Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Secundi tractatus
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octauas / ↄ̨ñs eſt motus eaꝝ ſe habere in ꝓportione
<
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ſubtripla ad ꝓportionē triplã ſuꝑtripartiētē octa
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nas / vt ptꝫ ex ↄ̨cluſiõe: et talis eſt ꝓportio ſexq̇alte-
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ra / vt oſtenſū eſt in ſcḋo correlario octaue ↄ̨cluſiõis
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huiꝰ capitis / igr̄ ꝓpoſitū: de ꝓportiõe autē ſperaꝝ et
<
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de motuū eaꝝ ꝓportiõe videas theodoſiū deſperꝪ et
<
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pulchrã doctinã necnõ ſubtile artificiū cõcluſionū
<
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qua in hac materia thomas brauardibꝰ et in capi-
<
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/>
tulo quarto et vltimo tractatꝰ ꝓportionū / quas edi
<
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dit mathematico apparatu īducit: his poſitis ſit.</
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<
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xml:space
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onē. </
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>
<
s
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N1DC2B
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xml:space
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preserve
">Quēadmodū ꝓbabile eſt velocitatē motus de
<
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quo eſt p̄ſens inq̇ſitio attēdi debere penes lineã de-
<
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ſcriptã a pūcto in quo eſt g̈dus mediꝰ aut penes re-
<
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/>
ductionē ad vniformitatē denoīatiõis: ita ꝓbile eſt
<
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/>
talē motū attēdi debere penes lineã a pūcto velo-
<
lb
/>
ciſſime moto deſcriptã ſiue talis punctꝰ velociſſime
<
lb
/>
motꝰ ſit verꝰ ſiue ymaginariꝰ: prima pars huiꝰ ↄ̨clu
<
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/>
ſionis aliq̈liter ptꝫ ex p̄dictīs et et declabit̄̄ ꝑ ãplius
<
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in argumētoꝝ ſolutiõibꝰ. </
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xml:space
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cluſiõe quīta huiꝰ.
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xml:space
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</
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>
<
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xml:space
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">Si tñ plus affectas hãc ſecundã
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partē ↄ̨cluſiõis īueſtigare p̄ſto erit tibi guillermus
<
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/>
hentiſber in ſuo tractatu de motu locali capite pri
<
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/>
mo illã cū ſuis ↄ̨mētariis ad extremū vſ diſcutiēs</
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<
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xml:space
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">Ad rationes ante oppoſitū q2 vtrã
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opinionē ſuſtinemꝰ oꝑe p̄ciū eſt oēs illas rõnes ſol-
<
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/>
uere: ̄uis ille q̄ ſūt ↄ̨tra vnã opinione ſint ꝓ altera</
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</
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>
<
p
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<
s
xml:id
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xml:space
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">Ad prṫmã dico / vt dictū eſt ibi cū dice-
<
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bat̄̄ / ideo velocitas motꝰ difformis quo ad ſubie-
<
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/>
ctū attendi d3 penes punctū velociſſime motū q2 di
<
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/>
gnū eſt vnūqḋ a digniori denoīri. </
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>
<
s
xml:id
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xml:space
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">Itē q2 aliqñ
<
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nõ datur punctꝰ tardiſſime motus vt ibi dr̄: et ad re-
<
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/>
plicã reſpõdeo / ̄uis nõ detur aliqñ pūctꝰ qui ve-
<
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/>
lociſſime mouet̄̄ verꝰ: datur tñ ymaginariꝰ / qḋ ſuffi
<
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/>
cit: et ſimiliter nõ detur linea vera datur tñ ymagi-
<
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/>
naria quã deſcribit: et loquor in ꝓpoſito de o vel
<
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/>
ymaginario vt ad ꝓpoſitū cõducit. </
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>
<
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xml:space
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">Et ꝑ hoc ptꝫ ad
<
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primã cõfirmationē cū ſua replica prima. </
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>
<
s
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xml:space
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">Et ad ſe-
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cundã replicã / q̄ ponit rotã cõtinuo rarefieri ita
<
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/>
cõtinuo magis diſtent pūcta extra a centro admit-
<
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/>
to caſum et nego añs: et ad ꝓbationē nego / nullaꝫ
<
lb
/>
lineã deſcribat: et cū ꝓbat̄̄ / q2 nec rectã nec circularē
<
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/>
cõcedo añs: et nego cõſequētiã. </
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>
<
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xml:space
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">Multe em̄ linee ſunt
<
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que nec recte nec circulares ſunt / vt patꝫ de linea pro
<
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/>
media parte recta et ꝓ media circulari. </
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>
<
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xml:id
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xml:space
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">Hoc idē ptꝫ
<
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de linea giratiua et de filio ad globum redacto. </
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<
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xml:space
