Alvarus, Thomas
,
Liber de triplici motu
,
1509
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<
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Secundi tractatus
"
file
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0139
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n
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139
"/>
miter difformis q̊ ad ſubiectū nõ d3 attendi penes
<
lb
/>
velocitatē pūcti exiſtētis in medio mobilis quãtū
<
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/>
ad lõgitudinē. </
s
>
<
s
xml:id
="
N1D86C
"
xml:space
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preserve
">Ptꝫ hec ↄ̨cluſio ex eodē argumēto.</
s
>
</
p
>
<
p
xml:id
="
N1D86F
">
<
s
xml:id
="
N1D870
"
xml:space
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">Tertia concluſio </
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>
<
s
xml:id
="
N1D873
"
xml:space
="
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">Uelocitas motꝰ vni
<
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formiter difformis quo ad ſubiectū cõmēſurari d3
<
lb
/>
penes gradū mediū totiꝰ latitudinis talis motus
<
lb
/>
vniformiter difformis vbicū fuerit talis gradus
<
lb
/>
ſiue in medio corꝑis ̄tū ad magnitudinē ſiue non
<
lb
/>
(non eſt cura) </
s
>
<
s
xml:id
="
N1D880
"
xml:space
="
preserve
">Probat̄̄ hec cõcluſio / qm̄ ceteri modi
<
lb
/>
cognoſcēdi velocitatē motꝰ vniformiter difformis
<
lb
/>
quo ad ſubiectū ſuperioribꝰ argumētis īprobãtur
<
lb
/>
reſtat / igitur vt penes modum datum cognoſcatur</
s
>
</
p
>
<
p
xml:id
="
N1D889
">
<
s
xml:id
="
N1D88A
"
xml:space
="
preserve
">Quarta cõcluſio. </
s
>
<
s
xml:id
="
N1D88D
"
xml:space
="
preserve
">Uelocitas motꝰ dif-
<
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/>
formiter difformis quo ad ſubiectum cognoſci põt
<
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/>
penes denoīationē partiū quantū ad longitudinē
<
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/>
</
s
>
<
s
xml:id
="
N1D895
"
xml:space
="
preserve
">Intelligēdo ꝑ lõgitudinē diſtantiã a nõ gradu ta-
<
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/>
lis motꝰ vel a g̈du tardiſſimo ſus g̈dus velociores /
<
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/>
vt declaratū eſt in vltimo argumēto. </
s
>
<
s
xml:id
="
N1D89C
"
xml:space
="
preserve
">Probat̄̄ hec
<
lb
/>
ↄ̨cluſio / q2 nõ occurrit alter modꝰ facilior ad cogno
<
lb
/>
ſcendū huiuſmodi velocitatem per denominationē /
<
lb
/>
igr̄ tali modo īueſtiganda eſt motꝰ difformiter dif-
<
lb
/>
formis quo ad ſubiectū velocitas. </
s
>
<
s
xml:id
="
N1D8A7
"
xml:space
="
preserve
">Nec replica fa-
<
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/>
cta de linea giratiua in vltīo argumēto huiꝰ capitꝪ
<
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/>
hãc ↄ̨cluſionē valet vllo pacto infirmare / vt patebit
<
lb
/>
ex ſolutione eiuſdem replice.</
s
>
</
p
>
<
p
xml:id
="
N1D8B0
">
<
s
xml:id
="
N1D8B1
"
xml:space
="
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">Quinta concluſio. </
s
>
<
s
xml:id
="
N1D8B4
"
xml:space
="
preserve
">Probabile eſt ve-
<
lb
/>
locitatē motꝰ difformis quo ad ſubiectū attēdi de-
<
lb
/>
bere penes gradū ſummū.
