Alvarus, Thomas
,
Liber de triplici motu
,
1509
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111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
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capitulum
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<
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chead
="
Prime partis
"
file
="
0011
"
n
="
11
"/>
<
p
xml:id
="
N10C08
">
<
s
xml:id
="
N10C09
"
xml:space
="
preserve
">Quinta ſuppoſitio. </
s
>
<
s
xml:id
="
N10C0C
"
xml:space
="
preserve
">Si quantitatis
<
lb
/>
moioris ad aliquã partē aliquota quãtitatis mi-
<
lb
/>
noris ſit proportio rationalis: eiuſdē quãtitatis
<
lb
/>
maioris ad totã quantitatē minorē erit ꝓportio-
<
lb
/>
rationalis. </
s
>
<
s
xml:id
="
N10C17
"
xml:space
="
preserve
">Probatur. </
s
>
<
s
xml:id
="
N10C1A
"
xml:space
="
preserve
">q2 ſi quantitatis maioris
<
lb
/>
ad partē aliquotã quantitatis minoris eſt ꝓpor-
<
lb
/>
tio rationalis: iam quantitas maior: et pars ali-
<
lb
/>
quota minoris quantitatis ſe habent vt duo nu-
<
lb
/>
meri. </
s
>
<
s
xml:id
="
N10C25
"
xml:space
="
preserve
">et ꝑ cõſequens pars aliquota minoris quati
<
lb
/>
tatis ſe habet vt numerus. </
s
>
<
s
xml:id
="
N10C2A
"
xml:space
="
preserve
">et cū nõ ſit maior ratio
<
lb
/>
de vna parte aliquota quã de qualibet tanta: ſe-
<
lb
/>
quitur / quelibet tanta: ſe habet vt numerꝰ. </
s
>
<
s
xml:id
="
N10C31
"
xml:space
="
preserve
">et per
<
lb
/>
ↄ̨ñs aggregatū ex oībus partibꝰ aliquotꝪ ipſius
<
lb
/>
mīoris: ſe habet vt nūerꝰ. </
s
>
<
s
xml:id
="
N10C38
"
xml:space
="
preserve
">vt ptꝫ ex ṗma ſuppoſiti
<
lb
/>
one: et illud aggregatū eſt ipſa mīor quãtitas: igr̄
<
lb
/>
tp̄a mīor quãtitas ſe hꝫ vt numerꝰ: ad maiorē et ſic
<
lb
/>
inter illas eſt ꝓportio rõnalis. </
s
>
<
s
xml:id
="
N10C41
"
xml:space
="
preserve
">et ſic ptꝫ ſuppoſitio</
s
>
</
p
>
<
p
xml:id
="
N10C44
">
<
s
xml:id
="
N10C45
"
xml:space
="
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">Sexta ſuppoſitio. </
s
>
<
s
xml:id
="
N10C48
"
xml:space
="
preserve
">Si due quantita
<
lb
/>
tes inequales ſe habeant in ꝓportione rationali.
