Journal . F I tt r VOL. LI. 94 Newtons Interpolation Formulas. [Oct. I. METHODUS DIFFEREXTIALIS. {Iranalation.) Prop. I. If the ahscissa of a curve consist of a given quantity A and anindeterminate quantity :c, and if the ordinate consist of any number ofquantities h, c, d, e, &c., multiplied respectively into a correspondingnumber of terms of the G. P. x, 9?, o?, j-}, dx., and if ordinatcs beerected at as many points of the ahscissa; then the first differences of theordinates are divisible by their intervals; and the differences of thedifferences so divided are divisible by the intervals
Journal . F I tt r VOL. LI. 94 Newtons Interpolation Formulas. [Oct. I. METHODUS DIFFEREXTIALIS. {Iranalation.) Prop. I. If the ahscissa of a curve consist of a given quantity A and anindeterminate quantity :c, and if the ordinate consist of any number ofquantities h, c, d, e, &c., multiplied respectively into a correspondingnumber of terms of the G. P. x, 9?, o?, j-}, dx., and if ordinatcs beerected at as many points of the ahscissa; then the first differences of theordinates are divisible by their intervals; and the differences of thedifferences so divided are divisible by the intervals between alternateordinates ; and the differences of these differences so divided are divisibleby the intervals beticeen every third ordinate, and so on indefinitely. Thus if given quantities p, q, r, s, t, &c., be substituted insuccession for the indeterminate portion of the abscissa, andordinates a, ft, y, 8, e, &c., be erected at the extremities of theabscissae so determined; the abscisste and the ordinat
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