Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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que ſectio communis BD; certè habebitur baſis pyramidis, cuius axis
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erit AC, quæ omnia conſtant. </
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Theorema
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18.
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Determinari poteſt centrum percuſſionis in latere orthogonij ſubtenſo angulo
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recto
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; </
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">ſit enim AGB, latuſque ſubtenſum angulo recto AB, ſit Trape
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zus KD, eo modo quo diximus, cuius centrum grauitatis ſit H, ducatur
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AH, aſſumatur IH 1/4: </
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">AH, ducatur IM perpendicularis in AH: dico
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punctum M eſſe centrum percuſſionis, quod demonſtratur per Theo
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rema 17. </
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Theorema
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19.
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Si voluatur triangulum prædictum, circa angulum rectum, determinari
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poteſt
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centrum percuſſionis
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; </
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">ſit enim triangulum ABH, quod voluatur
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circa centrum B; </
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">motus puncti A eſt ad motum H, vt BA, ad BH; </
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">ſit ergo
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Trapezus MG, cuius latus ML ſit æquale AB, & GI æquale BH; </
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pyramis, eo modo, quo diximus ſuprà; </
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">ſit autem D centrum grauitatis
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baſis, ſeu Trapezij, & AD axis; </
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">ſit KD 1/4 BD; </
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">ſit denique KE perpen
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dicularis in DB: dico punctum E eſſe centrum percuſſionis, quod co
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dem modo demonſtratur, quo ſuprà. </
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Corollarium.
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<
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">Hinc colligo primò, de omni triangulo idem prorſus dicendum eſſe,
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eſt enim eadem ratio, vt conſideranti patebit. </
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<
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">Secundò, ſi voluatur circa punctum aliquod lateris, poſſe determinari
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centrum percuſſionis; </
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M, circa quod voluatur mode prædicto, motus puncti C, eſt ad motum
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puncti A, vt MC, vel DX, ad MA, vel PO; </
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">hinc Trapezus DPOX, id eſt
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baſis pyramidis, cuius axis eſt MG, & centrum grauitatis K: </
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habetur Trapezus DRNX; </
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<
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">id eſt baſis alterius pyramidis, cuius axis eſt
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MV, & centrum grauitatis H; </
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">fiat autem vt vtraque pyramis ad eam, cuius
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axis eſt MG, ita tota HK, ad HI; </
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tatis; </
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">ducatur IL perpendicularis in IM; dico L eſſe centrum percuſ
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ſionis quæſitum. </
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">Tertiò, ſi voluatur circa aliud punctum, res eodem modo ſuc
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cedet. </
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">Quartò, ſi ſit ſolidum ad inſtar cunei, conſtans ſcilicet ex multis pla
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nis triangularibus, quæ probè inter ſe conueniant; idem etiam accidet,
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quæ omnia ex ſuprà dictis clariſſima efficiuntur. </
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">Quintò, ſi ſit triangulum EAD, fig. </
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A, vt latus AE, modò accedat ad CB, modò recedat; </
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">ſitque ita diuiſa AS
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in R, vt RS ſit 1/4 AS, ſi ducatur RN, centrum percuſſionis erit in N,
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quia R eſt centrum grauitatis geminæ pyramidis; </
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">igitur RN linea di
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rectionis inſtanti percuſſionis; ſi verò producatur AS in G, ſintque I &
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M centra grauitatis pyramidum ducanturque IF, MF perpendiculares
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in AI. AM, centrum percuſſionis erit F, vt conſtat ex dictis. </
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