Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Table of Notes
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<
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Tertii tractatus
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file
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0209
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209
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Probat̄̄ antecedens / qm̄ ille proportiones acqui-
<
lb
/>
ſite ↄ̨tinuo ſe habent in ꝓportione dupla et prima
<
lb
/>
illaꝝ eſt dupla: ergo totū eſt vna ꝓportio q̈drupla /
<
lb
/>
vt ſepius argutū eſt. </
s
>
<
s
xml:id
="
N24926
"
xml:space
="
preserve
">Q, autē continuo ſe habēt in
<
lb
/>
ꝓportiõe dupla. </
s
>
<
s
xml:id
="
N2492B
"
xml:space
="
preserve
">Ptꝫ / q2 in prima parte ꝓportiõa-
<
lb
/>
bili acq̇rit illud corpꝰ ꝓportionē dupla: et in ſcḋa
<
lb
/>
medietatē duple: qm̄ ſi eque velociter augmētaret̄̄
<
lb
/>
in ſcḋa ſicut in prima acq̇reret vnã quartã duple:
<
lb
/>
ſed mõ in duplo velociꝰ auget̄̄ ꝙ̄ tūc: g̊ acq̇rit vnam
<
lb
/>
medietatē duple: et ſic ꝓbabis / in tertia parte ac
<
lb
/>
quirit vnã quartã: et ſic ↄ̨ñter: igr̄ ↄ̨tinuo acq̇rit ꝓ-
<
lb
/>
portiões ſe habētes in ꝓportiõe ſubdupla, et ſub-
<
lb
/>
dupla / qḋ fuit ꝓbandū.
<
note
position
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left
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xlink:href
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note-0209-01a
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note-0209-01
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xml:id
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N24988
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xml:space
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preserve
">Cõfirma
<
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tio .2.</
note
>
</
s
>
<
s
xml:id
="
N24943
"
xml:space
="
preserve
">¶ Cõfirmat̄̄ ſcḋo / q2 ſi poſi-
<
lb
/>
tio eſſet uera: ſeq̄ret̄̄ / aliqḋ corpꝰ augmētaret̄̄, et
<
lb
/>
in nulla ꝓportiõe fierit maiꝰ: ↄ̨ñs eſt falſñ: igr̄ et il-
<
lb
/>
lud ex quo ſequit̄̄. </
s
>
<
s
xml:id
="
N2494C
"
xml:space
="
preserve
">Seq̄la ꝓbat̄̄: et volo / vnū peda-
<
lb
/>
le in prima parte ꝓportiõali hore ꝓportiõe dupla
<
lb
/>
diuiſe aliq̈liter augmētet̄̄: et in ſcḋa in ſuꝑbipartiē
<
lb
/>
te tertias velociꝰ, et in tertia in ſuꝑtripartiēte quī-
<
lb
/>
tas, et ī quarta in ſupraq̈dripartiēte ſeptīas, ī .5. et
<
lb
/>
ſupraquītipartiēte vndecimas, et ſic ↄ̨ñter ꝓcedēdo
<
lb
/>
ꝑ nūeros īpares primos et incõpoſitos. </
s
>
<
s
xml:id
="
N2495B
"
xml:space
="
preserve
">Quo poſi
<
lb
/>
to ſic argr̄: tale corpꝰ augmētat̄̄ vt notū eſt: et tñ in
<
lb
/>
nulla ꝓportiõe ſit maiꝰ: igr̄. </
s
>
<
s
xml:id
="
N24962
"
xml:space
="
preserve
">Probat̄̄ mīor: q2 nec
<
lb
/>
in multiplici, nec ī ſuꝑparticulari, nec in ſuprapar
