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
>
121
(109)
122
(110)
123
(111)
124
(112)
125
(113)
126
(114)
127
(115)
128
(116)
129
(117)
130
(118)
<
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
|<
<
(129)
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-div308
"
type
="
chapter
"
level
="
2
"
n
="
2
">
<
div
xml:id
="
echoid-div322
"
type
="
section
"
level
="
3
"
n
="
8
">
<
p
>
<
s
xml:id
="
echoid-s1573
"
xml:space
="
preserve
">
<
pb
o
="
129
"
rhead
="
DE PERSPECT.
"
n
="
141
"
file
="
0141
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0141
"/>
vera altitudo ipſius
<
var
>.M.T.</
var
>
et
<
var
>I.s.</
var
>
duxi ſupponendo eſſe
<
var
>.I.</
var
>
<
reg
norm
="
punctum
"
type
="
context
">punctũ</
reg
>
pſpectiuæ
<
reg
norm
="
ſecundum
"
type
="
context
">ſecundũ</
reg
>
<
lb
/>
antiquos, ideſt angulum ſupremum trianguli antiquorum à punctoq́ue
<
var
>.k.</
var
>
meo duxi
<
lb
/>
<
var
>k.f.</
var
>
parallelam ipſi
<
var
>.c.m.p.</
var
>
vſque ad
<
var
>.i.x.</
var
>
in puncto
<
var
>.f.</
var
>
& à puncto à communi ipſis
<
var
>.k.f.</
var
>
<
lb
/>
et
<
var
>.i.x.</
var
>
vſque ad
<
var
>.I.s.</
var
>
duxi quoque
<
var
>.A.B.</
var
>
parallelam ipſi
<
var
>.i.x.</
var
>
atque hæc omnia ex more
<
lb
/>
antiquo præſtiti.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1574
"
xml:space
="
preserve
">Nunc verò eum conſiderans modum, quem ego de figuris
<
var
>.G.H.</
var
>
antecedentibus
<
lb
/>
præſcripſi, videndum eſt, an punctum
<
var
>.B.</
var
>
tribus lineis
<
var
>.A.B.I.s.</
var
>
et
<
var
>.R.V.</
var
>
quarum hęc vl
<
lb
/>
tima à me iam ducta fuit, commune exiſtat, ideſt vtrum
<
var
>.A.B.</
var
>
æqualis exiſtat ipſi
<
var
>.K.
<
lb
/>
R.</
var
>
quam ſecundum modum à me adinuentum, reuera ſcimus eſſe deſideratam altitu
<
lb
/>
dinem in perſpectiua. </
s
>
<
s
xml:id
="
echoid-s1575
"
xml:space
="
preserve
">Quod tunc à nobis probatum erit, quando rationibus clarè
<
lb
/>
patebit ipſam
<
var
>.A.B.</
var
>
æqualem eſſe ipſi
<
var
>.f.V</
var
>
. </
s
>
<
s
xml:id
="
echoid-s1576
"
xml:space
="
preserve
">Quamobrem ducamus
<
var
>.I.f.</
var
>
vſque ad
<
var
>.ω.</
var
>
<
lb
/>
lineæ
<
var
>.c.p.</
var
>
vnde ratione ſimilitudinis triangulorum manifeſtè intelligemus, eandem
<
lb
/>
proportionem eſſe ipſius
<
var
>.m.T.</
var
>
ad
<
var
>.f.V.</
var
>
quæ eſt
<
var
>.m.o.</
var
>
ad
<
var
>.f.o.</
var
>
& eius, quæ eſt
<
var
>.m.o.</
var
>
ad
<
var
>.f.
<
lb
/>
o.</
var
>
quæ eſt
<
var
>.ω.I.</
var
>
ad
<
var
>.f.I.</
var
>
& eius, quæ eſt
<
var
>.ω.I.</
var
>
ad
<
var
>.f.I.</
var
>
quæ eſt
<
var
>.x.I.</
var
>
ad
<
var
>.A.I.</
var
>
& eius, quæ eſt
<
var
>.x.
<
lb
/>
I.</
var
>
ad
<
var
>.A.I.</
var
>
quæ eſt
<
var
>.x.s.</
var
>
ad
<
var
>.A.B.</
var
>
ideſt vt eius, quæ eſt
<
var
>.m.T.</
var
>
ad
<
var
>.A.B.</
var
>
ſed idem
<
reg
norm
="
quoque
"
type
="
simple
">quoq;</
reg
>
erat
<
lb
/>
de
<
var
>.m.T.</
var
>
ad
<
var
>.f.V</
var
>
. </
s
>
<
s
xml:id
="
echoid-s1577
"
xml:space
="
preserve
">Vnde ſequitur
<
var
>.A.B.</
var
>
æqualem eſſe
<
var
>.f.V.</
var
>
ex .9. quinti Eucli.
