Alvarus, Thomas
,
Liber de triplici motu
,
1509
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[Figure 1]
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[Figure 9]
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[Figure 10]
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[Figure 11]
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[Figure 12]
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[Figure 13]
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[Figure 14]
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Secundi tractatus
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0139
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139
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miter difformis q̊ ad ſubiectū nõ d3 attendi penes
<
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velocitatē pūcti exiſtētis in medio mobilis quãtū
<
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ad lõgitudinē. </
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>
<
s
xml:id
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N1D86C
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xml:space
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preserve
">Ptꝫ hec ↄ̨cluſio ex eodē argumēto.</
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</
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<
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="
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<
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<
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N1D873
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xml:space
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">Uelocitas motꝰ vni
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formiter difformis quo ad ſubiectū cõmēſurari d3
<
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penes gradū mediū totiꝰ latitudinis talis motus
<
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/>
vniformiter difformis vbicū fuerit talis gradus
<
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/>
ſiue in medio corꝑis ̄tū ad magnitudinē ſiue non
<
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(non eſt cura) </
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>
<
s
xml:id
="
N1D880
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xml:space
="
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">Probat̄̄ hec cõcluſio / qm̄ ceteri modi
<
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cognoſcēdi velocitatē motꝰ vniformiter difformis
<
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quo ad ſubiectū ſuperioribꝰ argumētis īprobãtur
<
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reſtat / igitur vt penes modum datum cognoſcatur</
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>
</
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>
<
p
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="
N1D889
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<
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">Quarta cõcluſio. </
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<
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xml:id
="
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xml:space
="
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">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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</
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>
<
s
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="
N1D895
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xml:space
="
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">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. </
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>
<
s
xml:id
="
N1D89C
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xml:space
="
preserve
">Probat̄̄ hec
<
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ↄ̨cluſio / q2 nõ occurrit alter modꝰ facilior ad cogno
<
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ſcendū huiuſmodi velocitatem per denominationē /
<
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/>
igr̄ tali modo īueſtiganda eſt motꝰ difformiter dif-
<
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formis quo ad ſubiectū velocitas. </
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>
<
s
xml:id
="
N1D8A7
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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
<
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ex ſolutione eiuſdem replice.</
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>
</
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>
<
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<
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>
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xml:space
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">Probabile eſt ve-
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locitatē motꝰ difformis quo ad ſubiectū attēdi de-
<
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bere penes gradū ſummū.
<
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position
="
left
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xlink:href
="
note-0139-01a
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note-0139-01
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xml:id
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xml:space
="
preserve
">Opinio hentiſbe
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ri.</
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>
</
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<
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="
N1D8C0
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xml:space
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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.</
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>
</
p
>
<
p
xml:id
="
N1D8D3
">
<
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xml:id
="
N1D8D4
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xml:space
="
preserve
">Sexta cõcluſio. </
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>
<
s
xml:id
="
N1D8D7
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xml:space
="
preserve
">Diſtantia punctorū
<
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a cētro a q̊ ꝓcedit motꝰ difformis q̊ ad ſubiectū te-
<
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net ſe ex ꝑte potētie: et auget ꝓportionē poñe ad re
<
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ſiſtentiã. </
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>
<
s
xml:id
="
N1D8E0
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xml:space
="
preserve
">necnõ eidē potētie eſt adiumento. </
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<
s
xml:id
="
N1D8E3
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xml:space
="
preserve
">et ꝑ op-
<
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poſitū ꝓpinq̇tas. </
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>
<
s
xml:id
="
N1D8E8
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xml:space
="
preserve
">nec magnitudo aut paruitans a-
<
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liq̇d facit. </
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>
<
s
xml:id
="
N1D8ED
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xml:space
="
preserve
">Probat̄̄ facile hec cõcluſio ex deductiõe
<
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q̈rti argumēti huiꝰ capitis.
