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
>
71
(59)
72
(60)
73
(61)
74
(62)
75
(63)
76
(64)
77
(65)
78
(66)
79
(67)
80
(70)
<
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
|<
<
(46)
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-div138
"
type
="
math:theorem
"
level
="
3
"
n
="
70
">
<
p
>
<
s
xml:id
="
echoid-s605
"
xml:space
="
preserve
">
<
pb
o
="
46
"
rhead
="
IO. BAPT. BENED.
"
n
="
58
"
file
="
0058
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0058
"/>
<
var
>g.m.</
var
>
<
reg
norm
="
cogiteturque
"
type
="
simple
">cogiteturq́;</
reg
>
rectangulum
<
var
>.y.x.</
var
>
& rectangulum
<
var
>.k.x</
var
>
. </
s
>
<
s
xml:id
="
echoid-s606
"
xml:space
="
preserve
">Itaque dabitur eadem pro
<
lb
/>
portio
<
var
>.k.m.</
var
>
ad
<
var
>.m.x.</
var
>
nempe
<
var
>.k.x.</
var
>
rectanguli ad
<
var
>.m.g.</
var
>
quæ eſt
<
var
>.b.a.</
var
>
ad
<
var
>.o.e.</
var
>
et
<
var
>.y.x.</
var
>
ad
<
var
>.m.
<
lb
/>
g.</
var
>
quæ
<
var
>.b.a.</
var
>
ad
<
var
>.a.o.</
var
>
ſed ex prima ſexti aut .18. vel .19. ſeptimi, ſic ſe habet rectangu-
<
lb
/>
lum
<
var
>.k.y.</
var
>
ad
<
var
>.x.y.</
var
>
ſicut
<
var
>.k.m.</
var
>
ad
<
var
>.m.x.</
var
>
</
s
>
<
s
xml:id
="
echoid-s607
"
xml:space
="
preserve
">quare ſicut
<
var
>.b.a.</
var
>
ad
<
var
>.o.e.</
var
>
ex .11. quinti, & eiuſdem
<
lb
/>
rectanguli
<
var
>.k.y.</
var
>
ad rectangulum
<
var
>.k.x.</
var
>
ſicut
<
var
>.y.m.</
var
>
ad
<
var
>.x.m.</
var
>
nempe
<
var
>.b.a.</
var
>
ad
<
var
>.a.o</
var
>
. </
s
>
<
s
xml:id
="
echoid-s608
"
xml:space
="
preserve
">Quare
<
lb
/>
ex communi ſcientia, ſic ſe habebit duplum rectanguli
<
var
>.k.y.</
var
>
ad ſummam
<
var
>.y.x.</
var
>
cum
<
var
>.
<
lb
/>
k.x.</
var
>
rectangulorum, ſicut duplum
<
var
>.b.a.</
var
>
ad ſummam
<
var
>.a.o.e.</
var
>
et proportio ſummæ re-
<
lb
/>
ctangulorum
<
var
>.y.x.</
var
>
et
<
var
>.k.x.</
var
>
duplo
<
var
>.g.m.</
var
>
ſicut duplum
<
var
>.b.a.</
var
>
ad
<
var
>.a.o.e</
var
>
. </
s
>
<
s
xml:id
="
echoid-s609
"
xml:space
="
preserve
">Igitur ſumma duo-
<
lb
/>
rum rectangulorum
<
var
>.y.x.</
var
>
et
<
var
>.x.k.</
var
>
media proportionalis erit inter duplum rectanguli
<
var
>.
<
lb
/>
k.y.</
var
>
& duplum vnitatis ſuperſicialis
<
var
>.g.m</
var
>
. </
s
>
<
s
xml:id
="
echoid-s610
"
xml:space
="
preserve
">Nunc terminetur rectangulum
<
var
>.a.r.</
var
>
ex quo
<
lb
/>
dabitur eadem proportio dupli
<
var
>.a.s.</
var
>
ad
<
var
>.a.r.</
var
>
ſicut dupli
<
var
>.b.a.</
var
>
ad
<
var
>.a.e.</
var
>
ex propoſitioni-
<
lb
/>
bus notatis, ſexti aut ſeptimi. </
s
>
<
s
xml:id
="
echoid-s611
"
xml:space
="
preserve
">Quare etiam ſicut dupli rectanguli
<
var
>.k.y.</
var
>
ad
<
reg
norm
="
ſummam
"
type
="
context
">ſummã</
reg
>
<
lb
/>
rectangulorum
<
var
>.y.x.</
var
>
et
<
var
>.k.x</
var
>
. </
s
>
<
s
xml:id
="
echoid-s612
"
xml:space
="
preserve
">Iam verò ſi conſtituatur
<
var
>.e.c.</
var
>
pro vnitate lineari ipſius
<
var
>.
<
lb
/>
e.r.</
var
>
certi erimus numerum
<
var
>.a.c.</
var
>
æqualem eſſe
<
var
>.a.e.</
var
>
& proportionem
<
var
>.r.e.</
var
>
ad
<
var
>.e.c.</
var
>
hoc
<
lb
/>
eſt
<
var
>.a.r.</
var
>
ad
<
var
>.a.c.</
var
>
eandem quæ
<
var
>.y.x.</
var
>
et
<
var
>.x.k.</
var
>
rectangulorum ad
<
var
>.m.g.</
var
>
ex prædictis rationi-
<
lb
/>
bus, & ex hypotheſi, nempe quòd
<
var
>.
