Alvarus, Thomas
,
Liber de triplici motu
,
1509
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Figures
Content
Thumbnails
Table of figures
<
1 - 14
[out of range]
>
<
1 - 14
[out of range]
>
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
="
N16349
"
level
="
4
"
n
="
5
"
type
="
chapter
"
type-free
="
capitulum
">
<
p
xml:id
="
N168C7
">
<
s
xml:id
="
N168DD
"
xml:space
="
preserve
">
<
pb
chead
="
Primi tractatus
"
file
="
0067
"
n
="
67
"/>
tis ex vigeſimaſeptima concluſione.</
s
>
</
p
>
<
p
xml:id
="
N168E5
">
<
s
xml:id
="
N168E6
"
xml:space
="
preserve
">Quadrageſima concluſio </
s
>
<
s
xml:id
="
N168E9
"
xml:space
="
preserve
">Si aliqua
<
lb
/>
potentia non variata mouetur per mediuꝫ vnifor
<
lb
/>
miter difforme incipiendo ab extremo intenſiori:
<
lb
/>
talis potentia continuo velocius et velocius intē-
<
lb
/>
dit motū ſuum. </
s
>
<
s
xml:id
="
N168F4
"
xml:space
="
preserve
">Patet / quia continuo velocius et
<
lb
/>
velocius decreſcit ſibi de reſiſtentia: igitur conti-
<
lb
/>
nuo velocius et velocius intendit motuꝫ ſuum </
s
>
<
s
xml:id
="
N168FB
"
xml:space
="
preserve
">Pa
<
lb
/>
tet conſequentia ex vigeſimaoctaua concluſione.</
s
>
</
p
>
<
p
xml:id
="
N16900
">
<
s
xml:id
="
N16901
"
xml:space
="
preserve
">Quadrageſimaprima ↄ̨̨cluſio </
s
>
<
s
xml:id
="
N16904
"
xml:space
="
preserve
">Stat
<
lb
/>
duas potētias equales moueri per mediū vnifor
<
lb
/>
miter difforme incipiendo ab extremo remiſſiori
<
lb
/>
eiuſdē medii ipſis et medio ſimplicter inuariatis
<
lb
/>
et tamē vnam moueri velocius altera </
s
>
<
s
xml:id
="
N1690F
"
xml:space
="
preserve
">Probatur
<
lb
/>
hec concluſio et capio vnum mediū quadratū vni
<
lb
/>
formiter difforme a non gradu vſ ad octauū vel
<
lb
/>
a certo gradu (in idē redit) / et volo / a. et b. ſint due
<
lb
/>
potentie equales: et incipiat vna moueri ab extre
<
lb
/>
mo remiſſiori per diametrū et alia per lineam re-
<
lb
/>
ctã ab eodem extremo: quo poſito ſic arguo a. et b.
<
lb
/>
mouebuntur: et a. non mouebitur tardius ipſo b.
