Ceva, Giovanni, Geometria motus, 1692

Table of figures

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              ſimplices ex B in H, & ex C in G, ex quibus fiunt accele­
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              rati, geneſes habebunt, quarum primæ velocitates, ſeu am­
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              plitudines proportionales ſunt altitudinibus earundem,
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              ſpatijs nimirum CG, BH accelerato motu exigendis; qua­
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              mobrem componentur ex ratione ipſarum velocitatum,
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              ſeu amplitudinum CG ad BH, & ex ea quadratorum tem­
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              porum, quæ proinde æqualitatis erit; itaque etiam huius
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              ſubduplicata; hoc eſt tempora in tranſitibus accelarato
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              motu exactis, erunt paria. </s>
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              pr.
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              4.
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              huius.
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              Corollarium.
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              Hinc patet, vbi æquè craſſis filis eiuſdemque materiei vel
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              cedentiæ ſuſpenſa ſint æqualia pondera, tunc primas velocita­
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              tes, ſubductis ponderibus, fore in eadem ratione
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              ,
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              vel longitudinum filorum.
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              PROP. XXXVIII. THEOR. XXXI.
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              <s id="s.000794">SI extremitatibus funiculorum ex vna parte
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              ,
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              ac eandem craſſitiem habentium, nec non eiuſdem
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              cædentiæ exiſtentium, fuerint ſuſpenſa æqualia pondera,
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              quæ inde ijſdem longitudinibus ſeruatis, quomodo opor­
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              tet tollantur, erunt ſpatia recurſuum, temporibus ſimpli­
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              cium motuum exacta in ratione longitudinum pendulo­
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              rum. </s>
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            <p type="main">
              <s id="s.000795">Sit funiculus AC æquè craſſus ac BD, & ſuſpenſis
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              hinc inde ponderibus æqualibus, elongatio primi funiculi
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              ſit CE, & alterius ſit DF. </s>
              <s id="s.000796">Dico ſpatia temporibus ſimpli­
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              cium imaginum, ab extremitatibus ſolutis exacta, fore iņ
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              ratione longitudinum ipſorum funiculorum. </s>
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            <p type="main">
              <s id="s.000797">Iam conſtat CE ad DF eſſe, vt AC ad BD, in qua ratione
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              ſunt etiam velocitates à quiete, dum pondera ſubduceren­
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              tur ex E, et F, vel ex alijs punctis quibuſcunque ſi æqualia </s>
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