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
="
N1C8AF
"
level
="
3
"
n
="
2
"
type
="
other
"
type-free
="
tractatus
">
<
div
xml:id
="
N1DD6A
"
level
="
4
"
n
="
3
"
type
="
chapter
"
type-free
="
capitulum
">
<
p
xml:id
="
N1FC64
">
<
s
xml:id
="
N1FD46
"
xml:space
="
preserve
">
<
pb
chead
="
Secundi tractatus
"
file
="
0163
"
n
="
163
"/>
velocitates ſe habeant in ꝓportione ſexquiquarta
<
lb
/>
omnium vero parium in ꝓportione ſexquiquinta:
<
lb
/>
excedat velocitas ṗme partis paris velocitatem
<
lb
/>
ṗme partis imparis in proportiõe ſexquiſexta: tūc
<
lb
/>
inueſtiga ꝓportionem totius ſpacii ad ſpaciuꝫ per
<
lb
/>
tranſitū in prima innitendo p̄cedentibus. </
s
>
<
s
xml:id
="
N1FD5C
"
xml:space
="
preserve
">Itē parti
<
lb
/>
ta hora in partes ꝓportionales ꝓportiõe quadru
<
lb
/>
pla: mobili in omni īpari ſequente mouēte in ſex
<
lb
/>
quiſexto velocius ꝙ̄ in immediate ꝓcedente impari
<
lb
/>
et in omni pari ſequente in ſexquiſeptimo velocius
<
lb
/>
quã in pari immediate precedente: ſuperet veloci
<
lb
/>
tas prime partis paris velocitatem prime imparis
<
lb
/>
in ꝓportione ſexquioctaua: tunc cõmenſura totale
<
lb
/>
ſpacium ſpacio prime partis ꝓportionalis precedē
<
lb
/>
tibus ſuffultus </
s
>
<
s
xml:id
="
N1FD71
"
xml:space
="
preserve
">Et ſic aſcendendo per ſpecies ꝓpor-
<
lb
/>
tionis multiplicis in diuidenda hora velocitatibꝰ
<
lb
/>
ſe habentibus continuo in diuerſis ꝓportionibus
<
lb
/>
ſuperparticularibus infinitam multitudinem ſe ſe
<
lb
/>
ↄ̨ſequētiū cõcluſionum inferre valebis. </
s
>
<
s
xml:id
="
N1FD7C
"
xml:space
="
preserve
">Deinde diui
<
lb
/>
ſa hora aliqua multipli ſimplici vel compoſita ve-
<
lb
/>
locitatibus partiuꝫ imparium cõtinuo ſe habētibꝰ
<
lb
/>
in ꝓportione aliqua ſuprapartiente: et partium pa
<
lb
/>
riū immediatarum velocitatibus continuo ſe habē
<
lb
/>
tibus in aliqua alia ꝓportione ſuprapartiente: ex-
<
lb
/>
cedente velocitate prime partis paris velocita-
<
lb
/>
tem prime partis imparis in aliqua alia propor-
<
lb
/>
tione ſuperpartiente infinita correlaria inferre po
<
lb
/>
teris. </
s
>
<
s
xml:id
="
N1FD91
"
xml:space
="
preserve
">Preterea partita hora per partes pro
<
lb
/>
portionales ꝓportione multipici: quarūcun dua
<
lb
/>
rum ꝑtium ꝑ .4. partes ꝓportionales diſtantiū ve-
<
lb
/>
locitatibus ſe habentibus in aliqua ꝓportione ſu
<
lb
/>
perparticulari vel ſuperpartiente ita vt ṗme diſtã
<
lb
/>
tes ꝑ .4. partes ꝓportionales vt puta prima et ſex
<
lb
/>
ta ſe habeant in velocitate in ꝓportione ſexquial-
<
lb
/>
tera: et ſeptime velocitas ad velocitatem ſecunde in
<
lb
/>
ꝓportione ſexquitertia: et octaue velocitas ad velo
<
lb
/>
citatem tertie in ꝓportione ſexquiq̈rta: et none ve-
<
lb
/>
locitas ad velocitatem quarte in ꝓportione ſexqui
<
lb
/>
quinta: et decime velocitas ad velocitatem quinte ī
<
lb
/>
ꝓportione ſexquiſexta: et vndecime velocitas ad ve
<
lb
/>
locitatem ſexte in ꝓportione ſexquialtera: et ſic ite-
<
lb
/>
rum aſcendendo vſ ad proportionem ſexquiſextã
<
lb
/>
et deinde redeundo vſ ad ꝓportionem ſexquial-
<
lb
/>
teram / et ſic conſequenter: ita omnes diſtantes ꝑ
<
lb
/>
