Ceva, Giovanni, Geometria motus, 1692

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              tudinum E ad C; temporum igitur quadrata erunt vt E ad
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              D, ipſa verò tempora vt E ad F. </s>
              <s id="s.000736">Quod &c. </s>
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              Tab.
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              8.
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              Fig.
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              1.</s>
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              27.
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              huiuij
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              lem. </s>
              <s id="s.000740">pr.
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              3.
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              pri­
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              mi huius.
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              PROP. XXXII. PROB. VII.
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              <s id="s.000742">EXdatis ſpatijs accelerato motu tranſactis, datis item
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              primis velocitatibus ſimilium, ſimpliciumque mo­
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              tuum, inuenire altitudines ſimplicium geneſum, ex quibus
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              propoſita ſpatia effecta ſunt. </s>
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              Tab.
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              7.
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              fig.
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              1.
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              30.
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              huius.
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            <p type="main">
              <s id="s.000744">Spatia ſint E, D reliquis, vt ſupra, manentibus: quoniam
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              ſpatia accelerato motu tranſacta componuntur ex ratio­
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              nibus amplitudinum geneſum ſimplicium, ſimiliumquę
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              motuum reciprocè ſumptarum B ad A, ſiue E ad C, & ex
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              ea quadratorum altitudinum ipſarum geneſum; erit ratio
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              dictarum altitudinum duplicata C ad D; quare F, ſi ſit me­
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              dia proportionalis, non inter E, & D (vt antea poſuimus)
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              ſed inter C ad D; erit ſanè C ad F ratio altitudinum gene­
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              ſum ſimplicium, ſimiliumque motuum, quam quereba­
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              mus. </s>
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              Exemplum primum.
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            <p type="main">
              <s id="s.000746">SI idem graue naturaliter cadens percurrerit à quiete
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              duo ſpatia; tempora erunt in ratione ſubduplicatą
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              eorundem ſpatiorum. </s>
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              <s id="s.000747">Ex Cor. </s>
              <s id="s.000748">pr: 4. huius conſtat rectangula eſſe geneſes ſim­
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              plicium motuum grauium naturaliter deſcendentium, &
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              ex def. 7. primi liquet eaſdem geneſes eſſe motuum ſimi­
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              lium. </s>
              <s id="s.000749">Cumque eiuſdem mobilis naturaliter cadentis ve­
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              locitas à quiete ſit vna, eademque; ſimplices motus erunt
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              ij, vt geneſum ſimilium, ſimpliciumque motuum amplitu­
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              dines æquales ſint, proptereaque, vt in figura præcedentis
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              propoſitionis æquales erunt C, E, atque adeo ſpatium̨
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              C, ſiue E ad D erit in duplicata ratione temporum E ad F. </s>
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