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">Et
<
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ideo dico / talis linea habet ſe quaſi ad modum
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linee giratiue vel curue.</
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>
</
p
>
<
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<
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xml:space
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">Ad ſecūdã cõfirmationē dico breuiṫ /
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talis rota mouet̄̄ ita velociter ſicut pūctꝰ eiꝰ extre
<
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/>
mꝰ mouet̄̄ in toto tꝑe adequate. </
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>
<
s
xml:id
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xml:space
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preserve
">Et ſi queras cui cor
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reſpõdet velocitas illiꝰ pūcti ī toto illo tꝑe adeq̈te.</
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>
</
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>
<
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<
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xml:space
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">Reſpõdeo / vt michi videt̄̄ ꝓ nūc / cor
<
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reſpõdet velocitati quã talis pūctꝰ hꝫ in inſtanti me-
<
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/>
dio totiꝰ tꝑis. </
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>
<
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xml:space
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">Nã ymaginor illū punctū moueri vni
<
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formiter quo ad tēpꝰ cõtinuo vniformiter intēden-
<
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do motū: et cū dicis / qḋ hoc eſt cõicidere cū alia opi
<
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/>
nione, nego tibi illud, et ratio eſt / q2 alia opinio di-
<
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/>
ceret in illo caſu rotã illã moueri cõtinuo ita velo-
<
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cīter ſicut pūctꝰ / qui eſt in medio ſemidiametri inter
<
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centrū et circūferentiã q̇ lõge tardiꝰ moue^ quã pū-
<
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/>
ctus peripherie: et ↄ̨ñter diceret / velocitas motus
<
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totiꝰ rote corrñdet velocitati motꝰ qua hꝫ ille pūctꝰ
<
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qui eſt in medio illius ſemidiametri mouetur in me
<
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dio totius temporis in quo mouetur.</
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>
</
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>
<
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<
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xml:space
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">Ad ſcḋm argumentū reſponſum eſt
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Capitulū tertiū.
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ibi vſ ad vltimã replicã ad quã reſpõdeo ↄ̨ceden
<
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do / qḋ īfert̄̄, et negãdo falſitatē ↄ̨ñtis, et cū ꝓbat̄̄ fal
<
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/>
ſitas ↄ̨ñtis nego ſeq̄lã vcꝫ / ſtabit punctū extremū
<
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moueri ita velociṫ ſicut ãtea mouebat̄̄ q̈libet parte
<
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/>
ꝓportiõali carēte velocitate ſiue q̇eſcēte. </
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<
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">Sꝫ dico /
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cū aliq̈ pars ꝓportiõalis deuenerit ad nõ graduꝫ
<
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velocitatꝪ tota rota q̇eſcit.
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</
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<
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xml:space
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">Utrū aūt poſſet fieri / qḋ
<
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in calce argumēti ponit̄̄ vcꝫ / a q̈libet ꝑ parte ꝓpo-
<
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/>
tionali ſcḋm certã diuiſionē demat̄̄ medietas velo-
<
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citatis abſ hoc / demat̄̄ aliq̇d a pūcto exiſtēte in
<
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/>
peripheria rote nõ eſt michi certū: nichilominꝰ vi
<
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/>
detur / pari ratione concedendum ſit ſicut conce-
<
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ditur procedens illatum.</
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>
</
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<
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<
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xml:space
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<
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cluſiões huiꝰ capitis poſite in corꝑe huiꝰ queſtiõis.</
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>
</
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>
<
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<
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xml:id
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xml:space
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">Ad quartū argumentū dictum eſt ibi
<
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/>
vſ ad vltimã replicã ad quã reſpõdet ſeptīa ↄ̨clu-
<
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/>
ſio cū ſuo correlario: diſtãtia em̄ pūctoꝝ vĺ ꝓpinq̇-
<
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tas nichil cõfert ad velocitatē circūgirationis, nec
<
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/>
auget, nec minuit ꝓportionē ſꝫ dūtaxat īpedimētū
<
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circūgirandi / qḋ forte eſt g̈uitas exiſtēs in corꝑe cir
<
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cunducto. </
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>
<
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xml:space
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">Si nulla em̄ eſſet g̈uitas aut aliqḋ aliud
<
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īpedimentū eque cito giraretur magna rota ſicut
<
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parua: et ſi potentia circungirans eſſet naturalis
<
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ſubito circungiraretur.</
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</
