Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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JAC. GREG. RESPONS.
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perientiam enim feci ſolummodo de primis & </
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minis, non conſiderando tertios cum primis coincidere, nam
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ratiociniis inſiſtebam, de exemplis parum ſolicitus. </
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<
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xml:space
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tem appareat in hoc nihil contineri contra noſtram Doctri-
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nam, agedum hoc loco 10: </
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<
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<
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">totidem verbis, ſed cum
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legitimo exemplo repetamus.</
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<
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">Ex data quantitate eodem modo compoſita à duobus
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terminis convergentibus cujuſcunque ſeriei convergen-
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tis, quo componitur ex terminis convergentibus ejuſ-
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dem ſeriei immediate ſequentibus; </
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<
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xml:space
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">ſeriei propoſitæ
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terminationem invenire.</
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<
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</
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<
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<
s
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xml:space
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">Sit ſeries convergens, cujus duo termini convergentes qui-
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cunque ſint a, b, & </
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<
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xml:space
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">termini convergentes immediatè ſe-
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quentes {2 a b/a + b}, {a + b/2}, termini priores inter ſe multiplicati effi-
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ciunt eandem a b, item ſequentes inter ſe multiplicati effi-
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ciunt eandem a b; </
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<
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xml:space
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">ex his invenienda ſit propoſitæ ſeriei ter-
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minatio. </
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<
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">Manifeſtum eſt, quantitatem a b eodem modo
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fieri à terminis convergentibus a, b, quo à terminis conver-
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gentibus immediatè ſequentibus {2 a b/a + b}, {a + b/z}: </
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<
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titates a, b, indefinitè ponuntur pro quibuslibet totius ſe-
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riei terminis convergentibus, evidens eſt, duos quoſcunque
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terminos convergentes propoſitæ ſeriei inter ſe multiplica-
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tos idem efficere productum, quod faciunt termini imme-
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diatè ſequentes etiam inter ſe multiplicati; </
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<
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mini convergentes duos terminos convergentes ſemper im-
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mediatè ſequantur, manifeſtum eſt, duos quoſcunque ter-
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minos convergentes inter ſe multiplicatos idem ſemper effi-
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cere productum, nempe a b; </
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gentes ſunt æquales, & </
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ſeriei terminatio Z, quæ in ſe ipſam multiplicata facit
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