Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of Notes
<
1 - 8
[out of range]
>
[Note]
Page: 50
[Note]
Page: 50
[Note]
Page: 50
[Note]
Page: 50
[Note]
Page: 51
[Note]
Page: 51
[Note]
Page: 53
[Note]
Page: 55
[Note]
Page: 55
[Note]
Page: 55
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 57
[Note]
Page: 57
[Note]
Page: 58
[Note]
Page: 58
[Note]
Page: 59
[Note]
Page: 59
[Note]
Page: 59
[Note]
Page: 60
[Note]
Page: 60
[Note]
Page: 61
[Note]
Page: 61
[Note]
Page: 61
[Note]
Page: 61
[Note]
Page: 61
[Note]
Page: 62
[Note]
Page: 63
<
1 - 8
[out of range]
>
page
|<
<
(41)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div128
"
type
="
section
"
level
="
1
"
n
="
89
">
<
p
>
<
s
xml:id
="
echoid-s1093
"
xml:space
="
preserve
">
<
pb
o
="
41
"
file
="
0061
"
n
="
61
"
rhead
="
LIBERI.
"/>
vt incidentes) ynde etiam figuræ eſſent æquales, & </
s
>
<
s
xml:id
="
echoid-s1094
"
xml:space
="
preserve
">ſi minores, etiam
<
lb
/>
ipſa figura, TDF, eſſet minor figura, BVO, contra ſuppoſitum,
<
lb
/>
eſtigitur, DC, maior ipſa, BR, eſt autem, vt, DC, ad, BR, ita,
<
lb
/>
PH, ad, NK, nam vt, DG, ad, BM, itaeſt, PH, ad, NK, & </
s
>
<
s
xml:id
="
echoid-s1095
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-01
"
xlink:href
="
note-0061-01a
"
xml:space
="
preserve
">A. Defin.
<
lb
/>
10.</
note
>
etiamita, CG, ad, RM, ergo reliqua, DC, ad reliquam, BR,
<
lb
/>
erit vt, PH, ad, NK, ſic etiam eſſe oſtendemus, EF, ad, IO, vt,
<
lb
/>
PH, ad, NK, & </
s
>
<
s
xml:id
="
echoid-s1096
"
xml:space
="
preserve
">quia, DC, eſt maior ipſa, BR, vel, EF, ipſa,
<
lb
/>
IO, ideò, HP, erit maior, KN, ſi igitur iunxerimus puncta, PN,
<
lb
/>
HK, ipſæ, PN, HK, ſi producantur ad partes ipſius, NK, con-
<
lb
/>
current, vt in, A. </
s
>
<
s
xml:id
="
echoid-s1097
"
xml:space
="
preserve
">Dico, A, eſſe verticem conici, cuius eſt baſis ipſa,
<
lb
/>
<
figure
xlink:label
="
fig-0061-01
"
xlink:href
="
fig-0061-01a
"
number
="
30
">
<
image
file
="
0061-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0061-01
"/>
</
figure
>
TDF, & </
s
>
<
s
xml:id
="
echoid-s1098
"
xml:space
="
preserve
">explano ipſi,
<
lb
/>
TDF, ęquidiſtanter du-
<
lb
/>
cto eſt in ipſo concepta
<
lb
/>
figura, VBO. </
s
>
<
s
xml:id
="
echoid-s1099
"
xml:space
="
preserve
">Quia er-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-02
"
xlink:href
="
note-0061-02a
"
xml:space
="
preserve
">4. Sexti
<
lb
/>
Elem.</
note
>
go, NK, eſt parallela
<
lb
/>
ipſi, PH, erunt triangu-
<
lb
/>
la, ANK, APH, ęqui-
<
lb
/>
angula, & </
s
>
<
s
xml:id
="
echoid-s1100
"
xml:space
="
preserve
">circa æquales
<
lb
/>
angulos latera propor-
<
lb
/>
tionalia, igitur, HP, ad,
<
lb
/>
PA, erit vt, KN, ad, N
<
lb
/>
A, &</
s
>
<
s
xml:id
="
echoid-s1101
"
xml:space
="
preserve
">, permutando, H
<
lb
/>
P, ad, NK, erit vt, PA,
<
lb
/>
ad, AN, vt autem, PH,
<
lb
/>
ad, NK, ita eſt, PG, ad, NM, nam ipſa, HP, KN, ſimiliter
<
lb
/>
ſunt diuiſæ in punctis, G, M, ergo, PA, ad, AN, erit vt, PG,
<
lb
/>
ad, NM, & </
s
>
<
s
xml:id
="
echoid-s1102
"
xml:space
="
preserve
">ſunt parallelæ ipſæ, PG, NM, ergo puncta, G, M,
<
lb
/>
A, erunt in vna recta linea, ſit illa, AG, igitur, vt, PG, ad, NM,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-03
"
xlink:href
="
note-0061-03a
"
xml:space
="
preserve
">Ex Lem-
<
lb
/>
mate leq.</
note
>
vel, PH, ad, NK, ita erit, GA, ad, AM, eſt autem, PH, ad,
<
lb
/>
NK, vt, FG, ad, OM, & </
s
>
<
s
xml:id
="
echoid-s1103
"
xml:space
="
preserve
">vt, EG, ad, IM, & </
s
>
<
s
xml:id
="
echoid-s1104
"
xml:space
="
preserve
">tandem, vt, D
<
lb
/>
G, ad, BM, ergo, vt, GA, ad, AM, ita erit, FG, ad, OM; </
s
>
<
s
xml:id
="
echoid-s1105
"
xml:space
="
preserve
">E
<
lb
/>
G, ad, IM; </
s
>
<
s
xml:id
="
echoid-s1106
"
xml:space
="
preserve
">CG, ad, RM; </
s
>
<
s
xml:id
="
echoid-s1107
"
xml:space
="
preserve
">&</
s
>
<
s
xml:id
="
echoid-s1108
"
xml:space
="
preserve
">, DG, ad, BM, ergo, cum ſint
<
lb
/>
parallelæ, erunt tum puncta, AOF, tum, AIE, ARC, tum etiam,
<
lb
/>
ABD, in vna recta linea, extendantur ergo dictæ rectæ lineæ, quę
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-04
"
xlink:href
="
note-0061-04a
"
xml:space
="
preserve
">Ex Lem-
<
lb
/>
mate leq.</
note
>
erunt, AF, AE, AD, AC. </
s
>
<
s
xml:id
="
echoid-s1109
"
xml:space
="
preserve
">Eodem modo, ſi per duas quaslibet
<
lb
/>
homologas figurarum, VBO, TDF, planum extendamus, fiet in
<
lb
/>
cæteris demonſtratio; </
s
>
<
s
xml:id
="
echoid-s1110
"
xml:space
="
preserve
">igitur ſi ſumantur in ambitu figurę, TDF,
<
lb
/>
quęcumq; </
s
>
<
s
xml:id
="
echoid-s1111
"
xml:space
="
preserve
">puncta, quę iungantur cum puncto, A, ſemper iungen-
<
lb
/>
tes tranſibunt per circuitum figuræ, VBO, ergo figurę, TDF, &</
s
>
<
s
xml:id
="
echoid-s1112
"
xml:space
="
preserve
">,
<
lb
/>
VBO, erunt fruſti conici oppoſitę baſes, quod à conico, ATDF,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0061-05
"
xlink:href
="
note-0061-05a
"
xml:space
="
preserve
">Defin. 4.</
note
>
abſcinditur per figuram, VBO, quod erat demonſtrandum.</
s
>
<
s
xml:id
="
echoid-s1113
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>