Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
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
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 213
>
51
(20)
52
53
(21)
54
55
(22)
56
57
(23)
58
59
(24)
60
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 213
>
page
|<
<
(42)
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div175
"
type
="
section
"
level
="
1
"
n
="
55
">
<
p
style
="
it
">
<
s
xml:id
="
echoid-s2486
"
xml:space
="
preserve
">
<
pb
o
="
42
"
file
="
0095
"
n
="
95
"
rhead
="
DE IIS QVAE VEH. IN AQVA.
"/>
clinata, ut baſis humidum non contingat, ſectur plano per axem,
<
lb
/>
recto ad ſuperficiem humidi, ut ſectio ſit a m o l rectanguli coni ſe-
<
lb
/>
ctio: </
s
>
<
s
xml:id
="
echoid-s2487
"
xml:space
="
preserve
">ſuperficiei humidi ſectio ſit i o: </
s
>
<
s
xml:id
="
echoid-s2488
"
xml:space
="
preserve
">axis portionis, & </
s
>
<
s
xml:id
="
echoid-s2489
"
xml:space
="
preserve
">ſectionis
<
lb
/>
diameter b d; </
s
>
<
s
xml:id
="
echoid-s2490
"
xml:space
="
preserve
">quæ in eaſdem, quas diximus, partes ſecetur: </
s
>
<
s
xml:id
="
echoid-s2491
"
xml:space
="
preserve
">duca-
<
lb
/>
turq; </
s
>
<
s
xml:id
="
echoid-s2492
"
xml:space
="
preserve
">m n quidem ipſi i o æquidiſtans, ut in puncto m ſectionem
<
lb
/>
cótingat: </
s
>
<
s
xml:id
="
echoid-s2493
"
xml:space
="
preserve
">mt uero æquidiſtans ipſi b d: </
s
>
<
s
xml:id
="
echoid-s2494
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2495
"
xml:space
="
preserve
">m s ad eandem perpen
<
lb
/>
dicularis. </
s
>
<
s
xml:id
="
echoid-s2496
"
xml:space
="
preserve
">Demonſtrandum eſt non manere portionem, ſed inclinari
<
lb
/>
ita, ut in uno puncto contingat ſuperficiem humidi. </
s
>
<
s
xml:id
="
echoid-s2497
"
xml:space
="
preserve
">ducatur enim p c
<
lb
/>
ad ipſam b d perpendicularis: </
s
>
<
s
xml:id
="
echoid-s2498
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2499
"
xml:space
="
preserve
">iuncta a f uſque ad ſectionem
<
lb
/>
producatur in q: </
s
>
<
s
xml:id
="
echoid-s2500
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2501
"
xml:space
="
preserve
">per p ducatur p φ ipſi a q æquidiſtans. </
s
>
<
s
xml:id
="
echoid-s2502
"
xml:space
="
preserve
">erunt
<
lb
/>
iam ex ijs, quæ demonſtrauimus a f, f q inter ſe ſe æquales. </
s
>
<
s
xml:id
="
echoid-s2503
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2504
"
xml:space
="
preserve
">cum
<
lb
/>
portio ad humi-
<
lb
/>
<
figure
xlink:label
="
fig-0095-01
"
xlink:href
="
fig-0095-01a
"
number
="
61
">
<
image
file
="
0095-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0095-01
"/>
</
figure
>
dum eam in gra-
<
lb
/>
uitate proportio
<
lb
/>
nem habeat, quá
<
lb
/>
quadratú p f ad
<
lb
/>
b d quadratum:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2505
"
xml:space
="
preserve
">atque eandem ha
<
lb
/>
beat portio ipſi-
<
lb
/>
us demerſa ad to
<
lb
/>
tam portionem; </
s
>
<
s
xml:id
="
echoid-s2506
"
xml:space
="
preserve
">
<
lb
/>
hoc eſt quadratú
<
lb
/>
m t ad quadratú
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0095-01
"
xlink:href
="
note-0095-01a
"
xml:space
="
preserve
">8. quinti.</
note
>
b d: </
s
>
<
s
xml:id
="
echoid-s2507
"
xml:space
="
preserve
">erit quadra
<
lb
/>
tum m t quadra-
<
lb
/>
to p f æquale: </
s
>
<
s
xml:id
="
echoid-s2508
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2509
"
xml:space
="
preserve
">
<
lb
/>
idcirco linea m t
<
lb
/>
æqualis lmeæ p
<
lb
/>
f. </
s
>
<
s
xml:id
="
echoid-s2510
"
xml:space
="
preserve
">Itaque quoniam in portionibus æqualibus, & </
s
>
<
s
xml:id
="
echoid-s2511
"
xml:space
="
preserve
">ſimilibus a p q l, a
<
lb
/>
m o l ductæ ſunt lineæ a q, i o, quæ æquales portiones abſcindunt;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2512
"
xml:space
="
preserve
">illa quidem ab extremitate baſis; </
s
>
<
s
xml:id
="
echoid-s2513
"
xml:space
="
preserve
">hæc uero non ab extremitate: </
s
>
<
s
xml:id
="
echoid-s2514
"
xml:space
="
preserve
">ſe-
<
lb
/>
quitur ut a q, quæ ab extremitate ducitur, minorem acutum angulú
<
lb
/>
contineat cum diametro portionis, quàm ipſa i o. </
s
>
<
s
xml:id
="
echoid-s2515
"
xml:space
="
preserve
">Sed linea p φ li-
<
lb
/>
neæ a q æquidiſtat, & </
s
>
<
s
xml:id
="
echoid-s2516
"
xml:space
="
preserve
">m n ipſi i o. </
s
>
<
s
xml:id
="
echoid-s2517
"
xml:space
="
preserve
">angulus igitur ad φ angulo ad </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>