4. incipiendo a ṗma ſe habeant in ꝓportione ſexq̇
<
lb
/>
altera in velocitate: et incipiendo a ſecunda in ſexq̇
<
lb
/>
tertia: et a tertia in ſexquiquarta: et a quarto in ſex
<
lb
/>
quiquinta: et a quinta in ſexquiſexta: et non plus.</
s
>
</
p
>
<
p
xml:id
="
N1FDC6
">
<
s
xml:id
="
N1FDC7
"
xml:space
="
preserve
">Ita poteris facere de partibus inter quas cõtinuo
<
lb
/>
mediant octo ꝑtes aſcendendo a prima vſ ad de-
<
lb
/>
cimã: et ſic in infinitum poteris variare caſus reten
<
lb
/>
ta ſemper aliqua vniformiter ꝓportionum </
s
>
<
s
xml:id
="
N1FDD0
"
xml:space
="
preserve
">Et ſi-
<
lb
/>
cut inferuntur multa correlaria quando velocitas
<
lb
/>
maior coextenditur ꝑtibꝰ minoribus. </
s
>
<
s
xml:id
="
N1FDD7
"
xml:space
="
preserve
">ita plura alia
<
lb
/>
poſſunt inferri quando continuo velocitas maior
<
lb
/>
coextenditur partibus minoribus que omnia ex ṗ-
<
lb
/>
oribus facile inducuntur. </
s
>
<
s
xml:id
="
N1FDE0
"
xml:space
="
preserve
">Et quia nimium in iſtis
<
lb
/>
immorari vltra modum eis inherere, eſt a melio
<
lb
/>
ribus ſublimioribuſ ꝓſtergari: </
s
>
<
s
xml:id
="
N1FDE7
"
xml:space
="
preserve
">Ideo calculator
<
lb
/>
his dedaleis laberinthulis implicitꝰ: verbiſ mul
<
lb
/>
tiplicibus multiformibuſ ꝓportionibus implica
<
lb
/>
tus: inflate bucce garritum contineat.</
s
>
</
p
>
<
p
xml:id
="
N1FDF0
">
<
s
xml:id
="
N1FDF1
"
xml:space
="
preserve
">Decima concluſio </
s
>
<
s
xml:id
="
N1FDF4
"
xml:space
="
preserve
">Diuiſa hora ꝑ par
<
lb
/>
tes ꝓportionales ꝓportione dupla et a. mobile in
<
lb
/>
prima ꝑte ꝓportionali moueatur aliquantula ve-
<
lb
/>
locitate: et in ſecunda in ſexquialtero maiori veloci
<
lb
/>
tate: et in tertia in ſexquiquarto maiori velocitate
<
lb
/>
̄ in prima: et in quinta in ſexquiſexdecimo maiori
<
lb
/>
quã in prima / et ſic conſequenter aſcendendo ꝑ ſpe-
<
cb
chead
="
Capitulum tertium
"/>
cies ꝓportionis ſuperparticularis denominatas
<
lb
/>
a numeris pariter paribus </
s
>
<
s
xml:id
="
N1FE08
"
xml:space
="
preserve
">(Meliꝰ tñ diceret̄̄ deſcē
<
lb
/>
dēdo: q2 ꝓportiões ſuꝑparticulares ſūt mīores quã
<
lb
/>
to a maiori numero denominantur hoc eſt a parte
<
lb
/>
aliquota denominata a maiori numero) ſpacium ꝑ
<
lb
/>
trauſitum in totali hora ſe habet ad ſpacium per-
<
lb
/>
tranſitum in prima ꝑte ꝓportionali in ꝓportione
<
lb
/>
dupla ſexquitertia. </
s
>
<
s
xml:id
="
N1FE17
"
xml:space
="
preserve
">Probatur et ſit gratia exempli
<
lb
/>
velocitas ṗme ꝑtis ꝓportionalis vt duo, ꝑtrãſeat
<
lb
/>
a. mobile mediante illa velocitate in prima ꝑte ꝓ
<
lb
/>
portionali bipedale: et arguitur ſic / illa velocitas vt
<
lb
/>
duo coextenditur toti hore, quia in qualibet parte
<
lb
/>
ꝓportionali hore velocitas eſt maior quam vt duo
<
lb
/>
vt habetur ex caſu et tota hora eſt dupla ad primaꝫ
<
lb
/>
partem ꝓportionalem eius in qua mobile pertran
<
lb
/>
ſit bipcdale mediante velocitate vt duo: igitur me-
<
lb
/>
diante illa velocitate coextenſa toti hore pertran-
<
lb
/>
ſit quadrupedale: et mediantibus exceſſibus parti-
<
lb
/>
um ꝓportionalium ſupra illam velocitatem vt duo
<
lb
/>
pertranſit duas tertias pedalis que faciūt vnã ter
<
lb
/>
