Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Prime partis
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0013
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13
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<
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<
s
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xml:space
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">His poſitis ſit prima cõcluſio. </
s
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<
s
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xml:space
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">Quã
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docun aliquod corpus diuiditur quouis genere
<
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proportionis: totū corpus ſe debet habere ad ag
<
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gregatum ex omnibus partibus proportionalibꝰ
<
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/>
ſequentibus primam: in ea proportione qua cor
<
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pus diuiditur. </
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>
<
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xml:id
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N10F7E
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xml:space
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preserve
">Exemplum / vt ſi corpus diuidatur
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proportione ſexquialtera: oportet / illud corpus
<
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/>
ſe habeat ad aggregatum ex omnibus partibus
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/>
proportionabilibꝰ. </
s
>
<
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xml:id
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N10F87
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xml:space
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preserve
">ſequentibus primam: in pro
<
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portione ſexquialtera. </
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>
<
s
xml:id
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N10F8C
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xml:space
="
preserve
">Probatur hec concluſio: et
<
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/>
volo / b. corpꝰ diuidatur in partes proportiona
<
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/>
les proportione a. in infinitum: et arguo ſic / b. cor-
<
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/>
pus diuiditur in partes proportionales propor
<
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/>
tione .a. in infinitum: igitur deperdendo primam
<
lb
/>
partem proportionalem proportione a. ipſum ef
<
lb
/>
ficitur in a. proportione minus: patet conſequētia
<
lb
/>
ex ſecunda parte quarte ſuppoſitionis: et vltra il
<
lb
/>
lud corpus b. deperdendo primã partem propor-
<
lb
/>
tionalem a. efficitur ſiue manet in a. proportione
<
lb
/>
minus et non manet niſi aggregatum ex omībus
<
lb
/>
ſequentibus primam partem proportionalē: igi
<
lb
/>
tur illud corpus b. ſe habet ad aggregatum ex om
<
lb
/>
nibus partibus proportionabilibus ſequentibus
<
lb
/>
primam eius partem proportionalem proportio
<
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/>
ne a. in eadem proportione a. / quod fuit ꝓbanduꝫ.
<
lb
/>
</
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>
<
s
xml:id
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N10FAE
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xml:space
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preserve
">Patet hec conſequentia: quia ſi illud aggregatū
<
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ex omnibus ſequentibus primã. etc̈. eſt minus ipſo
<
lb
/>
b. corpore in a proportione: ſequitur / ipſum b.
<
lb
/>
corpus eſt maius illo aggregato ex omnibus ſe-
<
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/>
quentibus primam in a. proportione.</
s
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</
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<
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xml:space
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">Secunda cõcluſio. </
s
>
<
s
xml:id
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N10FBD
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xml:space
="
preserve
">Ad inueniendū
<
lb
/>
reſiduū a prima parte ꝓportionali quauis ꝓpor
<
lb
/>
tione rationali corpus diuidatur: capiãtur primi
<
lb
/>
numeri talis ꝓportionis: et diuidat̄̄ corpus in tot
<
lb
/>
vnitates quotus eſt numerꝰ maior illius propor
<
lb
/>
tionis: et ex illis partibꝰ ꝓ reſiduo a prima parte
<
lb
/>
capiantur tot: quotus eſt numerus minor talis ꝓ-
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lb
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portionis. </
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>
<
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xml:id
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N10FCE
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xml:space
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preserve
">Exēplum / vt ſi vis diuidere corpꝰ ꝓpor-
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tione ſexquitertia: et videre quid reſtabit pro reſi-
<
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/>
duo a prima parte proportionali: capias .4. et .3.
