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
>
31
(19)
32
(20)
33
(21)
34
(22)
35
(23)
36
(24)
37
(25)
38
(26)
39
(27)
40
(28)
<
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
|<
<
(15)
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-div7
"
type
="
chapter
"
level
="
2
"
n
="
1
">
<
div
xml:id
="
echoid-div48
"
type
="
math:theorem
"
level
="
3
"
n
="
21
">
<
p
>
<
s
xml:id
="
echoid-s216
"
xml:space
="
preserve
">
<
pb
o
="
15
"
rhead
="
THEOREM. ARIT.
"
n
="
27
"
file
="
0027
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0027
"/>
eſſe
<
reg
norm
="
producto
"
type
="
simple
">ꝓducto</
reg
>
<
var
>.q.p.</
var
>
in
<
var
>.g.k.</
var
>
<
reg
norm
="
quod
"
type
="
wordlist
">qđ</
reg
>
<
reg
norm
="
autem
"
type
="
context
">autẽ</
reg
>
ſit
<
var
>.o</
var
>
. </
s
>
<
s
xml:id
="
echoid-s217
"
xml:space
="
preserve
">Patet enim
<
reg
norm
="
proportionem
"
type
="
context
">proportionẽ</
reg
>
<
var
>.o.</
var
>
ad
<
var
>.q.p.</
var
>
<
reg
norm
="
eandem
"
type
="
context
">eandẽ</
reg
>
eſſe
<
lb
/>
cum proportione
<
var
>.g.k.</
var
>
ad ſuam vnitatem linearem, ex decimaoctaua, aut decima-
<
lb
/>
nona ſeptimi, hæc vero vnitas linearis ſit
<
var
>.t.</
var
>
cuius ſuperficialis ſit
<
var
>.u.</
var
>
vnitas ſcilicet to-
<
lb
/>
ties in ſeipſam multiplicata quoties propoſita dignitas patitur, tametſi in præſen
<
lb
/>
ti exemplo quadrata dignitas ſumatur. </
s
>
<
s
xml:id
="
echoid-s218
"
xml:space
="
preserve
">
<
reg
norm
="
Itaque
"
type
="
simple
">Itaq;</
reg
>
ex eiſdem propoſitionibus decimaocta
<
lb
/>
ua aut decimanona, ſic ſe habet
<
var
>.m.</
var
>
ad
<
var
>.n.</
var
>
ſicut
<
var
>.i.</
var
>
ad
<
var
>.u</
var
>
. </
s
>
<
s
xml:id
="
echoid-s219
"
xml:space
="
preserve
">Scimus pręterea
<
reg
norm
="
proportionem
"
type
="
context
">proportionẽ</
reg
>
<
var
>.
<
lb
/>
m.</
var
>
ad
<
var
>.n.</
var
>
(eo quod in propoſito exemplo ſint quadrata) duplam eſſe proportioni
<
var
>.b.
<
lb
/>
d.</
var
>
ad
<
var
>.q.p.</
var
>
et ipſius
<
var
>.i.</
var
>
ad
<
var
>.u.</
var
>
pariter duplam proportioni
<
var
>.g.k.</
var
>
ad
<
var
>.t.</
var
>
iam autem dictum
<
lb
/>
fuit ſic ſe habere
<
var
>.m.</
var
>
ad
<
var
>.n.</
var
>
ſicut
<
var
>.i.</
var
>
ad
<
var
>.u</
var
>
. </
s
>
<
s
xml:id
="
echoid-s220
"
xml:space
="
preserve
">
<
reg
norm
="
Itaque
"
type
="
simple
">Itaq;</
reg
>
<
var
>.