tiam duorum pedalium: igitur totuꝫ ſpacium ſe ha
<
lb
/>
bebit ad ſpacium pertranſitum in prima parte ꝓ-
<
lb
/>
portionali in proportione dupla ſexquitertia cuiuſ
<
lb
/>
modi eſt ꝓportio ipſoꝝ quatuor cum duabus ter-
<
lb
/>
tiis vnius ad duo </
s
>
<
s
xml:id
="
N1FE3C
"
xml:space
="
preserve
">Probo tamen / mediantibꝰ il-
<
lb
/>
lis exceſſibus ꝑtranſeat duas tertias pedalis: quo
<
lb
/>
niam cum velocitas ſecunde ꝑtis ꝓportionalis ſit
<
lb
/>
ſexquialtera ad velocitatem prime que eſt vt duo ſe
<
lb
/>
quitur / exceſſus velocitatis ſecunde ad velocitatē
<
lb
/>
prime eſt vnus gradus et quia tertia excedit primã
<
lb
/>
in ꝓporeione ſexquiquarta / ſequitur / exceſſus eius
<
lb
/>
eſt medietas vnius gradus quoniam duorum cū di
<
lb
/>
midio ad duo eſt proportio ſexquiquarta, et veloci
<
lb
/>
tas quarte partis ſe habet ad velocitatem prime ī
<
lb
/>
ꝓportione ſexquioctaua: igitur exceſſus eius ē vna
<
lb
/>
quarta: igitur in illo caſu exceſſus ſecunde ad exceſ
<
lb
/>
ſum tertie eſt ꝓportio dupla et exceſſus tertie ad ex-
<
lb
/>
ceſſum quarte dupla ſimiliter: et ſic conſequenter re
<
lb
/>
peries illos exceſſus ſe habere in ꝓportione ſubdu
<
lb
/>
pla et ſubdupla. et coextenduntur partibus cõtinuo
<
lb
/>
ſe habentibus in ꝓportione ſubdupla et ſubdupla /
<
lb
/>
igitur continuo illa ſpacia mediantibus illis velo
<
lb
/>
citatibus ꝑtranſita ſe habet in ꝓportione ſubqua-
<
lb
/>
drupla / et ꝑ conſequens aggregatum ex omnibꝰ eis
<
lb
/>
ſe habebit ad primum illorum in ꝓportione ſexqui
<
lb
/>
tertia et ṗmum illorum eſt vnum ſemipedale: ergo
<
lb
/>
totum erit vnum ſemipedale cum vna ſexta peda-
<
lb
/>
lis: et ꝑ conſequens due tertie vnius pedalis / qḋ fuit
<
lb
/>
ꝓbandum. </
s
>
<
s
xml:id
="
N1FE6F
"
xml:space
="
preserve
">Sed iam ꝓbo / p̄mum illorum ſit vnum
<
lb
/>
ſemipedale quoniam primum illorum ꝑtranſit̄̄ me
<
lb
/>
diante exceſſu ſecunde ꝑtis ꝓportionalis ſupra pri
<
lb
/>
mam qui exceſſus eſt vnus gradus mediante quo ī
<
lb
/>
prima parte ꝓportionali pertranſitur vnum peda
<
lb
/>
le: igitur mediante illo in ſecunda parte ꝓportiõa-
<
lb
/>
li ſubdupla ad illam pertranſitur vnum ſemipeda
<
lb
/>
le / quod fuit ꝓbandum. </
s
>
<
s
xml:id
="
N1FE80
"
xml:space
="
preserve
">Patet conſequentia ex ſecū
<
lb
/>
da ꝑte prime ꝓpoſitionis ſecundi notabilis.</
s
>
</
p
>
<
p
xml:id
="
N1FE85
">
<
s
xml:id
="
N1FE86
"
xml:space
="
preserve
">¶ Ex hac concluſione ſequitur primo / ſi fuerit ho
<
lb
/>
ra diuiſa ꝓportione dupla: et in prima illarum par
<
lb
/>
tium moueatur aliquod mobile aliquanta velocita
<
lb
/>
te, et in ſecunda in ſupertripartiente quartas maio
<
lb
/>
ri velocitate, et in tertia in ſupertripartiente octa-
<
lb
/>
uas maiori velocitate ꝙ̄ in prima: et in quarta in ſu
<
lb
/>
ꝑtripartiente ſexdecimas maiori ꝙ̄ in prima et in
<
lb
/>
quinta in ſuꝑtripartiente triceſimas ſecundas ma
<
lb
/>
iori velocitate ꝙ̄ in prima / et ſic conſequenter ꝓcedē
<
lb
/>
do per ſpecies ꝓportionis ſupertripartientis de-
<
lb
/>
nominatas a numeris pariter paribus ſiue a par-
<
lb
/>
tibus aliquotis denominatis ab illis numeris: ſpa </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>