Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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natim ad vtramque diametrorum applicatarum, iunctis
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que AB, BC, ſit ſecta BD bifariam in puncto G.
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>Dico G eſse centrum grauita tis duarum portionum AEB,
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BFE ſimul. </
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>Si enim hoc non eſt, ſit aliud punctum L. &
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compleantur parallelogramma ANBD, DBRC, hoc
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eſt totum AR parallelogrammum: & ſecta BG bifariam
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in puncto H, ponatur DK ipſius BD pars tertia, vt pun
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ctum K ſit trianguli ABC centrum grauitatis. </
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tem ſeſquialtera BP ipſius PN, & BQ ipſius QR, iun
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ctisque AP, CQ, duoatur per punctum H ipſi AC, vel
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NR parallela, cum ipſis AP, CQ conueniens in punctis
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ST: & iuncta LG,
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ſi punctum L non
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ſit in linea BD,
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eſto LM quintu
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pla ipſius MG.
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>Quoniam igitur ob
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parallelas AC, P
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Q, ST in trape
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zio APQC, eſt
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vt DH ad HB, ita
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AS ad SP, & CT
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ad TQ, erit AS ipſius SP, & CT ipſius TQ tripla:
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ſed eſt BP ſeſquialtera ipſius PN, & BQ ipſius QR;
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mixti igitur trianguli ANB centrum grauitatis erit S, &
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trianguli mixti CRB centrum grauitatis T. cum igitur
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BP, BQ proportionales æqualibus NB, BR inter ſe
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ſint æquales, & ſecta AC bifariam in puncto D; etiam
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ijs parallela ST ſecta erit bifariam in puncto H: iungit
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autem ST centra grauitatis mixtorum triangulorum AN
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B, BRC; compoſiti igitur ex vtroque centrum grauita
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tis erit H. </
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>Rurſus quoniam ex quadratura parabolæ, ſe
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miparabola ABD ſeſquitertia eſt trianguli BDA, erit
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triangulum BDA ſeſquialterum mixti trianguli ANB: </
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