<
lb
/>
</
s
>
<
s
xml:id
="
N10C4E
"
xml:space
="
preserve
">vtra illaꝝ ſe habet ad exceſſum quo maior exce-
<
lb
/>
dit minorē in ꝓportione rationali: vĺ equalitatis
<
lb
/>
</
s
>
<
s
xml:id
="
N10C54
"
xml:space
="
preserve
">Probatur hec ſuppoſitio. </
s
>
<
s
xml:id
="
N10C57
"
xml:space
="
preserve
">qm̄ ſi ille quantitates:
<
lb
/>
ſe habent in ꝓportione rationali: ſe habēt vt duo
<
lb
/>
numeri. </
s
>
<
s
xml:id
="
N10C5E
"
xml:space
="
preserve
">et vltra ſe habent vt duo numeri: ergo ex-
<
lb
/>
ceſſus quo vna excedit alterã eſt numerꝰ. </
s
>
<
s
xml:id
="
N10C63
"
xml:space
="
preserve
">qm̄ ſemꝑ
<
lb
/>
numerꝰ excedit numerū ꝑ numerū. </
s
>
<
s
xml:id
="
N10C68
"
xml:space
="
preserve
">et vltra exceſſus
<
lb
/>
eſt numerꝰ: et quelibet aliarū ſe habet vt numerus
<
lb
/>
reſpectu illiꝰ exceſſus. </
s
>
<
s
xml:id
="
N10C6F
"
xml:space
="
preserve
">igr̄ inter illū exceſſū et quãli
<
lb
/>
bet illarum quantitatem eſt proportio ratiõalis
<
lb
/>
vel equalitatis: quod fuit probandum.</
s
>
</
p
>
<
p
xml:id
="
N10C76
">
<
s
xml:id
="
N10C77
"
xml:space
="
preserve
">His ſuppoſitionibus poſitis: ſit pri-
<
lb
/>
ma cõcluſio </
s
>
<
s
xml:id
="
N10C7C
"
xml:space
="
preserve
">Infinite ſunt ſpecies ꝓportionis irra
<
lb
/>
tionalis minores dupla: et illarū in īfinitū parua
<
lb
/>
eſt aliqua. </
s
>
<
s
xml:id
="
N10C83
"
xml:space
="
preserve
">Probatur prima pars huiꝰ cõcluſiõis /
<
lb
/>
et capio coſtã vniꝰ quadrati: et ſuã diametrū. </
s
>
<
s
xml:id
="
N10C88
"
xml:space
="
preserve
">et vo
<
lb
/>
lo / vniformiter in hora diminuat̄̄ exceſſus quo
<
lb
/>
diameter excedit coſtã ad nõ quantū. </
s
>
<
s
xml:id
="
N10C8F
"
xml:space
="
preserve
">ita in fine
<
lb
/>
diameter et coſta erūt equalia. </
s
>
<
s
xml:id
="
N10C94
"
xml:space
="
preserve
">quo poſito ſic argr̄
<
lb
/>
</
s
>
<
s
xml:id
="
N10C98
"
xml:space
="
preserve
">Inter diametrū que ſic diminuitur et coſtaꝫ erunt
<
lb
/>
infinite ꝓportiones irratiõales cõtinuo minores
<
lb
/>
dupla: igitur infinite ſunt ſpecies ꝓportiõis irra-
<
lb
/>
tionalis minores dupla. </
s
>
<
s
xml:id
="
N10CA1
"
xml:space
="
preserve
">Probatur ãtecedēs. </
s
>
<
s
xml:id
="
N10CA4
"
xml:space
="
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">qm̄
<
lb
/>
quãdo exceſſus: quo diameter excedit coſtã ꝑdide-
<
lb
/>
rit medietatē ſui / tūc aggregatū ex alia medietate
<
lb
/>
et coſta ſe habebit ad coſtã in ꝓportiõe irratiõali
<
lb
/>
minori dupla. / et quãdo exceſſus diametri fuerit di
<
lb
/>
minutꝰ ad vnã quartã ſui: tūc aggregati ex coſta
