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
Table of Notes
<
1 - 22
[out of range]
>
<
1 - 22
[out of range]
>
page
|<
<
(331)
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-div639
"
type
="
section
"
level
="
3
"
n
="
27
">
<
div
xml:id
="
echoid-div639
"
type
="
letter
"
level
="
4
"
n
="
1
">
<
p
>
<
s
xml:id
="
echoid-s4008
"
xml:space
="
preserve
">
<
pb
o
="
331
"
rhead
="
EPISTOL AE.
"
n
="
343
"
file
="
0343
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0343
"/>
dabit .64. (nam duo triangula
<
var
>.V.S.*.</
var
>
et
<
var
>.V.E.ω.</
var
>
ſunt inuicem ſimilia eadem ratio-
<
lb
/>
ne) vnde
<
var
>.E.ω.</
var
>
veniet nobis extalibus partibus .462.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4009
"
xml:space
="
preserve
">Coniungatur nunc quadratum ipſius
<
var
>.E.V.</
var
>
quod eſt .4096. cum quadrato ipſius
<
var
>.
<
lb
/>
E.ω.</
var
>
quod eſt .213444. & habebimus quadratum ipfius
<
var
>.V.ω.</
var
>
talium
<
reg
norm
="
partium
"
type
="
context
">partiũ</
reg
>
.217540.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4010
"
xml:space
="
preserve
">Dicemus poſtea ſi .217540. dat nobis .4096. quid dabit quadratum ipſius
<
var
>.V.ω.</
var
>
vt
<
lb
/>
ſinus totus quod eſt .10000000000. vnde veniet pro quadrato ipſius
<
var
>.V.E.</
var
>
talium
<
lb
/>
partium, ſuperficialium ſcilicet .18827211. cuius radix erit .13721. & erit ſinus an-
<
lb
/>
guli
<
var
>.V.ω.E.</
var
>
qui erit grad .7. min .53. vnde angulus
<
var
>.ω.V.E.</
var
>
erit grad .82. min .7. eius
<
lb
/>
vero ſinus erit partium .99054.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4011
"
xml:space
="
preserve
">Nunc autem quia angulus
<
var
>.E.V.ω.</
var
>
eſt acutus, imaginemur
<
var
>.E.Ŕ.</
var
>
ductam eſſe ad re
<
lb
/>
ctos ipſi
<
var
>.V.ω.</
var
>
<
reg
norm
="
ſitque
"
type
="
simple
">ſitq́;</
reg
>
etiam ducta ipſa
<
var
>.E.G</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4012
"
xml:space
="
preserve
">Vnde habebimus angulum
<
var
>.Ŕ.E.V.</
var
>
gra-
<
lb
/>
duum .7. min .53. eius vero ſinus
<
var
>.Ŕ.V.</
var
>
partium .13721. (propter ſimilitudinem trian
<
lb
/>
gulorum
<
var
>.E.Ŕ.V.</
var
>
et
<
var
>.ω.E.V.</
var
>
) talium ſcilicet, qualium
<
var
>.E.V.</
var
>
fuerit .100000. </
s
>
<
s
xml:id
="
echoid-s4013
"
xml:space
="
preserve
">Sed qua-
<
lb
/>
lium
<
var
>.E.V.</
var
>
eſt .64. talium erit .8. cum tribus quartis, cuius
<
var
>.Ŕ.V.</
var
>
quadratum erit par
<
lb
/>
tium .76. cum dimidio ſimilium ſed ſuperſicialium, quo quidem quadrato dempto
<
lb
/>
ex quadrato ipſius .64. quod eſt .4096. remanebit quadratum ipſius
<
var
>.E.Ŕ.</
var
>
partium
<
num
value
="
2871
">.
<
lb
/>
2871.</
num
>
quo etiam quadrato
<
var
>.E.Ŕ.</
var
>
dempto ex quadrato
<
var
>.E.G.</
var
>
partium .14400. remane
<
lb
/>
bit quadratum ipſius
<
var
>.Ŕ.G.</
var
>
partium .11529. cuius radix
<
var
>.Ŕ.G.</
var
>
erit partium .107.
<
reg
norm
="
talium
"
type
="
context
">taliũ</
reg
>
<
lb
/>
qualium
<
var
>.E.G.</
var
>
eſt .120. ſed qualium
<
var
>.E.G.</
var
>
erit .100000. talium
<
var
>.Ŕ.G.</
var
>
erit partium
<
num
value
="
89166
">.
