Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Secundi tractatus
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in eodem tempore. </
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<
s
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xml:space
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<
s
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xml:space
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">Sed contra / quia tunc ſequeretur / ſi
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motus vt .4. vel aliquis alter intendatur ad ſuum
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duplum vniformiter / et alter motus ei equalis remi
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tatur in eadem hora ad non gradum ſiue ad quietē /
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tunc ille qui remittitur in infinitum velocius remit
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titur quam alter qui intenditur intendatur </
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<
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xml:space
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tamen eſt falſum cum tantam latitudinem vnus ac
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quirat ſicut alter deperdat.</
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<
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">dicitur.</
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<
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<
s
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xml:space
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">¶ Dices et bene diſtinguendo illatum aut ī infini
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tum velocius remittatur in eodem tempore veloci-
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tate geometrica: et ſic conceditur aut arithmetica: et
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ſic negatur.</
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<
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xml:space
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">Sed cõtra quia tunc ſequeretur / nõ
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eſſet poſſibile / ita velociter geometrice intendere
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tur vnus motus in tempore finito vniformiter ſicut
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motus ei eq̈lis remitteretur vniformiter ad nõ gra
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dū in eodē tꝑe: ſed conſequens videtur falſum (cum
<
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/>
equalem latitudineꝫ vnus motus deperdat ſicut al
<
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ter acquirit) / igitur illud ex quo ſequitur. </
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<
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tamen probatur quoniam / vt patet ex reſponſione
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motus qui remittitur ad non gradum infinitam ꝓ-
<
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portionem deperdit, et motus qui intenditur ſoluꝫ
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finitam: igitur non eque velociter geometrice vnus
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motus intenditur ſicut alter ei equalis remittitur ī
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/>
eodem tempore.
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xml:space
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">2. confir.</
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<
s
xml:id
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xml:space
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">¶ Confirmatur ſecundo / quo
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niam ſi motus vniformiter difformis correſponde
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ret ſuo gradui medio ſequeretur / quando duo mo-
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/>
tus equales vniformiter difformes remitterentur ī
<
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hora vnus ī duplo velocius altero ille qui tardiꝰ re
<
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/>
mittitur / quando eſt remiſſus ad ſubduplum: alter
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eſſet remiſſus ad ſubquadruplum et non ad quieteꝫ
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ſiue ad non gradum: ſed conſequens falſum / vt pa-
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tet intuenti: igitur illud ex quo ſequitur: </
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">Sequela
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tamen probatur quoniam / ſi in eodem tempore vnꝰ
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continuo in duplo velocius altero remittitur ſeq̄re
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tur / quando vnus deperdit proportionem duplam
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alter deperdit proportionem quadruplam / et in tē-
<
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pore quo vnus quadruplam alter ſexdecuplaꝫ que
<
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eſt dupla ad quadruplam. </
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>
<
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xml:space
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">vt patet ex ſecunda par
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te capite ſexto.
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xml:id
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xml:space
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">.3. confir.</
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>
</
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<
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xml:space
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">¶ Confirmatur tertio / qm̄ ſi mo-
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tus vniformiter difformis correſponderet gradui
<
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medio ſequeretur / ſi eſſent duo motus vniformi-
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ter difformes equales incipientes ab eodem gra-
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du terminati ad eundem vel ad non gradum et vnꝰ
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illorum puta a. in duplo velocius continuo intende
<
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/>
retur quam alter puta b. / et talis intenſio duraret ī
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infinitum / aliquando a. eſſet motus duplus ad b. /
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ſed conſequens eſt falſuꝫ: igitur illud ex quo ſequit̄̄
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</
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<
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">Seq̄la probatur / q2 qñcū b. acq̇rit aliquã latitudi
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nē a. acq̇rit duplã: et ſꝑ in duplo velociꝰ a. acq̇ret ali
<
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/>
quem gradum / quam eundem acquirit b. / et hec inten
<
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ſio procedit in infinitum: igitur aliquãdo a. erit mo
<
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tus duplus ad b. </
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<
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xml:space
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">Probatur hec conſequentia / quo
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niam per infinitam latitudinem excedet latitudo ac
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/>
quiſita ipſi a. latitudinem acquiſitam ipſi b. / igitur
<
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aliquando totus motus a. erit duplus ad totuꝫ mo
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tuꝫ b. </
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">Cõſequētia apparet nota et arguit̄̄ añs / q2 ī in
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finitum maior erit latitudo acquiſita ipſi a. quã la-
<
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/>
titudo acquiſita ipſi b. / quia per infinitos gradꝰ la-
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titudo acquiſita ipſi a. excedet latitudinem ipſiꝰ b. /
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igitur ꝑ infinitã latitudinē excedit latitudo acquiſi
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ta ipſi a. latitudinē acquiſitã ipſi b. </
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<
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">Probat̄̄ ante
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cedens / quoniam latitudo acquiſita ipſi a. cum ſem
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per erit dupla ad latitudinem acquiſitam ipſi b. / qñ
<
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erit vt .4. excedit latitudineꝫ ipſius b, per duos gra
<
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dus et quando vt .8. per .4. et quando vt centum per
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50. et quando vt .1000. per .500. / et ſic in infinitum: igi
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Capitulum tertium
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tur per infinitos gradus latitudo acquiſita ipſi a.
