Alvarus, Thomas
,
Liber de triplici motu
,
1509
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Figures
Content
Thumbnails
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
>
21
22
23
24
25
26
27
28
29
30
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
>
page
|<
<
of 290
>
>|
<
echo
version
="
1.0
">
<
text
xml:lang
="
la
">
<
div
xml:id
="
N10132
"
level
="
1
"
n
="
1
"
type
="
body
">
<
div
xml:id
="
N1194D
"
level
="
2
"
n
="
2
"
type
="
other
"
type-free
="
pars
">
<
div
xml:id
="
N11E85
"
level
="
3
"
n
="
2
"
type
="
chapter
"
type-free
="
capitulum
">
<
p
xml:id
="
N1255B
">
<
s
xml:id
="
N12699
"
xml:space
="
preserve
">
<
pb
chead
="
Secūde partis
"
file
="
0027
"
n
="
27
"/>
bus quã ſit pars aliquota denoīata a numero ſub
<
lb
/>
duplo ad numerum parem in quo ſunt conſtituti
<
lb
/>
dati termini: et aggregatum ex duobus mediis
<
lb
/>
immediatis equaliter diſtantibus ab extremis
<
lb
/>
eſt maius quaꝫ talis pars aliquota. </
s
>
<
s
xml:id
="
N126B1
"
xml:space
="
preserve
">vt captis his
<
lb
/>
terminis .12.11.9.6. aggregatum ex .12. et ſex. eſt
<
lb
/>
minus quam medietas aggregati oīm illorū me
<
lb
/>
dietas denomīatur a numero binario qui eſt ſub
<
lb
/>
duplus ad numerū quaternariū in quo illi termi-
<
lb
/>
ni ſunt conſtituti: et aggregatum ex .11. et .9. eſt ma
<
lb
/>
ius quã medietas. </
s
>
<
s
xml:id
="
N126C0
"
xml:space
="
preserve
">Probatur: et ſint a.b.c.d.e.f.6.
<
lb
/>
termini continuo minores et minores maiori con
<
lb
/>
tinuo dnr̄ia ſeſe excedentes: et q2 illi ſunt conſtitu
<
lb
/>
ti in numero ſenario dico / aggregatū ex primo
<
lb
/>
et vltimo eſt minor pars totius ꝙ̄ pars aliquota
<
lb
/>
eiuſdem totius denoīata a numero ſubduplo ad
<
lb
/>
ſenarium que eſt vna tertia. / et aggregatū ex duo
<
lb
/>
bus intermediis īmediatis equaliter diſtantibus
<
lb
/>
ab extremis puta c.d. eſt maius quã talis pars ali
<
lb
/>
quota totius puta quã tertia. </
s
>
<
s
xml:id
="
N126D5
"
xml:space
="
preserve
">Probat̄̄ / q2 tale ag
<
lb
/>
gregatū cõponitur ex tribus partialibus aggre
<
lb
/>
gatis adequate puta ex aggregato ex a. et f. et ex
<
lb
/>
aggregato ex b. et e. et aggregato et c. et d. et ag-
<
lb
/>
gregatū ex a. et f. eſt minus ſecundo aggregato et
<
lb
/>
ſecundū minus tertio. </
s
>
<
s
xml:id
="
N126E2
"
xml:space
="
preserve
">igitur aggregatū ex a. et f.
<
lb
/>
eſt minus quaꝫ tertia totius: et aggregatū ex c.d.
