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
>
431
(419)
432
(420)
433
(421)
434
(422)
435
(423)
436
(424)
437
(425)
438
(426)
439
440
<
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
|<
<
(367)
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-div477
"
type
="
chapter
"
level
="
2
"
n
="
6
">
<
div
xml:id
="
echoid-div713
"
type
="
section
"
level
="
3
"
n
="
37
">
<
div
xml:id
="
echoid-div713
"
type
="
letter
"
level
="
4
"
n
="
1
">
<
p
>
<
s
xml:id
="
echoid-s4379
"
xml:space
="
preserve
">
<
pb
o
="
367
"
rhead
="
EPISTOL AE.
"
n
="
379
"
file
="
0379
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0379
"/>
e
<
unsure
/>
<
var
>.g.</
var
>
vnde angulus
<
var
>.g.e.q.</
var
>
æqualis erit angulo
<
var
>.b.a.g.</
var
>
portionis, cum duplus ſit angulo
<
lb
/>
<
var
>q.p.g.</
var
>
medietati anguli ipſius portionis ex .19. tertij, ita quod angulus
<
var
>.q.e.g.</
var
>
nobis
<
lb
/>
cognitus erit, & ſimiliter arcus
<
var
>.g.q.</
var
>
& conſequenter ar-
<
lb
/>
cus
<
var
>.p.g.</
var
>
reſiduum medij circuli, & ſic
<
var
>.m.g.</
var
>
eius ſinus re
<
lb
/>
<
figure
xlink:label
="
fig-0379-01
"
xlink:href
="
fig-0379-01a
"
number
="
419
">
<
image
file
="
0379-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0379-01
"/>
</
figure
>
ctus, & etiam chorda
<
var
>.p.g.</
var
>
vt dupla ſinus dimidij arcus
<
var
>.
<
lb
/>
p.g.</
var
>
& ſic
<
var
>.p.m.</
var
>
eius ſinus verſus, vel vt tertium latus trian
<
lb
/>
guli orthogonij
<
var
>.p.g.m.</
var
>
vnde nobis cognita erit propor
<
lb
/>
tio ipſius
<
var
>.b.g.</
var
>
(quæ dupla eſt ipſi
<
var
>.m.g.</
var
>
) ad
<
var
>.m.p.</
var
>
& quia
<
lb
/>
productum
<
var
>.p.m.</
var
>
in
<
var
>.m.q.</
var
>
æquale eſt ei, quod fit ex
<
var
>.b.m.</
var
>
<
lb
/>
in
<
var
>m.g.</
var
>
ex .34. tertij, quapropter nobis cognita erit pars
<
lb
/>
<
var
>q.m.</
var
>
quæ cum
<
var
>.p.m.</
var
>
complet totum diametrum
<
var
>.q.p.</
var
>
vn
<
lb
/>
de nobis cognita erit proportio ipſius
<
var
>.b.g.</
var
>
ad
<
var
>.q.p.</
var
>
qua
<
lb
/>
mediante cognoſcemus diametrum ſecundum partes il
<
lb
/>
las quibus propoſita ſuerit
<
var
>.b.g</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4380
"
xml:space
="
preserve
">Hoc autem problema non in numeris ſed in continuo ab Euclid. ponitur in .32
<
unsure
/>
.
