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
Table of contents
<
1 - 30
31 - 60
61 - 90
91 - 97
[out of range]
>
<
1 - 30
31 - 60
61 - 90
91 - 97
[out of range]
>
page
|<
<
of 213
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div123
"
type
="
section
"
level
="
1
"
n
="
41
">
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1761
"
xml:space
="
preserve
">
<
pb
file
="
0072
"
n
="
72
"
rhead
="
ARCHIMEDIS
"/>
quindecim ad quatuor; </
s
>
<
s
xml:id
="
echoid-s1762
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1763
"
xml:space
="
preserve
">ad eam, quæ uſque ad axem maiorem pro
<
lb
/>
portionem habeat: </
s
>
<
s
xml:id
="
echoid-s1764
"
xml:space
="
preserve
">erit quæ uſ que ad axem minor ipſa k c.</
s
>
<
s
xml:id
="
echoid-s1765
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
left
"
xml:space
="
preserve
">10. quinti</
note
>
<
p
>
<
s
xml:id
="
echoid-s1766
"
xml:space
="
preserve
">Sit ei, quæ uſque ad axem æ qualis k r.</
s
>
<
s
xml:id
="
echoid-s1767
"
xml:space
="
preserve
">] _Hac nos addidimus,_
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0072-02
"
xlink:href
="
note-0072-02a
"
xml:space
="
preserve
">G</
note
>
_quæ in translatione non erant._</
s
>
<
s
xml:id
="
echoid-s1768
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1769
"
xml:space
="
preserve
">_Eſt autem & </
s
>
<
s
xml:id
="
echoid-s1770
"
xml:space
="
preserve
">s b ſeſquialtera ipſius b r.</
s
>
<
s
xml:id
="
echoid-s1771
"
xml:space
="
preserve
">]_ Ponitur enim
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0072-03
"
xlink:href
="
note-0072-03a
"
xml:space
="
preserve
">H</
note
>
d b ſeſquialtera ipſius b k; </
s
>
<
s
xml:id
="
echoid-s1772
"
xml:space
="
preserve
">itémq; </
s
>
<
s
xml:id
="
echoid-s1773
"
xml:space
="
preserve
">d ſ ſeſquialtera k r. </
s
>
<
s
xml:id
="
echoid-s1774
"
xml:space
="
preserve
">quare ut to
<
lb
/>
ta d b ad totam b K, ita pars d s ad partem K r. </
s
>
<
s
xml:id
="
echoid-s1775
"
xml:space
="
preserve
">ergo & </
s
>
<
s
xml:id
="
echoid-s1776
"
xml:space
="
preserve
">reliqua
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0072-04
"
xlink:href
="
note-0072-04a
"
xml:space
="
preserve
">19. quinti</
note
>
s b ad reliquim b r, ut d b ad b k.</
s
>
<
s
xml:id
="
echoid-s1777
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1778
"
xml:space
="
preserve
">_Quæ ſimiles ſint portioni a b l.</
s
>
<
s
xml:id
="
echoid-s1779
"
xml:space
="
preserve
">]_ Similes portiones coni ſe-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0072-05
"
xlink:href
="
note-0072-05a
"
xml:space
="
preserve
">K</
note
>
ctionum Apollonius it. </
s
>
<
s
xml:id
="
echoid-s1780
"
xml:space
="
preserve
">i diffiniuit in ſexto libro conicorum, ut ſcri-
<
lb
/>
bit Eutocius, εν οἱς α χ θεισω
<
unsure
/>
νἐν ἑηάστω παραλλήλων τῆ βάσει, ἵσωι
<
lb
/>
τὸ πλῆθος, ὰι παρὰλληλοι, καὶ αἱ βάσ{ει}ς πρ
<
unsure
/>
ὸς τὰςἀποτεμνομένας
<
lb
/>
ἀπὸ τῶν διαμέ τρων ταῖς νορυφαῖς ἐν τοῖς αὐτοῖ ς λὄγοιςεἰσἰ, καὶἁι
<
lb
/>
ἀποτεμνόμεναι πρ
<
unsure
/>
ὸς τάς ἀποτεμνομένας; </
s
>
<
s
xml:id
="
echoid-s1781
"
xml:space
="
preserve
">hoc est. </
s
>
<
s
xml:id
="
echoid-s1782
"
xml:space
="
preserve
">in quibus ſi du-
<
lb
/>
cantnr lineæ æquidistantes baſi numero æquales: </
s
>
<
s
xml:id
="
echoid-s1783
"
xml:space
="
preserve
">æquidiſtantes atq;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1784
"
xml:space
="
preserve
