Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Content
Thumbnails
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
>
Scan
Original
61
25
62
63
26
64
65
27
66
67
22
68
69
29
70
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
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
>
page
|<
<
(22)
of 213
>
>|
DE IIS QVAE VEH. IN AQVA.
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
type
="
section
"
level
="
1
"
n
="
38
">
<
p
>
<
s
xml:space
="
preserve
">
<
pb
o
="
22
"
file
="
0067
"
n
="
67
"
rhead
="
DE IIS QVAE VEH. IN AQVA.
"/>
dum eam, quæ per g ſurſum eleuabitur. </
s
>
<
s
xml:space
="
preserve
">non igitur manebit
<
lb
/>
portio ſic inclinata, nec conuertetur ita, ut axis ad ſuperfi-
<
lb
/>
ciem humidi ſit perpendicularis: </
s
>
<
s
xml:space
="
preserve
">quoniam quæ ex parte 1
<
lb
/>
<
anchor
type
="
note
"
xlink:label
="
note-0067-01a
"
xlink:href
="
note-0067-01
"/>
deorſum; </
s
>
<
s
xml:space
="
preserve
">quæ uero ex parte a ſurſum ferentur, ut ex iam de
<
lb
/>
monſtratis apparere poteſt. </
s
>
<
s
xml:space
="
preserve
">Quòd ſi axis cum ſuperficie
<
lb
/>
humidi fecerit angulum minorem angulo b, ſimiliter de-
<
lb
/>
<
anchor
type
="
note
"
xlink:label
="
note-0067-02a
"
xlink:href
="
note-0067-02
"/>
monſtrabitur, nõ manere portionem, ſed inclinari, donec
<
lb
/>
utique axis cum ſuperficie humidi faciat angulum angulo
<
lb
/>
b æqualem.</
s
>
<
s
xml:space
="
preserve
"/>
</
p
>
<
div
type
="
float
"
level
="
2
"
n
="
1
">
<
figure
xlink:label
="
fig-0064-01
"
xlink:href
="
fig-0064-01a
">
<
image
file
="
0064-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0064-01
"/>
</
figure
>
<
note
position
="
left
"
xlink:label
="
note-0064-01
"
xlink:href
="
note-0064-01a
"
xml:space
="
preserve
">A</
note
>
<
note
position
="
right
"
xlink:label
="
note-0065-01
"
xlink:href
="
note-0065-01a
"
xml:space
="
preserve
">B</
note
>
<
note
position
="
right
"
xlink:label
="
note-0065-02
"
xlink:href
="
note-0065-02a
"
xml:space
="
preserve
">C</
note
>
<
note
position
="
right
"
xlink:label
="
note-0065-03
"
xlink:href
="
note-0065-03a
"
xml:space
="
preserve
">D</
note
>
<
note
position
="
right
"
xlink:label
="
note-0065-04
"
xlink:href
="
note-0065-04a
"
xml:space
="
preserve
">E</
note
>
<
figure
xlink:label
="
fig-0066-01
"
xlink:href
="
fig-0066-01a
">
<
image
file
="
0066-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0066-01
"/>
</
figure
>
<
note
position
="
right
"
xlink:label
="
note-0067-01
"
xlink:href
="
note-0067-01a
"
xml:space
="
preserve
">F</
note
>
<
note
position
="
right
"
xlink:label
="
note-0067-02
"
xlink:href
="
note-0067-02a
"
xml:space
="
preserve
">G</
note
>
</
div
>
</
div
>
<
div
type
="
section
"
level
="
1
"
n
="
39
">
<
head
xml:space
="
preserve
">COMMENTARIVS.</
head
>
<
p
>
<
s
xml:space
="
preserve
">QVARE quadratum b d magis excedit quadratum
<
lb
/>
<
anchor
type
="
note
"
xlink:label
="
note-0067-03a
"
xlink:href
="
note-0067-03
"/>
f q, quàm b c quadratum: </
s
>
<
s
xml:space
="
preserve
">& </
s
>
<
s
xml:space
="
preserve
">idcirco linea f q minor eſt,
<
lb
/>
quàm b c: </
s
>
<
s
xml:space
="
preserve
">itemq; </
s
>
<
s
xml:space
="
preserve
">f minor quam b r.</
s
>
<
s
