Alvarus, Thomas
,
Liber de triplici motu
,
1509
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121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
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Secundi tractatus
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147
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plex eſt: </
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>
<
s
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N1E503
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xml:space
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preserve
">Nam quidam eſt vniformiter difformis ter
<
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minatus ad non gradum in altero extremo. </
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>
<
s
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N1E508
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xml:space
="
preserve
">Alter
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vero eſt vniformiter difformis vtrobi ad graduꝫ
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terminatus. </
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>
<
s
xml:id
="
N1E50F
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xml:space
="
preserve
">Et de vtro iſtorum dicitur / gradui
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ſuo medio correſpondet: id eſt gradui motus quem
<
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habet in medio temporis. </
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>
<
s
xml:id
="
N1E516
"
xml:space
="
preserve
">Nam quanto velociꝰ mo
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/>
uetur mobile motum vniformiter difformiter medi
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ante medietate talis motus intenſiori tanto tardiꝰ
<
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/>
mouetur mediãte medietate remiſſiori, et ſic eque ve
<
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/>
lociter mouetur ac ſi moueretur gradu medio. </
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>
<
s
xml:id
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N1E521
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xml:space
="
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">Et
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ad cognitionem talis gradus medii pono aliq̈s ꝓ
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poſitiones.</
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</
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>
<
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N1E528
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<
s
xml:id
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N1E529
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xml:space
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">Prima propoſitio </
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>
<
s
xml:id
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N1E52C
"
xml:space
="
preserve
">In omni latitudīe
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vniformiter difformi incipiente a gradu a termina
<
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/>
ta ad non gradum: gradus medius eſt ſubduplus
<
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/>
ad extremuꝫ intenſius: ita ſi latitudo incipiat ad
<
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/>
octauo et terminatur ad nõ gradū: gradus medius
<
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/>
eſt gradus quartus q2 quartus gradꝰ eſt ſnbduplꝰ
<
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/>
ad octauum. </
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>
<
s
xml:id
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N1E53B
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xml:space
="
preserve
">Ad quam ꝓpoſitionem oſtendendam
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ſupponendum eſt / quandocun ſunt iufiniti ter
<
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/>
mini cõtinuo ꝓportionales ꝓportione dupla / tūc to
<
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/>
tum aggregatum ex eis eſt duplum ad totuꝫ aggre
<
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/>
gatū ex oībus ſequētibus primū. </
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>
<
s
xml:id
="
N1E546
"
xml:space
="
preserve
">Secūdo ſupponē
<
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dum eſt / medium eſt illḋ quod equaliter dlſtat ab
<
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extremis </
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>
<
s
xml:id
="
N1E54D
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xml:space
="
preserve
">Hee ſuppoſitiones ſatis aperte ſunt ex ṗ
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ma et ſecunda partibus. </
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>
<
s
xml:id
="
N1E552
"
xml:space
="
preserve
">His ſuppoſitis arguitur ꝓ
<
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/>
poſitio: et volo / diuidatur latitudo vniformiter
<
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/>
difformis a nõ gradu vſ ad certum gradum ī par
<
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/>
tes ꝓportionales continuo ſe habentes ī ꝓportio
<
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/>
ne dupla: et arguo ſic / gradus initians aggregatuꝫ
<
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/>
ex omnibus latitudinibus ſequentibus primam eſt
<
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/>
medius: et talis eſt ſubduplus ad gradum intenſio
<
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/>
rem illius latitudinis / igitur talis latitudinis vni-
<
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/>
formiter difformis terminate ad non gtadum: gra
<
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/>
dus medius eſt ſubduplus ad extremum intenſius
<
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/>
eiuſdem latitudinis: et ſic ꝓbabis de qualibet alia
<
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/>
</
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>
<
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xml:space
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">Conſequentia patet, et arguitur maior / q2 talis gra
<
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/>
dus equaliter diſtat ab extremis illius latitudinis /
<
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/>
vt patet ex prima ſuppoſitione </
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>
<
s
xml:id
="
N1E571
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xml:space
="
preserve
">Nam initiat ſecun
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dam medietatem latitudinis: et terminat primam:
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igitur eſt medius gradus: </
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>
<
s
xml:id
="
N1E578
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xml:space
="
preserve
">Patet conſequentia ex
<
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ſecunda ſuppoſitione. </
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>
<
s
xml:id
="
N1E57D
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xml:space
="
preserve
">Sed iſte ſit ſubduplus ad
<
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extremum intenſius probatur: quia ipſe bis ſūptꝰ
<
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/>
conſtituit extremum intenſius adequate: igitur.</
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>
</
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>
<
p
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="
N1E584
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<
s
xml:id
="
N1E585
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xml:space
="
preserve
">Alio modo Hentiſber deducit hanc concluſionem
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in ſuo tractatu de motu locali capite primo.</
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>
</
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>
<
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xml:id
="
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<
s
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="
N1E58B
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xml:space
