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
>
341
(311)
342
(312)
343
(313)
344
(314)
345
(315)
346
(316)
347
(317)
348
(318)
349
(319)
350
(320)
<
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
|<
<
(317)
of 450
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div907
"
type
="
section
"
level
="
1
"
n
="
318
">
<
pb
o
="
317
"
file
="
347
"
n
="
347
"
rhead
="
LIBER SEPTIMVS.
"/>
<
p
>
<
s
xml:id
="
echoid-s14854
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Sit</
emph
>
hexagonum datum A, æquilaterum quidem, ſed non æquiangulum, ita
<
lb
/>
vt B, ad latus quadrati illi æqualis inuentum maius non ſit ſemiſſe,
<
note
symbol
="
a
"
position
="
right
"
xlink:label
="
note-347-01
"
xlink:href
="
note-347-01a
"
xml:space
="
preserve
">14. ſecundi.</
note
>
ambitus hexagoni. </
s
>
<
s
xml:id
="
echoid-s14855
"
xml:space
="
preserve
">Sumpta ergo recta C D, æquali ſemiſsi ambitus hexagoni;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s14856
"
xml:space
="
preserve
">erit B, recta non maior ſemiſſe ipſius C D, ſed vel æqualis, vel minor. </
s
>
<
s
xml:id
="
echoid-s14857
"
xml:space
="
preserve
"> Secta
<
note
symbol
="
b
"
position
="
right
"
xlink:label
="
note-347-02
"
xlink:href
="
note-347-02a
"
xml:space
="
preserve
">ſchol. 13.
<
lb
/>
ſexti.</
note
>
tem CD, in E, ita vt B, ſit media proportionalis inter ſegmenta DE, EC, fiatre-
<
lb
/>
ctangulum E G, contentum ſub ſegmentis D E, E C. </
s
>
<
s
xml:id
="
echoid-s14858
"
xml:space
="
preserve
">Dico rectangulum E G,
<
lb
/>
æquale eſſe, & </
s
>
<
s
xml:id
="
echoid-s14859
"
xml:space
="
preserve
">iſoperimetrum hexagono A. </
s
>
<
s
xml:id
="
echoid-s14860
"
xml:space
="
preserve
">Quoniam enim tres D E, B, E C,
<
lb
/>
continuè proportionales ſunt; </
s
>
<
s
xml:id
="
echoid-s14861
"
xml:space
="
preserve
"> erit rectangulum E G, quadrato B, id eſt,
<
note
symbol
="
c
"
position
="
right
"
xlink:label
="
note-347-03
"
xlink:href
="
note-347-03a
"
xml:space
="
preserve
">17. ſexti.</
note
>
xagono A, æquale. </
s
>
<
s
xml:id
="
echoid-s14862
"
xml:space
="
preserve
">Et quia duo latera DE, EF, æqualia ſunt rectæ CD, hoc eſt,
<
lb
/>
ſemiſsi ambitus hexagoni A, ideo que reliquæ duæ FG, GD, alteri ſemiſsi: </
s
>
<
s
xml:id
="
echoid-s14863
"
xml:space
="
preserve
">@erit
<
lb
/>
totum rectangulum E G, hexagono A, iſoperimetrum. </
s
>
<
s
xml:id
="
echoid-s14864
"
xml:space
="
preserve
">Dato ergo rectilineo
<
lb
/>
parallelogrammum rectangulum ęquale, & </
s
>
<
s
xml:id
="
echoid-s14865
"
xml:space
="
preserve
">iſo perimetrum conſtituimus: </
s
>
<
s
xml:id
="
echoid-s14866
"
xml:space
="
preserve
">quod
<
lb
/>
erat faciendum.</
s
>
<
s
xml:id
="
echoid-s14867
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div909
"
type
="
section
"
level
="
1
"
n
="
319
">
<
head
xml:id
="
echoid-head346
"
xml:space
="
preserve
">SCHOLIVM.</
head
>
<
figure
number
="
239
">
<
image
file
="
347-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/347-01
"/>
</
figure
>
<
p
>
<
s
xml:id
="
echoid-s14868
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Qvod</
emph
>
ſi B, latus quadrati foret maius ſemiſſe di-
<
lb
/>
midij ambitus rectilinei A, hoc eſt, maius recta CD,
<
lb
/>
non poſſet C D, ita ſecari, vt B, eſſet medio loco pro-
<
lb
/>
portionalis inter ſegmenta, vt liquidò conſtat.</
s
>
<
s
xml:id
="
echoid-s14869
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s14870
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Iam</
emph
>
verò ſi ſumatur punctum H, inter C, & </
s
>
<
s
xml:id
="
echoid-s14871
"
xml:space
="
preserve
">E,
<
lb
/>