<
lb
/>
tiente, nec in multiplici ſupraparticulari, nec ī mul
<
lb
/>
tiplici ſuprabprrtiēte, et ſi hoc negas des illã. </
s
>
<
s
xml:id
="
N2496B
"
xml:space
="
preserve
">Itē
<
lb
/>
poſito / in prima parte ꝓportiõali vnū pedale ac
<
lb
/>
quirit ꝓportionē ſaꝑbipartientē tertias, et in ſcḋa
<
lb
/>
acq̇rat ꝓportionē ſuꝑbipartientē quītas, et in ter-
<
lb
/>
tia ſuꝑbipartientē ſeptīas, et in q̈rta ſuprabipar-
<
lb
/>
tiēte nonas, et ſic ↄ̨ñter ꝓcedendo ꝑ ſpecies ꝓporti-
<
lb
/>
onis ſuꝑbipartiētes: tale corpꝰ augmentabit̄̄: et in
<
lb
/>
nulla uroportione fiet maius quam erat antea igr̄</
s
>
</
p
>
<
p
xml:id
="
N24990
">
<
s
xml:id
="
N24991
"
xml:space
="
preserve
">Sexto principaliṫ ad idē argr̄ ſic. </
s
>
<
s
xml:id
="
N24994
"
xml:space
="
preserve
">Si
<
lb
/>
illa poſitio eſſet a ſeq̄ret̄̄ / ſi duo corpora equa-
<
lb
/>
lia augmētarent̄̄ talr̄ / medietas vniꝰ augmētaret̄̄
<
lb
/>
ad duplū, et quarta alteriꝰ ad quadruplū: illa cor
<
lb
/>
pora eq̄ velociter augmētarent̄̄: ſed ↄ̨ñs eſt falſum /
<
lb
/>
igr̄ illud ex quo ſequit̄̄. </
s
>
<
s
xml:id
="
N249A1
"
xml:space
="
preserve
">Seq̄la ptꝫ. </
s
>
<
s
xml:id
="
N249A4
"
xml:space
="
preserve
">qm̄ ſi eq̈lis aug-
<
lb
/>
mentatio aut acq̇ſitio ꝓportiõis in parte alicuiꝰ to
<
lb
/>
tius aliq̇d facit ad denoīationē augmētatiõis to-
<
lb
/>
tius, ſequit̄̄ qḋ dupla ꝓportio acq̇ſita parti in du
<
lb
/>
plo mīori tm̄ facit ſicut ſubdupla ꝓportio acq̇ſita
<
lb
/>
parti in duplo maiori: igr̄ in ꝓpoſito illa acq̇ſitio
<
lb
/>
ꝓportiõis in medietate tm̄ adequate facit ad aug-
<
lb
/>
mentū totiꝰ ſicut acq̇ſitio ꝓportiõis in duplo maio
<
lb
/>
ris in vna quarta. </
s
>
<
s
xml:id
="
N249B7
"
xml:space
="
preserve
">Ptꝫ añs a ſimili de denoīatiõe
<
lb
/>
q̈litatis et denſitatis. </
s
>
<
s
xml:id
="
N249BC
"
xml:space
="
preserve
">Iam ꝓbo falſitatē ↄ̨ñtis qm̄
<
lb
/>
in tali caſu corpꝰ cuiꝰ vna medietas auget̄̄ ad du-
<
lb
/>
plum ſui acq̇rit ꝓportionē ſexq̇alterã, et aliud acq̇-
<
lb
/>
rit ꝓportionē ſuꝑtripartientē quartas q̄ maior eſt /
<
lb
/>
igr̄ nõ eque velociter augmentat̄̄, et ꝑ ↄ̨ñs illatum
<
lb
/>
falſū. </
s
>
<
s
xml:id
="
N249C9
"
xml:space
="
preserve
">Probat̄̄ maior / q2 ſi medietas acq̇ſiuit ꝓpor
<
lb
/>
tionē duplã ſequit̄̄ tale corpꝰ acq̇ſiut tm̄ quantū
<
lb
/>
eſt medietas eiꝰ, et ꝑ ↄ̨ñs ſexq̇alterã ꝓportionē. </
s
>
<
s
xml:id
="
N249D0
"
xml:space
="
preserve
">Mi
<
lb
/>
nor ꝓbat̄̄: q2 ſi vna quarta alteriꝰ corporis facta
<
lb
/>
eſt in q̈druplo maior, ſequit̄̄ qḋ acq̇ſiuit ter tm̄ ſi-
<
lb
/>
cut ipſa eſt, et ſic acq̇ſiuit tres quartas totiꝰ, et per
<
lb
/>
ↄ̨ñs in fine illud totū componitur ex ſeptem parti-
<
lb
/>
bus quaꝝ q̄libet eſt equalis vni quarte totiꝰ corpo
<
lb
/>
ris in principio augmētatiõis, et ſic illud corpꝰ erit
<
lb
/>
in ſupratripartiēte quartas maiꝰ quã erat antea /
<
lb
/>
qḋ fuit ꝓbandū.
