Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
List of thumbnails
<
0 - 9
10 - 19
20 - 29
30 - 39
40 - 49
50 - 59
60 - 69
70 - 79
80 - 89
90 - 99
100 - 109
110 - 119
120 - 129
130 - 139
140 - 149
150 - 159
160 - 169
170 - 179
180 - 189
190 - 199
200 - 209
210 - 219
220 - 229
230 - 239
240 - 249
250 - 259
260 - 269
270 - 279
280 - 289
290 - 299
300 - 309
310 - 319
320 - 329
330 - 339
340 - 349
350 - 359
360 - 369
370 - 379
380 - 389
390 - 399
400 - 409
410 - 419
420 - 429
430 - 439
440 - 445
>
121
(109)
122
(110)
123
(111)
124
(112)
125
(113)
126
(114)
127
(115)
128
(116)
129
(117)
130
(118)
<
0 - 9
10 - 19
20 - 29
30 - 39
40 - 49
50 - 59
60 - 69
70 - 79
80 - 89
90 - 99
100 - 109
110 - 119
120 - 129
130 - 139
140 - 149
150 - 159
160 - 169
170 - 179
180 - 189
190 - 199
200 - 209
210 - 219
220 - 229
230 - 239
240 - 249
250 - 259
260 - 269
270 - 279
280 - 289
290 - 299
300 - 309
310 - 319
320 - 329
330 - 339
340 - 349
350 - 359
360 - 369
370 - 379
380 - 389
390 - 399
400 - 409
410 - 419
420 - 429
430 - 439
440 - 445
>
page
|<
<
(190)
of 445
>
>|
<
echo
version
="
1.0
">
<
text
type
="
book
"
xml:lang
="
la
">
<
div
xml:id
="
echoid-div7
"
type
="
body
"
level
="
1
"
n
="
1
">
<
div
xml:id
="
echoid-div387
"
type
="
chapter
"
level
="
2
"
n
="
4
">
<
div
xml:id
="
echoid-div432
"
type
="
section
"
level
="
3
"
n
="
32
">
<
pb
o
="
190
"
rhead
="
IO. BAPT. BENED.
"
n
="
202
"
file
="
0202
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0202
"/>
</
div
>
<
div
xml:id
="
echoid-div433
"
type
="
section
"
level
="
3
"
n
="
33
">
<
head
xml:id
="
echoid-head307
"
style
="
it
"
xml:space
="
preserve
">Pytagoreorum opinionem de ſonitu corporum cælestium non
<
lb
/>
fuiſſe ab Aristotele ſublatam.</
head
>
<
head
xml:id
="
echoid-head308
"
xml:space
="
preserve
">CAP. XXXIII.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2289
"
xml:space
="
preserve
">SEnſerunt Pythagorici orbes cæleſtes dum circunuoluuntur, non autem corpora
<
lb
/>
ſtellarum ſolum, æd ere ſonu. </
s
>
<
s
xml:id
="
echoid-s2290
"
xml:space
="
preserve
">Quibus dum Ariſtoteles contradicere cogitat,
<
lb
/>
maximè fauet. </
s
>
<
s
xml:id
="
echoid-s2291
"
xml:space
="
preserve
">Eatamen opinio è phyloſophorum ſcholis eſt explodenda, quia aut
<
lb
/>
orbes ſunt ſibi ipſis contigui, aut inuicem diſtantes: </
s
>
<
s
xml:id
="
echoid-s2292
"
xml:space
="
preserve
">ſi ab inuicem diſtant (quod
<
lb
/>
nemo adhuc conceſſit, quia hac ratione vacuum introduceretur) clarum eſt, quod
<
lb
/>
cum ſe minime tangant, ſonum edere nequeunt: </
s
>
<
s
xml:id
="
echoid-s2293
"
xml:space
="
preserve
">Si verò eorum vnus alteri ſit conti
<
lb
/>
guus,
<
reg
norm
="
neque
"
type
="
simple
">neq;</
reg
>
etiam ab ipſis ſonus reſultare poterit, quia pro certo putandum eſt,
<
reg
norm
="
ipſorum
"
type
="
context
">ipſorũ</
reg
>
<
lb
/>
ſuperficies tam politas eſſe, ac lenas, vt nihil omnino aſperitatis, aut inæqualitatis
<
lb
/>
contineant. </
s
>
<
s
xml:id
="
echoid-s2294
"
xml:space
="
preserve
">Vt exempli gratia, ſi aliquis duo ſpecula plana inuicem confricaret, nul
<
lb
/>
lum planè ſonum audiret, ſed ſi hoc faceret cum duabus ſuperficiebus a ſperis,
<
reg
norm
="
ſonum
"
type
="
context
">ſonũ</
reg
>
<
lb
/>
perſentiret, & tanto maiorem; </
s
>
<
s
xml:id
="
echoid-s2295
"
xml:space
="
preserve
">quantò aſperiores eſſent dictæ ſuperficies, & qui vult
<
lb
/>
vtarcus lirę, ex corda ſonum eliciat, colophonia dictum arcum illinet, vt aſperiorem
<
lb
/>
reddat. </
s
>
<
s
xml:id
="
echoid-s2296
"
xml:space
="
preserve
">Neceſſarium quoque eſt vt tremat ſiue trepidet corpus, quod
<
reg
norm
="
ſonum
"
type
="
context
">ſonũ</
reg
>
edere
<
lb
/>
debet; </
s
>
<
s
xml:id
="
echoid-s2297
"
xml:space
="
preserve
">Neque etiam abſque aere ſonus efficipotelt, quia aer ſonat ingrediendo