<
lb
/>
89166.</
num
>
quæ vt ſinus anguli
<
var
>.Ŕ.E.G.</
var
>
habebit pro ipſo angulo, gra .63. min .5. qui colle
<
lb
/>
cti cum gra .7. min .53. anguli
<
var
>.V.E.Ŕ.</
var
>
dabunt totum angulum
<
var
>.A.E.G.</
var
>
grad .70.
<
lb
/>
min .58. cuius complementum ex grad .90. erit
<
var
>.G.D.</
var
>
graduum .19. min .2. & non .24.
<
lb
/>
vt omnes ferè putant.</
s
>
</
p
>
</
div
>
</
div
>
<
div
xml:id
="
echoid-div642
"
type
="
section
"
level
="
3
"
n
="
28
">
<
div
xml:id
="
echoid-div642
"
type
="
letter
"
level
="
4
"
n
="
1
">
<
head
xml:id
="
echoid-head495
"
xml:space
="
preserve
">DE REFLEXIONIBVS RADIORVM.</
head
>
<
head
xml:id
="
echoid-head496
"
style
="
it
"
xml:space
="
preserve
">Excellentißimo Philoſopbo Franciſco Vimercato.</
head
>
<
p
>
<
s
xml:id
="
echoid-s4014
"
xml:space
="
preserve
">
<
emph
style
="
sc
">QVoniam</
emph
>
non videbatur quieſcere animus tuus, cum paucis ab hinc die-
<
lb
/>
bus tibi ſiſcitanti reſpondiſſem, nec tamen rationem omnium, quæ dixe-
<
lb
/>
ram exactè explicare per tem poris anguſtiam potuiſſem, cogitaui ad te
<
lb
/>
per hanc occaſionem ſcribens, & iam dicta repetere, & omnium tibi ra-
<
lb
/>
tionem ſubiungere, & vt mihi plenius ſatisfaciam, & tibi commodè perlegenti faci
<
lb
/>
lius ſit veritatem intueri. </
s
>
<
s
xml:id
="
echoid-s4015
"
xml:space
="
preserve
">Scripſiſti enim in tuis diſputationibus, vir doctiſſime, quod
<
lb
/>
omnis res viſa per
<
reg
norm
="
ſpeculum
"
type
="
context
">ſpeculũ</
reg
>
<
reg
norm
="
quodcunque
"
type
="
context
">quodcũque</
reg
>
, ſub breuiſſimis lineis
<
reg
norm
="
compræhendatur
"
type
="
context
">cõpræhendatur</
reg
>
à vifu.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4016
"
xml:space
="
preserve
">Propoſitio hæc non eſt vniuerſaliter vera (quamuis etiam ab alijs omnibus pro ta
<
lb
/>
li poſita ſit) cum in ſpeculis concauis non ſemper verificetur, vt nunc tibi demon-
<
lb
/>
ſtrabo.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4017
"
xml:space
="
preserve
">Eſto quod linea recta
<
var
>.b.d.</
var
>
tangat circulum
<
lb
/>
<
figure
xlink:label
="
fig-0343-01
"
xlink:href
="
fig-0343-01a
"
number
="
367
">
<
image
file
="
0343-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0343-01
"/>
</
figure
>
<
var
>b.o.q.n.</
var
>
qui ſit communis ſectionis ſup crficiei re
<
lb
/>
flexionis, & ſphæricę alicuius ſpeculi ſphærici
<
lb
/>
concaui, & punctum contingentiæ ſit
<
var
>.b.</
var
>
à quo
<
lb
/>
exeant duæ lineæ
<
var
>.b.q.</
var
>
et
<
var
>.b.n.</
var
>
efficientes duos an
<
lb
/>
gulos inuicem æquales circa perpendicularem
<
var
>.
<
lb
/>
b.c.</
var
>
res autem viſa primò ſit in ipſa circunferen-
<
lb
/>
tia huiuſmodi circuli in puncto
<
var
>.n.</
var
>
oculus vero in
<
lb
/>
puncto
<
var
>.q.</
var
>
ipſius circunferentię. </
s
>
<
s
xml:id
="
echoid-s4018
"
xml:space
="
preserve
">Dico nunc duas </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>