Gassendi, Pierre, De proportione qua gravia decidentia accelerantur, 1646

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              decurri temporibus æqualibus in ratione continuò dupla:
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            <p type="main">
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              Atqui in motu accelerato grauium decidentium velocitates
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              acquiſitę ſe habent vt emenſa spatia:
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              Igitur in motu accelerato grauium decidentium neceſſe eſt
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              spatia decurri æqualibus temporibus in ratione continuò du­
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              pla.
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              <s id="s.000845">Propoſitionis conſequutio probatur. </s>
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            <p type="main">
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              Diuiſo ſpatio in quotcumque æqualeis parteis lubuerit, ſi
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              in fine primæ partis vnus velocitatis gradus acquiſitus ſit, in
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              fine ſecundi acquiſiti ſint duo, in fine tertij tres, & ita dein­
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              ceps; oportet tempus, quo percurritur ſecunda pars, æquale eſſe
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              tempori, quo percurritur dimidium inferius primæ partis,
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              quòd velocitas per illam acquiſita ſit dupla velocitatis acqui­
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              ſitæ per hoc, vti & spatium duplum eſt; ac deinde tempus,
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              quo percurruntur tertia, & quarta (tempus, inquam, aliun­
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              de æquale tempori, quo ſigillatim percurrerentur triens,
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              & quadrans infimi eiuſdem primæ partis) eſſe ſimiliter
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              æquale, quòd vt ambarum ſpatium duplum eſt ſpatij ſecun­
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              dæ, ita dupla velocitas acquiſita per illas ſit: & iterùm tem­
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              pus, quo percurruntur quinta, ſexta, ſeptima, octaua, pari
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              ratione eſſe æquale, quod vt ſpatium illarum iunctim spatij
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              ſecundæ, & tertiæ eſt duplum, ſic dupla velocitas ſit; atque ita
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              de cæteris:
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              Igitur, ſi in motu accelerato grauium decidentium veloci­
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              tates acquiſitæ ſe habent vt emenſa ſpatia; neceſſe eſt spatia
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              decurri temporibus æqualibus in ratione continuò dupla.
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            <p type="main">
              <s id="s.000848">Aſſumptio autem ita probatur. </s>
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            <p type="main">
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              Conſtat experientia clara, facili, & indubitata, ſi globus
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              quilibet aſſumatur, & Bilanx ita ſuspendatut, vt lance al­
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              tera ſuſtentata cum impoſito tanto pondere, quantum ipſius
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