DelMonte, Guidubaldo - Mechanicorvm Liber

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69[Figure 69]

Sit libra AB, cuius centrum C; ſintq; vt in primo caſu duo pon
dera EF ex punctis BG ſuſpenſa: ſitq; GH ad HB, vt pondus
F ad pondus E. Dico pondera EF tàm in GB ponderare, quàm
ſi vtraq; ex diuiſionis puncto H ſuſpendantur. Conſtruantur ea
dem, hoc eſt fiat AC ipſi CH æqualis, & ex puncto A duo ap
pendantur pondera LM, ita vt pondus E ad pondus L, ſit vt
CA ad CG; vt autem CB ad CA, ita ſit pondus M ad pondus
F. pondera LM ipſis EF in GB appenſis (vt ſupra dictum eſt)
æqueponderabunt. Sint deinde puncta NO centra grauitatis pon
derum EF; connectanturq; GN BO; iungaturq; NO, quæ tan
quam libra erit; quæ etiam efficiat lineas GN BO inter ſe ſe æqui
diſtantes eſſe; à punctoq; H horizonti perpendicularis ducatur
HP, quæ NO ſecet in P, atq; ipſis GN BO ſit æquidiſtans.
deniq; connectatur GO, quæ HP ſecet in R. Quoniam igitur
HR eſt lateri BO trianguli GBO æquidiſtans; erit GH ad HB,
vt GR ad RO. ſimiliter quoniam RP eſt lateri GN trianguli
OGN æquidiſtans; erit GR ad RO, vt NP ad PO. quare
vt GH ad HB, ita eſt NP ad PO. vt autem GH ad HB, ita
eſt pondus F ad pondus E; vt igitur NP ad PO, ita eſt pondus
F ad pondus E. punctum ergo P centrum erit grauitatis magni
tudinis ex vtriſq; EF ponderibus compoſitæ. Intelligantur itaq;
pondera EF ita eſſe à libra NO connexa, ac ſi vna tantùm eſſet
magnitudo ex vtriſq; EF compoſita, in punctiſq; BG appenſa. ſi
igitur ponderum ſuſpenſiones BG ſoluantur, manebunt pondera
EF ex HP ſuſpenſa; ſicuti in GB prius manebant. pondera verò EF
in GB appenſa ipſis LM ponderibus æqueponderant, & pondera

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Scan	Original
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Scan	Original
81
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90
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