<
lb
/>
maius quã tertia totius. </
s
>
<
s
xml:id
="
N126E9
"
xml:space
="
preserve
">Patet hec conſequentia /
<
lb
/>
quia quando aliquid cõponitur ex tribus quoruꝫ
<
lb
/>
quodlibet cuilibet alteri eſt inequale: maius illoꝝ
<
lb
/>
eſt maius quã tertia: et ſic dices quando cõponitur
<
lb
/>
ex quatuor adequate quorū quodlibet cuilibet al
<
lb
/>
teri eſt īequale: et ex .5. et ex .6. / et ſic deinceps vt po
<
lb
/>
ſtea oſtendetur. </
s
>
<
s
xml:id
="
N126F8
"
xml:space
="
preserve
">Iam probo minorem videlicet /
<
lb
/>
aggregatū ex a. et f. eſt minus ſecundo aggrega-
<
lb
/>
to puta ex b. et e. / q2 ſi tanto exceſſu. </
s
>
<
s
xml:id
="
N126FF
"
xml:space
="
preserve
">et dnr̄a a exce-
<
lb
/>
deret b. quanta e. excedit f. / tunc aggregatū ex a. et
<
lb
/>
f. eſſet equale aggregato ex b. et e. / vt patet ex ſecū
<
lb
/>
da concluſione: ſed modo aggregatū ex a.f. eſt mi
<
lb
/>
nus quã tunc: quia a. eſt tãtum ſicut tunc et f. eſt mi
<
lb
/>
nus quã tunc: quia maiori dnr̄ia exceditur modo
<
lb
/>
quã tunc ab eodē puta e. / igitur aggregatū ex a. et
<
lb
/>
f. eſt minus quã aggregatū ex b. et e. / et eadē ratio
<
lb
/>
ne ꝓbabis / aggregatū ex b. et e. eſt minus aggre
<
lb
/>
gato ex c. et d. / et ſic patet minor et totū correlariū /
<
lb
/>
quoniã et ſi iſta ſit particularis demonſtratio tñ
<
lb
/>
dat formã vniuerſaliter ꝓbandi quibuſcū ter-
<
lb
/>
minis paribus conſtitutis. </
s
>
<
s
xml:id
="
N1271A
"
xml:space
="
preserve
">¶ Similia correlaria
<
lb
/>
poteris inferre q̇buſcun termīs īpari nūero cõ
<
lb
/>
ſtitutis ſiue continuo maioribus et maioribus ma
<
lb
/>
iori continuo dnr̄a ſe excedentibus: ſiue eocontra
<
lb
/>
etc. / que omnia predictorum auxilio facile monſtra
<
lb
/>
ri poſſunt.</
s
>
</
p
>
<
note
position
="
left
"
xml:id
="
N12743
"
xml:space
="
preserve
">1. ele. ior.
<
lb
/>
3. con.
<
lb
/>
4. ꝓprie
<
lb
/>
tas arith
<
lb
/>
metice
<
lb
/>
medieta
<
lb
/>
tis.</
note
>
<
p
xml:id
="
N12753
">
<
s
xml:id
="
N12754
"
xml:space
="
preserve
">Tertia concluſio in hac medietate
<
lb
/>
arithmetica / quod ſub extremis continetur cum q̈
<
lb
/>
drato differentie. </
s
>
<
s
xml:id
="
N1275B
"
xml:space
="
preserve
">equale eſt quadrato medii. </
s
>
<
s
xml:id
="
N1275E
"
xml:space
="
preserve
">Hec
<
lb
/>
concluſio eſt tertia decimi elementorum iordani et
<
lb
/>
breuitatis cauſa hic non demonſtratur / quia eius
<
lb
/>
demõſtratio prolixa eſt eo dependet ex decima
<
lb
/>
quarta et decima nona primi elementorum eiuſ-
<
lb
/>
dem iordani. </
s
>
<
s
xml:id
="
N1276B
"
xml:space
="
preserve
">¶ Aduerte tamen pro intelli
<
lb
/>
gentia contextus ipſius concluſionis / illud dici
<
lb
/>
tur contineri. </
s
>
<
s
xml:id
="
N12772
"
xml:space
="
preserve
">ſub extremis arithmetice ꝓportio-
<
lb
/>
nalitatis quod reſultat ex ductu vnius extremi in
<
lb
/>
alterum: vt numerus octonarius continetur ſub
<
lb
/>
extremis huius ꝓportionalitatis .4.3.2. quia du-
<
lb
/>
cendo .4. per .2. reſultant octo. </
s
>
<
s
xml:id
="
N1277D
"
xml:space
="
preserve
">Bis em̄ .4. ſūt octo
<
cb
chead
="
Capitulum ſecundum
"/>
</
s
>
<
s
xml:id
="
N12783
"
xml:space
="
preserve
">Item .32. continētur ſub extremis huius ꝓportio
<
lb
/>
nalitatis arithmetice .8.7.4. qm̄ ducendo .8. per .
