Ceva, Giovanni
,
Geometria motus
,
1692
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
>
51
52
53
54
55
56
57
58
59
60
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
>
page
|<
<
of 110
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
pb
pagenum
="
52
"
xlink:href
="
022/01/058.jpg
"/>
<
p
type
="
margin
">
<
s
id
="
s.000531
">
<
margin.target
id
="
marg118
"/>
<
emph
type
="
italics
"/>
Pr.
<
emph.end
type
="
italics
"/>
13.
<
emph
type
="
italics
"/>
huius.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.000532
">
<
margin.target
id
="
marg119
"/>
<
emph
type
="
italics
"/>
Pr.
<
gap
/>
. </
s
>
<
s
id
="
s.000533
">prima.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.000534
">
<
margin.target
id
="
marg120
"/>
<
emph
type
="
italics
"/>
Pr.
<
emph.end
type
="
italics
"/>
2.
<
emph
type
="
italics
"/>
prima.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.000535
">
<
margin.target
id
="
marg121
"/>
<
emph
type
="
italics
"/>
Pr.
<
emph.end
type
="
italics
"/>
8.
<
emph
type
="
italics
"/>
huius &
<
lb
/>
Cor. </
s
>
<
s
id
="
s.000536
">pr.
<
emph.end
type
="
italics
"/>
13.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.000537
">
<
margin.target
id
="
marg122
"/>
<
emph
type
="
italics
"/>
Pr.
<
emph.end
type
="
italics
"/>
2.
<
emph
type
="
italics
"/>
huius.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000538
">
<
emph
type
="
center
"/>
<
emph
type
="
italics
"/>
Corollarium.
<
emph.end
type
="
italics
"/>
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000539
">
<
emph
type
="
italics
"/>
Hinc aparet, ſpiralem DB ad ſpiralem DBG eandem habe
<
lb
/>
re rationem, quam quadrilineum QIKN ad quadrilineum
<
lb
/>
HIKP; pariterque rectam DA ad eandem ſpiralem DCB ha
<
lb
/>
bere ipſam rationem, ac rectangulum HIKL ad dictum qua
<
lb
/>
drilineum HIKP. </
s
>
<
s
id
="
s.000540
">Eodem ferè modo exhiberi pißet ratio ſpi
<
lb
/>
ralis ad ſpiralem, licèt plurium interſe circulationum, eritque
<
lb
/>
prorſus ea, quam habet vnum ad alterum eiuſdem illius na
<
lb
/>
turæ, quadrilineorum.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000541
">
<
emph
type
="
center
"/>
PROP. XV. THEOR. XI.
<
emph.end
type
="
center
"/>
<
lb
/>
<
arrow.to.target
n
="
marg123
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.000542
">
<
margin.target
id
="
marg123
"/>
<
emph
type
="
italics
"/>
Tab.
<
emph.end
type
="
italics
"/>
5.
<
emph
type
="
italics
"/>
Fig.
<
emph.end
type
="
italics
"/>
4.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000543
">SPiralis orta ex motu naturaliter accelerato per
<
expan
abbr
="
radiũ
">radium</
expan
>
<
lb
/>
circuli comprehendentis ſpiralem ipſam, & ex motu
<
lb
/>
æquabili circa
<
expan
abbr
="
circumferentiã
">circumferentiam</
expan
>
eiuſdem circuli, æqualis eſt
<
lb
/>
ei curuæ parabolicæ natæ ex motu compoſito, cuius vnum
<
lb
/>
latus curritur iuxta imaginem trianguli, nempe motu gra
<
lb
/>
uium, alterum verò latus iuxta imaginem trilinei ſecundi,
<
lb
/>
habebitque parabola ipſa axim æqualem radio, & baſim̨
<
lb
/>
tertiæ parti circunferentiæ eiuſdem circuli ſpiralem com
<
lb
/>
prehendentis. </
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000544
">Eſto ſpiralis ACB, quæ ſignatur ex motu
<
expan
abbr
="
pũcti
">puncti</
expan
>
A æqua
<
lb
/>
biliter lati circa circumferentiam ADA, dum nempe
<
expan
abbr
="
eodẽ
">eodem</
expan
>
<
lb
/>
tempore IF, punctum B currit à quiete lineam BA motu
<
lb
/>
grauium deſcendentium; ſit verò imago velocitatum dicti
<
lb
/>
motus æquabilis per ADA rectangulum HGFI, & alte
<
arrow.to.target
n
="
marg124
"/>
<
lb
/>
rius motus imago, (quæ triangulum erit) eſto FEIM. Pa
<
lb
/>
<
arrow.to.target
n
="
marg125
"/>
<
lb
/>
tet, quia ipſæ imagines ponuntur homogeneæ, eſſe rectan
<
lb
/>
gulum HGFI ad triangulum IFM vt ADA circumferentia
<
lb
/>
ad radium BA, & propterea IM ad IH erit vt BA ad dimi
<
lb
/>
dium circunferentiæ AEDA. </
s
>
<
s
id
="
s.000546
">Sumatur quodlibet
<
expan
abbr
="
momẽ-tum
">momen
<
lb
/>
tum</
expan
>
K, & ducatur ONKL æquidiſtans HM, puteturque </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>