<
lb
/>
tertij.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div715
"
type
="
letter
"
level
="
4
"
n
="
2
">
<
head
xml:id
="
echoid-head542
"
style
="
it
"
xml:space
="
preserve
">De inuentione alterius trianguli conditionati.</
head
>
<
head
xml:id
="
echoid-head543
"
xml:space
="
preserve
">AD EVNDEM.</
head
>
<
p
>
<
s
xml:id
="
echoid-s4381
"
xml:space
="
preserve
">QVotieſcunque etiam inuenire voluerimus triangulum aliquem, puta
<
var
>.n.q.o.</
var
>
<
lb
/>
æqualem triangulo
<
var
>.t.</
var
>
(exempli gratia) propoſito, qui habeat angulum
<
var
>.n.</
var
>
æ-
<
lb
/>
qualem angalo
<
var
>.a.</
var
>
dato, latera vero continentia ipſum angulum
<
var
>.n.</
var
>
ſint inuicem pro-
<
lb
/>
portionata vt
<
var
>.x.</
var
>
et
<
var
>.y.</
var
>
ita faciemus, accipiemus lineam
<
var
>.n.m.</
var
>
cuius volueris magnitu-
<
lb
/>
dinis, ſupra quam conſtituemus triangulum
<
var
>.m.n.p.</
var
>
æqualem triangulo
<
var
>.t.</
var
>
hac metho-
<
lb
/>
do, hoc eſt prolungando latus
<
var
>.r.z.</
var
>
trianguli
<
var
>.t.</
var
>
quod ſit
<
var
>.r.e.</
var
>
ita vt duplum ſit ipſi
<
var
>.r.z.</
var
>
<
lb
/>
ducendo poſtea
<
var
>.c.e.</
var
>
habebimus ex .38. primi triangulum
<
var
>.t.</
var
>
eſſe dimidium totius
<
lb
/>
trianguli
<
var
>.r.c.e.</
var
>
deſignabimus deinde ex .44. dicti ſuperficiem
<
var
>.p.n.m.b.</
var
>
parallelo
<
lb
/>
grammam
<
reg
norm
="
æqualemque
"
type
="
simple
">æqualemq́;</
reg
>
triangu
<
lb
/>
lo
<
var
>.r.c.e.</
var
>
habentem angulum
<
var
>.
<
lb
/>
<
figure
xlink:label
="
fig-0379-02
"
xlink:href
="
fig-0379-02a
"
number
="
420
">
<
image
file
="
0379-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0379-02
"/>
</
figure
>
n.</
var
>
æqualem angulo
<
var
>.a.</
var
>
ducatur
<
lb
/>
poſtea
<
var
>.p.m.</
var
>
& habebimus
<
reg
norm
="
triam
"
type
="
context
">triã</
reg
>
<
lb
/>
gulum
<
var
>.m.n.p.</
var
>
æqualem
<
var
>.t.</
var
>
cum
<
lb
/>
angulo
<
var
>.n.</
var
>
æquali angulo
<
var
>.a.</
var
>
pro
<
lb
/>
ducatur poſtea
<
var
>.n.p.</
var
>
ita vt
<
var
>.n.K.</
var
>
<
lb
/>
ſe habeat .ad
<
var
>.n.m.</
var
>
quemadmo
<
lb
/>
dum
<
var
>.x.</
var
>
ad
<
var
>.y.</
var
>
quod erit facilli-
<
lb
/>
mum producendo
<
var
>.n.m.</
var
>
et
<
var
>.n.
<
lb
/>
K.</
var
>
indeterminatè ſi oportuerit,
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4382
"
xml:space
="
preserve
">deinde eas ad æqualitatem ſe-
<
lb
/>
can
<
unsure
/>
do ipſis
<
var
>.x.</
var
>
et
<
var
>.y.</
var
>
efficiendo
<
lb
/>
exempli gratia quod
<
var
>.n.i.</
var
>
ſit
<
lb
/>
æqualis ipſi
<
var
>.x.</
var
>
et
<
var
>.n.u.</
var
>
ipſi
<
var
>.y.</
var
>
du
<
lb
/>
cendo poſtea
<
var
>.u.i.</
var
>
deinde à puncto
<
var
>.m.</
var
>
ducendo
<
var
>.m.K.</
var
>
æquidiſtanter
<
var
>.u.i.</
var
>
ex .31.
<
lb
/>
primi. </
s
>
<
s
xml:id
="
echoid-s4383
"
xml:space
="
preserve
">& ſic habebimus ex .4. ſexti proportionem
<
var
>.x.</
var
>
ad
<
var
>.y.</
var
>
eſſe inter
<
var
>.n.K.</
var
>
et
<
var
>.n.</
var
>
</
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>