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

DETERMINANTS IN GENERAL (DEL GROSSO, 1857) 99

DEL GROSSO, R. (1857).
[Sulla regola secondo la quale debbono procedere i segni nello
sviluppo d'un determinante in prodotti di determinanti
minori. Rendic..... Accad. Pontaniana (Napoli), Ann. v.
pp. 196-198. See also pp. 198-206.]
When a determinant is expressed in accordance with Laplace's
theorem as an aggregate of products of complementary minors,
Del Grosso directs that the sign of any product is to be (-1),
where cr is the sum of the odd row-numbers and odd columnnumbers of one of the factors. The rule is not stated with
sufficient care, and the author in reaching it concludes too
hastily that the simplest case is all that need be established.
JANNI, G. (1858).
[SAGGIO DI UNA TEORICA ELEMENTARE DE' DETERMINANTI, del
Sacerdote Giuseppe Janni.... 40 pp. Napoli.]
Janni's professed object was to make determinants more readily
accessible, previous text-books having, he says, either totally
neglected demonstrations or used those of great difficulty. He
speaks of the work as the first of a series, and its contents
certainly look like the first five chapters of a text-book planned
on a fairly large scale. The theorems, twenty-three in number,
are carefully enunciated and are printed in italics; but, although
the proofs receive every attention, it is very doubtful whether
the object aimed at was to any extent accomplished. There is
at any rate nothing sufficiently fresh in the treatment to warrant
attention here.
ZEHFUSS, G. (1858).
[Ueber die Auflisung der linearen endlichen Differenzengleichungen mit variabeln Coefficienten. Zeitschrift f. Math. u.
Phys., iii. pp. 175-177.]
His solution suggests to Zehfuss the remark (p. 177) that every
determinant can be expressed as a multiple integral. It will