<
lb
/>
4. reſultant: 32. </
s
>
<
s
xml:id
="
N1278A
"
xml:space
="
preserve
">Quater enim octo ſunt .32.
<
note
position
="
right
"
xlink:href
="
note-0027-01a
"
xlink:label
="
note-0027-01
"
xml:id
="
N127D7
"
xml:space
="
preserve
">quadra-
<
lb
/>
tū medii</
note
>
</
s
>
<
s
xml:id
="
N12792
"
xml:space
="
preserve
">¶ Ad
<
lb
/>
uerte vlterius / quadratū medii termini eſt illud
<
lb
/>
quod reſultat ex ductu medii termini in ſeipſuꝫ:
<
note
position
="
right
"
xlink:href
="
note-0027-02a
"
xlink:label
="
note-0027-02
"
xml:id
="
N127DF
"
xml:space
="
preserve
">q̈dratuꝫ
<
lb
/>
dnr̄ie.</
note
>
vt
<
lb
/>
numerus nouenarius eſt quadratum medii in hac
<
lb
/>
arithmetica proportionalitate .4.3.2. quia reſul-
<
lb
/>
tat ex ductu numeri ternarii in ſeipſum. </
s
>
<
s
xml:id
="
N127A4
"
xml:space
="
preserve
">Nam ter
<
lb
/>
tria ſunt nouē. </
s
>
<
s
xml:id
="
N127A9
"
xml:space
="
preserve
">¶ Quadratū autē differentie eſt il
<
lb
/>
lud quod reſultat ex ductu differentie in ſeipſum:
<
lb
/>
vt in hac arithmetica medietate .8.6.4. numerus
<
lb
/>
quaternarius eſt quadratū dnr̄e. </
s
>
<
s
xml:id
="
N127B2
"
xml:space
="
preserve
">Nã differentia
<
lb
/>
eſt numerus binarius / vt conſtat. </
s
>
<
s
xml:id
="
N127B7
"
xml:space
="
preserve
">Binarius enim
<
lb
/>
ductus in ſeipſum quaternarium educit / vt cõſtat.
<
lb
/>
</
s
>
<
s
xml:id
="
N127BD
"
xml:space
="
preserve
">¶ His dictis ſenſus concluſionis eſt talis. </
s
>
<
s
xml:id
="
N127C0
"
xml:space
="
preserve
">Nume-
<
lb
/>
rus reſultans ex ductu vnius extremi in alterū in
<
lb
/>
medietate arithmetica continua cum numero re-
<
lb
/>
ſultante ex ductu differentie in ſeipſam eſt equalis
<
lb
/>
numero qui fit ex ductu medii in ſeipſū: vt in hac
<
lb
/>
medietate .8. que fiunt ex ductu vnius extremi in al
<
lb
/>
terum iuncto quaternario numero qui fit ex dictu
<
lb
/>
differentie in ſeipſaꝫ ſunt equalia .36. que fiunt ex
<
lb
/>
ductu ſenarii medii termini in ſeipſum.</
s
>
</
p
>
<
note
position
="
right
"
xml:id
="
N127E7
"
xml:space
="
preserve
">4. cõclu-
<
lb
/>
ſio prīa
<
lb
/>
ꝓprietaſ
<
lb
/>
medieta
<
lb
/>
tis geo-
<
lb
/>
metrice.</
note
>
<
p
xml:id
="
N127F5
">
<
s
xml:id
="
N127F6
"
xml:space
="
preserve
">Quarta concluſio in medietate geo-
<
lb
/>
metrica q̈tuor terminis conſtituta ſi primus ad ſe
<
lb
/>
cundū ſicut tertius ad quartum: ita primus ad ter
<
lb
/>
tiū ſicut tertius ad quartū ſe habeat neceſſe eſt: vt
<
lb
/>
quia ſicut ſe habent octo ad quatuor ita ſe habēt
<
lb
/>
ſex. ad .tria. / conſequens eſt / ſicut ſe habent .octo
<
lb
/>
ad .ſex. ita quatuor ad tria. </
s
>
<
s
xml:id
="
N12805
"
xml:space
="
preserve
">Probatur / ſint a.b.
