Alvarus, Thomas
,
Liber de triplici motu
,
1509
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[Figure 1]
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[Figure 2]
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[Figure 3]
Page: 9
[Figure 4]
Page: 16
[Figure 5]
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[Figure 6]
Page: 67
[Figure 7]
Page: 72
[Figure 8]
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[Figure 9]
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[Figure 10]
Page: 131
[Figure 11]
Page: 131
[Figure 12]
Page: 210
[Figure 13]
Page: 275
[Figure 14]
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capitulum
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<
s
xml:id
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xml:space
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<
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chead
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Prime partis
"
file
="
0010
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n
="
10
"/>
laris: eſt ſexquialtera: vel ſexquitertia: vel minor
<
lb
/>
ſexquitertia: et nulla proportio diametri ad coſtã
<
lb
/>
eſt ſexquialtera: vel ſexquitertia vel minor ſexq̇ter
<
lb
/>
tia. / ergo nulla proportio diametri ad coſtã: eſt ſu-
<
lb
/>
perparticularis. </
s
>
<
s
xml:id
="
N10A08
"
xml:space
="
preserve
">Cõſequētia ptꝫ cū maiore mani-
<
lb
/>
feſte: et probatur minor. </
s
>
<
s
xml:id
="
N10A0D
"
xml:space
="
preserve
">qm̄ oīs proportio ſexqui-
<
lb
/>
altera: vel ſexquitertia: vel minor ſexquitertia. eſt
<
lb
/>
maior vel minor: medietate duple. et nulla propor
<
lb
/>
tio diametri ad coſtã: eſt maior vel minor medieta
<
lb
/>
te duple. q2 eſt equalis medietati duple. / vt patꝫ ex
<
lb
/>
tertia ſuppoſitiõe. </
s
>
<
s
xml:id
="
N10A1A
"
xml:space
="
preserve
">igitur nulla ꝓportio diametri
<
lb
/>
ad coſtã: eſt ſexquialtera. vel ſexq̇tertia: vel minor
<
lb
/>
ſexquitertia. </
s
>
<
s
xml:id
="
N10A21
"
xml:space
="
preserve
">Cõſequētia patet cū minore: et maior
<
lb
/>
probatur: q2 ſexquialtera eſt maior quã medietas
<
lb
/>
duple. et ſexquitertia minor quã medietas duple / et
<
lb
/>
ex cõſequēti: ꝑ locū a maiori: quelibet minor ſexq̇-
<
lb
/>
tertia: eſt minor quã medietas duple. / ergo oīs pro
<
lb
/>
portio ſexquialtera. vel ſexquitertia: vĺ minor ſex
<
lb
/>
quitertia: eſt maior: vel minor: medietate duple.
<
lb
/>
</
s
>
<
s
xml:id
="
N10A31
"
xml:space
="
preserve
">Probatur tamē ãtecedēs. </
s
>
<
s
xml:id
="
N10A34
"
xml:space
="
preserve
">q2 dupla. cõponit̄̄ ade-
<
lb
/>
quate ex ſexquialtera: et ſexquitertia. / vt patet ex
<
lb
/>
ſecūda parte. </
s
>
<
s