<
note
position
="
left
"
xlink:href
="
note-0139-01a
"
xlink:label
="
note-0139-01
"
xml:id
="
N1D8CB
"
xml:space
="
preserve
">Opinio hentiſbe
<
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/>
ri.</
note
>
</
s
>
<
s
xml:id
="
N1D8C0
"
xml:space
="
preserve
">Ptꝫ / q2 ad illã opinionē
<
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/>
q̄ eſt hentiſberi nullū incõueniēs ſequit̄̄: īmo oīa ar
<
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/>
gumēta q̄ in eū adducūiur facillime diſſoluūtur.</
s
>
</
p
>
<
p
xml:id
="
N1D8D3
">
<
s
xml:id
="
N1D8D4
"
xml:space
="
preserve
">Sexta cõcluſio. </
s
>
<
s
xml:id
="
N1D8D7
"
xml:space
="
preserve
">Diſtantia punctorū
<
lb
/>
a cētro a q̊ ꝓcedit motꝰ difformis q̊ ad ſubiectū te-
<
lb
/>
net ſe ex ꝑte potētie: et auget ꝓportionē poñe ad re
<
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/>
ſiſtentiã. </
s
>
<
s
xml:id
="
N1D8E0
"
xml:space
="
preserve
">necnõ eidē potētie eſt adiumento. </
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>
<
s
xml:id
="
N1D8E3
"
xml:space
="
preserve
">et ꝑ op-
<
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/>
poſitū ꝓpinq̇tas. </
s
>
<
s
xml:id
="
N1D8E8
"
xml:space
="
preserve
">nec magnitudo aut paruitans a-
<
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/>
liq̇d facit. </
s
>
<
s
xml:id
="
N1D8ED
"
xml:space
="
preserve
">Probat̄̄ facile hec cõcluſio ex deductiõe
<
lb
/>
q̈rti argumēti huiꝰ capitis.
<
note
position
="
left
"
xlink:href
="
note-0139-02a
"
xlink:label
="
note-0139-02
"
xml:id
="
N1D91A
"
xml:space
="
preserve
">correĺ.</
note
>
</
s
>
<
s
xml:id
="
N1D8F7
"
xml:space
="
preserve
">¶ Ex q̊ ſequit̄̄ / nõ ſtat
<
lb
/>
aliquã rotã q̄ mouet̄̄ a tute ſortis vt q̈tuor rare-
<
lb
/>
fieri et maiorari ꝑ ↄ̨tinuã elõgationē pūctoꝝ a cētro
<
lb
/>
et ipſã cõtinuo ab eadē ꝓportiõe moueri ceteris pa
<
lb
/>
ribꝰ. </
s
>
<
s
xml:id
="
N1D902
"
xml:space
="
preserve
">Ptꝫ correlariū hoc, q2 diſtãtia pūctoꝝ. </
s
>
<
s
xml:id
="
N1D905
"
xml:space
="
preserve
">adau-
<
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/>
get ꝓportionē. </
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>
<
s
xml:id
="
N1D90A
"
xml:space
="
preserve
">Similiter dicendū eſt / ſi cõdenſaret̄̄
<
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/>
rota ſorte cõtinuo mouēte a tute vt q̈tuor. </
s
>
<
s
xml:id
="
N1D90F
"
xml:space
="
preserve
">tunc em̄
<
lb
/>
totalis ꝓportio cõtinuo diminuit̄̄ ꝓpṫ deꝑditionē
<
lb
/>
diſtante punctorum a centro.</
s
>
</
p
>
<
p
xml:id
="
N1D920
">
<
s
xml:id
="
N1D921
"
xml:space
="
preserve
">Septima cõcluſio. </
s
>
<
s
xml:id
="
N1D924
"
xml:space
="
preserve
">Propīquitas aut
<
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/>
diſtãtia pūctoꝝ a cētro nichil cõducit ceterꝪ paribꝰ
<
lb
/>
ad velocitatē circūgiratiõis ſiue circuitiõis / qḋ idē
<
lb
/>
eſt. </
s
>
<
s
xml:id
="
N1D92D
"
xml:space
="
preserve
">Probat̄̄ / q2 eq̄ velociter oīa pūcta cõplēt circu-
<
lb
/>
los ſuos / vt ptꝫ ī rota in ſpera lune ſolis, et ſic ↄ̨ñter
<
lb
/>
ꝓcedēdo et eq̈les ãgulos faciūt circa centrū: igr̄ eq̄
<
lb
/>
velociter circueūt / et ꝑ ↄ̨ñs diſtãtia nichil ↄ̨fert
<
note
position
="
left
"
xlink:href
="
note-0139-03a
"
xlink:label
="
note-0139-03
"
xml:id
="
N1D9D4
"
xml:space
="
preserve
">1. correĺ:</
note
>
</
s
>
<
s
xml:id
="
N1D93B
"
xml:space
="
preserve
">¶ Ex
<
lb
/>
q̊ ſequit̄̄ / nū̄ ↄ̨cēdendū eſt ab eq̈libꝰ ꝓportiõibꝰ
<
lb
/>
īeq̈les motꝰ circulares ꝓuenire, aut ab ineq̈libꝰ ꝓ-
<
lb
/>
portiõibꝰ eq̈les circuitiões / vt ſolutio q̈rti argumēti
<
lb
/>
oñdit.
