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
|<
<
(15)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div61
"
type
="
section
"
level
="
1
"
n
="
51
">
<
p
>
<
s
xml:id
="
echoid-s537
"
xml:space
="
preserve
">
<
pb
o
="
15
"
file
="
0035
"
n
="
35
"
rhead
="
LIBER I.
"/>
tinget figuram, ABC, contingatin ſitu ipſius, FG, & </
s
>
<
s
xml:id
="
echoid-s538
"
xml:space
="
preserve
">in pun-
<
lb
/>
cto, A, igitur, A, erit vertex figuræ, ABC, reſpectu ipſius, B
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0035-01
"
xlink:href
="
note-0035-01a
"
xml:space
="
preserve
">A. Def. 1.</
note
>
C, à nobis inuentus, qui in huius Problematis priori parte inue-
<
lb
/>
niendus proponebatur.</
s
>
<
s
xml:id
="
echoid-s539
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s540
"
xml:space
="
preserve
">Sit nunc figura ſolida, ſiue ſolidum, ADE, in quo reſpectu
<
lb
/>
plani, BECD, ſit vertex inueniendus, ſumpto igitur exrra pla-
<
lb
/>
num figuræ, vtcumque puncto, N, per ipſum agatur planum, K
<
lb
/>
HVX, ipſi, BECD, æquidiſtans, quod vel continget ſolidum,
<
lb
/>
BAC, vel non, ſi autem non contingat, moueatur accedendo,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0035-02
"
xlink:href
="
note-0035-02a
"
xml:space
="
preserve
">Poſtul. 2.</
note
>
velrecedendo, à plano, BECD, tandem igitur contingetipſum,
<
lb
/>
tangatin, A, puncto, igitur punctum, A, erit vertex ſolidi, AD
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0035-03
"
xlink:href
="
note-0035-03a
"
xml:space
="
preserve
">A. Def. 2.</
note
>
E, reſpectu plani, BECD, qui inueniendus proponebatur.</
s
>
<
s
xml:id
="
echoid-s541
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div64
"
type
="
section
"
level
="
1
"
n
="
52
">
<
head
xml:id
="
echoid-head63
"
xml:space
="
preserve
">COROLLARIVM.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s542
"
xml:space
="
preserve
">_H_Inc manifeſtum eſt, ſi recta, BC, tangat planam figuram, AB
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0035-04
"
xlink:href
="
note-0035-04a
"
xml:space
="
preserve
">_B. Def. 1._</
note
>
C, quod ductæ erunt oppoſitę tangentes ipſius figuræ, ABC,
<
lb
/>
reſpectu datæ rectæ lineæ, quæ fuit vna ex eiſdem tangentibus, nem-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0035-05
"
xlink:href
="
note-0035-05a
"
xml:space
="
preserve
">_B. Def. 2._</
note
>
pè, BC; </
s
>
<
s
xml:id
="
echoid-s543
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s544
"
xml:space
="
preserve
">ita ſi figura, BDCE, tangit ſolidum, ADE, ducta erunt
<
lb
/>
oppoſita tangentia plana ſolidi, ADE, reſpectu plani, BECD, in
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0035-06
"
xlink:href
="
note-0035-06a
"
xml:space
="
preserve
">_A. Def. 2._</
note
>
quibus puncta contactuum erunt oppoſiti vertices earumdem figura-
<
lb
/>
rum, boc pacto inuenti: </
s
>
<
s
xml:id
="
echoid-s545
"
xml:space
="
preserve
">Siverò recta linea, BC, ſecaret figuran, A
<
lb
/>
BC, vel planum, BECD, ſecaret ſolidum, ADE, eodem pacto ex
<
lb
/>
alia parte lineæ, BC, vel plani, BDCE, inueniemus verticem, vn-
<
lb
/>
de inuenti erun@ propoſitæ figuræ planæ oppoſiti vertices, & </
s
>
<
s
xml:id
="
echoid-s546
"
xml:space
="
preserve
">ductæ op-
<
lb
/>
poſitæ tangentes reſpectu datæ lineæ BC; </
s
>
<
s
xml:id
="
echoid-s547
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s548
"
xml:space
="
preserve
">in ſolido iuuenti erunt
<
lb
/>
oppoſiti vertices, & </
s
>
<
s
xml:id
="
echoid-s549
"
xml:space
="
preserve
">ducta oppoſita tangentia plana reſpectu dati
<
lb
/>
plani, BDCE, quæ cum tangunt in figuris planis, figuræ contactuum
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0035-07
"
xlink:href
="
note-0035-07a
"
xml:space
="
preserve
">_C. Def. 2._</
note
>
vocantur etiam oppoſitæ baſes, & </
s
>
<
s
xml:id
="
echoid-s550
"
xml:space
="
preserve
">earum ſingulæ baſes, & </
s
>
<
s
xml:id
="
echoid-s551
"
xml:space
="
preserve
">baſes li-
<
lb
/>
neares, ſi contactus fieret in lineis: </
s
>
<
s
xml:id
="
echoid-s552
"
xml:space
="
preserve
">binc ergo diſcimus inuenire op-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0035-08
"
xlink:href
="
note-0035-08a
"
xml:space
="
preserve
">_A. B. Def._
<
lb
/>
_1. & 2._</
note
>
poſitos vertices figuræ planæ, vel ſolidæ cuiuſcumque, & </
s
>
<
s
xml:id
="
echoid-s553
"
xml:space
="
preserve
">eorum op-
<
lb
/>
poſita tangentia ducere reſpectu datæ in figura plana rectæ lineæ, & </
s
>
<
s
xml:id
="
echoid-s554
"
xml:space
="
preserve
">
<
lb
/>
dati plani par@ter in ſolida figura.</
s
>
<
s
xml:id
="
echoid-s555
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div66
"
type
="
section
"
level
="
1
"
n
="
53
">
<
head
xml:id
="
echoid-head64
"
xml:space
="
preserve
">PROBLEMA II. PROPOS. II.</
head
>
<
p
>
<
s
xml:id
="
echoid-s556
"
xml:space
="
preserve
">CVilibct figuræ planæ parallelogrammum circumſcri-
<
lb
/>
bere, cuius latera duabus datis rectis lineis, in pro-
<
lb
/>
poſitæ figuræ plano ſe ſecantibus, ſint parallela.</
s
>
<
s
xml:id
="
echoid-s557
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>