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
>
51
(39)
52
(40)
53
(41)
54
(42)
55
(43)
56
(44)
57
(45)
58
(46)
59
(47)
60
(48)
<
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
|<
<
(45)
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-div137
"
type
="
math:theorem
"
level
="
3
"
n
="
69
">
<
p
>
<
s
xml:id
="
echoid-s599
"
xml:space
="
preserve
">
<
pb
o
="
45
"
rhead
="
THEOREM. ARIT.
"
n
="
57
"
file
="
0057
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0057
"/>
componendo ſic ſe habebit
<
var
>.k.y.</
var
>
ad
<
var
>.m.y.</
var
>
ſicut
<
var
>.e.a.</
var
>
ad
<
var
>.o.a.</
var
>
& permutando
<
var
>.k.y.</
var
>
ad
<
var
>.e.
<
lb
/>
a.</
var
>
ſicut
<
var
>.m.y.</
var
>
ad
<
var
>.o.a.</
var
>
& ex .19. quinti ita
<
var
>.k.m.</
var
>
ad
<
var
>.e.o.</
var
>
ſicut
<
var
>.k.y.</
var
>
ad
<
var
>.e.a.</
var
>
& permutando
<
var
>.
<
lb
/>
k.m.</
var
>
ad
<
var
>.k.y.</
var
>
ſicut
<
var
>.e.o.</
var
>
ad
<
var
>.e.a</
var
>
. </
s
>
<
s
xml:id
="
echoid-s600
"
xml:space
="
preserve
">Nunc producatur
<
var
>.f.t.</
var
>
donec
<
var
>.t.i.</
var
>
æqualis ſit
<
var
>.k.y.</
var
>
<
reg
norm
="
produ- ctaque
"
type
="
simple
">produ-
<
lb
/>
ctaq́;</
reg
>
<
var
>.m.t.</
var
>
done
<
var
>c.t.s.</
var
>
æqualis ſit vnitati
<
var
>.x.</
var
>
<
reg
norm
="
termineturque
"
type
="
simple
">termineturq́;</
reg
>
rectangulum
<
var
>.s.i.</
var
>
ex quo da-
<
lb
/>
bitur proportio numeri
<
var
>.f.m.</
var
>
ad numerum
<
var
>.s.i.</
var
>
compoſita ex
<
var
>.m.t.</
var
>
ad
<
var
>.t.s.</
var
>
et
<
var
>.f.t.</
var
>
ad
<
var
>.t.i.</
var
>
<
lb
/>
ex .24. ſexti, aut quinta octaui, ſed ita etiam proportio
<
var
>.q.b.</
var
>
ad
<
var
>.a.e.</
var
>
componitur ex
<
lb
/>
eiſdem proportionibus, nempe ex
<
var
>.q.b.</
var
>
ad
<
var
>.o.e.</
var
>
æquali
<
var
>.m.t.</
var
>
ad
<
var
>.t.s.</
var
>
& ex proportione
<
var
>.
<
lb
/>
o.e.</
var
>
ad
<
var
>.a.e.</
var
>
æquali
<
var
>.f.t.</
var
>
ad
<
var
>.t.i.</
var
>
ita que proportio numeri
<
var
>.f.m.</
var
>
ad
<
var
>.s.i.</
var
>
hoc eſt ad
<
reg
norm
="
numerum
"
type
="
context
">numerũ</
reg
>
<
lb
/>
ipſius
<
var
>.k.y.</
var
>
ęqualis eſt proportioni numeri
<
var
>.q.b.</
var
>
ad
<
var
>.a.e.</
var
>
<
reg
norm
="
nempe
"
type
="
context
">nẽpe</
reg
>
<
var
>.k.g.</
var
>
ad
<
var
>.k.u.</
var
>
hoc eſt
<
var
>.k.p.</
var
>
ad
<
lb
/>
<
var
>x.y.</
var
>
ex quo ſequitur
<
var
>.k.p.</
var
>
conſtare numero ęquali
<
var
>.f.m.</
var
>
proueniens igitur ex diuiſione
<
lb
/>
numeri
<
var
>.k.z.</
var
>
per
<
var
>.f.m.</
var
>
æquale eſt numero ipſius
<
var
>.a.e</
var
>
.</
s
>
</
p
>
<
figure
position
="
here
"
number
="
77
">
<
image
file
="
0057-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0057-01
"/>
</
figure
>
</
div
>
<
div
xml:id
="
echoid-div138
"
type
="
math:theorem
"
level
="
3
"
n
="
70
">
<
head
xml:id
="
echoid-head86
"
xml:space
="
preserve
">THEOREMA
<
num
value
="
70
">LXX</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s601
"
xml:space
="
preserve
">HAEC porrò concluſio alia etiam via demonſtrari poteſt.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s602
"
xml:space
="
preserve
">Significetur numerus diuidendus atque multiplicandus linea
<
var
>.b.a</
var
>
. </
s
>
<
s
xml:id
="
echoid-s603
"
xml:space
="
preserve
">Deinde
<
lb
/>
diuidentes &
<
reg
norm
="
multiplicantes
"
type
="
context
">multiplicãtes</
reg
>
ſint
<
var
>.k.m.</
var
>
et
<
var
>.m.y.</
var
>
prouenientia ex diuiſione ſint
<
var
>.a.o.</
var
>
et
<
var
>.o.
