Valerio, Luca - De centro gravitatis solidorvm libri tres

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PROPOSITIO XXI.

Omnis polygoni æquilateri, & æquianguli
idem eſt centrum grauitatis, & figuræ.

Sit polygonum æquilaterum, & æquiangulum ABC
DEFG, cuius ſit primo laterum numerus impar, centrum
autem ſit L. Dico punctum L, eſse centrum grauitatis
polygoni ABCDEFG; ſectis enim duobus lateribus
DE, FG, bifariam in punctis K, H, ducantur ab angulis
oppoſitis rectæ AH, CK. & rectæ BMG, CNF, CM,
MF, iungantur. Quoniam igitur ex decima tertia quar
ti Elem. quemadmodum in pentagono, ita in omni præ
dicto polygono imparium multitudine laterum plane col
ligitur centrum po
lygoni eſse in qua
libet recta, quæ ab
angulo ad medium
lateris oppoſiti du
citur, quoniam ab
omnibus angulis ſic
ductæ ſecant ſe ſe
in eadem proportio
ne æqualitatis, ita
vt eadem ſit propor
tio ſegmentorum,
quæ ad angulos, ad
ea, quæ ad latera

30[Figure 30]
illis angulis oppoſita; rectæ AH, CK, ſecabunt ſe ſe in
puncto L. Rurfus quoniam ex eadem Euclidis angulus
BAL, æqualis eſt angulo GAL, ſed AB, eſt æqualis
AG, & AM, communis, erit baſis BM, æqualis baſi

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