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
>
351
(339)
352
(340)
353
(341)
354
(342)
355
(343)
356
(344)
357
(345)
358
(346)
359
(347)
360
(348)
<
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
|<
<
(296)
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-div564
"
type
="
section
"
level
="
3
"
n
="
17
">
<
div
xml:id
="
echoid-div571
"
type
="
letter
"
level
="
4
"
n
="
4
">
<
pb
o
="
296
"
rhead
="
IO. BAPT. BENED.
"
n
="
308
"
file
="
0308
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0308
"/>
<
p
>
<
s
xml:id
="
echoid-s3659
"
xml:space
="
preserve
">Sed etiam alio vniuerſaliori modo potes probare, quod ita ſit
<
var
>.u.x.</
var
>
ad
<
var
>.x.y.</
var
>
vt
<
var
>.c.e.</
var
>
<
lb
/>
ad
<
var
>.e.a.</
var
>
cogitando in linea
<
var
>.c.a.</
var
>
punctum quoddam quod vocabimus ſimiliter
<
var
>.y.</
var
>
in
<
lb
/>
tali ſitu locatum, quod diuidat
<
var
>.c.a.</
var
>
eadem proportione qua
<
var
>.y.</
var
>
diuidit
<
var
>.u.s.</
var
>
vnde cum
<
lb
/>
<
var
>e.s.</
var
>
diuiſa eodem modo etiam ſit à puncto
<
var
>.s.</
var
>
ex ſupradicta quinta lib. de quadratura
<
lb
/>
parabolæ, erit igitur proportio
<
var
>.a.y.</
var
>
ad
<
var
>.y.c.</
var
>
vt
<
var
>.e.s.</
var
>
ad
<
var
>.s.c.</
var
>
per .11. quinti Eucli. </
s
>
<
s
xml:id
="
echoid-s3660
"
xml:space
="
preserve
">& com
<
lb
/>
ponendo ita erit
<
reg
norm
="
totius
"
type
="
simple
">totiꝰ</
reg
>
<
var
>.a.c.</
var
>
ad totum
<
var
>.y.c.</
var
>
vt abſcisſi
<
var
>.s.c.</
var
>
ad abſciſsum
<
var
>.s.c.</
var
>
</
s
>
<
s
xml:id
="
echoid-s3661
"
xml:space
="
preserve
">quare reſidui
<
lb
/>
<
var
>a.e.</
var
>
ad reſiduum
<
var
>.y.s.</
var
>
erit vt totius
<
var
>.a.c.</
var
>
ad totum
<
var
>.y.c.</
var
>
& permutando, ita erit
<
var
>.a.c.</
var
>
ad
<
var
>.a.
<
lb
/>
e.</
var
>
vt
<
var
>.y.c.</
var
>
ad
<
var
>.y.s.</
var
>
& diuidendo, ita erit
<
var
>.
<
lb
/>
c.e.</
var
>
ad
<
var
>.e.a.</
var
>
ut
<
var
>.c.s.</
var
>
ad
<
var
>.s.y.</
var
>
& quia pun-
<
lb
/>
<
figure
xlink:label
="
fig-0308-01
"
xlink:href
="
fig-0308-01a
"
number
="
331
">
<
image
file
="
0308-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0308-01
"/>
</
figure
>
ctum
<
var
>.s.</
var
>
diuidit
<
var
>.c.a.</
var
>
eodem modo, quo
<
lb
/>
x. diuidit
<
var
>.u.s.</
var
>
per ſupradictam
<
reg
norm
="
quintam
"
type
="
context
">quintã</
reg
>
,
<
lb
/>
ergo ita erit
<
var
>.c.s.</
var
>
ad
<
var
>.s.y.</
var
>
in linea
<
var
>.c.a.</
var
>
vt
<
lb
/>
<
var
>u.x.</
var
>
ad
<
var
>.x.y.</
var
>
</
s
>
<
s
xml:id
="
echoid-s3662
"
xml:space
="
preserve
">vnde ex .11. quinti
<
var
>.c.e.</
var
>
ad
<
lb
/>
<
var
>e.a.</
var
>
erit, vt
<
var
>.u.x.</
var
>
ad
<
var
>.x,y</
var
>
. </
s
>
<
s
xml:id
="
echoid-s3663
"
xml:space
="
preserve
">quare ſequitur,
<
lb
/>
primum, ſecundum, tertium, & quartum lemma ſuperflua eſſe.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3664
"
xml:space
="
preserve
">Quod deinde ponit pro corellario in fine .6. lemmatis, aliter quam per .6. lemma
<
lb
/>
poteſt demonſtrari, hoc mode. </
s
>
<
s
xml:id
="
echoid-s3665
"
xml:space
="
preserve
">Nam ſuperius demonſtrauimus eandem propor-
<
lb
/>
tionem eſſe
<
var
>.l.b.</
var
>
ad
<
var
>.b.m.</
var
>
quæ
<
var
>.c.e.</
var
>
ad
<
var
>.e.a.</
var
>
<
reg
norm
="
idem
"
type
="
context
">idẽ</
reg
>
dico de proportione
<
var
>.u.x.</
var
>
ad
<
var
>.x.y.</
var
>
& om-
<
lb
/>
nium æquidiſtantium ad
<
var
>.h.e.</
var
>
quibus rationibus mediantibus codem modo ſcies,
<
reg
norm
="
quod
"
type
="
simple
">ꝙ</
reg
>
<
lb
/>
<
var
>u.y.</
var
>
ad
<
var
>.y.r.</
var
>
erit, vt
<
var
>.c.d.</
var
>
ad
<
var
>.d.c.</
var
>
& ita dico de omnibus
<
reg
norm
="
æquidiſtantibus
"
type
="
context
">æquidiſtãtibus</
reg
>
. ad
<
var
>.h.e.</
var
>
</
s
>
<
s
xml:id
="
echoid-s3666
"
xml:space
="
preserve
">vnde
<
var
>.l.b.</
var
>
<
lb
/>
ad
<
var
>.b.m.</
var
>
erit vt
<
var
>.u.x.</
var
>
ad
<
var
>.x.y.</
var
>
et
<
var
>.l.m.</
var
>
ad
<
var
>.m.d.</
var
>
vt
<
var
>.u.y.</
var
>
ad
<
var
>.y.r.</
var
>
per .11. quinti, ſed cum ſit
<
var
>.l.
