Gassendi, Pierre
,
De proportione qua gravia decidentia accelerantur
,
1646
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repetam, quod iam inſinuaui, velle te AN, & ND,
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quod ſpatium eſt triplum, æquali tempore percurri, ac
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ita rationem incipere triplam, deberéque eodem pro
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gredi tenore ex D in T ipſius ND triplam, & ita
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deinceps; ne id, inquam, repetam: accipiatur non NC,
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ſed XC infimus triens primæ partis. </
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XC, & DE eſſe æqualia, quoniam XC eſt triens ip
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ſius DE, eo modo, quo vis tempora per NC, & CD,
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eſſe æqualia; quoniam NC eſt dimidium ipſius CD:
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Quare, vt, aſſumendo partem analogam ipſi NC, vt
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putà CD, progrederis deinceps in ratione dupla CD,
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DF, FK, &c. </
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<
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">ita aſſumendo partem analogam ipſi
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XC, progredi deinceps licebit in ratione tripla DE,
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EH, HB, &c. </
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">Sequitur quoque te recidiſſe in illud
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ipſum incommodum, quod deduxi antè aduerſus
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eandem rationem duplam: nempe, vt debeas admit
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tere, peracto primo tempore in percurrendo aliquo
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ſpatio, percurri deinceps debere ſpatia omninò infini
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ta, priuſquam finis temporis alterius æqualis adueniat.
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">Quippe, ſi vt tu biſecuiſti partem primam AC in N,
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ita cæteræ biſcentur in S, V, &c. </
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tempus NC fit per te dimidium temporis AN, ita
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tempus CS erit dimidium temporis NC, & tempus
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SD dimidium temporis CS, &c. </
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tendas iam, incipiendum eſſe non à puncto A, ſed à
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puncto N: idem nihilominùs ſequetur. </
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nente eadem biſectiore partium, ac habentibus, ſe
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dimidiis eadem ratione, qua habent tota; cùm ſi ex
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N in C certus velocitatis gradus acquiratur, is ſit dein
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de in S duplus, ac pari ratione eſſe debeat in D qua-</
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