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
>
91
(79)
92
(80)
93
(81)
94
(82)
95
(89)
96
(84)
97
(85)
98
(96)
99
(87)
100
(88)
<
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
|<
<
(42)
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-div130
"
type
="
math:theorem
"
level
="
3
"
n
="
64
">
<
pb
o
="
42
"
rhead
="
IO. BAPT. BENED.
"
n
="
54
"
file
="
0054
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0054
"/>
</
div
>
<
div
xml:id
="
echoid-div131
"
type
="
math:theorem
"
level
="
3
"
n
="
65
">
<
head
xml:id
="
echoid-head81
"
xml:space
="
preserve
">THEOREMA
<
num
value
="
65
">LXV</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s557
"
xml:space
="
preserve
">CVR propoſito numero in tres qualeſcunque partes diuiſo, ſi prima in
<
lb
/>
tertiam multiplicetur, & huic producto, ſecundæ in primam productum
<
lb
/>
coniungatur,
<
reg
norm
="
itemque
"
type
="
simple
">itemq́;</
reg
>
ſecundæ in tertiam, hæc ſumma duplicata æqualis ſit ſummæ
<
lb
/>
productorum ſingularum in cæteras duas.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s558
"
xml:space
="
preserve
">Exempli gratia, ſi proponatur .20. diuiſus in tres partes nempe .12. 5. 3. multipli-
<
lb
/>
cato primo .12. per .3. tertiam partem dabitur .36. ſecunda verò multiplicata per re
<
lb
/>
liquas duas, hoc eſt .5. per .12. et .3. in primis dabitur .60. poſtea .15.
<
reg
norm
="
quorum
"
type
="
context
">quorũ</
reg
>
<
reg
norm
="
trium
"
type
="
context
">triũ</
reg
>
pro
<
lb
/>
ductorum ſumma erit .111. quæ duplicata dabit .222. qui numerus æqualis eſſe di-
<
lb
/>
citur ſummæ productorum ſingularum partium in reliquas duas, nempe ſummæ .60.
<
lb
/>
36. 60. 15. 36. 15. hoc eſt ipſis .222.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s559
"
xml:space
="
preserve
">Cuius rei per ſe patet ſpeculatio, cum in his ſex vltimis productis, ſingula tria
<
lb
/>
prima duplicentur.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div132
"
type
="
math:theorem
"
level
="
3
"
n
="
66
">
<
head
xml:id
="
echoid-head82
"
xml:space
="
preserve
">THEOREMA
<
num
value
="
66
">LXVI</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s560
"
xml:space
="
preserve
">CVR propoſito numero in .3. qualeſcunque partes diuiſo, ſi in reliquas duas ſin-
<
lb
/>
gulæ multiplicentur, & hæc producta cum ſumma ſuorum quadratorum con-
<
lb
/>
iungantur, tota ſumma hæc vltima æqualis erit quadrato totali propoſiti numeri.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s561
"
xml:space
="
preserve
">Exempli gratia, ſi fuerit idem numerus .20. in .3. partes diuiſus .12. 5. 3. </
s
>
<
s
xml:id
="
echoid-s562
"
xml:space
="
preserve
">Si .12. in
<
lb
/>
5. et .3. producatur, ſumma productorum erit .96. at .5. in .12. et .3. erit .75. poſtmo-
<
lb
/>
dum .3. in .12. et .5. erit .51. nempe in vniuerſum .222. quadratorum porrò ſumma
<
lb
/>
erit .178 quæ coniuncta .222. dabit .400. quadratum ipſius .20.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s563
"
xml:space
="
preserve
">Erit autem huiuſce rei facillima ſpeculatio, ſi ſequentem figuram mente conce-
<
lb
/>
perimus, in qua
<
var
>.a.b.</
var
>
propoſitum numerum ſignificet, cuius partes diſtinctæ ſint me-
<
lb
/>
dio
<
var
>.e.</
var
>
et
<
var
>.c</
var
>
. </
s
>
<
s
xml:id
="
echoid-s564
"
xml:space
="
preserve
">Ip ſum autem
<
var
>.q.b.</
var
>
ſit quadratum
<
lb
/>
totale parallelis
<
var
>.e.s.</
var
>
et
<
var
>.c.x.</
var
>
diuiſum, quæ qua
<
lb
/>
<
figure
xlink:label
="
fig-0054-01
"
xlink:href
="
fig-0054-01a
"
number
="
74
">
<
image
file
="
0054-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0054-01
"/>
</
figure
>
dratum in triarectangula diuident, quorum
<
lb
/>
primum erit
<
var
>.q.e.</
var
>
compoſitum ex producto
<
var
>.a.
<
lb
/>
e.</
var
>
in ſemetipſam, nempe quadratum
<
var
>.o.e.</
var
>
&
<
lb
/>
ex producto eiuſdem
<
var
>.a.e.</
var
>
in
<
var
>.e.b.</
var
>
quod erit re
<
lb
/>
ctangulum
<
var
>.o.s.</
var
>
ex quo tria rectangula
<
var
>.o.s.</
var
>
et
<
var
>.
<
lb
/>
n.x.</
var
>
et
<
var
>.t.u.</
var
>
tria producta erunt ſingularum par
<
lb
/>
tium in cæteras duas, et
<
var
>.e.o</
var
>
:
<
var
>c.n</
var
>
:
<
var
>b.t.</
var
>
tria qua-
<
lb
/>
drata erunt: </
s
>
<
s
xml:id
="
echoid-s565
"
xml:space
="
preserve
">quibus ſex quantitatibus quadra
<
lb
/>
tum totale
<
var
>.q.b.</
var
>
completur.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div134
"
type
="
math:theorem
"
level
="
3
"
n
="
67
">
<
head
xml:id
="
echoid-head83
"
xml:space
="
preserve
">THEOREMA
<
num
value
="
67
">LXVII</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s566
"
xml:space
="
preserve
">
<
emph
style
="
sc
">VEteres</
emph
>
aliud quoque problema indefinitum propoſuerunt, quod tamen à
<
lb
/>
nobis determinabitur.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s567
"
xml:space
="
preserve
">Cur diuiſuri propoſitum numerum in duas eiuſmodi partes, vt mutuò diuiſis, &
<
lb
/>
per ſummam prouenientium diuiſa ſumma qua dratorum partium, oriatur proue-
<
lb
/>
niens alter numerus propoſitus.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s568
"
xml:space
="
preserve
">Propoſito deinde tertio quolibet numero diuidendo per ſingulas partes primi, </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>