<
note
position
="
left
"
xlink:href
="
note-0139-02a
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xlink:label
="
note-0139-02
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xml:id
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xml:space
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">correĺ.</
note
>
</
s
>
<
s
xml:id
="
N1D8F7
"
xml:space
="
preserve
">¶ Ex q̊ ſequit̄̄ / nõ ſtat
<
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aliquã rotã q̄ mouet̄̄ a tute ſortis vt q̈tuor rare-
<
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/>
fieri et maiorari ꝑ ↄ̨tinuã elõgationē pūctoꝝ a cētro
<
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/>
et ipſã cõtinuo ab eadē ꝓportiõe moueri ceteris pa
<
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/>
ribꝰ. </
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>
<
s
xml:id
="
N1D902
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xml:space
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">Ptꝫ correlariū hoc, q2 diſtãtia pūctoꝝ. </
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>
<
s
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="
N1D905
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="
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">adau-
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get ꝓportionē. </
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>
<
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">Similiter dicendū eſt / ſi cõdenſaret̄̄
<
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rota ſorte cõtinuo mouēte a tute vt q̈tuor. </
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>
<
s
xml:id
="
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xml:space
="
preserve
">tunc em̄
<
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totalis ꝓportio cõtinuo diminuit̄̄ ꝓpṫ deꝑditionē
<
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diſtante punctorum a centro.</
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>
</
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>
<
p
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="
N1D920
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<
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="
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">Septima cõcluſio. </
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>
<
s
xml:id
="
N1D924
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xml:space
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">Propīquitas aut
<
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diſtãtia pūctoꝝ a cētro nichil cõducit ceterꝪ paribꝰ
<
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/>
ad velocitatē circūgiratiõis ſiue circuitiõis / qḋ idē
<
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eſt. </
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>
<
s
xml:id
="
N1D92D
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xml:space
="
preserve
">Probat̄̄ / q2 eq̄ velociter oīa pūcta cõplēt circu-
<
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los ſuos / vt ptꝫ ī rota in ſpera lune ſolis, et ſic ↄ̨ñter
<
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/>
ꝓcedēdo et eq̈les ãgulos faciūt circa centrū: igr̄ eq̄
<
lb
/>
velociter circueūt / et ꝑ ↄ̨ñs diſtãtia nichil ↄ̨fert
<
note
position
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left
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xlink:href
="
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="
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xml:space
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">1. correĺ:</
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>
</
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<
s
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="
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xml:space
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">¶ Ex
<
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q̊ ſequit̄̄ / nū̄ ↄ̨cēdendū eſt ab eq̈libꝰ ꝓportiõibꝰ
<
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/>
īeq̈les motꝰ circulares ꝓuenire, aut ab ineq̈libꝰ ꝓ-
<
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portiõibꝰ eq̈les circuitiões / vt ſolutio q̈rti argumēti
<
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oñdit.
<
note
position
="
left
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xlink:href
="
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="
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xml:id
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xml:space
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">2. correĺ.</
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>
</
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>
<
s
xml:id
="
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xml:space
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">¶ Sequit̄̄ ex hac ſolutiõe ſcḋo / ſi in eodem
<
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/>
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-
<
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/>
at oēs illas rotas mediãte illo axe: in īfinitū tarde
<
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/>
mouet̄̄ ibi aliqua rota: nichilominꝰ tñ q̄libet rota
<
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/>
ita velociter circuit ſicut prima. </
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>
<
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xml:id
="
N1D95A
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xml:space
="
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">Patꝫ prima pars /
<
lb
/>
q2 īfinite modicū circulū deſcribit aliqua illaꝝ ro-
<
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tarū in eodē tꝑe: igr̄. </
s
>
<
s
xml:id
="
N1D961
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xml:space
="
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">Scḋa pars ꝓbat̄̄ / q2 eque cito
<
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q̄libet circuitionē ſuã ſicut prima cõplet: igr̄ q̄libet
<
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eque velociter circuit ſicut prima. </
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>
<
s
xml:id
="
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xml:space
="
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">Ite ↄ̨tinuo cuiuſli
<
cb
chead
="
Capitulū ſecundū.
