Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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ET HYPERBOLÆ QUADRATURA.
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ſtrari poſſunt de duobus quibuſcunque polygonis
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complicatis loco polygonorum complicatorum ABIP,
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A B D L P; </
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">polygonum enim à tangentibus comprehenſum
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tot continet æqualia trapezia, quot continet polygonum à
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ſubtendentibus comprehenſum æqualia triangula: </
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<
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xml:space
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">atque hinc
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evidens eſt has polygonorum analogias ita ſe habere in infi-
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nitum, ducendo nimirum rectas AN, AK, AG, AC, per
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puncta R, T, S, V, & </
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<
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<
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">alia polygona intra & </
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<
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extra ſemper ſcribendo: </
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<
s
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xml:space
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gonorum inſcriptionem & </
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<
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">circumſcriptionem, inſcriptionem
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& </
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<
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">circumſcriptionem ſubduplam, ex prædictis patet (ſi po-
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natur triangulum A B P =
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, & </
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<
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xml:space
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">trapezium A B F P =
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) tra-
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pezium A B I P eſſe vqab & </
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<
s
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xml:space
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">polygonum A B D L P {2ab/a + vqab}:
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</
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<
s
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xml:space
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">eodem modo poſito trapezio A B I P =
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, & </
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<
s
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A B D L P =
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, erit polygonum A B E I O P = vqcd & </
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<
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xml:space
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lygonum A B C G K N P = {2cd/c + vqcd,}, ita ut evidens ſit hanc
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polygonorum ſeriem eſſe convergentem; </
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<
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xml:space
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">atque in infinitum
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illam continuando, manifeſtum eſt tandem exhiberi quanti-
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tatem ſectori circulari, elliptico vel hyperbolico A B E I O P
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æqualem; </
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<
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">differentia enim polygonorum complicatorum in
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ſeriei continuatione ſemper diminuitur, ita ut omni exhibita
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quantitate fieri poſſit minor, ut in ſequentis theorematis
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Scholio demonſtrabimus: </
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<
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">ſi igitur prædicta polygonorum ſe-
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ries terminari poſſet, hoc eſt, ſi inveniretur ultimum illud
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polygonum inſcriptum (ſi ita loqui liceat) æquale ultimo
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illi polygono circumſcripto, daretur infallibiliter circuli & </
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hyperbolæ quadratura: </
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<
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<
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metria omnino fortaſſe inauditum tales ſeries terminare; </
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mittendæ ſunt quædam propoſitiones è quibus inveniri poſ-
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ſint hujuſmodi aliquot ſerierum terminationes, & </
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