<
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/>
primos numeros ꝓportionis ſexquitertie: et diui
<
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/>
das totū corpus in quatuor partes equales: quia
<
lb
/>
numerus maior eſt quaternarius: et pro reſiduo a
<
lb
/>
prima ꝑte ꝓportionali capias tres partes ex illis
<
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/>
q2 numerus minor eſt ternarius. </
s
>
<
s
xml:id
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N10FDF
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xml:space
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preserve
">Probat̄̄ hec con
<
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cluſio et volo / b. corpus diuidatur proportione
<
lb
/>
a. cuius proportionis primi numeri ſint c. maior
<
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/>
numerus et d. minor / et arguo ſic. </
s
>
<
s
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="
N10FE8
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xml:space
="
preserve
">Iſtud corpus eſt
<
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/>
diuiſum per partes ꝓportionales proportione a /
<
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/>
ergo totū iſtud b. corpus ſe habet ad aggregatuꝫ
<
lb
/>
ex oībus partibus ꝓportionabilibus ꝓportione
<
lb
/>
a. ſequētibus primã in proportione a. </
s
>
<
s
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N10FF3
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xml:space
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preserve
">Patet ↄ̨ña
<
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ex priori concluſione: et vltra totum b. ſe habet ad
<
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/>
aggregatum .etc̈. in ꝓportione a. / ergo ſequitur /
<
lb
/>
ipſuꝫ b. ſe habet ad illud aggregatū ſicut c. nume
<
lb
/>
reus ad d. numerū / vt cõſtat et d. numerꝰ eſt nume
<
lb
/>
rus minor: ergo ſequitur / aggregatū ex omībꝰ
<
lb
/>
partibus ꝓportionalibꝰ proportione a. ſequē-
<
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/>
tibus primã ſe habet vt numerus mīor primorum
<
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/>
numerorū proportionis a. reſpectu maioris nu-
<
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/>
meri: et nõ poteſt ſic ſe habere: niſi fiat diuiſio ta-
<
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/>
lis corporis modo dicto in concluſione vel equiua
<
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/>
lenti / vt conſtat: igitur ſequitur concluſio.</
s
>
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<
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">Tertia cõcluſio. </
s
>
<
s
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N11010
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xml:space
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">Ad diuidendū cor-
<
lb
/>
pus per partes proportionales qua vis ꝓportõe
<
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Capitulum quintū
"/>
multiplici capiēda eſt pro reſiduo a prima parte
<
lb
/>
proportionali vna pars aliquota denoīata a nu
<
lb
/>
mero talē proportionē multiplicem denominante
<
lb
/>
vt in diuiſione dupla proportione capiēda eſt vna
<
lb
/>
medietas pro reſiduo a prima parte ꝓportionali
<
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/>
et proportione tripla vna tertia et quadrupla vna
<
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/>
quarta quintupla vero vna quinta et ſic ī infinitū
<
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/>
</
s
>
<
s
xml:id
="
N11025
"
xml:space
="
preserve
">Probatur hec cõcluſio: qm̄ ſemper corpus diuiſū
<
lb
/>
per partes proportionales aliqua proportione ſe
<
lb
/>
debet habere ad reſiduū a prima parte ꝓportio-
<
lb
/>
nali in eadeꝫ ꝓportione qua diuiditur: vt patet ex
<
lb
/>
prima concluſione: ſed quodlibet corpus ſe hab3
<
lb
/>
ad ſuã medietatē in proportiõe dupla et quodlib3
<
lb
/>
ad ſuã tertiã in tripla: ad quartã in quadrupla: et
<
lb
/>
ſic conſequēter: ergo in qualibet diuiſione corpo-
<
lb
/>
ris ꝓportione dupla debet capi ꝓ reſiduo a pri-
<
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/>
ma parte proportionali medietas. </
s
>
<
s
xml:id
="
N1103A
"
xml:space
="
preserve
">et proportione
<
lb
/>
tripla vna tertia: et q̈drupla vna quarta et quintu
<
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pla vna quīta. </
s
>
<
s
xml:id
="
N11041
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xml:space
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preserve
">et ſic in infinituꝫ: quod fuit ꝓbandū
<
lb
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<
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xml:id
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xml:space
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">Correla
<
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riū ṗmū.</
note
>
</
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<
s
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xml:space
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preserve
">¶ Ex hac cõcluſione ſequitur primo: diuidendo
<
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corpus proportiõe dupla prima pars erit medie
<
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tas, et ſecūda medietas reſidui: et tertia medietas
<
lb
/>
reſidui, et ſic cõſequenter. </
s
>
<
s
xml:id
="
N11054
"
xml:space
="
preserve
">ꝓportione tripla prima
<
