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
71
30
72
73
37
74
75
32
76
77
25
78
79
34
80
81
35
82
83
36
84
85
37
86
87
38
88
89
39
90
91
40
92
93
41
94
95
42
96
97
43
98
99
44
100
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
>
page
|<
<
(43)
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div281
"
type
="
section
"
level
="
1
"
n
="
94
">
<
p
>
<
s
xml:id
="
echoid-s4926
"
xml:space
="
preserve
">
<
pb
o
="
43
"
file
="
0197
"
n
="
197
"
rhead
="
DE CENTRO GRAVIT. SOLID.
"/>
b m. </
s
>
<
s
xml:id
="
echoid-s4927
"
xml:space
="
preserve
">ergo circulus a c circuli _k_ g: </
s
>
<
s
xml:id
="
echoid-s4928
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4929
"
xml:space
="
preserve
">idcirco cylindrus
<
lb
/>
a h cylindri _k_ l duplus erit. </
s
>
<
s
xml:id
="
echoid-s4930
"
xml:space
="
preserve
">quare & </
s
>
<
s
xml:id
="
echoid-s4931
"
xml:space
="
preserve
">linea o p dupla
<
lb
/>
ipſius p n. </
s
>
<
s
xml:id
="
echoid-s4932
"
xml:space
="
preserve
">Deinde inſcripta & </
s
>
<
s
xml:id
="
echoid-s4933
"
xml:space
="
preserve
">circumſcripta portioni
<
lb
/>
alia figura, ita ut inſcripta conſtituatur ex tribus cylin-
<
lb
/>
dris q r, s g, tu: </
s
>
<
s
xml:id
="
echoid-s4934
"
xml:space
="
preserve
">circumſcripta uero ex quatuor a x, y z,
<
lb
/>
_K_ ν, θ λ: </
s
>
<
s
xml:id
="
echoid-s4935
"
xml:space
="
preserve
">diuidantur b o, o m, m n, n d bifariam in punctis
<
lb
/>
μ ν π ρ. </
s
>
<
s
xml:id
="
echoid-s4936
"
xml:space
="
preserve
">Itaque cylindri θ λ centrum grauitætis eſt punctum
<
lb
/>
μ: </
s
>
<
s
xml:id
="
echoid-s4937
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4938
"
xml:space
="
preserve
">cylindri
<
emph
style
="
sc
">K</
emph
>
ν centrum ν. </
s
>
<
s
xml:id
="
echoid-s4939
"
xml:space
="
preserve
">ergo ſi linea μ ν diuidatur in σ,
<
lb
/>
ita ut μ σ ad σ ν proportionẽ eã habeat, quam cylindrus K ν
<
lb
/>
ad cylindrum θ λ, uidelicet quam quadratum
<
emph
style
="
sc
">K</
emph
>
m ad qua-
<
lb
/>
dratum θ o, hoc eſt, quam linea m b ad b o: </
s
>
<
s
xml:id
="
echoid-s4940
"
xml:space
="
preserve
">erit σ centrum
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0197-01
"
xlink:href
="
note-0197-01a
"
xml:space
="
preserve
">20. primi
<
lb
/>
conicorũ</
note
>
magnitudinis compoſitæ ex cylindris
<
emph
style
="
sc
">K</
emph
>
ν, θ λ. </
s
>
<
s
xml:id
="
echoid-s4941
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4942
"
xml:space
="
preserve
">cum linea
<
lb
/>
m b ſit dupla b o, erit & </
s
>
<
s
xml:id
="
echoid-s4943
"
xml:space
="
preserve
">μ σ ipſius σ ν dupla. </
s
>
<
s
xml:id
="
echoid-s4944
"
xml:space
="
preserve
">præterea quo-
<
lb
/>
niam cylindri y z centrum grauitatis eſt π, linea σ π ita diui
<
lb
/>
ſa in τ, ut σ τ ad τ π eam habeat proportionem, quam cylin
<
lb
/>
drus y z ad duos cylindros K ν, θ λ: </
s
>
<
s
xml:id
="
echoid-s4945
