Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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HUGENII EXCEPTIO
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& </
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">in ſequentibus dicam de Circulo debet intelligi pariter de
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ſectore Circuli.</
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">Præter hanc approximationem D. </
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ponit in fine ſuæ
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Propoſitionis, quam admirandam di-
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cit, cujus demonſtrationem ſe ignorare fatetur; </
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<
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">hæc eſt, in-
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ter duos terminos, ſtatim memoratos {1/3} a + {2/3} d & </
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<
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">{4/3} c - {1/3} a,
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inventis quatuor mediis quantitatibus in proportione Arith-
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metica, aſſerit maximam harum quantitatum adeo Circuli
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magnitudini vicinam eſſe, ut, ſi in numeris, qui deſignant
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Polygona ſimilia a & </
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<
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">d, prima notarum triens ſit eadem,
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error ad unitatem non pertingat.</
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">Sed invenio hanc approximationem in Circulo veram non
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eſſe licet in Hyperbola locum habeat, &</
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">, dum in hac utimur
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maxima quatuor mediarum Arithmeticarum proportiona-
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lium, minimam pro approximatione Circuli adhibendam
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eſſe.</
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">Ita minima quatuor mediarum proportionalium inter
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terminos dictos primæ approximationis erit {16 c + 2 d - 3 a/15}, uti
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facile eſt videre per Calculum; </
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">probare poſſum non ſo-
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lum experientiâ, ſed & </
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hanc, poſitis numeris quorum prima notarum triens eadem
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eſt, ex primentibus polygonis a & </
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<
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gnitudine non aberrare niſi in duabus ultimis notis, & </
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rumque in omnibus notis & </
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<
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ne conincidere, quam tamen ſemper ſuperat, cum e contra-
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rio maxima quatuor Mediarum, qua utitur D
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Gregorius in
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Hyperbola deficiat.</
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<
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">Inveni præterea, approximationem hanc pro Circulo non
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æque accuratam eſſe, ac eſt illa quam dedi in Tractatu deCircu-
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li magnitudine, juxta quam, quando a, c & </
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<
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">d deſignant eadem
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Polygona, ac ſupra, terminus excedens contentum Circuli
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eſt a + {10cc - 10aa /6c + 9a} Neque demonſtratio difficilis eſt,
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p. 383. in
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ſ
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ine.</
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ſi neges illum terminum eſſe minorem ideoque magis </
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