Valerio, Luca
,
De centro gravitatis solidorvm libri tres
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
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 - 283
>
51
52
53
54
55
56
57
58
59
60
<
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 - 283
>
page
|<
<
of 283
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
043/01/053.jpg
"
pagenum
="
45
"/>
MG, & angulus ABM, angulo AGM, ſed totus ABC,
<
lb
/>
toti AGF, eſt æqualis; reliquus igitur angulus CBG,
<
lb
/>
reliquo BGF, æqualis erit: ſed circa hos æquales an
<
lb
/>
gulos recta BM, oſtenſa eſt æqualis rectæ MG, & CB,
<
lb
/>
eſt æqualis GF; baſis igitur CM, baſi GF, & angulus
<
lb
/>
CMB, angulo FMG, æqualis erit; ſed totus BMN,
<
lb
/>
æqualis eſt toti GMN; quia vterque rectus; reliquus
<
lb
/>
igitur CMN, reliquo NMF, æqualis erit, quos circa
<
lb
/>
recta CM, eſt æqualis MF, & MN, communis; baſis
<
lb
/>
igitur CN, baſi NF, & anguli, qui ad N, æquales erunt,
<
lb
/>
atque ideo recti: ſed & qui ad M, ſunt recti, & BM, eſt
<
lb
/>
æqualis GM; parallelæ igitur ſunt BG, CF, & trape
<
lb
/>
zij CBGF, centrum grauitatis eſt in linea MN: ſed &
<
lb
/>
trianguli ABG, centrum grauitatis eſt in linea AM; to
<
lb
/>
tius igitur figuræ ABCFG, centrum grauitatis eſt in li
<
lb
/>
nea AN; hoc eſt in linea AH. </
s
>
<
s
>Rurſus quoniam omnis
<
lb
/>
quadrilateri quatuor anguli ſunt æquales quatuor rectis:
<
lb
/>
& tres anguli ABM, BMN, MNC, ſunt æquales tri
<
lb
/>
bus angulis FGM, GMN, MNF, reliquus angulus
<
lb
/>
BCF, reliquo CFG, æqualis erit: ſed totus angulus
<
lb
/>
BCD, eſt æqualis toti angulo GFE; reliquus ergo
<
lb
/>
DCF, reliquo CFE, æqualis erit: ſed linea CN, eſt
<
lb
/>
æqualis NF, & anguli, qui ad N, ſunt recti; ſimiliter
<
lb
/>
ergo vt antea, centrum grauitatis trapezij CDEF, erit
<
lb
/>
in linea AH: ſed & totius figuræ ABCFG, eſt in li
<
lb
/>
nea AH; totius igitur polygoni ABCDEFG, in li
<
lb
/>
nea AH, eſt centrum grauitatis, quod idem ſimiliter in
<
lb
/>
linea CK, eſse oftenderemus; in communi igitur ſectione
<
lb
/>
puncto L, eſt centrum grauitatis polygoni ABCDEFG.
<
lb
/>
</
s
>
<
s
>Similiter quotcumque plurium laterum numero impa
<
lb
/>
rium eſset polygonum æquilaterum, & æquiangulum,
<
lb
/>
ſemper deueniendo ab vno triangulo ad quotcumque eius
<
lb
/>
trapezia; propoſitum concluderemus. </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>