"
xml:space
="
preserve
">erit τ centrum magnitu
<
lb
/>
dinis, quæ ex dictis tribus cylindris conſtat. </
s
>
<
s
xml:id
="
echoid-s4946
"
xml:space
="
preserve
">cylindrus au-
<
lb
/>
tẽ y z ad cylindrum θ λ eſt, ut linea n b ad b o, hoc eſt ut 3
<
lb
/>
ad 1: </
s
>
<
s
xml:id
="
echoid-s4947
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4948
"
xml:space
="
preserve
">ad cylindrum k ν, ut n b ad b m, uidelicet ut 3 ad 2.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4949
"
xml:space
="
preserve
">quare y z cylĩdrus duobus cylindris k ν, θ λ æqualis erit. </
s
>
<
s
xml:id
="
echoid-s4950
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4951
"
xml:space
="
preserve
">
<
lb
/>
propterea linea σ τ æqualis ipſi τ π. </
s
>
<
s
xml:id
="
echoid-s4952
"
xml:space
="
preserve
">denique cylindri a x
<
lb
/>
centrum grauitatis eſt punctum ρ. </
s
>
<
s
xml:id
="
echoid-s4953
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4954
"
xml:space
="
preserve
">cum τ ζ diuiſa fuerit
<
lb
/>
in eã proportionem, quam habet cylindrus a x ad tres cy-
<
lb
/>
lindros y z, _k_ ν, θ λ: </
s
>
<
s
xml:id
="
echoid-s4955
"
xml:space
="
preserve
">erit in eo puncto centrum grauitatis
<
lb
/>
totius figuræ circũſcriptæ. </
s
>
<
s
xml:id
="
echoid-s4956
"
xml:space
="
preserve
">Sed cylindrus a x ad ipſum y z
<
lb
/>
eſt ut linea d b ad b n: </
s
>
<
s
xml:id
="
echoid-s4957
"
xml:space
="
preserve
">hoc eſt ut 4 ad 3: </
s
>
<
s
xml:id
="
echoid-s4958
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4959
"
xml:space
="
preserve
">duo cylindri _k_ ν
<
lb
/>
θ λ cylindro y z ſunt æquales. </
s
>
<
s
xml:id
="
echoid-s4960
"
xml:space
="
preserve
">cylindrns igitur a x ad tres
<
lb
/>
iam dictos cylindros eſt ut 2 ad 3. </
s
>
<
s
xml:id
="
echoid-s4961
"
xml:space
="
preserve
">Sed quoniã μ σ eſt dua-
<
lb
/>
rum partium, & </
s
>
<
s
xml:id
="
echoid-s4962
"
xml:space
="
preserve
">σ ν unius, qualium μ π eſt ſex; </
s
>
<
s
xml:id
="
echoid-s4963
"
xml:space
="
preserve
">erit σ π par-
<
lb
/>
tium quatuor: </
s
>
<
s
xml:id
="
echoid-s4964
"
xml:space
="
preserve
">proptereaq; </
s
>
<
s
xml:id
="
echoid-s4965
"
xml:space
="
preserve
">τ π duarum, & </
s
>
<
s
xml:id
="
echoid-s4966
"
xml:space
="
preserve
">ν π, hoc eſt π ρ
<
lb
/>
trium. </
s
>
<
s
xml:id
="
echoid-s4967
"
xml:space
="
preserve
">quare ſequitur ut punctum π totius figuræ circum
<
lb
/>
ſcriptæ ſit centrum. </
s
>
<
s
xml:id
="
echoid-s4968
"
xml:space
="
preserve
">Itaque fiat ν υ ad υ π, ut μ σ ad σ ν. </
s
>
<
s
xml:id
="
echoid-s4969
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4970
"
xml:space
="
preserve
">υ ρ
<
lb
/>
bifariam diuidatur in φ. </
s
>
<
s
xml:id
="
echoid-s4971
"
xml:space
="
preserve
">Similiter ut in circumſcripta figu
<
lb
/>
ra oſtendetur centrum magnitudinis compoſitæ ex </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>