<
lb
/>
e.r.</
var
>
æqualis ſit numero
<
var
>.k.m.y.</
var
>
<
lb
/>
<
figure
xlink:label
="
fig-0058-01
"
xlink:href
="
fig-0058-01a
"
number
="
79
">
<
image
file
="
0058-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0058-01
"/>
</
figure
>
hoc eſt rectangulorum
<
var
>.y.x.</
var
>
et
<
var
>.x.
<
lb
/>
k</
var
>
. </
s
>
<
s
xml:id
="
echoid-s613
"
xml:space
="
preserve
">Quamobrem
<
var
>.a.r.</
var
>
ex communi
<
lb
/>
ſcientia
<
reg
norm
="
medium
"
type
="
context
">mediũ</
reg
>
proportionale erit
<
lb
/>
inter duplum
<
var
>.a.s.</
var
>
& duplum
<
var
>.a.c.</
var
>
<
reg
norm
="
ea demque
"
type
="
context simple
">ea
<
lb
/>
dẽq́;</
reg
>
<
reg
norm
="
proportio
"
type
="
simple
">ꝓportio</
reg
>
dupli prędicti
<
var
>.a.s.</
var
>
ad
<
lb
/>
duplum
<
var
>.a.c.</
var
>
ex æqualitate propor-
<
lb
/>
tionum ſimul collectarum, eadem
<
lb
/>
erit qùæ proportio dupli rectangu-
<
lb
/>
li
<
var
>.k.y.</
var
>
ad duplum
<
var
>.m.g.</
var
>
hoc eſt
<
var
>.a.s.</
var
>
<
lb
/>
ſimplicis ad ſimplicem
<
var
>.a.c.</
var
>
quæ ſim
<
lb
/>
plicis rectanguli
<
var
>.k.y.</
var
>
ad ſimplicem
<
lb
/>
vnitatem
<
var
>.g.m.</
var
>
ſic enim ſe habet ſim
<
lb
/>
plex ad ſimplex, ſicut duplum ad
<
lb
/>
duplum. </
s
>
<
s
xml:id
="
echoid-s614
"
xml:space
="
preserve
">Sed pariter ita ſe habet
<
var
>.a.s.</
var
>
ad
<
var
>.a.</
var
>
c
<
unsure
/>
. cogitato
<
var
>.a.c.</
var
>
tamquam proueniente
<
lb
/>
ex diuiſione
<
var
>.a.s.</
var
>
per rectangulum
<
var
>.k.y.</
var
>
vt conſtitutum eſt, ſicut
<
var
>.k.y.</
var
>
ad
<
var
>.m.g.</
var
>
ex defi-
<
lb
/>
nitione diuiſionis vt iam dictum eſt, </
s
>
<
s
xml:id
="
echoid-s615
"
xml:space
="
preserve
">quare numerus
<
var
>.a.c.</
var
>
æqualis erit numero
<
var
>.a.o.e</
var
>
.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div140
"
type
="
math:theorem
"
level
="
3
"
n
="
71
">
<
head
xml:id
="
echoid-head87
"
xml:space
="
preserve
">THEOREMA
<
num
value
="
71
">LXXI</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s616
"
xml:space
="
preserve
">CVR propoſitis .4. numeris, duobus nempe diuidentibus ac duobus diuiden-
<
lb
/>
dis, ſi
<
reg
norm
="
adinuicem
"
type
="
context
">adinuicẽ</
reg
>
diuiſi fuerint,
<
reg
norm
="
duoque
"
type
="
simple
">duoq́;</
reg
>
<
reg
norm
="
prouenientia
"
type
="
context
">proueniẽtia</
reg
>
<
reg
norm
="
inuicem
"
type
="
context
">inuicẽ</
reg
>
multiplicata
<
reg
norm
="
quenuis
"
type
="
context
">quẽuis</
reg
>
nu
<
lb
/>
merum producant, qui ſeruetur, ſi deinde ijdem numeri verſa vice mutuo diuiſi fue
<
lb
/>
rint, & inter ſe multiplicata prouenientia,
<
reg
norm
="
productum
"
type
="
context
">productũ</
reg
>
hoc, primo ſeruato numero
<
lb
/>
æquale erit.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s617
"
xml:space
="
preserve
">Exempli gratia propoſitis his .4. numeris .20. 30. 5. 10. duo autem .20. ſcilicet
<
lb
/>
et .30. ſint numeri diuidendi, porrò .5. et .10. numeri diuidentes,
<
reg
norm
="
nempe
"
type
="
context
">nẽpe</
reg
>
vt primo .20
<
lb
/>
per .5. diuidatur, tum .30. per .10. producetur .4. et .3. qui ſimul multiplicati
<
reg
norm
="
proferent
"
type
="
context
">proferẽt</
reg
>
<
num
value
="
12
">.
<
lb
/>
12.</
num
>
tum .20. per .10. d iuiſo et .30. per .5. prouenientia erunt .2. 6. quæ inter ſe multi-
<
lb
/>
plicata producent etiam .12.</
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>