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
>
1
2
3
4
5
6
7
8
9
<
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
|<
<
(25)
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-div83
"
type
="
math:theorem
"
level
="
3
"
n
="
38
">
<
p
>
<
s
xml:id
="
echoid-s343
"
xml:space
="
preserve
">
<
pb
o
="
25
"
rhead
="
THEOREM. ARIT.
"
n
="
37
"
file
="
0037
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0037
"/>
noni,
<
reg
norm
="
hocque
"
type
="
simple
">hocq́;</
reg
>
rectangulum
<
var
>.g.r.</
var
>
quadratum eſt primi numeri propoſiti ex .19. theo-
<
lb
/>
remate huius libri,
<
reg
norm
="
itaque
"
type
="
simple
">itaq;</
reg
>
cognitum erit. </
s
>
<
s
xml:id
="
echoid-s344
"
xml:space
="
preserve
">vnà etiam gnomon
<
var
>.u.g.t.</
var
>
cognoſcetur,
<
lb
/>
quare totum quadratum
<
var
>.g.y.</
var
>
<
reg
norm
="
eiusque
"
type
="
simple
">eiusq́;</
reg
>
radix
<
var
>.b.g.</
var
>
manifęſta erit, cui coniuncta
<
var
>.q.b.</
var
>
<
lb
/>
data, maius quadratum
<
var
>.q.g.</
var
>
cognoſcetur, ex qua
<
var
>.b.g.</
var
>
detracta
<
var
>.b.i.</
var
>
data, cogno-
<
lb
/>
ſcetur
<
var
>.i.g.</
var
>
quadratum minus conſequenter, etiam eorum radices notæ erunt.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div85
"
type
="
math:theorem
"
level
="
3
"
n
="
39
">
<
head
xml:id
="
echoid-head55
"
xml:space
="
preserve
">THEOREMA
<
num
value
="
39
">XXXIX</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s345
"
xml:space
="
preserve
">
<
emph
style
="
sc
">ALia</
emph
>
etiam ratione idipſum definiri poteſt, prætermiſſa antiquorum via,
<
lb
/>
nempe multiplicatis in ſemetipſis primo & ſecundo, numeris propoſitis, qua-
<
lb
/>
<
reg
norm
="
druplicatoque
"
type
="
simple
">druplicatoq́;</
reg
>
quadrato primi, qua ſumma coniuncta cum quadrato ſecundi nume-
<
lb
/>
ri, & ex hac altera ſumma eruta radice quadrata, ex qua detracto ſecundo nume-
<
lb
/>
ro, & è reliquo ſumpto dimidio, quod erit
<
reg
norm
="
quadratum
"
type
="
context
">quadratũ</
reg
>
minus, quo detracto ex radi-
<
lb
/>
ce poſtremo iuncta, ſupererit quadrarum maius.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s346
"
xml:space
="
preserve
">Exempli gratia, ſi proponeretur numerus .8. cui productum duorum numerorum
<
lb
/>
quæſitorum æquandum eſt, proponeretur idem .12. cui differentia quadratorum
<
lb
/>
duorum numerorum æqualis eſſe debet. </
s
>
<
s
xml:id
="
echoid-s347
"
xml:space
="
preserve
">Iubeo primum numerum, nempe .8. in ſe
<
lb
/>
ipſum multiplicari, ex quo exurget .64. pro numero ſui quadrati, quod quadru-
<
lb
/>
plicari volo,
<
reg
norm
="
eritque
"
type
="
simple
">eritq́;</
reg
>
productum .256. quod cenſeo
<
reg
norm
="
coniungendum
"
type
="
context
">coniũgendum</
reg
>
cum quadrato ſe-
<
lb
/>
cundi numeri propoſiti, nempe .144.
<
reg
norm
="
eritque
"
type
="
simple
">eritq́;</
reg
>
ſumma .400. ex quaſumetur radix, ſci
<
lb
/>
licet .20. & ex hac detrahetur ſecundus numerus .12.
<
reg
norm
="
reſiduique
"
type
="
simple
">reſiduiq́;</
reg
>
dimidium, nempe
<
num
value
="
4
">.