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/>
pars eſt due tertie totius: et ſecūda due tertie reſi-
<
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/>
dui, et tertia due tertie reſidui a prima et ſecunda:
<
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/>
et ſic ſine termino. </
s
>
<
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="
N1105D
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xml:space
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preserve
">ꝓportione vero quadrupla pri
<
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ma pars eſt tres quarte, et ſecunda tres quarte re
<
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/>
ſidui. </
s
>
<
s
xml:id
="
N11064
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xml:space
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">ꝓportiõe vero quītupla prima pars eſt qua
<
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tuor quinte. </
s
>
<
s
xml:id
="
N11069
"
xml:space
="
preserve
">et ſextupla quin ſexte et ſeptupla ſex
<
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ſeptime: et ſic ſine termino. </
s
>
<
s
xml:id
="
N1106E
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xml:space
="
preserve
">Probatur hoc correla
<
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/>
riū: quia diuidendo proportione dupla: totum re
<
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/>
ſiduū a prima parte ꝓportõali eſt vna medietas /
<
lb
/>
vt patet ex cõcluſione: igitur prima pars erit vna
<
lb
/>
medietas </
s
>
<
s
xml:id
="
N11079
"
xml:space
="
preserve
">Patet cõſequētia ex ſecūda ſuppoſitio
<
lb
/>
ne / qm̄ omnes partes proportionales totū corpꝰ
<
lb
/>
abſoluūt. </
s
>
<
s
xml:id
="
N11080
"
xml:space
="
preserve
">Item diuidendo ꝓportione tripla reſi
<
lb
/>
duū a prima parte ꝓportionali eſt vna tertia / igit̄̄
<
lb
/>
prima erit due tertie. </
s
>
<
s
xml:id
="
N11087
"
xml:space
="
preserve
">Itē diuidēdo quadrupla re
<
lb
/>
ſiduū a ṗma eſt vna quarta / igit̄̄ prima eſt 3 quar-
<
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/>
te. </
s
>
<
s
xml:id
="
N1108E
"
xml:space
="
preserve
">Quītupla vero eſt vna quīta / igitur prima erit
<
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/>
quatuor quinte. </
s
>
<
s
xml:id
="
N11093
"
xml:space
="
preserve
">Et ſimiliter arguēdū eſt de ꝓpor
<
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/>
tione ſextupla ſeptupla / et ſic cõſequenter. </
s
>
<
s
xml:id
="
N11098
"
xml:space
="
preserve
">igit̄̄ cor-
<
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relarium verū. </
s
>
<
s
xml:id
="
N1109D
"
xml:space
="
preserve
">Antecedentia harū cõſequētiarum
<
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patēt ex ꝓxima concluſione et ipſe conſequentie ex
<
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/>
ſecunda ſuppoſitione.
<
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="
right
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xlink:href
="
note-0013-02a
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xlink:label
="
note-0013-02
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xml:id
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xml:space
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preserve
">Corelari
<
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riū ſcḋm</
note
>
</
s
>
<
s
xml:id
="
N110A9
"
xml:space
="
preserve
">¶ Sequitur ſecūdo / diui
<
lb
/>
dēdo corpus per partes proportionales ꝓportõe
<
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/>
dupla: reſiduum a prima eſt equale prime parti: et
<
lb
/>
ꝓportione tripla eſt ſubduplū ad ṗmã: et quadru
<
lb
/>
pla ſubtriplū: et quītupla ſubquadruplū: et ſextu-
<
lb
/>
pla ſubquintuplū: et ſic ſine termīo. </
s
>
<
s
xml:id
="
N110B6
"
xml:space
="
preserve
">Patet hec cor
<
lb
/>
relariū facile ex priori et concluſione. </
s
>
<
s
xml:id
="
N110BB
"
xml:space
="
preserve
">Si em̄ diui-
<
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/>
dendo ꝓportione tripla prima pars eſt due tertie
<
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/>
et reſiduū vna tertia cū vna tertia ſit ſubduplū ad
<
lb
/>
duas tertias reſiduū a prima diuidēdo ꝓportiõe
<
lb
/>
tripla erit ſubduplū ad primã. </
s
>
<
s
xml:id
="
N110C6
"
xml:space
="
preserve
">Item cū diuidēdo
<
lb
/>
corpus ꝓportione quadrupla prima pars ſit tres
<
lb
/>
quarte et reſiduuꝫ a prima vna quarta vna: autem
<
lb
/>
quarta eſt ſubtripla ad tres quartas: igitur reſi-
<
lb
/>
duū a prima parte diuidendo proportõe quadru
<
lb
/>
pla eſt ſubtriplum ad primã partem. </
s
>
<
s
xml:id
="
N110D3
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xml:space
="
preserve
">Et hoc mo-
<
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do de aliis probabis.</
s
>
</
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p
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<
s
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">Quarta cõcluſio. </
s
>
<
s
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="
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"
xml:space
="
preserve
">Ad diuidendū cor
<
lb
/>
pus qua vis ꝓportione ſuperparticulari: capiēda
<
lb
/>
eſt ꝓ ṗma parte ꝓportionali vna pars aliquota
<
lb
/>
denoīata a maiori numero ṗmorū numeroꝝ talis
<
lb
/>
ꝓportionis. </
s
>
<
s
xml:id
="
N110FB
"
xml:space
="
preserve
">puta diuidendo ꝓportione ſexquial- </
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>
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