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 - 41
>
[Note]
Page: 6
[Note]
Page: 7
[Note]
Page: 7
[Note]
Page: 7
[Note]
Page: 7
[Note]
Page: 7
[Note]
Page: 7
[Note]
Page: 7
[Note]
Page: 8
[Note]
Page: 8
[Note]
Page: 8
[Note]
Page: 8
[Note]
Page: 8
[Note]
Page: 8
[Note]
Page: 8
[Note]
Page: 8
[Note]
Page: 8
[Note]
Page: 8
[Note]
Page: 8
[Note]
Page: 9
[Note]
Page: 10
[Note]
Page: 11
[Note]
Page: 13
[Note]
Page: 13
[Note]
Page: 14
[Note]
Page: 14
[Note]
Page: 16
[Note]
Page: 16
[Note]
Page: 16
[Note]
Page: 17
<
1 - 30
31 - 41
>
page
|<
<
of 290
>
>|
<
echo
version
="
1.0
">
<
text
xml:lang
="
la
">
<
div
xml:id
="
N10132
"
level
="
1
"
n
="
1
"
type
="
body
">
<
div
xml:id
="
N10136
"
level
="
2
"
n
="
1
"
type
="
other
"
type-free
="
pars
">
<
div
xml:id
="
N10E2D
"
level
="
3
"
n
="
5
"
type
="
chapter
"
type-free
="
capitulum
">
<
p
xml:id
="
N11215
">
<
s
xml:id
="
N11282
"
xml:space
="
preserve
">
<
pb
chead
="
Prime partis
"
file
="
0015
"
n
="
15
"/>
qm̄ iuxta illam cõcluſionē reſiduū a prima parte
<
lb
/>
ꝓportionali quauis ꝓportione rationali debet ſe
<
lb
/>
habere vt numerꝰ minor talis ꝓportionis: et ꝑ cõ
<
lb
/>
ſequēs manebit ꝓ prima parte ꝓportiõali nume
<
lb
/>
rus ille quo numerꝰ maior talis ꝓportionis exce-
<
lb
/>
dit minorē. </
s
>
<
s
xml:id
="
N11294
"
xml:space
="
preserve
">Patet hec cõſequētia / q2 ſemꝑ corpus
<
lb
/>
debet diuidi in tot partes quotus eſt numerꝰ ma-
<
lb
/>
ior et primus ꝓportiõis qua debet fieri diuiſio: vt
<
lb
/>
patet ex ſecūda cõcluſione: et pro reſiduo a prima
<
lb
/>
debent capi tot partes ex illis quotus eſt numerꝰ
<
lb
/>
minor vt dictum eſt. </
s
>
<
s
xml:id
="
N112A1
"
xml:space
="
preserve
">igitur relique partes remanē
<
lb
/>
tes erunt prima pars. </
s
>
<
s
xml:id
="
N112A6
"
xml:space
="
preserve
">Patet cõſequētia ex prima
<
lb
/>
ſuppoſitione: et ille partes remanentes ſunt nume
<
lb
/>
rus quo numerus maior excedit minorē, vt patet:
<
lb
/>
igitur prima pars ꝓportionalis eſt numerus quo
<
lb
/>
maior numerꝰ et primꝰ proportionis qua ſit diui
<
lb
/>
ſio excedit minorē. </
s
>
<
s
xml:id
="
N112B3
"
xml:space
="
preserve
">Habet ſe / igitur totū reſiduū a
<
lb
/>
prima parte proportionali ad primã partē pro-
<
lb
/>
portionalē in ea proportione qua numerꝰ minor
<
lb
/>
et primus talis proportionis ſe habet ad numerū
<
lb
/>
quo maior et primus eiuſdem proportiõis excedit
<
lb
/>
minorem. </
s
>
<
s
xml:id
="
N112C0
"
xml:space
="
preserve
">quod fuit probandum </
s
>
<
s
xml:id
="
N112C3
"
xml:space
="
preserve
">¶ Ad habendam
<
lb
/>
autē praxim huius correlarii in cõpoſitis propor
<
lb
/>
tionibus conſtituētur alique figure: quibus facile
<
lb
/>
iudicabitur in qua proportiõe ſe habet reſiduū a
<
lb
/>
prima parte ꝓportionali ad primã partē ꝓpor-
<
lb
/>
tionalē. </
s
>
<
s
xml:id
="
N112D0
"
xml:space
="
preserve
">Ad quod facile inſpiciendū in ꝓportioni
<
lb
/>
bus duplis ſuperparticularibus conſtituatur na
<
lb
/>
turalis ſeries numeroꝝ incipiēdo a binario in īfe
<
lb
/>
riori linea: et in ſuperiori linea conſtituatur natu
<
lb
/>
ralis ordo numerorū incipiendo a ternario: tunc
<
lb
/>
referendo primum inferioris ordinis. </
s
>
<
s
xml:id
="
N112DD
"
xml:space
="
preserve
">primo ſu-
<
lb
/>
periois: habebis in qua ꝓportione ſe habet reſi-
<
lb
/>