="
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">Secunda propoſitio </
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>
<
s
xml:id
="
N1E58E
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xml:space
="
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">Gradus mediꝰ
<
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/>
motus vniformiter difformis vtrobi ad gradum
<
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/>
terminati eſt intenſior quaꝫ ſubduplus ad extremū
<
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/>
intenſius. </
s
>
<
s
xml:id
="
N1E597
"
xml:space
="
preserve
">Probatur hec ꝓpoſitio / quia omnis gra
<
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/>
dus ſubduplus ad extremum intenſius tantum di-
<
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/>
ſtat ab extremo intenſiori quantum a nõ gradu: ſꝫ
<
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/>
uullus gradus medius latitudinis vtrobi ad gra
<
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/>
dum terminate tantum diſtat ab extremo intenſio-
<
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/>
ri eius quantum a non gradu: igitur nullus gradꝰ
<
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/>
medius latitudinis vtrobi ad gradum terminate
<
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/>
eſt ſubduplus ad extremum intenſius eiuſdem lati-
<
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/>
tudinis: nec remiſſior / vt ꝓbabītur: ergo intenſior.</
s
>
</
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>
<
p
xml:id
="
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<
s
xml:id
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"
xml:space
="
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">Conſequentia patet in ſecundo ſecunde. </
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>
<
s
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="
N1E5AE
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xml:space
="
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">Et maior
<
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patet ex precedēti propoſitione: et minor probatur /
<
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/>
quia tantum talis gradus diſtat ab extremo inten
<
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/>
ſiori quantū diſtet adequate ab extremo remiſſiori
<
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/>
ſed non tantum talis gradus medius diſtat ab ex-
<
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/>
tremo intenſiori quantum diſtat a non gradu / vt ſa
<
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/>
tis patet de ſe: igitur non tantuꝫ diſtat ab extremo
<
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/>
intenſiori quãtum a non gradu </
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>
<
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xml:id
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N1E5BF
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xml:space
="
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">Patet conſequētia
<
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per hanc maximam </
s
>
<
s
xml:id
="
N1E5C4
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xml:space
="
preserve
">Quando aliqua duo ſunt eq̈-
<
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chead
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Capitulum tertium
"/>
lia q̇cq̇d eſt maius vno eſt maius altero. </
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>
<
s
xml:id
="
N1E5CA
"
xml:space
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">Et per hoc
<
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patet facile / talis gradꝰ ē intenſior gradu ſudu-
<
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/>
plo ad extremum intenſius. </
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>
<
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xml:id
="
N1E5D1
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xml:space
="
preserve
">q2 magis diſtat a non
<
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gradu quam gradus ſubduplus ad extremum in-
<
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tenſius / et ſic patet propoſitio.</
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>
</
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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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">Tertia proportio </
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>
<
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xml:id
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xml:space
="
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">Cuiuſlibet latitudi
<
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/>
nis motus vniformiter difformis terminati ad nõ
<
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/>
gradum: medietas intenſior eſt in triplo intenſior
<
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/>
medietate remiſſiori. </
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>
<
s
xml:id
="
N1E5E5
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xml:space
="
preserve
">Probatur hec ꝓpoſitio ſup-
<
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ponendo / quando ſunt tres termini continuo ꝓ-
<
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/>
portionabiles ꝓportione dupla / tūc extremi ad ex-
<
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/>
tremū eſt proportio duplicata / et per conſequens q̈
<
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/>
drupla. </
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>
<
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xml:id
="
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xml:space
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">Hoc ſuperius oſtenſum eſt in ſecunda par-
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te ſexti capitis octaua concluſione. </
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>
<
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xml:id
="
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xml:space
="
preserve
">Secundo ſup-
<
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/>
ponendum eſt / in qualibet tali latitudine motus
<
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/>
vniformiter difformis terminati ad non gradum
<
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/>
gradus initians ſecundam partem proportionalē
<
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/>
ꝓportione dupla eſt ſubduplus ad extremum inten
<
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/>
ſius: et gradus initians tertia tem proportio
<
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/>
nalem eſt ſubduplus ad gradum initiantē ſecundã:
<
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/>
et ſic conſequenter (loquor de partibus proportiõa
<
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/>
libus quantitatiuis) </
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>
<
s
xml:id
="
N1E608
"
xml:space
="
preserve
">Suppono vlterius / ſubſexq̇
<
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/>
tertium ad quadruplum alicuius eſt triplum ad il-
<
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/>
lud ſubquadruplum. </
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>
<
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xml:id
="
N1E60F
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xml:space
="
preserve
">Quod probatur facile / quia ſi
<
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eſt ſubſexquitertium ad illud eſt tres quarte eius: et
<
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/>
ſubquadruplum ad illud quadruplum eſt vna quar
<
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/>
ta: igitur illud ſubſexquitertium erit triplum ad il
<
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/>
lud ſubquadruplum. </
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>
<
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xml:id
="
N1E61A
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xml:space
="
preserve
">Patet conſequentia / q2 triuꝫ
<
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/>
quartarum ad vnam quartam eſt ꝓportio tripla.
