Alvarus, Thomas
,
Liber de triplici motu
,
1509
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Figures
Content
Thumbnails
Table of Notes
<
1 - 30
31 - 60
61 - 81
>
[Note]
Page: 20
[Note]
Page: 20
[Note]
Page: 20
[Note]
Page: 20
[Note]
Page: 20
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 22
[Note]
Page: 22
[Note]
Page: 24
[Note]
Page: 24
[Note]
Page: 24
[Note]
Page: 24
[Note]
Page: 24
[Note]
Page: 24
[Note]
Page: 24
<
1 - 30
31 - 60
61 - 81
>
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
="
N15C22
"
level
="
3
"
n
="
1
"
type
="
other
"
type-free
="
tractatus
">
<
div
xml:id
="
N17BB3
"
level
="
4
"
n
="
8
"
type
="
chapter
"
type-free
="
capitulum
">
<
p
xml:id
="
N182F4
">
<
s
xml:id
="
N18366
"
xml:space
="
preserve
">
<
pb
chead
="
Primi tractatus
"
file
="
0084
"
n
="
84
"/>
velociꝰ ipſa poña a. / vt patet ex hypotheſi / quo po
<
lb
/>
ſito arguitur ſic / latitudinis motus deperdite ab
<
lb
/>
ipſa b. potentia tranſeundo .ef. partem in g. tem
<
lb
/>
pore adequate ad latitudinem motus deperditaꝫ
<
lb
/>
ab eadem poña b. tranſeundo d. partem non eſt ꝓ
<
lb
/>
portio quadrupla nec maior: ergo latitudinis de
<
lb
/>
perdite ab b. poña tranſeundo .ef. partem in tēpo
<
lb
/>
re g. ad latitudinem motus deperditam ab a. po-
<
lb
/>
tentia ſtante inuariata vel remittente poñam ſuã
<
lb
/>
tranſeundo d. partem in g. tempore adequate nõ
<
lb
/>
eſt proportio quadrupla nec maior quadrupla: ſꝫ
<
lb
/>
conſequens eſt falſum: igitur illud ex quo ſequit̄̄.
<
lb
/>
</
s
>
<
s
xml:id
="
N18393
"
xml:space
="
preserve
">Patet conſequentia / quia omnes poñe inuariate
<
lb
/>
idem medium tranſeuntes etc. equalem latitudinē
<
lb
/>
motus deperdunt. </
s
>
<
s
xml:id
="
N1839A
"
xml:space
="
preserve
">et ſi aliqua poña tranſeūdo idē
<
lb
/>
medium īuariatum remittendo motum ſuum etc.
<
lb
/>
remittat poñam ſuam: ipſa maiorem latitudineꝫ
<
lb
/>
motus deperdit quam ſi ſtaret idem medium inua
<
lb
/>
riatum tranſeundo: vt conſtat ex quarto argumē
<
lb
/>
to ſexti capitis. </
s
>
<
s
xml:id
="
N183A7
"
xml:space
="
preserve
">Sed falſitas conſequentis proba
<
lb
/>
tur / quia ſi latitudinis deperdite ab ipſa b. poten
<
lb
/>
tia tranſeundo .ef. partem in g. tempore ad veloci
<
lb
/>
tatem deperditam ab a. poña tranſeundo d. par-
<
lb
/>
tem in eodem g. tempore non eſt ꝓportio quadru-
<
lb
/>
pla nec maior: et a principio latitudinis motus ip
<
lb
/>
ſius b. ad latitudinem motus ipſius a. eſt ꝓportio
<
lb
/>
quadrupla: ſequitur / facta tali variatione lati-
<
lb
/>
tudinis motus ipſius b. ad latitudinem motus ip
<
lb
/>
ſius a. non eſt ꝓportio quadrupla: quod eſt cõtra
<
lb
/>
hypotheſim. </
s
>
<
s
xml:id
="
N183BE
"
xml:space
="
preserve
">Conſequentia tamen patet ex primo
<
lb
/>
correlario et ſecundo quinte concluſionis ſecundi
<
lb
/>
capitis ſecunde partis. </
s
>
<
s
xml:id
="
N183C5
"
xml:space
="
preserve
">Iam ꝓbatur antecedens
<
lb
/>
videlicet / latitudinis motus deperdite a b. poña
<
lb
/>
tranſeundo in g. tempore .ef. partem ad latitudi-
<
lb
/>
nem deꝑditam ab eadem b. poña tranſeundo d. ꝑ
<
lb
/>
tem nõ eſt ꝓportio quadrupla nec maior: quia ip̄i
<
lb
/>
us .ef. ꝑtis ad d. partem eſt ꝓportio quadrupla ex
<
lb
/>
caſu: et ipſa poña b. tranſeundo quãlibet ꝑtem ex
<
lb
/>
ceſſus ip̄ius .ef. ꝑtis minorem d. ꝑte: mouetur cum
<
lb
/>
minori reſiſtentia quam tranſeundo quamlibet ꝑ
<
lb
/>
tem equalem ipſius d. ꝑtis: cum quelibet pars ex-
<
lb
/>
ceſſus quo .ef. pars excedit d. ꝑtem minus diſtet a
<
lb
/>
puncto iniciatiuo c. medii a quo incipit motus (ſi
<
lb
/>
gno enim exceſſum illum verſus punctum remiſſiꝰ
<
lb
/>
c. medii a quo incipit motus) / ergo latitudinis de
<
lb
/>
perdite ab ipſa b. poña tranſeundo .ef. ꝑtem in g.