<
note
position
="
left
"
xlink:href
="
note-0139-04a
"
xlink:label
="
note-0139-04
"
xml:id
="
N1D9DA
"
xml:space
="
preserve
">2. correĺ.</
note
>
</
s
>
<
s
xml:id
="
N1D94B
"
xml:space
="
preserve
">¶ Sequit̄̄ ex hac ſolutiõe ſcḋo / ſi in eodem
<
lb
/>
axe ponant̄̄ īfinite rote ↄ̨tinuo mīores et mīores ita
<
lb
/>
diametri prime ſit dupla ad diametrū ſecūde, et
<
lb
/>
ſcḋe ad diametrū tertie, et ſic ↄ̨ñter: et ſortes moue-
<
lb
/>
at oēs illas rotas mediãte illo axe: in īfinitū tarde
<
lb
/>
mouet̄̄ ibi aliqua rota: nichilominꝰ tñ q̄libet rota
<
lb
/>
ita velociter circuit ſicut prima. </
s
>
<
s
xml:id
="
N1D95A
"
xml:space
="
preserve
">Patꝫ prima pars /
<
lb
/>
q2 īfinite modicū circulū deſcribit aliqua illaꝝ ro-
<
lb
/>
tarū in eodē tꝑe: igr̄. </
s
>
<
s
xml:id
="
N1D961
"
xml:space
="
preserve
">Scḋa pars ꝓbat̄̄ / q2 eque cito
<
lb
/>
q̄libet circuitionē ſuã ſicut prima cõplet: igr̄ q̄libet
<
lb
/>
eque velociter circuit ſicut prima. </
s
>
<
s
xml:id
="
N1D968
"
xml:space
="
preserve
">Ite ↄ̨tinuo cuiuſli
<
cb
chead
="
Capitulū ſecundū.
"/>
bet illaꝝ ãguīus deſcriptꝰ circa cētrū eſt eq̈lis ãgu-
<
lb
/>
lo deſcripto a ṗma rota: igr̄ quelibet illaꝝ cõtinuo
<
lb
/>
equaliter circuit cū prima </
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>
<
s
xml:id
="
N1D972
"
xml:space
="
preserve
">Ex quo facile apparet
<
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/>
magnitudo ſiue diſtãtia pūctoꝝ nihil facit ad velo
<
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/>
citatē circuitiõis: ſed bene ad velocitatē motꝰ circu-
<
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/>
laris.
