Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Primi tractatus
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0063
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tiam vt .2. aliquanta velocitate neceſſe eſt eandem
<
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potentiam vt octo natam eſſe mouere duplam re-
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ſiſtentiaꝫ in ſubdupla velocitate. </
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>
<
s
xml:id
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N16262
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xml:space
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preserve
">et potentia vt .8
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eſt aliqua potentia: et reſiſtentia vt duo aliqua re
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ſiſtentia: igitur. </
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>
<
s
xml:id
="
N16269
"
xml:space
="
preserve
">Si aliqua potētia moueat aliquã
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/>
reſiſtentiã in aliquo tempore alīta velocitate: ea
<
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/>
dem mouebit duplam reſiſtentiã in ſubdupla ve-
<
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/>
locitate / quod eſt oppoſitum regule. </
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>
<
s
xml:id
="
N16272
"
xml:space
="
preserve
">Patet hec cõ
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ſequentia ab inferiori ad ſuuꝫ ſuperius.</
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>
</
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>
<
p
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="
N16277
">
<
s
xml:id
="
N16278
"
xml:space
="
preserve
">Quarto contra ſeptimam arguitur
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/>
ſic / quoniã ſi potētia vt ſex moueat reſiſtentiaꝫ vt
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/>
quatuor et potentia vt .8. moueat reſiſtentiã etiaꝫ
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/>
vt .4. diuiſim ille potentie coniuncte non mouebūt
<
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/>
eaſdem potentias coniunctas in duplo velocius.
<
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/>
</
s
>
<
s
xml:id
="
N16284
"
xml:space
="
preserve
">igitur regula falſa. </
s
>
<
s
xml:id
="
N16287
"
xml:space
="
preserve
">Probatur antecendens / quoni
<
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/>
am proportio reſultans ex illis duabus potētiis
<
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/>
ſimul ſumptis et duabus reſiſtentiis etiam ſimul
<
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/>
ſumptis eſt proportio .14. ad .8. que eſt minor du-
<
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/>
pla. eſt enim proportio ſupertripartiēs quartas.
<
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/>
</
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>
<
s
xml:id
="
N16293
"
xml:space
="
preserve
">Modo illa eſt minor dupla / vt ptꝫ ex tertia ſuppo
<
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/>
ſitiõe ſuperiꝰ allegati q̈rti capitis / g̊ ſequit̄̄ / nõ
<
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/>
eque velociter manebit talis proportio ſicut ãtea
<
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/>
mouebat dupla que eſt .8. ad .4.</
s
>
</
p
>
<
p
xml:id
="
N1629C
">
<
s
xml:id
="
N1629D
"
xml:space
="
preserve
">Ad iſta reſpondetur ꝑ ordinē ad pri-
<
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/>
ma duo argumenta reſpondet paulus venetus et
<
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/>
brauardinus ille regule philoſophi intelligun
<
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/>
tur preciſe de proportione dupla: modo inſtantie
<
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/>
fuerunt adducte in alia ſpecie proportionis </
s
>
<
s
xml:id
="
N162A8
"
xml:space
="
preserve
">¶ Ad
<
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/>
tertium reſpondeo / non eſt ad propoſitum ma-
<
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/>
terie non valet eni3 conſequentia ab inferiori ad
<
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/>
ſuum ſuperius cum dictione illatiua. </
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>
<
s
xml:id
="
N162B1
"
xml:space
="
preserve
">Adduxi ta-
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men illud argumentum / qm̄ ſemper tenet in pro-
<
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/>
portione quadrupla. </
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>
<
s
xml:id
="
N162B8
"
xml:space
="
preserve
">¶ Ad quartuꝫ reſpondeo /
<
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/>
regula philoſophi ſeptima intelligitur dūmodo
<
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/>
ille proportiões ſint equales. </
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>
<
s
xml:id
="
N162BF
"
xml:space
="
preserve
">Que aūt ſunt equa
<
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/>
les patet ex tertia ſuppoſitione quarti capitis ſe
<
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/>
cunde partis. </
s
>
<
s
xml:id
="
N162C6
"
xml:space
="
preserve
">Sed quia ex ſolutione quã dat bra-
<
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/>
uardinus ad primū argumentū / ſequitur philoſo
<
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/>
phum poſuiſſe regulas ſatis inſufficientes: que p̄
<
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/>
ciſe in vna ſpecie proportionis tenerent.
