^{note * page 129} For the early history see Favaro's Notizie storiche sulle frazioni continue dal secolo decimoterzo al decimosettimo published in vol. vii. of Boncompagni's Bollettino: and as regards Bombelli see a paper by G. Wertheim in the Abhandl. zur Gesch. d. Math., viii. pp. 147–160.

^{note * page 130} The state of the theory in 1833 can best be gathered from Stern's monograph published in vol. x. of Crelle's Journal.Google Scholar

^{note * page 134} This is the author's date at the end of the paper (p. 381). The first two parts of the volume, however, are dated 1855, and the remaining two 1856.Google Scholar

^{note * page 137} An interesting extension of this is given by Brioschi, in the Nouvelles Annales de Math., xiv. (Jan. 1854) p. 20.Google Scholar

^{note * page 139} v. The theory of orthogonants … in Proc. Roy. Soc. Edinburgh, xxiv. p. 261.

^{note * page 142} It is in this mode of writing A_κ^ι, viz., with the negative sign, that Jacobi's peculiarity consists. Not content with removing from R_n the row and column in which α _κ^ι occurs and prefixing to the minor thus obtained the sign factor (−l)^ι+κ, he takes the further step of moving the row with the index κ over κ − ι +1 rows, thus arriving at

Of course there is at the second step the option of moving the column with the index ι over κ-ι + 1 columns, and this Ramus does.

^{note * page 154} To obtain the cofactor of the product of a number of a set of elements in a determinant Worpitzky puts a 1 in the determinant in place of each element occurring in the said product, O's in all the other places of the rows to which these elements belong, and O's for all the other elements of the set.

^{note * page 157} In giving to N_{s+1, s} N_s+2,s, N_{s + 3,s} the values 1, 1, 0 which are necessitated by assuming the generality of the recursion-formula

Worpitzky forgets to note that in these cases the proposition N_k,n = N_n,k;, used by him in the demonstration, does not hold.