Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Primi tractatus
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0092
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et ſic conſequenter: igitur ꝓpoſitum. </
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>
<
s
xml:id
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N18F8A
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xml:space
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preserve
">Arguitur an-
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tecedens / quoniam qualitas acquiſita in ſecunda ꝑ
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te propoſtiouali eſt equalis qualitati acquiſite in
<
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medietate prime partis proportionalis </
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>
<
s
xml:id
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N18F93
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xml:space
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preserve
">(Uolo em̄
<
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acquirat vniformiter) et aquiritur in duplo mino
<
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ri tempore quam ſit illa medietas prime partis ꝓ-
<
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portionalis / vt conſtat intelligenti quintum caput
<
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prime partis: igitur ī duplo velocius acquiritur il
<
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/>
la qualitas in ſecunda parte ꝓportionali quam in
<
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prima. </
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>
<
s
xml:id
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N18FA2
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xml:space
="
preserve
">Et iſto modo arguatur de qualitate acquiſi
<
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ta in tertia parte ꝓportionali reſpectu qualitatis
<
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acquiſite in ſecunda. </
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>
<
s
xml:id
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N18FA9
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xml:space
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preserve
">Bene tamen concedo pro reſo
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lutione argumenti / illa poña verſus extremum in
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tenſius deueniendo in infinitum velociter intendi-
<
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/>
tur / vt probat argumentum.
<
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note-0092-01
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xml:id
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xml:space
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">1. correl.</
note
>
</
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<
s
xml:id
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N18FB7
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xml:space
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preserve
">¶ Ex quo ſequitur pri-
<
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mo / ſtat aliquid in infinitum velociter augeri ac-
<
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quirendo preciſe quantitatem pedalem in hora.</
s
>
</
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<
s
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xml:space
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">Patet hoc ſupponendo / hora diuidatur per par
<
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/>
tes proportionales proportione quadrupla, aut
<
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quintupla (in idem redit) et vnum corpus in prima
<
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/>
parte ꝓportionali acquirat ſemipedale, et in ſecun
<
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/>
da quartam partem pedalis, et in tertia octauaꝫ, et
<
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/>
ſic conſequenter in ſubdupla ꝓportione. </
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>
<
s
xml:id
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N18FD6
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xml:space
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preserve
">quo poſi-
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to manifeſtū ē (vt patet ex ſolutione argumenti) /
<
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illud corpus in infinitum velociter augetur: et tamē
<
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ſolum finite augetur acquirendo adequate quan-
<
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titatem pedalem in hora: </
s
>
<
s
xml:id
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N18FE1
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xml:space
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preserve
">Nam acquirit infinita cõ
<
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tinue ſe habentia in ꝓportione dupla: igit̄̄ reſiduū
<
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a primo eſt equale primo / vt patet ex ſecundo corre-
<
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lario tertie concluſionis quinti capitis preallega-
<
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to: et primo acquiſitum eſt ſemipedale: ergo totum
<
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/>
eſt pedale.