duū a prima parte proportiõali ad primã diuidē
<
lb
/>
do corpus prima ſpecie ꝓportionis duple ſuper-
<
lb
/>
particularis: et referendo ſecundū inferioris ordi
<
lb
/>
nis ſecundo ſuperioris habebis illud idem in ſe-
<
lb
/>
cunda ſpecie ꝓportionis duple ſuperparticula
<
lb
/>
ris. </
s
>
<
s
xml:id
="
N112EE
"
xml:space
="
preserve
">et ſic conſequenter vt patet in figura.</
s
>
</
p
>
<
xhtml:table
xml:id
="
N112FD
">
<
xhtml:tr
xml:id
="
N112FE
">
<
xhtml:td
xml:id
="
N112FF
"
xml:space
="
preserve
"/>
</
xhtml:tr
>
</
xhtml:table
>
<
p
xml:id
="
N11301
">
<
s
xml:id
="
N11302
"
xml:space
="
preserve
">Sed ad praxim huiꝰ negocii in ſpeciebus ꝓporti
<
lb
/>
onis triple ſuꝑparticularis cõſtituatur in inferio
<
lb
/>
ri ſerie naturalis ordo numerorū incipiendo a bi
<
lb
/>
nario: et in ſuperiori conſtituãtur oēs numeri īpa
<
lb
/>
res incipiendo a quinario: et tunc referēdo primū
<
lb
/>
inferioris ordinis primo ſuperioris: et ſecundū in
<
lb
/>
ferioris ſecūdo ſuperioris: et tertiū inferioris ter-
<
lb
/>
tio ſuperioris: et ſic conſequenter. </
s
>
<
s
xml:id
="
N11313
"
xml:space
="
preserve
">cõſpicies in qua
<
lb
/>
ꝓportione ſe habet reſiduum a prima parte pro
<
lb
/>
portionali ad primã diuiſione corporis facto pro
<
lb
/>
portione tripla ſuperparticulari: vt ptꝫ in figura</
s
>
</
p
>
<
xhtml:table
xml:id
="
N1131C
">
<
xhtml:tr
xml:id
="
N1131D
">
<
xhtml:td
xml:id
="
N1131E
"
xml:space
="
preserve
"/>
</
xhtml:tr
>
</
xhtml:table
>
<
p
xml:id
="
N11320
">
<
s
xml:id
="
N11321
"
xml:space
="
preserve
">Ad praticandū autē ita in ſpeciebus quadruple
<
lb
/>
ſuꝑparticularis quintuple ſuꝑparticularis .etc̈. / cõ
<
lb
/>
ſtituatur naturalis ſeries numerorū incipiendo a
<
lb
/>
binario in linea inferiori: et in ſuperiori oēs nume
<
lb
/>
ros excedentes ſe continuo ternario incipiendo a
<
lb
/>
ſeptenario: et ſic habebis quod queris in ſpeciebꝰ
<
lb
/>
ꝓportionis quadruple ſuꝑparticularis </
s
>
<
s
xml:id
="
N11330
"
xml:space
="
preserve
">Ad quod
<
lb
/>
inueniēdū in ſpeciebus ꝓportionis quītuple ſuꝑ
<
lb
/>
particularis cõſtituas in ſuperiori ordine oēs nu
<
lb
/>
meros excedentes ſe quaternario incipiendo a nu
<
lb
/>
mero nouenario: et in ſpecie ſequeuti coſtituas in
<
lb
/>
ſuperiori ordine oēs numeros excedentes ſe qui
<
cb
chead
="
Capitulum ſextū.
"/>
nario incipiendo a numero vndenario: et ſic conſe
<
lb
/>
quenter in aliis ſpeciebus operaberis </
s
>
<
s
xml:id
="
N11342
"
xml:space
="
preserve
">Patet hoc
<
lb
/>
in figuris ſequentibus.</
s
>
</
p
>
<
xhtml:table
xml:id
="
N11347
">
<
xhtml:tr
xml:id
="
N11348
">
<
xhtml:td
xml:id
="
N11349
"
xml:space
="
preserve
"/>
</
xhtml:tr
>
</
xhtml:table
>
<
p
xml:id
="
N1134B
">
<
s
xml:id
="
N1134C
"
xml:space
="
preserve
">¶ Sed ad exercitiū huiꝰ vltimi correlarii in ſpecie
<
lb
/>
bus multipliciū ſuprapartientiū quedã etiaꝫ con-
<
lb
/>
ſtituentur figuere. </
s
>
<
s
xml:id
="
N11353
"
xml:space
="
preserve
">Unde ac facile īueniendã ꝓpor
<
lb
/>
tionē reſidui a prima parte ꝓportionali ad ipſaꝫ
<
lb
/>
primã in ſpeciebus ꝓportionis duple ſupraparti
<
lb
/>
entis cõſtituatur naturalis ſeries incipiēdo a ter
<
lb
/>
nario inferiori linea: in ſuperiori vero cõſtituan-
<
lb
/>
tur oēs numeri īpares incipiēdo a quinario: et tūc
<
lb
/>
referēdo primū inferioris ordinis primo ſuperio
