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
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
>
Scan
Original
131
10
132
133
11
134
135
12
136
137
13
138
139
14
140
141
15
142
143
15
144
16
145
17
146
147
18
148
149
19
150
151
20
152
153
21
154
155
22
156
157
23
158
159
24
160
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
>
page
|<
<
(21)
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div84
"
type
="
section
"
level
="
1
"
n
="
34
">
<
pb
o
="
21
"
file
="
0053
"
n
="
53
"
rhead
="
DE IIS QVAE VEH. IN AQVA.
"/>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1210
"
xml:space
="
preserve
">Producatur enim u s ad lineam qm in x: </
s
>
<
s
xml:id
="
echoid-s1211
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1212
"
xml:space
="
preserve
">à puncto x duca
<
lb
/>
tur ad diametrum x y ipſi bd æquidistans. </
s
>
<
s
xml:id
="
echoid-s1213
"
xml:space
="
preserve
">erit gt minor quàm
<
lb
/>
gy, quoniam u s minor eſt quàm ux: </
s
>
<
s
xml:id
="
echoid-s1214
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1215
"
xml:space
="
preserve
">ex primo lemmate yg
<
lb
/>
ad uc erit, ut h g ad n c; </
s
>
<
s
xml:id
="
echoid-s1216
"
xml:space
="
preserve
">uidelicet ut g b ad c k, quod proxime de
<
lb
/>
monstrauimus: </
s
>
<
s
xml:id
="
echoid-s1217
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1218
"
xml:space
="
preserve
">permutando yg ad gb, ut uc ad c k. </
s
>
<
s
xml:id
="
echoid-s1219
"
xml:space
="
preserve
">Sed t g
<
lb
/>
cum ſit ipſa y g minor, habet ad g b proportionem minorem, quàm
<
lb
/>
y g ad eandem. </
s
>
<
s
xml:id
="
echoid-s1220
"
xml:space
="
preserve
">ergo u c ad c K maiorem proportioné habet, quàm
<
lb
/>
t g ad g b. </
s
>
<
s
xml:id
="
echoid-s1221
"
xml:space
="
preserve
">quod demonstraſſe oportuit. </
s
>
<
s
xml:id
="
echoid-s1222
"
xml:space
="
preserve
">Itaque poſitione data g K
<
lb
/>
unum duntaxat erit in ſectione punctum, uidelicet m, à quo ductis
<
lb
/>
duabus lineis m e h, mno, habeat n c ad c K proportionem ean-
<
lb
/>
dem, quam h g ad g b. </
s
>
<
s
xml:id
="
echoid-s1223
"
xml:space
="
preserve
">nam ſi ab alijs omnibus ducantur, ſemper
<
lb
/>
ea, quæ inter a c, & </
s
>
<
s
xml:id
="
echoid-s1224
"
xml:space
="
preserve
">lineam ipſi æquidistantem interijcitur, ad c K
<
lb
/>
proportionem maiorem habebit, quàm quæ inter g K atque ei æqui
<
lb
/>
diſtantem, ad ipſam g b. </
s
>
<
s
xml:id
="
echoid-s1225
"
xml:space
="
preserve
">Conſtat igitur id, quod ab Archimede di-
<
lb
/>
ctum est; </
s
>
<
s
xml:id
="
echoid-s1226
"
xml:space
="
preserve
">nempe lineam pi ad p h uel eandem, quam n ω ad ω o,
<
lb
/>
uel maiorem habere proportionem.</
s
>
<
s
xml:id
="
echoid-s1227
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1228
"
xml:space
="
preserve
">Quare p h ipſius h i aut dupla eſt, aut minor quàm du
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0053-01
"
xlink:href
="
note-0053-01a
"
xml:space
="
preserve
">D</
note
>
pla.</
s
>
<
s
xml:id
="
echoid-s1229
"
xml:space
="
preserve
">] _Si quidé_
<
lb
/>
<
figure
xlink:label
="
fig-0053-01
"
xlink:href
="
fig-0053-01a
"
number
="
33
">
<
image
file
="
0053-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0053-01
"/>
</
figure
>
_minor, quàm du-_
<
lb
/>
_pla, ſit pt dupl. </
s
>
<
s
xml:id
="
echoid-s1230
"
xml:space
="
preserve
">2_
<
lb
/>
_ti. </
s
>
<
s
xml:id
="
echoid-s1231
"
xml:space
="
preserve
">erit centrum_
<
lb
/>
_grauitatis eius,_
<
lb
/>
_quod in humido_
<
lb
/>
_est, punctumt. </
s
>
<
s
xml:id
="
echoid-s1232
"
xml:space
="
preserve
">ſi_
<
lb
/>
_uero p h ſit ip-_
<
lb
/>
_ſius h i dupla,_
<
lb
/>
_erit h grauitatis_
<
lb
/>
_centrum: </
s
>
<
s
xml:id
="
echoid-s1233
"
xml:space
="
preserve
">ductâq;_
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1234
"
xml:space
="
preserve
">_h f, & </
s
>
<
s
xml:id
="
echoid-s1235
"
xml:space
="
preserve
">producta_
<
lb
/>
_ad centrum eius,_
<
lb
/>
_quod est extra humidum, uidelicct ad g, alia ſimiliter demonstra-_
<
lb
/>
_buntur. </
s
>
<
s
xml:id
="
echoid-s1236
"
xml:space
="
preserve
">atque idem intelligendum est in propoſitione, quæ ſe_-
<
lb
/>
_quitur._</
s
>
<
s
xml:id
="
echoid-s1237
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1238
"
xml:space
="
preserve
">Reuoluetur ergo ſolidum a p o l, & </
s
>
<
s
xml:id
="
echoid-s1239
"
xml:space
="
preserve
">baſis ipſius nullo
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0053-02
"
xlink:href
="
note-0053-02a
"
xml:space
="
preserve
">E</
note
>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>