xml:space
="
preserve
">] _Quoniani exceſſus, quo_
<
lb
/>
_quadratum b d excedit quadratum b c ad quadratum b d minorem_
<
lb
/>
_proportionem habet, quàm exceſſus, quo quadratum b d excedit qua_
<
lb
/>
_dratum f q, ad idem quadratum: </
s
>
<
s
xml:space
="
preserve
">erit ex octaua quinti exceſſus, quo_
<
lb
/>
_quadratum b d excedit quadratum b c, minor quàm exceſſus, quo ex_
<
lb
/>
_cedit quadratum f q. </
s
>
<
s
xml:space
="
preserve
">ergo quadratum f q minus est quadrato b c: </
s
>
<
s
xml:space
="
preserve
">&_</
s
>
<
s
xml:space
="
preserve
">
<
lb
/>
_propterea linea f q minor linea b c. </
s
>
<
s
xml:space
="
preserve
">Sed f q ad f eandem proportionẽ_
<
lb
/>
_habet, quam b c ad b r; </
s
>
<
s
xml:space
="
preserve
">utraque enim utriuſque ſeſquialtera est. </
s
>
<
s
xml:space
="
preserve
">cum_
<
lb
/>
<
anchor
type
="
note
"
xlink:label
="
note-0067-04a
"
xlink:href
="
note-0067-04
"/>
_igitur f q ſit minor b c, & </
s
>
<
s
xml:space
="
preserve
">f ipſa b r minor erit_.</
s
>
<
s
xml:space
="
preserve
"/>
</
p
>
<
div
type
="
float
"
level
="
2
"
n
="
1
">
<
note
position
="
right
"
xlink:label
="
note-0067-03
"
xlink:href
="
note-0067-03a
"
xml:space
="
preserve
">A</
note
>
<
note
position
="
right
"
xlink:label
="
note-0067-04
"
xlink:href
="
note-0067-04a
"
xml:space
="
preserve
">14. quinti</
note
>
</
div
>
<
p
>
<
s
xml:space
="
preserve
">Et propterea k r ad ſ y maiorem habet, quàm dimidium
<
lb
/>
<
anchor
type
="
note
"
xlink:label
="
note-0067-05a
"
xlink:href
="
note-0067-05
"/>
ipſius k r ad ψ b.</
s
>
<
s
xml:space
="
preserve
">] _Est enim k r ad ſ y, ut quadratum p s ad qua_
<
lb
/>
_dratum ſ y
<
unsure
/>
: </
s
>
<
s
xml:space
="
preserve
">& </
s
>
<
s
xml:space
="
preserve
">dimidium lineæ K r ad lineam ψ b, ut quadratum e ψ_
<
lb
/>
_ad quadratum ψ b_.</
s
>
<
s
xml:space
="
preserve
"/>
</
p
>
<
div
type
="
float
"
level
="
2
"
n
="
2
">
<
note
position
="
right
"
xlink:label
="
note-0067-05
"
xlink:href
="
note-0067-05a
"
xml:space
="
preserve
">B</
note
>
</
div
>
<
p
>
<
s
xml:space
="
preserve
">Et s o minor quàm ψ b] _Est enim ſ y dupla ipſius ſ o._</
s
>
<
s
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
right
"
xml:space
="
preserve
">C</
note
>
<
p
>
<
s
xml:space
="
preserve
">Et p h maior, quàm f.</
s
>
<
s
xml:space
="
preserve
">] _Nam p h eſt æqualis ſ ω, & </
s
>
<
s
xml:space
="
preserve
">r ψ_
<
lb
/>
<
anchor
type
="
note
"
xlink:label
="
note-0067-07a
"
xlink:href
="
note-0067-07
"/>
_ipſi f_.</
s
>
<
s
xml:space
="
preserve
"/>
</
p
>
<
div
type
="
float
"
level
="
2
"
n
="
3
">
<
note
position
="
right
"
xlink:label
="
note-0067-07
"
xlink:href
="
note-0067-07a
"
xml:space
="
preserve
">D</
note
>
</
div
>
<
p
>
<
s
xml:space
="
preserve
">Habebit ergo tota portio ad eam, quæ eſt extra humi-
<
lb
/>
<
anchor
type
="
note
"
xlink:label
="
note-0067-08a
"
xlink:href
="
note-0067-08
"/>
dum proportionem eandem, quam quadratum b d ad qua
<
lb
/>
dratum f q.</
s
>
<
s
xml:space
="
preserve
">] _Cum pars demerſa ad totam portionem ita ſit, ut_
<
lb
/>
_exceſſus, quo quadratum b d excedit quadratum f q ad b d quadratu
<
unsure
/>
:_</
s
>
<
s
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>