Alvarus, Thomas
,
Liber de triplici motu
,
1509
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Figures
Content
Thumbnails
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
="
N1C8AF
"
level
="
3
"
n
="
2
"
type
="
other
"
type-free
="
tractatus
">
<
div
xml:id
="
N2063E
"
level
="
4
"
n
="
4
"
type
="
chapter
"
type-free
="
capitulum
">
<
p
xml:id
="
N20B13
">
<
s
xml:id
="
N20B6A
"
xml:space
="
preserve
">
<
pb
chead
="
De motu locali mixto difformi tꝑe ſubiecto quo ad effectū
"
file
="
0172
"
n
="
172
"/>
Patet ↄ̨ña cū minore et ꝓbatur maior: q2 tota ꝑs
<
lb
/>
citra centrum mundi continet b. partem equalem
<
lb
/>
parti citra centrū mūdi ex hypotheſi: et inſuꝑ cõti-
<
lb
/>
net d. et c. / igr̄ ꝑ d. et c. pars citra centrū mūdi exce-
<
lb
/>
dit partē vltra centrū mundi / qḋ fuit ꝓbandū. </
s
>
<
s
xml:id
="
N20B79
"
xml:space
="
preserve
">Ptꝫ
<
lb
/>
ↄ̨ña intelligenti / quid ſit vnū excedere alterum per
<
lb
/>
aliquid: et ſic patet ſuppoſitio .</
s
>
</
p
>
<
p
xml:id
="
N20B80
">
<
s
xml:id
="
N20B81
"
xml:space
="
preserve
">Scḋa ſuppoſitio. </
s
>
<
s
xml:id
="
N20B84
"
xml:space
="
preserve
">Qñ inter aliquos
<
lb
/>
terminos eſt ꝓportio maioris īequalitatis et ma-
<
lb
/>
iore quartã exceſſus quo minorē excedit deꝑdente
<
lb
/>
adequate: minore eandē dūtaxat quartã acq̇ren-
<
lb
/>
te que a minori deperdit̄̄: ꝓportio inter datos ter-
<
lb
/>
minos pluſ̄ ad ſubduplum ſui diminuit̄̄ et ex ↄ̨ñti
<
lb
/>
data ꝓportio vltra ſuã medietatē deꝑdit. </
s
>
<
s
xml:id
="
N20B93
"
xml:space
="
preserve
">Probat̄̄
<
lb
/>
ſit ꝓportio f. īter a. terminū maiorem et e. terminū
<
lb
/>
minorē: diuidat̄̄ exceſſus quo a. excedit e: in q̈tuor
<
lb
/>
partes equales adequate hoc eſt in quatuor q̈rtas
<
lb
/>
et ſignētur ibi īter a. et e. ãnumeratis extremis q̇n
<
lb
/>
termini cõtinuo arithmetice ꝓportionabiles quoꝝ
<
lb
/>
primꝰ ſit a. ſecūdus b. qui excedit̄̄ ab a. ꝑ vnã quar-
<
lb
/>
tã illiꝰ exceſſus quo a. excedit e. adequate, et tertius
<
lb
/>
ſit c. qui excedat̄̄ a b. ꝑ aliã quartã illius exceſſus, et
<
lb
/>
quartꝰ ſit d. que excedat̄̄ a c. ꝑ vnã aliã quartã ex-
<
lb
/>
ceſſus, et quītus ſit e. terminꝰ minor ꝓportiõis date
<
lb
/>
qui excedit̄̄ ab ipſo d. ꝑ vltimam quartã exceſſus: et
<
lb
/>
manifeſtū eſt illos quī termīos cõtinuo eſſe arith
<
lb
/>
metice ꝓportionabiles cū equali exceſſu exupe
<
lb
/>
rent. </
s
>
<
s
xml:id
="
N20BB2
"
xml:space
="
preserve
">deꝑdat igr̄ a. terminꝰ maior vnã quartã exceſ-
<
lb
/>
ſus illã vcꝫ ꝑ quã b. terminū excedit: et illã adequate
<
lb
/>
acq̇rat e. terminꝰ minor. </
s
>
<
s
xml:id
="
N20BB9
"
xml:space
="
preserve
">Tūc dico / data ꝓportio
<
lb
/>
diminuit̄̄ et plus quã ſuã medietatē deꝑdit et ex hoc
<
lb
/>
plus quã ad ſubduplū diminuit̄̄. </
s
>
<
s
xml:id
="
N20BC0
"
xml:space
="
preserve
">Quod ſic oſtendi
<
lb
/>
tur / q2 ꝓportio f. diminuit̄̄ et plus quã ſui medieta-
<
lb
/>
tem deꝑdit ꝓpoſitū. </
s
>
<
s
xml:id
="
N20BC7
"
xml:space
="
preserve
">Maior ptꝫ manifeſte ex ſe
<
lb
/>
cūdo correlario tertie concluſionis octaui capitis
<
lb
/>
ſecūde partis auxiliãte hypotheſi: et minor ꝓbatur /
<
lb
/>
q2 illa ꝓportio f. q̄ eſt inter a. et e. cõponit̄̄ adequate
<
lb
/>
ex quatuor proportionibꝰ puta ex ꝓportiõe d. ad e.
