Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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CHRIST. HUGENII
"/>
meratoris partis alterius e carentes, omitti poſſe, cum quan-
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titates inde ortæ eædem utrinque eſſent futuræ ideoque de-
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lendæ. </
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<
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xml:space
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">Quare in terminis poſterioribus ii tantum ab ini-
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tio ſcribendi erant in quibus unum e, omiſſis omnibus reli-
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quis, ut æquatio hîc futura ſit iſta
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{bx
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- ccxx - 2bccx/bcc + x
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} = {3bexx - 2ccex - 2bcce/3exx}</
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</
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<
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<
s
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xml:space
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">Hîc jam multiplicationes alternæ per denominatores in-
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ſtituendæ eſſent ad tollendas fractiones. </
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<
s
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xml:space
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preserve
">Verum examinan-
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do diligentius quænam futura ſint harum multiplicationum
<
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producta, aliud adhuc compendium inveniemus, & </
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<
s
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xml:space
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ſcribendos quidem omnino eſſe terminos poſteriores: </
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<
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xml:space
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">quia
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enim deſcribuntur ex prioribus mutato x in e, præpoſito-
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que numero dimenſionum ipſius x, non difficile eſt col-
<
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ligere ex ſolis terminis prioribus quænam futura ſint iſta
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omnia producta.</
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<
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</
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<
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xml:space
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">Ita quoniam propter - ccxx in prioribus, habetur -
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2ccex in poſterioribus; </
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<
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xml:space
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">& </
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<
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xml:space
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">propter x
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in denominatore prio-
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rum, in poſteriorum denominatore eſt 3exx; </
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<
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ſpicitur utraque producta ex - ccxx in 3exx & </
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xml:space
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2ccex in x
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, quæ ſunt - 3ccex
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& </
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<
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xml:space
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">- 2ccex
<
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>
, eaſdem
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literas habitura, ſed diverſos numeros præpoſitos 3 & </
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xml:space
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idque inde fieri quòd in termino ccxx unam dimenſio-
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nem minus habeat x quam in termino x
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. </
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">au-
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ferendo poſtea ex utraque parte æquationis, - 2ccex
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>
, ap-
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paret ſuperfuturum - ccex
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à parte terminorum priorum.
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</
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<
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xml:space
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">Quare ab initio hoc ſciri poteſt, multiplicando tantum in
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terminis prioribus - ccxx numeratoris in x
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>
denomina-
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toris, unumque x in e mutando, ac productum ſimplex ſcri-
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bendo; </
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<
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xml:space
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minis eſt unitas.</
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</
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<
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<
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">Eadem ratione producta ex - 2bccx in 3exx, & </
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xml:space
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">ex -
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2bcce in x
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, quæ eaſdem literas habent, ſunt enim -
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6bccex
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& </
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<
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xml:space
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, habebunt numeros præpoſitos </
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