Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Secundi tractatus
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137
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laris eſt ita velox circulatio ſicut antea vt conclu-
<
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datur maior extremitas de minori. </
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>
<
s
xml:id
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N1D4E5
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xml:space
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preserve
">Quãuis enim
<
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idē ſit circulatio et motus circularis nõ tamen pe-
<
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nes idem iudicari debet velocitas circuitiõis et ve-
<
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locitas motus localis circularis / vt poſtea dicetur.</
s
>
</
p
>
<
p
xml:id
="
N1D500
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<
s
xml:id
="
N1D501
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xml:space
="
preserve
">Sed ↄ̨̨tra. </
s
>
<
s
xml:id
="
N1D504
"
xml:space
="
preserve
">Q2 ſi illa ſolutio eſſet bona
<
lb
/>
ſeq̄ret̄̄ / ab eadē ꝓportione potētie ad ſuã reſiſtē-
<
lb
/>
tiã ꝓuenirēt īequales motꝰ, et equales circuitiones /
<
lb
/>
qḋ eſt falſū. </
s
>
<
s
xml:id
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N1D50D
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xml:space
="
preserve
">Seq̄la ptꝫ facile ex ſolutiõe. </
s
>
<
s
xml:id
="
N1D510
"
xml:space
="
preserve
">Poſitum
<
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eſt em̄ / poña moueret ab eodē conamine rotã cõti
<
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/>
nuo equaliter reſiſtentē / et dictū eſt / a tali ꝓporti-
<
lb
/>
one ꝓueniebãt īequales motꝰ. </
s
>
<
s
xml:id
="
N1D519
"
xml:space
="
preserve
">eq̈les aūt circuitiões
<
lb
/>
<
note
position
="
left
"
xlink:href
="
note-0137-01a
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xlink:label
="
note-0137-01
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xml:id
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N1D545
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xml:space
="
preserve
">Dicitur.</
note
>
</
s
>
<
s
xml:id
="
N1D523
"
xml:space
="
preserve
">¶ Dices forte / iã / tūc nõ eſt eadē ꝓportio īter mo-
<
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/>
uēs et mobile ſed eſt mīor. </
s
>
<
s
xml:id
="
N1D528
"
xml:space
="
preserve
">Sed hoc nõ põt dici qm̄
<
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/>
volo / poña ſit naturalis: et maneat in rota tanta
<
lb
/>
reſiſtētia ſicut ãtea erat vt poſitū eſt. </
s
>
<
s
xml:id
="
N1D52F
"
xml:space
="
preserve
">Et ſi hoc non
<
lb
/>
admittas equa lance currit ↄ̨tra te argumentū de
<
lb
/>
circuitiõibꝰ q2 tūc ex īequalibꝰ ꝓportiõibꝰ ꝓuenirēt
<
lb
/>
equales circuitiões et īequales motꝰ / qḋ tã incõueni
<
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/>
ens videt̄̄ ſicut reliquū. </
s
>
<
s
xml:id
="
N1D53A
"
xml:space
="
preserve
">¶ Et ideo dices forte / vt di-
<
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/>
cūt alii nõ eſt incõueniēs ab eq̈li ꝓportiõe eq̈les
<
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/>
circuitiões īequales autē motꝰ ꝓuenire / vt dictū eſt.</
s
>
</
p
>
<
p
xml:id
="
N1D54B
">
<
s
xml:id
="
N1D54C
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xml:space
="
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">Sed ↄ̨̨tra. </
s
>
<
s
xml:id
="
N1D54F
"
xml:space
="
preserve
">Q2 hoc dato iã deſtruit̄̄ fū
<
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/>
damentū totiꝰ materie: et iã pari facilitate ꝓteruus
<
lb
/>
phiſicꝰ cõcederet a ꝓportiõe dupla, et a ꝓportio-
<
lb
/>
ne quadrupla equales velocitates nate ſunt ꝓueni
<
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/>
re. </
s
>
<
s
xml:id
="
N1D55A
"
xml:space
="
preserve
">et multa ſimilia q̄ ſunt abſona calculatori pḣo
<
lb
/>
<
note
position
="
left
"
xlink:href
="
note-0137-02a
"
xlink:label
="
note-0137-02
"
xml:id
="
N1D595
"
xml:space
="
preserve
">Reſpon
<
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ſio cõis.</
note
>
</
s
>
<
s
xml:id
="
N1D564
"
xml:space
="
preserve
">¶ Qua ꝓpter dicūt alii ad argumētū concedendo
<
lb
/>
conſequentiã, et negãdo falſitatē ↄ̨ñtis: et ad pun-
<
