Borelli, Giovanni Alfonso, De motionibus naturalibus a gravitate pendentibus, 1670

Table of figures

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              minus verò pondus B pendeat nedùm ex D, ſed
                <expan abbr="etiã">etiam</expan>
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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;
                <expan abbr="pa-riterq;">pa­
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                riterque</expan>
              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
                <expan abbr="velocitatẽ">velocitatem</expan>
              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,
                <expan abbr="atq;">atque</expan>
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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
                <expan abbr="cẽ-tris">cen­
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                tris</expan>
              grauitat
                <expan abbr="ũlibrarum">ullibrarum</expan>
              L, & I, &
                <expan abbr="ſuſpẽduntur">ſuſpenduntur</expan>
              ex
                <expan abbr="pũ-">pun­
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                </expan>
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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. </s>
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