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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omnes ſeriei convergentis terminationem eodem modo eſſe
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compoſitam ex terminis convergentibus primis quo ex termi-
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nis convergentibus ſecundis, tertiis, vel quartis, &</
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">Dico ſectorem circuli, ellipſeos vel hyperbolæ A B I P
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Fig. 1. 2. 3.</
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non eſſe compoſitum analyticè à triangulo
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A B P & </
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& </
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: </
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nifeſtum eſt ex prædictis trapezium A B I P eſſe Vqab & </
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polygonum A B D L P {2 ab/a + Vqab}, item ſectorem A B I P eſſe
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hujus ſeriei convergentis terminationem. </
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nis auferantur ſigna radicis & </
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primis
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ſeriei terminis convergentibus, hoc eſt pro triangulo A B P
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& </
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+ a
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b & </
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+ b
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que ſecundi ſeriei termini convergentes, hoc eſt trapezium
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A B I P & </
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+ b
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a & </
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">2 b
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a, di-
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co ſeriei convergentis (cujus primi termini convergentes ſunt
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a
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+ a
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b, ab
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+ b
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& </
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+ b
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a, 2 b
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a) termina-
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tionem non eſſe compoſitam analyticè a terminis a
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+ a
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b,
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ab
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+ b
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terminis convergentibus a
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+ a
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b, ab
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+ b
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; </
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<
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eadem terminatio analyticè & </
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nis convergentibus ba
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+ b
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a, 2b
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a; </
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titas, nempe prædicta terminatio, eodem modo componitur
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analyticè ex terminis a
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+ a
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b, ab
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+ b
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, quo componitur ex
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terminis ba
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+ b
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a, 2b
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a,
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a
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b # ab
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ba
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a # 2b
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a
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ſed nulla quantitas poteſt
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eodem modo analyticè com-
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poni ex terminis a
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+ a
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b,
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ab
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+ b
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, quo componitur
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ex terminis ba
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+ b
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a, 2b
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a, quod ſic demonſtro. </
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ticè componeretur quantitas ex terminis a
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+ a
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b, ab
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+ b
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