Journal . ntia colligi debent auferendoinferiores quantirates de fuperioribus, A2B2 de AB, A^B? de A2B2,^2 de ^, 8cc. et faciendo ut fint AB —A2B2=Z, A2B2—A3B3=/^2,b — hi=c., &e. adeoque quando differentia: ills hoc modo prodeuntnegativa: figna earum mutanda funt. PROP. IV. Si reHa aliqua in partes quotcunque inaequaks A A 2,A2A3, A3A4, A4A5, istccfividatur^ is ad^un^a divi-fioriumerigantur faralieice AB, A2B2, A3B3, isc, Inve-nire Curvam Geometricam generis Parabolici qu A6A7 — A7B7- a8b8 A7A» hi. T)sinde— =c,-^ = C2, -^ = c3, &c. AA4 Et ^i - e ^^ AA5 ~ ^: A2A4 A3A5 A2A5rf2 -d> = £2, ^3,8c
Journal . ntia colligi debent auferendoinferiores quantirates de fuperioribus, A2B2 de AB, A^B? de A2B2,^2 de ^, 8cc. et faciendo ut fint AB —A2B2=Z, A2B2—A3B3=/^2,b — hi=c., &e. adeoque quando differentia: ills hoc modo prodeuntnegativa: figna earum mutanda funt. PROP. IV. Si reHa aliqua in partes quotcunque inaequaks A A 2,A2A3, A3A4, A4A5, istccfividatur^ is ad^un^a divi-fioriumerigantur faralieice AB, A2B2, A3B3, isc, Inve-nire Curvam Geometricam generis Parabolici qu A6A7 — A7B7- a8b8 A7A» hi. T)sinde— =c,-^ = C2, -^ = c3, &c. AA4 Et ^i - e ^^ AA5 ~ ^: A2A4 A3A5 A2A5rf2 -d> = £2, ^3,8cc. A2A6 • A^A7 Sic pergendum eft ad ultiraam differentiam B b. 50 Newlons Interpolation Formulas. [Oct. 98 METHODUS DIFFERENTIALIS DifFerentiisfitcollectis & divifis per intervalla Ordinatim applicatarum 5in akernis earum Columnis five Seriebus vel Ordinibus excerpe medias,incipiendo ab ultima, &in reliquis Columnis excerpe media Arithmeticainter duas,medias, pergendo ufque ad firiem primorum rerminorum, AB,A2B2, 8cc. Sunto hsc i, /, m,«, 0,;;, 7, r, &-c. quorum ultimus terminusfignificet ultimam differentiam j penultimus medium Arithmeticun; interduas penultimas ^ antepenaltimus mediam mum antepenultimirum, & primus I erit media Ordinatim applicata, fi numerus darorum pun-ftorum eft impar ^ vel medium Arithraeticum inter duas n»edias, fi nu-merus eorum eft par. CAS. I. In Cafu priori/ic A4B4 ifta media Ordinatim appUcata,hoc ell,fit A^Bi^^zh^^31^ = /, C3 =»«, ^^ =r, e2 = 0, -^-^ =p,g = q. Et erefta Ordi-natim applicata PQ., & in Bafi AA5: furapto quovis punftoO, die OP=;f,^ due in fe gradatim terminos hujus Progreffio
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