<
lb
/>
et ex ꝓportiõe c. ad d. et ex ꝓportiõe b. ad c. et ex q̈rta
<
lb
/>
ꝓportione ipſiꝰ a. ad b. / vt cõſtat cõſideranti hypo-
<
lb
/>
theſim: et ille ꝓportiones ſunt cõtinuo minores et
<
lb
/>
minores et minori exceſſu continuo ſeſe excedunt:
<
lb
/>
igitur aggregatum ex duabus extremis proporti-
<
lb
/>
onibus puta ex ꝓportione d. ad e. et ex ꝓportione a.
<
lb
/>
ad b. eſt maiꝰ quã medietas aggregati ex illis qua
<
lb
/>
tuor ꝓportionibꝰ: et ꝑ ↄ̨ñs eſt maius quã medietas
<
lb
/>
ipſiꝰ f. ꝓportionis adequate ex illis quatuor ꝓpor
<
lb
/>
tionibꝰ cõpoſite. </
s
>
<
s
xml:id
="
N20BE6
"
xml:space
="
preserve
">Ptꝫ hec ↄ̨ña ex quarto correlario
<
lb
/>
ſecūde cõcluſionis ſecūdi capitis ſecunde partis: et
<
lb
/>
aggregatū ex illis extremis ꝓportiõibꝰ ꝑdit ꝓpor
<
lb
/>
tio f. / vt ptꝫ ex hypotheſi auxiliãte primo correlario
<
lb
/>
ſexte concluſiõis octaui capitis ſecūde partis. </
s
>
<
s
xml:id
="
N20BF1
"
xml:space
="
preserve
">(Ter-
<
lb
/>
minꝰ em̄ maior puta a. cū deꝑdit exceſſum quo exce
<
lb
/>
dit b. deꝑdit ꝓportionē q̄ eſt ipſiꝰ a. ad b. et terminꝰ
<
lb
/>
minor puta e. cū acq̇rit illū exceſſum quo excedit̄̄ a
<
lb
/>
d. acq̇rit illã ꝓportionē adequate q̄ eſt ipſiꝰ d. ad e.) /
<
lb
/>
igr̄ ꝓportio f. plus quã ſui medietatē deꝑdit / qḋ fuit
<
lb
/>
ꝓbandū. </
s
>
<
s
xml:id
="
N20C00
"
xml:space
="
preserve
">Prima pars mīoris vcꝫ ille ꝓportiões
<
lb
/>
ſunt cõtinuo minores et mīoris ꝓbat̄̄ / q2 qñ īter ali-
<
lb
/>
quos termīos eſt aliqua ꝓportio maioris inequa-
<
lb
/>
litatis: et maiores equali exceſſu excedūt ſuos mīo-
<
lb
/>
res ſemꝑ inter maiores eſt minor ꝓportio quã inter
<
lb
/>
mīores / vt ptꝫ ex octaua ſuppoſitiõe quarti capitis
<
lb
/>
ſecūde partis: ſed oēs illi termini .a. b.c.d. excedūt
<
lb
/>
ſuos minores eq̈li exceſſu et d. et e. ſunt minores quã
<
lb
/>
d. et c. et d. et c. mīores quã c. et b. et c. et b. minores quã
<
lb
/>
b. et a. / igr̄ ꝓportio ipſiꝰ d. ad e. eſt maior ꝓportiõe
<
lb
/>
c. ad d. et ꝓportio c. ad d. maior eſt ꝓportionē b. ad
<
lb
/>
c. et ꝓportio b. ad c. maior ꝓportiõe a. ad b. et ſic ille
<
cb
chead
="
De motu locali mixto difformi tꝑe ſubiecto quo ad effectū
"/>
ꝓportiones ſunt ↄ̨tinuo minores et mīores / qḋ fuit
<
lb
/>
ꝓbandū. </
s
>
<
s
xml:id
="
N20C1E
"
xml:space
="
preserve
">Sed iã ꝓbo aliã partē minoris vcꝫ cõti
<
lb
/>
nuo minori exceſſu ſe excedant: q2 ꝓportio ipſiꝰ d.