<
lb
/>
b.</
var
>
ad
<
var
>.b.m.</
var
>
vt
<
var
>.u.x.</
var
>
ad
<
var
>.x.y.</
var
>
componendo erit
<
var
>.l.m.</
var
>
ad
<
var
>.b.m.</
var
>
vt
<
var
>.u.x.</
var
>
ad
<
var
>.x.y.</
var
>
& euerſim
<
var
>.b.
<
lb
/>
m.</
var
>
ad
<
var
>.m.b.</
var
>
erit, vt
<
var
>.x.y.</
var
>
ad
<
var
>.y.u.</
var
>
& per æquam proportionalitatem erit
<
var
>.b.m.</
var
>
ad
<
var
>.m.d.</
var
>
vt
<
unsure
/>
<
lb
/>
<
var
>x.y.</
var
>
ad
<
var
>.y.r.</
var
>
quod eſt propoſitum.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3667
"
xml:space
="
preserve
">Non video etiam, quare ipſe ducat lineam
<
var
>.s.r.</
var
>
cum in ipſo contextu nihil ſaciac
<
lb
/>
de dicta
<
var
>.s.r</
var
>
.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3668
"
xml:space
="
preserve
">Comentum poſtea contextus
<
var
>.P.</
var
>
pulchrius eſſet, ſi diceret, quod cum ita ſit totius,
<
lb
/>
<
var
>l.a.</
var
>
ad totum
<
var
>.a.d.</
var
>
ſic ſe habebit abſciſſum
<
var
>.a.i.</
var
>
ad abſciſſum
<
var
>.a.z.</
var
>
eo quod ita eſt, vt ſcis,
<
lb
/>
hoc eſt in proportione dupla, ergo reſidui
<
var
>.i.l.</
var
>
ad reſiduum
<
var
>.d.z.</
var
>
erit vt totius
<
var
>.a.l.</
var
>
ad
<
lb
/>
totum
<
var
>.a.d.</
var
>
hoc eſt in proportione dupla.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div573
"
type
="
letter
"
level
="
4
"
n
="
5
">
<
head
xml:id
="
echoid-head438
"
style
="
it
"
xml:space
="
preserve
">De Viſu.</
head
>
<
head
xml:id
="
echoid-head439
"
xml:space
="
preserve
">AD EVNDEM.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3669
"
xml:space
="
preserve
">RAtio vnde ſiat, vt videamus diſtinctè omnes eolores, cum in qualibet aeris par
<
lb
/>
te, quo lumina reſlexa poſſunt peruenire mixta ſint, & non diſtincta, oritur à
<
lb
/>
paruitate ipſius pupillæ oculorum, & à magna expanſione virtutis viſiuæ in ſuperſi-
<
lb
/>
cie concaua orbis continentis humores diaphanos oculorum per ramuſculos nerui
<
lb
/>
optici remotè ab ipſa pupilla. </
s
>
<
s
xml:id
="
echoid-s3670
"
xml:space
="
preserve
">& quamuis radii luminoſi frangantur ab vnoquoque
<
lb
/>
humore diuerſimodè, hoc nihilominus maximè iuuat ad diſtinctionem radiorum,
<
lb
/>
ſed & ſi directè procederent, idem ferè eueniret, non tamen ſuis locis, cogita exem-
<
lb
/>
pli gratia lineam
<
var
>.a.u.e.</
var
>
vt communis ſectio cuiuſdam plani ſecantis ſphæram oculi,
<
lb
/>
per centrum ipſius, & pupillæ, et
<
var
>.o.</
var
>
punctum ſit proximum centro ipſius pupillæ,
<
lb
/>
ſed interius aliquantulum, extra
<
reg
norm
="
autem
"
type
="
context
">autẽ</
reg
>
<
reg
norm
="
oculum
"
type
="
context
">oculũ</
reg
>
, ſint varij colores, vt
<
var
>.c.n.t.</
var
>
in dicto plano.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3671
"
xml:space
="
preserve
">Iam nulli dubium eſt quod lumina quæ producuntur ab
<
var
>.c.n.t.</
var
>
ad
<
var
>.o.</
var
>
in ipſo
<
var
>.o.</
var
>
mi- </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>