Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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VERA CIRCULI
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ut ſemper quilibet terminus unius ſeriei ſit major quam idem
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numero terminus alterius ſeriei; </
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<
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longius producuntur, eò minor eſt eorundem numero termi-
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norum differentia: </
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<
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producuntur, eò magis differunt iidem numero termini, ſicut
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facillimè demonſtrari poteſt.</
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<
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">Experientia obſervo differentiam inter ſecundam duarum
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mediarum arithmetice proportionalium & </
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<
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mediarum geometricè proportionalium ſemper eſſe multò
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majorem differentia inter ſecundam duarum mediarum geo-
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metricè proportionalium & </
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<
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">ſectorem circuli, ellipſeos vel
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hyperbolæ; </
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">quod notatu dignum exiſtimo, hinc enim col-
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ligitur ſectorem differre vix ultra unitatem à ſecunda duarum
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mediarum arithmeticè continuè proportionalium, quando
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medium arithmeticum non excedit medium geometricum ul-
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tra unitatem, quod ſummopere notandum, nam ex hoc evi-
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dens eſt approximationem audacter eſſe adhibendam, quan-
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do ita continuatur ſeries ut medietas prima notarum ſit
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eadem in utroque termino convergente, quod experientia
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etiam evincit; </
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<
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">nunquam enim in hoc caſu differt ſector
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unitate à ſecunda duarum mediarum arithmeticè continuè
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proportionalium.</
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admiranda, etiamſi mihi non contingat illam demonſtratio-
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ne geometrica munire; </
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">nempe ſi primus notarum triens in
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utroque termino convergente ſit eadem, ſector circuli, el-
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lipſeos vel hyperbolæ ſemper differt infra unitatem à maxi-
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mo quatuor arithmeticè continuè proportionalium inter ter-
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minos noſtræ approximationis.</
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fig. 4.</
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ptota A B, A O; </
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circum ſcripto A F L: </
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cantur rectæ F D, I M; </
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