"/>
bet illaꝝ ãguīus deſcriptꝰ circa cētrū eſt eq̈lis ãgu-
<
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/>
lo deſcripto a ṗma rota: igr̄ quelibet illaꝝ cõtinuo
<
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equaliter circuit cū prima </
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>
<
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xml:id
="
N1D972
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xml:space
="
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">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
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">3. correĺ.</
note
>
</
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>
<
s
xml:id
="
N1D980
"
xml:space
="
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">¶ Sequit̄̄ vlteriꝰ / in caſu p̄dicto nõ ab eadē
<
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proportiõe adequate ſortes mouet primam rotã et
<
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ſcḋam: ſed a maiori primã quã ſcḋam. </
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>
<
s
xml:id
="
N1D987
"
xml:space
="
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">q2 diſtantia
<
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pūctoꝝ medioꝝ eſt adiumēto potētie ſortis. </
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>
<
s
xml:id
="
N1D98C
"
xml:space
="
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">¶ Hic
<
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tñ tu aduerte nõ volo dicere / quãlibet illaꝝ rotaꝝ
<
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moueri adeq̈te a certa ꝓportiõe: ſed bene q̄libet il-
<
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/>
larū mouet̄̄ a certa ꝓportiõe inadequate. </
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>
<
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. </
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>
<
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xml:id
="
N1D99E
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xml:space
="
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">Qḋ ideo dixerim / qm̄ ſi cõcedat̄̄ ſortē potētie vt
<
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4. circūgirare rotã in octuplo minorē prima a cer
<
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/>
ta ꝓportiõe adequate cū oporteat talē ꝓportionē
<
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/>
eſſe maiorē ꝓportiõe a qua ſortes circūducit primã
<
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rotã (cū maior rota magis reſiſtit ſue circūgiratiõi
<
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/>
quã mīor) / tã ſeq̄ret̄̄ / ab īeq̈libꝰ ꝓportiõibꝰ equa-
<
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/>
les circuitiões ꝓuenirēt qḋ vitare intēdit ſeptīa cõ
<
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cluſio. </
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>
<
s
xml:id
="
N1D9AF
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xml:space
="
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">Et ideo in ꝓpoſito ymaginandū eſt de illis
<
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/>
rotis ſicut de īfinitis rotis partialibꝰ cõcētricis ro
<
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/>
te alicui cuiꝰ ſūt partes. </
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>
<
s
xml:id
="
N1D9B6
"
xml:space
="
preserve
">Manifeſtū eſt em̄ / q̄libet
<
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/>
illaꝝ rotaꝝ eque velociter circuit cū qualꝫ aliarū: et
<
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/>
cuiuſlꝫ illaꝝ circuitio ꝓuēit ab eadē ꝓportiõe inade
<
lb
/>
quate ſiue partialiter qm̄ ꝓuenit ab eadē ꝓportiõe
<
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/>
a qua circuitio totalis rote efficit̄̄ ſicut em̄ dicere-
<
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mus ſortē potētie / vt .4. mouentē põdus reſiſtentie
<
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/>
vt .2. velocitate vt .4. mouere quãlibet partē illiꝰ põ
<
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/>
deris velocitate vt q̈tuor et a ꝓportione dupla: ſed
<
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/>
hoc īadequate. </
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>
<
s
xml:id
="
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"
xml:space
="
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">¶ Ad īducēdã octauã ↄ̨cluſionē ſolu
<
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/>
tiuam quinti argumenti preſentis queſtiõis pono
<
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/>
aliquas ſuppoſitiones geometricas.</
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>
</
p
>
<
p
xml:id
="
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">
<
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xml:id
="
N1D9E7
"
xml:space
="
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">Prima ſuppoſitio </
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>
<
s
xml:id
="
N1D9EA
"
xml:space
="
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">Si ſūt due quãtita
<
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/>
tes equalis ꝓfunditatis vniformiter, et eq̄ late vni-
<
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/>
formiter, et vna lõgior allera in q̈cū ꝓportiõe eſt
<
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/>
lõgior in eadē eſt maior. </
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>
<
s
xml:id
="
N1D9F3
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xml:space
="
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">Exēplū / vt ſi ſit vnū pedale
<
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/>
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
<
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/>
cõtinet duo pedalia. </
s
>
<
s
xml:id
="
N1D9FE
"
xml:space
="
preserve
">Probat̄̄ hec ſuppoſitio facile /
<
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/>
qm̄ cū tales latitudines ſint vniformes in latitudī
<
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/>
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
<
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/>
illḋ ē eq̄ magnū adeq̈te ſicut tã lõga ꝑs mīoris quã
<
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/>
tatis: igr̄ in q̈cū ꝓportiõe lõgitudo maioris ex
<
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/>
cedit longitudinem minoris in eadeꝫ proportione
<
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/>
magnitudo maioris excedit magnitudinis mīoris</
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>
</
p
>
<
p
xml:id
="
N1DA11
">
<
s
xml:id
="
N1DA12
"
xml:space
="
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">Secūda ſuppoſitio </
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>
<
s
xml:id
="
N1DA15
"
xml:space
="
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">Si due quantita
<
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/>
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. </
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>
<
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
>