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

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              <s id="s.000642">
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                <emph type="italics"/>
              heic ſermo eſt, pars ſecunda DE tribus minutis percurri
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              deberet, hoc eſt dimidia parte primi temporis; & pars ter­
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              tia EF duobus minutis, nempe tertia parte eiuſaem primi
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              temporis, & ita de cæteris.
                <emph.end type="italics"/>
              </s>
              <s id="s.000643"> Quamobrem verò id non
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              fieret; cùm ſuppoſito tuo illo principio de velocita­
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              tibus ſeſe habentibus vt ſpatijs, & nullus ſit paralo­
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              giſmus, & res ſponte ſua ſe prodat, neque videatur
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              euerti poſſe, abs te, vt mox tentas euertere, niſi tua
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              ipſius euertas principia, & falſitatem prodens conſe­
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              quentis, quod tamen ex tuis principiis tam neceſſa­
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              riò deducitur, videaris etiam prodere falſitatem ante­
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              cedentis? </s>
              <s id="s.000644">Pergis itaque,
                <emph type="italics"/>
              At rem non ita accidere facilè
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              intelligimus, diuiſa bifariam parte AD in S, & parte
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              item DE ſimiliter in X. </s>
              <s id="s.000645">Tunc enim ob eandem ratio­
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              nem neceſſe fuerit, vt pars SD percurratur in dimidio
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              eius temporis, quo pars AS decurritur; & DX in ter­
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              tia parte, itemque XE in quarta parte eiuſdem temporis,
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              vt manifeſtum eſt.
                <emph.end type="italics"/>
              </s>
              <s id="s.000646"> Quorſum verò id neceſſe non fue­
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              rit; cùm eadem ſit ratio dimidij ad dimidium, quæ
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              totius ad totum, & nulla ſit obſeruatio, aut ratio, ex
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              qua aliud inferatur potiùs de partibus AD, DE, EF,
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              &c. </s>
              <s id="s.000647">quàm de partibus AS, SD, DX, &c. </s>
              <s id="s.000648">aut de
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              quibuſlibet minoribus, dummodò ſint omnes inter
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              ſe æquales? </s>
              <s id="s.000649">Pergis iterum, C
                <emph type="italics"/>
              ùm igitur ſupponamus
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              totam AD minutis ſex pertranſiri, neceſſe erit, vt decur­
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              ſus per AS quatuor minuta, & deſcenſus per SD duo
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              tantum minuta inſumat: vt ſcilicet ea ratione tempus deſ­
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              cenſus per SD ſit dimidia pars temporis in deſcenſu per AS
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              inſumpti; ideoque etiam pars DX minuti.
                <emph.end type="italics"/>
              (1 1/5)
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              nempe tertia
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              parte temporis AS; & pars XE minuto vno, ſiue
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