<
lb
/>
tempore adequate ad latitudinem deꝑditaꝫ ab ea
<
lb
/>
dem b. poña tranſeundo d. ꝑtem non eſt ꝓportio
<
lb
/>
quadrupla nec maior: quod fuit ꝓbandum. </
s
>
<
s
xml:id
="
N183EA
"
xml:space
="
preserve
">Pa-
<
lb
/>
tet conſequentia ex quarta ſuppoſitione huius</
s
>
</
p
>
<
p
xml:id
="
N183EF
">
<
s
xml:id
="
N183F0
"
xml:space
="
preserve
">Q, autem a. poña remittit motum ſuum ad non
<
lb
/>
gradum: ꝓbatur / quoniam cõtinuo ex hypotheſi ī
<
lb
/>
ter motum ipſius b. et motum ipſius a. eſt ꝓportio
<
lb
/>
quadrupla: vtro illorum motuum decreſcente:
<
lb
/>
et motus ipſius b. poñe tranſeuntis quatuor quar
<
lb
/>
tas ipſius c. medii in extremo intenſiori eiuſdeꝫ c.
<
lb
/>
medii remittitur ad non gradum: igitur etiã mo-
<
lb
/>
tus ipſius a. poñe mouentis in quadruplo tardiꝰ
<
lb
/>
in eodem tempore tranſeundo vltimam quartam
<
lb
/>
c. medii in extremo intenſiori remittitur ad nõ gra
<
lb
/>
dum. </
s
>
<
s
xml:id
="
N18407
"
xml:space
="
preserve
">Patet conſequētia ex octauo correlario q̈r
<
lb
/>
te concluſionis octaui capitis ſecunde ꝑtis: </
s
>
<
s
xml:id
="
N1840C
"
xml:space
="
preserve
">Et ſic
<
lb
/>
patet concluſio. </
s
>
<
s
xml:id
="
N18411
"
xml:space
="
preserve
">¶ Ex quo ſequitur / vbi aliqua
<
lb
/>
poña non variata aliquod medium tranſeūdo vni
<
lb
/>
formiter remittit motum ſuum: omnis minor hñs
<
lb
/>
ꝓportionem maioris inequalitatis ad punctū in
<
lb
/>
itiatiuum eiuſdem medii in extremo remiſſiori vni
<
lb
/>
formiter continuo remittit motum ſuum idē medi
<
lb
/>
um tranſeundo īuariatum per continuam ſui intē
<
cb
chead
="
Capitulum octauum
"/>
ſſonem. </
s
>
<
s
xml:id
="
N18423
"
xml:space
="
preserve
">Probatur / ſit b. poña que variata totuꝫ c.
<
lb
/>
medium inuariatum tranſeundo vniformiter re-
<
lb
/>
mittit motum: et a poña minor habens ad initiati
<
lb
/>
uum punctum c. medii in extremo remiſſiori ꝓpor
<
lb
/>
tionem maioris inequalitatis: et cum ipſa a. poña
<
lb
/>
habeat ad aliquem punctum intrinſecum eiuſdeꝫ
<
lb
/>
c. medii etiam ꝓportionem maioris inequalitatis
<
lb
/>
ponatur ip̄a poña a. in tali puncto et b. poña in ṗn
<
lb
/>
cipio c. medii in extremo remiſſiori: et ꝓportionis
<
lb
/>
ipſius b. ad punctum initiatiuum c. medii ad pro-
<
lb
/>
portionem ipſius a. quam habet ad punctum in-
<
lb
/>
trinſecum ad quod ponitur ſit h. ꝓportio: et incipi
<
lb
/>
at ī eodē īſtãti ab illis pūctis moueri a. et b. ſꝫ b. cõ
<
lb
/>
tinuo in h. ꝓportione velocius ip̄a poña a. / et mani
<
lb
/>
feſtum eſt / non ſubito b. poña deueniet ad pūctū
<
lb
/>
a quo incipit moueri a. poña: capio igitur ſpaciuꝫ /
<
lb
/>
quod abſoluet a. poña in tempore in quo b. poña
<
lb
/>
deueniet ad pūctum a quo incipit moueri a. poña
<
lb
/>
et ſit illud ſpacium d. / et tunc dico / tam a. quam b.
<
lb
/>
tranſeundo d. mediū vniformiter remittet motuꝫ
<
lb
/>
ſuum: et a. poña continuo d. medium tranſeundo ī
<
lb
/>
tendit poñam ſuam. </
s
>
<
s
xml:id
="
N18450
"
xml:space
="
preserve
">Quod ſic oſtenditur / quia a.
