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
>
161
(131)
162
(132)
163
(133)
164
(134)
165
(135)
166
(163)
167
(137)
168
(138)
169
(139)
170
(140)
<
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
|<
<
(183)
of 450
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div484
"
type
="
section
"
level
="
1
"
n
="
177
">
<
p
>
<
s
xml:id
="
echoid-s7756
"
xml:space
="
preserve
">
<
pb
o
="
183
"
file
="
213
"
n
="
213
"
rhead
="
LIBER QVARTVS.
"/>
Octogoniæqualis, cadet punctumk, citra F, & </
s
>
<
s
xml:id
="
echoid-s7757
"
xml:space
="
preserve
">i, citra H, quod E T, minor ſit
<
lb
/>
ſemidiametro circuli, & </
s
>
<
s
xml:id
="
echoid-s7758
"
xml:space
="
preserve
">ambitus Octogoni minor peripheria eiuſdem circuli. </
s
>
<
s
xml:id
="
echoid-s7759
"
xml:space
="
preserve
">I-
<
lb
/>
gitur ducta recta ki, erit triangulum G k i, minus triangulo F G H, pars toto. </
s
>
<
s
xml:id
="
echoid-s7760
"
xml:space
="
preserve
">Eſt
<
lb
/>
autem triangulum k Gi, Octogono æquale: </
s
>
<
s
xml:id
="
echoid-s7761
"
xml:space
="
preserve
">quippe cum ex ſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s7762
"
xml:space
="
preserve
">41.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7763
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s7764
"
xml:space
="
preserve
">1, Euclid. </
s
>
<
s
xml:id
="
echoid-s7765
"
xml:space
="
preserve
">æquale ſit rectangulo ſub G k, & </
s
>
<
s
xml:id
="
echoid-s7766
"
xml:space
="
preserve
">ſemiſſe ipſius Gi, comprehenſo,
<
lb
/>
quod per propoſitionem 2. </
s
>
<
s
xml:id
="
echoid-s7767
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s7768
"
xml:space
="
preserve
">7. </
s
>
<
s
xml:id
="
echoid-s7769
"
xml:space
="
preserve
">de Iſoperimetris Octogono æquale eſt. </
s
>
<
s
xml:id
="
echoid-s7770
"
xml:space
="
preserve
">O-
<
lb
/>
ctogonum ergo minus eſt triangulo F G H. </
s
>
<
s
xml:id
="
echoid-s7771
"
xml:space
="
preserve
">Non ergo maius eſt: </
s
>
<
s
xml:id
="
echoid-s7772
"
xml:space
="
preserve
">ac proinde cir-
<
lb
/>
culus triangulo maius eſſe nequit.</
s
>
<
s
xml:id
="
echoid-s7773
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7774
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Sit</
emph
>
deinde, ſi fieri poteſt, circulus ABCD, minor quam triangulum FGH,
<
lb
/>
magnitudinez. </
s
>
<
s
xml:id
="
echoid-s7775
"
xml:space
="
preserve
">Circumſcribatur circulo quadratum IKL M, cuius latera cir-
<
lb
/>
culum tangantin punctis A, B, C, D. </
s
>
<
s
xml:id
="
echoid-s7776
"
xml:space
="
preserve
">quod maius erit triangulo FGH. </
s
>
<
s
xml:id
="
echoid-s7777
"
xml:space
="
preserve
">Cum
<
lb
/>
enim eius ambitus (vt lib. </
s
>
<
s
xml:id
="
echoid-s7778
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s7779
"
xml:space
="
preserve
">propoſ. </
s
>
<
s
xml:id
="
echoid-s7780
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s7781
"
xml:space
="
preserve
">probabimus) maior ſit peripheria circuli,
<
lb
/>
hoc eſt, recta G H, & </
s
>
<
s
xml:id
="
echoid-s7782
"
xml:space
="