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/>
ctū ꝓbationis negant / talis rota ãtea et poſt mo
<
lb
/>
uebat̄̄ ab equali ꝓportione / q2 vt dicūt magnitudo
<
lb
/>
rote tenet ſe ex ꝑte poñe. </
s
>
<
s
xml:id
="
N1D56F
"
xml:space
="
preserve
">Mõ manēte eodē conamīe
<
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/>
poñe rota tardiꝰ mouet̄̄ et a minore ꝓportione quia
<
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/>
ãtea magnitudo iṗiꝰ rote iuuabat poñaꝫ ad deſcri
<
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/>
bendã lineã. </
s
>
<
s
xml:id
="
N1D578
"
xml:space
="
preserve
">Mõ vero cū ipſa rota cõtinuo efficiat̄̄
<
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/>
minor nõ ita iuuat poñam ſicut añ </
s
>
<
s
xml:id
="
N1D57D
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xml:space
="
preserve
">Qḋ facile exem
<
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/>
plo declarart põt. </
s
>
<
s
xml:id
="
N1D582
"
xml:space
="
preserve
">Manifeſtū eſt em̄ / ſi in ſuꝑficie
<
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/>
alicuiꝰ rote addat̄̄ aliq̇d eiuſdē ſpeciei cõtinuatū cū
<
lb
/>
rota nulliꝰ grauitatis: et ſortes giret totū illud ab
<
lb
/>
eodē conamine illa totalis rota velociꝰ mouet̄̄ quã
<
lb
/>
mouebat̄̄ ãtea pars eiꝰ et tñ poña manet eq̈lis et re-
<
lb
/>
ſiſtentia rote: ſed totalis proportio eſt maior quia
<
lb
/>
iuuatur ibi poña ſortis a magnitudine rote.</
s
>
</
p
>
<
p
xml:id
="
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<
s
xml:id
="
N1D59E
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xml:space
="
preserve
">Sed ↄ̨̨tra. </
s
>
<
s
xml:id
="
N1D5A1
"
xml:space
="
preserve
">Q2 magnitudo tenet ſe ex
<
lb
/>
parte reſiſtētie: g̊ nõ ex parte potētie etiã manente
<
lb
/>
eq̈li g̈uitate oīno. </
s
>
<
s
xml:id
="
N1D5A8
"
xml:space
="
preserve
">Probat̄̄ añs de orbe / qui maio-
<
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/>
ratur ꝑ rarefactionē quovſ fiat ſpera ſolida qui
<
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/>
tūc tardiꝰ mouet̄̄ quã qñ erat minor / vt patꝫ ex ſcḋa
<
lb
/>
replica huiꝰ quarti argumēti.
<
note
position
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left
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xlink:href
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note-0137-03a
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xlink:label
="
note-0137-03
"
xml:id
="
N1D5DB
"
xml:space
="
preserve
">Dicitur.</
note
>
</
s
>
<
s
xml:id
="
N1D5B6
"
xml:space
="
preserve
">¶ Dices ſicut dicēdū
<
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/>
eſt / nec magnitudo, nec paruitas in talibꝰ tenet
<
lb
/>
ſe ex parte poñe vt ſatis ꝓbat replica: ſed diſtãtia
<
lb
/>
pūcti a cētro penes cuiꝰ motū d3 attēdi velocitas to
<
lb
/>
tiꝰ mobilis puta ipſiꝰ pūcti ī q̊ eſt g̈dꝰ mediꝰ totiꝰ la-
<
lb
/>
titudīs motꝰ tenet ſe ex ꝑte poñe. </
s
>
<
s
xml:id
="
N1D5C3
"
xml:space
="
preserve
">CeterꝪ em̄ paribꝰ
<
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/>
iuuat poñaꝫ ad velociꝰ deſcribēdū lineã / ꝙ̄ deſcribit
<
lb
/>
qñ recedit a cētro: et ꝑ contrariū iuuat ad deſcribē-
<
lb
/>
dam tardiꝰ qñ magis accedit ad centrū a quo exori
<
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/>
tur motus. </
s
>
<
s
xml:id
="
N1D5CE
"
xml:space
="
preserve
">Et ſic dico / qñ rota rarefit verſus cir-
<
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/>
cunferentiam mouente circūferentia: tota ꝓportio
<
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/>
efficitur maior, et quando condenſatur ordine con-
<
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/>
uerſo tota ꝓportio efficitur minor.</
s
>
</
p
>
<
p
xml:id
="
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<
s
xml:id
="
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xml:space
="
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">Sed ↄ̨̨tra </
s
>
<
s
xml:id
="
N1D5E5
"
xml:space
="
preserve
">Q2 iſta ſolutio nõ ſatiſfacit
<
lb
/>
adhuc em̄ ſequit̄̄ / ab īeq̈libꝰ ꝓportiõibꝰ eq̈les cir-
<
lb
/>
cuitiões ꝓueniūt / qḋ eſt īpoſſibile. </
s
>
<
s
xml:id
="
N1D5EC
"
xml:space
="
preserve
">Ptꝫ ↄ̨ña / q2 ſorte
<
lb
/>
cū eq̈li cõamīe ↄ̨tinuo girante ſiue rota rarefiat ſi-
<
lb
/>
ue ↄ̨dēſet̄̄ ipſe eque velociter ↄ̨tinuo circuit et tñ ꝑ te
<
lb
/>
ꝓportio eſt continuo maior vel minor: igr̄ ꝓpoſitū.</
s
>
</
p
>
<
cb
chead
="
Capitulū ſecundū.
