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
|<
<
(347)
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-div642
"
type
="
section
"
level
="
3
"
n
="
28
">
<
div
xml:id
="
echoid-div666
"
type
="
letter
"
level
="
4
"
n
="
8
">
<
p
>
<
s
xml:id
="
echoid-s4201
"
xml:space
="
preserve
">
<
pb
o
="
347
"
rhead
="
EPISTOL AE.
"
n
="
359
"
file
="
0359
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0359
"/>
mine deſtitutæ
<
reg
norm
="
interuallumque
"
type
="
simple
">interuallumq́;</
reg
>
tantummodò inter
<
var
>.y.x.</
var
>
illuminatum erit, ſed ſi in
<
lb
/>
loco
<
var
>.c.u.</
var
>
poſitum fuerit, </
s
>
<
s
xml:id
="
echoid-s4202
"
xml:space
="
preserve
">tunc totum
<
var
>.c.u.</
var
>
illuminatum erit, ſed debili modo propter
<
lb
/>
detractionem factam à reflexione in ſuperficie corporis ſphærici, vt ſupra diximus.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4203
"
xml:space
="
preserve
">Poſito deinde obiecto in loco
<
var
>.i.z.H.f.</
var
>
tunc partes
<
var
>.z.i.</
var
>
et
<
var
>.H.f.</
var
>
rectos Solis radios
<
lb
/>
habebunt cum aliquibus refractis, ſed
<
var
>.z.H.</
var
>
pauciſſimum habebit lumen, pro-
<
lb
/>
pter diſgregationem radiorum. </
s
>
<
s
xml:id
="
echoid-s4204
"
xml:space
="
preserve
">Poſito poſtea ipſo obiecto in loco
<
var
>.t.l.r.s.</
var
>
tanto
<
lb
/>
minus lumen habebit pars
<
var
>.l.r.</
var
>
propter dictam
<
reg
norm
="
diſgregationem
"
type
="
context
">diſgregationẽ</
reg
>
, ſeu
<
reg
norm
="
diſſipationem
"
type
="
context
">diſſipationẽ</
reg
>
radio
<
lb
/>
rum, & ſic ſucceſſiuè quanto remotius poſitum fuerit ipſum obiectum, tanto minus
<
lb
/>
illuminabitur. </
s
>
<
s
xml:id
="
echoid-s4205
"
xml:space
="
preserve
">vnde ita remotum poterit locari, ut nullus actus luminis in eo
<
lb
/>
videatur, de radijs ſcilicet, qui per ſphæram chryſtallinam tranſibunt, ſed videbi-
<
lb
/>
tur vmbra ipſius ſphęrę in obiecto propoſito, cum nullum actum illuminationis in
<
lb
/>
eo loco obiecti habeant radij tranſeuntes per dictam ſphęram. </
s
>
<
s
xml:id
="
echoid-s4206
"
xml:space
="
preserve
">quapropter partes
<
var
>.
