The force of this contention lies in the close verbal identities between Crawford's account of the Darnley-Mary interviews (see Crawford's Declaration of December 9, 1568, in Lang's Mystery of Mary Stuart, pp. 428-431; from State Papers Scotland, Elizabeth vol.

The identities are, in particular, of service in reducing symbolic products to standard forms. A symbolical expression may be always so transformed that the power of any determinant factor (ab) is even.

He probably thought we'd have talked her out of leaving, or at least into leaving their new identities with us.

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The verbal identities can only be explained in one of the following ways.

All propositions not concerned with the existence of individual facts ultimately analyse out into identities - obviously lend themselves to the design of this algebra of thought, though the mathematician in Leibnitz should have been aware that a significant equation is never an identity.

And we may suppose such identities between the symbols that on the whole only two, three, or more of the sets of umbrae are not equivalent; we will then obtain invariants of two, three, or more sets of binary forms. The symbolic expression of a covariant is equally simple, because we see at once that since AE, B, Ce,...

Betsy suggested we each assign our new identities without telling each other except our spouses.

Symbolic Identities.- For the purpose of manipulating symbolic expressions it is necessary to be in possession of certain simple identities which connect certain symbolic products.

If we were to say that on his view the essential step must be the establishment of identities or equivalences, we should probably be doing justice to his doctrine of numerical reasoning, but should have some difficulty in showing the application of the method to geometrical reasoning.

Similarly, by putting one or more of the deleted rows or columns equal to rows or columns which are not deleted, we obtain, with Laplace, a number of identities between products of determinants of complementary orders.