Baliani, Giovanni Battista, De motu naturali gravium solidorum, 1638

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              <s id="s.000077">PROPOSITIO TERTIA.
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                <s id="s.000078">Lineae descensus gravium, dum naturali motu perpendicula-
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                riter feruntur, sunt in duplicata ratione diuturnitatum.
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              <s id="s.000079">Sint LN, KM linea descensus gravium L, K, & sint P
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              O ipsorum diuturnitates.
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              <s id="s.000080">Dico LN, KM esse in duplicata ratione ipsarum P, O.
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              <s id="s.000081">Sint pendula AH, AI, dependentia a puncto A, & eleven-
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              tur ad libellam ipsius A usque ad E, B, quae in elevatione
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              producant arcus HB, IE, & sint talis longitudinis, ut du-
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              cta ACF, secet arcus BC, & EF, portionis minimae, aequa-
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              les quo ad sensum lineis LN, KM, & sit S, quadratum
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              diuturnitatis P, & T quadratum O, & Q, R, diuturni-
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              tates vibrationum BC, & EF.
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              <s id="s.000082">Quoniam diuturnitates Q, R sunt aequales diuturnitatibus
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              P, O
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              ; S, T, sunt etiam quadrata ipsarum Q, R
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              , & quia
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              vibrationes integrae pendulorum AH, AI sunt ut qua-
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              dratum T ad quadratum S
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              , portiones BC, EF, sunt pa-
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              riter inter se ut quadratum T ad quadratum S
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              , sed
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              BC, & EF sunt aequales lineis KM, LN
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              , ergo etiam K
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              M, LN sunt ut quadrata S, T
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              , & proinde in duplicata
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              ratione P, O, temporum seu diuturnitatum earumdem.
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              <s id="s.000083">Quod, &c.
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