<
lb
/>
c.d. quatuor termini in medietate geometrica: et
<
lb
/>
habeat ſe a. ad .b. ſicut c. ad d. / tūc dico / ſicut ſe hꝫ
<
lb
/>
a. ad .c. ita b. ad d. </
s
>
<
s
xml:id
="
N1280E
"
xml:space
="
preserve
">Qḋ ſic ꝓbat̄̄ et ṗmo ī nūerꝪ / q2 ſi
<
lb
/>
ſicut ſe habet a. ad b. ita .c. ad .d.b. eſt pars vel par
<
lb
/>
tes aliquote reſpectu a. eiuſdem denoīationis ſi-
<
lb
/>
cut d. ipſius c. et vltra b. eſt pars aliquota vel par
<
lb
/>
tes aliq̊te eiuſdē denoīationis reſpectu a. ſicut d.
<
lb
/>
reſpectu c. / ergo ſicut ſe habet a. ad c. ita b. ad d. / qḋ
<
lb
/>
fuit probandū. </
s
>
<
s
xml:id
="
N1281D
"
xml:space
="
preserve
">Secunda conſequētia patet ex vn-
<
lb
/>
decima ſuppoſitione huius capitis: et prima ptꝫ
<
lb
/>
ex hoc / quod inferius probabitur. </
s
>
<
s
xml:id
="
N12824
"
xml:space
="
preserve
">Si aliqui duo
<
lb
/>
numeri maiores habent ↄ̨ſimiles proportiones
<
lb
/>
ad duos minores: illi minores numeri ſūt partes
<
lb
/>
aliquote maiorū conſimilis denoīationis. </
s
>
<
s
xml:id
="
N1282D
"
xml:space
="
preserve
">Et ſit
<
lb
/>
hec prima proprietas geometrice medietatis.</
s
>
</
p
>
<
p
xml:id
="
N12832
">
<
s
xml:id
="
N12833
"
xml:space
="
preserve
">Probatur iaꝫ vniuerſaliter / ſint a.b.c.d. quatuor
<
lb
/>
termini in hac medietate geometrica conſtituti ſi
<
lb
/>
ue continuo ꝓportionabiles, ſiue diſcontinue, ſi-
<
lb
/>
ue proportione rationali, ſiue irrationali. </
s
>
<
s
xml:id
="
N1283C
"
xml:space
="
preserve
">et ipſi-
<
lb
/>
us a. ad b. ſit f. proportio: et ſimiliter ipſius c. ad
<
lb
/>
ipſum d. ſit f. proportio: et ſit a. ad .c.g. ꝓportio. </
s
>
<
s
xml:id
="
N12843
"
xml:space
="
preserve
">et
<
lb
/>
tunc dico / etiam b. ad d. eſt g. proportio. </
s
>
<
s
xml:id
="
N12848
"
xml:space
="
preserve
">Quod
<
lb
/>
probatur ſic / et capio ꝓportionem g. / que eſt a. ad
<
lb
/>
c. / et volo / a deperdat ꝓportioneꝫ f. quam habet
<
lb
/>
ad b. ita in fine maneat equale ipſi b. / vt oportet
<
lb
/>
et c. perdat eandem proportionem f. quam ex hy-
<
lb
/>
potheſi habet ad ipſum d. ita in fine maneat eq̈
<
lb
/>
le ipſi d. / et arguo ſic. </
s
>
<
s
xml:id
="
N12857
"
xml:space
="
preserve
">huius ꝓportionis g. que eſt a
<
lb
/>
ad c. equalem omnino ꝓportionē deperdit termi-
<
lb
/>
nus maior ſicut minor: quia vter f. proportioneꝫ /
<
lb
/>
vt patet ex hypotheſi: igitur facta tali diminutio
<
lb
/>
ne adhuc manet inter reſiduum maioris termini et
<
lb
/>
minoris. </
s
>
<
s
xml:id
="
N12864
"
xml:space
="
preserve
">eadem proportio g. / vt patet ex ſecunda
<
lb
/>
parte decime ſuppoſitionis ſecundi capitis ſecun
<
lb
/>
de partis ſed reſiduū maioris termini eſt b. et reſi
<
lb
/>
duū mīoris d. / vt pꝫ ex hypotheſi: igit̄̄ b. ad d. ē g. ꝓ </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>