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
111
112
113
1
114
115
2
116
117
3
118
119
4
120
121
5
122
123
6
124
125
7
126
127
8
128
129
9
130
131
10
132
133
11
134
135
12
136
137
13
138
139
14
140
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
>
page
|<
<
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div192
"
type
="
section
"
level
="
1
"
n
="
64
">
<
p
>
<
s
xml:id
="
echoid-s2960
"
xml:space
="
preserve
">
<
pb
file
="
0118
"
n
="
118
"
rhead
="
FED. COMMANDINI
"/>
do in reliquis figuris æquilateris, & </
s
>
<
s
xml:id
="
echoid-s2961
"
xml:space
="
preserve
">æquiangulis, quæ in cir-
<
lb
/>
culo deſcribuntur, probabimus cẽtrum grauitatis earum,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s2962
"
xml:space
="
preserve
">centrum circuli idem eſſe. </
s
>
<
s
xml:id
="
echoid-s2963
"
xml:space
="
preserve
">quod quidem demonſtrare
<
lb
/>
oportebat.</
s
>
<
s
xml:id
="
echoid-s2964
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2965
"
xml:space
="
preserve
">Ex quibus apparet cuiuslibet figuræ rectilineæ
<
lb
/>
in circulo plane deſcriptæ centrum grauitatis idẽ
<
lb
/>
eſſe, quod & </
s
>
<
s
xml:id
="
echoid-s2966
"
xml:space
="
preserve
">circuli centrum.</
s
>
<
s
xml:id
="
echoid-s2967
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2968
"
xml:space
="
preserve
">Figuram in circulo plane deſcriptam appella-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0118-01
"
xlink:href
="
note-0118-01a
"
xml:space
="
preserve
">γνωρ@ μω@</
note
>
mus, cuiuſmodi eſt ea, quæ in duodecimo elemen
<
lb
/>
torum libro, propoſitione ſecunda deſcribitur.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2969
"
xml:space
="
preserve
">ex æqualibus enim lateribus, & </
s
>
<
s
xml:id
="
echoid-s2970
"
xml:space
="
preserve
">angulis conſtare
<
lb
/>
perſpicuum eſt.</
s
>
<
s
xml:id
="
echoid-s2971
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div199
"
type
="
section
"
level
="
1
"
n
="
65
">
<
head
xml:id
="
echoid-head72
"
xml:space
="
preserve
">THEOREMA II. PROPOSITIO II.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2972
"
xml:space
="
preserve
">Omnis figuræ rectilineæ in ellipſi plane deſcri-
<
lb
/>
ptæ centrum grauitatis eſt idem, quod ellipſis
<
lb
/>
centrum.</
s
>
<
s
xml:id
="
echoid-s2973
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2974
"
xml:space
="
preserve
">Quo modo figura rectilinea in ellipſi plane deſcribatur,
<
lb
/>
docuimus in commentarijs in quintam propoſitionem li-
<
lb
/>
bri Archimedis de conoidibus, & </
s
>
<
s
xml:id
="
echoid-s2975
"
xml:space
="
preserve
">ſphæroidibus.</
s
>
<
s
xml:id
="
echoid-s2976
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2977
"
xml:space
="
preserve
">Sit ellipſis a b c d, cuius maior axis a c, minor b d: </
s
>
<
s
xml:id
="
echoid-s2978
"
xml:space
="
preserve
">iun-
<
lb
/>
ganturq́; </
s
>
<
s
xml:id
="
echoid-s2979
"
xml:space
="
preserve
">a b, b c, c d, d a: </
s
>
<
s
xml:id
="
echoid-s2980
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2981
"
xml:space
="
preserve
">bifariam diuidantur in pun-
<
lb
/>
ctis e f g h. </
s
>
<
s
xml:id
="
echoid-s2982
"
xml:space
="
preserve
">à centro autem, quod ſit k ductæ lineæ k e, k f,
<
lb
/>
k g, k h uſque ad ſectionem in puncta l m n o protrahan-
<
lb
/>
tur: </
s
>
<
s
xml:id
="
echoid-s2983
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2984
"
xml:space
="
preserve
">iungantur l m, m n, n o, o l, ita ut a c ſecet li-
<
lb
/>
neas l o, m n, in z φ punctis, & </
s
>
<
s
xml:id
="
echoid-s2985
"
xml:space
="
preserve
">b d ſecet l m, o n in χ ψ.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2986
"
xml:space
="
preserve
">erunt l k, k n linea una, itemq́ue linea unaipſæ m k, k o: </
s
>
<
s
xml:id
="
echoid-s2987
"
xml:space
="
preserve
">
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s2988
"
xml:space
="
preserve
">lineæ b a, c d æquidiſtabunt lineæ m o: </
s
>
<
s
xml:id
="
echoid-s2989
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2990
"
xml:space
="
preserve
">b c, a d ipſi
<
lb
/>
l n. </
s
>
<
s
xml:id
="
echoid-s2991
"
xml:space
="
preserve
">rurſus l o, m n axi b d æquidiſtabunt: </
s
>
<
s
xml:id
="
echoid-s2992
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2993
"
xml:space
="
preserve
">l </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>