Clavius, Christoph
,
Geometria practica
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
>
231
(201)
232
(202)
233
(203)
234
(204)
235
(205)
236
(206)
237
(207)
238
(208)
239
(209)
240
(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
>
page
|<
<
(206)
of 450
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div558
"
type
="
section
"
level
="
1
"
n
="
204
">
<
p
>
<
s
xml:id
="
echoid-s9217
"
xml:space
="
preserve
">
<
pb
o
="
206
"
file
="
236
"
n
="
236
"
rhead
="
GEOMETR. PRACT.
"/>
ſunt & </
s
>
<
s
xml:id
="
echoid-s9218
"
xml:space
="
preserve
">æqualia, & </
s
>
<
s
xml:id
="
echoid-s9219
"
xml:space
="
preserve
">ſimilia, & </
s
>
<
s
xml:id
="
echoid-s9220
"
xml:space
="
preserve
">parallela; </
s
>
<
s
xml:id
="
echoid-s9221
"
xml:space
="
preserve
">alia verò parallelogramma. </
s
>
<
s
xml:id
="
echoid-s9222
"
xml:space
="
preserve
">Vt eſt ſo-
<
lb
/>
lidum ADF, cuius baſes ſunt pentagona ABCDE, FGHIK, parallela, & </
s
>
<
s
xml:id
="
echoid-s9223
"
xml:space
="
preserve
">æqua-
<
lb
/>
lia. </
s
>
<
s
xml:id
="
echoid-s9224
"
xml:space
="
preserve
">Hanc figuram ſolidam repræſentat columna aliqua laterata æqualis craſsi-
<
lb
/>
tudinis, cuiu, baſes oppoſitæ ſunt æquales, ſimiles, ac parallelę, ſiue hæ triangu-
<
lb
/>
la ſint, ſiue quadrangula, ſiue pentagona, &</
s
>
<
s
xml:id
="
echoid-s9225
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s9226
"
xml:space
="
preserve
">Ex quo fit, vt priſma quodcun-
<
lb
/>
que ambiant tot parallelo gramma, quot latera, vel anguli in vnoquo que op-
<
lb
/>
poſitorum planorum reperiuntur. </
s
>
<
s
xml:id
="
echoid-s9227
"
xml:space
="
preserve
">Vt propoſitum priſma ambiunt quinque
<
lb
/>
parallelogramma ABGF, BCHG, CDIH, DEKI, EAFK. </
s
>
<
s
xml:id
="
echoid-s9228
"
xml:space
="
preserve
">Area porro cuiusli-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-236-01
"
xlink:href
="
note-236-01a
"
xml:space
="
preserve
">Area priſma-
<
lb
/>
tis, tam recti,
<
lb
/>
quam obliqui.</
note
>
bet priſmatis inuenietur, ſi area baſis inquiratur, atque in altitudinem ducatur.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s9229
"
xml:space
="
preserve
">Nam ſi concipiatur parallelepipedum eiuſdem
<
lb
/>
<
figure
xlink:label
="
fig-236-01
"
xlink:href
="
fig-236-01a
"
number
="
152
">
<
image
file
="
236-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/236-01
"/>
</
figure
>
altitudinis cum priſmate, habens baſem, rectan-
<
lb
/>
gulũ baſi priſmatis æquale; </
s
>
<
s
xml:id
="
echoid-s9230
"
xml:space
="
preserve
"> erit hoc
<
note
symbol
="
a
"
position
="
left
"
xlink:label
="
note-236-02
"
xlink:href
="
note-236-02a
"
xml:space
="
preserve
">2. coroll. 7.
