Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Secūdi tractatus
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<
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xml:space
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">1. confir-
<
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matio.</
note
>
<
p
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<
s
xml:id
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xml:space
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">¶ Et confirmatur / quia cuiuſlibet motus vniformi-
<
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/>
ter difformis gradꝰ velociſſimꝰ .i. quo mouet̄̄ pun-
<
lb
/>
ctus velociſſime motꝰ tm̄ excedit gradū mediū ̄tū
<
lb
/>
gradꝰ mediꝰ excedit gradū quo mouet̄̄ pūctus tar-
<
lb
/>
diſſime motꝰ vt cõcedit hec opinio et cõis ſcola: ſed
<
lb
/>
motꝰ talis q̈drati a.b.c.d. nõ eſt huiuſmodi, igr̄ ta-
<
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/>
lis motꝰ nõ eſt vniformiter difformis. </
s
>
<
s
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xml:space
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preserve
">Minor ꝓbat̄̄ /
<
lb
/>
q2 gradꝰ velociſſimꝰ illiꝰ partis eſt gradus octauꝰ
<
lb
/>
cū quadratū illud applicet̄̄ circūferētie rote: et me-
<
lb
/>
dius eſt vt quatuor, et motꝰ illiꝰ nõ terminat̄̄ ad nõ
<
lb
/>
gradū: ergo ſeq̇tur / gradus velociſſimꝰ ꝑ maiorē
<
lb
/>
latitudinem excedit mediuꝫ quam medius excedat
<
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/>
infimum / quod fuit probandum.</
s
>
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left
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xml:id
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xml:space
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preserve
">2. confir-
<
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matio.</
note
>
<
p
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<
s
xml:id
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xml:space
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preserve
">¶ Confirmatur ſecundo principale argumentum /
<
lb
/>
q2 ſi motꝰ talis rote eſſet vniformiter difformis a
<
lb
/>
nõ gradū vſ ad octauū / ſeq̄ret̄̄ / adequata velo-
<
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/>
citas illiꝰ rote eſſet vt quatuor: ſed ↄ̨ñs eſt falſū: igr̄
<
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/>
illud ex quo ſeq̇tur. </
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>
<
s
xml:id
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N1CB97
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xml:space
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preserve
">Cõſequētia eſt nota, et falſitas
<
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/>
ↄ̨ñtis argr̄ / q2 velocitas totiꝰ illiꝰ partis q̄ claudit̄̄
<
lb
/>
circulo minori .d.e.f. eſt vt duo cuꝫ ſit a quarto vſ
<
lb
/>
ad nõ gradū, et velocitas totiꝰ reſidui eſt vt ſex cum
<
lb
/>
ſit a quarto vſ ad octauum, et ſi eſſet in medietate
<
lb
/>
adequate faceret ad denoīationē totiꝰ motꝰ vt tria.
