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
|<
<
(14)
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-div46
"
type
="
math:theorem
"
level
="
3
"
n
="
20
">
<
p
>
<
s
xml:id
="
echoid-s206
"
xml:space
="
preserve
">
<
var
>
<
pb
o
="
14
"
rhead
="
IO. BAPT. BENED.
"
n
="
26
"
file
="
0026
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0026
"/>
q.</
var
>
radicem eſſe quadratam producti
<
var
>.l.e.</
var
>
in
<
var
>.e.p.</
var
>
quod
<
reg
norm
="
productum
"
type
="
context
">productũ</
reg
>
ſit quadratuni
<
unsure
/>
<
lb
/>
corporeum
<
var
>.c.g.</
var
>
cogitemus pariter duo quadrata
<
var
>.l.e.</
var
>
et
<
var
>.e.p.</
var
>
eſſe pariter corpo-
<
lb
/>
rea, tantę profunditatis, quantam, vnitas linearis radicum
<
var
>.m.e.</
var
>
et
<
var
>.e.q.</
var
>
requirit.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s207
"
xml:space
="
preserve
">Hæc duo corpora producentur à ſuperficie in vnitatem,
<
reg
norm
="
vocenturque
"
type
="
simple
">vocenturq́;</
reg
>
<
var
>.l.x.</
var
>
et
<
var
>.x.p.</
var
>
quo
<
lb
/>
facto, cogitemus corpus
<
var
>.a.g.</
var
>
tamquam productum cubi
<
var
>.l.b.</
var
>
in quadratum
<
var
>.e.p</
var
>
. </
s
>
<
s
xml:id
="
echoid-s208
"
xml:space
="
preserve
">Vn-
<
lb
/>
de ex decimaoctaua, aut decimanona ſeptimi, eadem erit proportio
<
var
>.a.g.</
var
>
ad
<
var
>.c.g.</
var
>
<
lb
/>
quæ eſt
<
var
>.l.b.</
var
>
ad
<
var
>.l.x.</
var
>
corporeum, ſed ex .25. vndecimi & prima ſexti, ita ſe habet
<
var
>.a.K.</
var
>
<
lb
/>
ad
<
var
>.K.c.</
var
>
vnitatem linearé ſicut
<
var
>.a.g.</
var
>
ad
<
var
>.c.g.</
var
>
& ex
<
reg
norm
="
eiſdem
"
type
="
context
">eiſdẽ</
reg
>
ita ſe habebit
<
var
>.b.e.</
var
>
ad
<
var
>.e.x.</
var
>
vnita-
<
lb
/>
tem linearem, ſicut
<
var
>.l.b.</
var
>
ad quadratum
<
var
>.l.x.</
var
>
corporeum. </
s
>
<
s
xml:id
="
echoid-s209
"
xml:space
="
preserve
">Itaque ſic ſe habebit
<
var
>.b.e.</
var
>
ad
<
lb
/>
vnitatem linearem
<
var
>.e.x.</
var
>
videlicet
<
var
>.K.c.</
var
>
ſicut
<
var
>.a.K.</
var
>
ad ipſam
<
var
>.K.c</
var
>
. </
s
>
<
s
xml:id
="
echoid-s210
"
xml:space
="
preserve
">Vnde ex nona quinti
<
var
>.
