Valerio, Luca - De centro gravitatis solidorvm libri tres

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Sed eſto polygonum æquilaterum, & æquiangulum,
ABCDEF, cuius laterum numerus ſit par, & centrum
eſto G. Dico idem G, eſse centrum grauitatis polygoni
ABCDEF. Iungantur enim angulorum oppoſitorum
puncta rectis lineis AD, BE, CF. Ex quarto igitur
Elem. ſecabunt ſeſe hæ rectæ omnes bifariam in vno pun
cto, quod talis figuræ centrum definiuimus: ſed G poni
tur centrum; in puncto igitur G. Quoniam igitur duo
rum triangulorum CBG, GFE, anguli ad verticem
BGC, FGE, ſunt æquales; & vterlibet angulorum CBG,
GCB, æqualis eſt vtrilibet ipſorum EFG, GEF; ex
quarto Elem. & circa æquales angulos latera proportio
nalia horum triangu
lorum ſunt æqualia;
ſimilia, & æqualia
erunt triangula BC
G, GFE: poſitis
igitur centris graui
tatis K, H, duorum
triangulorum EFG,
GBC, iunctifque
KG, GH, erit v
terlibet angulorum
BGH, HGC, æ
qualis vtrilibet an

31[Figure 31]
gulorum CGK, KGE, propter ſimilitudinem poſitio
nis centrorum K, H, in iſoſcelijs triangulis CBG,
GFE: (nam GH, ſi produceretur latus BC, bifariam
ſecaret: ſimiliter GK, latus EF) ſed CG, eſt in directum
poſita ipſi GF; igitur & GH ipſi GK: & ſunt æquales,
vtpote lateribus triangulorum BCG, GFE, æqualibus
homologæ; cum igitur eorundem triangulorum centra
grauitatis ſint K, H; centrum grauitatis duorum triangu
lorum CBG, GFE, ſimul, erit punctum G. Eadem

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