<
lb
/>
modo eſt in ſexquialtero maiori parte medietate: g̊
<
lb
/>
ſeq̇tur / motꝰ eiꝰ facit ad denoīationē totiꝰ in ſex-
<
lb
/>
q̇altero magis: et ꝑ ↄ̨ñs / vt quatuor cū dimidio (cum
<
lb
/>
quatuor cū dimidio ad tria ſit ꝓportio ſexq̇altera) /
<
lb
/>
g̊ ſeq̇tur / talis motus adequate eſt velocior quã vt
<
lb
/>
quatuor cū dimidio, et ꝑ ↄ̨ñs velocior quã vt quatu
<
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/>
tor / qḋ fuit ꝓbandū. </
s
>
<
s
xml:id
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N1CBB2
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xml:space
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preserve
">Sed iã ꝓbo / illa pars rote q̄
<
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/>
eſt totū reſiduū a minori circulo eſt in ſexquialtero
<
lb
/>
maior medietate, q2 illa pars eſt tres quarte totiꝰ
<
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/>
rote: igr̄ in ſexq̇altero eſt maior medietate </
s
>
<
s
xml:id
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N1CBBB
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xml:space
="
preserve
">Probat̄̄ /
<
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/>
q2 medietas eſt due q̈rte: mõ triū quartaꝝ ad duas
<
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/>
q̈rtas eſt ꝓportio ſexq̇altera. </
s
>
<
s
xml:id
="
N1CBC2
"
xml:space
="
preserve
">Sed iã ꝓbo añs vcꝫ /
<
lb
/>
reſiduū illius rote a minori circulo ſit tres quarte
<
lb
/>
illius rote quia totius rote ad minorem totum cir-
<
lb
/>
culū eſt ꝓportio quadrupla: g̊ totū reſiduū a mīori
<
lb
/>
circulo qui eſt vna quarta eſt tres q̈rte: ſꝫ illa ꝑs eſt
<
lb
/>
totū reſiduū a mīori circulo / vt notū eſt: g̊ illa ē tres
<
lb
/>
q̈rte totiꝰ rote / qḋ fuit ꝓbandū.
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position
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xlink:href
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note-0131-01a
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xlink:label
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note-0131-01
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xml:id
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xml:space
="
preserve
">Brauar-
<
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dinꝰ ī tra
<
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/>
ctatu ꝓ-
<
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/>
portio-
<
lb
/>
nū capi-
<
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/>
te .4.</
note
>
</
s
>
<
s
xml:id
="
N1CBD6
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xml:space
="
preserve
">Sꝫ iã ꝓbo / totius
<
lb
/>
rote ad mīorē circulū ei cõcētricū ſit ꝓportio q̈dru-
<
lb
/>
pla, q2 vt demõſtrat brauardinꝰ ī tractatu ꝓporti-
<
lb
/>
onū capite q̈rto ſēꝑ īter duos circulos īeq̈les eſt du
<
lb
/>
plicata ꝓportio ad ꝓportionē q̄ eſt īter diametros
<
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/>
eorūdē circuloꝝ. </
s
>
<
s
xml:id
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N1CBE3
"
xml:space
="
preserve
">ita ꝓportio circuloꝝ eſt ꝓportio
<
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/>
diametroꝝ duplicata / vt etiã facile poteſt intueri in
<
lb
/>
<
figure
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fig-0131-01a
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fig-0131-01
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10
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0131-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0131-01
"/>
</
figure
>
figura ſuppoſita
<
lb
/>
ſꝫ diametri totiꝰ
<
lb
/>
rote ad diametꝝ
<
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/>
circĺi d.e.f. ē ꝓpor
<
lb
/>
tio dupla: g̊ totiꝰ
<
lb
/>
rote ad circulū .d
<
lb
/>
e.f. eſt ꝓportio q̈-
<
lb
/>
drupla q̄ ē dupla
<
lb
/>
ad duplã / qḋ fuit
<
lb
/>
ꝓbandū. </
s
>
<
s
xml:id
="
N1CC01
"
xml:space
="
preserve
">Qḋ o
<
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/>
diametri ad dia
<
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metꝝ ſit ꝓportio
<
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/>
dupla / ptꝫ ex caſu
<
lb
/>
prīcipalis argu-
<
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/>
mēti. </
s
>
<
s
xml:id
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xml:space
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">Et ſic ex hac deductiõe ptꝫ / totꝰ ille motꝰ eſt
<
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/>
vt quī q2 ille tres q̈rte denominã vt q̈tuor cū di-
<
lb
/>
midio, et alia q̈rta eſt mīor circulꝰ denoīat vt di-
<
lb
/>
midiū (cū ſit vt duo) / igr̄ totꝰ motꝰ eſt vt quī et ſic nõ
<
lb
/>
eſt adequate vt quatuor / quod fuit probandum.</
s
>
</
p
>
<
p
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<
s
xml:id
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xml:space
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">Scḋo prīcipaliṫ arguit̄̄ ſic </
s
>
<
s
xml:id
="
N1CC37
"
xml:space
="
preserve
">Si illa dif
<
lb
/>
finitio eſſet bona ſeq̄ret̄̄ / motꝰ celi nõ eſſet vnifor-
<
cb
chead
="
Capitulū primū.