<
lb
/>
a.K.</
var
>
æqualis erit
<
var
>.e.b.</
var
>
& conſequenter æqualis
<
var
>.m.e</
var
>
. </
s
>
<
s
xml:id
="
echoid-s211
"
xml:space
="
preserve
">Iam verò ſit
<
var
>.u.g.</
var
>
productum
<
var
>.l.b.</
var
>
<
lb
/>
cubi, in cubum
<
var
>.o.p.</
var
>
vt ſupra dictum eſt, Hinc patebit ex quauis duarum propoſitio-
<
lb
/>
num, decimaoctaua, aut decimanona ſeptimi, eandem futuram proportionem
<
var
>.u.g.</
var
>
<
lb
/>
ad
<
var
>.a.g.</
var
>
quæ eſt
<
var
>.o.p.</
var
>
ad
<
var
>.x.p.</
var
>
quadratum corporeum. </
s
>
<
s
xml:id
="
echoid-s212
"
xml:space
="
preserve
">Quare ex poſtremis, dictis ratio-
<
lb
/>
nibus, eadem erit proportio
<
var
>.u.K.</
var
>
ad
<
var
>.a.K.</
var
>
quæ eſt
<
var
>.o.e.</
var
>
ad vnitatem linearem
<
var
>.e.x.</
var
>
at
<
lb
/>
ex dictis decimaoctaua & decimanona ſeptimi, ita ſe habet
<
reg
norm
="
numerus
"
type
="
simple
">numerꝰ</
reg
>
<
var
>.m.q.</
var
>
ad
<
reg
norm
="
numerum
"
type
="
context
">numerũ</
reg
>
<
lb
/>
<
reg
norm
="
ſuperficialem
"
type
="
context
">ſuperficialẽ</
reg
>
<
var
>.m.e.</
var
>
qui
<
reg
norm
="
producitur
"
type
="
simple
">ꝓducitur</
reg
>
à lineari
<
var
>.m.e.</
var
>
in vnitaté
<
reg
norm
="
linearem
"
type
="
context
">linearẽ</
reg
>
ipſius
<
var
>.e.q.</
var
>
ſicut nume
<
lb
/>
rus
<
var
>.q.e.</
var
>
ad ſuam vnitaté, ſed
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
numerus
<
var
>.a.K.</
var
>
æqualis ſit numero
<
var
>.m.e.</
var
>
vt
<
reg
norm
="
probatum
"
type
="
context
">probatũ</
reg
>
eſt
<
lb
/>
erit ergo ex vndecima & nona quinti, numerus
<
var
>.u.K.</
var
>
æqualis numero
<
var
>.m.q</
var
>
. </
s
>
<
s
xml:id
="
echoid-s213
"
xml:space
="
preserve
">At
<
var
>.f.g.</
var
>
<
lb
/>
pariter æqualis eſt numero
<
var
>.m.q.</
var
>
ex præcedenti theoremate, vnde
<
var
>.K.u.</
var
>
pariter æqua
<
lb
/>
lis erit
<
var
>.f.g</
var
>
. </
s
>
<
s
xml:id
="
echoid-s214
"
xml:space
="
preserve
">Itaque ſequitur
<
var
>.u.g.</
var
>
cubum eſſe, &
<
var
>f.g.</
var
>
radicem ipſius, æqualem numero
<
var
>.
<
lb
/>
m.q.</
var
>
quod quærebatur.</
s
>
</
p
>
<
figure
position
="
here
"
number
="
29
">
<
image
file
="
0026-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0026-01
"/>
</
figure
>
<
figure
position
="
here
"
number
="
30
">
<
image
file
="
0026-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0026-02
"/>
</
figure
>
</
div
>
<
div
xml:id
="
echoid-div48
"
type
="
math:theorem
"
level
="
3
"
n
="
21
">
<
head
xml:id
="
echoid-head37
"
xml:space
="
preserve
">THEOREMA
<
num
value
="
21
">XXI</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s215
"
xml:space
="
preserve
">VT autem in uniuerſum ſciri poſſit totum
<
reg
norm
="
infinitum
"
type
="
context
">infinitũ</
reg
>
dignitatum, hoc eſt radicem
<
lb
/>
producti duarum dignitatum ſimilium, productum eſſe duarum radicum ea-
<
lb
/>
rundem dignitatum.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s216
"
xml:space
="
preserve
">Ponamus, exempli gratia, duas radices quadratas
<
var
>.q.p.</
var
>
et
<
var
>.g.K.</
var
>
incognitas, quas
<
lb
/>
qui velit adinuicem multiplicare, cogatur earum quadrata cognita
<
var
>.n.</
var
>
cum
<
var
>.i.</
var
>
multi-
<
lb
/>
plicare, quorum productum ſit quadratum
<
var
>.m.</
var
>
radix cuius ſit
<
var
>.b.d.</
var
>
quam dico æqualé </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>