- Some of Laplace's results in the theory of
**probabilities**are simplified in S. - Thus the
**probabilities**are delicately balanced. - A volume entitled Opera posthuma (Leiden, 1703) contained his "Dioptrica," in which the ratio between the respective focal lengths of object-glass and eye-glass is given as the measure of magnifying power, together with the shorter essays De vitris figurandis, De corona et parheliis, &c. An early tract De ratiociniis tin ludo aleae, printed in 16J7 with Schooten's Exercitationes mathematicae, is notable as one of the first formal treatises on the theory of
**probabilities**; nor should his investigations of the properties of the cissoid, logarithmic and catenary curves be left unnoticed. - The assumption may be a reasonable one, and if the results agree with
**probabilities**as deduced from the rest of the evidence it is wise to adopt it; if on the other hand the other evidence seems in any serious degree contrary to those results it may be surmised that the assumption is faulty in some particular. - The
**probabilities**seem in favour of the Academy cartoon.

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