<
lb
/>
ris: et ſcḋm ſcḋo: et tertiū tertio id quod queris fa-
<
lb
/>
cile reperies / vt patet in figura ſequenti.</
s
>
</
p
>
<
xhtml:table
xml:id
="
N11366
">
<
xhtml:tr
xml:id
="
N11367
">
<
xhtml:td
xml:id
="
N11368
"
xml:space
="
preserve
"/>
</
xhtml:tr
>
</
xhtml:table
>
<
p
xml:id
="
N1136A
">
<
s
xml:id
="
N1136B
"
xml:space
="
preserve
">¶ Ad īueniendã autē proportionē reſidui a prima
<
lb
/>
parte ꝓportionali ad ipſam primã diuiſione cor
<
lb
/>
poris facta ꝓportione tripla ſuprapartiente con
<
lb
/>
ſtituatur ſupra naturalē ſeriē numeroꝝ incipiēdo
<
lb
/>
a ternario vna ſeries omnium numerorum conti-
<
lb
/>
nuo excedentium ſe ternario incipiendo ab octo-
<
lb
/>
nario numero: vt patet in figura.</
s
>
</
p
>
<
xhtml:table
xml:id
="
N1137A
">
<
xhtml:tr
xml:id
="
N1137B
">
<
xhtml:td
xml:id
="
N1137C
"
xml:space
="
preserve
"/>
</
xhtml:tr
>
</
xhtml:table
>
<
p
xml:id
="
N1137E
">
<
s
xml:id
="
N1137F
"
xml:space
="
preserve
">¶ Ad īueniendū autē ꝓpoſitū in ſpeciebus ꝓpor-
<
lb
/>
tionis quadruple ſuprapartiētis ſupra naturalē
<
lb
/>
ſeriē numeroꝝ incipiendo a ternario conſtituatur
<
lb
/>
ſeries numeroꝝ ↄ̨tinuo excedentiū ſe quaternario
<
lb
/>
incipiendo ab vndeuario: et ſic cõſequenter ſupra
<
lb
/>
eandē naturalē ſeriē numeroꝝ incipiendo a terna
<
lb
/>
rio cõſtituatur ſeries numeroꝝ cõtinuo exedentiū
<
lb
/>
ſe numero quinario īcipiēdo a numero quarto de
<
lb
/>
cimo: et ſic cõſequenter operaberis in aliis. </
s
>
<
s
xml:id
="
N11392
"
xml:space
="
preserve
">Et hec
<
lb
/>
de diuiſione corpoꝝ ꝓportione rationali.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
N11397
"
level
="
3
"
n
="
6
"
type
="
chapter
"
type-free
="
capitulum
">
<
head
xml:id
="
N1139C
"
xml:space
="
preserve
">Capitulū ſextū / ī quo datur modus di
<
lb
/>
uidendi corpus in partes proportiona-
<
lb
/>
les proportione irrationali.</
head
>
<
p
xml:id
="
N113A3
">
<
s
xml:id
="
N113A4
"
xml:space
="
preserve
">QUemadmodū quodlibet cor-
<
lb
/>
pus diuidi poteſt ꝓportione rationali
<
lb
/>
infinitiſ ſpeciebus eius / vt caput prece
<
lb
/>
dens oſtendit: ita etiã ꝓportione irrationali infi-
<
lb
/>
nitiſ ſpeciebus eiꝰ quodlibet corpꝰ diuidi poteſt
<
lb
/>
</
s
>
<
s
xml:id
="
N113B0
"
xml:space
="
preserve
">Pro cuius diuiſionis noticia ſit</
s
>
</
p
>
<
p
xml:id
="
N113B3
">
<
s
xml:id
="
N113B4
"
xml:space
="
preserve
">Prima concluſio </
s
>
<
s
xml:id
="
N113B7
"
xml:space
="
preserve
">Quodlibet corpus
<
lb
/>
diuiſū aliqua ꝓportione irrationali ſe debet ha
<
lb
/>
bere ad aggregatū ex oībus partibus ꝓportiona
<
lb
/>
bilibus tali ꝓportione ſequētibus primam in ea
<
lb
/>
proportione qua totum diuidatur. </
s
>
<
s
xml:id
="
N113C2
"
xml:space
="
preserve
">Hec concluſio
<
lb
/>
claram et euidentem ex prima precedentis capitis
<
lb
/>
demonſtrationem ſortitur.</
s
>
</
p
>
<
p
xml:id
="
N113C9
">
<
s
xml:id
="
N113CA
"
xml:space
="
preserve
">Secunda cõcluſio. </
s
>
<
s
xml:id
="
N113CD
"
xml:space
="
preserve
">Ad diuidendum
<
lb
/>
corpus infinitis ꝓportionibꝰ irrationabilibꝰ mi
<
lb
/>
noribus dupla: vt puta ꝓportione diametri ad co
<
lb
/>
ſtam: aggregati ex medietate exceſſus quo diame
<
lb
/>
ter excedit coſtã et ipſa coſta ipſammet coſtam: </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>