"/>
<
p
xml:id
="
N1D5F7
">
<
s
xml:id
="
N1D5F8
"
xml:space
="
preserve
">Quīto ↄ̨̨tra eandē partē arguit̄̄ ſic / ali
<
lb
/>
q̇s motꝰ eſt vniformiṫ difformis q̊ ad ſubiectū: et tñ
<
lb
/>
eiꝰ velocitas nõ corrñdet g̈dui medio: igr̄. </
s
>
<
s
xml:id
="
N1D5FF
"
xml:space
="
preserve
">Añs ꝓba
<
lb
/>
tur et ſuppono / rarefactio ſit motꝰ localis diffor-
<
lb
/>
mis q̊ ad ſubiectū. </
s
>
<
s
xml:id
="
N1D606
"
xml:space
="
preserve
">q̊ ſuppoſito pono / ſint duo pe-
<
lb
/>
dalia ſcḋm oēm dimēſionē puta a.b. / et volo / a ra-
<
lb
/>
refiat vniformiṫ quovſ efficiat̄̄ in duplo longiꝰ et
<
lb
/>
in duplo latiꝰ vniformiṫ, et b. rarefiat vniformiter
<
lb
/>
q̊vſ efficiat̄̄ in ſexq̇altero lõgiꝰ, et in ſexq̇altero la
<
lb
/>
tius vniformiṫ ita a. in fine ſit vnū q̈dratū cuiꝰ co
<
lb
/>
ſta ſit dupla ad coſtã eiuſdē in prīcipio rarefactõis
<
lb
/>
et b. ſit aliud q̈dratū cuiꝰ coſta in fine rarefactionis
<
lb
/>
ſit ſexq̇altera ad coſtã eiꝰ in prīcipio rarefactiõis / q̊
<
lb
/>
poſito ſic argr̄: ſi ille motꝰ q̊ mouet̄̄ a. et etiã q̊ mouet̄̄
<
lb
/>
b. debeãt ↄ̨mēſurari penes pūctū mediū / ſequit̄̄ / a
<
lb
/>
adeq̈te in duplo velociꝰ moueret̄̄ quã b. / ſed ↄ̨ñs eſt
<
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/>
falſum: igitur illud ex quo ſequitur. </
s
>
<
s
xml:id
="
N1D621
"
xml:space
="
preserve
">Seq̄la ꝓbatur /
<
lb
/>
quia pūctus medius ipſius a. in toto illo tempore
<
lb
/>
rarefactionis pertrãſibit vnū ſemipedale q2 pūctꝰ
<
lb
/>
extremius mouet̄̄ ꝑ pedale: et pūctus medius ipſius
<
lb
/>
b. mouet̄̄ ꝑ quartã pedalis cū pūctꝰ extremꝰ eiuſdeꝫ
<
lb
/>
b. moueat̄̄ ꝑ ſemipedale: ſed ſemipedalis ad quar-
<
lb
/>
tã pedalis eſt ꝓportio dupla / vt ptꝫ: igitur in duplo
<
lb
/>
velociꝰ mouet̄̄ a. quã b. / qḋ fuit ꝓbãdū. </
s
>
<
s
xml:id
="
N1D632
"
xml:space
="
preserve
">Sed falſitas
<
lb
/>
ↄ̨ñtis arguitur ſuppoſita illa concluſione geome-
<
lb
/>
trica vcꝫ ſemꝑ quadrata ꝑfecta equalis craſſitu-
<
lb
/>
dinis ſe habent in proportione duplicata ad ꝓpor
<
lb
/>
tionē ſuarū cõſtarū / vt poſtea dicetur ī capitulo de
<
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/>
augmentatione. </
s
>
<
s
xml:id
="
N1D63F
"
xml:space
="
preserve
">ſi vero ſint vndiqua quadrata
<
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/>
ꝑfecta tunc ſe habēt in ꝓportione triplicata ad pro
<
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/>
portionē ſuarū coſtarū. </
s
>
<
s
xml:id
="
N1D646
"
xml:space
="
preserve
">Quo ſuppoſito ſic arguit̄̄ /
<
lb
/>
pedale a. in duplo ſuprabipartiente quintas velo
<
lb
/>
cius rarefit quã pedale b. et ipſa rarefactio eſt motꝰ
<
lb
/>
localis vt ſuppoſitū eſt: ergo in duplo ſuprabipar
<
lb
/>
tiente quintas velocius mouetur a. quã b. / et per cõ-
<
lb
/>
ſequēs nõ in duplo adequate / quod fuit probandū.