<
lb
/>
e.</
var
>
atque
<
var
>.a.o.</
var
>
ex
<
var
>.m.y</
var
>
:
<
var
>o.e.</
var
>
verò ex
<
var
>.k.m.</
var
>
proueniat, quorum ſumma ſit
<
var
>.a.e</
var
>
: productum
<
lb
/>
autem
<
var
>.b.a.</
var
>
in
<
var
>.k.m.</
var
>
ſit
<
var
>.b.p.</
var
>
et
<
var
>.p.s.</
var
>
productum
<
var
>.b.a.</
var
>
in
<
var
>.m.y.</
var
>
ad hæc rectangulum
<
var
>.k.y.</
var
>
ſit
<
lb
/>
productum
<
var
>.k.m.</
var
>
in
<
var
>.m.y</
var
>
: quo to-
<
lb
/>
tum productum
<
var
>.a.s.</
var
>
diuidatur, pro
<
lb
/>
<
figure
xlink:label
="
fig-0057-02
"
xlink:href
="
fig-0057-02a
"
number
="
78
">
<
image
file
="
0057-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0057-02
"/>
</
figure
>
<
reg
norm
="
ueniensque
"
type
="
simple
">ueniensq́;</
reg
>
ſit
<
var
>.a.c.</
var
>
cui,
<
var
>a.c</
var
>
:
<
reg
norm
="
productum
"
type
="
context
">productũ</
reg
>
<
var
>.
<
lb
/>
a.s.</
var
>
<
reg
norm
="
eandem
"
type
="
context context
">eãdẽ</
reg
>
<
reg
norm
="
proportionem
"
type
="
context
">proportionẽ</
reg
>
ſeruabit,
<
reg
norm
="
quam
"
type
="
context
">quã</
reg
>
<
lb
/>
<
var
>k.y.</
var
>
rectangulum ad vnitatem ex
<
lb
/>
definitione diuiſionis, hoc autem
<
lb
/>
proueniens
<
var
>.a.c.</
var
>
<
reg
norm
="
conſtare
"
type
="
context
">cõſtare</
reg
>
numero æ-
<
lb
/>
quali aſſero ſummæ
<
var
>.a.e</
var
>
. </
s
>
<
s
xml:id
="
echoid-s604
"
xml:space
="
preserve
">Primum
<
lb
/>
enim ex dicta definitione diuiſio-
<
lb
/>
nis habemus eandem eſſe propor-
<
lb
/>
tionem
<
var
>.b.a.</
var
>
ad
<
var
>.a.o.</
var
>
quæ
<
var
>.m.y.</
var
>
ad
<
lb
/>
vnitatem, & quod ſic ſe habet
<
var
>.b.a.</
var
>
<
lb
/>
ad
<
var
>.o.e.</
var
>
ſicut
<
var
>.k.m.</
var
>
ad eandem vnita
<
lb
/>
tem. </
s
>
<
s
xml:id
="
echoid-s605
"
xml:space
="
preserve
">Itaque vnitas hæc linearis ſi-
<
lb
/>
gnificetur per
<
var
>.m.x.</
var
>
in ſingulis late-
<
lb
/>
ribus
<
var
>.k.m.</
var
>
et
<
var
>.m.y.</
var
>
producentibus rectangulum
<
var
>.k.y</
var
>
: ſuperficialis autem vnitas ſit. </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>