<
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/>
</
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>
<
s
xml:id
="
N1E620
"
xml:space
="
preserve
">His ſuppoſitis probatur ꝓpoſitio: et diuido vnam
<
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/>
talem latitudinem per partes ꝓportionales ꝓpor
<
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/>
tione dupla: quo poſito arguitur ſic / gradus mediꝰ
<
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/>
medietatis intenſioris eſt triplus ad graduꝫ medi
<
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/>
um medietatis remiſſioris et penes tales gradꝰ me
<
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/>
tri habent velocitates illarum medietatū / vt dictū
<
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/>
eſt. </
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>
<
s
xml:id
="
N1E62F
"
xml:space
="
preserve
">igitur medietas intenſior eſt triple intenſionis
<
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/>
ad medietatem remiſſiorem / quod fuit probandum
<
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/>
</
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>
<
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xml:id
="
N1E635
"
xml:space
="
preserve
">Patet conſequentia cuꝫ minore / et arguitur maior /
<
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/>
quia vt patet ex ſecunda ſuppoſitione gradus ini-
<
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/>
tians tertiã partem proportionalem eſt ſubduplꝰ
<
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/>
ad initiantem ſecundam: et intians ſecundam ad in
<
lb
/>
itiantiantem primam: igitur initians primaꝫ eſt q̈
<
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/>
druplus ad initiantem tertiam / vt patet ex prīa ſup
<
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/>
poſitione: et ille eſt gradus medius ſecunde medie-
<
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/>
tatis puta remiſſioris: igitur gradus medius me-
<
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/>
dietatis remiſſioris ē ſubquadruplus ad extremuꝫ
<
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/>
intenſius medietatis intenſioris: et gradus mediꝰ
<
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/>
medietatis intenſioris eſt ſubſexquitertius ad ex-
<
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/>
tremum intenſius: ergo eſt triplus ad gradum me
<
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/>
dium medietatis remiſſioris qui eſt ſubquadruplꝰ
<
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/>
ad extremum intenſius latitudinis. </
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>
<
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xml:id
="
N1E652
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xml:space
="
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">Patet conſe-
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quentia ex tertia ſuppoſitione. </
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>
<
s
xml:id
="
N1E657
"
xml:space
="
preserve
">Sed reſtat ꝓbare /
<
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/>
gradus medius medietatis ītenſioris eſt ſubſex
<
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/>
quitertius ad extremum intenſius eiuſdcm medie
<
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/>
tatis: </
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>
<
s
xml:id
="
N1E660
"
xml:space
="
preserve
">Quod probatur ſic / quia talis gradus ē me-
<
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/>
dius inter duplum et ſubduplum puta inter extre-
<
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/>
mum intenſius illius medietatis et extremuꝫ remiſ
<
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/>
ſius eiuſdem qui eſt ſubduplus ad illum: igitur ta-
<
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/>
lis gradus medius eſt ſubſexquitertius ad illū du
<
lb
/>
plum puta ad illud extremum intenſius / quod fuit
<
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/>
probandum. </
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>
<
s
xml:id
="
N1E66F
"
xml:space
="
preserve
">Patet conſequētia per hanc maximã
<
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/>
</
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>
<
s
xml:id
="
N1E673
"
xml:space
="
preserve
">Omnis gradus medius inter duplum et ſubduplū
<
lb
/>
eſt ſexquialterꝰ ad ſubduplum et ſexquitertius ad
<
lb
/>
duplum / vt patet de ſenario mediãte inter .4. et .8.
<
lb
/>
de ternario mediante inter binarium et quarterna
<
lb
/>
rium et de nouenario mediante inter ſenariū et duo
<
lb
/>
denarium: et vniuerſaliter in omnibus.</
s
>
</
p
>
<
p
xml:id
="
N1E680
">
<
s
xml:id
="
N1E681
"
xml:space
="
preserve
">Quarta ꝓpoſitio / que ſequit̄̄ ex priori
<
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/>
</
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>
<
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xml:id
="
N1E685
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xml:space
="
preserve
"/>
</
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