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
>
21
22
23
24
25
26
27
28
29
30
<
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
="
19
"
xlink:href
="
022/01/025.jpg
"/>
<
p
type
="
main
">
<
s
id
="
s.000216
">
<
emph
type
="
center
"/>
PROP. IX. THEOR. IX.
<
emph.end
type
="
center
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000217
">REctangulum ſub altitudine, & baſi vnius auuerſarum
<
lb
/>
ad ipſam auuerſam figuram, eandem habet
<
expan
abbr
="
rationẽ
">rationem</
expan
>
,
<
lb
/>
ac altera auuerſa figura ad rectangulum ex baſi in altitudi
<
arrow.to.target
n
="
marg43
"/>
<
lb
/>
nem eiuſdem huius figuræ. </
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.000219
">
<
margin.target
id
="
marg43
"/>
<
emph
type
="
italics
"/>
Tab.
<
emph.end
type
="
italics
"/>
<
gap
/>
.
<
emph
type
="
italics
"/>
fig.
<
emph.end
type
="
italics
"/>
7.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000220
">Sint auuerſæ figuræ ACB, GFDEG. </
s
>
<
s
id
="
s.000221
">Dico rectangu
<
lb
/>
lum DF in DE ad figuram GFDEG, eandem habere ratio
<
lb
/>
nem ac figura ACBA ad rectangulum AB in BC. </
s
>
<
s
id
="
s.000222
">Sint pri
<
lb
/>
mùm ABC, FDE anguli recti, & ducta qualibet HI paral
<
lb
/>
<
arrow.to.target
n
="
marg44
"/>
<
lb
/>
lela BC, ſit BAC ad HIA vt DF ad KF, erit ob naturam
<
lb
/>
auuerſarum KL ad DE vt BC ad HI; itaque ſi ponatur eſſe
<
lb
/>
quidam motus ab F in D iuxta imaginem
<
expan
abbr
="
velocitatũ
">velocitatum</
expan
>
BAC,
<
lb
/>
<
arrow.to.target
n
="
marg45
"/>
<
lb
/>
erit GFDEG imago temporis eiuſdem motus; nam imago
<
lb
/>
<
arrow.to.target
n
="
marg46
"/>
<
lb
/>
BAC ad imaginem HIA eſt vt ſpatium DF ad ſpatium FK
<
lb
/>
& velocitas BC ad
<
expan
abbr
="
velocitatẽ
">velocitatem</
expan
>
HI vt reciprocè KL ad DE.
<
lb
/>
</
s
>
<
s
id
="
s.000223
">Sit etiam alius motus, ſed æquabilis, cuius imago velocita
<
lb
/>
tum æqualis ſit, & homogenea ipſi BAC, rectangulum
<
expan
abbr
="
nẽ-pe
">nen
<
lb
/>
pe</
expan
>
AB in BM, & ideo ſi fiat BM ad BC ſicut DE ad DN,
<
lb
/>
concipiaturque rectangulum FD in DN, erit hoc imago
<
lb
/>
<
arrow.to.target
n
="
marg47
"/>
<
lb
/>
temporis dicti motus æquabilis, homogenea, & æqualis
<
lb
/>
imagini GFDEG; nam
<
expan
abbr
="
tẽpora
">tempora</
expan
>
, ſcilicet imagines GFDEG,
<
lb
/>
<
arrow.to.target
n
="
marg48
"/>
<
lb
/>
FD in DN rectangulum componuntur ex rationibus ſpa
<
lb
/>
<
arrow.to.target
n
="
marg49
"/>
<
lb
/>
tiorum, hoc eſt imaginum velocitatum interſe æqualium,
<
lb
/>
ABM, ACB, & reciproca æquatricum pariter æqualium
<
lb
/>
BM, BM. </
s
>
<
s
id
="
s.000224
">Cum igitur rectangulum FD in DN æquale ſit
<
lb
/>
<
arrow.to.target
n
="
marg50
"/>
<
lb
/>
imagini, ſeu figuræ GFDEG, habebit eadem figurą
<
lb
/>
GFDEG ad rectangulum FD in DE eandem rationem,
<
lb
/>
quam DN ad DE, hoc eſt quam BC ad BM, ſeu quam re
<
lb
/>
ctangulum AB in BC ad rectangulum AB in BM, aut ad ei
<
lb
/>
æqualem figuram ABC; & conuertendo, manifeſtum eſt
<
lb
/>
quod propoſuimus, nempe rectangulum FD in DE ad fi
<
lb
/>
guram GFDEG habere eandem
<
expan
abbr
="
rationẽ
">rationem</
expan
>
, ac figura ACBA </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>