Borelli, Giovanni Alfonso
,
De motionibus naturalibus a gravitate pendentibus
,
1670
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minus verò pondus B pendeat nedùm ex D, ſed
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etiã
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ex G; & vt A ad B, ita fiat DI ad IC, nec non GL ad
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LF, erunt I, & L centra grauitatum librarum, fiat po
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ſtea HN media proportionalis inter HL, & EI;
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pa-riterq;
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riterque</
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ponatur HO media proportionalis inter HG,
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& ED; patet HG ad HO ſubduplicatam proportio
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nem habere radij HG ad ED; dico velocitatem reuo
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lutionis libræ FG ad
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velocitatẽ
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vertiginis libræ CD
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eamdem proportionem habe
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re, quam HG ad HO; quia vt
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A ad B, ita erat GL ad LF,
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atq;
">atque</
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DI ad IC, ergo componendo
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GF ad FL erit vt DC ad CI, &
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antecedentium ſemiſſes HF ad
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FL, atque EC ad CI proporti
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onales erunt, & per conuerſio
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nem rationis HF ad HL erit vt CE ad EI, & permu
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tando FH ad CE, ſeu HG ad ED erit vt LH ad IE, &
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earum ſubduplicatæ proportiones eædem quoquę
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erunt, nimirùm HG ad HO, vt HL ad HN; poſteą
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quia duo pondera A, & B exercent eorum vim in
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cẽ-tris
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tris</
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grauitat
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ũlibrarum
">ullibrarum</
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L, & I, &
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ſuſpẽduntur
">ſuſpenduntur</
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ex
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pũ-
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ctis H, & E, ergo efficiunt duo funependula HL, &
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EI, quæ conantur deſcendere per arcus LM, IK, ſed
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pendulorum velocitates ſubduplicatam proportio
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nem habent longitudinum eorum, igitur velocitas
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deſcenſus libræ FG ad velocitatem deſcenſus libræ
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CD eamdem proportionem habebit, quam LH ad
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HN, ſeu quam habet HG ad HO, quod erat primum. </
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