vtcunque; </
s
>
<
s
xml:id
="
echoid-s14872
"
xml:space
="
preserve
">erit rectangulum ſub D H, H C, adhuc
<
lb
/>
iſoperimetrum figuræ A, ſed tamen minus. </
s
>
<
s
xml:id
="
echoid-s14873
"
xml:space
="
preserve
">Si verò ac-
<
lb
/>
cipiatur punctum I, vtcunque inter E, & </
s
>
<
s
xml:id
="
echoid-s14874
"
xml:space
="
preserve
">L, punctum
<
lb
/>
medium rectæ C D; </
s
>
<
s
xml:id
="
echoid-s14875
"
xml:space
="
preserve
">erit adhuc rectangulum ſub D I,
<
lb
/>
I C, figuræ A, iſoperimetrum, maius tamen. </
s
>
<
s
xml:id
="
echoid-s14876
"
xml:space
="
preserve
">Sic et-
<
lb
/>
iam quadratum ſemiſsis D L, erit iſo perimetrum ei-
<
lb
/>
dem figuræ & </
s
>
<
s
xml:id
="
echoid-s14877
"
xml:space
="
preserve
">maius; </
s
>
<
s
xml:id
="
echoid-s14878
"
xml:space
="
preserve
">quæ omnia demonſtrabun-
<
lb
/>
tur, vt in ſcholio præcedentis problematis dictum
<
lb
/>
eſt.</
s
>
<
s
xml:id
="
echoid-s14879
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div910
"
type
="
section
"
level
="
1
"
n
="
320
">
<
head
xml:id
="
echoid-head347
"
xml:space
="
preserve
">APPENDIX.</
head
>
<
p
>
<
s
xml:id
="
echoid-s14880
"
xml:space
="
preserve
">De circulo per lineas quadrando.</
s
>
<
s
xml:id
="
echoid-s14881
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s14882
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s14883
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Locvs</
emph
>
hic me admonet, vt quoniam hoc libro demonſtratum eſt, cir-
<
lb
/>
culum figurarum omnium ſibi iſoperimetrarum eſſe maximum, breuiter do-
<
lb
/>
ceam, quaratione dato circulo quadratum conſtrui poſsit æquale, & </
s
>
<
s
xml:id
="
echoid-s14884
"
xml:space
="
preserve
">viciſsim
<
lb
/>
dato quadrato circulus æqualis; </
s
>
<
s
xml:id
="
echoid-s14885
"
xml:space
="
preserve
">atqueid per lineas: </
s
>
<
s
xml:id
="
echoid-s14886
"
xml:space
="
preserve
">cum lib. </
s
>
<
s
xml:id
="
echoid-s14887
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s14888
"
xml:space
="
preserve
">cap 7. </
s
>
<
s
xml:id
="
echoid-s14889
"
xml:space
="
preserve
">copiosè
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-347-04
"
xlink:href
="
note-347-04a
"
xml:space
="
preserve
">Quo pacto re-
<
lb
/>
periatur per
<
lb
/>
numeros qua-
<
lb
/>
dratum cir-
<
lb
/>
culo æquale,
<
lb
/>
& contra ex
<
lb
/>
doctrina Ar-
<
lb
/>
chimedis.</
note
>
traditum ſit, quo pacto ex inuentis ab Archimede, per numeros circulus qua-
<
lb
/>
drandus ſit, hoc eſt, qua ratione area circuli, ſiue capacitas tum ex diametro, tum
<
lb
/>
ex circumferentia cognita ſit inuenienda: </
s
>
<
s
xml:id
="
echoid-s14890
"
xml:space
="
preserve
">Huius enim areæ radix quadrata, la-
<
lb
/>
tus eſt quadrati, quod circulo æquale eſt. </
s
>
<
s
xml:id
="
echoid-s14891
"
xml:space
="
preserve
">Sic è contrario cap. </
s
>
<
s
xml:id
="
echoid-s14892
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s14893
"
xml:space
="
preserve
">eiuſdem lib. </
s
>
<
s
xml:id
="
echoid-s14894
"
xml:space
="
preserve
">re-
<
lb
/>
gula 1. </
s
>
<
s
xml:id
="
echoid-s14895
"
xml:space
="
preserve
">Num. </
s
>
<
s
xml:id
="
echoid-s14896
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s14897
"
xml:space
="
preserve
">docuimus qua via ex data circuli area indaganda ſit tam circum-
<
lb
/>
ferentia, quam diameter illius circuli: </
s
>
<
s
xml:id
="
echoid-s14898
"
xml:space
="
preserve
">hoc eſt, propoſito quadrato, inſtar areæ
<
lb
/>
circuli alicuius, quomodo circulus deſcribendus ſit illi quadrato æqualis. </
s
>
<
s
xml:id
="
echoid-s14899
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>