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>
<
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<
s
xml:id
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xml:space
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">Ad quintū negat̄̄ añs: ad ꝓbationē
<
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/>
admiſſo caſu et ſuppoſitiõe ↄ̨cedo illatū vcꝫ / a. ade
<
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/>
quate in duplo velociꝰ mouet̄̄ ꝙ̄ b. / et nego falſitateꝫ
<
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ↄ̨ñtis, et ad ꝓbationē admiſſa ↄ̨cluſiõe geometrica /
<
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q̄ ibi ſupponit̄̄ cõcedo / a. pedale in duplo ſuꝑbi-
<
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partiēti quītas velociꝰ rarefit quã pedale b. et ra
<
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refactio eſt motꝰ localis et cū infert̄̄ / g̊ in duplo ſuꝑ-
<
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bipartiēti quãtas velociꝰ mouet̄̄ a. ꝙ̄ b. / nego ↄ̨ñam
<
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̄uis em̄ idē ſit rarefactio et motꝰ: penes tñ aliud cõ
<
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mēſurari habet velocitas rarefactiõis et motus lo
<
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calis ſicut dictū eſt de circuitione et motu circulari.</
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<
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xml:space
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">Ad ſextã rõnē dictū eſt ibi vſ ad re-
<
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plicã de linea girãte columnã: ad quã dico / motꝰ
<
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/>
talis linee giratiue nõ d3 reduci ad vniformitatē vt
<
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/>
ſupponit replica: ſed totū reſiduū illius linee qḋ
<
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/>
eſt ſupra pūctū in quo eſt mediꝰ g̈dus motꝰ quo mo
<
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uet̄̄ totalis rota d3 capi ac ſi eſſet medietas totius
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linee. </
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>
<
s
xml:id
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N1DD48
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xml:space
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preserve
">Tã velociter em̄ mouet̄̄ illa linea giratiua ſi-
<
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cut vna linea recta exiēs a cētro rote vſ ad circū-
<
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/>
feretiã eiꝰ. </
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>
<
s
xml:id
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N1DD4F
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xml:space
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preserve
">Et ideo velocitas illiꝰ linee giratiue cõ-
<
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mēſurari hꝫ penes velocitatē talis linee recte. </
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>
<
s
xml:id
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xml:space
="
preserve
">Et ſi
<
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hec ſolutio tibi nõ placet vexes īteīlectū ad cõperiē-
<
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dã aliã. </
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>
<
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xml:id
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="
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">Nõ em̄ ꝓ nūc alia michi occurit. </
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>
<
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xml:id
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N1DD5E
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xml:space
="
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">Argumē
<
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tū in oppoſitū nõ eſt magis ꝓ vna opiniõe quã pro
<
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/>
reliqua. </
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>
<
s
xml:id
="
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xml:space
="
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">Et ideo queſtio noſtra his paucis contēta
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terminum ſumat.</
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</
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<
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xml:space
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preserve
">Capitulū tertiū / in quo oſtendit̄̄ modꝰ cogno-
<
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ſcendi ſiue cõmenſurandi motū vniformieer diffor-
<
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/>
mem et difformiter difformem quo ad tempus quo
<
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/>
ad velocitatem et tarditatem in omni ſpecie .etc̈.
<
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/>
In oī ſpecie ꝓportiõis rõnalis et irrõalis
<
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per modū q̄ſtiõis ꝓcedendo.</
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>
<
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<
s
xml:id
="
N1DD7D
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xml:space
="
preserve
">Exactis vt potuimus difficulta-
<
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tibus circa motꝰ difformis quo ad ſubiectū ↄ̨tingē
<
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tibꝰ: iã reſtat accedere ad difficultates circa cogno
<
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/>
dã et ↄ̨mēſurandã velocitatē motꝰ difformis quo ad
<
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tēpꝰ occureētes. </
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>
<
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xml:id
="
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xml:space
="
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">Circa qḋ talē q̄ro q̄ſtionē. </
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>
<
s
xml:id
="
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"
xml:space
="
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">¶ Utrum
<
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oīs motus vniformiter difformis quo ad tempus
<
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menſurari habet penes gradum medium: et omīs
<
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difformiter difformis quo ad tēpus penes reducti
<
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/>
onē ad vniformitatē ſiue pēnes cõmenſurationem
<
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denoīatiõis q̈ denoīatiõe denoīat mobile moueri.</
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