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of vibration are investigated
Analytical development of Fresnels optical
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algebraical application becomes Bezoutiant canonical form characteristic coefﬁcients coeﬂicients cogredient coincident combined commutant complete determinant concomitant conics consequently contain continued fraction contravariants corresponding covariant cubic equation cubic function curve deﬁned demonstration denote derived dimensions elimination equal roots evectant expressed ﬁnal derivee ﬁnd ﬁnding ﬁrst minors ﬁve ﬁxed four given function Hence Hessian homogeneous function identical indeﬁnitely inﬁnite integer intersection invariant linear functions linear transformations matrix method minor determinants modulus multiplicity number of letters number of variables obtain pairs permutations Philosophical Magazine plexus positive preﬁxed proposition quadratic functions quantities quintic function quotients rational real roots relations remarkable represent respectively resultant right lines rotation satisﬁed simpliﬁed residue solution square Sturm’s substituted suppose surface symmetrical symmetrical function synthemes syzygetic tangent plane theorem theory theory of elimination third degree transformation values vanish zero