preserve
">perpendicularis E A, ipſi F G, æqualis, erit triangulum re-
<
lb
/>
ctangulum latus vnum habens æqualeipſi F G, & </
s
>
<
s
xml:id
="
echoid-s7783
"
xml:space
="
preserve
">alterum maius latere GH, (æ-
<
lb
/>
quale nimirum ambitui quadrati I K L M.) </
s
>
<
s
xml:id
="
echoid-s7784
"
xml:space
="
preserve
">maius triangulo FGH. </
s
>
<
s
xml:id
="
echoid-s7785
"
xml:space
="
preserve
">Cum ergo
<
lb
/>
triangulum illud, per ſcholium propoſ. </
s
>
<
s
xml:id
="
echoid-s7786
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s7787
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s7788
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s7789
"
xml:space
="
preserve
">Euclid. </
s
>
<
s
xml:id
="
echoid-s7790
"
xml:space
="
preserve
">ſit æquale rectangulo
<
lb
/>
ſub FG, & </
s
>
<
s
xml:id
="
echoid-s7791
"
xml:space
="
preserve
">ſemiſſe ambitus quadrati IKLM, comprehenſo: </
s
>
<
s
xml:id
="
echoid-s7792
"
xml:space
="
preserve
">hoc autem rectan-
<
lb
/>
gulum per propoſ. </
s
>
<
s
xml:id
="
echoid-s7793
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s7794
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s7795
"
xml:space
="
preserve
">7. </
s
>
<
s
xml:id
="
echoid-s7796
"
xml:space
="
preserve
">de Iſoperimetris, qua drato IKLM, æquale; </
s
>
<
s
xml:id
="
echoid-s7797
"
xml:space
="
preserve
">erit quo-
<
lb
/>
que quadratum IKLM, maius triangulo F G H. </
s
>
<
s
xml:id
="
echoid-s7798
"
xml:space
="
preserve
">Et quia triangulum F G H, po-
<
lb
/>
nitur æquale circulo, & </
s
>
<
s
xml:id
="
echoid-s7799
"
xml:space
="
preserve
">magnitudini z. </
s
>
<
s
xml:id
="
echoid-s7800
"
xml:space
="
preserve
">ſimul, ac proinde maius quã z, erit quo-
<
lb
/>
que quadratum IKLM, (quod maius eſſe oſtendimus triangulo FGH,) maius,
<
lb
/>
quam z. </
s
>
<
s
xml:id
="
echoid-s7801
"
xml:space
="
preserve
">Siigitur ex quadrato IKLM, auferatur plus, quam dimidium, & </
s
>
<
s
xml:id
="
echoid-s7802
"
xml:space
="
preserve
">à reſi-
<
lb
/>
dio plus etiam quam dimidium, at queita deinceps, relin quetur tandem
<
note
symbol
="
a
"
position
="
right
"
xlink:label
="
note-213-01
"
xlink:href
="
note-213-01a
"
xml:space
="
preserve
">1. decimi.</
note
>
gnitudo minor, quam z.</
s
>
<
s
xml:id
="
echoid-s7803
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s7804
"
xml:space
="
preserve
">Hæc autem detractio continua fiet, ſi primo loco auferatur circul{us} A B C D: </
s
>
<
s
xml:id
="
echoid-s7805
"
xml:space
="
preserve
">Hic
<
lb
/>
<
figure
xlink:label
="
fig-213-01
"
xlink:href
="
fig-213-01a
"
number
="
135
">
<
image
file
="
213-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/213-01
"/>
</
figure
>
enim maior eſt ſemiſſe quadrati I K L M, propterea quod
<
lb
/>
quadratum inſcriptum (quod min{us} eſt circulo, pars toto)
<
lb
/>
ſemiſſis eſt quadrati circumſcripti, exſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s7806
"
xml:space
="
preserve
">9. </
s
>
<
s
xml:id
="
echoid-s7807
"
xml:space
="
preserve
