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
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
|<
<
(27)
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div111
"
type
="
section
"
level
="
1
"
n
="
38
">
<
p
>
<
s
xml:id
="
echoid-s1562
"
xml:space
="
preserve
">
<
pb
o
="
27
"
file
="
0065
"
n
="
65
"
rhead
="
DE IIS QVAE VEH. IN AQVA.
"/>
æqualis r ψ: </
s
>
<
s
xml:id
="
echoid-s1563
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1564
"
xml:space
="
preserve
">ducatur ψ r perpendicularis ad b d, quæ
<
lb
/>
posſit dimidium eius, quod ipſis k r, ψ b, continetur. </
s
>
<
s
xml:id
="
echoid-s1565
"
xml:space
="
preserve
">Dico
<
lb
/>
portionem in humidum demiſſam adeo, ut baſis ipſius to-
<
lb
/>
ta ſit in humido, ita conſiſtere, ut axis cum ſuperficie humi
<
lb
/>
di faciat angulum angulo b æqualem. </
s
>
<
s
xml:id
="
echoid-s1566
"
xml:space
="
preserve
">Demittatur enim
<
lb
/>
portio in humidum, ſicuti dictum eſt; </
s
>
<
s
xml:id
="
echoid-s1567
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1568
"
xml:space
="
preserve
">axis cum humidi
<
lb
/>
ſuperficie non faciat angulum æqualẽ ipſi b, ſed primo ma
<
lb
/>
iorem: </
s
>
<
s
xml:id
="
echoid-s1569
"
xml:space
="
preserve
">ſecta autem ipſa plano per axem, recto ad ſuperfi-
<
lb
/>
ciem humidi, ſectio portionis ſit a p o l rectanguli coni ſe-
<
lb
/>
ctio; </
s
>
<
s
xml:id
="
echoid-s1570
"
xml:space
="
preserve
">ſuperficiei humidi ſectio c i; </
s
>
<
s
xml:id
="
echoid-s1571
"
xml:space
="
preserve
">ſitq, axis portionis, & </
s
>
<
s
xml:id
="
echoid-s1572
"
xml:space
="
preserve
">ſe
<
lb
/>
ctionis diameter n o, quæ fecetur in punctis ω t, ut prius. </
s
>
<
s
xml:id
="
echoid-s1573
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1574
"
xml:space
="
preserve
">
<
lb
/>
ducantur y p quidem ipſi ci æquidiſtans, contingensq; </
s
>
<
s
xml:id
="
echoid-s1575
"
xml:space
="
preserve
">ſe
<
lb
/>
ctionem in p; </
s
>
<
s
xml:id
="
echoid-s1576
"
xml:space
="
preserve
">m p uero æquidiſtans n o: </
s
>
<
s
xml:id
="
echoid-s1577
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1578
"
xml:space
="
preserve
">p s ad axem
<
lb
/>
perpendicularis. </
s
>
<
s
xml:id
="
echoid-s1579
"
xml:space
="
preserve
">Quoniam igitur axis portionis cum ſu-
<
lb
/>
perficie humidi facit angulum maiorem angulo b; </
s
>
<
s
xml:id
="
echoid-s1580
"
xml:space
="
preserve
">erit & </
s
>
<
s
xml:id
="
echoid-s1581
"
xml:space
="
preserve
">
<
lb
/>
angulus s y p angulo b maior. </
s
>
<
s
xml:id
="
echoid-s1582
"
xml:space
="
preserve
">quare quadratum p s ad
<
lb
/>
quadratum s y maiorem habet proportionem, quàm qua
<
lb
/>
dratum ψ e ad quadratum ψ b: </
s
>
<
s
xml:id
="
echoid-s1583
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1584
"
xml:space
="
preserve
">propterea _K_ r ad s y ma
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0065-01
"
xlink:href
="
note-0065-01a
"
xml:space
="
preserve
">B</
note
>
iorem habet, quàm dimidium ipſius κ r ad ψ b. </
s
>
<
s
xml:id
="
echoid-s1585
"
xml:space
="
preserve
">ergo s y
<
lb
/>
minor eſt, quam dupla ψ b; </
s
>
<
s
xml:id
="
echoid-s1586
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1587
"
xml:space
="
preserve
">s o minor, quam ψ b. </
s
>
<
s
xml:id
="
echoid-s1588
"
xml:space
="
preserve
">quare
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0065-02
"
xlink:href
="
note-0065-02a
"
xml:space
="
preserve
">C</
note
>
s ω maior, quàm r ψ; </
s
>
<
s
xml:id
="
echoid-s1589
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1590
"
xml:space
="
preserve
">p h maior, quàm f. </
s
>
<
s
xml:id
="
echoid-s1591
"
xml:space
="
preserve
">Itaque quoniã
<
lb
/>
portio ad humidum in grauitate eam habet proportionẽ,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0065-03
"
xlink:href
="
note-0065-03a
"
xml:space
="
preserve
">D</
note
>
quam exceſſus, quo quadratum b d excedit quadratum f q
<
lb
/>
ad quadratum b d: </
s
>
<
s
xml:id
="
echoid-s1592
"
xml:space
="
preserve
">quam uero proportionem habet por-
<
lb
/>
tio ad humidum in grauitate, eandem pars ipſius demerſa
<
lb
/>
habet ad totam portionẽ: </
s
>
<
s
xml:id
="
echoid-s1593
"
xml:space
="
preserve
">ſequitur partẽ demerſam ad to
<
lb
/>
tam portionem, eam proportionem habere, quã exceſſus,
<
lb
/>
quo quadratum b d excedit quadratũ f q, ad quadratū b d.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1594
"
xml:space
="
preserve
">habebit ergo tota portio ad eam, quæ eſt extra humidum
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0065-04
"
xlink:href
="
note-0065-04a
"
xml:space
="
preserve
">E</
note
>
proportionem eandem, quam quadratum b d ad quadra-
<
lb
/>
tum f q. </
s
>
<
s
xml:id
="
echoid-s1595
"
xml:space
="
preserve
">Sed quam proportionem habet tota portio ad eã,
<
lb
/>
quæ eſt extra humidum, eandem habet quadratum n o ad
<
lb
/>
quadratum p m. </
s
>
<
s
xml:id
="
echoid-s1596
"
xml:space
="
preserve
">ergo p m ipſi f q æ qualis etit. </
s
>
<
s
xml:id
="
echoid-s1597
"
xml:space
="
preserve
">demonſtra
<
lb
/>
ta eſt autem p h maior, quàm f: </
s
>
<
s
xml:id
="
echoid-s1598
"
xml:space
="
preserve
">quare m h minor </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>