<
note
position
="
right
"
xlink:href
="
note-0139-05a
"
xlink:label
="
note-0139-05
"
xml:id
="
N1D9E0
"
xml:space
="
preserve
">3. correĺ.</
note
>
</
s
>
<
s
xml:id
="
N1D980
"
xml:space
="
preserve
">¶ Sequit̄̄ vlteriꝰ / in caſu p̄dicto nõ ab eadē
<
lb
/>
proportiõe adequate ſortes mouet primam rotã et
<
lb
/>
ſcḋam: ſed a maiori primã quã ſcḋam. </
s
>
<
s
xml:id
="
N1D987
"
xml:space
="
preserve
">q2 diſtantia
<
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/>
pūctoꝝ medioꝝ eſt adiumēto potētie ſortis. </
s
>
<
s
xml:id
="
N1D98C
"
xml:space
="
preserve
">¶ Hic
<
lb
/>
tñ tu aduerte nõ volo dicere / quãlibet illaꝝ rotaꝝ
<
lb
/>
moueri adeq̈te a certa ꝓportiõe: ſed bene q̄libet il-
<
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/>
larū mouet̄̄ a certa ꝓportiõe inadequate. </
s
>
<
s
xml:id
="
N1D995
"
xml:space
="
preserve
">Nec volo
<
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/>
dicere / ̄libet illaꝝ circūgirare ſiue ꝓpriã circuitio
<
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/>
nē efficere a certa ꝓportiõe adeq̊te: ſed bene īadeq̈-
<
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/>
te. </
s
>
<
s
xml:id
="
N1D99E
"
xml:space
="
preserve
">Qḋ ideo dixerim / qm̄ ſi cõcedat̄̄ ſortē potētie vt
<
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/>
4. circūgirare rotã in octuplo minorē prima a cer
<
lb
/>
ta ꝓportiõe adequate cū oporteat talē ꝓportionē
<
lb
/>
eſſe maiorē ꝓportiõe a qua ſortes circūducit primã
<
lb
/>
rotã (cū maior rota magis reſiſtit ſue circūgiratiõi
<
lb
/>
quã mīor) / tã ſeq̄ret̄̄ / ab īeq̈libꝰ ꝓportiõibꝰ equa-
<
lb
/>
les circuitiões ꝓuenirēt qḋ vitare intēdit ſeptīa cõ
<
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/>
cluſio. </
s
>
<
s
xml:id
="
N1D9AF
"
xml:space
="
preserve
">Et ideo in ꝓpoſito ymaginandū eſt de illis
<
lb
/>
rotis ſicut de īfinitis rotis partialibꝰ cõcētricis ro
<
lb
/>
te alicui cuiꝰ ſūt partes. </
s
>
<
s
xml:id
="
N1D9B6
"
xml:space
="
preserve
">Manifeſtū eſt em̄ / q̄libet
<
lb
/>
illaꝝ rotaꝝ eque velociter circuit cū qualꝫ aliarū: et
<
lb
/>
cuiuſlꝫ illaꝝ circuitio ꝓuēit ab eadē ꝓportiõe inade
<
lb
/>
quate ſiue partialiter qm̄ ꝓuenit ab eadē ꝓportiõe
<
lb
/>
a qua circuitio totalis rote efficit̄̄ ſicut em̄ dicere-
<
lb
/>
mus ſortē potētie / vt .4. mouentē põdus reſiſtentie
<
lb
/>
vt .2. velocitate vt .4. mouere quãlibet partē illiꝰ põ
<
lb
/>
deris velocitate vt q̈tuor et a ꝓportione dupla: ſed
<
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/>
hoc īadequate. </
s
>
<
s
xml:id
="
N1D9C9
"
xml:space
="
preserve
">¶ Ad īducēdã octauã ↄ̨cluſionē ſolu
<
lb
/>
tiuam quinti argumenti preſentis queſtiõis pono
<
lb
/>
aliquas ſuppoſitiones geometricas.</
s
>
</
p
>
<
p
xml:id
="
N1D9E6
">
<
s
xml:id
="
N1D9E7
