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
>
41
42
43
44
45
46
47
48
49
50
<
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
="
N14B3F
"
level
="
3
"
n
="
7
"
type
="
chapter
"
type-free
="
capitulum
">
<
pb
chead
="
Secunde partis.
"
file
="
0050
"
n
="
50
"/>
<
p
xml:id
="
N14DA1
">
<
s
xml:id
="
N150E9
"
xml:space
="
preserve
">
<
note
position
="
left
"
xlink:href
="
note-0052-01a
"
xlink:label
="
note-0052-01
"
xml:id
="
N1511F
"
xml:space
="
preserve
">Branar
<
lb
/>
dinus.</
note
>
Iſta cõncluſio / vt dicit thomos branardinꝰ in ſua
<
lb
/>
geometria in capitulo de proportionalitate con-
<
lb
/>
cluſione quarta longã et prolixã expetit demõſtra
<
lb
/>
tionem.
<
note
position
="
left
"
xlink:href
="
note-0052-02a
"
xlink:label
="
note-0052-02
"
xml:id
="
N15127
"
xml:space
="
preserve
">Eu. 6. ele</
note
>
</
s
>
<
s
xml:id
="
N15100
"
xml:space
="
preserve
">Ideo ſufficiat ad eam euclidis auctoritas
<
lb
/>
ſexto elementoꝝ propoſitione decima tertia.</
s
>
</
p
>
<
p
xml:id
="
N1512D
">
<
s
xml:id
="
N1512E
"
xml:space
="
preserve
">Nona cõcluſio. </
s
>
<
s
xml:id
="
N15131
"
xml:space
="
preserve
">Ad inueniendã pro-
<
lb
/>
portionē ſubduplã duple, aut alicuiꝰ alterius, cõ-
<
lb
/>
ſtituantur due linee ſe habentes in ꝓportione illa
<
lb
/>
cuiꝰ medietas queritur: et inueniatur media linea
<
lb
/>
inter eas per artem precedentis cõcluſionis: et tūc
<
lb
/>
maioris linee ad illam mediã et etiam illius medie
<
lb
/>
ad minimã erit proportio que eſt media ſiue me-
<
lb
/>
dietas talis proportionis. </
s
>
<
s
xml:id
="
N15142
"
xml:space
="
preserve
">Et ſi velis īuenire ſub-
<
lb
/>
quadruplã proportionē īuenias lineã mediã inter
<
lb
/>
primã, et ſecundã et vnã aliam inter ſecundã et ter-
<
lb
/>
tiam, et tunc quelibet illarū intermediarū erit ſub
<
lb
/>
quadrupla: q2 erūt ibi .5. termini continuo ꝓpor-
<
lb
/>
tionabiles: igitur proportio extremi ad extremū
<
lb
/>
eſt quadrupla ad quãlibet intermediam. </
s
>
<
s
xml:id
="
N15151
"
xml:space
="
preserve
">Et ſi vis
<
lb
/>
īuenire ſuboctuplã poſtquã īueniſti ſubq̈druplam
<
lb
/>
inter quaſlibet duas lineas īmediate ſe habentes
<
lb
/>
eleua vnã. </
s
>
<
s
xml:id
="
N1515A
"
xml:space
="
preserve
">Et ſi vis īuenire ſubſexdecuplã poſtquã
<
lb
/>
īueniſti ſuboctuplã: īter quaſlibet duas eleua vnã
<
lb
/>
artificio precedentis cõcluſionis / et ſic in infinitum
<
lb
/>
duplicando. </
s
>
<
s
xml:id
="
N15163
"
xml:space
="
preserve
">Hec concluſio patet ex priori patro-
<
lb
/>
cinio octaue concluſionis precedentis capitis.</
s
>
</
p
>
<
p
xml:id
="
N15168
">
<
s
xml:id
="
N15169
"
xml:space
="
preserve
">Decima cõcluſio. </
s
>
<
s
xml:id
="
N1516C
"
xml:space
="
preserve
">Quãuis facile ſit
<
lb
/>
cuilibet ꝓportioni īuenirē ſubduplã, ſubquadru-
<
lb
/>
plam, ſuboctuplã, ſubſexdecuplã, et ſic in infinitū
<
lb
/>
aſcendendo per numeros pariter pares: difficile
<
lb
/>
tamen eſt ſubtriplã, ſubquintuplã, ſubſextuplam /
<
lb
/>
et ſic in infinitū per numeros impares vel impari
<
lb
/>
ter pares aſcendendo īuenire. </
s
>
<
s
xml:id
="
N1517B
"
xml:space
="
preserve
">Prima pars patet
<
lb
/>
ex priori concluſione: et ſecūda eſt michi experimē
<
lb
/>
to cõperta: quãuis nicholaꝰ horen in ſuo tractatu
<
lb
/>
ꝓportionū capite quarto velit dare modum per
<
lb
/>
artem medie rei inuentionis ad īueniendam pro-
<
lb
/>
portionem et ſubduplam, et ſubtriplam, et ſubſex-
<
lb
/>
quialteram.