<
lb
/>
nec eque velociter adequate: ergo velocius. </
s
>
<
s
xml:id
="
N16922
"
xml:space
="
preserve
">Ma-
<
lb
/>
ior ptꝫ cum conſequentia. </
s
>
<
s
xml:id
="
N16927
"
xml:space
="
preserve
">et minor probatur. </
s
>
<
s
xml:id
="
N1692A
"
xml:space
="
preserve
">q2 ſi
<
lb
/>
mouerentur equaliter ſequeretur / equales potē
<
lb
/>
tie cum inequalibus reſiſtentiis equaliter mouerē
<
lb
/>
tur / et per conſequens ab inequalibus proportio-
<
lb
/>
nibus equales motus proueniunt: quod eſt contra
<
lb
/>
primã ſuppoſitionē huius capitis et directe cõtra
<
lb
/>
opinionem. </
s
>
<
s
xml:id
="
N16939
"
xml:space
="
preserve
">Sequela tamen probatur / quoniam
<
lb
/>
capto quocū pūcto diametri equaliter diſtante
<
lb
/>
ab angulo quadrati: hoc eſt a linea quadrati fa-
<
lb
/>
ciente angulum ſicut certus pūctus: eſt minoris re
<
lb
/>
ſiſtentie quã pūctus exiſtens in linea recta equali-
<
lb
/>
ter diſtante cum ipſo. </
s
>
<
s
xml:id
="
N16946
"
xml:space
="
preserve
">ergo ſequitur / ſemꝑ a. ha-
<
lb
/>
bebit minorē reſiſtentiam / et per conſequens maio
<
lb
/>
rem proportionem ad talem pūctū quã b. in pun-
<
lb
/>
cto ſibi correſpondente: et tamen per te a. et b. mo
<
lb
/>
uentur equaliter: igitur ꝓpoſituꝫ. </
s
>
<
s
xml:id
="
N16951
"
xml:space
="
preserve
">Q, aūt in tali
<
lb
/>
puncto diametri ſit ſemper reſiſtentia minor quã
<
lb
/>
in puncto ſibi correſpõdente ī linea directe / et per-
<
lb
/>
pendiculariter ꝓcedente ꝓbatur / quoniaꝫ ſemper
<
lb
/>
talis punctus plus diſtat a gradu ſūmo illius cor
<
lb
/>
poris / quam punctus ſibi correſpondens in linea
<
lb
/>
directe et perpēdiculariter procedente. </
s
>
<
s
xml:id
="
N16960
"
xml:space
="
preserve
">igitur ſem
<
lb
/>
per in eo eſt minor reſiſtentia et per conſequens ꝓ
<
lb
/>
portio maior </
s
>
<
s
xml:id
="
N16967
"
xml:space
="
preserve
">Patet hec demonſtratio aſpicienti
<
lb
/>
figuram quadrataꝫ vniformiter difformē quo ad
<
lb
/>
reſiſtentiam / que ſit .a.b. et .c.d. et extremū remiſſiſ
<
lb
/>
ſimū ſit .ac. et linea diametralis ꝑ quã a. mouetur
<
lb
/>
ſit .ad. et linea per quam mouetur b. ſit .cd.</
s
>
</
p
>
<
figure
xml:id
="
N16972
"
number
="
6
">
<
image
file
="
0067-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0067-01
"/>
</
figure
>
<
p
xml:id
="
N16976
">
<
s
xml:id
="
N16977
"
xml:space
="
preserve
">qua figura inſpecta patet facile ꝓpoſitum. </
s
>
<
s
xml:id
="
N1697A
"
xml:space
="
preserve
">Et hec
<
lb
/>
de his concluſionibus in quibus ferme ſequutus
<
lb
/>
ſum calculatorem in capitulo de motu locali dem
<
lb
/>
pta vltima quam adiunxi.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
N16983
"
level
="
4
"
n
="
6
"
type
="
chapter
"
type-free
="
capitulum
">
<
head
xml:id
="
N16988
"
xml:space
="
preserve
">Sextum capitulum / in quo ponūtur
<
lb
/>
alique obiectiones contra aliquas
<
lb
/>
concluſiones ſuperioris capitis.</
head
>
<
p
xml:id
="
N1698F
">
<
s
xml:id
="
N16990
"
xml:space
="
preserve
">COntra quintam concluſio-
<
lb
/>
nem arguitur ſic. </
s
>
<
s
xml:id
="
N16995
"
xml:space
="
preserve
">per intenſionem et cre
<
lb
/>
mētum alicuius reſiſtētie reſpectu dua
<
lb
/>
rum potentiarum inequalium minor potentia ve
<
cb
chead
="
Capitulum ſextum
"/>
locius remittit motū ſuum quã maior: igitur ſex-
<
lb
/>
ta ↄ̨cluſio falſa. </
s
>
<
s
xml:id
="
N169A1
"
xml:space
="
preserve
">Arguit̄̄ antecedēs et pono / ſit a.
<
lb
/>
potētia vt .8. et b. potētia vt .4. et c. reſiſtētia vt 2.