<
lb
/>
et illa quarta exceſſus diametri ad coſtã erit ꝓpor
<
lb
/>
tio irrationalis. </
s
>
<
s
xml:id
="
N10CB5
"
xml:space
="
preserve
">et ſic cõſequēter ſemꝑ aggregatū
<
lb
/>
ex coſta: et aliqua parte aliquota exceſſus ſe habe
<
lb
/>
bit ad coſtã in ꝓportione irratiõali mīori dupla:
<
lb
/>
et infinita ſunt talia aggregata ex coſta et aliqua
<
lb
/>
parte aliquota exceſſus: igitur infinite erūt ꝓpor
<
lb
/>
tiones irrationales cõtinuo minores dupla. </
s
>
<
s
xml:id
="
N10CC2
"
xml:space
="
preserve
">Ptꝫ
<
lb
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cõſequētia. </
s
>
<
s
xml:id
="
N10CC7
"
xml:space
="
preserve
">et arguit̄̄ maior videlicet / aggregatū
<
lb
/>
ex coſta et medietate exceſſus diametri: ſe habet in
<
lb
/>
ꝓportione irrationali ad coſtã: q2 ſi nõ. </
s
>
<
s
xml:id
="
N10CCE
"
xml:space
="
preserve
">ſed ſe ba-
<
lb
/>
bent in ꝓportione rationali. </
s
>
<
s
xml:id
="
N10CD3
"
xml:space
="
preserve
">ſequitur: vtra il
<
lb
/>
laꝝ: ſe habet ad exceſſum quo maior excedit mino
<
lb
/>
rem in ꝓportione rationali vel equalitatis. </
s
>
<
s
xml:id
="
N10CDA
"
xml:space
="
preserve
">Ptꝫ
<
lb
/>
ↄ̨ña ex ſexta ſuppoſitione. </
s
>
<
s
xml:id
="
N10CDF
"
xml:space
="
preserve
">et cõſequēs eſt falſū. </
s
>
<
s
xml:id
="
N10CE2
"
xml:space
="
preserve
">qm̄
<
lb
/>
ſi vtra illarū ſe haberet ad exceſſum quo diame
<
lb
/>
ter excedit coſtã: in ꝓportione rationali .etc̈. cū al-
<
lb
/>
tera illarum ſit coſta: et exceſſus quo maior excedit
<
lb
/>
minorē ſit medietas exceſſus diametri: ſequitur /
<
cb
chead
="
Capitulum quartū.
"/>
coſte ad medietatē exceſſus diametri erit ꝓportio
<
lb
/>
rationalis. </
s
>
<
s
xml:id
="
N10CF2
"
xml:space
="
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">Patet hec cõſequētia ex ſe. </
s
>
<
s
xml:id
="
N10CF5
"
xml:space
="
preserve
">et vltra ſe-
<
lb
/>
quitur / coſte: ad exceſſum diametri erit ꝓportio
<
lb
/>
rationalis. </
s
>
<
s
xml:id
="
N10CFC
"
xml:space
="
preserve
">Patet cõſequētia ex quīta ſuppoſitio
<
lb
/>
ne. </
s
>
<
s
xml:id
="
N10D01
"
xml:space
="
preserve
">hoc addito / medietas exceſſus eſt pars aliq̊ta
<
lb
/>
illius: cõſequēs eſt falſum: vt patet ex quarta igit̄̄
<
lb
/>
et ãtecedēs. </
s
>
<
s
xml:id
="
N10D08
"
xml:space
="
preserve
">Et ſic ꝓbabis. </
s
>
<
s
xml:id
="
N10D0B
"
xml:space
="
preserve
"> aggregatū ex coſta et
<
lb
/>
quarta parte exceſſus diametri ſe habet in ꝓpor-
<
lb
/>
tione irratiõali ad coſtã: et ſimiliter aggregatū
<
lb
/>
ex coſta et octaua parte exceſſus / et ſic cõſequenter.