">baſes ad partes diametrorum, quæ ab ipſis ad uerticem abſcindũtur,
<
lb
/>
eandem proportionem babent: </
s
>
<
s
xml:id
="
echoid-s1785
"
xml:space
="
preserve
">it émq; </
s
>
<
s
xml:id
="
echoid-s1786
"
xml:space
="
preserve
">partes abſciſſæ ad abſciſſas. </
s
>
<
s
xml:id
="
echoid-s1787
"
xml:space
="
preserve
">
<
lb
/>
ducuntur autem lineæ baſi æquidistantes: </
s
>
<
s
xml:id
="
echoid-s1788
"
xml:space
="
preserve
">ut opinor, deſcripta in ſin
<
lb
/>
gulis plane rectilinea figura, quæ lateribus numero æqualibus conti
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0072-06
"
xlink:href
="
note-0072-06a
"
xml:space
="
preserve
">γνωρίμως</
note
>
neatur. </
s
>
<
s
xml:id
="
echoid-s1789
"
xml:space
="
preserve
">Itaq; </
s
>
<
s
xml:id
="
echoid-s1790
"
xml:space
="
preserve
">portiones ſimiles à ſimilibus coni ſectionibus abſcindũ
<
lb
/>
tur: </
s
>
<
s
xml:id
="
echoid-s1791
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1792
"
xml:space
="
preserve
">earum diametri ſiue ad baſes rectæ, ſiue cum baſibus æ qua-
<
lb
/>
les angulos facientes, ad ipſas baſes eandem habent proportionem.</
s
>
<
s
xml:id
="
echoid-s1793
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1794
"
xml:space
="
preserve
">_Tranſibit igitur a e i coni ſectio per k.</
s
>
<
s
xml:id
="
echoid-s1795
"
xml:space
="
preserve
">]_ Sienim fieri po
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0072-07
"
xlink:href
="
note-0072-07a
"
xml:space
="
preserve
">L</
note
>
teſt non tranſeat per k, ſed per aliud punctum lineæ d b, ut per u.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1796
"
xml:space
="
preserve
">Quoniam igitur in rectáguli coni ſectione a e i, cuius diameter e z,
<
lb
/>
ducta eſt a e, & </
s
>
<
s
xml:id
="
echoid-s1797
"
xml:space
="
preserve
">producta: </
s
>
<
s
xml:id
="
echoid-s1798
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1799
"
xml:space
="
preserve
">d b diametro æquidistans utraſque
<
lb
/>
a e, a i ſecat; </
s
>
<
s
xml:id
="
echoid-s1800
"
xml:space
="
preserve
">a e quidem in b, ai uero in d: </
s
>
<
s
xml:id
="
echoid-s1801
"
xml:space
="
preserve
">habebit d b ad b u
<
lb
/>
proportionem eandem, quam a z, ad z d, ex quarta propoſitione li
<
lb
/>
bri. </
s
>
<
s
xml:id
="
echoid-s1802
"
xml:space
="
preserve
">Archimedis de quadratura parabol
<
unsure
/>
æ. </
s
>
<
s
xml:id
="
echoid-s1803
"
xml:space
="
preserve
">Sed a z ſeſquialtera eſt
<
lb
/>
ipſius z d: </
s
>
<
s
xml:id
="
echoid-s1804
"
xml:space
="
preserve
">eſt enim ut tria ad duo, quod mox demonſtrabimus. </
s
>
<
s
xml:id
="
echoid-s1805
"
xml:space
="
preserve
">ergo
<
lb
/>
d b ſeſquialtera eſt ipſius b u. </
s
>
<
s
xml:id
="
echoid-s1806
"
xml:space
="
preserve
">eſt auté d b & </
s
>
<
s
xml:id
="
echoid-s1807
"
xml:space
="
preserve
">ipſius b k ſeſquialte
<
lb
/>
ra. </
s
>
<
s
xml:id
="
echoid-s1808
"
xml:space
="
preserve
">quare lineæ b u, b k inter ſe æ quales ſunt; </
s
>
<
s
xml:id
="
echoid-s1809
"
xml:space
="
preserve
">quod fieri non po-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0072-08
"
xlink:href
="
note-0072-08a
"
xml:space
="
preserve
">2. quinti.</
note
>
teſt. </
s
>
<
s
xml:id
="
echoid-s1810
"
xml:space
="
preserve
">restanguli igitur com ſectio a e i per punctum k tranſibit.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1811
"
xml:space
="
preserve
">quod demonstrare uolebamus.</
s
>
<
s
xml:id
="
echoid-s1812
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>