<
lb
/>
b.d.</
var
>
ſic ſe habebit ad
<
var
>.q.p.</
var
>
ſicut
<
var
>.g.k.</
var
>
ad
<
var
>.t.</
var
>
<
lb
/>
<
figure
xlink:label
="
fig-0027-01
"
xlink:href
="
fig-0027-01a
"
number
="
31
">
<
image
file
="
0027-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0027-01
"/>
</
figure
>
quandoquidem ſic ſe habeattotum ad
<
reg
norm
="
to- tum
"
type
="
context
">to-
<
lb
/>
tũ</
reg
>
, ſicut pars ad
<
reg
norm
="
partem
"
type
="
context
">partẽ</
reg
>
,
<
reg
norm
="
dum
"
type
="
context
">dũ</
reg
>
ſimiles ſint, proba
<
lb
/>
<
reg
norm
="
tum
"
type
="
context
">tũ</
reg
>
<
reg
norm
="
autem
"
type
="
context
">autẽ</
reg
>
eſt ſuperius ita ſe habere
<
var
>.o.</
var
>
ad
<
var
>.q.p.</
var
>
<
lb
/>
ſicut
<
var
>.g.k.</
var
>
ad
<
var
>.t.</
var
>
<
reg
norm
="
itaque
"
type
="
simple
">itaq;</
reg
>
<
var
>.o.</
var
>
ſic ſe habebit ad
<
var
>.q.p.</
var
>
<
lb
/>
ſicut
<
var
>.b.d.</
var
>
ad
<
var
>.q.p.</
var
>
vnde
<
var
>.o.</
var
>
æqualis erit
<
var
>.b.d.</
var
>
<
lb
/>
Hocipſum cęteris dignitatibus conueniet,
<
lb
/>
mutatis tantummodo proportionibus
<
var
>.m.
<
lb
/>
n.</
var
>
ad proportionem
<
var
>.b.d</
var
>
:
<
var
>q.p.</
var
>
ſic propor-
<
lb
/>
tionibus duarum dignitatum
<
var
>.i.u.</
var
>
ad pro-
<
lb
/>
portionem ſuarum radicum
<
var
>.g.k.t</
var
>
.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div50
"
type
="
math:theorem
"
level
="
3
"
n
="
22
">
<
head
xml:id
="
echoid-head38
"
xml:space
="
preserve
">THEOREMA
<
num
value
="
22
">XXII</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s221
"
xml:space
="
preserve
">
<
emph
style
="
sc
">DOcent</
emph
>
veteres, quòd ſi quilibet numerus in duas partes inæquales diuiſus
<
lb
/>
fuerit,
<
reg
norm
="
totumque
"
type
="
simple
">totumq́</
reg
>
diuiſum per
<
reg
norm
="
vnam
"
type
="
context
">vnã</
reg
>
partium, & per eandem pars altera diuiſa fue-
<
lb
/>
rit: </
s
>
<
s
xml:id
="
echoid-s222
"
xml:space
="
preserve
">differentia prouenientium ſemper vnitas erit. </
s
>
<
s
xml:id
="
echoid-s223
"
xml:space
="
preserve
">quodquidem veriſſimum eſt.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s224
"
xml:space
="
preserve
">Detur enim
<
var
>.b.d.</
var
>
propoſitus numerus in duas partes inæquales diuiſus
<
var
>.b.c.</
var
>
et
<
var
>.c.d.</
var
>
<
lb
/>
& in primis
<
reg
norm
="
totum
"
type
="
context
">totũ</
reg
>
<
var
>.b.d.</
var
>
per
<
var
>.c.d.</
var
>
diuidatur, ex quo oriatur
<
var
>e.o.</
var
>
vnitas autem
<
reg
norm
="
per
"
type
="
punctuation simple
">.ꝑ</
reg
>
<
var
>.i.o.</
var
>
ſigni-
<
lb
/>
ficetur, tum pars ipſa
<
var
>.b.c.</
var
>
<
reg
norm
="
per
"
type
="
simple punctuation
">ꝑ.</
reg
>
<
reg
norm
="
eandem
"
type
="
context
">eãdem</
reg
>
<
var
>.c.d.</
var
>
diuidatur,
<
reg
norm
="
ſitque
"
type
="
simple
">ſitq́;</
reg
>
<
reg
norm
="
proueniens
"
type
="
context
">proueniẽs</
reg
>
<
var
>.a</
var
>
. </
s
>
<
s
xml:id