<
note
position
="
left
"
xlink:href
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note-0209-02a
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xlink:label
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note-0209-02
"
xml:id
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xml:space
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">ↄ̨firma°.</
note
>
</
s
>
<
s
xml:id
="
N249E8
"
xml:space
="
preserve
">¶ Cõfirmat̄̄ / q2 ſi iſta poſitio eſſet
<
lb
/>
vera, ſeq̄ret̄̄ / uõ eſſet poſſibile aliq̇d īcipere auge-
<
lb
/>
ri a nõ quanto vniformiṫ, aut īfinite tarde ſed ↄ̨ñs
<
lb
/>
eſt flm̄: igr̄ illud ex q̊ ſequit̄̄. </
s
>
<
s
xml:id
="
N249F1
"
xml:space
="
preserve
">Seq̄la ꝓbat̄̄ / q2 qḋlibet
<
lb
/>
qḋ a nõ quãto īcipit augeri īfinite velociter incipit
<
lb
/>
augeri: igr̄ nullū tale / qḋ a nõ quãto incipit augeri
<
cb
chead
="
Capitulū ſecundum.
"/>
incipit vniformiter aut infinitū tarde augeri. </
s
>
<
s
xml:id
="
N249FB
"
xml:space
="
preserve
">Con
<
lb
/>
ſequētia ſatis apparet, et añs ꝓbat̄̄ vcꝫ / quodli-
<
lb
/>
bet tale incipit infinite velociter augeri: qm̄ quod-
<
lb
/>
libet tale incipit infinitã magnã ꝓportionē acqui-
<
lb
/>
rere: igr̄. </
s
>
<
s
xml:id
="
N24A06
"
xml:space
="
preserve
">Probat̄̄ tñ falſitas ↄ̨ñtis: q2 aliq̇d incipit
<
lb
/>
a nõ quanto augeri īfinite tarde: et illud idē incipit
<
lb
/>
a nõ quãto īfinite velociter augeri, et illud idē etiã
<
lb
/>
a nõ quanto incipit vniformiter augeri. </
s
>
<
s
xml:id
="
N24A0F
"
xml:space
="
preserve
">igr̄ poſſi-
<
lb
/>
bile eſt aliq̇d incipere a nõ quãto vniformiter, et in-
<
lb
/>
finitū tarde augeri: et ꝑ ↄ̨ñs illud ↄ̨ñs eſt flm̄. </
s
>
<
s
xml:id
="
N24A16
"
xml:space
="
preserve
">Pro-
<
lb
/>
bat̄̄ añs, et volo / diuidat̄̄ hora futura in partes
<
lb
/>
ꝓportionales ꝓportione dupla, et capio tres ordi
<
lb
/>
nes partiū ꝓportionaliū qui ordines continuo ſe
<
lb
/>
habēt in ꝓportione octupla puta pro primo ordīe
<
lb
/>
primã partē et quartã: et ſeptimã et decimã / et ſic cõ-
<
lb
/>
ſequēter omittendo duas, et ꝓ ſecūdo ordine capio
<
lb
/>
ſcḋam, et quintã, et octauã, et vndecimã, et ſic ↄ̨ñter:
<
lb
/>
ſimiliter omittēdo duas. </
s
>
