Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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SUPER HUGENII EXCEPT.
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dem modo, quo Z. </
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<
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xml:space
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Vax {2ax/a + Vax}
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m
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n
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B, 2 B; </
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<
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quantitatibus Vax, {2ax/a + Vax}: </
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<
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xml:space
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">quantitates m, n, non
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ſunt indefinite æquales ex prop. </
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<
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ter m & </
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<
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<
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">a manente quantitate indefinita,
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æquatio inter m & </
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<
s
xml:id
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xml:space
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">n tot habebit radices ſeu quantitates, in
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quas reſolvitur x, quot quantitatum, inter ſe diverſas ra-
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tiones habentium, binarii ſunt in rerum natura, quæ vices
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quantitatum a, x, ſubire poſſunt, h. </
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<
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">e. </
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<
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">quæ eandem quan-
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titatem Analyticè ex ſe ipſis componit eodem modo, quo
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eandem quantitas componitur ex ipſarum media Geometri-
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ca Vax, & </
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<
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Geometricam & </
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<
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">x, nempe {2ax/a + Vax,} ita ut compoſitio ſit eo-
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dem modo quo Z componitur ex B & </
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<
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<
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ctario Prop. </
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">omnes quantitatum binarii, rationes quoque
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diverſas inter ſe habentium, B 2 B, C D, E F, G H, &</
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<
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</
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<
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">in infinitum, poſſunt ſupplere vices quantitatum a, x, quo-
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niam Z eodem modo componitur ex B 2 B, quo ex C D, E F,
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vel G H, &</
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numero infinitas. </
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">Sed omnis æquatio habet ad ſummum tot
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radices, quot habet dimenſiones; </
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">& </
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m & </
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<
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xml:space
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">n dimenſiones habet numero infinitas, quod eſt abſur-
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dum; </
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xml:space
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">ideoque Z ſeu Circuli Sector non poteſt analyticè
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componi ex Polygonis definitis B, 2B. </
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dum erat. </
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<
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">Hinc manifeſtum eſt, Terminationem cujuſlibet
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ſeriei convergentis, ſi non poſſit componi ex terminis con-
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vergentibus indefinitè, nec poſſe componi definitè; </
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que evaneſcit ſimul cum noſtra diſtinctione Objectio Huge-
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nii prima.</
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<
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">Idem in Objectione ſua ſecunda non videtur advertiſſe,
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me non ſolum in Prop. </
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<
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tulo intelligere per Extractionem radicum, Reſolutionem
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omnium poteſtatum ſive purarum ſive affectarum; </
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quippe eadem eſt ratio, neque ulla imaginabilis eſt in de-
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monſtratione diverſitas, ſive Sector ſupponatur Radix </
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