<
lb
/>
4.</
num
>
pro quadrato minore, quo in ſummam collecto cum, 12. dabit quadratum
<
lb
/>
maius .16.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s348
"
xml:space
="
preserve
">Cuius ſpeculationis cauſa, quadratum maius per lineam
<
var
>.q.g.</
var
>
minus per
<
var
>.g.p.</
var
>
ſi-
<
lb
/>
gnificetur: </
s
>
<
s
xml:id
="
echoid-s349
"
xml:space
="
preserve
">ſuper integram autem
<
var
>.q.p.</
var
>
erigatur quadratum integrum
<
var
>.d.p.</
var
>
diuiſum,
<
lb
/>
vt quadratum
<
var
>.f.g.</
var
>
vigeſimiſeptimi theorematis huius libri, (idipſum accideret di-
<
lb
/>
uiſo quadrato modo octauæ ſecundi Euclidis) quæ quidem diuiſio, eſt via quatuor
<
lb
/>
productorum
<
var
>.q.g.</
var
>
in
<
var
>.g.p.</
var
>
è quibus vnum ſit
<
var
>.g.r.</
var
>
quod erit cognitum ex .19. theore
<
lb
/>
mate cum ſit
<
reg
norm
="
quadratum
"
type
="
context
">quadratũ</
reg
>
primi numeri ppoſiti, ex quo illa quatuor cognita
<
reg
norm
="
erunt
"
type
="
context
">erũt</
reg
>
. </
s
>
<
s
xml:id
="
echoid-s350
"
xml:space
="
preserve
">Iam
<
lb
/>
verò ſi cogitemus
<
var
>.q.p.</
var
>
ſectam in puncto
<
var
>.t.</
var
>
ita vt
<
var
>.q.t.</
var
>
æqualis ſit
<
var
>.p.g.</
var
>
dabitur differen
<
lb
/>
tia
<
var
>.t.g.</
var
>
cognita, vt radix quadrati
<
var
>.e.o.</
var
>
cum ex præſup-
<
lb
/>
poſito
<
var
>.r.n.</
var
>
æqualis ſit
<
var
>.q.g.</
var
>
et
<
var
>.r.e</
var
>
:
<
var
>g.p.</
var
>
ex quo etiam
<
var
>.q.t.</
var
>
<
lb
/>
<
figure
xlink:label
="
fig-0037-01
"
xlink:href
="
fig-0037-01a
"
number
="
52
">
<
image
file
="
0037-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0037-01
"/>
</
figure
>
ita pariter
<
var
>.e.n.t.g.</
var
>
æqualis erit. </
s
>
<
s
xml:id
="
echoid-s351
"
xml:space
="
preserve
">Collecto
<
reg
norm
="
itaque
"
type
="
simple
">itaq;</
reg
>
quadra
<
lb
/>
to
<
var
>.e.o.</
var
>
ipſius
<
var
>.t.g.</
var
>
cum quadruplo
<
var
>.g.r</
var
>
: cognitum erit
<
lb
/>
quadratum
<
var
>.d.p.</
var
>
ipſius
<
var
>.q.p.</
var
>
</
s
>
<
s
xml:id
="
echoid-s352
"
xml:space
="
preserve
">quare cognoſcetur
<
var
>.q.p.</
var
>
de
<
lb
/>
quo numero detracta differétia quadratorum cognita
<
var
>.
<
lb
/>
t.g.</
var
>
ſupererit aggregatum
<
var
>.p.g.</
var
>
et
<
var
>.q.t.</
var
>
cognitum. </
s
>
<
s
xml:id
="
echoid-s353
"
xml:space
="
preserve
">Qua-
<
lb
/>
re ex conſequenti, dimidium aggregati, nempe
<
var
>.g.p.</
var
>
<
lb
/>
cognoſcetur, tanquam minus duorum quadratorum.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s354
"
xml:space
="
preserve
">cui iuncta
<
var
>.g.t.</
var
>
aut detracta
<
var
>.p.g.</
var
>
ex
<
var
>.p.q.</
var
>
quadratum
<
var
>.q.
<
lb
/>
g.</
var
>
maius cognitum remanebit.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div87
"
type
="
math:theorem
"
level
="
3
"
n
="
40
">
<
head
xml:id
="
echoid-head56
"
xml:space
="
preserve
">THEOREMA
<
num
value
="
40
">XL</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s355
"
xml:space
="
preserve
">CVR ijs, qui volunt duos eiuſmodi numeros inuenire, vt eorum maior mi-
<
lb
/>
norem, numero propoſito ſuperet, & productum vnius in alterum, alteri nu-
<
lb
/>
mero propoſito adęquetur, conſultiſsimum ſit dimidium primi numeri propoſiti, </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>