<
s
xml:id
="
N24A29
"
xml:space
="
preserve
">Et ꝓ tertio ordine capio
<
lb
/>
tertiã, ſextã, nonã, duodecimã, et ſic cõſeqnēter etiã
<
lb
/>
omittendo duas: et volo / in qualibet parte ꝓpor
<
lb
/>
tionali primi ordinis vnū pedale perdat ꝓportio-
<
lb
/>
nē duplã: et in prima parte ſcḋi ordinis perdat etiã
<
lb
/>
duplã: et in ſcḋa eiuſdē ordinis ꝓportiouē in octu-
<
lb
/>
plo minorē quã in ſcḋa: et ſic ↄ̨ñter. </
s
>
<
s
xml:id
="
N24A38
"
xml:space
="
preserve
">ita in ſcḋo or
<
lb
/>
dine in ea ꝓportione qua partes ſunt minores in
<
lb
/>
ea ↄ̨tinuo ꝓportionē minorē deṗerdat. </
s
>
<
s
xml:id
="
N24A3F
"
xml:space
="
preserve
">In prima
<
lb
/>
vero parte tertii ordinis idē pedale deꝑdat ꝓpor-
<
lb
/>
tionē duplã, et in ſcḋa eiuſdē tertii ordinis in ſexde
<
lb
/>
cuplo minorē, et in tertia eiuſdē ordinis in ſexdecu-
<
lb
/>
plo minorē quã in ſcḋa / et ſic ↄ̨ñter. </
s
>
<
s
xml:id
="
N24A4A
"
xml:space
="
preserve
">Quo poſito ma
<
lb
/>
nifeſtū eſt / hoc corpꝰ diminuet̄̄ ad nõ quantñ vſ
<
lb
/>
et in īfinitū velociter diminuet̄̄ ad nõ quantū in par
<
lb
/>
tibꝰ ꝓportionabilibꝰ primi ordinis, et in partibus
<
lb
/>
ꝓportiõalibꝰ ſcḋi ordīs ↄ̨tinuo vniformiter dimi-
<
lb
/>
nuet̄̄ / vt ptꝫ ex caſu et in partibꝰ ꝓportiõalibꝰ tertii
<
lb
/>
ordinis in īfinitū tarde diminuit̄̄ ad nõ quantum.
<
lb
/>
</
s
>
<
s
xml:id
="
N24A5A
"
xml:space
="
preserve
">Uolo igr̄ / cū corpꝰ fuerit ad nõ quantū redactū.
<
lb
/>
</
s
>
<
s
xml:id
="
N24A5E
"
xml:space
="
preserve
">Iteꝝ īcipiat in hora ſeq̄nti augeri a nõ quãto oīno
<
lb
/>
eodē mõ ſicut diminuebat̄̄. </
s
>
<
s
xml:id
="
N24A63
"
xml:space
="
preserve
">Et argr̄ ſic. </
s
>
<
s
xml:id
="
N24A66
"
xml:space
="
preserve
">illud corpꝰ
<
lb
/>
īcipit in īfinitū velociter augeri puta in partibꝰ pri
<
lb
/>
mi ordinis, et incipit etiã vniformiter puta in par-
<
lb
/>
bꝰ ſcḋi ordīs: et ↄ̨ſimiliter īcipit in īfinitū tarde au-
<
lb
/>
geri / vt īdicat diminutio fucta in partibꝰ tertii or-
<
lb
/>
dinis: igr̄ aliq̇d īcipit a nõ quãto in īfinitū tarde, et
<
lb
/>
īfinitū velociter, et vniformiṫ augeri / qḋ fuit ꝓbãdū</
s
>
</
p
>
<
p
xml:id
="
N24A7F
">
<
s
xml:id
="
N24A80
"
xml:space
="
preserve