"/>
miter difformis q̊ ad ſubiectū: ſꝫ ↄ̨ñs eſt falſū / et ↄ̨tra
<
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/>
cõiṫ opinãtes / ir̄ illḋ ex q̊ ſeq̇tur. </
s
>
<
s
xml:id
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N1CC41
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xml:space
="
preserve
">Seq̄la ꝓbat̄̄ / et diuido
<
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/>
ṗmū mobile in duas medietates ꝑ coluꝝ vcꝫ ꝓcedē
<
lb
/>
tē a polo artico ꝑ polū antarticū et ꝑ capita arietꝪ
<
lb
/>
et libre / q̊ poſito arguo ſic / nulla illaꝝ medietatū mo
<
lb
/>
uet̄̄ vniformiṫ difformiṫ: igr̄ nec celū mouet̄̄ vnifor-
<
lb
/>
miṫ difformiṫ. </
s
>
<
s
xml:id
="
N1CC4E
"
xml:space
="
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">Cõſequētia ptꝫ, et argr̄ añs / qm̄ neu-
<
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/>
triꝰ illaꝝ medietatū pūctꝰ q̇ eſt ī medio tãtū excedi-
<
lb
/>
tur in velocitate a pūcto velociſſime moto ̄tū exce-
<
lb
/>
dit pūctū tardiſſime motū ſiue nõ g̈dū cū pūctꝰ exi-
<
lb
/>
ſtēs in medio ſit pūctꝰ exñs in circulo eq̇noctiali q̇ ē
<
lb
/>
pūctꝰ velociſſime motꝰ: igr̄ a nullo excedit̄̄ in veloci
<
lb
/>
tate / et ꝑ ↄ̨ñs nõ tm̄ excedit a pūcto velociſſime moto
<
lb
/>
quantum excedit punctū tardiſſime motum vel nõ
<
lb
/>
gradum velocitatis / quod fuit probandum.</
s
>
</
p
>
<
p
xml:id
="
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">
<
s
xml:id
="
N1CC62
"
xml:space
="
preserve
">¶ Et confirmat̄̄ / q2 ſi eſſet aliquis motus vniformi-
<
lb
/>
ter difformis q̊ ad ſubiectū maxīe eſſet motꝰ localis
<
lb
/>
q̊ ꝑ rarefactionē mouet̄̄ vnū q̈dratū qḋ rarefit vni-
<
lb
/>
formiter a nõ g̈du in extremo q̇eſcēte vſ ad octauū
<
lb
/>
in altero extremo: ſꝫ hec nõ, igr̄. </
s
>
<
s
xml:id
="
N1CC6D
"
xml:space
="
preserve
">Maior eſt nota cū
<
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/>
ↄ̨ña, et ꝓbat̄̄ mīor / q2 nõ cuiuſlꝫ ꝑtis illiꝰ g̈dus mediꝰ
<
lb
/>
tm̄ excedit̄̄ a velociſſimo quãto excedit g̈dū tardiſſi
<
lb
/>
mū illiꝰ ꝑtis vĺ nõ g̈dū: igr̄ totū illud q̈dratū nõ mo
<
lb
/>
uet̄̄ vniformiṫ difformiṫ q̊ ad ſubiectū. </
s
>
<
s
xml:id
="
N1CC78
"
xml:space
="
preserve
">Cõſequētia
<
lb
/>
ptꝫ ex definitiõe, et argr̄ añs, et ſigno vnã partē ī me
<
lb
/>
dietate illiꝰ q̈drati q̄ velociꝰ rarefit: et ſit illa pars
<
lb
/>
figurata ꝑ modū duoꝝ lateꝝ vniꝰ triãguli faciētis
<
lb
/>
vnū angulū ſupra punctū mediū ex vno latere et ex
<
lb
/>
alio infra vt apparet in figura hic infra ſcripta.</
s
>
</
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>
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number
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0131-02
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xlink:href
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Tunc
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type
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ſic
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arguitur
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type
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/ illa
<
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pars
"
type
="
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>
eſt
<
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="
pars
"
type
="
wordlist
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>
<
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norm
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illius
"
type
="
simple
">illiꝰ</
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>
q̈dra-
<
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ti: et
<
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tamen
