Valerio, Luca - De centro gravitatis solidorum

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1tes A deficiens, cuius baſis BC. Dico fieri poſse quod
proponitur: ducta enim per verticem figuræ A, baſi BC,
parallela, atque ideo figuram ipſam contingente, abſol
uatur parallelogrammum BL, ſectaque diametro AD,
bifariam, & ſingulis eius partibus ſemper bifariam, du
cantur per puncta ſectionum rectæ lineæ baſi BC, & in
ter ſe parallelæ, atque ita multiplicatæ ſint ſectiones,
vt ſecti parallelogrammi in parallelogramma æqua
lia, & eiuſdem altitudinis quælibet pars, vt paralle
logrammum BF, ſit minus ſuperficie propoſita, cu
ius parallelogram
mi latus EF, ſe
cet figuræ termi
num BAC, in
punctis GH, &
diametrum AD, in
puncto K. erit igi
tur GK, æqualis
KH: per omnia
igitur puncta ſe
ctionum termini

12[Figure 12]
BAC, quæ à prædictis fiunt lineis parallelis, ſi ducan
tur diametro AD parallelæ, figura quædam ipſi ABC,
inſcribetur, & altera circumſcribetur ex parallelogram
mis æqualium altitudinum. Dico harum figurarum
inſcriptam ſuperari à circumſcripta minori ſpacio ſuper
ficie propoſita. Quoniam enim omnia parallelogramma,
quibus figura circumſcripta ſuperat inſcriptam ſimul ſum
pta ſunt æqualia BF parallelogrammo: ſed parallelo
grammum BF, eſt minus ſuperficie propoſita: exceſſus
igitur quo figura circumſcripta inſcriptam ſuperat, minor
erit ſuperficie propoſita. Fieri igitur poteſt, quod propo
nebatur.

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