"
xml:space
="
preserve
">Prima ſuppoſitio </
s
>
<
s
xml:id
="
N1D9EA
"
xml:space
="
preserve
">Si ſūt due quãtita
<
lb
/>
tes equalis ꝓfunditatis vniformiter, et eq̄ late vni-
<
lb
/>
formiter, et vna lõgior allera in q̈cū ꝓportiõe eſt
<
lb
/>
lõgior in eadē eſt maior. </
s
>
<
s
xml:id
="
N1D9F3
"
xml:space
="
preserve
">Exēplū / vt ſi ſit vnū pedale
<
lb
/>
pedaliter latū, et pedaliter ꝓfundū, et ſit alia quã-
<
lb
/>
titas eq̄ ꝓfunda et eq̄ lata vniformiter, et in duplo
<
lb
/>
longior: manifeſtū eſt / illa eſt in duplo maior q2
<
lb
/>
cõtinet duo pedalia. </
s
>
<
s
xml:id
="
N1D9FE
"
xml:space
="
preserve
">Probat̄̄ hec ſuppoſitio facile /
<
lb
/>
qm̄ cū tales latitudines ſint vniformes in latitudī
<
lb
/>
ne et ꝓfūditate illud qḋ maior plꝰ cõtinet ē eque la-
<
lb
/>
tū et eque ꝓfundū vniformiter ſicut mīor: ergo alia
<
lb
/>
quãtitas maior cõtinet totã minorē et illud vltra: et
<
lb
/>
illḋ ē eq̄ magnū adeq̈te ſicut tã lõga ꝑs mīoris quã
<
lb
/>
tatis: igr̄ in q̈cū ꝓportiõe lõgitudo maioris ex
<
lb
/>
cedit longitudinem minoris in eadeꝫ proportione
<
lb
/>
magnitudo maioris excedit magnitudinis mīoris</
s
>
</
p
>
<
p
xml:id
="
N1DA11
">
<
s
xml:id
="
N1DA12
"
xml:space
="
preserve
">Secūda ſuppoſitio </
s
>
<
s
xml:id
="
N1DA15
"
xml:space
="
preserve
">Si due quantita
<
lb
/>
tes ineq̈les ſint eq̄ profunde vniformiter et eq̄ longe
<
lb
/>
vniformiter et vna latior altera: in q̈cū ꝓportiõe
<
lb
/>
vna eſt latior in eadē eſt maior. </
s
>
<
s
xml:id
="
N1DA1E
"
xml:space
="
preserve
">Exēplū / vt ſi ſit vna
<
lb
/>
quãtitas bipedalis ſcḋm lõgitudinē pedalis ſcḋ3 la
<
lb
/>
titudinē et ꝓfūditatē vniformiter et alia vniformiṫ
<
lb
/>
eque lõga et eq̄ ꝓfunda et ī ſexquialtero latior: erit
<
lb
/>
ī ſexquialtero maior. </
s
>
<
s
xml:id
="
N1DA29
"
xml:space
="
preserve
">Ptꝫ hec ſuppoſitio ſicut ṗor.</
s
>
</
p
>
<
p
xml:id
="
N1DA2C
">
<
s
xml:id
="
N1DA2D
"
xml:space
="
preserve
">Tertia ſuppoſitio </
s
>
<
s
xml:id
="
N1DA30
"
xml:space
="
preserve
">Si ſint due quan-
<
lb
/>
titates eq̄ longe eque late vniformiter: et vna ſit in
<
lb
/>
aliq̈ ꝓqortione ꝓfundior altera: in eadē ꝓportione
<
lb
/>
in q̈ eſt ꝓfundior ē maior. </
s
>
<
s
xml:id
="
N1DA39
"
xml:space
="
preserve
">Exemplū / vt ſi ſit vna ma-
<
lb
/>
gnitudo bipedaliter lõga pedaliter lata et pedali-
<
lb
/>
ter ꝓfunda et vna alia bipedaliter lõga et pedaliter
<
lb
/>
lata et ſemipedaliter profunda / tūc dico / alia quã
<
lb
/>
titas maior in ea ꝓportione in q̈ eſt ꝓfundior ī ea ē
<
lb
/>
maior puta in dupla. </
s
>
<
s
xml:id
="
N1DA46
"
xml:space
="
preserve
">Patet etiam hec ſicut prima
<
lb
/>
</
s
>
<
s
xml:id
="
N1DA4A
"
xml:space
="
preserve
">His ſuppoſitionibus premiſſis ſit hec.</
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>