum: ergo inter illud in
<
lb
/>
ſtans et īſtans initiatiuū illud acquiſiuit infinitam
<
lb
/>
proportionem: et per cõſequēs ſequit̄̄ / ipſum infi-
<
lb
/>
nite velociter incipit augeri. </
s
>
<
s
xml:id
="
N24185
"
xml:space
="
preserve
">patet conſequentia ex
<
lb
/>
poſitione.
<
note
position
="
right
"
xlink:href
="
note-0203-03a
"
xlink:label
="
note-0203-03
"
xml:id
="
N241A8
"
xml:space
="
preserve
">Dictur.</
note
>
</
s
>
<
s
xml:id
="
N2418F
"
xml:space
="
preserve
">¶ Dices et bene concedendo cõcluſioneꝫ
<
lb
/>
illatam / vt bene ꝓbat argumentū / et negando falſi
<
lb
/>
tatem conſequentis: et ad probationē nego iſtam
<
lb
/>
conſequentiã infinite velociter incipit augeri: ergo
<
lb
/>
infinite velociter incipit a. acquirerere de quãtitate / </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>