1MG, & angulus ABM, angulo AGM, ſed totus ABC,
toti AGF, eſt æqualis; reliquus igitur angulus CBG,
reliquo BGF, æqualis erit: ſed circa hos æquales an
gulos recta BM, oſtenſa eſt æqualis rectæ MG, & CB,
eſt æqualis GF; baſis igitur CM, baſi GF, & angulus
CMB, angulo FMG, æqualis erit; ſed totus BMN,
æqualis eſt toti GMN; quia vterque rectus; reliquus
igitur CMN, reliquo NMF, æqualis erit, quos circa
recta CM, eſt æqualis MF, & MN, communis; baſis
igitur CN, baſi NF, & anguli, qui ad N, æquales erunt,
atque ideo recti: ſed & qui ad M, ſunt recti, & BM, eſt
æqualis GM; parallelæ igitur ſunt BG, CF, & trape
zij CBGF, centrum grauitatis eſt in linea MN: ſed &
trianguli ABG, centrum grauitatis eſt in linea AM; to
tius igitur figuræ ABCFG, centrum grauitatis eſt in li
nea AN; hoc eſt in linea AH. Rurſus quoniam omnis
quadrilateri quatuor anguli ſunt æquales quatuor rectis:
& tres anguli ABM, BMN, MNC, ſunt æquales tri
bus angulis FGM, GMN, MNF, reliquus angulus
BCF, reliquo CFG, æqualis erit: ſed totus angulus
BCD, eſt æqualis toti angulo GFE; reliquus ergo
DCF, reliquo CFE, æqualis erit: ſed linea CN, eſt
æqualis NF, & anguli, qui ad N, ſunt recti; ſimiliter
ergo vt antea, centrum grauitatis trapezij CDEF, erit
in linea AH: ſed & totius figuræ ABCFG, eſt in li
nea AH; totius igitur polygoni ABCDEFG, in li
nea AH, eſt centrum grauitatis, quod idem ſimiliter in
linea CK, eſse oftenderemus; in communi igitur ſectione
puncto L, eſt centrum grauitatis polygoni ABCDEFG.
Similiter quotcumque plurium laterum numero impa
rium eſset polygonum æquilaterum, & æquiangulum,
ſemper deueniendo ab vno triangulo ad quotcumque eius
trapezia; propoſitum concluderemus.
toti AGF, eſt æqualis; reliquus igitur angulus CBG,
reliquo BGF, æqualis erit: ſed circa hos æquales an
gulos recta BM, oſtenſa eſt æqualis rectæ MG, & CB,
eſt æqualis GF; baſis igitur CM, baſi GF, & angulus
CMB, angulo FMG, æqualis erit; ſed totus BMN,
æqualis eſt toti GMN; quia vterque rectus; reliquus
igitur CMN, reliquo NMF, æqualis erit, quos circa
recta CM, eſt æqualis MF, & MN, communis; baſis
igitur CN, baſi NF, & anguli, qui ad N, æquales erunt,
atque ideo recti: ſed & qui ad M, ſunt recti, & BM, eſt
æqualis GM; parallelæ igitur ſunt BG, CF, & trape
zij CBGF, centrum grauitatis eſt in linea MN: ſed &
trianguli ABG, centrum grauitatis eſt in linea AM; to
tius igitur figuræ ABCFG, centrum grauitatis eſt in li
nea AN; hoc eſt in linea AH. Rurſus quoniam omnis
quadrilateri quatuor anguli ſunt æquales quatuor rectis:
& tres anguli ABM, BMN, MNC, ſunt æquales tri
bus angulis FGM, GMN, MNF, reliquus angulus
BCF, reliquo CFG, æqualis erit: ſed totus angulus
BCD, eſt æqualis toti angulo GFE; reliquus ergo
DCF, reliquo CFE, æqualis erit: ſed linea CN, eſt
æqualis NF, & anguli, qui ad N, ſunt recti; ſimiliter
ergo vt antea, centrum grauitatis trapezij CDEF, erit
in linea AH: ſed & totius figuræ ABCFG, eſt in li
nea AH; totius igitur polygoni ABCDEFG, in li
nea AH, eſt centrum grauitatis, quod idem ſimiliter in
linea CK, eſse oftenderemus; in communi igitur ſectione
puncto L, eſt centrum grauitatis polygoni ABCDEFG.
Similiter quotcumque plurium laterum numero impa
rium eſset polygonum æquilaterum, & æquiangulum,
ſemper deueniendo ab vno triangulo ad quotcumque eius
trapezia; propoſitum concluderemus.