By L. P. Bouckaert (auth.), L. P. Bouckaert, B. L. van der Waerden (eds.)
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6. 10. 21. &c. 6+3. CorolI. 2. In omnibus seriebus tertü ordinis est terminus quivis = quadruplo ultimi minus sextuplo penultimi plus quadruplo antepenultimi minus penantepenultimo. Exempli gratia sint cubi numerorum naturalium 1. 8. 27. 64. 343. &c. 64+4. 27-8. 5. Apparet ex praecedente theoremate, quanam lege series recurrentes construi debeant, ita ut flant algebraicae. Si vero alia, quam quae modo definita fuit, lex flngatur, semper series orientur transcendentes, seu potius exponentiales, quarum terminus generalis ut inveniatur, sequens propositio inserviet.
4. Exemplum huius rei eum mihi aliquando occurreret, volui perieulum facere, an aliquod hae in parte auxilium praestare posset methodus illa singularis, quam in Comment. Tom. ' exhibui pro inveniendis radieibus aequationum algebraicarum euiuseunque ordinis, idque sola terminorum additione vel substraetione continua, quod eum tentarem, vidi istam methodum minime nos defieere appropinquare volentes ad radieem aequationis sine fine progredientis, dum modo eerta ratione utamur: in eo autem eardo rei vertitur, ut series, quae ad leges loeo citato exhibitas formanda est pro norma aequationis propositae, quaeque incipit a tot terminis arbitrariis, quot dimensiones habet eadem aequatio, hie incipere fmgatur ab infinitis nullionibus, quos omnes excipiat unitas.
B. 1 5 1730 C. B. B. B. B. B. B. 5 4 1732 L. B. B. apres 2 6 1735 26 10 1735 L. EULER L. EULER 12 91736 1736 L. EULER 18 5 1737 L. EULER L. B. B. 13 9 1738 8 11 1738 L. B. L. B. L. B. 14 11 1739 L. B. 12 1 1740 L. EULER 13 3 1740 L. EULER 3 1740 L. B. 28 1-1 2 1741 L. B. 20 9 1741 L. EULER L. EULER 20 1 1742 L. B. B. B. B. B. Analysis L. L. L. L. L. B. B. B. B. L. L. L. L. II1, p. 85-100. 1728 (1732) 11. 16 1. Anni sunt fere quinque, quod Venetiis agens tumultuarias quasdam circa series observationes cum Nobili Veneto communicaveram, quas paulo post idem Nobilis, meo tarnen nomine, imprimi curavit una cum alüs theorematibus geometricis sub titulo Exercitationum Geometricarum'.