<
note
position
="
left
"
xlink:href
="
note-0063-01a
"
xlink:label
="
note-0063-01
"
xml:id
="
N1630F
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xml:space
="
preserve
">Qūo in-
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telligunt̄̄
<
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regule
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phī.</
note
>
</
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>
<
s
xml:id
="
N162D4
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xml:space
="
preserve
">Ideo di
<
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/>
co aliter / philoſophus capit potentiaꝫ pro pro
<
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portione maioris inequalitatis. </
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>
<
s
xml:id
="
N162DB
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xml:space
="
preserve
">Et iſto modo ca-
<
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/>
piendo regule habēt veritatem in omni genere ꝓ
<
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/>
protionum. </
s
>
<
s
xml:id
="
N162E2
"
xml:space
="
preserve
">Et argumentum nichil concludit / qm̄
<
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oportet quando duplatur potentia duplare pro-
<
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/>
portionem: et non curare de potentia: ita ſit ſen
<
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/>
ſus prime regule ſi aliqua potētia moueat aliquã
<
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/>
reſiſtentiã per aliquod ſpacium in aliquo tempo-
<
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/>
re etc. eadem mouebit ſubduplam reſiſtentiam etc.
<
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/>
id eſt ſi aliqua virtus moueat aliquã reſiſtentiam
<
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/>
ab aliqua proportione eadem virtus mouebit re-
<
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/>
ſiſtentiam ad quam habet proportionem duplaꝫ
<
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/>
ad aliam proportionem .i. ad quam habet ꝓpor-
<
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/>
tionē duplicatã in duplo velocius. </
s
>
<
s
xml:id
="
N162F9
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xml:space
="
preserve
">Et ſenſus huiꝰ
<
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/>
regule eſt ſi aliqua potentia moueat aliquam reſi
<
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/>
ſtentiam in aliquo tempore etc. dupla virtus mo-
<
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/>
uebit eandem reſiſtentiam in duplo velocius hoc ē
<
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/>
ſi aliqua virtus moueat aliquam reſiſtentiam ab
<
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/>
aliqua proportione: dupla proportio mouebit in
<
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/>
duplo velocius. </
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>
<
s
xml:id
="
N16308
"
xml:space
="
preserve
">Et ſic intelliguntur alie regule.</
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>
</
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>
<
note
position
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left
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xml:id
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N1631B
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xml:space
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">1. correl.</
note
>
<
p
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<
s
xml:id
="
N16320
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xml:space
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preserve
">¶ Ex quo ſequitur / ſi virtus ſe habens ad aliquã
<
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reſiſtentiam in proportione irrationali diametri
<
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/>
ad coſtam moueat alītum velociter: proportio
<
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/>
dupla ad eandē reſiſtentiã mouebit in duplo velo
<
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cius.
<
note
position
="
left
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xlink:href
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note-0063-02a
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note-0063-02
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xml:id
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xml:space
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">2. correl.</
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>
</
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<
s
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N16330
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xml:space
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">¶ Secundo igitur / non oportet q̄rere in q̈-
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libet proportione proportionem rationalem ī du
<
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plo tardius mouentem eam reſiſtentiam: ſed ſa-
<
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tis eſt / detur ꝓportio rationalis vel irrationa-
<
cb
chead
="
Capitulum quintum
"/>
lis. </
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>
<
s
xml:id
="
N1633C
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xml:space
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preserve
">et hec de regulis philoſophi.</
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>
</
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</
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<
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xml:id
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N16349
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level
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4
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type
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type-free
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capitulum
">
<
head
xml:id
="
N1634E
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xml:space
="
preserve
">Capitulum quintum / in quo ponuntur
<
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/>
regule ſiue concluſiones velocitatis et tar
<
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/>
ditatis motus penes proportionem pro
<
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/>
portionum conformiter ad intentionem
<
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/>
calculatoris.</
head
>
<
p
xml:id
="
N16359
">
<
s
xml:id
="
N1635A