<
lb
/>
poña tranſeundo d. medium continuo vniformi-
<
lb
/>
ter remittit motum ſuum / vt ſupra in concluſione
<
lb
/>
quarta probatum eſt: et ipſa a. poña continuo trã
<
lb
/>
ſeundo d. ꝑtem intendit poñam ſuam: igitur ꝓpo
<
lb
/>
poſitum. </
s
>
<
s
xml:id
="
N1845D
"
xml:space
="
preserve
">Probatur minor / quia ſi a. per aliquod
<
lb
/>
tempus d. medium inuariatum tranſeundo ſtat ī-
<
lb
/>
uariata vel remittit potentiam ſuam. </
s
>
<
s
xml:id
="
N18464
"
xml:space
="
preserve
">detur illud
<
lb
/>
tempus et ſit g. et pars pertranſita ab a. in g. tēpo
<
lb
/>
re adequate ſit e. et pars pertranſita adequate in
<
lb
/>
eodem g. tempore ab ip̄a poña b. ſit .ef. / et manife-
<
lb
/>
ſtum eſt / ip̄ius .ef. partis ad e. partem eſt ꝓportio
<
lb
/>
h. quia continuo potentia b. in h. ꝓportione velo-
<
lb
/>
cius mouetur quaꝫ ipſa potentia a. / vt patet ex hy
<
lb
/>
potheſi. </
s
>
<
s
xml:id
="
N18475
"
xml:space
="
preserve
">Quo poſito arguitur ſic / latitudinis mo-
<
lb
/>
tus deperdite ab ipſa b. potentia tranſeundo .ef.
<
lb
/>
partem in g. tempore adequate ad latitudinē mo
<
lb
/>
tus deperditam ab eadeꝫ potentia b. tranſeundo
<
lb
/>
e. partem non eſt proportio h. nec maior: ergo la-
<
lb
/>
titudinis deperdite ab ip̄a b. poña tranſeundo .ef:
<
lb
/>
ꝑtem in g. tempore adequate ad latitudinem mo-
<
lb
/>
tus deperditam ab a. potentia ſtãte inuariata vel
<
lb
/>
remittente potentiam ſuam tranſeundo e. parteꝫ
<
lb
/>
in g. tempore adequate non eſt ꝓportio h. nec ma
<
lb
/>
ior: ſed conſequens eſt falſum: igitur illud ex quo
<
lb
/>
ſequitur. </
s
>
<
s
xml:id
="
N1848E
"
xml:space
="
preserve
">Conſequentia patet cum antecedente ex
<
lb
/>
ꝓbatione concluſionis: et ſimiliter falſitas conſe
<
lb
/>
quentis </
s
>
<
s
xml:id
="
N18495
"
xml:space
="
preserve
">Patet igitur correlarinm.</
s
>
</
p
>
<
note
position
="
right
"
xml:id
="
N18498
"
xml:space
="
preserve
">q̈drageſi
<
lb
/>
ma q̈rta
<
lb
/>
ↄ̨clu. cal.</
note
>
<
p
xml:id
="
N184A0
">
<
s
xml:id
="
N184A1
"
xml:space
="
preserve
">Quinta concluſio </
s
>
<
s
xml:id
="
N184A4
"
xml:space
="
preserve
">Ubi aliqua poten
<
lb
/>
tia inuariata inuariarum medium tranſeundo
<
lb
/>
vniformiter continuo remittit motum ſuum ad nõ
<
lb
/>
gradum: aliqua minor per cõtinuam ſui remiſſio
<
lb
/>
nem continuo vniformiter remittit motum ſuum
<
lb
/>
ad non gradum in aliquo puncto intrinſeco dati
<
lb
/>
medii idem medium inuariatum trãſeundo </
s
>
<
s
xml:id
="
N184B3
"
xml:space
="
preserve
">Pro
<
lb
/>
batur / ſit b. poña que vniformiter continuo remit
<
lb
/>
tit motum ſuum totum c. medium tranſeundo vſ
<
lb
/>
ad nõ gradum: ſit a. poña minor que habeat ad
<
lb
/>
punctum initiatiuum c. medii in extremo remiſſio
<
lb
/>
ri ꝓportionem in ſexquialtero maiorem quam b.
<
lb
/>
poña habeat ad punctum initiatiuum vltime q̈r-
<
lb
/>
te magis reſiſtentis: ponatur a. poña in puncto
<
lb
/>
initiatiuo c. medii in extremo remiſſiori: et b. poña
<
lb
/>
in puncto initiatiuo vltime quarte magis reſiſten
<
lb
/>
tis: et in eodem inſtanti incipiant ab illis punctis
<
lb
/>
moueri a. cõtinuo in ſexquialtero velocius ip̄o b.
<
lb
/>
quo ad b. deueniat ad extremum intenſius c. medii
<
lb
/>
in quo habet non gradum motus: et manifeſtū eſt / </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>