<
note
position
="
left
"
xlink:href
="
note-0052-03a
"
xlink:label
="
note-0052-03
"
xml:id
="
N15208
"
xml:space
="
preserve
">Contra
<
lb
/>
horeu:</
note
>
</
s
>
<
s
xml:id
="
N1518F
"
xml:space
="
preserve
">¶ Sed ſaluo meliori indicio et aucto-
<
lb
/>
ritate tam circuaſpecti viri ſignanter in mathe-
<
lb
/>
mathicis ſciētiis: videtur michi / per artē medie
<
lb
/>
rei īuentionis nõ poſſunt īueniri quatuor linee cõ
<
lb
/>
tinuo proportionabiliter ſe habentes. </
s
>
<
s
xml:id
="
N1519A
"
xml:space
="
preserve
">Quod ſic
<
lb
/>
oſtendo: quia captis duabus lineis ſe habentibꝰ
<
lb
/>
in ꝓportione dupla ad īueniendã quatuor lineas
<
lb
/>
cõtinuo ꝓpprtionabiles: oportet inter illas duas
<
lb
/>
īuenire alias duas cõtinuo ꝓportionabiles inter
<
lb
/>
ſe et cū extremis / vt ipſemet fatetur: ſed hoc nõ põt
<
lb
/>
fieri per medii rei īuentionē igitur. </
s
>
<
s
xml:id
="
N151A9
"
xml:space
="
preserve
">Minor proba
<
lb
/>
tur / q2 vel prima illarū duarū linearū que īuenit̄̄
<
lb
/>
inter illas duas īuenitur per illã artē vel nõ. </
s
>
<
s
xml:id
="
N151B0
"
xml:space
="
preserve
">ſi non
<
lb
/>
habeo ꝓpropoſitū / oportet dare aliã artē: ſi ſic tū
<
lb
/>
manifeſtū eſt / illa erit medio loco ꝓportionabi
<
lb
/>
lis inter lineas ſe habentes in ꝓportione dupla:
<
lb
/>
et per cõſequens maioris linee ad ipſam / et etiam
<
lb
/>
ipſius ad minimū erit proportio que eſt medietas
<
lb
/>
duple: et tūc quero de īuentione ſecūde linee inter
<
lb
/>
medie: q2 vel ille īuenietur per artem medie rei in-
<
lb
/>
uentionis vel nõ: ſi nõ habeo ꝓpoſitū: ſi ſic quero
<
lb
/>
vel illa debet īueniri per illam artem inter illam
<
lb
/>
mediam lineam et vltimam: vel inter primã et illã
<
lb
/>
mediam: ſed neutrū iſtorum eſt diceudum igitur.
<
lb
/>
</
s
>
<
s
xml:id
="
N151CA
"
xml:space
="
preserve
">Probatur minor: quoniã ſi inueniatur inter me-
<
lb
/>
diam et vltimam: iam ille quatuor linee nõ erunt
<
lb
/>
continuo proportionabiles: quoniã prime ad ſe-
<
lb
/>
cundam erit medietas duple: et ſecunde ad tertiã
<
lb
/>
et etiam tertie ad quartam erit ſubquadrupla du
<
cb
chead
="
Capitulū octauū.