<
lb
/>
</
s
>
<
s
xml:id
="
N10D15
"
xml:space
="
preserve
">Quod autē ille ꝓportiones cõtinuo ſint minores
<
lb
/>
dupla: patet. </
s
>
<
s
xml:id
="
N10D1A
"
xml:space
="
preserve
">q2 a principio ꝓportio diametri ad
<
lb
/>
coſtã erat minor dupla. cū eſſet medietas duple: et
<
lb
/>
cõtinuo diminuet̄̄ vſ ad nõ gradū: vt ptꝫ ex ſcḋa
<
lb
/>
parte. </
s
>
<
s
xml:id
="
N10D23
"
xml:space
="
preserve
">igr̄ cõtinuo erit minor dupla. </
s
>
<
s
xml:id
="
N10D26
"
xml:space
="
preserve
">Itē continuo
<
lb
/>
exceſſus erit minor et minor reſpectu eiuſdē quãti-
<
lb
/>
tatis: ergo cõtinuo ꝓportio erit minor et mīor. </
s
>
<
s
xml:id
="
N10D2D
"
xml:space
="
preserve
">Et
<
lb
/>
ex hoc ptꝫ ſcḋa pars cõclſionis. </
s
>
<
s
xml:id
="
N10D32
"
xml:space
="
preserve
">q2 in infinitū mo-
<
lb
/>
dicus erit exceſſus quãtitatis maioris ad quãtita
<
lb
/>
tē minorē: et ipſa quãtitas minor cõtinuo manebit
<
lb
/>
equalis et īuariata. </
s
>
<
s
xml:id
="
N10D3B
"
xml:space
="
preserve
">igitur infinite modica erit ꝓ-
<
lb
/>
portio maioris ad quantitatem minorem. </
s
>
<
s
xml:id
="
N10D40
"
xml:space
="
preserve
">Conſe
<
lb
/>
quentia patet ex ſecūda parte. </
s
>
<
s
xml:id
="
N10D45
"
xml:space
="
preserve
">Et ſic patet prima
<
lb
/>
concluſio.
<
note
position
="
right
"
xlink:href
="
note-0011-01a
"
xlink:label
="
note-0011-01
"
xml:id
="
N10D67
">
<
s
xml:id
="
N10D6B
"
xml:space
="
preserve
">Correla-
<
lb
/>
rium.
<
lb
/>
</
s
>
<
s
xml:id
="
N10D71
"
xml:space
="
preserve
">Gñatio
<
lb
/>
infinitoꝝ
<
lb
/>
ſpecierū
<
lb
/>
ꝓportio-
<
lb
/>
nis irra-
<
lb
/>
tionalis.</
s
>
</
note
>
</
s
>
<
s
xml:id
="
N10D4F
"
xml:space
="
preserve
">¶ Ex hac concluſione ſequitur: infini-
<
lb
/>
tis modis poſſunt generari infinite ſpecies mino
<
lb
/>
res dupla irrationalis ꝓportiõis: vtpote ſi exceſ-
<
lb
/>
ſus diametri diminuatur per partes ꝓportiona-
<
lb
/>
les ꝓportione dupla: </
s
>
<
s
xml:id
="
N10D5A
"
xml:space
="
preserve
">Alio modo ꝓportiõe tripla
<
lb
/>
alio quadrupla. alio ſexquialtera. / et ſic in infinitū
<
lb
/>
</
s
>
<
s
xml:id
="
N10D60
"
xml:space
="
preserve
">Patet correlariū intelligēti ꝓbationē cõculſiõis</
s
>
</
p
>
<
p
xml:id
="
N10D7E
">
<
s
xml:id
="
N10D7F
"
xml:space
="
preserve
">Secūda cõcluſio. </
s
>
<
s
xml:id
="
N10D82
"
xml:space
="
preserve
">Infinite ſunt ſpe-
<
lb
/>
cies ꝓportionis irratiõalis maioris dupla: et illa
<
lb
/>
rū infinite magna eſt aliqua. </
s
>
<
s
xml:id
="
N10D89
"
xml:space
="
preserve
">Probatur hec con-
<
lb
/>
cluſio: et pono / exceſſus quo diameter excedit co-
<
lb
/>
ſtam: diminuatur vniformiter in hora vſ ad nõ
<
lb
/>
quantū. </
s
>
<
s
xml:id
="
N10D92
"
xml:space
="
preserve
">et capio ꝓportionē que eſt coſte ad exceſſū
<
lb
/>
diametri: et arguo ſic. </
s
>
<
s
xml:id
="
N10D97
"
xml:space
="
preserve
">Illa ꝓportio eſt maior du-
<
lb
/>
pla irrationalis. </
s
>
<
s
xml:id
="
N10D9C
"
xml:space
="
preserve
">et ꝓportio coſte ad medietatē il-
<
lb
/>
lius exceſſus eſt etiã irratiõalis maior: et ꝓ-
<
lb
/>
portio coſte ad quartã eſt etiã irrationalis maior
<
lb
/>
dupla: et ſic in infinitū quelibet ꝓportio coſte ad
<
lb
/>
aliquã partē aliquotã exceſſus eſt ꝓportio irrati-
<
lb
/>
onalis et ſunt īfinite partes aliquote cõtinuo mi-
<
lb
/>
nores et minores / ergo īfinite ſunt ꝓportiões irra
<
lb
/>
tiõales minores dupla. </
s
>
<
s
xml:id
="
N10DAD
"
xml:space
="
preserve
">Probat̄̄ maior. </
s
>
<
s
xml:id
="
N10DB0
"
xml:space
="
preserve
">qm̄ coſte
<
lb
/>
ad exceſſū q̊ diameṫ excedit coſtã eſt ꝓportio irra-
<
lb
/>
tionalis: ex q̈rta ſuppoſitiõe maior dupla: vt con-
<
lb
/>
ſtat. </
s
>
<
s
xml:id
="
N10DB9
"
xml:space
="
preserve
">qm̄ ille exceſſus eſt minor quã medietas coſte.