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xml:space
="
preserve
">AD inducendas ſeriatim ma
<
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thematico more concluſiones docētes
<
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velocitatem et tarditatē motus penes
<
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cauſam iuxta opinionem quartam ſit.</
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>
</
p
>
<
p
xml:id
="
N16363
">
<
s
xml:id
="
N16364
"
xml:space
="
preserve
">Prima ſuppoſitio / ab equalibus pro
<
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/>
portionibus equales velocitates proueniunt: et ab
<
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/>
inequalibus inequales. </
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>
<
s
xml:id
="
N1636B
"
xml:space
="
preserve
">et a rationalibus rationa
<
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/>
les: et ab incõmēſurabilibus īcõmēſurabiles </
s
>
<
s
xml:id
="
N16370
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xml:space
="
preserve
">Pa
<
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/>
tet hec ſuppoſitio ex opinione que ponit velocita
<
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tem ſequi proportionem ꝓproportionum.</
s
>
</
p
>
<
p
xml:id
="
N16377
">
<
s
xml:id
="
N16378
"
xml:space
="
preserve
">Secundua ſuppoſitio ab equalibꝰ pro
<
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/>
portionibus que ſunt partes aliarum proportio
<
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/>
num ſiue equalium ſiue inequalium equales velo
<
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/>
citates proueniunt. </
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>
<
s
xml:id
="
N16381
"
xml:space
="
preserve
">Declaro hanc ſuppoſitionem
<
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et capio proportionem triplam et duplam: et ma
<
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/>
nifeſtum eſt: vtriuſ proportio ſexquialtera eſt
<
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/>
pars. </
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>
<
s
xml:id
="
N1638A
"
xml:space
="
preserve
">dico tunc / quãtam velocitatē producit ſex
<
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/>
quialtera que eſt pars duple tantam velocitatem
<
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ꝓducit ſexquialtera que eſt pars triple. </
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>
<
s
xml:id
="
N16391
"
xml:space
="
preserve
">Proba-
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tur ex priori ſuppoſitione / quia ſexquialtera que
<
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/>
eſt pars duple et ſexquialtera que eſt pars triple
<
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/>
ſunt equales proportiones.</
s
>
</
p
>
<
p
xml:id
="
N1639A
">
<
s
xml:id
="
N1639B
"
xml:space
="
preserve
">Tertia ſuppoſitio / ꝑ additionē equa
<
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/>
lium proportionum ſuper proportiones equales
<
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/>
vel inequales: velocitates equaliter intenduntur
<
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/>
</
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>
<
s
xml:id
="
N163A3
"
xml:space
="
preserve
">Declaro hoc in terminis et capio proportionem
<
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/>
duplam et quadruplam / et volo / vtri addatur
<
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/>
proportio ſexquialtera: qua addita dico / equa
<
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/>
liter intendunt proportiones ille ſiue ille potentie
<
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/>
motū ſuum intendunt / et tantam velocitatem acq̇-
<
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/>
rit proportio maior ſicut et minor ſupra velocita
<
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/>
tem habitam ante additionem proportionis ſexq̇
<
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/>
altere. </
s
>
<
s
xml:id
="
N163B4
"
xml:space
="
preserve
">Probatur hec ſuppoſitio ex ſecūda / quia il
<
lb
/>
la proportio ſexquialtera efficitur pars duaꝝ ꝓ-
<
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/>
portionum inequalium / igitur cum vtra equalē
<
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/>
velocitatem producet.</
s
>
</
p
>
<
p
xml:id
="
N163BD
">
<
s
xml:id
="
N163BE
"
xml:space
="
preserve
">Quarta ſuppoſitio / ꝑ decremētū dua
<
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/>
rum proportionū equalium que ſunt partes dua
<
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/>
rum proportionū ſiue equalium ſiue inequalium:
<
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/>
equales velocitates perdētur. </
s
>
<
s
xml:id
="
N163C7
"
xml:space
="
preserve
">¶ Declarat̄̄ hec ſup
<
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poſitio et capio proportionem duplam et triplaꝫ /
<
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/>
et volo / vtra deperdat proportionem ſexqui-
<
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/>
alterã / tunc dico / ſi proportio dupla ꝑdat duos
<
lb
/>
gradus velocitatis etiam duos adequate perdit
<
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/>
proportio tripla. </
s
>
<
s
xml:id
="
N163D4
"
xml:space
="
preserve
">Patet hec ſuppoſitio ex priori /
<
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/>
quoniam ille due proportiones deperdite cū eēnt
<
lb
/>
equales: equalē velocitatem producebant: igitur
<
lb
/>
per decrementum illarum equales velocitates ꝑ-
<
lb
/>
duntur / quia perduntur ipſemet quas ipſe produ
<
lb
/>
cebant.</
s
>
</
p
>
<
p
xml:id
="
N163E1
">
<
s
xml:id
="
N163E2
"
xml:space
="
preserve
">Quinta ſpupoſitio / ꝑ additionē equa
<
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/>
lis ̄titatis maiori et minori ̄titati maior ꝓpor
<
lb
/>
tio acquiritur minori ̄titati ꝙ̄ maiori. </
s
>
<
s
xml:id
="
N163E9
"
xml:space
="
preserve
">¶ Hec eſt
<
lb
/>
octaua ſuppoſitio quarti capitis ſecunde partis.</
s
>
</
p
>
<
p
xml:id
="
N163EE
">
<
s
xml:id
="
N163EF
"
xml:space
="
preserve
">Sexta ſuppoſitio eq̄ velociṫ intēde
<
lb
/>
re motum: eſt in equali tempore equales ꝑtes ade
<
lb
/>
quate acquirere: et eque proportionabiliter intē-
<
lb
/>
dere eſt in equali tempore equales proportiones
<
lb
/>
acquirere: </
s
>
<
s
xml:id
="
N163FA
"
xml:space
="
preserve
">Et ſimiliter dicendum eſt de eque velo-
<
lb
/>
citer remittere et eque proportionabiliter / vt ſi nu </
s
>
</
p
>
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