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
>
221
(201)
222
(202)
223
(203)
224
(204)
225
(205)
226
(206)
227
(207)
228
(208)
229
(209)
230
(210)
<
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
|<
<
(205)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div508
"
type
="
section
"
level
="
1
"
n
="
305
">
<
p
>
<
s
xml:id
="
echoid-s5052
"
xml:space
="
preserve
">
<
pb
o
="
205
"
file
="
0225
"
n
="
225
"
rhead
="
LIBER III.
"/>
ad quadratum, IM, ergo per conuerſionem rationis rectangulum,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0225-01
"
xlink:href
="
note-0225-01a
"
xml:space
="
preserve
">Ex 40. l. 1.
<
lb
/>
& ex eius
<
lb
/>
Scholio.</
note
>
<
figure
xlink:label
="
fig-0225-01
"
xlink:href
="
fig-0225-01a
"
number
="
138
">
<
image
file
="
0225-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0225-01
"/>
</
figure
>
HEB, .</
s
>
<
s
xml:id
="
echoid-s5053
"
xml:space
="
preserve
">i. </
s
>
<
s
xml:id
="
echoid-s5054
"
xml:space
="
preserve
">quadratum, BE, ad qua-
<
lb
/>
dratum, ME, (quod eſt exceſſus re
<
lb
/>
ctanguli, HEB, ſub rectangulum, H
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0225-02
"
xlink:href
="
note-0225-02a
"
xml:space
="
preserve
">5. 2. elem.</
note
>
MB,) erit vt quadratum, RM, ad ſui
<
lb
/>
reliquum, dempto quadrato, MI, ſed
<
lb
/>
vt quadratum, BE, ad quadratum, E
<
lb
/>
M, ita quadratum, BC, ideſt quadra-
<
lb
/>
tum, MR, ad quadratum, MN, quia
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0225-03
"
xlink:href
="
note-0225-03a
"
xml:space
="
preserve
">4. 6. elem.</
note
>
triangula, BEC, MEN, ſunt æquian-
<
lb
/>
gula; </
s
>
<
s
xml:id
="
echoid-s5055
"
xml:space
="
preserve
">ergo quadratum, BC, ideſt qua-
<
lb
/>
dratum, MR, ad quadratum, MN,
<
lb
/>
erit vt idem quadratum, MR, ad ſui
<
lb
/>
reliquum, dempto quadrato, MI, & </
s
>
<
s
xml:id
="
echoid-s5056
"
xml:space
="
preserve
">
<
lb
/>
eorum quadrupla .</
s
>
<
s
xml:id
="
echoid-s5057
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s5058
"
xml:space
="
preserve
">quadratum, SN, æquabitur reliquo quadrati,
<
lb
/>
VR, dempto quadrato, TI, quod erat oſtendendum.</
s
>
<
s
xml:id
="
echoid-s5059
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div510
"
type
="
section
"
level
="
1
"
n
="
306
">
<
head
xml:id
="
echoid-head323
"
xml:space
="
preserve
">COROLLARIV M.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s5060
"
xml:space
="
preserve
">_Q_VONIAM autem punctum, M, ſumptum eſt vtcumque hinc
<
lb
/>
patet, quod omnia quadrata trianguli, AEC, (regula, DF,)
<
lb
/>
æquantur reliquo omnium quadratorum parallelogrammi, AF, dem-
<
lb
/>
ptis omnibus quadratis ſemicirculi, vel ſemiellipſis, DBF, & </
s
>
<
s
xml:id
="
echoid-s5061
"
xml:space
="
preserve
">duabus
<
lb
/>
vtcunq; </
s
>
<
s
xml:id
="
echoid-s5062
"
xml:space
="
preserve
">ductis ipſis, DF, parallelis, vt, XG, VR, patet, quod om-
<
lb
/>
nia quadra@a trapezij, γSN℟, æquabuntur reſiduo omnium quadra-
<
lb
/>
torumpar allelogrammi, XR, demptis omnibus quadratis portionis ſe-
<
lb
/>
micirculi, vel ſemiellipſis inter, ZL, TI, concluſæ: </
s
>
<
s
xml:id
="
echoid-s5063
"
xml:space
="
preserve
">Quia verò oſten-
<
lb
/>
ſa eſtratio omnium quadratorum cuiuſuis parallelogrammorum in alti-
<
lb
/>
tudine eadem cum portionibus, baſi autem æquali ſecundæ diametre,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0225-04
"
xlink:href
="
note-0225-04a
"
xml:space
="
preserve
">_24, & 28._
<
lb
/>
_lib. 2._</
note
>
ad omnia quadrata trapeziorum, vel triangulorum in ijſdem exiſten-
<
lb
/>
tium, hine manifeſta eſt ratio eorundem ad dictareſidua, & </
s
>
<
s
xml:id
="
echoid-s5064
"
xml:space
="
preserve
">conſequen-
<
lb
/>
ter ad omnia quadrata portionum ſemicirculi, vel ſemiellipſis, DBF,
<
lb
/>
dictis parallelis interpoſitarum, vt ex. </
s
>
<
s
xml:id
="
echoid-s5065
"
xml:space
="
preserve
">gr. </
s
>
<
s
xml:id
="
echoid-s5066
"
xml:space
="
preserve
">nota erit ratio, quam babent
<
lb
/>
omnia quadrata parallelogrammi, XR, ad omnia quadrata portionis,
<
lb
/>
ZTIL, & </
s
>
<
s
xml:id
="
echoid-s5067
"
xml:space
="
preserve
">ſic in reliquis. </
s
>
<
s
xml:id
="
echoid-s5068
"
xml:space
="
preserve
">Quia verò omnia quadrata trianguli, AE
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0225-05
"
xlink:href
="
note-0225-05a
"
xml:space
="
preserve
">_F. Cor. 22_
<
lb
/>
_lib. 2._</
note
>
C, ad omnia quadrata trianguli, SEN, ſunt in tripla ratione ipſius,
<
lb
/>
BE, ad, EM, ideò etiam patebit, quod omnia quadrata parallelogram-
<
lb
/>
mi, AF, demptis omnibus quadratis ſemicirculi, vel ſemiellipſis, D
<
lb
/>
BF, ad omnia quadrata parallelogrammi, VF, demptis omnibus qua-
<
lb
/>
dratis fruſti, TDFR, ſint in tripla ratione ipſius, BE, ad, EM, ideſt
<
lb
/>
vt cubus, BE, ad cubum, EM.</
s
>
<
s
xml:id
="
echoid-s5069
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>