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
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
451 - 480
481 - 510
511 - 540
541 - 569
>
Scan
Original
21
1
22
2
23
3
24
4
25
5
26
6
27
7
28
8
29
9
30
10
31
11
32
12
33
13
34
14
35
15
36
16
37
17
38
18
39
19
40
20
41
21
42
22
43
23
44
24
45
25
46
26
47
27
48
28
49
29
50
30
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
451 - 480
481 - 510
511 - 540
541 - 569
>
page
|<
<
(26)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div93
"
type
="
section
"
level
="
1
"
n
="
68
">
<
p
>
<
s
xml:id
="
echoid-s753
"
xml:space
="
preserve
">
<
pb
o
="
26
"
file
="
0046
"
n
="
46
"
rhead
="
GEOMETRIÆ
"/>
ductæ, reperitur tamen earumdem portiones, quæiacent inter ip-
<
lb
/>
ſas, GL, BF, ex eadem parte, eodem ordine ſumptas, eſſe, vtip-
<
lb
/>
ſas, BF, GL, nam quia, DK, eſt æqualis ipſi, HN, &</
s
>
<
s
xml:id
="
echoid-s754
"
xml:space
="
preserve
">, BF, ipſi,
<
lb
/>
GL, vt, BF, ad, GL, ita eſt, DK, ad, HN, & </
s
>
<
s
xml:id
="
echoid-s755
"
xml:space
="
preserve
">ita eſſe oſtende-
<
lb
/>
mus, DE, ad, HM, DC, ad, HI, &</
s
>
<
s
xml:id
="
echoid-s756
"
xml:space
="
preserve
">, DP, ad, HO, nam iſtæ
<
lb
/>
ſunt æquales. </
s
>
<
s
xml:id
="
echoid-s757
"
xml:space
="
preserve
">Idem demonſtrabitur in cæteris, quæ ſimiliter ad ean-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0046-01
"
xlink:href
="
note-0046-01a
"
xml:space
="
preserve
">Def.10.</
note
>
dem partem diuidunt ipſas, BF, GL, igitur figuræ, APK, ZON,
<
lb
/>
ſunt ſimiles: </
s
>
<
s
xml:id
="
echoid-s758
"
xml:space
="
preserve
">Et quia earum homologæ, tum, PC, OI, tum, EK,
<
lb
/>
MN, ſunt ęquales, quod etiam de cæteris oſtendetur eodem pacto,
<
lb
/>
ſunt enim ſemper parallelogrammorum oppoſita latera, ideò figu-
<
lb
/>
ræ, APK, ZON, nedum erunt ſimiles, ſed etiam æquales, & </
s
>
<
s
xml:id
="
echoid-s759
"
xml:space
="
preserve
">re-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0046-02
"
xlink:href
="
note-0046-02a
"
xml:space
="
preserve
">Aequales
<
lb
/>
homolo-
<
lb
/>
gas argue
<
lb
/>
reęquales
<
lb
/>
ſimiles fi-
<
lb
/>
guras, &è
<
lb
/>
contra,
<
lb
/>
patebit
<
lb
/>
infra in
<
lb
/>
Cor.25.
<
lb
/>
huius, ab
<
lb
/>
hac inde
<
lb
/>
pendẽter.
<
lb
/>
D. Defin.
<
lb
/>
10.</
note
>
gulæ homologarum erunt ipſæ oppoſitæ tangentes, & </
s
>
<
s
xml:id
="
echoid-s760
"
xml:space
="
preserve
">ipſę, BF, G
<
lb
/>
L, earum incidentes. </
s
>
<
s
xml:id
="
echoid-s761
"
xml:space
="
preserve
">Quia verò figuræ, APK, ZON, ſunt in pla-
<
lb
/>
nis æquidiſtantibus ita conſtitutæ, vt earum incidentes ſint paralle-
<
lb
/>
læ, & </
s
>
<
s
xml:id
="
echoid-s762
"
xml:space
="
preserve
">homologæ figurarum, ZON, APK, ſunt ad eandem par-
<
lb
/>
tem incidentium poſitę, & </
s
>
<
s
xml:id
="
echoid-s763
"
xml:space
="
preserve
">item homologæ partes incidentium, B
<
lb
/>
F, GL, vt ipſæ, BD, GH, ſunt ad eandem partem pariter conſti-
<
lb
/>
tutæ, ideò figuræ, APK, ZON, nedum erunt ſimiles, & </
s
>
<
s
xml:id
="
echoid-s764
"
xml:space
="
preserve
">æqua-
<
lb
/>
les, ſed etiam ſimiliter poſitæ, quod oſtendere opus erat.</
s
>
<
s
xml:id
="
echoid-s765
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div95
"
type
="
section
"
level
="
1
"
n
="
69
">
<
head
xml:id
="
echoid-head80
"
xml:space
="
preserve
">COROLLARIV M.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s766
"
xml:space
="
preserve
">_M_Anifeſtum eſt autem, quia plana oppoſita tangentia cylindrici,
<
lb
/>
PN, ducta ſunt vtcumque, & </
s
>
<
s
xml:id
="
echoid-s767
"
xml:space
="
preserve
">eorum, & </
s
>
<
s
xml:id
="
echoid-s768
"
xml:space
="
preserve
">oppoſitarum baſium
<
lb
/>
productarum communes ſectiones ſunt regulæ homologarum earumdem,
<
lb
/>
quod ſi duxerimus duo alia oppoſita tangentia plana, habebimus etiam
<
lb
/>
earumdem figurarum homologas, regulis adbuc communibus ſectionibus
<
lb
/>
horum tangentium planorum poſtremò ductorum, & </
s
>
<
s
xml:id
="
echoid-s769
"
xml:space
="
preserve
">earumdem baſium
<
lb
/>
productarum, quæ communes ſectiones cum primò dictis angulos æqua-
<
lb
/>
les continebunt, nam quæ exiſtent ex. </
s
>
<
s
xml:id
="
echoid-s770
"
xml:space
="
preserve
">gr. </
s
>
<
s
xml:id
="
echoid-s771
"
xml:space
="
preserve
">in plano figuræ, APK, erunt
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0046-03
"
xlink:href
="
note-0046-03a
"
xml:space
="
preserve
">_10. Vnde-_
<
lb
/>
_cimi Ele._</
note
>
parallelæ exiſtentibus in plano figuræ, ZON, igitur in oppoſitis cylin-
<
lb
/>
dricorumbaſibus homologas babebimus etiam cum quibuſuis rectis lineis
<
lb
/>
æquales angulos cum duabus quibuſuis homologarum earumdem inuen-
<
lb
/>
tis regulis continentibus, quæ igitur cum regulis homologarum oppoſi-
<
lb
/>
tarum baſium cylindrici angulos ad eandem partem continent æquales,
<
lb
/>
ſunt & </
s
>
<
s
xml:id
="
echoid-s772
"
xml:space
="
preserve
">ipſæ homologarum earumdem regulæ, neonon earundem oppoſi-
<
lb
/>
tarum baſium, & </
s
>
<
s
xml:id
="
echoid-s773
"
xml:space
="
preserve
">oppoſitarum tangentium æquè ad prædictas inclinata-
<
lb
/>
rum, etiam incidentes licebit, vt ſupra, inuenire.</
s
>
<
s
xml:id
="
echoid-s774
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>