<
lb
/>
</
s
>
<
s
xml:id
="
N1D654
"
xml:space
="
preserve
">Conſequentia apparet, et arguitur maior / quia pe
<
lb
/>
dale a. efficitur quadruplū in fine rarefactionis ad
<
lb
/>
ipſum in principio quia in principio rarefactionis
<
lb
/>
coſte ipſius a. ad coſtam eius in fine rarefactionis
<
lb
/>
eſt proportio dupla cū ceteris poſitis in caſu: ergo
<
lb
/>
ipſius quadrati a. in fine ad ipſum in principio eſt
<
lb
/>
proportio quadrupla que eſt duplicata proportio
<
lb
/>
coſtarū, et antea erat illud pedale adequate: ergo
<
lb
/>
acquiſiuit tria pedalia: et aliud puta b. acquiſiuit
<
lb
/>
pedale cum quarta preciſe: igitur quantitatis ac-
<
lb
/>
acquiſite ipſi a. ad quãtitatē acquiſitã ipſi b. eſt pro
<
lb
/>
portio dupla ſuꝑbipartiēs q̇ntas: et tãta ē ꝓportio
<
lb
/>
rarefactionis ipſius a. ad rarefactionē ipſiꝰ b. igit̄̄
<
lb
/>
</
s
>
<
s
xml:id
="
N1D670
"
xml:space
="
preserve
">Sed iã ꝓbo / b. acq̇ſiuit pedale cū quarta q2 coſte
<
lb
/>
ipſiꝰ b. in fine ad coſtã eiuſdē in prīcipio rarefactio
<
lb
/>
nis eſt ꝓportio ſexq̇altera. </
s
>
<
s
xml:id
="
N1D677
"
xml:space
="
preserve
">g̊ totiꝰ quadrati b. in fi-
<
lb
/>
ne ad ipſū in prīcipio eſt ꝓportio dupla ſexquiq̈rta
<
lb
/>
q̄ eſt dupla ad ſexq̇alterã. </
s
>
<
s
xml:id
="
N1D67E
"
xml:space
="
preserve
">Ptꝫ ↄ̨ña ex ſuppoſitione
<
lb
/>
et antea b. erat pedale: g̊ acq̇ſiuit pedale cū quarta /
<
lb
/>
qḋ fuit ꝓbandū. </
s
>
<
s
xml:id
="
N1D685
"
xml:space
="
preserve
">Simile argumētū poſſet fieri de ra
<
lb
/>
refactione duarū ſperarū ſolidarū equaliū in ṗnci
<
lb
/>
pio rarefactiõis: et in fine ita ſe habētiū diametri
<
lb
/>
vnius ad diameirum alterius eſſet ꝓportio dupla.</
s
>
</
p
>
<
p
xml:id
="
N1D68E
">
<
s
xml:id
="
N1D68F
"
xml:space
="
preserve
">Sexto prīcipaliṫ arguit̄̄ hoc ↄ̨̨tra ter
<
lb
/>
tiã ꝑtē q̄ſtionis vcꝫ / debet attēdi motꝰ localis dif-
<
lb
/>
formis velocitas quo ad ſubiectū penes reductiõeꝫ
<
lb
/>
ad vniformitatē. </
s
>
<
s
xml:id
="
N1D698
"
xml:space
="
preserve
">q2 motus circularis in ſubiecto cir
<
lb
/>
culari nõ p̄t reduci ad vniformitatē: igitur nõ debet
<
lb
/>
attendi penes reductionē ad vniformitatē.
<
note
position
="
right
"
xlink:href
="
note-0137-04a
"
xlink:label
="
note-0137-04
"
xml:id
="
N1D73D
"
xml:space
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matio.</
note
>
</
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<
s
xml:id
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N1D6A4
"
xml:space
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preserve
">¶ Et cõ-
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firmatur / q2 ſi reduceretur ad vniformitateꝫ motus
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circularis alicuiꝰ rote a non gradu vſ ad octauū
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vel oporteret reducēdo ab aliqua parte capere ali </
s
>
</
p
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</
div
>
</
div
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</
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>
</
div
>
</
text
>
</
echo
>