<
reg
norm
="
atque
"
type
="
simple
">atq;</
reg
>
etiam
<
lb
/>
ipſi
<
var
>.k.R.</
var
>
quod à nobis propoſitum eſt inquirendum.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div324
"
type
="
section
"
level
="
3
"
n
="
9
">
<
head
xml:id
="
echoid-head185
"
xml:space
="
preserve
">CAP. IX.</
head
>
<
figure
position
="
here
"
number
="
196
">
<
image
file
="
0141-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0141-01
"/>
</
figure
>
<
p
>
<
s
xml:id
="
echoid-s1578
"
xml:space
="
preserve
">
<
emph
style
="
sc
">INstitvens</
emph
>
etiam ſermonem de figuris ſu-
<
lb
/>
perficialibus orizontalibus, ſeu de plantis,
<
lb
/>
pulcherrimum quendam modum, quem ego ad
<
lb
/>
locandum quodlibet punctum in perſpectiua,
<
lb
/>
(degradatum cum fuerit
<
reg
norm
="
parallelogrammum
"
type
="
context
">parallelogrãmum</
reg
>
quod
<
lb
/>
dam rectangulum, in noſtro plano perpendicula
<
lb
/>
ri orizonti, quemadmodum in ſuperioribus figu-
<
lb
/>
ris
<
var
>.A.</
var
>
demonſtrauimus) conſideraui, ſilentio
<
lb
/>
haud prætereundum eſſe.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1579
"
xml:space
="
preserve
">Sit igitur in ſubſcripta hîc figura
<
var
>.K.</
var
>
in paralle
<
lb
/>
<
reg
norm
="
logrammo
"
type
="
context
">logrãmo</
reg
>
perfecto
<
reg
norm
="
punctum
"
type
="
context
">pũctum</
reg
>
<
var
>.b.</
var
>
quod locari debeat
<
lb
/>
in degradato
<
var
>.e.q.d.r</
var
>
. </
s
>
<
s
xml:id
="
echoid-s1580
"
xml:space
="
preserve
">Nunc à duobus quorumli-
<
lb
/>
bet quatuor angulorum
<
var
>.q.u.a.d.</
var
>
ducuntur duæ li-
<
lb
/>
neæ occultæ
<
var
>.q.g.</
var
>
et
<
var
>.u.f.</
var
>
per punctum
<
var
>.b.</
var
>
vſque ad
<
lb
/>
latera
<
var
>.q.d.</
var
>
et
<
var
>.u.a.</
var
>
ita tamen vt eorum extremita-
<
lb
/>
tes
<
var
>.g.</
var
>
et
<
var
>.f.</
var
>
intus cadant inter
<
var
>.q.d.</
var
>
et
<
var
>.u.a.</
var
>
ipſorum
<
lb
/>
laterum, ideſt vt non ſecent duo latera
<
var
>.q.u.</
var
>
aut
<
var
>.d.
<
lb
/>
a</
var
>
. </
s
>
<
s
xml:id
="
echoid-s1581
"
xml:space
="
preserve
">Deinde punctum
<
var
>.f.</
var
>
inter
<
var
>.q.</
var
>
et
<
var
>.d.</
var
>
<
reg
norm
="
coniungatur
"
type
="
context
">cõiungatur</
reg
>
oc-
<
lb
/>
cultè cum angulo degradato
<
var
>.e.</
var
>
qui
<
reg
norm
="
correſpondet
"
type
="
context
">correſpõdet</
reg
>
<
var
>.
<
lb
/>
u.</
var
>
perfecti, mediante linea
<
var
>.e.f.</
var
>
quæ erit
<
var
>.u.f.</
var
>
degra
<
lb
/>
dita in noſtro plano. </
s
>
<
s
xml:id
="
echoid-s1582
"
xml:space
="
preserve
">Deinde ſumatur punctum
<
var
>.
<
lb
/>
n.</
var
>
in linea
<
var
>.q.d.</
var
>
tam diſtans à
<
var
>.q.</
var
>
quàm.g. diſtat ab
<
var
>.
<
lb
/>
u.</
var
>
ducaturq́ue linea
<
var
>.i.n.</
var
>
quæ lineam
<
var
>.e.r.</
var
>
in puncto
<
lb
/>
c. diuidet, quod exijs, quæ ſuperius iam diximus
<
lb
/>
ad ipſum
<
var
>.g.</
var
>
referetur. </
s
>
<
s
xml:id
="
echoid-s1583
"
xml:space
="
preserve
">Ducendo poſtea lineam oc
<
lb
/>
cultam
<
var
>.q.c.</
var
>
patebit eam correſpondere lineæ
<
var
>.q.g.</
var
>
quæ ſecans lineam
<
var
>.e.f.</
var
>
in puncto
<
var
>.
<
lb
/>
t.</
var
>
hoc, communi ſcientiæ ratione, reſpondebit ipſi
<
var
>.b.</
var
>
vt omnes cognoſcent.</
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>