<
lb
/>
et d. reſiſtētia vt vnū: et agat vtra illaꝝ potētiaꝝ
<
lb
/>
cū vtra illarum reſiſtentiarū: et creſcat c. reſiſten
<
lb
/>
tia vt .2. vniformiter / quo ad vſ ſit vt .4. et d. reſiſtē
<
lb
/>
tia itidem vniformiter creſcat / quo ad vſ ſit vt .4.
<
lb
/>
creſcat tamen reſiſtētia vt .2. in duplo velociꝰ quã
<
lb
/>
reſiſtentia vt vnū. </
s
>
<
s
xml:id
="
N169B2
"
xml:space
="
preserve
">ita quando reſiſtentia vt vnuꝫ
<
lb
/>
acquiſiuerit vnum gradum reſiſtentie: reſiſtentia
<
lb
/>
vt duo acquirat duos. </
s
>
<
s
xml:id
="
N169B9
"
xml:space
="
preserve
">quo poſito ſic argumentor
<
lb
/>
b. potentia vt .4. velocius remittit motum ſuum
<
lb
/>
cū c. reſiſtentia vt .2. quã a. potentia vt .8. cum ea-
<
lb
/>
dem reſiſtentia vt duo. </
s
>
<
s
xml:id
="
N169C2
"
xml:space
="
preserve
">igitur aſſumptum verum.</
s
>
</
p
>
<
p
xml:id
="
N169C5
">
<
s
xml:id
="
N169C6
"
xml:space
="
preserve
">Probatur antecedens / quoniaꝫ eque velociter po
<
lb
/>
tentia a. vt .8. remittet motū ſuum cum reſiſtentia
<
lb
/>
c. vt .2. ſicut potentia b. vt .4. cū reſiſtentia d. / vt vnū
<
lb
/>
quoniam proportiones erunt equales: et eque ve-
<
lb
/>
lociter ꝓportionabiliter deperduntur. </
s
>
<
s
xml:id
="
N169D1
"
xml:space
="
preserve
">igitur ſem
<
lb
/>
per manebunt equales ad inuicem ſed b. potentia
<
lb
/>
vt .4. velocius remittet motū ſuum cū c. reſiſtentia
<
lb
/>
vt .2. quam cū d. reſiſtentia vt vnum / ergo b. poten
<
lb
/>
tia vt .4. velocius remittet cum c. motū ſuum. </
s
>
<
s
xml:id
="
N169DC
"
xml:space
="
preserve
">quaꝫ
<
lb
/>
a. potentia vt .8. cū eodē c. / quod fuit probandum.
<
lb
/>
</
s
>
<
s
xml:id
="
N169E2
"
xml:space
="
preserve
">Conſequentia patet cū maiore: et minor probatur /
<
lb
/>
quoniam velocius deperditur proportio b. ad c.
<
lb
/>
quam proportio b. ad d. / ergo velocius remittitur
<
lb
/>
motus proueniens a proportione b. ad c. / quã mo
<
lb
/>
tus proueniens a proportione b. ad d. </
s
>
<
s
xml:id
="
N169ED
"
xml:space
="
preserve
">Conſequen
<
lb
/>
tia eſt nota et arguitur antecedens. </
s
>
<
s
xml:id
="
N169F2
"
xml:space
="
preserve
">quoniam pro
<
lb
/>
portio b. potētie vt 4. ad c. reſiſtētiã vt .2. ē ī duplo
<
lb
/>
minor ꝓportione b. potētie vt .4. ad d. reſiſtentiã vt
<
lb
/>
vnum: quoniam vna dupla et alia quadrupla. </
s
>
<
s
xml:id
="
N169FB
"
xml:space
="
preserve
">et
<
lb
/>
plꝰquã ī duplo citiꝰ remittet̄̄ ꝓportio b. ad c. quã
<
lb
/>
ꝓportio b. ad d. / igr̄ velociꝰ remittet̄̄ ꝓportio b. ad
<
lb
/>
c. quã b. ad .d. / quod fuit probandū. </
s
>
<
s
xml:id
="
N16A04
"
xml:space
="
preserve
">Conſequentia
<
lb
/>
eſt nota / vt apparet cum maiore: et minor ꝓbatur /
