The theory of determinants in the historical order of development, by Sir Thomas Muir.

CHAPTER XVI.

CONTINUANTS, FROM 1850 TO 1880.
IT has to be recalled that the corresponding chapter of the immediately preceding volume aimed at bringing the record up to the year
1870. On this account two of the papers here dealt with belong
properly to that volume. The approximate date assigned to the
first paper rests on the opinion of the editor of it. Jacobi died
in 1851.
JACOBI, C. G. J. (1850?).
[Allgemeine Theorie der kettenbruchahnlichen Algorithmen, in
welchen jede Zahl aus drei vorhergehenden gebildet wird.
Crelle's Journ., lxix. (1868), pp. 29-64; or Gesammelte Werke,
pp. 385-426.]
In this paper, published seventeen years after his death, Jacobi
constructs a series whose first three terms are
al, Ct2, a3,
and every other term a sum of multiples of the three terms preceding it; thus, the multiples in question being
1 11 Mnl.
1 12 M2,
the 4th, 5th, 6th... terms are
al + 11a2 + mq1a,
qn 2a+(1 ) + (+1'm2 + 1) ac + (7nln2 + 12).3,
(m,2n3 +I3) al + (m1n2m+l11 +m^3) a2+(mm2m, +n1l3 +l2i3 +1) a,,