"/>
ple: quia erit medietas medietatis duple: vt patet
<
lb
/>
ex nona concluſione huius: ſi vero īueniatur inter
<
lb
/>
primam et mediam idē ſequitur.
<
note
position
="
right
"
xlink:href
="
note-0052-04a
"
xlink:label
="
note-0052-04
"
xml:id
="
N15210
"
xml:space
="
preserve
">Correĺ.</
note
>
</
s
>
<
s
xml:id
="
N151E1
"
xml:space
="
preserve
">¶ Ex quo ſequi-
<
lb
/>
tur horen non tradidiſſe doctrinam ad inuenien-
<
lb
/>
dam proportionē compoſitam ex duabus tertiis
<
lb
/>
proportiõis duple puta ſubſequialterã ad duplã
<
lb
/>
</
s
>
<
s
xml:id
="
N151EB
"
xml:space
="
preserve
">Probatur / quia vt ſonant verba eius videtur in-
<
lb
/>
nuere illas lineas īueniendas eſſe per artē medie
<
lb
/>
rei īuentionis / quod ſtare nõ poteſt / vt probatū eſt
<
lb
/>
</
s
>
<
s
xml:id
="
N151F3
"
xml:space
="
preserve
">Et ſi hec nõ fuit intentio et mens venerabilis ma-
<
lb
/>
giſtri. </
s
>
<
s
xml:id
="
N151F8
"
xml:space
="
preserve
">Nicholai horen detur imbecillitati et par-
<
lb
/>
uitati ingenioli mei venia. </
s
>
<
s
xml:id
="
N151FD
"
xml:space
="
preserve
">Eligat igitur vnuſq̇ſ-
<
lb
/>
/ quod vult et me magis ſtudioſum quã maliuo-
<
lb
/>
lum probet.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
N15216
"
level
="
3
"
n
="
8
"
type
="
chapter
"
type-free
="
capitulum
">
<
head
xml:id
="
N1521B
"
xml:space
="
preserve
">Capitulum octauū / in quo agitur decre-
<
lb
/>
mento et decremento ꝓportionū.</
head
>
<
p
xml:id
="
N15220
">
<
s
xml:id
="
N15221
"
xml:space
="
preserve
">QUoniã inſequētibus plerū
<
lb
/>
ſeſe offert diminutio proportionis ex
<
lb
/>
augmento reſiſtentie: aut virtutis decre
<
lb
/>
mento / et etiam augmentatio proueniens ex decre
<
lb
/>
mento reſiſtētie aut virtutis augmento. </
s
>
<
s
xml:id
="
N1522C
"
xml:space
="
preserve
">Ideo ope
<
lb
/>
re precium eſt in huiꝰ ſecunde partis calce aliquid
<
lb
/>
de augmento et decremento ꝓportionū adiicere.</
s
>
</
p
>
<
p
xml:id
="
N15233
">
<
s
xml:id
="
N15234
"
xml:space
="
preserve
">Pro quo ſuppono primo. </
s
>
<
s
xml:id
="
N15237
"
xml:space
="
preserve
">Augere ſi-
<
lb
/>
ue augmentare aliquã proportionē cõtingit mul-
<
lb
/>
tipliciter: aut em̄ maiori numero aliquid additur
<
lb
/>
minore īuariato: aut decreſcente: aut minori ali-
<
lb
/>
quid demitur maiore nõ variato aut creſcēte. </
s
>
<
s
xml:id
="
N15242
"
xml:space
="
preserve
">aut
<
lb
/>
vtro creſcente velocius tamen ꝓportiõabiliter
<
lb
/>
creſcente maiore quã minore. </
s
>
<
s
xml:id
="
N15249
"
xml:space
="
preserve
">Aut vtro diminu-
<
lb
/>
to velocius tamē ꝓportionabiliter diminuto mi-
<
lb
/>
nore quã maiore. </
s
>
<
s
xml:id