">lib.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7808
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s7809
"
xml:space
="
preserve
">Euclid. </
s
>
<
s
xml:id
="
echoid-s7810
"
xml:space
="
preserve
">Quod ſi ducta recta E K, ſecante circulum in
<
lb
/>
O, ducatur per O, ad E K, perpendicularis V X, quæ
<
note
symbol
="
b
"
position
="
right
"
xlink:label
="
note-213-02
"
xlink:href
="
note-213-02a
"
xml:space
="
preserve
">16. tertij.</
note
>
culum tanget in O: </
s
>
<
s
xml:id
="
echoid-s7811
"
xml:space
="
preserve
">idemque fiat, ductis rectis EL, EM,
<
lb
/>
EI, &</
s
>
<
s
xml:id
="
echoid-s7812
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s7813
"
xml:space
="
preserve
">deſcriptum erit Octogonum a quilaterum, & </
s
>
<
s
xml:id
="
echoid-s7814
"
xml:space
="
preserve
">æ-
<
lb
/>
<
figure
xlink:label
="
fig-213-02
"
xlink:href
="
fig-213-02a
"
number
="
136
">
<
image
file
="
213-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/213-02
"/>
</
figure
>
quiangulũ VXY a b c d e V, vt conſtat ex conſtructione, demonſtratione propoſ. </
s
>
<
s
xml:id
="
echoid-s7815
"
xml:space
="
preserve
">12. </
s
>
<
s
xml:id
="
echoid-s7816
"
xml:space
="
preserve
">lib.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7817
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s7818
"
xml:space
="
preserve
">Eucl. </
s
>
<
s
xml:id
="
echoid-s7819
"
xml:space
="
preserve
">quippe cum ad E A, E O, & </
s
>
<
s
xml:id
="
echoid-s7820
"
xml:space
="
preserve
">adreliqu{as} ſemidiametros Octogoni inſcripti ductæ
<
lb
/>
ſint perpendiculares ve, V X, &</
s
>
<
s
xml:id
="
echoid-s7821
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s7822
"
xml:space
="
preserve
">Quoniã vero v A, v O, per 2. </
s
>
<
s
xml:id
="
echoid-s7823
"
xml:space
="
preserve
">coroll propoſ. </
s
>
<
s
xml:id
="
echoid-s7824
"
xml:space
="
preserve
">36. </
s
>
<
s
xml:id
="
echoid-s7825
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s7826
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s7827
"
xml:space
="
preserve
">Eucl. </
s
>
<
s
xml:id
="
echoid-s7828
"
xml:space
="
preserve
">
<
lb
/>
æqual{es} ſunt; </
s
>
<
s
xml:id
="
echoid-s7829
"
xml:space
="
preserve
"> & </
s
>
<
s
xml:id
="
echoid-s7830
"
xml:space
="
preserve
">eſt K V, maior quam v O: </
s
>
<
s
xml:id
="
echoid-s7831
"
xml:space
="
preserve
">erit quoque K V, maior quam v A, ideoque
<
note
symbol
="
c
"
position
="
right
"
xlink:label
="
note-213-03
"
xlink:href
="
note-213-03a
"
xml:space
="
preserve
">19. primi.</
note
>
& </
s
>
<
s
xml:id
="
echoid-s7832
"
xml:space
="
preserve
">triangulum K v O, triangulo v A O, mai{us} erit; </
s
>
<
s
xml:id
="
echoid-s7833
"
xml:space
="
preserve
"> cum ſit triangulum ad
<
note
symbol
="
d
"
position
="
right
"
xlink:label
="
note-213-04
"
xlink:href
="
note-213-04a
"
xml:space
="
preserve
">1. ſexti.</
note
>
vt baſis ad baſem. </
s
>
<
s
xml:id
="
echoid-s7834
"
xml:space
="
preserve
">Igitur triangulum K V O, mai{us} erit, quam dimidium </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>