Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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dicta quantitas eodem etiam modo componitur ex ul-
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timis ejus terminis convergentibus, qui æquales ſunt:
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<
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xml:space
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">ſit ultimus ille terminus
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qui multiplicatus in {mae-mbe/ad-bd} & </
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in
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efficit xm & </
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<
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xml:space
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">{xmae - xmbe/ad - bd}, quorum factorum ſumma nempe
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{xmae - xmbe + xmad - xmbd/ad - bd} æquatur {maae - mbae + mbad - mbbd/ad - bd} & </
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<
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ne reducta invenitur x ſeu ſeriei terminatio {aae - bae + bad - bbd/ae - be + ad - bd},
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quam invenire oportuit.</
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<
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">Ne minus exercitatis obſcurum videatur hoc problema,
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illud in numeris illuſtrabimus: </
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erunt ſe-
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cundi termini convergentes 32, 36, tertii 33 {1/7}, 34 {2/7}, & </
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<
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minatio 33 {3/5}.</
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">Neminem moveat, quod (etiamſi
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ſit minor quam
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)
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{ca + bd - ad/c} poſſit eſſe major quam {bc - be + ae/c}, analyticè enim major
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à minore poteſt ſubſtrahi, cnjus tamen exemplum non grava-
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bimus exhibere, ſit
<
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erunt ſecundi termini
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convergentes 38, 34, & </
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35 {7/9}.</
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<
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">Animadvertendum eſt hujus problematis ſolutionem eo-
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dem modo ſe habere, etiamſi loco
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ponatur cyphra ſeu me-
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rum nihil, Ex. </
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erunt ſecundi ter-
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mini convergentes 9, 12, & </
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tio 10 {2/7},</
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Gregorii à S. </
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methodo longe ab hac diverſa.</
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