="
N15250
"
xml:space
="
preserve
">Probat̄̄ / qm̄ capta proportione
<
lb
/>
dupla que eſt .8. ad .4. cõtingit eã augeri ꝑ cremen
<
lb
/>
tū ipſoꝝ .8. ipſis .4. īuariatis vel decreſcētibus. </
s
>
<
s
xml:id
="
N15257
"
xml:space
="
preserve
">vt
<
lb
/>
ſi .8: acquirãt vnitatē ipſis .4. īuariatis: manebit
<
lb
/>
ꝓportio maior dupla: nouē ad .4. q̄ eſt dupla ſex-
<
lb
/>
quiquarta: ſi quãdo .8. acquirūt vnitatē .4. deper
<
lb
/>
dūt vnitatē: etiã manebit proportio maior dupla
<
lb
/>
puta tripla. </
s
>
<
s
xml:id
="
N15264
"
xml:space
="
preserve
">Itē ſi quieſcētibꝰ .8.4. deꝑdant bina
<
lb
/>
riū: augmentabit̄̄ ꝓportio / vt cõſtat: et ſi etiã tūc .8
<
lb
/>
aliquid acquirãt: etiã augmētabitur ꝓportio. </
s
>
<
s
xml:id
="
N1526B
"
xml:space
="
preserve
">Si
<
lb
/>
vero .8. acquirãt quaternariū numeꝝ puta ꝓpor-
<
lb
/>
tionē ſexquialterã: et q̈ternariꝰ numerꝰ acq̇rat vni
<
lb
/>
tatē puta ꝓportionē ſexquiquartã: ꝓportio effi-
<
lb
/>
cietur maior: </
s
>
<
s
xml:id
="
N15276
"
xml:space
="
preserve
">Efficiet̄̄ em̄ dupla ſuprabipartiens
<
lb
/>
quītas. </
s
>
<
s
xml:id
="
N1527B
"
xml:space
="
preserve
">Si aūt .8: deꝑdant duo et .4. / ſiĺr duo aug-
<
lb
/>
mētabit̄̄ etiã ꝓportio: q2 maiorē ꝓportionē deꝑ-
<
lb
/>
dit numerꝰ mīor quã maior. </
s
>
<
s
xml:id
="
N15282
"
xml:space
="
preserve
">Et ſic ptꝫ ſuppoſitio.</
s
>
</
p
>
<
p
xml:id
="
N15285
">
<
s
xml:id
="
N15286
"
xml:space
="
preserve
">Secūda ſuppoſitio. </
s
>
<
s
xml:id
="
N15289
"
xml:space
="
preserve
">Augmētare pro
<
lb
/>
portionē eſt addere ꝓportioni ꝓportionē ceteris
<
lb
/>
paribꝰ: vt augere duplã eſt ei addere aliquã ꝓpor
<
lb
/>
tionē ceteris aliis manentibus paribus.</
s
>
</
p
>
<
p
xml:id
="
N15292
">
<
s
xml:id
="
N15293
"
xml:space
="
preserve
">Ex quo ſequit̄̄ tertia ſuppoſitio ꝓpo-
<
lb
/>
ſita vna ꝓportione quauis et duabꝰ aliis minori-
<
lb
/>
bus: īueſtigare vtrū illa maior ex illis duabꝰ mi-
<
lb
/>
noribꝰ adeq̈te ↄ̨ponit̄̄: vt ꝓpoſita ꝓportiõe dupla
<
lb
/>
et ſexq̇altera, et ſeq̇tertia minoribꝰ, videre vtrum
<
lb
/>
dupla ex ſexq̇altera et ſexq̇tertia adeq̈te cõponat̄̄.
<
lb
/>
</
s
>
<
s
xml:id
="
N152A1
"
xml:space
="
preserve
">Probat̄̄ / ſit a. ꝓportio maior b: et c: mīores: et volo
<
lb
/>
videre vtrū adeq̈te ↄ̨ponat̄̄ a. ex b. et c. </
s
>
<
s
xml:id
="
N152A6
"
xml:space
="
preserve
">Ad qḋ vidē-
<
lb
/>
dū: addã c. ipſi b. / et ſi tūc ꝓportio ↄ̨poſita ex b. et c.
<
lb
/>
adeq̈te eſt eq̈lis ipſi a. / ex illis adeq̈te cõponit̄̄ a.
<
lb
/>
ſin minus: nõ ex his adequate componitur: ſed ex
<
lb
/>
duabus maioribus, aut duabus minoribus.</
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>