xml:id
="
N10A3B
"
xml:space
="
preserve
">et ſexquialtera eſt maior. </
s
>
<
s
xml:id
="
N10A3E
"
xml:space
="
preserve
">et ſexquiter
<
lb
/>
tia mīor. </
s
>
<
s
xml:id
="
N10A43
"
xml:space
="
preserve
">igitur ſexquialtera eſt maior quã medie
<
lb
/>
tas duple. et ſexquitertia minor quã medietas du
<
lb
/>
ple. </
s
>
<
s
xml:id
="
N10A4A
"
xml:space
="
preserve
">Patet conſequētia ex ſexta ſuppoſitione q̈rti
<
lb
/>
capitis ſecūde partis.</
s
>
</
p
>
<
p
xml:id
="
N10A4F
">
<
s
xml:id
="
N10A50
"
xml:space
="
preserve
">Tertia concluſio. </
s
>
<
s
xml:id
="
N10A53
"
xml:space
="
preserve
">Nulla proportio
<
lb
/>
diametri ad coſtã eſt aliqua proportio ſuprapar-
<
lb
/>
tiens. </
s
>
<
s
xml:id
="
N10A5A
"
xml:space
="
preserve
">Probatur. </
s
>
<
s
xml:id
="
N10A5D
"
xml:space
="
preserve
">q2 oīs proportio ſuprapartiēs:
<
lb
/>
reperibilis eſt inter duos numeros: quoꝝ alter eſt
<
lb
/>
impar. </
s
>
<
s
xml:id
="
N10A64
"
xml:space
="
preserve
">et nulla proportio diametri ad coſtã: repe
<
lb
/>
ribilis eſt inter duos numeros: quoꝝ alter eſt īpar /
<
lb
/>
ergo nulla proporito diametri ad coſtã: eſt aliqua
<
lb
/>
proportio ſuprapartiens </
s
>
<
s
xml:id
="
N10A6D
"
xml:space
="
preserve
">Patet conſequentia in
<
lb
/>
ſcḋo ſcḋe vt prius. </
s
>
<
s
xml:id
="
N10A72
"
xml:space
="
preserve
">et maior ex quarta ſuppoſitiõe
<
lb
/>
et minor probat̄̄. </
s
>
<
s
xml:id
="
N10A77
"
xml:space
="
preserve
">q2 ſi nõ detur oppoſitū. </
s
>
<
s
xml:id
="
N10A7A
"
xml:space
="
preserve
">videlicet /
<
lb
/>
proportio diametri ad coſtã: reperitur inter du
<
lb
/>
os numeros: quoꝝ alter eſt impar. </
s
>
<
s
xml:id
="
N10A81
"
xml:space
="
preserve
">ita diameter
<
lb
/>
et coſta: ſe habere poſſūt vt duo nūeri: quoꝝ alter
<
lb
/>
eſt impar. </
s
>
<
s
xml:id
="
N10A88
"
xml:space
="
preserve
">vel igitur diameter erit numerꝰ impar:
<
lb
/>
vel coſta ſi diameter: ſequitur / quadratū ipſius
<
lb
/>
diametri: erit numerꝰ impar. </
s
>
<
s
xml:id
="
N10A8F
"
xml:space
="
preserve
">Patet cõſequētia ex
<
lb
/>
quinta ſuppoſitione. </
s
>
<
s
xml:id
="
N10A94
"
xml:space
="
preserve
">et vltra quadratū diametri:
<
lb
/>
eſt numerꝰ impar. </
s
>
<
s
xml:id
="
N10A99
"
xml:space
="
preserve
">ergo quadratū diametri: nõ eſt
<
lb
/>
duplū ad quadratū coſte. </
s
>
<
s
xml:id
="
N10A9E
"
xml:space
="
preserve
">Patet conſequentia ex
<
lb
/>
ſexta ſuppoſitione. </
s
>
<
s
xml:id
="
N10AA3
"
xml:space
="
preserve
">et cõſequēs eſt falſum: vt patet
<
lb
/>
ex ſecūda ſuppoſitione. </
s
>
<
s
xml:id
="
N10AA8
"
xml:space
="
preserve
">igitur et antecedens: </
s
>
<
s
xml:id
="
N10AAB
"
xml:space
="
preserve
">Non
<
lb
/>