<
lb
/>
duodec.</
note
>
pipedum priſmati ęquale. </
s
>
<
s
xml:id
="
echoid-s9231
"
xml:space
="
preserve
">Cũ ergo parallelepi-
<
lb
/>
pedũ producatur ex ſua baſe in altitudinem,
<
lb
/>
procreabitur quoque priſma ex multiplicatio-
<
lb
/>
ne ſuę baſis in altitudinem. </
s
>
<
s
xml:id
="
echoid-s9232
"
xml:space
="
preserve
">Area porro baſis
<
lb
/>
cognoſcetur ex iis, quæ lib. </
s
>
<
s
xml:id
="
echoid-s9233
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s9234
"
xml:space
="
preserve
">ſcrip ſimus, & </
s
>
<
s
xml:id
="
echoid-s9235
"
xml:space
="
preserve
">altitudo priſmatis, ſi eius latera re-
<
lb
/>
cta non ſint ad baſem, exploranda
<
unsure
/>
erit, vt cap. </
s
>
<
s
xml:id
="
echoid-s9236
"
xml:space
="
preserve
">præcedente Num. </
s
>
<
s
xml:id
="
echoid-s9237
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s9238
"
xml:space
="
preserve
">altitudinem
<
lb
/>
parallelepidi inueſtigandam eſſe præ@p
<
unsure
/>
imus.</
s
>
<
s
xml:id
="
echoid-s9239
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s9240
"
xml:space
="
preserve
">5. </
s
>
<
s
xml:id
="
echoid-s9241
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Cylindrvs</
emph
>
eſt figura ſolida æqualis craſsitiei, quæ duobus circulis
<
lb
/>
æqualibus, & </
s
>
<
s
xml:id
="
echoid-s9242
"
xml:space
="
preserve
">æquidiſtantibus, & </
s
>
<
s
xml:id
="
echoid-s9243
"
xml:space
="
preserve
">rotunda ſuperficie inter ipſos interiecta con-
<
lb
/>
tinetur, inſtar columnę cuiuſpiam rotundæ. </
s
>
<
s
xml:id
="
echoid-s9244
"
xml:space
="
preserve
">Vt eſt ſolidum A C H, cuius baſes
<
lb
/>
ſunt duo circuli ABCD, EFGH, paralleli, & </
s
>
<
s
xml:id
="
echoid-s9245
"
xml:space
="
preserve
">æquales. </
s
>
<
s
xml:id
="
echoid-s9246
"
xml:space
="
preserve
">Huius quo que area pro-
<
lb
/>
creabitur ex multiplicatione baſis, ex cap. </
s
>
<
s
xml:id
="
echoid-s9247
"
xml:space
="
preserve
">7. </
s
>
<
s
xml:id
="
echoid-s9248
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s9249
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s9250
"
xml:space
="
preserve
">inuentę in altitudinem.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s9251
"
xml:space
="
preserve
">quod in Cylindro recto explicabitur, vt Num. </
s
>
<
s
xml:id
="
echoid-s9252
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s9253
"
xml:space
="
preserve
">in parallelepipedo recto fa-
<
lb
/>
ctum eſt. </
s
>
<
s
xml:id
="
echoid-s9254
"
xml:space
="
preserve
">Nam ſi verbi gratia baſis Cylindri circularis ABCD, continet 10. </
s
>
<
s
xml:id
="
echoid-s9255
"
xml:space
="
preserve
">pal-
<
lb
/>
mos quadratos, explebunt 10. </
s
>
<
s
xml:id
="
echoid-s9256
"
xml:space
="
preserve
">cubi palmares ſupra illos 10. </
s
>
<
s
xml:id
="
echoid-s9257
"
xml:space
="
preserve
">palmos quadratos
<
lb
/>
extructi, Cylindrum vſque ad primum palmum altitudinis; </
s
>
<
s
xml:id
="
echoid-s9258
"
xml:space
="
preserve
">at 20. </
s
>
<
s
xml:id
="
echoid-s9259
"
xml:space
="
preserve
">cubi eundem
<
lb
/>
explebunt vſque ad ſecundum palmum, &</
s
>
<
s
xml:id
="
echoid-s9260
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s9261
"
xml:space
="
preserve
">Quod ſi Cylindrus obliquus ſit,
<
lb
/>
exquirenda erit eius altitudo per lineam perpendicularem ex ſuperiore baſe de-
<
lb
/>
miſſam ad planum, in quo inferior baſis exiſtit, atque in hanc altitudinem area
<
lb
/>
baſis ex cap. </
s
>
<
s
xml:id
="
echoid-s9262
"
xml:space
="
preserve
">7. </
s
>
<
s
xml:id
="
echoid-s9263
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s9264
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s9265
"
xml:space
="
preserve
">inuenta multiplicanda. </
s
>
<
s
xml:id
="
echoid-s9266
"
xml:space
="
preserve
">Productus enim numerus dabit
<
lb
/>
aream Cylindri propoſiti, cum æqualis ſit Cylindro recto eandem cum
<
note
symbol
="
b
"
position
="
left
"
xlink:label
="
note-236-03
"
xlink:href
="
note-236-03a
"
xml:space
="
preserve
">coroll. 11.
<
lb
/>
duodec.</
note
>
baſem, & </
s
>
<
s
xml:id
="
echoid-s9267
"
xml:space
="
preserve
">altitudinem habenti.</
s
>
<
s
xml:id
="
echoid-s9268
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div565
"
type
="
section
"
level
="
1
"
n
="
205
">
<
head
xml:id
="
echoid-head219
"
xml:space
="
preserve
">DE AREA PYRAMIDVM
<
lb
/>
& Conorum.</
head
>
<
head
xml:id
="
echoid-head220
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Capvt</
emph
>
II.</
head
>
<
p
>
<
s
xml:id
="
echoid-s9269
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s9270
"
xml:space
="
preserve
">
<
emph
style
="
sc
">PYramis</
emph
>
eſt figura ſolida, quę planis continetur ab vno plano ad
<
note
symbol
="
c
"
position
="
left
"
xlink:label
="
note-236-04
"
xlink:href
="
note-236-04a
"
xml:space
="
preserve
">defin. 12.
<
lb
/>
vndec.</
note
>
num punctum conſtituta. </
s
>
<
s
xml:id
="
echoid-s9271
"
xml:space
="
preserve
">Vt figura ſolida A B C D E F, ad punctum
<
lb
/>
F, conſtituta ſupra baſem pentagonam A B C D E, & </
s
>
<
s
xml:id
="
echoid-s9272
"
xml:space
="
preserve
">quam </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>