<
lb
/>
</
s
>
<
s
xml:id
="
N10DBD
"
xml:space
="
preserve
">qm̄ ſi eſſet medietas coſte aut moior: iam ibi eſſet
<
lb
/>
ꝓportio ſexq̇altera īter diametrū et coſtã: vel ma-
<
lb
/>
ior ſexquialtera: quod eſt falſum. </
s
>
<
s
xml:id
="
N10DC4
"
xml:space
="
preserve
">vt ptꝫ ex pcedēti
<
lb
/>
capite. </
s
>
<
s
xml:id
="
N10DC9
"
xml:space
="
preserve
">ergo q̄libet ꝓportio coſte ad aliquã partē
<
lb
/>
aliquotã exceſſus quo diameter excedit coſtam eſt
<
lb
/>
ꝓportio irratiõalis maior dupla: qḋ fuit ꝓbãdū.
<
lb
/>
</
s
>
<
s
xml:id
="
N10DD1
"
xml:space
="
preserve
">Patet cõſequētia ex quīta ſuppoſitiõe. </
s
>
<
s
xml:id
="
N10DD4
"
xml:space
="
preserve
">qm̄ ex illa
<
lb
/>
ſuppoſitione. </
s
>
<
s
xml:id
="
N10DD9
"
xml:space
="
preserve
">ſi coſta ad aliquã partē aliquotã ex-
<
lb
/>
ceſſus quo diameter excedit coſtã ſe habet in pro-
<
lb
/>
portione ratiõali: ipſius coſte ad totū illū exceſſū
<
lb
/>
erit ꝓportio rationalis: ſed nõ ipſiꝰ coſte ad totū
<
lb
/>
illū exceſſū quo diameter excedit coſtã eſt ꝓportio
<
lb
/>
rationalis. </
s
>
<
s
xml:id
="
N10DE6
"
xml:space
="
preserve
">vt ptꝫ ex quarta ſuppoſitiõe. </
s
>
<
s
xml:id
="
N10DE9
"
xml:space
="
preserve
">igitur nõ
<
lb
/>
coſta ad aliquã partē aliquotã exceſſus quo dia-
<
lb
/>
meter excedit coſtã: ſe habet in ꝓportiõe ratiõali.
<
lb
/>
</
s
>
<
s
xml:id
="
N10DF1
"
xml:space
="
preserve
">Patet cõſequētia ꝑ ſyllogiſmū hypotheticum: a
<
lb
/>
tota cõditionali cū deſtructiõe cõſequētis .etc̈. / et ſic
<
lb
/>
patet prima pars. </
s
>
<
s
xml:id
="
N10DF8
"
xml:space
="
preserve
">Et ſcḋa ꝓbatur facile. </
s
>
<
s
xml:id
="
N10DFB
"
xml:space
="
preserve
">q2 in īfi- </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>