eſt igitur dicendū / diameter eſt numerus impar
<
lb
/>
reſpectu coſte. </
s
>
<
s
xml:id
="
N10AB2
"
xml:space
="
preserve
">ſi vero coſta ſit nūerꝰ īpar reſpectu
<
lb
/>
diametri: ſequit̄̄ / quadratū eiꝰ erit numerꝰ īpar
<
lb
/>
ſed quadratū eiꝰ: eſt etiã quadratū diametri. </
s
>
<
s
xml:id
="
N10AB9
"
xml:space
="
preserve
">qm̄
<
lb
/>
ipſa coſta: eſt diameter mīoris quadrati. </
s
>
<
s
xml:id
="
N10ABE
"
xml:space
="
preserve
">vt patet
<
lb
/>
in ſuperiori figura. </
s
>
<
s
xml:id
="
N10AC3
"
xml:space
="
preserve
">Igit̄̄ quadratū diametri: eſt
<
lb
/>
numerꝰ impar. </
s
>
<
s
xml:id
="
N10AC8
"
xml:space
="
preserve
">Patet cõſequētia ex quinta ſuppo
<
lb
/>
ſitione. </
s
>
<
s
xml:id
="
N10ACD
"
xml:space
="
preserve
">et per cõſequēs quadratū diametri: nõ eſt
<
lb
/>
duplū ad q̈dratū coſte. </
s
>
<
s
xml:id
="
N10AD2
"
xml:space
="
preserve
">Patet cõſequētia ex ſexta
<
lb
/>
ſuppoſitione. </
s
>
<
s
xml:id
="
N10AD7
"
xml:space
="
preserve
">et cõſequēs eſt falſum. </
s
>
<
s
xml:id
="
N10ADA
"
xml:space
="
preserve
">vt patet ex ſe
<
lb
/>
cūda ſuppoſitione: igitur et ãtecedēs. </
s
>
<
s
xml:id
="
N10ADF
"
xml:space
="
preserve
">Et ſic patet:
<
lb
/>
nec diameter ſe habet ſicut nūerꝰ īpar: nec coſta
<
lb
/>
<
note
position
="
left
"
xlink:href
="
note-0010-01a
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xlink:label
="
note-0010-01
"
xml:id
="
N10B21
"
xml:space
="
preserve
">Quid ſit
<
lb
/>
quãtita-
<
lb
/>
tē ſe hr̄e
<
lb
/>
vt nūerꝰ.</
note
>
</
s
>
<
s
xml:id
="
N10AEB
"
xml:space
="
preserve
">¶ Aliquam autem quantitatem: ſe habere vt nu-
<
lb
/>
merus impar reſpectu alterius: eſt ipſam diuidi
<
lb
/>
ſaltē ad ymaginationē: in partes equales denoīa
<
lb
/>
tas a numero impari. </
s
>
<
s
xml:id
="
N10AF4
"
xml:space
="
preserve
">vt in tres tertias: in quin
<
lb
/>
quītas in ſeptem ſeptimas / et ſic cõſequēter. </
s
>
<
s
xml:id
="
N10AF9
"
xml:space
="
preserve
">et hoc
<
lb
/>
reſpectu alterius quãtitatis: diuiſe in partes illis
<
cb
chead
="
Capitulū quartū.
"/>
equales. </
s
>
<
s
xml:id
="
N10B01
"
xml:space
="
preserve
">vt ſi pedale diuidatur in tres tertias et bi
<
lb
/>
pedale in ſexſexas quarum ſextarum quelibet eſt
<
lb
/>
equalis vni tertie pedalis: tūc dico: pedale ſe hꝫ
<
lb
/>
vt nūerꝰ impar: reſpectu bipedalis. </
s
>
<
s
xml:id
="
N10B0A
"
xml:space
="
preserve
">Tu tamē ad-
<
lb
/>
uerte etiã poteſt ſe habere vt nūerꝰ par: reſpectu
<
lb
/>
bipedalis. </
s
>
<
s
xml:id
="
N10B11
"
xml:space
="
preserve
">tamē ſemꝑ īter pedale et bipedale erit
<
lb
/>
ꝓportio dupla. </
s
>
<
s
xml:id
="
N10B16
"
xml:space
="
preserve
">Diameter autē et coſta: nū̄ ſic ſe
<
lb
/>
