Archimedes - Archimedis De iis qvae vehvntvr in aqva libri dvo

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116FED. COMMANDINI quæ quidem in centro conueniunt. idem igitur eſt centrum
grauitatis quadrati, & circuli centrum.

Sit pentagonum æquilaterum, & æquiangulum in circu-
lo deſcriptum a b c d e: & iun-

72[Figure 72] cta b d, bifariamq́; in ſ diuiſa,
ducatur c f, & producatur ad
circuli circumferentiam in g;
quæ lineam a e in h ſecet: de-
inde iungantur a c, c e. Eodem
modo, quo ſupra demonſtra-
bimus angulum b c f æqualem
eſſe angulo d c f; & angulos
ad f utroſque rectos: & idcir-
colineam c f g per circuli cen
trum tranſire. Quoniam igi-
tur latera c b, b a, & c d, d e æqualia ſunt; & æquales anguli
c b a, c d e: erit baſis c a baſi c e, & angulus b c a angulo
114. Primi. d c e æqualis. ergo & reliquus a c h, reliquo e c h. eſt au-
tem c h utrique triangulo a c h, e c h communis. quare
baſis a h æqualis eſt baſi h e: & anguli, quiad h recti: ſuntq́;
recti, qui ad f. ergo lineæ a e, b d inter ſe ſe æquidiſtant.
2208. primi. Itaque cum trapezij a b d e latera b d, a e æquidiſtantia à li
nea fh bifariam diuidantur; centrum grauitatis ipſius erit
in linea f h, ex ultima eiuſdem libri Archimedis. Sed trian-
3313. Archi-
medis. guli b c d centrum grauitatis eſt in linea c f. ergo in eadem
linea c h eſt centrum grauitatis trapezij a b d e, & trian-
guli b c d: hoc eſt pentagoni ipſius centrum & centrum
circuli. Rurſus ſi iuncta a d, bifariamq́; ſecta in k, duca-
tur e k l: demonſtrabimus in ipſa utrumque centrum in
eſſe. Sequitur ergo, ut punctum, in quo lineæ c g, e l con-
ueniunt, idem ſit centrum circuli, & centrum grauitatis
pentagoni.

Sit hexagonum a b c d e f æquilaterum, & æquiangulum
in circulo deſignatum: iunganturq́; b d, a c: & bifariam

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Scan	Original
81	35
82
83	36
84
85	37
86
87	38
88
89	39
90
91	40
92
93	41
94
95	42
96
97	43
98
99	44
100
101	43
102
103
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105
106
107
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109
110

Scan	Original
81	35
82
83	36
84
85	37
86
87	38
88
89	39
90
91	40
92
93	41
94
95	42
96
97	43
98
99	44
100
101	43
102
103
104
105
106
107
108
109
110