<
lb
/>
quoniam quando reſiſtentia c. acquiſiuerit duos
<
lb
/>
gradus reſiſtentie / tunc proportio b. ad c. erit omī
<
lb
/>
no deperdita. </
s
>
<
s
xml:id
="
N16A0F
"
xml:space
="
preserve
">et in eodem tempore adequate ꝑde
<
lb
/>
tur proportio dupla ipſi quadruple, et acquiretur
<
lb
/>
vnus gradus dūtaxat ipſi reſiſtentie d. / et reſtabūt
<
lb
/>
acquirendi duo qui debēt acquiri vniformiter: er
<
lb
/>
go illi acquirentur adequate ī duplo tempore ad
<
lb
/>
acquiſitionem primi: et ſic ſequitur / tempus de-
<
lb
/>
perditionis proportionis b. ad c. eſt ſubtriplū, ad
<
lb
/>
tempus deperditionis proportionis b. ad d. / et per
<
lb
/>
conſequens pluſquã in duplo citius deperditur ꝓ
<
lb
/>
portio b. ad c. quã b. ad d. / quod fuit probanduꝫ.</
s
>
</
p
>
<
p
xml:id
="
N16A24
">
<
s
xml:id
="
N16A25
"
xml:space
="
preserve
">Reſpondeo negando antecedens: et
<
lb
/>
ad probationē admiſſo caſu negat̄̄ añs: et ad pro-
<
lb
/>
bationē negatur hec minor b. velociꝰ remittet mo
<
lb
/>
tū ſuū cū c. quã cum d. / et ad ꝓbationē negatur an-
<
lb
/>
tecedens et ad probationē antecedētis negat̄̄ hec
<
lb
/>
ↄ̨ña in qua eſt virtus argumenti: proportio b. ad
<
lb
/>
c. ē in duplo minor ꝓportione b. ad d. / et pluſquaꝫ
<
lb
/>
in duplo citius deperdetur proportio b. ad c. quã
<
lb
/>
ꝓportio b. ad .d. / ergo velocius deperdetur propor
<
lb
/>
portio b. ad .c. / quã deperdetur proportio b. ad d. / ſi
<
lb
/>
cut eam eſſe negandam docet triceſimaſexta con-
<
lb
/>
cluſio
<
note
position
="
right
"
xlink:href
="
note-0067-01a
"
xlink:label
="
note-0067-01
"
xml:id
="
N16A56
"
xml:space
="
preserve
">inq̇rit̄̄ bo
<
lb
/>
uitaſ ↄ̨ña
<
lb
/>
rū calcu.</
note
>
</
s
>
<
s
xml:id
="
N16A43
"
xml:space
="
preserve
">In probatione tamē ↄ̨ñe negate adducit
<
lb
/>
calculator duas conditionales: quarū neutra eſt
<
lb
/>
bona ↄ̨ña. </
s
>
<
s
xml:id
="
N16A4A
"
xml:space
="
preserve
">Ipſe tamē nihil ad eas reſpondet </
s
>
<
s
xml:id
="
N16A4D
"
xml:space
="
preserve
">Pro
<
lb
/>
quarū impugnatione pono aliqua correlaria.</
s
>
</
p
>
<
note
position
="
right
"
xml:id
="
N16A60
"
xml:space
="
preserve
">1. correl.</
note
>
<
p
xml:id
="
N16A64
">
<
s
xml:id
="
N16A65
"
xml:space
="
preserve
">¶ Primū correlariū in caſu argumenti d. reſiſtē-
<
lb
/>
tia vt vnum et .c. reſiſtentia vt .2. / non vniformiter
<
lb
/>
creſcūt / et tamē vtra illarum vniformiter creſcit.
<
lb
/>
</
s
>
<
s
xml:id
="
N16A6D
"
xml:space
="
preserve
">Probatur / quia quando reſiſtentia vt vnum acq̇-
<
lb
/>
rit vnitatem: reſiſtentia vt .2. acquirit dualitē gra </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>