poſſunt habere: diameter ſe habeat vt numerus
<
lb
/>
impar reſpectu coſte: vel econtra / vt ꝓbatū eſt.</
s
>
</
p
>
<
p
xml:id
="
N10B2D
">
<
s
xml:id
="
N10B2E
"
xml:space
="
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">Quarta cõcluſio. </
s
>
<
s
xml:id
="
N10B31
"
xml:space
="
preserve
">Omnis proportio
<
lb
/>
diametri ad coſtã: eſt irrationalis </
s
>
<
s
xml:id
="
N10B36
"
xml:space
="
preserve
">Probatur hec
<
lb
/>
cõcluſio. </
s
>
<
s
xml:id
="
N10B3B
"
xml:space
="
preserve
">q2 oīs ꝓportio rationalis: eſt multiplex:
<
lb
/>
aut multiplex ſuꝑparticularis, aut multiplex ſu-
<
lb
/>
prapartiens, aut ſuꝑparticularis, aut ſuprapar
<
lb
/>
tiens, et nulla ꝓportio diametri ad coſtã: eſt mul-
<
lb
/>
tiplex, aut multiplex ſuperparticularis, aut mul-
<
lb
/>
tiplex ſuprapartiēs. </
s
>
<
s
xml:id
="
N10B48
"
xml:space
="
preserve
">vt patet ex prima cõcluſione
<
lb
/>
aut ſuꝑparticularis. </
s
>
<
s
xml:id
="
N10B4D
"
xml:space
="
preserve
">vt ptꝫ ex ſcḋa: aut ſuprapar-
<
lb
/>
tiens: vt patet ex tertia. / igitur nulla ꝓportio dia
<
lb
/>
metri ad coſtã: eſt rationalis. </
s
>
<
s
xml:id
="
N10B54
"
xml:space
="
preserve
">Cõſequētia patet vt
<
lb
/>
ſupra: et maior ex fine primi capitis. </
s
>
<
s
xml:id
="
N10B59
"
xml:space
="
preserve
">Illa enim eſt
<
lb
/>
ſūma diuiſio ꝓportiõis rationalis: et vltra nulla
<
lb
/>
ꝓportio diametri ad coſtã: eſt ratiõalis. </
s
>
<
s
xml:id
="
N10B60
"
xml:space
="
preserve
">et eſt pro
<
lb
/>
portio: igitur eſt proportio irrationalis. </
s
>
<
s
xml:id
="
N10B65
"
xml:space
="
preserve
">Patet
<
lb
/>
cõſequentia a ſufficienti diuiſione.</
s
>
</
p
>
</
div
>
<
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<
head
xml:id
="
N10B6F
"
xml:space
="
preserve
">Capitulum quartum / in quo agitur de
<
lb
/>
infinitis ſpeciebus proportionis irratio
<
lb
/>
nalis: et de earum procreatione.</
head
>
<
p
xml:id
="
N10B76
">
<
s
xml:id
="
N10B77
"
xml:space
="
preserve
">PRoportio irrationalis: per-
<
lb
/>
inde at rationalis: in infinitas di-
<
lb
/>
ſtribuitur ſpecies </
s
>
<
s
xml:id
="
N10B7E
"
xml:space
="
preserve
">Ad quod mathema
<
lb
/>
tica induſtria inferendū: ponūtur alique ſuppões</
s
>
</
p
>
<
p
xml:id
="
N10B83
">
<
s
xml:id
="
N10B84
"
xml:space
="
preserve
">Prima ſuppoſitio. </
s
>
<
s
xml:id
="
N10B87
"
xml:space
="
preserve
">Si due quantita
<
lb
/>
tes: ſe habent vt duo numeri: aggregatū ex eis: ſe
<
lb
/>
habebit vt vnꝰ numerꝰ. </
s
>
<
s
xml:id
="
N10B8E
"
xml:space
="
preserve
">Probatur. </
s
>
<
s
xml:id
="
N10B91
"
xml:space
="
preserve
">q2 ſemꝑ ex ad
<
lb
/>
ditiõe numeri ad numerū: reſultat numerꝰ maior</
s
>
</
p
>
<
p
xml:id
="
N10B96
">
<