<
lb
/>
ad e. ꝑ maiorē ꝓportionē excedit ꝓportionē ipſiꝰ c.
<
lb
/>
ad d. quã ꝓportio ipſius c. ad d. excedit ꝓportionē
<
lb
/>
ipſiꝰ b. ad c. et ꝓportio ipſiꝰ c. ad d. ꝑ maiorē ꝓpor-
<
lb
/>
tionē excedit ꝓportionē b. ad. c. quã ꝓportio b. ad c.
<
lb
/>
excedat ꝓportionē a. ad b. / igr̄ ille ꝓportiões conti-
<
lb
/>
nuo minori exceſſu ſe excedūt. </
s
>
<
s
xml:id
="
N20C2F
"
xml:space
="
preserve
">Maior ptꝫ ex quinto
<
lb
/>
correlario quīte cõcluſionis octaui capitis ſecūde
<
lb
/>
partis qm̄ .b.c.d.e. ſunt quatuor termini continuo
<
lb
/>
arithmetice ꝓportionabiles ex hypotheſi: igr̄ pro
<
lb
/>
portio q̄ eſt inter duos termīos mīores puta inter
<
lb
/>
d. et e. ꝑ plus excedit ſecūdã ꝓportionē q̄ eſt inter c.
<
lb
/>
et d. quã illa ſcḋa excedat tertia q̄ eſt ipſiꝰ b. ad c. / vt
<
lb
/>
ptꝫ ex correlario allegato. </
s
>
<
s
xml:id
="
N20C40
"
xml:space
="
preserve
">Et ſic ꝓbabis minorem
<
lb
/>
capiendo iſtos quatuor terminos cõtinuo arithme
<
lb
/>
tice ꝓportionabiles puta .a. b.c.d. </
s
>
<
s
xml:id
="
N20C47
"
xml:space
="
preserve
">Et ſic ptꝫ corre-
<
lb
/>
larium. </
s
>
<
s
xml:id
="
N20C4C
"
xml:space
="
preserve
">¶ Cõſimiliter ꝓbares / diuiſo exceſſu quo
<
lb
/>
maior terminꝰ excedit minorē in qñ partes eq̈les
<
lb
/>
maiore termino deꝑdente vnã illaꝝ quītaꝝ minore
<
lb
/>
acq̇rente eandē tūc ꝓportio inter datos termīos
<
lb
/>
perdit plus quã duas quītas ſui et ſi exceſſus diui-
<
lb
/>
datur in ſex partes equales maiore deꝑdente vnã
<
lb
/>
illaꝝ et minore acq̇rente eandē: ꝓportio īter datos
<
lb
/>
terminos perdit plus quam vnã tertiã: et ſi diuidat̄̄
<
lb
/>
exceſſus in ſeptē maiore deꝑdente vnã illaꝝ et mīore
<
lb
/>
acq̇rente eandē: ꝓportio inter datos termīos ꝑdit
<
lb
/>
plus quã duas ſeptimas / et ſic ↄ̨ñter. </
s
>
<
s
xml:id
="
N20C63
"
xml:space
="
preserve
">Oīa iſta patēt
<
lb
/>
ex deductionibꝰ quīti correlarii prime cõcluſionis
<
lb
/>
et quīti correlarii ſecūde cõcluſionis ſecūdi capitis
<
lb
/>
ſecūde partis. </
s
>
<
s
xml:id
="
N20C6C
"
xml:space
="
preserve
">¶ Ex his inducit̄̄ et demõſtratur ꝓpo
<
lb
/>
ſitū vcꝫ illud quadratū terreū ꝑpetuo moueret̄̄
<
lb
/>
in tali caſu. </
s
>
<
s
xml:id
="
N20C73
"
xml:space
="
preserve
">Sit vna pars illiꝰ q̈drati vltra centruꝫ
<
lb
/>
mūdi minor medietate: et diuidat̄̄ pars intercepta
<
lb
/>
inter centrū illiꝰ quadrati et centrū mūdi q̄ eſt me-
<
lb
/>
dietas totiꝰ exceſſus partis citra centrū mundi ad
<
lb
/>
partē vltra centrū mūdi ex prima ſuppoſitione et
<
lb
/>
hoc ꝑ partes ꝓportionales ꝓportione dupla ma-
<
lb
/>
ioribꝰ ſus centrū mundi terminatis: q̄ pars ſit d.
