Archimedes
,
Archimedis De insidentibvs aqvae
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Handwritten
Figures
Content
Thumbnails
Page concordance
<
1 - 30
31 - 51
>
Scan
Original
21
3
22
23
4
24
25
5
26
27
6
28
29
7
30
31
8
32
33
9
34
35
10
36
37
11
38
39
12
40
41
13
42
43
14
44
45
15
46
47
16
48
49
50
<
1 - 30
31 - 51
>
page
|<
<
of 51
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div34
"
type
="
section
"
level
="
1
"
n
="
25
">
<
p
style
="
it
">
<
s
xml:id
="
echoid-s432
"
xml:space
="
preserve
">
<
pb
file
="
0030
"
n
="
30
"
rhead
="
DE INSIDENTIBVS AQVAE
"/>
K, recta ducatur ſuper p, f, erit autem minor, quæ r, ***, quàm e, a, quæ
<
lb
/>
uſque ad axem. </
s
>
<
s
xml:id
="
echoid-s433
"
xml:space
="
preserve
">Accipiatur igitur ei quæ uſque ad axem æqũas quæ
<
lb
/>
r, h, & </
s
>
<
s
xml:id
="
echoid-s434
"
xml:space
="
preserve
">quæ quidem c, o, ducatur contingens ſectiones penes o, exiſtens
<
lb
/>
_æquedistans_ ipſi a, s, & </
s
>
<
s
xml:id
="
echoid-s435
"
xml:space
="
preserve
">quæ n, o, & </
s
>
<
s
xml:id
="
echoid-s436
"
xml:space
="
preserve
">_æquedistans_ ipſi p, f. </
s
>
<
s
xml:id
="
echoid-s437
"
xml:space
="
preserve
">Secet autem
<
lb
/>
quæ n, o, ipſam K, ***, prius ſecundum i. </
s
>
<
s
xml:id
="
echoid-s438
"
xml:space
="
preserve
">Conſimiliter autem præcedenti
<
lb
/>
demõſtrabitur, quòd quæn, o, aut hemiolia eſt ipſius o, i, aut maior quàm
<
lb
/>
bemiolia, ſit autẽ, quæ o, t, ipſi t, n, minor, quàm dupla. </
s
>
<
s
xml:id
="
echoid-s439
"
xml:space
="
preserve
">Sit igitur quæ o,
<
lb
/>
b, dupla ipſius b, n, & </
s
>
<
s
xml:id
="
echoid-s440
"
xml:space
="
preserve
">diſponantur tandem prioribus. </
s
>
<
s
xml:id
="
echoid-s441
"
xml:space
="
preserve
">Similiter igitur de
<
lb
/>
monstrabitur, quæ r, f, faciens angulos rectos ad c, o, & </
s
>
<
s
xml:id
="
echoid-s442
"
xml:space
="
preserve
">ad ſuperficiem
<
lb
/>
humidi, & </
s
>
<
s
xml:id
="
echoid-s443
"
xml:space
="
preserve
">ab ipſis b, g, productæ æquedistanter ipſi r, f, erunt perpendi
<
lb
/>
culares ſuper ſuperficiem humidi. </
s
>
<
s
xml:id
="
echoid-s444
"
xml:space
="
preserve
">Portio igitur, quę quidem extra hu-
<
lb
/>
midum deorſum ferretur in humidum, ſecundum eam, quæ per b, perpen
<
lb
/>
dicularem. </
s
>
<
s
xml:id
="
echoid-s445
"
xml:space
="
preserve
">Quæ autem inter humidum ſurſum ferretur, ſecũdum eam,
<
lb
/>
quàm per g. </
s
>
<
s
xml:id
="
echoid-s446
"
xml:space
="
preserve
">Maximum igitur, quod ad uoluit ſolidum ita, ut baſis ip-
<
lb
/>
ſius, necſecundum vnum contingat ſuperficiem humidi, quoniam nunc,
<
lb
/>
ſecundum vnum tangens ad deorſum, ferret ex parte a. </
s
>
<
s
xml:id
="
echoid-s447
"
xml:space
="
preserve
">Manifestum
<
lb
/>
autem quòd & </
s
>
<
s
xml:id
="
echoid-s448
"
xml:space
="
preserve
">ſi quæ n, o, non ſecuerit ***, K, eandem demonſtrabũtur.</
s
>
<
s
xml:id
="
echoid-s449
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div36
"
type
="
section
"
level
="
1
"
n
="
26
">
<
head
xml:id
="
echoid-head36
"
xml:space
="
preserve
">OCTAVVS.</
head
>
<
p
>
<
s
xml:id
="
echoid-s450
"
xml:space
="
preserve
">Recta portio rectanguli conoy dalis, quando axem habue
<
lb
/>
rit maiorem, quàm hemiolium eius, quæ uſque ad axem mi-
<
lb
/>
norem, autem ut ad eam, quæ ad axem habeat proportionẽ,
<
lb
/>
quam habet quindecim ad quatuor. </
s
>
<
s
xml:id
="
echoid-s451
"
xml:space
="
preserve
">Si grauis ad humidum
<
lb
/>
habeat proportionem minorem proportione, quam habet
<
lb
/>
tetragonum, quod ab ex ceſſu, quo axis eſt maior, quàm he-
<
lb
/>
miolius eius, quæ uſque ad axem ad tetragonum, quod ab
<
lb
/>
axe dimiſſa in humidum, it a ut baſis ipſius non tangat humi
<
lb
/>
dum, nec in rectum reſtituetur, nec manebit inclinata, niſi
<
lb
/>
quando axis ipſius ad ſuperficiem humidi fecerit angulum
<
lb
/>
æqualem ei qui dicendus eſt.</
s
>
<
s
xml:id
="
echoid-s452
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s453
"
xml:space
="
preserve
">_S_It portio qualis dicta est : </
s
>
<
s
xml:id
="
echoid-s454
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s455
"
xml:space
="
preserve
">ſit quæ b, d,@ æquales axi, & </
s
>
<
s
xml:id
="
echoid-s456
"
xml:space
="
preserve
">quæ qui-
<
lb
/>
dem b, K, ſit duplaipſius k, d. </
s
>
<
s
xml:id
="
echoid-s457
"
xml:space
="
preserve
">Quæ autem r, k, æqualis ei, quæ uſ-
<
lb
/>
que ad axem. </
s
>
<
s
xml:id
="
echoid-s458
"
xml:space
="
preserve
">Sit autem, & </
s
>
<
s
xml:id
="
echoid-s459
"
xml:space
="
preserve
">quæ quidem e, b, hemiolia ipſius b, r.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s460
"
xml:space
="
preserve
">Quam autem proportionem habet portio in grauitate ad bumidum hãc
<
lb
/>
quod a, b, f, q, tetragonum ad id, quod a, d, b. </
s
>
<
s
xml:id
="
echoid-s461
"
xml:space
="
preserve
">Sit autem, & </
s
>
<
s
xml:id
="
echoid-s462
"
xml:space
="
preserve
">quæ f, dupla
<
lb
/>
ipſius q, palam, igitur quòd quæ f, g, ad ipſam d, b, proportionem habet
<
lb
/>
minorem proportione, quàm habet, quæ t, b, ad ipſam b, d, exceſſus enim
<
lb
/>
quòdg, d, eſt quo axis eſt. </
s
>
<
s
xml:id
="
echoid-s463
"
xml:space
="
preserve
">maior, quàm bemiolius eius, quæuſque </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>