s
xml:id
="
N10B97
"
xml:space
="
preserve
">Secūda ſuppoſitio </
s
>
<
s
xml:id
="
N10B9A
"
xml:space
="
preserve
">Si alique quan
<
lb
/>
titates. </
s
>
<
s
xml:id
="
N10B9F
"
xml:space
="
preserve
">ſe habeant in ꝓportione rationali: ille ſe
<
lb
/>
habebunt: vt duo numeri: et econtra. </
s
>
<
s
xml:id
="
N10BA4
"
xml:space
="
preserve
">Patet ſup-
<
lb
/>
poſitio hec ex diffinitione ꝓportiõis ratioalis: cū
<
lb
/>
ſuo correlario: primo capite poſita.</
s
>
</
p
>
<
p
xml:id
="
N10BAB
">
<
s
xml:id
="
N10BAC
"
xml:space
="
preserve
">Tertia ſuppoſitio. </
s
>
<
s
xml:id
="
N10BAF
"
xml:space
="
preserve
">Si due quantita
<
lb
/>
tes ſe habeant in ꝓportione ratiõali: aggregatū
<
lb
/>
ex eis: ſe habet in ꝓportione ratiõali: ad quãlibet
<
lb
/>
illaꝝ quantitatū. </
s
>
<
s
xml:id
="
N10BB8
"
xml:space
="
preserve
">Probatur hec ſuppoſitio. </
s
>
<
s
xml:id
="
N10BBB
"
xml:space
="
preserve
">qm̄ ſi
<
lb
/>
ſe habent in ꝓportione rationali: iã quelib3 illaꝝ
<
lb
/>
ſe habet vt numerꝰ: vt patet ex ſecūda ſuppoſitõe
<
lb
/>
et ſi quelibet illaꝝ ſe habet vt uūerꝰ: ſe aggregatū
<
lb
/>
ex eis: ſe habet vt nūerꝰ. </
s
>
<
s
xml:id
="
N10BC6
"
xml:space
="
preserve
">vt patet ex prima ſuppo
<
lb
/>
ſitiõe. </
s
>
<
s
xml:id
="
N10BCB
"
xml:space
="
preserve
">et ꝑ cõſequens illiꝰ agggregati: quod ſe ha
<
lb
/>
bet vt numerꝰ: ad vtrã illarū quantitatū: que ſe
<
lb
/>
habent vt numeri: erit ꝓportio rationalis. </
s
>
<
s
xml:id
="
N10BD2
"
xml:space
="
preserve
">vt ptꝫ
<
lb
/>
ex ſecūda ſuppoſitione: quod fuit ꝓbandum.</
s
>
</
p
>
<
p
xml:id
="
N10BD7
">
<
s
xml:id
="
N10BD8
"
xml:space
="
preserve
">Qurata ſuppoſitio. </
s
>
<
s
xml:id
="
N10BDB
"
xml:space
="
preserve
">Coſte: ad exceſſū
<
lb
/>
quo diameter excedit coſtã: ꝓportio irrationalis
<
lb
/>
</
s
>
<
s
xml:id
="
N10BE1
"
xml:space
="
preserve
">Probatur. </
s
>
<
s
xml:id
="
N10BE4
"
xml:space
="
preserve
">q2 ſi eſſet rationalis: iã ſe haberent vt
<
lb
/>
duo numeri. </
s
>
<
s
xml:id
="
N10BE9
"
xml:space
="
preserve
">vt patet ex ſecūda ſuppoſitiõe. </
s
>
<
s
xml:id
="
N10BEC
"
xml:space
="
preserve
">et ſi ſe
<
lb
/>
haberēt vt duo numeri: aggregatū ex eis: qḋ ade
<
lb
/>
q̈te eſt diameter haberet ſe in ꝓportione ratiõali
<
lb
/>
ad vtrū illoꝝ. </
s
>
<
s
xml:id
="
N10BF5
"
xml:space
="
preserve
">et ꝑ cõſequēs ad coſtam. </
s
>
<
s
xml:id
="
N10BF8
"
xml:space
="
preserve
">vt patet ex
<
lb
/>
tertia ſuppoſitione: et ſic diametri ad coſtam: eſſet
<
lb
/>
rationalis proportio. </
s
>
<
s
xml:id
="
N10BFF
"
xml:space
="
preserve
">quod eſt contra quratã cõ
<
lb
/>
cluſionem precedentis capitis.</
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>