<
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left
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note-0092-02
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xml:id
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N18FFC
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xml:space
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preserve
">2. correl.</
note
>
</
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<
s
xml:id
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N18FF3
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xml:space
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">¶ Sequitur ſecundo / aliquid in infini-
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tum tarde intenditur: et tamen finite intenditur.</
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>
</
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<
s
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xml:space
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">Probatur ponendo / hora diuidatur per partes
<
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ꝓportionales ꝓportione dupla: et in prima parte
<
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ꝓportiõali aliquod corpus acquirat quatuor gra
<
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dus, et in ſecunda vnum, et in tertia vnam quartam
<
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vnius gradus: et ſic conſequenter procedendo per ꝑ
<
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tes ꝓportionales proportione quadrupla. </
s
>
<
s
xml:id
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N19010
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xml:space
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">quo po
<
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ſito manifeſtum eſt / illud corpus in infinitum tar
<
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de intenditur: quoniaꝫ in ſecunda parte proportio
<
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/>
nali in duplo tardius quaꝫ in prima, et ī tertia ī du
<
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/>
plo tardius quam in ſecunda, et ſic conſequēter: igi
<
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tur in infinitum tarde intenditur. </
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>
<
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xml:space
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">Probatur ante-
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cedens / quoniam in ſecunda parte tale corpꝰ acqui
<
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rit ſubduplam intenſionem ad intenſionem acqui-
<
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ſitam in medietate prime partis: et medietas prime
<
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/>
et ſecunda ſunt equales: igitur ī equali tempore ſub
<
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duplam intenſionem acquirit / et per conſequens in
<
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duplo tardius intenditur. </
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>
<
s
xml:id
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N1902C
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xml:space
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preserve
">Et ſic ꝓbabitur de qua-
<
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litate acquiſita in tertia, et de quacun alia reſpe-
<
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ctu qualitatis acquiſite in parte precedenti eaꝫ im
<
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mediate. </
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>
<
s
xml:id
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xml:space
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">igitur propoſitum. </
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<
s
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xml:space
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">Sed finite intenda-
<
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tur patet: quia preciſe in toto tempore illo acquirit
<
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quin gradus cum tertia. </
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>
<
s
xml:id
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xml:space
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">Nam in prima parte ꝓ-
<
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portionali acquirit quatuor gradus: et in ſecunda
<
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vnum: et ſic conſequenter ꝓcedendo per partes pro
<
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portionales proportione quadrupla: ergo reſiduū
<
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/>
ab acquiſito in prima eſt ſubtriplum ad illud / vt pa
<
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tet ex ſecundo correlario preallegato: ſed acquiſi-
<
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tum in prima eſt quatuor graduum: igitur acquiſi-
<
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tum in omnibus ſequentibus a prima eſt gradꝰ cū
<
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tertia: et ſic totum eſt quin graduum cuꝫ tertia / qḋ
<
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fuit probandum.
<
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left
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note-0092-03
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xml:id
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xml:space
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preserve
">3. correl.</
note
>
</
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<
s
xml:id
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N19059
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xml:space
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">¶ Sequitur tertio / infinite intē
<
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di eſt infinitam qualitatem acquirere vel infinitam
<
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intenſionem: ſed in infinitum velociter intendi eſt in
<
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aliquo tempore aliquam qualitatē acquirere ali-
<
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quanta velocitate: et aliam in duplo maiori veloci-
<
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tate (ſiue ſit tanta ſiue minor non eſt cura) et aliam
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Capitulum nonum
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in triplo maiori: et ſic conſequenter vt poteſt exem-
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plo primi correlarii oſtendi. </
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<
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as in infinnitum tarde intendi.</
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<
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xml:id
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xml:space
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">4. correl.</
note
>
<
p
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<
s
xml:id
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xml:space
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">¶ Sequitur quarto / quamuis poña non variata
<
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/>
intendens motum ſuum per medium vniformiter
<
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/>
difforme velocius intendat motum ſuum continuo
<
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/>
tranſeundo partem minus reſiſtentem quam ma-
<
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/>
gis reſiſtentem: nichilominus tamen poña non va-
<
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/>
