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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ope ſolius regulæ & </
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<
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">circini peracta, hanc in his non ſolum
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eſſe impoſſibilem ſed etiam in omnibus problematis quæ ad
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æquationem quadratic
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am reduci non poſſunt, ſicut facile
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demonſtrari poſſet; </
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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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">ſi per geometricum intelligatur redu-
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ctio problematis ad æquationem analyticam, omnia hæc
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problemata ſunt geometrice impoſſibilia, cum ex hic demon-
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ſtratis, manifeſtum ſit talem reductionem fieri non poſſe:
<
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</
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<
s
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xml:space
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">ſi verò per geometricum intelligatur methodus omnium poſ-
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ſibilium ſimpliciſſima; </
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<
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xml:space
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">invenietur fortaſſe poſt maturam con-
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ſiderationem omnia prædicta problemata eſſe geometriciſſi-
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mè reſoluta, diligenter animadvertendum totam ſerierum
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convergentium doctrinam poſſe etiam nullo negotio applicari
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ſeriebus ſimplicibus. </
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<
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">Sit enim ſeries A, B, C, D, E, &</
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talis naturæ ut tertius terminus C eodem modo
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A
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B
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C
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D
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E
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Z
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</
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componatur ex primo & </
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">ſecundo A, B, quo
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quartus D componitur ex ſecundo & </
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">tertio B, C,
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& </
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">quintus E ex tertio & </
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<
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xml:space
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">ſic dein-
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ceps in infinitum; </
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<
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">ſitque differentia anteceden-
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tium A, B, major ſemper differentia immediatè
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ſequentium B, C; </
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<
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xml:space
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">ſupponamus hanc ſeriem ita in infinitum
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continuari donec duorum terminorum immediate ſe invicem
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ſequentium nulla ſit differentia, ſitque unus ex illis terminis
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z, quem ſeriei terminationem appellamus: </
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<
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modo componi ex A & </
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monſtratio vix differt ab hujus 10 & </
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<
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ratione ſi ponatur triangulum, ſectori circulari vel elliptico
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inſcriptum, vel ſectori hyperbolico circumſcriptum a, & </
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trapezium, ſectori circulari vel elliptico regulariter in-
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ſcriptum vel hyperbolico regulariter circumſcriptum b;
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</
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<
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">erit hexagonum ſectori circulari vel elliptico regulari-
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ter inſcriptum vel hyperbolico regulariter circumſcri-
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ptum Vq {2 b3/a + b;</
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<
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">} & </
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læ eodem modo componitur ex a & </
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atque hinc etiam demonſtrari poteſt, quod ratio inter ſecto-
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rem & </
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