<
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excedet latitudinem acquiſitam ipſi b. / quod fuit ꝓ
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bandum. </
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<
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">Sed iam probatur falſitas conſequentis
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quoniam / ſi aliquando totus motus a. ad totuꝫ mo
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tum b. erit duplus. </
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<
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">ſignetur illud inſtans / in quo ita
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erit / et arguitur ſic / totus motus a. ad totum motum
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b. eſt duplus / ergo ſi vna pars ipſius a. eſt dupla ad
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vnam partem b. totum reſiduum de a. eſt dupluꝫ ad
<
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reſiduum de b. / ſed conſequens eſt falſum: igitur illḋ
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ex quo ſequitur. </
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<
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">Falſitas conſequētis probatur / q2
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in illo inſtanti totum acquiſitum a. eſt duplū ad to
<
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tum acquiſitum b. / et tamen reſidua pars de a. non
<
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eſt dupla ad reſiduam partem de b. / ſed ille partes
<
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ſunt equales ſicut erant in principio: et ſic ſequitur /
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quando vna pars a. eſt dupla ad vnam partem
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b. totum reſiduum a. non eſt duplum ad totum reſi-
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duum b. / et ſic a. non eſt duplum ad b. </
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<
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ſequentia ex ſeptimo correlario q̈rte concluſionis
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octaui capitis ſecunde partis.</
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<
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xml:space
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">¶ Et confirmatur quarto et vltimo / quia ſi oīs mo-
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tus vniformiter difformis commenſurari hꝫ gradu
<
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medio: vel igitur in quolibet tali motu ille gradus
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medius eſt ſubduplus adequate ad intenſius extre
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mum talis motus vel maior ſubduplo: vel minor:
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nullum iſtorum eſt dicendum igitur. </
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<
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">Probatur mi
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nor / quia capto motu vniformiter difformi ab octa
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uo vſ ad quartum gradus medius eius eſt vt .6. /
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et talis eſt dumtaxat ſubſexquitertius ad gradum ī
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tenſiorem: et non ſubduplus: igitur non in omni mo
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tu vniformiter difformi gradus medius eſt ſubdu-
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plus ad gradum intenſiorem. </
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<
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vniformiter difformi ab octauo vſ ad non gradū
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medius gradus eius eſt ſubduplus ad extremū in-
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tenſius: igitur non in omni motu vniformiter dif-
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formi gradus medius eſt maior quam ſubduplus.
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</
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<
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">Item nullus gradus medius alicuius motꝰ vnifor-
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miter difformis eſt minor quam ſubduplus ad ex-
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tremum intenſius / vt facile eſt intueri: igitur illa mi
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nor vera.
<
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">dicitur.</
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>
</
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<
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xml:space
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">¶ Dices ſicut dicendum eſt negando illaꝫ
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minorem: immo in aliquibus motibus vniformiter
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difformibus gradus medius eſt preciſe ſubduplus
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ad gradum ſummū eiuſdem motus / vt patet in om
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ni motu vniformiter difformi terminato ad nõ gra
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dum. </
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<
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xml:space
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">In omni motu vero vniformiter difformi ter-
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minato vtrim ad gradum. </
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<
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xml:id
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xml:space
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">gradus medius eſt ma
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ior quam ſubduplus ad extremum intenſius / vt po
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ſtea oſtenditur.</
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<
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">Sed contra / quia tunc ſequeretur /
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aliquando gradus medius alicuius motus vnifor
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miter difformis vtrim terminati ad gradum eēt
<
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ſubſexquitertius ad gradum ſummum: aliquando
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ſubſexquialterius: aliquando ſubſexquiquartus:
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et ſic in infinitum. </
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<
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">Quod ſi concedis ſicut conceden
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dum eſt ſequitur / nulla poteſt inueniri certa regu
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la et vniuerſalis ad ſciendum in quolibet motu vni
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formiter difformi quanto plus pertranſitur per to
<
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tum motum in medietate intenſiori quam in medie
<
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tate remiſſiori: quod videtur ſatis inconueniens.</
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<
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<
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">Secundo principaliter tangendo ve
<
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locitatem, motus difformiṫ difformis cuius nulla
<
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pars eſt vniformis comparando ipſum ad vnifor
<
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miter difformem: arguitur ſic. </
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>
<
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xml:id
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N1E081
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xml:space
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preserve
">quia ſi prima pars et
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ſecunda queſtionis eſſent vere: ſequeretur / aliqui
<
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duo motus ſunt modo equales: et in tempore equa-
<
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li equales latitudines deperdent ſucceſſiue ita in
<
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fine illius temporis erunt equales: et tamen ꝑ vnuꝫ
<
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illorum motuum maius ſpacium continuo pertrã-
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ſitur quã per alium: hoc videtur īpoſſibile: igitur </
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