riata difformiter intendens motum ſuum per me-
<
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dium difforme per quod poña minor continuo vni
<
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/>
formiter intendit motum ſuum: velocius ītendit ip
<
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/>
ſa potentia maior non variata motum ſuum tran-
<
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ſeundo partem magis reſiſtentem quam minus re-
<
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ſiſtentem. </
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>
<
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N19096
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">Prima pars correlarii patet ex quadra
<
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geſima concluſione quinti capitis huius tractatus
<
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</
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<
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xml:space
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">Et ſecunda probatur / quia quacun parte data ꝓ-
<
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portionabili illius medii procedendo a minoribus
<
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verſus maiores in qua aliqualiter ītendit talis po
<
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/>
tentia maior motum ſuum: in aliqua minore prece
<
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/>
dente magis reſiſtente velocius intendebat motum
<
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/>
ſuum cum in infinitum velociter antea intendebat
<
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/>
motum ſuum / vt patet ex tertio correlario quinte cõ
<
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cluſionis ſeptimi capitis huius tractatus: igitur ve
<
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/>
locius intendebat talis potentia motum ſuum cum
<
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parte magis reſiſtente / quod fuit probandum.</
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>
</
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<
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xml:space
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">Quarto contra ſecundam concluſio-
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nem octaui capitis arguitur ſic / quia ſi illa eſſet ve-
<
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ra ſequeretur / vbi aliqua potentia inuariata ali
<
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/>
quod medium inuariatum tranſeundo cõtinuo vni
<
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/>
formiter remittit motum ſuum ad non gradum in
<
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/>
puncto terminatiuo eiuſdem medii in extremo intē
<
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/>
ſiori: omnem potentiam maiorem idem mediã trã
<
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/>
ſeundo adequate vniformiter continuo poſſe remit
<
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/>
tere motum ſuum ad non gradum in eodem puncto
<
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/>
terminatiuo per continuam ſue potentie remiſſio-
<
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nem / ſed hoc eſt falſum: igitur et concluſio. </
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>
<
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N190C9
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xml:space
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">Falſitas
<
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conſequentis probatur / et capio a. poñam que habe
<
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at ad punctum initiatiuum c. medii quod inuaria-
<
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/>
tum b. poña inuariata pertranſit continuo vnifor-
<
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/>
miter remittēdo motum ſuum ad non gradum etc.
<
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/>
ꝓportionem in ſexquialtero maiorem quam b. ad
<
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/>
idem punctum: et arguo ſic / a. potentia tranſeūdo c.
<
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/>
medium non valet vniformiter continuo remittere
<
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/>
motum ſuum vſ ad non gradum in puncto termi
<
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/>
natiuo c. medii in extremo intenſiori per continuaꝫ
<
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/>
ſue potentie remiſſionem: igitur non vbi potentia ī
<
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/>
uariata aliquod medium tranſeundo inuariatum
<
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/>
etc. ad non gradum in puncto terminatiuo etc. om-
<
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nis potentia maior idem medium tranſeundo ade
<
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quate, vniformiter continuo poteſt remittere motū
<
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ſnum vſ ad non gradum in eodem puncto termi-
<
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natiuo per continuam ſue potentie remiſſionem. </
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>
<
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N190EC
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">qḋ
<
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eſt oppoſitum conſequentis. </
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>
<
s
xml:id
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N190F1
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xml:space
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">Antecedens probatur /
<
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quia ſi a. potentia tranſeundo c. medium valet re-
<
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/>
mittere motum ſuum vſ ad non gradum in pūcto
<
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/>
terminatiuo etc. per continuam ſue poñe remiſſio-
<
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/>
nem: maxime remitteret vniformiter continuo mo-
<
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/>
tum ſuum vſ ad non gradum in puncto termina-
<
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/>
tiuo etc. caſu quo b. poña inuariata inciperet moue
<
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/>
ri a puncto initiatiuo ſecunde partis ꝓportionalis
<
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c. medii diuiſi in partes ꝓportionales ꝓportione
<
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ſexquialtera verſus extremum intenſius eiuſdem c.
<
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medii: et a. potentia a puncto initiatiuo c. medii ver
<
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/>
ſus extremum intenſius eiuſdem: taliter cõtinuo
<
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/>
per ſui variationem in ſexquialtero velocius moue
<
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/>
retur a. quam b. ſed hoc non: igitur </
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<
s
xml:id
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N1910E
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xml:space
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preserve
">Maior ptꝫ / q2
<
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tunc tam a. quam b. eque primum deuenirent ad pū
<
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/>
ctum terminatiuum c. medii in quo vtra remitte-
<
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ret motū ſuum ad non gradum: cū a. per caſum in </
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