">Septimo prīcipaliṫ ↄ̨̨tra aliã partē
<
lb
/>
q̄ſtiõis argr̄ ſic. </
s
>
<
s
xml:id
="
N24A85
"
xml:space
="
preserve
">Quia ſi velocitas augmētationis
<
lb
/>
deberet attēdi penes abſolutã acq̇ſitionē quãtita-
<
lb
/>
tia ſeq̄ret̄̄ / aliq̇d augmētaret̄̄ / qḋ tñ nõ fierit maiꝰ
<
lb
/>
ↄ̨ñs eſt falſū: igr̄ illud ex quo ſequit̄̄. </
s
>
<
s
xml:id
="
N24A8E
"
xml:space
="
preserve
">Seq̄la ꝓbat̄̄:
<
lb
/>
et capio vnū bipedale, et volo / vna medietas eius
<
lb
/>
vniformiter acq̇rat vnū ſemipedale, et tm̄ cõtinuo
<
lb
/>
deꝑdat alia medietas ſicut altera acq̇rit, q̊ poſito
<
lb
/>
argr̄ ſic. </
s
>
<
s
xml:id
="
N24A99
"
xml:space
="
preserve
">Illud bipedale nõ ſit maiꝰ vt conſtat: et tñ
<
lb
/>
augmentat̄̄: igr̄ ꝓpoſitū. </
s
>
<
s
xml:id
="
N24A9E
"
xml:space
="
preserve
">argr̄ minor. </
s
>
<
s
xml:id
="
N24AA1
"
xml:space
="
preserve
">Q2 acq̇rit a-
<
lb
/>
liquã ̄titatē cū vna medietas eiꝰ acq̇rat ſemipeda
<
lb
/>
lē quãtitatē: igr̄ augmētat̄̄. </
s
>
<
s
xml:id
="
N24AA8
"
xml:space
="
preserve
">Ptꝫ ↄ̨ña ꝑ poſitione q̄
<
lb
/>
ponit / augmētatio d3 attēdi penes abſolutã acq̇
<
lb
/>
ſitionē quãtitatis.
<
note
position
="
right
"
xlink:href
="
note-0209-03a
"
xlink:label
="
note-0209-03
"
xml:id
="
N24B98
"
xml:space
="
preserve
">Dictur</
note
>
</
s
>
<
s
xml:id
="
N24AB4
"
xml:space
="
preserve
">¶ Dices et bñ: negãdo ſequelã, et
<
lb
/>
ad ꝓbationē admiſſo caſu negãdo / illud bipeda
<
lb
/>
le augeat̄̄, qm̄ ſemꝑ manet pedale: et cū ꝓbat̄̄ / q2 ac
<
lb
/>
q̇rit aliquã quãtitatē negando illud, ̄uis em̄ vna
<
lb
/>
medietas eiꝰ acq̇rit quãtitatē totū nõ. </
s
>
<
s
xml:id
="
N24ABF
"
xml:space
="
preserve
">Ad hoc em̄
<
lb
/>
acq̇reret oporteret / vltra illã quã habet. </
s
>
<
s
xml:id
="
N24AC4
"
xml:space
="
preserve
">haberet
<
lb
/>
maiorē, hoc eſt acq̇reret aliquē exceſſum ſuꝑ illã
<
lb
/>
qḋ nõ ſit in ꝓpoſito: q2 quãtū vna medietas acq̇rit
<
lb
/>
tm̄ alia deꝑdit. </
s
>
<
s
xml:id
="
N24ACD
"
xml:space
="
preserve
">¶ Sed ↄ̈ / q2 ſi alia medietas nõ di-
<
lb
/>
minueret̄̄: ſequeret̄̄ / hec medietas que auget̄̄ eque
<
lb
/>
velociter augeretur cum toto: ſed conſequens eſt </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>