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type
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ipſa
<
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non
"
type
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<
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mouetur
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type
="
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<
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vniformiter
"
type
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reg
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<
reg
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dif- formiter
"
type
="
simple
">dif-
<
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formiṫ</
reg
>
:
<
reg
norm
="
igitur
"
type
="
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">igr̄</
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>
<
reg
norm
="
propoſitum
"
type
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. </
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<
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Arguitur
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type
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<
reg
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="
antecedens
"
type
="
wordlist
">añs</
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>
/
<
reg
norm
="
quia(?)
"
type
="
wordlist
">q2</
reg
>
<
reg
norm
="
pun ctus
"
type
="
context
">pū
<
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/>
ctus</
reg
>
<
reg
norm
="
exiſtens
"
type
="
wordlist
">exñs</
reg
>
in medio
<
reg
norm
="
illius
"
type
="
simple
">illiꝰ</
reg
>
<
reg
norm
="
partis
"
type
="
wordlist
">ꝑtis</
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>
in linea
<
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<
reg
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="
procedente
"
type
="
simple context
">ꝓcedēte</
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>
a
<
reg
norm
="
puncto
"
type
="
context
">pūcto</
reg
>
<
reg
norm
="
non
"
type
="
wordlist
">nõ</
reg
>
moto
<
reg
norm
="
vſque
"
faithful
="
vſ
"
type
="
simple
">vſqꝫ</
reg
>
ad
<
reg
norm
="
pun ctum
"
type
="
context context
">pū
<
lb
/>
ctū</
reg
>
velociſſime
<
reg
norm
="
motum
"
type
="
context
">motū</
reg
>
<
reg
norm
="
ipſius
"
type
="
simple
">ipſiꝰ</
reg
>
q̈drati eſt
<
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/>
<
reg
norm
="
punctus
"
type
="
context
">pūctus</
reg
>
<
reg
norm
="
medius
"
type
="
simple
">mediꝰ</
reg
>
<
reg
norm
="
totius
"
type
="
simple
">totiꝰ</
reg
>
q̈drati qui
<
reg
norm
="
mouetur
"
type
="
simple
">mouet̄̄</
reg
>
vt quatuor / vt
<
lb
/>
<
reg
norm
="
patet
"
type
="
wordlist
">ptꝫ</
reg
>
in figura:
<
reg
norm
="
igitur
"
type
="
wordlist
">igr̄</
reg
>
ſi talis
<
reg
norm
="
mouetur
"
type
="
simple
">mouet̄̄</
reg
>
vniformiter diffor-
<
lb
/>
miter
<
reg
norm
="
ſequitur
"
type
="
simple
">ſequit̄̄</
reg
>
/
<
reg
norm
="
quae
"
type
="
wordlist
"></
reg
>
<
reg
norm
="
totus
"
type
="
simple
">totꝰ</
reg
>
<
reg
norm
="
motus
"
type
="
simple
">motꝰ</
reg
>
<
reg
norm
="
eius
"
type
="
simple
">eiꝰ</
reg
>
eſt vt quatuor / ſed
<
reg
norm
="
conſequens
"
type
="
wordlist
">ↄ̨ñs</
reg
>
<
lb
/>
eſt
<
reg
norm
="
falſum
"
type
="
context
">falſū</
reg
>
:
<
reg
norm
="
igitur
"
type
="
wordlist
">igr̄</
reg
>
illud ex quo
<
reg
norm
="
ſequitur
"
type
="
simple
">ſequit̄̄</
reg
>
. </
s
>
<
s
xml:id
="
N1CCA2
"
xml:space
="
preserve
">Falſitas ↄ̨ñtis
<
reg
norm
="
pro batur
"
type
="
simple
">pro
<
lb
/>
bat̄̄</
reg
>
/
<
reg
norm
="
quia(?)