<
lb
/>
ſit totū illud quadratū vniforme in grauitate: ſit
<
lb
/>
etiã ꝓportio totiꝰ partis citra centrū mūdi ad par
<
lb
/>
tē vltra centrū mūdi f. </
s
>
<
s
xml:id
="
N20C88
"
xml:space
="
preserve
">Quo poſito ſic argr̄ q̈dratū
<
lb
/>
illud tamdiu mouebit̄̄ quãdiu aliqua pars ipſius
<
lb
/>
d. partis intercepte inter centrū q̈drati et centrum
<
lb
/>
mundi fuerit citra centrū mūdi qm̄ tamdiu excedet
<
lb
/>
pars citra centrū partē vltra centrū q2 tūc cõtinuo
<
lb
/>
erit maior: ſed ꝑpetuo aliqua pars ipſiꝰ d. partis
<
lb
/>
erit citra centrū mūdi: g̊ ꝑpetuo tale q̈dratū moue
<
lb
/>
bitur / qḋ fuit ꝓbandū. </
s
>
<
s
xml:id
="
N20C99
"
xml:space
="
preserve
">Cõſequētia ptꝫ cū maiore et
<
lb
/>
ꝓbat̄̄ minor / q2 ꝑpetuo aliqua pars aggregati ex
<
lb
/>
oībus partibꝰ ꝓportionalibꝰ ipſiꝰ d. partis deſcē
<
lb
/>
det: g̊ ꝑpetuo aliqua pars ipſiꝰ d. partis erit citra
<
lb
/>
centrū mūdi / qḋ fuit ꝓbandū, </
s
>
<
s
xml:id
="
N20CA4
"
xml:space
="
preserve
">Cõſequētia ptꝫ et pro
<
lb
/>
batur añs / q2 prima pars ꝓportionalis ipſius d.
<
lb
/>
partis incipit deſcēdere a ꝓportiõe f. vt habet̄̄ hy-
<
lb
/>
potheſi: et ſecūda pars ꝓportiõalis ipſiꝰ d. partis
<
lb
/>
incipit deſcēdere a ꝓportiõe ſubdupla ad ꝓportio
<
lb
/>
nē f. vel a minori: et tertia īcipit deſcēdere a ſubdu-
<
lb
/>
pla vel minori ſubdupla ad ꝓportionē a q̈ incipit
<
lb
/>
deſcēdere ſcḋa / et ſic ↄ̨ñter q̄libet pars ꝓportiõalis
<
lb
/>
ipſiꝰ d. ſequēs īcipiet deſcēdere a ꝓportione ſubdu
<
lb
/>
pla vel minori ad ꝓportionē a qua īcipit deſcēde-
<
lb
/>
re pars īmediate p̄cedēſupra: et q̄libet pars quãdiu ali-
<
lb
/>
q̇d eiꝰ deſcēdit cõtinuo deſcēdit ſiue mouet̄̄ a mīori
<
lb
/>
ꝓportione ꝙ̄ ſit illa a qua incipit illa eadem pars
<
lb
/>
deſcēdere (cū cõtinuo partis citra centrū mūdi ad
<
lb
/>
partē vltra centrū mūdi ꝓportio a qua partes ille
<
lb
/>
deſcendūt cõtinuo diminuatur: continuo em̄ pars </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>