Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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mologa; puncta igitur K, H, in prædictis triangulis ſunt
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ſimiliter poſita. </
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<
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>Rurſus quoniam angulus ABC, non
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eſt minor recto, acuti erunt reliqui ACB, BAC; igitur
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latus AC, maximum erit: ponitur autem AB maius,
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quàm BC; triangulum igitur ABC, ſcalenum erit.
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</
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<
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>Eadem ratione ſcalenum eſt triangulum ACD. </
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in triangulo ACD, vnum duntaxat punctum K, ſimili
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ter poſitum erit, ac punctum H, in triangulo ABC. </
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<
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>Cum
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igitur H ſit centrum grauitatis trianguli ABC, erit &
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K, centrum grauitatis trianguli ACD. </
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<
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>Sed longitudo
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GK, æqualis eſt longitudini GH; punctum igitur G erit
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centrum grauitatis parallelogrammi ABCD, in quo ni
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mirum ſecta eſt bifariam diameter AC: quare ſi ducatur
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altera diameter BD, in medio etiam diametri BD, erit
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idem centrum grauitatis G. </
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<
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>Sed ſint omnia latera æqualia
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parallelogrãmi
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ABCD,
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Sectisque duobus lateribus AD, BC, bifariam in E, F
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iungantur EF, AE, ED,
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AGC, & per punctum G,
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ducatur ipſi AD, vel BC,
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parallela HGK. </
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<
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>Quoniam
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igitur EC, eſt æqualis
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AF, erit CG æqualis AG,
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& EG, æqualis GF, pro
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pter ſimilitudinem triangu
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lorum: nec non EH, ipſi
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AH, & EK, ipſi KD: tres
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igitur diametri AC, AE,
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ED, erunt ſectæ bifariam
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in punctis K, G, H: & quoniam ex æquali propter triangu
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la ſimilia eſt vt AF, ad FD, ita HG, ad GK, erit HG,
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æqualis ipſi GK: ſed puncta K, H, ſunt centra grauitatis
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parallelogrammorum BF, FC; igitur totius parallelo
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grammi ABCD, centrum grauitatis erit G, in medio </
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