<
lb
/>
velociter ad implendum locum, vt non remaneat vacuus. </
s
>
<
s
xml:id
="
echoid-s2298
"
xml:space
="
preserve
">Sed ſupponendo in æche
<
lb
/>
rea regione neque aerem eſſe, neque corpus aliquod fluidum, clarè patebit orbes
<
lb
/>
cœleſtes ex ſeſe nullum emittere ſonum. </
s
>
<
s
xml:id
="
echoid-s2299
"
xml:space
="
preserve
">Idem affirmo de fricatione ſuperficiei con
<
lb
/>
cauæ infimi orbis lunaris cum conuexa materiæ à dicto orbe contentæ, ſuperioribus
<
lb
/>
rationibus fultus, vt etiam experientia à corpore aliquo fluido, quod in alio velociſ
<
lb
/>
ſimè moueretur deſumpta fretus, cuius corporis ſuperficies tamen lenis eſſet, à quo
<
lb
/>
ſonus non gigneretur. </
s
>
<
s
xml:id
="
echoid-s2300
"
xml:space
="
preserve
">Et non minus dicere poſſum, corpus fluidum moueri in con-
<
lb
/>
tinente loco immobili, quam dictum corpus continens illud eſſe, quod moueretur,
<
lb
/>
& non fluidum corpus. </
s
>
<
s
xml:id
="
echoid-s2301
"
xml:space
="
preserve
">Cuius rei poſſumus etiam exemplum habere à quouis
<
lb
/>
corpore perfectè rotundo, quod circa ſuum axem velociſſimè moueatur, nullum ſo-
<
lb
/>
num efficiet, quia nullam aeris partem extra ſuum
<
reg
norm
="
locum
"
type
="
context
">locũ</
reg
>
impellit dum mouetur non
<
lb
/>
ſecundum totum, ſed ſecundum ſuas partes, quarum quælibet abſque reſiſtentia im-
<
lb
/>
mediatè ſubintrat locum alterius, abſque temporis interpoſitione. </
s
>
<
s
xml:id
="
echoid-s2302
"
xml:space
="
preserve
">nec huiuſmodi
<
lb
/>
locum aliquo modo eadem materia dicti corporis, quod circunuoluitur: </
s
>
<
s
xml:id
="
echoid-s2303
"
xml:space
="
preserve
">deſtitutum
<
lb
/>
dimittat. </
s
>
<
s
xml:id
="
echoid-s2304
"
xml:space
="
preserve
">Sed ſi Pythagorici de alia quadam harmoniæ ſpecie ab ea, quæ eſt ſono-
<
lb
/>
rum, vt à diuerſis velocitatibus motuum, aut à diuerſis magnitudinibus aut diſtantiis,
<
lb
/>
aut ſtellarum influxibus intellexiſſent, rectè ſenſiſſent exparte, non autem omnino,
<
lb
/>
quia ea harmoniam efficere nequeunt, quæ ad
<
reg
norm
="
inuicem
"
type
="
context
">inuicẽ</
reg
>
ſecundum interualla harmoni-
<
lb
/>
ca proportionata non ſunt, vt ſunt dupla, ſeſquial tera, ſeſquitertia, ſeſquiquarta, ſeſ-
<
lb
/>
quiquinta, ſupertripartientia quintas,
<
reg
norm
="
ſuperbipartientia
"
type
="
context
">ſuperbipartiẽtia</
reg
>
tertias, & quę ab ijs
<
reg
norm
="
dependent
"
type
="
context
">dependẽt</
reg
>
<
lb
/>
ideſt coniuncta ſunt cum duplis; </
s
>
<
s
xml:id
="
echoid-s2305
"
xml:space
="
preserve
">de conſonantijs loquendo. de diſſonantiis idem di
<
lb
/>
co, quæ harmonicis inſeruiunt modulationibus, vt
<
reg
norm
="
ſeſquioctauum
"
type
="
context
">ſeſquioctauũ</
reg
>
,
<
reg
norm
="
ſeſquinonum
"
type
="
context
">ſeſquinonũ</
reg
>
, ſeſqui
<
lb
/>
<
reg
norm
="
quintundecimum
"
type
="
context context
">quintũdecimũ</
reg
>
,
<
reg
norm
="
ſequiuigeſimunquartum
"
type
="
context context
">ſequiuigeſimũquartũ</
reg
>
,
<
reg
norm
="
ſeſquioctuogeſimum
"
type
="
context
">ſeſquioctuogeſimũ</
reg
>
, & ſuperbipartiens vigeſi
<
lb
/>
masquintas. </
s
>
<
s
xml:id
="
echoid-s2306
"
xml:space
="
preserve
">
<
reg
norm
="
Verum
"
type
="
context
">Verũ</
reg
>
quidem eſt nonnulla harmonica interualla in aſpectibus
<
reg
norm
="
comperta
"
type
="
context
">cõperta</
reg
>
<
lb
/>
fuiſſe, vt Prolomeus oſtendit, & alii quoque aſſerunt. </
s
>
<
s
xml:id
="
echoid-s2307
"
xml:space
="
preserve
">ineſt tamen huic rei nonnihil
<
lb
/>
difficultatis. </
s
>
<
s
xml:id
="
echoid-s2308
"
xml:space
="
preserve
">vt exempli gratia, ſi ſubtrahamus diateſſaron extra diapaſon, remanet
<
lb
/>
diapente, & ſi à diapente ſubtrahamus ſemiditonum, remanet ditonum (quæ duæ </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>