Classical projective geometry is rich in relations between the extrinsic invariants (e.g., order, double tangents, number of nodes, triple points, •) associated with an algebraic map /: M —• CPN of a projective algebraic manifold M. It has also long been known that these extrinsic invariants may be sometimes used to define birational or intrinsic invariants of the manifold. For example, the Pliicker formulas for an algebraic plane curve may be interpreted as a definition of the 1st Chern class of an algebraic manifold of dimension 1, or the postulation formula as the arithmetic genus in terms of the projective characters of an algebraic surface. The object of this note is: (a) to obtain descriptions of the Chern classes of an algebraic manifold in terms of the extrinsic invariants associated with an algebraic map /: M —> CPN which is nonsingular of order 1, i.e., the derivative of / has maximal rank everywhere, (b) to show how the Chern classes affect well-known geometric invariants, associated with an imbedding satisfying the above condition.