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
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 540
541 - 550
551 - 560
561 - 569
>
61
(41)
62
(42)
63
(43)
64
(44)
65
(45)
66
(46)
67
(47)
68
(48)
69
(49)
70
(50)
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 540
541 - 550
551 - 560
561 - 569
>
page
|<
<
(34)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div114
"
type
="
section
"
level
="
1
"
n
="
80
">
<
p
style
="
it
">
<
s
xml:id
="
echoid-s929
"
xml:space
="
preserve
">
<
pb
o
="
34
"
file
="
0054
"
n
="
54
"
rhead
="
GEOMETRIÆ
"/>
communem ſectionem borum duorum planorum fore intra figuram in,
<
lb
/>
conico productan à plano omnibus eiuſdem lateribus coincidente, vt
<
lb
/>
patet in conico, ACD qui ſecatur plano, ACD, & </
s
>
<
s
xml:id
="
echoid-s930
"
xml:space
="
preserve
">alio, BNEO,
<
lb
/>
quorum com nunis ſectio ſit, BE. </
s
>
<
s
xml:id
="
echoid-s931
"
xml:space
="
preserve
">Dico n. </
s
>
<
s
xml:id
="
echoid-s932
"
xml:space
="
preserve
">ſi, CD, ſit intra figuram, C
<
lb
/>
MDV, etiam, BE, fore intra figuram, BNEO, nam, ACVD, e§t
<
lb
/>
conicus, & </
s
>
<
s
xml:id
="
echoid-s933
"
xml:space
="
preserve
">quia latera non vniuntur, niſi in puncto, A, ideo, BOE,
<
lb
/>
eſt aliqua figura, vt etiam, BNE, & </
s
>
<
s
xml:id
="
echoid-s934
"
xml:space
="
preserve
">ideò, BE, cadit intra figuram,
<
lb
/>
BNEO.</
s
>
<
s
xml:id
="
echoid-s935
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div115
"
type
="
section
"
level
="
1
"
n
="
81
">
<
head
xml:id
="
echoid-head92
"
xml:space
="
preserve
">THEOREMA XV. PROPOS. XVIII.</
head
>
<
p
>
<
s
xml:id
="
echoid-s936
"
xml:space
="
preserve
">SI per verticem conici, & </
s
>
<
s
xml:id
="
echoid-s937
"
xml:space
="
preserve
">rectam tangentem eius baſim
<
lb
/>
extendatur planum, hoc tanget ipſum conicum in vna,
<
lb
/>
vel pluribus rectis lineis, quę erunt latera conici, velin pla-
<
lb
/>
no tranſeunte per eiuſdem latera, quod erit triangulum, ſiue
<
lb
/>
in plurib us triangulis.</
s
>
<
s
xml:id
="
echoid-s938
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s939
"
xml:space
="
preserve
">Sit conicus, cuius vertex, A, baſis, BCE, quam tangat recta,
<
lb
/>
DF, in puncto, vel punctis, ſiue in linea. </
s
>
<
s
xml:id
="
echoid-s940
"
xml:space
="
preserve
">Dico planum, ADF,
<
lb
/>
tangere dictum conicum in recta linea, ſiue in pluribus rectis lineis,
<
lb
/>
ſiue in plano, quod erit triangulum per eiuſdem latera tranſiens.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s941
"
xml:space
="
preserve
">
<
figure
xlink:label
="
fig-0054-01
"
xlink:href
="
fig-0054-01a
"
number
="
27
">
<
image
file
="
0054-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0054-01
"/>
</
figure
>
Tangat igitur, DF, figuram, BCE,
<
lb
/>
in puncto, B, & </
s
>
<
s
xml:id
="
echoid-s942
"
xml:space
="
preserve
">iungatur, AB, perq;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s943
"
xml:space
="
preserve
">AB, &</
s
>
<
s
xml:id
="
echoid-s944
"
xml:space
="
preserve
">, DF, dictum ſit extenſum pla-
<
lb
/>
num, ergo, AB, erit latus conici, A
<
lb
/>
CE, nam latus, quod reuoluitur tran-
<
lb
/>
ſiens per, B, congruit rectę, AB, alio-
<
lb
/>
quin duæ rectæ lineæ clauderent ſuper-
<
lb
/>
ficiem, eſt ergo, AB, in ſuperficie co-
<
lb
/>
niculari, eſt etiam in plano per, A, &</
s
>
<
s
xml:id
="
echoid-s945
"
xml:space
="
preserve
">,
<
lb
/>
DF, tranſeunte, ergo, AB, eſt com-
<
lb
/>
munis tum ſuperſiciei coniculari, tum
<
lb
/>
plano per, A, &</
s
>
<
s
xml:id
="
echoid-s946
"
xml:space
="
preserve
">, DF, ducto, nullus
<
lb
/>
autem punctus rectę, AB, eſt intra ſu-
<
lb
/>
perſiciem cylindraceam, ergo planum
<
lb
/>
per, AB, DF, ductum tangit conicum
<
lb
/>
in recta, AB: </
s
>
<
s
xml:id
="
echoid-s947
"
xml:space
="
preserve
">Eodem pacto oſtendemus idem tangere conicum in
<
lb
/>
quibuſuis alijs lateribus, quæ ducuntur à punctis contactus rectæ li-
<
lb
/>
neæ, DF, qui fi ſint plures, fit etiam contactus in omnibus lineis,
<
lb
/>
fi vero contactus rectæ, DF, fiat in recta linea tunc contactus plani
<
lb
/>
per, AB, DF, fit in ſingulis rectis lineis, quæ à recta talis </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>