<
lb
/>
t.l.</
var
>
et
<
var
>.r.s.</
var
>
illuminatæ erunt à Sole, et
<
var
>.l.r.</
var
>
omnino lumine deſtituta.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4207
"
xml:space
="
preserve
">Quòd vero tolerabilior ſit oculis radius reflexus Solis à ſuperſicie aquæ, quàm
<
lb
/>
à ſuperficie alicuius ſpeculi, oritur ab eo, quod ſupra diximus, hoc eſt, quod ma-
<
lb
/>
gna parsipſius luminis penetrat in aquam, & non totum reflectit, quod quidem non
<
lb
/>
accidit ſpeculis opacis.</
s
>
</
p
>
</
div
>
</
div
>
<
div
xml:id
="
echoid-div670
"
type
="
section
"
level
="
3
"
n
="
29
">
<
div
xml:id
="
echoid-div670
"
type
="
letter
"
level
="
4
"
n
="
1
">
<
head
xml:id
="
echoid-head511
"
xml:space
="
preserve
">DE LONGITVDINE DVORVM LATERVM
<
lb
/>
cuiuſuis trianguli ſupra tertium.</
head
>
<
head
xml:id
="
echoid-head512
"
style
="
it
"
xml:space
="
preserve
">Hieronymo Fenarolo.</
head
>
<
p
>
<
s
xml:id
="
echoid-s4208
"
xml:space
="
preserve
">
<
emph
style
="
sc
">
<
reg
norm
="
QVod
"
type
="
conjecture
">QVo'd</
reg
>
</
emph
>
quælibet duo latera continentia rectum angulum cuiuſuis triangu-
<
lb
/>
li orthogonij, longiora ſint tertio latere, per diametrum circuli in eo in-
<
lb
/>
ſcripti, ab alijs iam demonſtratum fuit. </
s
>
<
s
xml:id
="
echoid-s4209
"
xml:space
="
preserve
">Sed quòd quælibet duo latera
<
lb
/>
cuiuſuis trianguli longiora ſint tertio per latus tetragonicum, quadrupli
<
lb
/>
producti cuiuſuis lineæ deſcendentis ab angulo contento à dictis duobus lateribus
<
lb
/>
ad oppoſitam partem circuli inſcripti, in partem extrinſecam ipſius lineæ, nullus
<
lb
/>
(quod ſciam) vnquam ſcripſit, vel animaduertit.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4210
"
xml:space
="
preserve
">Sit exempli gratia triangulus
<
var
>.a.b.c.</
var
>
quem volueris, in quo deſcribatur circulus
<
var
>.
<
lb
/>
u.s.n.</
var
>
& puncta contingentiæ ſint eadem
<
var
>.u.s.n.</
var
>
à puncto vero
<
var
>.a.</
var
>
deſcendat linea
<
var
>.a.
<
lb
/>
i.e.</
var
>
quæ terminetur à circunferentia in puncto
<
var
>.e.</
var
>
ipſius circunferentiæ, vbi volue-
<
lb
/>
ris. </
s
>
<
s
xml:id
="
echoid-s4211
"
xml:space
="
preserve
">Dico nunc latera
<
var
>.a.b.</
var
>
et
<
var
>.a.c.</
var
>
longiora eſſe latere
<
var
>.b.c.</
var
>
per latus
<
reg
norm
="
tetragonicum
"
type
="
context
">tetragonicũ</
reg
>
qua-
<
lb
/>
drupli producti ipſius
<
var
>.a.e.</
var
>
in
<
var
>.a.i</
var
>
. </
s
>
<
s
xml:id
="
echoid-s4212
"
xml:space
="
preserve
">Nam certi ſamus ex vltima parte penultimæ ter-
<
lb
/>
tij Eucli
<
var
>.n.c.</
var
>
et
<
var
>.s.c.</
var
>
æquales inuicem eſſe, & ſimiliter
<
var
>.b.s.</
var
>
et
<
var
>.b.u.</
var
>
vnde ex communi
<
lb
/>
conceptu dicta latera maiora erunt
<
lb
/>
<
figure
xlink:label
="
fig-0359-01
"
xlink:href
="
fig-0359-01a
"
number
="
394
">
<
image
file
="
0359-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0359-01
"/>
</
figure
>
ipſo
<
var
>.b.c.</
var
>
per
<
var
>.a.u.</
var
>
et
<
var
>.a.n.</
var
>
quæ duæ
<
lb
/>
partes ſunt inuicem æquales di-
<
lb
/>
cta ratione, & quadratum lineæ
<
lb
/>
æqualis aggregato earum, eſſet qua
<
lb
/>
druplum quadrato cuiuſuis earum
<
lb
/>
ex .4. ſecundi, ſed ex penultima ter
<
lb
/>
tij, productum
<
var
>.a.e.</
var
>
in
<
var
>.a.i.</
var
>
æquale eſt
<
lb
/>
quadrato ipſius
<
var
>.a.u.</
var
>
vel ipſius
<
var
>.a.n</
var
>
.</
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>