"
type
="
wordlist
">q2</
reg
>
<
reg
norm
="
vtraque
"
faithful
="
vtra
"
type
="
simple
">vtraqꝫ</
reg
>
medietas talis partis
<
reg
norm
="
velocius
"
type
="
simple
">velociꝰ</
reg
>
<
reg
norm
="
mouetur
"
type
="
simple
">mouet̄̄</
reg
>
<
lb
/>
<
reg
norm
="
per
"
type
="
wordlist
">ꝑ</
reg
>
<
reg
norm
="
rarefactionem
"
type
="
context
">rarefactionē</
reg
>
<
reg
norm
="
quam
"
type
="
context
">quã</
reg
>
vt quatuor
<
reg
norm
="
quia(?)
"
type
="
wordlist
">q2</
reg
>
<
reg
norm
="
vtriuſque
"
faithful
="
vtriuſ
"
type
="
simple
">vtriuſqꝫ</
reg
>
<
reg
norm
="
illarum
"
type
="
simple
">illaꝝ</
reg
>
<
reg
norm
="
pun- ctus
"
type
="
context
">pū-
<
lb
/>
ctus</
reg
>
<
reg
norm
="
medius
"
type
="
simple
">mediꝰ</
reg
>
eſt
<
reg
norm
="
intenſior
"
type
="
context
">intēſior</
reg
>
<
reg
norm
="
quam
"
type
="
wordlist
">ꝙ̄</
reg
>
vt .4.
<
reg
norm
="
cum
"
type
="
context
">cū</
reg
>
<
reg
norm
="
vtriuſque
"
faithful
="
vtriuſ
"
type
="
simple
">vtriuſqꝫ</
reg
>
<
reg
norm
="
illarum
"
type
="
simple
">illaꝝ</
reg
>
<
reg
norm
="
me- dietatum
"
type
="
context
">me-
<
lb
/>
dietatū</
reg
>
<
reg
norm
="
punctus
"
type
="
context
">pūctus</
reg
>
<
reg
norm
="
medius
"
type
="
simple
">mediꝰ</
reg
>
ſit ſupra
<
reg
norm
="
punctum
"
type
="
context
">punctū</
reg
>
<
reg
norm
="
exiſtentem
"
type
="
context
">exiſtentē</
reg
>
in
<
lb
/>
medio
<
reg
norm
="
illius
"
type
="
simple
">illiꝰ</
reg
>
q̈drati: et ſic
<
reg
norm
="
vtraque
"
faithful
="
vtra
"
type
="
simple
">vtraqꝫ</
reg
>
<
reg
norm
="
illarum
"
type
="
simple
">illaꝝ</
reg
>
<
reg
norm
="
mouetur
"
type
="
simple
">mouet̄̄</
reg
>
<
reg
norm
="
velocius
"
type
="
simple
">velociꝰ</
reg
>
<
lb
/>
̄ vt quatuor:
<
reg
norm
="
ergo
"
type
="
wordlist
">g̊</
reg
>
<
reg
norm
="
per
"
type
="
wordlist
">ꝑ</
reg
>
<
reg
norm
="
conſequens
"
type
="
wordlist
">ↄ̨ñs</
reg
>
tota illa pars
<
reg
norm
="
cuius
"
type
="
simple
">cuiꝰ</
reg
>
ille
<
reg
norm
="
ſunt
"
type
="
context
">ſūt</
reg
>
me
<
lb
/>
dietates
<
reg
norm
="
mouetur
"
type
="
simple
">mouet̄̄</
reg
>
<
reg
norm
="
velocius
"
type
="
simple
">velociꝰ</
reg
>
<
reg
norm
="
quam