="
echoid-s225
"
xml:space
="
preserve
">Sanè ex defini-
<
lb
/>
tione diuiſionis, eadem erit proportio
<
var
>.b.d.</
var
>
ad
<
var
>.e.o.</
var
>
quæ eſt
<
var
>.c.d.</
var
>
ad
<
var
>.i.o.</
var
>
et ita
<
var
>.b.c.</
var
>
ad
<
var
>.a.</
var
>
<
lb
/>
ſicut
<
var
>.c.d.</
var
>
ad
<
var
>.i.o</
var
>
. </
s
>
<
s
xml:id
="
echoid-s226
"
xml:space
="
preserve
">Ex
<
ref
id
="
ref-0009
">.19. autem quinti</
ref
>
, ita ſe habet
<
var
>.b.c.</
var
>
ad
<
var
>.e.i.</
var
>
ſicut
<
var
>.b.d.</
var
>
ad
<
var
>.e.o.</
var
>
at
<
var
>.b.d.</
var
>
<
lb
/>
ad
<
var
>.e.o.</
var
>
ſic ſe habet ſicut
<
var
>.c.d.</
var
>
ad
<
var
>.i.o.</
var
>
hoc eſt ſicut
<
var
>.b.c.</
var
>
ad
<
var
>.a</
var
>
. </
s
>
<
s
xml:id
="
echoid-s227
"
xml:space
="
preserve
">Quare ex .11. quinti ſic ſe
<
lb
/>
habebit
<
var
>.b.c.</
var
>
ad
<
var
>.e.i.</
var
>
ſicut .ad
<
var
>.a.</
var
>
ex quo ex .9.
<
reg
norm
="
praedi cti
"
type
="
simple
">prędi
<
lb
/>
cti</
reg
>
<
var
>.a.</
var
>
æqualis erit
<
var
>.e.i.</
var
>
ſed
<
var
>.e.i.</
var
>
minor eſt
<
var
>.e.o.</
var
>
<
lb
/>
<
figure
xlink:label
="
fig-0027-02
"
xlink:href
="
fig-0027-02a
"
number
="
32
">
<
image
file
="
0027-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0027-02
"/>
</
figure
>
per
<
var
>.i.o</
var
>
. </
s
>
<
s
xml:id
="
echoid-s228
"
xml:space
="
preserve
">Quare ſequitur propoſitum verum eſ
<
lb
/>
ſe. </
s
>
<
s
xml:id
="
echoid-s229
"
xml:space
="
preserve
">Quod ipſum pauciſſimis verbis ſic definiri
<
lb
/>
poteſt, ſi dixerimus, eiuſmodi diuidens .in par-
<
lb
/>
te diuiſibili,
<
reg
norm
="
quam
"
type
="
context
">quã</
reg
>
in toto, ſemel minus ingredi,
<
lb
/>
quandoquidem altera pars eſt, ex qua totum integrum perficitur.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div52
"
type
="
math:theorem
"
level
="
3
"
n
="
23
">
<
head
xml:id
="
echoid-head39
"
xml:space
="
preserve
">THEOREMA
<
num
value
="
23
">XXIII</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s230
"
xml:space
="
preserve
">HOcipſum alia ratione contemplari po
<
lb
/>
<
figure
xlink:label
="
fig-0027-03
"
xlink:href
="
fig-0027-03a
"
number
="
33
">
<
image
file
="
0027-03
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0027-03
"/>
</
figure
>
terimus.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s231
"
xml:space
="
preserve
">Significetur enim totalis numerus per
<
var
>.a.e.</
var
>
<
lb
/>
in duas partes diuiſus
<
var
>.a.u.</
var
>
et
<
var
>.u.e.</
var
>
totius autem diuidens ſit
<
var
>.u.e.</
var
>
& partis alterius
<
var
>.a.u.</
var
>
<
lb
/>
totius verò
<
reg
norm
="
proueniens
"
type
="
context
">proueniẽs</
reg
>
ſit
<
var
>.a.c.</
var
>
partis
<
reg
norm
="
autem
"
type
="
context
">autẽ</
reg
>
, ſit
<
reg
norm
="
proueniens
"
type
="
context
">proueniẽs</
reg
>
<
var
>.a.n.</
var
>
tum differentia ſit
<
var
>.n.c.</
var
>
vni </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>