Valerio, Luca, De centro gravitatis solidorvm libri tres

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1
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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