"
type
="
wordlist
">ꝙ̄</
reg
>
vt
<
reg
norm
="
quatuor
"
type
="
wordlist
">q̈tuor</
reg
>
/
<
reg
norm
="
quod
"
type
="
simple
">qḋ</
reg
>
eſt
<
reg
norm
="
oppoſitum
"
type
="
simple
">oppoſituꝫ</
reg
>
<
lb
/>
aut
<
reg
norm
="
ſaltem
"
type
="
context
">ſaltē</
reg
>
<
reg
norm
="
infert
"
type
="
context
">īfert</
reg
>
<
reg
norm
="
oppoſitum
"
type
="
context
">oppoſitū</
reg
>
<
reg
norm
="
conſequentis
"
type
="
wordlist
">ↄ̨ñtis</
reg
>
/
<
reg
norm
="
quod
"
type
="
simple
">qḋ</
reg
>
erat
<
reg
norm
="
probandum
"
type
="
simple context context
">ꝓbãdū</
reg
>
<
reg
norm
="
falſum
"
type
="
context
">falſū</
reg
>
.</
s
>
</
p
>
<
p
xml:id
="
N1CCB5
">
<
s
xml:id
="
N1CCB6
"
xml:space
="
preserve
">In oppoſitū tñ arguit̄̄ / ꝑ cõmunē au-
<
lb
/>
ctoritatem recentiū pḣoꝝ hãc definitionē ponentiū</
s
>
</
p
>
<
p
xml:id
="
N1CCBB
">
<
s
xml:id
="
N1CCBC
"
xml:space
="
preserve
">Pro ſolutiõe enodatiõe huiꝰ q̄ſtiõis
<
lb
/>
pono aliquas cõcluſiones quibꝰ mediantibꝰ adīue
<
lb
/>
niatur definitio motus vniformiter difformis quo
<
lb
/>
ad ſubiectum.</
s
>
</
p
>
<
p
xml:id
="
N1CCC5
">
<
s
xml:id
="
N1CCC6
"
xml:space
="
preserve
">Prima ↄ̨̨cluſio. </
s
>
<
s
xml:id
="
N1CCC9
"
xml:space
="
preserve
">Motꝰ vniformiṫ dif-
<
lb
/>
formis quo ad ſubiectū nõ bene definit̄̄ iſto modo.
<
lb
/>
</
s
>
<
s
xml:id
="
N1CCCF
"
xml:space
="
preserve
">Motus vniformiter difformis quo ad ſubiectū eſt
<
lb
/>
cuiꝰ oēs partes īmediate ſcḋm extenſionē ſunt īme-
<
lb
/>
diate ſcḋm intenſionē motus ſiue velocitatū ita
<
lb
/>
remiſſiſſimus gradus velocitatis qui eſt in intēſio-
<
lb
/>
ri ſit remiſſiſſimus qui non eſt in remiſſiori illarum
<
lb
/>
duarum partium ſibi immediatarum. </
s
>
<
s
xml:id
="
N1CCDC
"
xml:space
="
preserve
">Probatur
<
lb
/>
hec concluſio: quia pono caſum / ſit vna rota que
<
lb
/>
que mouetur a non gradu vſ ad certum gradum
<
lb
/>
ita a centro eius q̇eſcente vſ ad mediū ſemidia
<
lb
/>
metri ſit motus vniformiter difformis a nõ gradu
<
lb
/>
vſ ad quatuor et a pūcto medio ſemidiametri vſ-
<
lb
/>
ad circūferentiã ſit motus vniformiter difformis </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>