1natim ad vtramque diametrorum applicatarum, iunctis
que AB, BC, ſit ſecta BD bifariam in puncto G.
Dico G eſse centrum grauita tis duarum portionum AEB,
BFE ſimul. Si enim hoc non eſt, ſit aliud punctum L. &
compleantur parallelogramma ANBD, DBRC, hoc
eſt totum AR parallelogrammum: & ſecta BG bifariam
in puncto H, ponatur DK ipſius BD pars tertia, vt pun
ctum K ſit trianguli ABC centrum grauitatis. Poſita au
tem ſeſquialtera BP ipſius PN, & BQ ipſius QR, iun
ctisque AP, CQ, duoatur per punctum H ipſi AC, vel
NR parallela, cum ipſis AP, CQ conueniens in punctis
ST: & iuncta LG,
ſi punctum L non
ſit in linea BD,
eſto LM quintu
pla ipſius MG.
Quoniam igitur ob
parallelas AC, P
Q, ST in trape
zio APQC, eſt
vt DH ad HB, ita
AS ad SP, & CT
166[Figure 166]
ad TQ, erit AS ipſius SP, & CT ipſius TQ tripla:
ſed eſt BP ſeſquialtera ipſius PN, & BQ ipſius QR;
mixti igitur trianguli ANB centrum grauitatis erit S, &
trianguli mixti CRB centrum grauitatis T. cum igitur
BP, BQ proportionales æqualibus NB, BR inter ſe
ſint æquales, & ſecta AC bifariam in puncto D; etiam
ijs parallela ST ſecta erit bifariam in puncto H: iungit
autem ST centra grauitatis mixtorum triangulorum AN
B, BRC; compoſiti igitur ex vtroque centrum grauita
tis erit H. Rurſus quoniam ex quadratura parabolæ, ſe
miparabola ABD ſeſquitertia eſt trianguli BDA, erit
triangulum BDA ſeſquialterum mixti trianguli ANB:
que AB, BC, ſit ſecta BD bifariam in puncto G.
Dico G eſse centrum grauita tis duarum portionum AEB,
BFE ſimul. Si enim hoc non eſt, ſit aliud punctum L. &
compleantur parallelogramma ANBD, DBRC, hoc
eſt totum AR parallelogrammum: & ſecta BG bifariam
in puncto H, ponatur DK ipſius BD pars tertia, vt pun
ctum K ſit trianguli ABC centrum grauitatis. Poſita au
tem ſeſquialtera BP ipſius PN, & BQ ipſius QR, iun
ctisque AP, CQ, duoatur per punctum H ipſi AC, vel
NR parallela, cum ipſis AP, CQ conueniens in punctis
ST: & iuncta LG,
ſi punctum L non
ſit in linea BD,
eſto LM quintu
pla ipſius MG.
Quoniam igitur ob
parallelas AC, P
Q, ST in trape
zio APQC, eſt
vt DH ad HB, ita
AS ad SP, & CT
166[Figure 166]ad TQ, erit AS ipſius SP, & CT ipſius TQ tripla:
ſed eſt BP ſeſquialtera ipſius PN, & BQ ipſius QR;
mixti igitur trianguli ANB centrum grauitatis erit S, &
trianguli mixti CRB centrum grauitatis T. cum igitur
BP, BQ proportionales æqualibus NB, BR inter ſe
ſint æquales, & ſecta AC bifariam in puncto D; etiam
ijs parallela ST ſecta erit bifariam in puncto H: iungit
autem ST centra grauitatis mixtorum triangulorum AN
B, BRC; compoſiti igitur ex vtroque centrum grauita
tis erit H. Rurſus quoniam ex quadratura parabolæ, ſe
miparabola ABD ſeſquitertia eſt trianguli BDA, erit
triangulum BDA ſeſquialterum mixti trianguli ANB:
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